Science of Weather, Climate and Ocean Extremes (Volume 2) (Developments in Weather and Climate Science, Volume 2) [1 ed.] 0323855415, 9780323855419

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SCIENCE OF WEATHER, CLIMATE AND OCEAN EXTREMES

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SCIENCE OF WEATHER, CLIMATE AND OCEAN EXTREMES JOHN E. HAY Adjunct Professor, The University of the South Pacific; Adjunct Professor, Griffith University, Australia; Adjunct Professor, University of Auckland, New Zealand

Series editor

PAUL D. WILLIAMS

Elsevier Radarweg 29, PO Box 211, 1000 AE Amsterdam, Netherlands The Boulevard, Langford Lane, Kidlington, Oxford OX5 1GB, United Kingdom 50 Hampshire Street, 5th Floor, Cambridge, MA 02139, United States Copyright © 2023 Royal Meteorological Society. Published by Elsevier Inc. in cooperation with The Royal Meteorological Society. All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher. Details on how to seek permission, further information about the Publisher’s permissions policies and our arrangements with organizations such as the Copyright Clearance Center and the Copyright Licensing Agency, can be found at our website: www.elsevier.com/permissions. This book and the individual contributions contained in it are protected under copyright by the Publisher (other than as may be noted herein). Notices Knowledge and best practice in this field are constantly changing. As new research and experience broaden our understanding, changes in research methods, professional practices, or medical treatment may become necessary. Practitioners and researchers must always rely on their own experience and knowledge in evaluating and using any information, methods, compounds, or experiments described herein. In using such information or methods they should be mindful of their own safety and the safety of others, including parties for whom they have a professional responsibility. To the fullest extent of the law, neither the Publisher nor the authors, contributors, or editors, assume any liability for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions, or ideas contained in the material herein. ISBN: 978-0-323-85541-9 For information on all Royal Meteorological Society e Elsevier publications visit our website at https://www.elsevier.com/books-and-journals Publisher: Candice Janco Acquisitions Editor: Jennette McClain Editorial Project Manager: Charlotte Kent Production Project Manager: Bharatwaj Varatharajan Cover Designer: Matthew Limbert Typeset by TNQ Technologies

Dedication Geographer in 1971, and a co-authored chapter in the North American volume of the World Survey of Climatology, published by Elsevier in 1974. I was exceedingly fortunate to be supported, mentored and motivated by a person who has been described, without exaggeration, as ‘a giant in Canadian and international climatology, geography and environmental sciences’. After serving as a meteorologist during World War II, Ken joined McGill University as an assistant professor. In 1950, he was awarded a PhD in Geography from the Université de Montréal. Ken was appointed Dean of Arts and Science at McGill in 1962. In 1964, he was appointed Head of Geography at Kings College, and subsequently Master of Birkbeck College from 1966 to 1968, during which time he also served as president of the Royal Meteorological Society. In 1968, Ken became the fifth president of the University of British Columbia. He subsequently became Professor of Geography and Physics at the University of Toronto, as well as Director of its Institute for Environmental Studies. From 1979 until 1986, he was Provost of Trinity College. From 1988 to 1995, Ken was the sixth Chancellor of Trent University. From 1992 until his death in 2002, Ken chaired Canada’s national Climate Program Planning Board. In 1978, Ken was appointed an Officer of the Order of Canada. He was promoted to Companion in 1987. During his illustrious career, Ken was awarded honorary degrees by 11 universities.

I am humbled and honoured to dedicate this book to: John N. Rayner John inspired my interest in climatology when I was an undergraduate in the Department of Geography, University of Canterbury, New Zealand. I am fortunate, indeed, to have walked through the scientific doors he opened for me. John was undertaking his own doctoral research at the time. It was his passion for research, as well as for life in general, that encouraged me to undertake doctoral studies overseas. Even before I had time to attend my graduation ceremony, and be awarded a BSc(Hons), I had taken his advice and started travelling. John departed New Zealand soon after me, initially taking up an appointment as an Associate Professor at Ohio State University. He continued there until his retirement. John was Chair of the Department of Geography for 20 years, Director of Atmospheric Sciences for 10 years and State Climatologist for 11 years. F. Kenneth Hare Ken supervised the doctoral research I undertook at Kings College, University of London. I arrived there, expecting to study extreme rainfall events in East Africa. Unrest in that region caused those plans to be postponed. Ken kindly found some work for the ‘naïve and inexperienced boy from the colonies’. Under his guidance, I was soon deeply immersed in researching the heat and water balance climatologies of North America. This launched my publishing career, with a co-authored paper in the Canadian

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DEDICATION

While I endeavour to follow in Ken’s footsteps, I am a mere shadow of this great man. Geert Jan van Oldenborgh Even though I never met Geert Jan, our interactions, his publications and his many other contributions have had a significant

influence on the later years of my research and writing. After his untimely death in 2021, Geert Jan was described as ‘a tireless advocate for inclusive science and a pioneer of event attribution science’. The world as a whole is all the poorer from his passing.

Contents Foreword ix Acknowledgements

Answering the question References 116

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116

4. Have the oceans also experienced changes in extreme events?

1. Introduction Overview 1 From means to yet-to-be-experienced extremes: a historical perspective 2 Scope of this book 4 Structure of this book 6 Terminology and definitions 7 Uncertainty and confidence 10 More than a review or an assessment 11 References 11

Introduction 127 Marine extremes in the pre-instrumental era 127 Marine extremes in the instrumental era 128 Answering the question 140 References 141

5. How are atmospheric extremes likely to change into the future? Introduction 145 Future changes in atmospheric extremes Answering the question 172 References 173

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Changes

145

6. How are marine extremes likely to change into the future?

2. Changes in characterising extremes Introduction 17 Detecting past changes in extremes 18 Change and extreme event detection 46 Projecting future changes in extremes 52 Uncertainties: types, sources, evaluations, corrections and implications 65 Conclusions 68 References 70

Introduction 181 Future changes in marine extremes Answering the question 189 References 189

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3. Have atmospheric extremes changed in the past?

Causes 7. Drivers of past and future changes in weather, climate and ocean extremes

Introduction 81 Atmospheric extremes in the pre-instrumental era 81 Changes in atmospheric extremes in the instrumental era 86

Introduction 195 Overview 195 Drivers of changes in specific extremes 198

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viii Summary and conclusions References 256

CONTENTS

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8. Attribution methods related to past and projected changes, and to extreme events Introduction 269 Methods for attribution of long-term observed and projected changes 273 Methods for extreme event attribution 285 Evaluating progress in extreme event attribution 315 Summary and conclusions 317 References 319

9. Atmospheric extremes: attribution of changes and events Introduction 327 Attribution findings for past and projected changes in extremes 328 Attribution findings for specific extreme events 336 Summary and conclusions 355 References 356

10. Marine extremes: attribution of changes and events Introduction 367 Attribution findings for past and projected changes 368 Extreme event attribution findings 369 Conclusions 370 References 370

11. Hindsights, insights and foresights Introduction 373 Hindsights e reflecting on the evidence of change 374 Insights e identifying and attributing the drivers of changes in extremes 375 Foresights e the implications for policies and actions 376 Is this the end of the story? 377 References 378

Index 379

Foreword as the evidence allows. In doing so, it provides robust evidence and explanations for the general increase in these extremes in the past. It also presents the key results of model-based future projections. These reveal how the same extremes are likely to change in the coming decades. Climate models also provide the opportunity to determine the extent to which observed changes in the frequency and intensity of the extremes can be attributed to human activities, rather than natural variability in the atmosphereeocean system. This analysis can also be undertaken for an individual extreme event. Science of Weather, Climate and Ocean Extremes is, therefore, a timely addition to Developments in Weather and Climate Science, the Royal Meteorological Society’s new book series, published in partnership with Elsevier. Hay’s contribution e drawing on his decades of unrivalled experience in academia, the private sector and governmental organisations e is consistent with the goal of the series being to combine the underpinning principles of the atmospheric, oceanic and climate sciences with recent developments in the field. Its multi-disciplinary approach brings together aspects of physics, mathematics, chemistry, computer science and other basic disciplines. In doing so, it cuts across these traditional subject boundaries, bringing together all the elements that are important for understanding atmospheric and ocean extremes. The book is thus an excellent

It seems that not a day goes by without the media reporting yet another extreme weather event. More and more often, these reported events are occurring close to home, in our country, if not our neighbourhood. What does this trend reflect? Is it a media that is increasingly captivated by these events, perhaps aided by the modern ubiquity of dramatic video footage shot on mobile telephones by the people affected? Or is there a real upsurge in their frequency, intensity and resulting impacts? While the media tends to focus on extreme weather events, longer-lasting climate extremes, such as droughts, receive less attention. This is despite their consequences being just as significant. The same applies to ocean extremes, although marine heatwaves are receiving more attention. The increased interest in marine heatwaves is not only a result of the growing awareness of the direct impact of ocean extremes on marine ecosystems but also because the increasing frequency and severity of marine heatwaves is paralleling the changes in atmospheric heatwaves and their serious consequences. A single, authoritative and highly readable book that covers the full array of weather, climate and ocean extremes is long overdue, which is why I jumped at the opportunity to commission and publish the book you are currently reading. The book considers past changes in these extremes, often extending back to previous millennia,

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FOREWORD

addition to the series. For this reason, I also look forward to Hay’s next contribution to the series, with the forthcoming publication of

Managing the Consequences of Weather, Climate and Ocean Extremes in Our Warming World.

Dr Paul D. Williams Professor of Atmospheric Science University of Reading United Kingdom and Editor Developments in Weather and Climate Science The Royal Meteorological Society and Elsevier

Acknowledgements their initial suggestion that I write a book on climate extremes to the appearance in print of a much more nuanced book. For this I give special thanks to six of Elsevier’s editorial team, namely Charlotte Kent, Amy Shapiro, Veronica III Santos, Bharatwaj Varatharajan, Narmatha Mohan and Peter Llewellyn. I deeply appreciate your patience, understanding and professionalism. I also acknowledge my colleagues and the staff at the University of the South Pacific, the University of Auckland and Griffith University. I am especially thankful to the librarians and others who facilitated my access to electronic and other library resources and services.

A large number of people and institutions have contributed to this work, either directly or indirectly. I fear that I may fail to acknowledge some of them or make totally inadequate references to those I do recognise. Please accept my apologies for any omissions. I offer heart-felt thanks to my wife, Helen Henry, as well as to my daughter, Joanne, and to my son, Anthony. Your love, interest and practical support have kept me motivated and engaged during the research and writing process. Similarly, I acknowledge my grandchildren, Matthew and Cassandra. The staff at Elsevier made the journey so much easier than it might have been, from

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C H A P T E R

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Introduction Studies on extremes have been proceeding at a furious pace, with important outcomes springing up. (Chen et al., 2018).1

Overview Science-based understanding of weather, climate and oceanic extremes has advanced markedly over recent decades, and on multiple fronts. The latter include improved characterisation of the changes captured in both the instrumental and geological records, developments in attribution science that have clarified the causes of the changing nature of extremes, numerical modelling of past and future changes in weather, climate and oceanic extremes, and being able to identify and predict the impacts of these extremes on human and natural systems, including their component parts. Related advances in the ability to foresee changes in the drivers of extremes, and in the extremes themselves, underpin recent improvements in the capacity to manage their current and anticipated impacts in a proactive and effective manner. Extreme weather, climate and oceanic events, such as heavy precipitation, droughts, heatwaves, damaging winds, and extreme ocean waves and sea levels, represent significant hazards to societies and economies, including agriculture, fisheries, transport, health and urban systems.2 The more recent systematic changes in weather, climate and oceanic extremes can be attributed, at least in large part, to increases in the concentration of greenhouse gases in the Earth’s atmosphere as a result of human activity. The build-up of these gases leads to an increase in the net radiant heat energy absorbed by the Earth3,4 e the Earth’s energy imbalance e and to what is commonly referred to as ‘global warming’ or, more broadly and correctly, as ‘anthropogenic climate change’. Greenhouse gas emissions resulting from human activity will continue, likely at an increasing rate despite international and other efforts to reverse the trend. As a result, we can expect changes in these extremes to accelerate further over the coming decades and centuries. In the absence of effective countermeasures, including adaptation, disaster risk reduction and disaster preparedness, the trajectory of increasing extremes will inevitably result in an alarming increase in the social, economic and environmental consequences of global

Science of Weather, Climate and Ocean Extremes https://doi.org/10.1016/B978-0-323-85541-9.00006-7

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© 2023 Elsevier Inc. All rights reserved.

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warming. These impacts will be further exacerbated by continuing increases in the exposure and vulnerability of natural and human assets. Importantly, our increasingly comprehensive and robust understanding of atmospheric and oceanic extremes, including the ability to anticipate future changes, underpins and drives concomitant improvements in the ability to plan for, and implement, proactive risk management initiatives. However, significant challenges still exist, largely as a result of the multiple sources and levels of uncertainty in both the science and management of these extremes.5,6 This results in the need to recognise multiple response pathways and to also adopt flexible and adaptive management approaches.

From means to yet-to-be-experienced extremes: a historical perspective While extreme weather, climate and oceanic events have always had significant detrimental consequences for both natural and human systems, initial concerns about the repercussions of the build-up of greenhouse gases in the Earth’s atmosphere focussed on the impacts of systematic changes in mean values of the temperature, precipitation, sea level and other variables. Calls for a greater focus on extremes began in the 1990s.7 However, while acknowledging that potentially the overall impact of a changing climate is determined more by the changes in the magnitude and frequency of extreme events than by changes in average conditions, in the 1990s, the authoritative Intergovernmental Panel on Climate Change (IPCC) could provide no evidence of an increasing incidence of extreme events in recent decades. It acknowledged that climate models were generally incapable of showing whether such extremes might increase in the future.8 Only a decade later the situation was markedly different, reflecting major improvements in the recovery and rehabilitation of observational data, in statistical methods and in climate modelling. By this time, systematic changes over the latter half of the 20th century for a variety of indicators of temperature and precipitation extremes had been detected, and similarly for projected changes during the 21st century.9 The improvements in both capabilities and understanding gained momentum, fuelled by an apparent increase in the frequency of extreme weather, climate and oceanic events, with these in turn causing severe and, in some instances, disastrous consequences (Fig. 1.1). The desire to determine the extent to which global warming was altering the incidence of extreme weather, climate and oceanic events also drove an increase in the use of the term ‘extreme event’, though with an initial focus on occurrences rather than on consequences. This relative dominance still prevails.10 But the balance is changing. Recently, there has been a rapid growth in efforts to understand the causes and manage the consequences of such events. This is exemplified by the increased attention given to weather, climate and oceanic extremes in the wider published scientific literature (Fig. 1.2). But management interventions still tend to focus on reducing the impacts of long-term changes in the mean climate, rather than addressing the consequences of changes in the frequency and intensity of extreme weather, climate and oceanic events.11 Publication of the Special Report on Extremes12 in 2012 was a significant milestone in the growing focus on extremes. The Report acknowledged that only during the previous few years had the science of extreme weather, climate and oceanic events, their impacts, and

From means to yet-to-be-experienced extremes: a historical perspective

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FIGURE 1.1 Number of reported extreme meteorological, climatological and hydrological events, and related losses, 1970e2021. Data from EM-DAT: The Emergency Events Database - Université catholique de Louvain (UCL) - CRED, D. Guha-Sapir - www.emdat.be, Brussels, Belgium.

options for dealing with them, advanced sufficiently to support the comprehensive assessment typical of special reports prepared by the Intergovernmental Panel on Climate Change. Similarly, its Sixth Assessment Report by Working Group I13 was the first time a chapter of an Assessment Report had been devoted to extreme weather and climate events. That chapter13 documented further recent progress in characterising observed and anticipated changes in weather and climate extremes, including formally attributing these to human influences. Compound extremes are the simultaneous or sequential occurrence of multiple extremes at single or several locations. Recent recognition that such events can cause disproportionately large socioeconomic and environmental consequences has resulted in a growing number of studies focussed on the statistical characterisation and modelling of compound extremes, their consequential impacts and on potential management options.14,15 Recently, and based on several case studies, a set of guidelines has been proposed for compound event analysis across disciplines and sectors.16 Another very recent advance is the ability to statistically characterise and plan for extreme events which have never been detected in the observed record, but might occur in the future as a result of climate change. This capability is due, in part, to increasing computer power making it possible to run large numbers of simulations using multi-model ensembles. Practical application of this quantitative information has been facilitated by the use of the probabilistic risk assessment methodology. It had its origins in the aerospace, nuclear and chemical process industries in the 1970s,17 and it is now being used increasingly for assessing current and future levels of weather, climate and oceanic risk,

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FIGURE 1.2

Annual number of scientific journal and research papers published between 1980 and 2021, based on a Web of Science search using the terms ‘climate extreme*’, ‘extreme climat(e/ic’, ‘weather extreme*’, ‘extreme weather’, ‘ocean extreme’ and ‘extreme ocean’.

including extreme events that have yet to be experienced.18 Thus the methodology plays an important role when assembling the evidence base that underpins the assessment and implementation of adaptation and other risk management options.19 This perspective has outlined the many advances in the detection, projection and attribution of weather, climate and oceanic extremes, especially in terms of conceptual and analytical frameworks, methods and physical and socio-economic insights. But as this book and its companion volume20 emphasise, further progress on all fronts is urgently needed.

Scope of this book While this book concentrates on extremes, it is important to highlight that mean conditions, including their systematic changes over time, continue to be highly relevant from scientific, environmental, socio-economic and political perspectives. Furthermore, changes in the mean climate often translate into changes in the frequency, magnitude, duration, location and other characteristics of weather, climate and ocean extremes.21 The changes in extremes, and their underlying causes, are examined not only for the Earth’s atmosphere but also for its oceans. Fig. 1.3 shows that analogous processes and

Scope of this book

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FIGURE 1.3 The time and space scales of the major marine and atmospheric processes. Adapted from Villas Bôas AB, Ardhuin F, Ayet A et al. Integrated Observations of Global Surface Winds, Currents, and Waves: Requirements and Challenges for the Next Decade. Front Mar Sci. 2019; 6(JUL):1e34. https://doi.org/10.3389/fmars.2019.00425

conditions occur in both domains. However, across all scales, atmospheric processes are in general about three orders of magnitude faster than those in the oceans. Nevertheless, in both domains, kinetic energy is concentrated at the synoptic scale (typical horizontal dimension and duration of 1000 km and three days, respectively), with a secondary peak in the microscale (10m and 1 min, respectively). This is essentially because the air density is about 1000 times less than that of water. In addition, in both the atmospheric and oceanic domains, larger-scale phenomena tend to evolve and/or move faster.22 Many of the chapters in both Parts I and II focus on either atmospheric or marine extremes. This is mainly a matter of simplification and convenience, while also reflecting in part the differences in data availability and the processes involved. Obviously, the boundaries between these two groupings of extremes are often blurred. This is not only in the case of compound extremes,23 and especially those occurring in coastal areas,24 but also as a result of more general airesea interactions.25 For example, 16% of droughts that affected the continents worldwide from 1981 to 2018 started over the ocean and travelled onto land. Compared to

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droughts that start and end completely over land, these ‘landfalling droughts’ are larger, more intense and grow faster after making landfall.26

Structure of this book This book covers methods, past changes, projections, drivers and attribution of weather, climate and ocean extremes. It does so in two substantive parts (Fig. 1.4). Part I (Changes) describes major advances in the availability and quality of data and other information on weather, climate and ocean extremes, as well as in the methods used to assess past and quantify future changes in these extremes. It also presents and discusses the important new findings resulting from studies which take advantage of these enhanced capabilities.

FIGURE 1.4 Book chapters are organised into two substantive parts which deal with changes and causes in weather, climate and ocean extremes.

Terminology and definitions

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A key conclusion is that the combined magnitude and velocity of anthropogenic climate change may well result in extreme events that have yet to be experienced. Part II (Causes) presents the key findings of recent studies which document the reasons why weather, climate and ocean extremes have changed and will continue to do so. It also details the methods used to attribute changes in these extremes, along with the significant findings. These include the increasingly robust evidence that anthropogenic forcing, which is due, in part, to rising atmospheric greenhouse gas concentrations, is often the main contributor to increases in the frequency and severity of many extremes, as well in individual extreme events. The final section of this book, Hindsights, Insights and Foresights, first summarises the key findings and messages from the individual chapters and presents them in a coherent and integrated manner. A discussion of the varying levels of confidence in the findings provides the context for an overview of where future efforts might focus in order to improve our understanding of past and future changes in extremes, and in extreme events, including the underlying causes. These insights are fundamental to strengthening our ability to identify and comprehend the growing and increasingly diverse consequences of future changes in extremes, and hence to being better placed to manage the increases in risk resulting from the changes in these hazards.

Terminology and definitions There are many dimensions to an extreme event. As a result, ‘extreme events are generally easy to recognise but difficult to define’.27 Hazards, including weather, climate and ocean extremes, can be characterised in terms of either their statistical rarity or their resulting impacts, or both. Impacts are highly context specific e the consequences of an extreme event are not only a function of the characteristics of the event itself but also of the exposure and vulnerability to that event.14 The latter encompasses both the sensitivity to the extreme, and the ability to cope with and adapt to it. Extreme events are in themselves highly variable, as described by their likelihood of occurrence, and their intensity, duration, spatial extent, timing and interdependencies. As already noted, it is often a combination of several such events occurring simultaneously or sequentially (compound extremes) that cause the most severe weather- and climate-related consequences e even if each event is not in itself extreme.28 Compound extremes may be distinguished as ‘preconditioned’, when a hazard causes or leads to an amplified impact because of a precondition; ‘multivariate’, when multiple co-occurring drivers and/or hazards cause an impact; ‘temporally compounding’ when sequential hazards cause an impact; and ‘spatially compounding’ when spatially co-occurring hazards cause an impact.23 The process of identifying an event as extreme varies between disciplines, and even within disciplines. As a result of the many complexities of extreme events, and given the growing interest in extreme events across the spectrum of disciplines from Architecture to Zoology, it is hardly surprising that there is no single, universally applicable and generally accepted definition of an extreme event.

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But despite such complexities, there have been many calls for increased consistency in defining extreme events, including extreme weather, climate and ocean events.29 The fact that these events and their resulting impacts are almost certain to increase over time underscores the need to report their occurrence, nature (magnitude, duration and extent) and evolution in a consistent manner.30 On a wider front, the transdisciplinary understanding and management of extreme events is facilitated by clearer and more consistent definitions and reporting.31 There has been a call for a comprehensive and consistent definition that not only covers all categories of extreme events, including their physical, temporal and spatial characteristics, but also extends to incorporating the consequential effects of such events.10 However, while there is a close connection between the magnitude of an extreme event and its consequential impacts, there is not a one-to-one relationship.32 This important reality underpins the widespread practice of not referring to impacts when defining an extreme event. Such an approach is taken by the Intergovernmental Panel on Climate Change, including having separate Working Groups consider the physical science of climate change on the one hand, and impacts, adaptation and vulnerability on the other. As defined by the Panel, extreme weather, climate and ocean events refer solely to the initial (e.g. intense rainfall) and directly associated (e.g. flood) physical hazards. The subsequent consequences for both human and biophysical systems, including ecosystems, are separately defined as ‘impacts’ and therefore are not considered an integral part of the extreme weather, climate or ocean event. Similarly, the World Meteorological Organization30 also argues that, as a general principle, the definitions of extreme weather, climate and ocean events should be impact independent. That organisation also sees this facilitating consistent reporting on the nature, occurrence and evolution of the event, including information on its magnitude, duration and extent. Even when the two Working Groups of the Intergovernmental Panel on Climate Change combined to prepare the Special Report on Extremes,12 the definitions of extreme weather, climate and oceanic events made no reference to impacts. More recently, both the Fifth and Sixth Assessment Reports of the Panel33,34 defined an extreme weather event as ‘an event that is rare at a particular place and time of year’ and an extreme climate event as ‘a pattern of extreme weather that persists for some time, such as a season’. Collectively, extreme events span a timescale of at least seven orders of magnitude, from an intense tornado lasting mere minutes to a persistent drought occurring over decades. Importantly, there is no clear distinction between these two categories of extreme event in terms of spatial scale. However, experience suggests such events differ with respect to not only the time scale (minutes to days and several months to years, respectively) but also spatially, with climate extremes generally covering larger areas (Fig. 1.3). This book uses the definitions of extreme weather, climate and ocean events agreed by the Intergovernmental Panel on Climate Change, as described above. For simplicity, when taken together, weather, climate and ocean extremes are referred to as ‘extremes’ or ‘extreme events’, according to the context. Fig. 1.5 presents a hierarchy of the physical attributes of extreme events, consistent with the definitional separation of extreme event and extreme impact. This contrasts to a proposed simple binary taxonomy of extreme events.27 It also considered the severity of the resulting impacts. Frequency is typically characterised by the probability of occurrence of the event, expressed with respect to given percentiles of the distribution function of the variable, or

Terminology and definitions

FIGURE 1.5

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Hierarchy of the physical attributes of extreme weather, climate and oceanic events.

with respect to specific return frequencies (e.g. ‘100-year event’). Magnitude is described with reference to a specific threshold, which may be characterised using an index.12 The duration or longevity of an event can be short-lived or longer-term, and continuous or spasmodic. Antecedent conditions for an event can lead to rapid or slow onset.35 In recent decades, regional extreme events are being given increasing attention.36 These meet statistical extreme criteria while also persisting in time and demonstrating regional characteristics that show simultaneous occurrences for a group of stations or grid points. This book uses the broader formal definition of climate change as adopted by the Intergovernmental Panel on Climate Change, namely ‘a change in the state of the climate that can be identified (e.g., by using statistical tests) by changes in the mean and/or the variability [including extremes] of its properties, and that persists for an extended period, typically decades or longer’.33 And for convenience, the terms ‘climate change’ and ‘global warming’ are used interchangeably, despite differences in how they are perceived more widely.37 The terms ‘anthropogenic climate change’ and ‘human-induced climate change’ can also be used interchangeably. They recognise the role of the enhanced greenhouse effect and other manifestations of anthropogenic forcing of the atmosphereeocean system, and they are consistent with the narrower definition of climate change used in the United Nations Framework Convention on Climate Change.12 Finally, with respect to terminology, two further clarifications are provided. The word ‘projection’ is used here when referring to model-based estimates of future climate conditions which have been forced by specified drivers such as changing atmospheric concentrations of greenhouse gases. The term ‘prediction’ is not used in this context. It normally refers to estimates of the future which also reflect the initial conditions of the climate system.38 Hurricanes, typhoons and tropical cyclones are all referred to as tropical cyclones, except when referring to a named system.

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Uncertainty and confidence This book relies on the definition of uncertainty provided by the Intergovernmental Panel on Climate Change e ‘a state of incomplete knowledge that can result from a lack of information or from disagreement about what is known or even knowable. It may have many types of sources, from imprecision in the data to ambiguously defined concepts or terminology, incomplete understanding of critical processes, or uncertain projections of human behaviour’.39 Uncertainty can be characterised using either quantitative measures or qualitative statements, such as when summarising expert judgment. Uncertainty challenges both the analysis and management of extremes, and results in varying levels of confidence in the evidence base and in the resulting findings and recommendations. Uncertainties are inherent in the geological and observational data that form the baseline against which future changes in extremes are assessed. There is also an incomplete understanding of the physical mechanisms linking extreme events and anthropogenic climate change. This challenges both the modelling of future changes and the interpretation of those findings. For example, there is still residual uncertainty in the response of climate models to changes in greenhouse gases and other forcing agents, and even more regarding how these drivers will change in the future. High-frequency variability of temperature has increased in low- to mid-latitude regions over recent decades, with this change being attributable to rising concentrations of greenhouse gases.40 A more variable climate is not only associated with an increased frequency of extremes, but also with greater uncertainty. Natural variability in the climate system overall, but especially in extreme events, is a further source of uncertainty, especially when assessing whether there is a significant change in extreme events, in both the past and the future. Natural variability is also a source of uncertainty when identifying the causes and attributing changes in extremes over time, as well as the occurrence of single extreme events. These uncertainties also have significant implications for both planning and decision-making related to addressing the consequences of weather, climate and oceanic extremes. The definition of confidence used by the Intergovernmental Panel on Climate Change is also adopted here. It defines confidence as ‘the robustness of a finding based on the type, amount, quality and consistency of evidence (e.g., mechanistic understanding, theory, data, models, expert judgment) and on the degree of agreement across multiple lines of evidence’.39 Typically, confidence is expressed in qualitative terms. Confidence statements are used to communicate judgments of the validity of findings, enabling relative comparisons of evidence-based conclusions. Increasing evidence and agreement is correlated with increasing confidence.41 Explicit descriptions of uncertainty and confidence strengthen risk communication, and especially if calibrated uncertainty and confidence language is used. But synthesising and communicating findings is especially difficult when there are substantial uncertainties and lower levels of confidence, as is often the case when detecting, projecting and attributing changes in weather, climate and oceanic extremes, and in extreme events. The opportunities and challenges related to reducing uncertainty and increasing confidence, and to working with the existing levels, will be explored in each relevant chapter of this book.

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More than a review or an assessment With respect to extremes, the present book covers many of the topics covered in the recent Sixth Assessment Report of the Intergovernmental Panel on Climate Change.34 But there is one significant difference. This book tells a previously untold story of change e changes in our ability to document past extremes, to monitor current extremes and to estimate future extremes, and to attribute causes to these past and future changes and to individual extreme events. The enhanced greenhouse effect is driving an increase in extreme weather, climate and oceanic events, and will continue to do so into the foreseeable future, at an accelerating rate. This unequivocal understanding, which comes largely as a result of the methodological and related advances summarised above, has been achieved comparatively recently. For example, the science of extreme events features prominently in a scan of the most important findings within climate changeerelated research in 2020.42 But significant gaps in our understanding remain.43 As a result, we and the systems on which we rely are relatively ill-prepared and equipped to plan for and implement effective countermeasures. Unfortunately, this is the case at global, national and sub-national levels. The hope is that telling this story will help further accelerate the rate at which our understanding of the science of weather, climate and ocean extremes is increasing.

References 1. Chen Y, Moufouma-Okia W, Masson-Delmotte V, Zhai P, Pirani A. Recent progress and emerging topics on weather and climate extremes since the Fifth Assessment Report of the Intergovernmental Panel on Climate Change. Annu Rev Environ Resour. 2018;43(1):35e59. https://doi.org/10.1146/annurev-environ-102017-030052. 2. Hay J, Mimura N. The changing nature of extreme weather and climate events: risks to sustainable development. Geomatics, Nat Hazards Risk. 2010;1(1):3e18. https://doi.org/10.1080/19475701003643433. 3. Loeb NG, Johnson GC, Thorsen TJ, Lyman JM, Rose FG, Kato S. Satellite and ocean data reveal marked increase in Earth’s heating rate. Geophys Res Lett. 2021;1(August):2e31. https://doi.org/10.1029/2021GL093047. 4. Raghuraman SP, Paynter D, Ramaswamy V. Anthropogenic forcing and response yield observed positive trend in Earth’s energy imbalance. Nat Commun. 2021;12(1):4577. https://doi.org/10.1038/s41467-021-24544-4. 5. Sillmann J, Thorarinsdottir T, Keenlyside N, et al. Understanding, modeling and predicting weather and climate extremes: challenges and opportunities. Weather Clim Extrem. 2017;18(October):65e74. https://doi.org/10.1016/ j.wace.2017.10.003. 6. Hay JE, Easterling D, Ebi KL, Kitoh A, Parry M. Conclusion to the special issue: observed and projected changes in weather and climate extremes. Weather Clim Extrem. 2016;11:103e105. https://doi.org/10.1016/ j.wace.2015.11.002. 7. Katz RW, Brown BG. Extreme events in a changing climate: variability is more important than averages. Clim Change. 1992;21(3):289e302. https://doi.org/10.1007/BF00139728. 8. IPCC. In: Houghton JT, Jenkins GJ, Ephraums JJ, eds. Climate Change, the IPCC Scientific Assessment. Contribution of Working Group I to the First Assessment Report of the Intergovernmental Panel on Climate Change (IPCC). Cambridge University Press; 1990. https://www.ipcc.ch/site/assets/uploads/2018/03/ipcc_far_wg_I_full_report. pdf. 9. IPCC. In: Houghton JT, Ding Y, Griggs DJ, et al., eds. Climate Change 2001: The Scientific Basis. Contribution of Working Group I to the Third Assessment Report of the Intergovernmental Panel on Climate Change (IPCC). Cambridge University Press; 2001. https://www.ipcc.ch/site/assets/uploads/2018/03/WGI_TAR_full_report.pdf. 10. Broska LH, Poganietz W-R, Vögele S. Extreme events definedda conceptual discussion applying a complex systems approach. Futures. 2020;115(November 2019):102490. https://doi.org/10.1016/j.futures.2019.102490. 11. Maxwell SL, Butt N, Maron M, et al. Conservation implications of ecological responses to extreme weather and climate events. Divers Distrib. 2019;25(4):613e625. https://doi.org/10.1111/ddi.12878.

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12. IPCC. In: Field CB, Barros V, Stocker TF, Dahe Q, eds. Managing the Risks of Extreme Events and Disasters to Advance Climate Change Adaptation. Cambridge University Press; 2012. https://doi.org/10.1017/ CBO9781139177245. 13. Seneviratne SI, Zhang X, Adam M, et al. Weather and climate extreme events in a changing climate. In: MassonDelmotte V, Zhai P, Pirani A, et al., eds. Climate Change 2021: The Physical Science Basis. Contribution of Working Group I to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change (IPCC). Cambridge University Press. https://www.ipcc.ch/report/ar6/wg1/downloads/report/IPCC_AR6_WGI_Chapter_11.pdf. 14. Raymond C, Horton RM, Zscheischler J, et al. Understanding and managing connected extreme events. Nat Clim Change. 2020;10(7):611e621. https://doi.org/10.1038/s41558-020-0790-4. 15. AghaKouchak A, Chiang F, Huning LS, et al. Climate extremes and compound hazards in a warming world. Annu Rev Earth Planet Sci. 2020;48(1):519e548. https://doi.org/10.1146/annurev-earth-071719-055228. 16. Bevacqua E, De Michele C, Manning C, et al. Guidelines for studying diverse types of compound weather and climate events. Earth’s Fut. 2021;9(11):1e23. https://doi.org/10.1029/2021EF002340. 17. Jensen U. Probabilistic risk analysis: foundations and methods. J Am Stat Assoc. 2002;97(459). https://doi.org/ 10.1198/016214502760301264, 925-925. 18. Woo G. A counterfactual perspective on compound weather risk. Weather Clim Extrem. 2021;32. https://doi.org/ 10.1016/j.wace.2021.100314. 19. Gignac-Eddy A, Gomes I, Ponte E, et al. Guidance Note on Using the Probabilistic Country Risk Profiles for Disaster Risk Management; 2020. https://www.undrr.org/publication/guidance-note-using-probabilistic-country-riskprofiles-disaster-risk-management. 20. Hay JE. Managing the Consequences of Weather, Climate and Ocean Extremes in Our Warming World. Elsevier and the Royal Meteorological Society; 2023. 21. IPCC. In: Field CB, Barros VR, Dokken D, et al., eds. Climate Change 2014: Impacts, Adaptation, and Vulnerability. Part A: Global and Sectoral Aspects. Contribution of Working Group II to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change (IPCC). Cambridge University Press; 2014:1132. https://www.ipcc.ch/site/ assets/uploads/2018/02/WGIIAR5-PartA_FINAL.pdf. 22. Geerts B, Linacre E. Climates and Weather Explained. Routledge; 1997. https://www.routledge.com/Climatesand-Weather-Explained/Geerts-Linacre/p/book/9780415125192. 23. Zscheischler J, Martius O, Westra S, et al. A typology of compound weather and climate events. Nat Rev Earth Environ. 2020;1(7):333e347. https://doi.org/10.1038/s43017-020-0060-z. 24. Bevacqua E, Vousdoukas MI, Zappa G, et al. More meteorological events that drive compound coastal flooding are projected under climate change. Commun Earth Environ. 2020;1(1):47. https://doi.org/10.1038/s43247-02000044-z. 25. Xie L, Liu B, Morrison J, Gao H, Wang J. Air-sea interactions and marine meteorology. Adv Meteorol. 2013;2013(2009):1e3. https://doi.org/10.1155/2013/162475. 26. Herrera-Estrada JE, Diffenbaugh NS. Landfalling droughts: global tracking of moisture deficits from the oceans onto land. Water Resour Res. 2020;56(9). https://doi.org/10.1029/2019WR026877. 27. Diaz HF, Murnane RJ. The significance of weather and climate extremes to society: an introduction. In: Diaz HF, Murnane RJ, eds. Climate Extremes and Society. Vol 9780521870. Cambridge University Press; 2008:1e8. https:// doi.org/10.1017/CBO9780511535840.003. 28. Leonard M, Westra S, Phatak A, et al. A compound event framework for understanding extreme impacts. WIREs Clim Chang. 2014;5(1):113e128. https://doi.org/10.1002/wcc.252. 29. Cattiaux J, Ribes A. Defining single extreme weather events in a climate perspective. Bull Am Meteorol Soc. 2018;99(8):1557e1568. https://doi.org/10.1175/BAMS-D-17-0281.1. 30. WMO. Guidelines on the Defintion and Monitoring of Extreme Weather and Climate Events; 2018. http://www.wmo. int/pages/prog/wcp/ccl/documents/GUIDELINESONTHEDEFINTIONANDMONITORINGOFEXTREME WEATHERANDCLIMATEEVENTS_09032018.pdf. 31. McPhillips LE, Chang H, Chester MV, et al. Defining extreme events: a cross-disciplinary review. Earth’s Fut. 2018;6(3):441e455. https://doi.org/10.1002/2017EF000686. 32. Zwiers FW, Alexander LV, Hegerl GC, et al. Climate extremes: challenges in estimating and understanding recent changes in the frequency and intensity of extreme climate and weather events. In: Asrar GR, Hurrell JW, eds. Climate Science for Serving Society. Springer Netherlands; 2013:339e389. https://doi.org/ 10.1007/978-94-007-6692-1_13.

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33. IPCC. In: Stocker TF, Qin D, Plattner G-K, et al., eds. Climate Change 2013: The Physical Science Basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change (IPCC). Cambridge University Press; 2013. https://www.ipcc.ch/site/assets/uploads/2018/02/WG1AR5_all_final.pdf. 34. IPCC. Climate Change 2021: The Physical Science Basis. Contribution of Working Group I to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change (IPCC). (Masson-Delmotte V, Zhai P, Pirani A, et al., eds.). Cambridge University Press. 2021. https://www.ipcc.ch/report/ar6/wg1/downloads/report/ IPCC_AR6_WGI_Full_Report.pdf. 35. Matias DM. Slow onset climate change impacts: global trends and the role of science-policy partnerships. Discuss Pap. 2017;24/2017:21 (October) https://www.die-gdi.de/uploads/media/DP_24.2017.pdf. 36. Ren F-M, Trewin B, Brunet M, et al. A research progress review on regional extreme events. Adv Clim Change Res. 2018;9(3):161e169. https://doi.org/10.1016/j.accre.2018.08.001. 37. Sonnett J. Climate change risks and global warming dangers: a field analysis of online US news media. Environ Sociol. 2021;00(00):1e11. https://doi.org/10.1080/23251042.2021.1960098. 38. Kirtman B, Power SB, Adedoyin JA, et al. Near-term climate change: projections and predictability. In: Stocker TF, Qin D, Plattner G-K, et al., eds. Climate Change 2013: The Physical Science Basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change (IPCC). Cambridge University Press; 2013. https://www.ipcc.ch/site/assets/uploads/2018/02/WG1AR5_Chapter11_FINAL.pdf. 39. IPCC. In: Pörtner H-O, Roberts DC, Masson-Delmotte V, et al., eds. IPCC Special Report on the Ocean and Cryosphere in a Changing Climate; 2019. https://www.ipcc.ch/site/assets/uploads/sites/3/2019/12/SROCC_ FullReport_FINAL.pdf. 40. Kotz M, Wenz L, Levermann A. Footprint of greenhouse forcing in daily temperature variability. Proc Natl Acad Sci USA. 2021;118(32). https://doi.org/10.1073/pnas.2103294118. e2103294118. 41. Mach KJ, Mastrandrea MD, Freeman PT, Field CB. Unleashing expert judgment in assessment. Global Environ Change. 2017;44:1e14. https://doi.org/10.1016/j.gloenvcha.2017.02.005. 42. Pihl E, Alfredsson E, Bengtsson M, et al. Ten new insights in climate science 2020 — a horizon scan. Glob Sustain. 2021;4:e5. https://doi.org/10.1017/sus.2021.2. 43. Chen D, Rodhe H, Emanuel K, et al. Summary of a workshop on extreme weather events in a warming world organized by the Royal Swedish Academy of Sciences. Tellus B. 2020;72(1):1e13. https://doi.org/10.1080/ 16000889.2020.1794236.

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P A R T I

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.. the confidence about past and future changes in weather and climate extremes has increased due to better physical understanding of processes, an increasing proportion of the scientific literature combining different lines of evidence, and improved accessibility to different types of climate models. (IPCC, 2021)1

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IPCC. Climate Change 2021: The Physical Science Basis. Contribution of Working Group I to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change (IPCC). (Masson-Delmotte V, Zhai P, Pirani A, et al., eds.). Cambridge University Press https://www. ipcc.ch/report/ar6/wg1/downloads/report/IPCC_AR6_WGI_Full_Report.pdf

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Changes in characterising extremes Given their importance and the prospect of changes in the future, it is very important to understand how and why weather and climate extremes have changed in the past, and how they will change in the future. (Zhang and Zwiers, 2013).1

Introduction A foundational review of extreme weather, climate and ocean events2 concluded that understanding these extremes is an important goal in the atmospheric and ocean sciences. All weather and climate risk assessments depend on characterising the tails of the distributions of these extremes. This book tells the story of the impressive progress that has been made in achieving that goal. The science community has embraced and advanced the study of extreme weather, climate and ocean events. The media and the public are also showing increasing interest in the role humans have played in the changing frequency and intensity of such events, and the implications for the future. But a relatively unrecognised substory relates to the increased access to quality data and other information on extremes, along with significant advances in the methods used to assess past changes and quantify future changes, and attribute these to natural processes and anthropogenic influences. The present chapter tells this substory. It involves many incremental and transformational changes. All are worthy of much greater recognition, individually and collectively. Importantly, the story is presented not just for its own sake. It also provides an essential context for the evidence on past and future changes in extremes which is presented in the four chapters that follow. Several approaches are used to describe and analyse extremes, including identifying the associated uncertainties. The methods include investigating unprecedented or recordbreaking events, calculating exceedances over absolute or percentile thresholds, and applying extreme value theory by fitting an extreme value distribution to the extremes of a relevant variable in order to calculate return periods, such as the intensity of a 100-year rainfall event.3 In this chapter, these general methods are contextualised and elaborated within a framework (Fig. 2.1) which distinguishes between the multiple sources of information and methods used to characterise past changes in extremes, and the reliance solely on modelling with respect to future changes. Importantly, the quality of these model-based projections is, in part, influenced by the effort made to ensure they are capable of simulating the occurrence

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FIGURE 2.1 Framework for the multiple sources of information and methods used to characterise changes in weather, climate and ocean extremes.

of extreme events as represented in observational and other records. Methods to detect and attribute changes in the frequency, intensity and other characterisations of extreme events are also common to studies that focus on the past or the future. So too are topics such as confidence and uncertainty. While the content of much of this chapter is applicable to both atmospheric and oceanic extremes, some sections distinguish between them. Despite oceanic extremes being strongly coupled to the circulation of both the upper ocean and the overlying atmosphere (Chapter 8), initiatives aimed at improving our understanding of oceanic and atmospheric extremes, through both the analysis of observations and by modelling, have proceeded somewhat independently.

Detecting past changes in extremes Overview Documenting and understanding past changes in extremes is important for three main reasons. Firstly, knowledge of past extremes places current extremes in context. Secondly, the information is fundamental to interpreting changes in systems which are sensitive to

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atmospheric and oceanic conditions, including food production, water supplies, transportation and tourism. This helps guide initiatives designed to improve the productivity and resilience of such systems. Thirdly, information on past changes is also critical to assessing and increasing the capacity to model changes in these extremes for the coming years, decades and centuries. Confidence in the ability of a model to characterise future changes in extremes is dependent, in large part, on being able to demonstrate how well it can replicate changes in those same extremes over past decades and to evaluate both model variability and model behaviour under historical forcing. Such validation efforts require high confidence in the historical observational record.4 Models with proven reliability can also form a key part of climate reanalysis systems. These are used to estimate past weather and its variations, complementing the sparser observational records. Most reanalysis systems have global coverage and provide estimates for at least the last 30 to 50 years.5 Until relatively recently, most studies designed to characterise systematic, longer-term changes in the global climate focussed on changes in mean values. But in the last decade or so, there has been substantial progress in the ability to characterise and detect past changes in extremes, especially those related to temperature and precipitation. This involved overcoming the many challenges to detecting systematic changes in extremes over time.6,7 These include reconciling information from multiple data sources (palaeo-reconstruction, stationbased, satellite and reanalysis) and ensuring adequate spatial coverage, temporal duration, completeness, homogeneity and accessibility of the data. Major advances have also been achieved in developing and applying the sophisticated statistical techniques required to detect temporal changes in the extremal portions of the distribution of the available data. But the complexity of extremes, the choice of multiple operational definitions of suitable indicators as well as reaching a consensus on reference periods (i.e. baselines) continue to present major challenges. Information on extremes differs significantly between the pre-instrumental and instrumental eras. The latter era extends back by only two centuries. Opportunities to assess changes in extremes prior to that time are provided by the use of indirect ‘proxy’ measures and climate model simulations. Some measures, such as those derived from the majority of preserved pollen and from low accumulation ice cores and sediment cores, are only capable of describing changes in climate on century or even longer time scales. On the other hand, historical documentary records, tree rings, laminated lake and ocean sediments, speleothems, corals and annually differentiated ice cores have the potential to provide annually or even seasonally resolved climate records.8 This latter grouping of proxy measures can provide useful insights into the changes in extremes in the pre-instrumental era, especially when combined with model simulations. Well-managed instrumental records are by far the most reliable of all available weather, climate and ocean data.9 They are able to resolve individual extreme events. But such data are only available on a relatively widespread basis back to 1850.10 Importantly, the more recent information available from surface and satellite observations, and from atmospheric reanalyses, is generally more comprehensive, detailed and reliable, especially after 1950, and since the 1980s for satellite data. This limits highly rigorous assessments of past changes in extremes to the more recent decades. This can limit the applicability of the findings.11,12

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Pre-instrumental era data Changes in weather, climate and ocean extremes during the pre-instrumental era may be examined using palaeo-reconstructions, documentary evidence and model-based analyses. The focus is usually on the last two millennia, the Common Era (CE), and largely on the immediate pre-industrial millennium, that is CE 850e1849. During the past two millennia, the basic boundary conditions of the Earth’s climate, including the continental arrangement, orography, Earth-orbital parameters and the spatial extent of continental ice sheets, did not change significantly. Potentially, therefore, the CE provides a baseline of the natural variability in weather, climate and ocean extremes, against which more recent changes in extremes can be assessed. However, the rarity of extreme events, and the limited information available for the CE, limits the ability to determine the likelihood of these extreme events occurring during that time. This is despite an increasing number of relevant studies. It is therefore challenging to assess whether the likelihood of an extreme event is different to that in the instrumental period. As noted above, key information is limited due to the shortage of high-resolution natural archives which can serve as proxies for past atmosphere and ocean variations at a temporal scale comparable to that of instrumental data.13 For the CE, tree rings, corals, ice cores, some speleothems, and lake and marine sediments, can provide high-resolution and generally welldated proxy records with decadal or better resolution. These are available for large regions of the Northern Hemisphere and some parts of the Southern Hemisphere.10 But even with such a resolution, only longer duration and larger spatial scale extremes are usually identifiable. These include multi-year droughts, and extensive and seasonal scale temperature extremes. Other proxy records can provide further insights, especially when used in combination. This includes historical documentary records, such as farming and phenological records, ecclesiastical documents, newspapers, paintings, logbooks and diaries. These can provide information on frost dates, droughts, famines, freezing and thawing of water bodies, duration of snow and sea ice cover and phenological evidence such as flowering dates.14 But such documentary information can sometimes overstate extreme conditions. Therefore, where possible, documentary evidence must undergo independent calibration using instrumental data in order to improve its reliability.10 Thus pre-instrumental documentary records will be of lower quality than later evidence from the same general sources. Importantly, there is now ‘a new age of research on the climate of the CE’.15 This is characterised by better coordinated, and hence more consistent investigations on temporal resolutions of years to centuries. These scaled-up efforts include assembling more climate proxy archives and interpreting the signals they contain, improving the statistical methods used to estimate past climate variability from the proxies, understanding the uncertainties in the resulting estimates, and comparing reconstructed climate variability and change with model simulations. One of the beneficiaries of improved coordination is paleotempestology, the study of storm occurrence before written records became available.16 The PAGES2k initiative exemplifies this ‘new age’ in the use of palaeo-reconstructions and documentary evidence to create an extreme event baseline for the pre-instrumental era.17 Nearly 700 temperature-sensitive proxy records from over 600 locations covering all continents and the major ocean basins have been assembled in an open access database. It forms a major resource for studies of global and regional temperature variability over the CE. The

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records, which range in length from 50 to 2000 years, are derived from trees, sediment, ice, corals, speleothems, documentary evidence and other archives. Temporal resolution ranges from biweekly to centennial. The higher resolution records are better suited to studies of extreme events. Validation included examining the ability of the proxy records to reflect the observed temperature variability at local and regional scales, as captured in an instrumental dataset covering CE 1850e2014.18 This dataset combines surface air temperature over land, and sea surface temperature over ocean regions. Nearly half of the proxy time series had significant correlations with observed surface temperatures. The complementary technique of palaeoclimate modelling has also undergone major improvements since it was first undertaken in the 1970s. The models used in palaeoclimate studies, and in climate studies, more generally, have evolved from comparatively simple three-dimensional representations of the atmosphere, to now include representations of the oceans and land cover, and incorporate the interactions between atmosphere, oceans, land and ice sheets. They also use time-dependent estimates of external influences (forcings) of climate, namely volcanic and solar natural radiative forcing, and anthropogenic greenhouse gas, aerosol and land-use forcing. These improving representations of the Earth system are now provided at significantly higher spatial and temporal resolution. Paleoclimate reconstructions based on proxy data, such as described above, play a critical role in both evaluating and improving the ability of climate models to simulate past changes and variability in the climate. Until recently, palaeoclimate modelling tended to focus on increasing our understanding of past changes in mean temperature and precipitation. However, combined model-data approaches have led to marked improvements in palaeo-reconstructions. This has made it possible to undertake rigorous analyses of the role and importance of longer-term climate extremes,19 thereby adding value to earlier studies based on palaeoclimate modelling alone.20 Specific examples of progress in paleoclimate reconstructions using various ways to combine proxy data and climate modelling are presented in Box 2.1. The proxy data ensure the reconstructions are as close as possible to the observations, while the modelling can provide reconstructions that are physically consistent and provide three-dimensional information on the state of the atmosphere for multiple variables and all points in time. The examples illustrate the progression from the use of statistical reconstruction techniques to physically consistent reconstructions based on climate model simulations. Given that before 1850 instrumental data are only available at limited locations, global three-dimensional climate reconstruction spanning the period between 1600 and 2005 provides an important bridge between pre-instrumental and instrumental era data. The resulting dataset,25 which has 2
resolution globally, was generated by blending atmospheric model simulations and various types of observations, including early instrumental measurements, documentary data and proxy records. The monthly resolution facilitates analysis of past climate variations, and of extreme events such as droughts.

Instrumental era data In situ land surface data The limitation of using in situ data, alone, to detect the occurrence of extreme events is highlighted by a recent calculation26 showing that the total area of the orifices of all

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BOX 2.1

Illustrative examples of progress in paleoclimate reconstruction methods Seven different statistical methods were used with the PAGES2k multiproxy database to reconstruct surface temperatures for the past 2000 years.21 The methods included basic composite-plus-scaling and regressionbased techniques, commonly used in previous reconstructions. These enabled the use of lower-than-annual resolution proxy records. Newer methods were also used. These included the linear methods of optimal information extraction and Bayesian hierarchical modelling, as well as pairwise intercomparison. The latter combines proxy records with different temporal resolution, and accounts for nonlinear relationships between those proxy values and temperature. Data assimilation was also used. This technique was used to combine proxy observations and pre-computed output from the NCAR Community Climate System Model in order to reconstruct multiple climate fields which were consistent with the underlying physics of the climate model. All methods used an interpolated version of an instrumental dataset covering 1850 to 200018 as a calibration dataset. Calibration was also performed from 1916 to 1995, allowing validation of reconstructions for 1881 to 1915. A 1000-member ensemble of reconstructions was generated for each method in order to provide a probabilistic assessment of uncertainties. Uncertainties for all reconstruction methods increased back in time. They were particularly large prior to medieval times due to the decreased number of proxy data. and to changes in the observing network.

The first monthly global paleo-reanalysis covered the period 1600 to 2005. Landbased instrumental temperature and surface pressure observations, as well as temperature indices derived from historical documents and climate sensitive tree-ring measurements, were assimilated into a 30-member ensemble from the ECHAM atmospheric general circulation model developed by the Max Planck Institute for Meteorology.22 The reconstructions were validated for the 20th century by using independent instrumental, documentary and proxy datasets. A data assimilation method was also used to generate the first global reconstructions of hydroclimate and associated atmosphereeocean states for the CE.23 Collectively, this information allows analyses of the causes of hydroclimate extremes. Proxy information from a network of 2978 annually resolved proxy data time series were assimilated into simulations of the Community Earth System Model Last Millennium Ensemble, using an offline approach. Temperature at 2 m, the Palmer Drought Severity Index and the Standardized PrecipitationEvapotranspiration Index24 were gridded at w2o resolution. Indices were calculated at annual, monthly and multi-monthly temporal resolutions, as appropriate, in order to illustrate linkages between hydroclimate variability and extremes globally. The resulting Paleo Hydrodynamics Data Assimilation product represents the first collection of global hydroclimate reconstructions, together with their associated dynamical variables. These can be used to characterise the dynamics

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BOX 2.1 (cont'd) associated with droughts and pluvials during the CE, on time scales ranging from seasons to centuries. The reconstructions were validated against observations primarily using two skill metrics computed for the years 1901e2000, for observations-based temperatures and for the Standardized Precipitation Evapotranspiration Index using land surface datasets. Skill metrics for the temperature-based climate indices were also determined for the 1871 e1919 period. Skill tended to be highest in the tropics, and nearby the proxy locations during the summer growing season. Results were generally consistent across the temporal windows and variables. The temperature reconstructions were generally more skilful than the Palmer Drought Severity Index and

the Standardized PrecipitationEvapotranspiration Index. The drought severity reconstructions were found to be in very close agreement with drought atlas products, particularly over North America and Europe. Agreement was much lower in the AustraliaeNew Zealand region, as well as in regions where there was limited or no proxy data. In these locations, the model ensembles were often insufficiently constrained, resulting in localised regions of low skill. Reconstructions of the various climate indices showed high skill for diverse regions. Overall, the validation tests showed that many variables were skilfully reconstructed, with the level of skill being dependent on the region, the variable, the time window and the timescale (e.g. annual versus decadal).

operational rain gauges worldwide is only 0.000000000593% of the Earth’s surface area. Of course, gauges provide useful information for more than just their specific location. But even if it is assumed that a gauge represents precipitation conditions within 5 km of its location, the coverage still represents only about 1% of the Earth’s surface. And the representation challenge does not end there. Analyses of changes or trends in extremes are most successful when using daily or sub-daily (one- to six-hourly) observed data.27 However, access to the original observations for these time resolutions continues to be one of the biggest impediments to assessing long-term changes in extremes over the globe.28 For large portions of the world, daily and sub-daily weather archives are often not readily accessible internationally due to restrictions imposed by the country where the observations were made. As a result, early global and regional analyses of daily extremes29 did not cover most of Africa, southern Asia and Central and South America. In a worrying recent trend, the density of observing stations reporting relevant data has decreased, in both developing30 and developed31 countries. Spatial coverage continues to be uneven, with large data gaps continuing to exist for regions such as Africa and South America.32 Fig. 2.2 shows the change over time in number of quality-controlled stations contributing data to a global land-based gridded dataset of daily precipitation.

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FIGURE 2.2 Number of quality-controlled stations contributing data to a global land-based gridded dataset of daily precipitation from 1950 to 2016. Published with permission. From Contractor S, Donat MG, Alexander L V. et al. Rainfall Estimates on a Gridded Network (REGEN) e a global land-based gridded dataset of daily precipitation from 1950 to 2016. Hydrol Earth Syst Sci. 2020;24(2):919e943. https://doi.org/10.5194/hess-24-919-2020.

Furthermore, many countries with relevant data continue to place high strategic or commercial value on daily and higher-resolution meteorological data, and are therefore unwilling to freely share their national weather archive with the international community. Other countries may be willing, but lack the capacity to mine, process and transfer large volumes of historic data. As a result of cooperative, concerted and well-coordinated international efforts, an elegant solution was found. The World Meteorological Organization’s Commission for Climatology, together with the World Climate Research Programme project on Climate Variability and Predictability, established the joint Expert Team on Climate Change Detection and Indices.a Its mandate was to address the need for the objective measurement and characterisation of climate variability and change, including through international coordination and collaboration on climate change detection, and the identification of indices relevant to climate change detection, and comparison of modelled data and observations. The joint Expert Team pursued two initiatives in parallel.34 The first involved the development of an internationally coordinated and agreed core set of 27 descriptive indices of extremes derived from daily in situ data, along with their precise definitions (Table 2.1). a In 2006 the Joint World Meteorological Organisation-Intergovernmental Oceanographic Commission of the United Nations Educational, Scientific and Cultural Organization Technical Commission for Oceanography and Marine Meteorology joined the two founding organisations to support the work of the Expert Team. This Team was disbanded in 2018. The Commission on Climatology’s Expert Team on Sector-specific Climate Indices was given the responsibility for operationalising sector-specific climate indices.

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Detecting past changes in extremes

TABLE 2.1 Descriptor

Extreme temperature and precipitation indices developed by the Expert Team.36 The last three indices are also included in HadEX2 and HadEX337. Description

Definition

Unit C

TXx

Hottest day

Monthly maximum value of daily maximum temperature




TNx

Warmest night

Monthly maximum value of daily minimum temperature




C

TXn

Coldest day

Monthly minimum value of daily maximum temperature




C

TNn

Coldest night

Monthly minimum value of daily minimum temperature




C

TN10p

Cool nights

Percentage of time when daily minimum temperature 90th percentile

%

DTR

Diurnal temperature range

Monthly mean difference between daily max and min temperature




GSL

Growing season length

Annual (1st Jan to 31st December in NH, 1st July to 30th June in SH) count between first span of at least six days with daily mean temperature >5
C and first span after July 1 (January 1 in SH) of six days with daily mean temperature 90th percentile

days

C

(Continued)

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26 TABLE 2.1

2. Changes in characterising extremes

Extreme temperature and precipitation indices developed by the Expert Team.36 The last three indices are also included in HadEX2 and HadEX337.dcont’d

Descriptor

Description

Definition

Unit

CSDI

Cold spell duration

Annual count when at least six consecutive days of minimum temperature 99th percentile

mm

PRCPTOT

Annual total wetday precipitation

Annual total precipitation from days 1 mm

mm

ETR

Extreme temperature range

Difference between hottest day and coldest night




R95pTOT

Contribution from very wet days

Annual rainfall from very wet days as percentage of annual total wet-day precipitation

%

R99pTOT

Contribution from extremely wet days

Annual rainfall from extremely wet days as percentage of annual total wet-day precipitation

%

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C

Detecting past changes in extremes

27

These allow comparable analyses of data for land areas across the world. The aggregation of raw data into indices also addresses the reluctance of many countries to share original archives of daily data. Many of the indices are based on the number of days in a year exceeding specific thresholds. These are usually based on percentile thresholds rather than categorical, physically-based thresholds, such as 0
C. The latter are unlikely to be evenly distributed across large regions, and may even result in zero returns in some parts of the world. In contrast, the number of days exceeding a given percentile will be more evenly distributed, and is therefore a meaningful index globally. The relative thresholds are set to capture extremes that typically occur a few times every year, rather than once-in-a-decade events (Box 2.2).

BOX 2.2

Extreme terminology Building on the more general definition of an extreme (Chapter 1, Terminology and Definitions), the Intergovernmental Panel on Climate Change has defined a climate extreme as ‘the occurrence of a value of a weather or climate variable above (or below) a threshold value near the upper (or lower) ends of the range of observed values of the variable’.41 Even then, this definition does not provide a precise specification as to what is considered to be extreme. In many ways, it simply reflects common practice. For example, some studies of extremes use indicators of the frequency or intensity of events based on parts of the distribution that are not very extreme, such as warm events that exceed the 90th percentile of daily maximum temperature. Since, on average, such events occur several times a year, they are often referred to as ‘moderate extremes’. Other studies consider values of climate variables that are generally not expected to recur each year. Such rare events are consistent with the concept of extreme in the statistical sciences, where powerful statistical tools based on extreme value theory have been developed in order to characterise the

occurrence of events more extreme than those captured in the observed record. This might, for example, involve estimating the magnitude of a 100-year event when only 30 years of observations are available. The same statistical tools are now also used in the analysis of past and future extremes. In this context, extremes are defined as very high quantiles, such as the 95th, 99th or 99.9th percentiles of annual maximum values. The shortness of the observational record in many parts of the world limits the chance of observing a rare event, such as one which occurs only once in several hundred years. When an event of this rarity does occur, it is often not only considered ‘unprecedented’, but also a ‘surprise’. Analysis of very rare events for a particular location is often expanded to assessing their likelihood of occurrence within a broader region with a similar climate. This provides an alternative way to make quantitative likelihood statements about events that are extremely rare at a single location.

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2. Changes in characterising extremes

The measures of climate extremes must be rigorous and clearly defined.27 For example, eight heat stress indicators were calculated using models participating in Phase 6 of the Coupled Model Intercomparison Project.35 Their future trends were assessed as a function of global mean temperature. The indicators showed a substantial spread, ranging from trends close to the rate of global mean temperature up to more than twice that rate. Even when the indicators were normalised by accounting for the different scales used in their definition, the large spread remained. This reflected, in part, differences in the definition of threshold levels. The second work stream of the joint Expert Team comprised a series of workshops in datasparse regions. These were designed to fill gaps in regional and global databases of extremes. Attendees learned how to undertake quality control procedures, including homogeneity testing to assess the impacts of any changes in instrumentation, observing practices, station location and site conditions.36 These procedures were informed by the history of each observing station. Participants then generated time series of the Expert Team indices, based on long-term daily data from meteorological stations in their respective countries. In many cases, only the compiled indices and station history would be made available to the international community. Development of a standardised software package of simplified procedures has since made it possible for individuals to calculate the indices without needing to attend a workshop. In this way, the spatial coverage and reliability of extreme indicator databases has improved over time, and now includes global gridded land-based datasets (Box 2.3). But despite the use of indices, some regions continue to be poorly represented. For example, long-term and high-quality data on precipitation extremes are available from less than half of the world’s arid regions.38 A recent case example39 highlighted the urgency to compile index-based information on extreme events in a disaster-prone country in order to inform both policy development and planning, and the practical impediments to generating such information.

BOX 2.3

Global datasets of gridded land-based extremesb The first global open-access dataset of gridded land-based temperature and precipitation extreme indices, HadEX, covered the period 1951e2003 only.37 Initially it contained all but one (Rnnmm e see Table 2.1) of the original 27 indices developed by the Expert Team. HadEX was subsequently extended to cover the period 1901 to 2010, along with an increased number of land surface stations. Both datasets included annual and, in some cases, monthly time

series, with the station data being interpolated to a 3.75
x 2.5
longitudeelatitude grid. HadEX and its successors (HadEX2 and HadEX3), also included three additional indices (Table 2.1). HadEX3 is based on 17 temperature and 12 precipitation indices covering the period 1901 to 2018, initially calculated for around 7000 locations for temperature and 17,000 for precipitation.37 A separate, open-access dataset, GHCNDEX, was developed in order to allow

I. Changes

Detecting past changes in extremes

BOX 2.3 (cont'd) for monthly or annual updating. This makes the dataset a valuable information source for climate monitoring reports.45 GHCNDEX uses the Global Historical Climatology Network Daily dataset rather than the combination of national and regional data used in the HadEX series. There are other significant differences, including the spatial coverage of HadEX2 being greater than that of GHCNDEX. For GHCNDEX, the daily station time series were first interpolated to a grid, and the indices calculated subsequently, while the opposite sequence was used for the HadEX suite of datasets. This difference in the sequence of steps leads to different values for the extremes, with less agreement for extreme precipitation than for extreme temperatures.46 These procedural differences, and the variations in the density of the observational network, contribute to uncertainties in the gridded indices. These are greatest when the long-term changes in the extremes are small, or in regions with few stations.47 EUSTACE is a global land dataset of quality-controlled in situ daily maximum and minimum temperature observations for 35,364 locations covering the period 1850 e2015.48 The data were selected to ensure both uniqueness and consistency, taking into account the heterogeneity that results from the diverse methods used to manage station networks. Coverage was subsequently extended to ocean and ice surfaces.49 A comprehensive review of 30 global precipitation datasets included consideration of their relative performance when analysing rainfall extremes.40 The archives include gauge-based, satellite-related and reanalysis datasets. Research into the nature and drivers

of intense precipitation is becoming increasingly focussed on sub-daily scale (1e6 h) rainfall data, as these extreme events cause damaging flash floods and can trigger landslides. But progress in characterising the changes in sub-daily rainfall extremes has been hampered by the lack of a global archive of sub-daily rainfall data. This was recently addressed by the release of the Global SubDaily Rainfall Dataset.50 The archive contains observed hourly data for over 23,000 gauges in over 200 countries and territories. Around a quarter of the stations have records longer than 30 years. But very few gauges have records exceeding 60 years. A global database of meteorological drought events has recently been compiled.51 Events were identified for three spatial scales (global, macro-regional and country level) using the Standardized Precipitation Index and the Standardized PrecipitationEvapotranspiration Index applied to two global land surface datasets from 1951 to 2016. Accumulation scales range from 3 to 72 months. The database includes approximately 4500 and 4800 events for each index, respectively. Each event is described by its start and end dates, duration, intensity, severity, and by the peak, average and maximum areas in drought. An index based on six of these descriptors has been used to identify 52 mega-droughts. The 23 macroregions are included in the database because many of the identified mega-droughts involved multiple countries, thus qualifying as regional extreme events. b

Some global gridded datasets are available at https://www.climdex.org/learn/datasets/.

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29

30

2. Changes in characterising extremes

Gridded precipitation datasets based entirely on gauge information reflect the problem of a declining number of observing sites providing the required data.40 For example, the Global Precipitation Climatology Centre’s Full Data Product is the most commonly used gridded global precipitation dataset, covering the period from 1901 to the present. Initially it was based on around 10,900 usable stations. The number increased steadily to a maximum of about 49,470 in 1970, but subsequently declined to 30,000 in 2005 and to only about 10,000 by 2012. The growing importance of, and interest in, compound extremes42 and regional extreme events43 has highlighted the benefits of integrating into one index multiple extreme indicators derived from in situ observations. Two examples are the Actuaries Climate Index44 and the Climate Extremes Index.27 The former is based on six extreme indicators. Values of these are determined relative to a baseline for which the mean and 10th and 90th percentile values are calculated: frequency of temperatures above the 90th percentile, frequency of temperatures below the 10th percentile, maximum five-consecutive-day rainfall, maximum number of consecutive days with precipitation less than 1 mm, frequency of wind speed above the 90th percentile and change in sea level. The raw values for each component are converted to standardised anomalies. The Index is the mean of these components, with the sign reversed for the extreme low-temperature component.52 It is routinely available for the United States and Canada53 and Australia,54 and its use is being contemplated for Europe and the United Kingdom.55 The Climate Extremes Index has undergone several revisions.56 A version of the Index is now used operationally for nine regions and the conterminous United States. It describes, for a season or year, a combination of the fractional area of a region, or of the country, that experienced extremes outside the 10th and 90th percentiles for multiple indicators. The indicators are maximum and minimum temperatures, the Palmer Drought Severity Index, proportion of precipitation from heavy-precipitation days, the number of days with or without precipitation and tropical system activity.57 The Index has also been applied to Australia,58 and subsequently to the United States, Europe and Australia.59,60 It has also been modified by using seven of the temperature and precipitation extreme indices listed in Table 2.1. This modified version has been applied to four continental regions and one hemispheric region, namely Europe, North America, Asia, Australia and the Northern Hemisphere.61 Several shortcomings in the Climate Extremes Index have led to even further revisions.62 Despite attempting to portray the overall extremeness of the weather and climate, the Index does not reflect tornadoes or multiple day extreme events such as heatwaves. Moreover, an indicator based on the area experiencing the highest and lowest 10% of the observed data will, on average, result in 20% of the area being assessed as always experiencing extreme conditions. In early versions of the Index, each indicator was the sum of the two areas calculated using each of the tails of the data distribution. This approach tended to make the Index more sensitive to changes in the spatial patterns of extremes. In later versions of the Index, these two areas have been subtracted, resulting in the Index being more sensitive to changes in the magnitude of the extremes.58 Further modifications have included using daily-scale rather than monthlyscale temperature extremes,58 and calculating the Index on a numerical scale using the nonparametric Z-score statistic. This reflects the fact that precipitation data are not normally distributed.62 This revised version of the Index has been applied to the United States.

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31

In situ ocean data The vast, remote and often violent nature of the world’s oceans, and being part of the global commons,63 has severely challenged the collection of information on the state of the ocean and its overlying atmosphere. As a result, there is a relative dearth of information describing oceanic extremes. But the situation is changing rapidly. Ocean observing systems now comprise ships, buoys, fixed and mobile platforms, aircraft and satellites.64 Yet there are still major shortcomings in spatial coverage and ongoing challenges in merging the various sources of information.65 Fig. 2.3 shows the total number of in situ ocean weather observations between 1850 and 2017, by platform type. While this shows a dramatic increase since the 1970s, the areal coverage has reduced due to the declining contribution by ships since the 1990s. This has been only partially compensated by an increase in coverage from buoys and coastal platforms.66 The increased use of autonomous remote and in situ platforms has revolutionised the ocean observing system. However, many of the datasets that can provide insights to the changes in marine extremes are of limited duration, especially relative to the time scales of variability, including trends and long-term cycles.65,67 A significant challenge arises when creating long-term ocean datasets. It relates to the major changes over the past century and a half in the technologies and procedures used to monitor such variables as sea surface temperature (Fig. 2.4). Even small changes in measurement methods can result in errors in the estimated trends being as large as 1.0
C, which is similar to the variation in sea surface temperature over the same period.68 Therefore, in order to assess changes in sea surface temperatures over time, these systematic errors must be corrected and the residual uncertainties must be quantified. Combining tide gauge and other systematic data with historical information such as news articles, flood water marks and

FIGURE 2.3 Total number of observations between 1850 and 2017 by platform type: ships, moored buoys, drifting buoys, oceanographic observations and coastal and other platforms. Reproduced with permission from Kent EC, Kennedy JJ. Historical Estimates of Surface Marine Temperatures. Ann Rev Mar Sci. 2021;13(1):283e311. https://doi.org/10. 1146/annurev-marine-042120-111807, http://www.annualreviews.org.

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2. Changes in characterising extremes

FIGURE 2.4

Relative contributions of methods (ERI represents engine room intake while Hull represents hull sensor measurements) used to provide sea surface temperature data assimilated into the ICOADS ship observations. Reproduced with permission from Kent EC, Kennedy JJ. Historical Estimates of Surface Marine Temperatures. Ann Rev Mar Sci. 2021;13(1):283e311. https://doi.org/10.1146/annurev-marine-042120-111807, http://www.annualreviews.org.

eye witness accounts can reduce uncertainties in estimates of extreme sea level and improve the representation of statistical outliers.69 The rapid growth in the frequency and spatial coverage of ocean observations led to a concomitant increase in the opportunity and the need to develop comprehensive datasets containing the original observations, as well as values and summary statistics interpolated on a regular grid. ICOADS Release 3.070 is the foundational global dataset of surface marine observations, serving as the basis for the production of gridded analyses of sea surface temperature and many other meteorological variables. The archive covers the period from 1662 to the present. Along with additional drifting buoy measurements, the ICOADS provides the input data for HadSST.4.0.0.0.68 The observed sea surface temperatures are averaged onto a 5
latitude by 5
longitude monthly grid. The data are presented as sea surface temperature anomalies from 1850 to 2018, relative to the 1961e90 average. They are considered representative of temperatures measured at a depth of 20 cm. Similar data sources and methods were used to produce ERSST v5.71 This is a global monthly sea surface temperature dataset on a 2
by 2
grid, covering the period from 1854 to the present. Spatial completeness is enhanced using statistical techniques. The need to quantify the risk of coastal flooding has resulted in notable progress in the development of global datasets of extreme sea levels and related variables. The GESLA-2 dataset72 contains hourly or higher frequency tide gauge data assembled from a number of national and international sea level archives. The records for 655 locations provide reasonable geographical coverage, although no data are available for some coastlines. The average length of record is 29 years, with a maximum of 167 years. Similar to ICOADS, GESLA provides the datasets needed to estimate extreme sea level parameters and validate73 earlier and widely used extreme sea level datasets such as DINAS-COAST.74 Remotely observed data Given the extensive spatial coverage, data from space-borne observing systems are a useful complement to in situ measurements. This is especially the case for regions with no or few

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Detecting past changes in extremes

33

direct observations. In such regions, satellites are the main source of information on observed changes in extremes. Polar-orbiting satellites provide the only effective remote sensing coverage for latitudes poleward of about 60 degrees. But unlike their geostationary counterparts, they do not observe any given location continuously. Single polar-orbiting satellites are not able to provide daily and sub-daily observations. However, coordinated, multi-satellite arrays can overcome this constraint.75 Satellite-based estimates of extremes have significant limitations, such as the estimation of heavy precipitation in complex mountain terrain. In this respect, there has once again been considerable progress, both generally76 and in specific instances.77 However, multiple studies of the ability of the many satellite-only products to characterise extreme precipitation events highlight that no single product is consistently better than the others. With few exceptions, satellite precipitation products tend to underestimate extreme precipitation events, with performance declining for increasing values of the percentile (90th percentile and higher) or threshold (above 50e100 mm day1).78 More specifically, when evaluating estimates using in situ data, performance varies with location, season and time scale, as well as with the metric used. But with recent increases in both spatial and temporal resolution, along with further improvements in precipitation retrieval methods, new opportunities for quantifying and monitoring precipitation extremes are becoming available globally, as well as for the many applications of such information. Satellite data do have the added advantage of being more spatially homogeneous. Until recently, the relatively short period of most satellite data archives has limited their use in assessments of longer-term changes in extremes. However, some satellite-based time series now cover several decades. These are becoming increasingly useful for assessing longer-term changes in extremes. Re- and cross-calibrations of data from many satellites are required in order to achieve global coverage for homogeneous, longer-term time series of relevant meteorological variables. Satellites provide only indirect estimates of temperature and precipitation. These can be biased if not adjusted using gridded values based on in situ measurements. Importantly, such corrections may not remove biases across the full frequency range of the data.28 Evaluations of the ability of satellite products to capture extreme precipitation are hampered by the availability of quality-controlled in situ data. But development of most products has involved the use of available data to adjust the satellite-based estimates for bias. It is important to ensure the in situ data used for validation are fully independent. Another challenge relates to the satellite estimates being for the area of the sensor pixel scan (typically between 5 and 25 km), while the in situ observations cover the gauge footprint. However, even for heavy rainfall, the in situ data may represent conditions some tens of kilometres from the gauge. For example, a study79 representative of mid-latitude precipitation conditions found that for two-hourly rainfall totals, the decorrelation distance80 varied from about 10 km in warm months to 50 km in cold months. In the former months, small-scale convection dominated, while stratified and long-lasting precipitation prevailed during the latter months. The decorrelation distance was found to increase with accumulation time. A further issue is that the gauge accumulation reporting time (e.g. 0900Z for a 24 h accumulation) may not match the daily accumulation time for satellite products. Typically, this is 0000Z-0000Z. An improved match is possible when using gauge data with a sub-daily temporal resolution. Box 2.4 provides examples of the use of in situ gauge data to evaluate

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BOX 2.4

Evaluation of selected satellite-based precipitation products The performances of two satellite-only products, IMERG (0.1
/0.5 h, Global 60
Ne60
S) and GSMaP (0.1
/1 h, Global 60
Ne60
S), were recently assessed against CPC, a gaugebased analysis of precipitation data with spatial and temporal resolutions of 0.5
/day over the global domain.81 The performance of both products improved with rainfall intensity, but generally IMERG outperformed GSMaP at the higher intensities indicative of heavy rainfall. A study82 which included a third satellite precipitation product, CHIRPS, used a high density of rain gauge stations (27 in situ rain gauges) at various elevations over Bali Island, Indonesia. The data covered three years, from 2015 to 2017. All three products tended to underestimate heavy rainfall events (>50 mm/day), with performance being best at middle and high altitudes. Consistent underestimates occurred at low-altitude locations. Of the three products, GSMaP agreed well with rain gauge observations at high altitudes in terms of the frequency of rainfall events of all intensities. For heavy-rain days (precipitation over 50 mm day1) in northern Vietnam, taking orographic convection into account was found to improve precipitation estimates based on GSMaP.83 Seven satellite precipitation products (CHIRPS v2.0 (0.25), CHIRPS v2.0 (0.05), CMORPH, IMERG, TRMM, PERSIANNCDR and PERSIANN-CCS) were examined for their ability to quantify the characteristics of drought and extreme rainfall events over the Yangtze River basin, China.77 The evaluation covered eight of the 11 extreme precipitation indexes listed in Table 2.1. These were calculated using daily precipitation data

for 198 locations. IMERG and CMORPH provided better estimates of extreme precipitation for all parts of the basin. Errors for both precipitation intensity and frequency were highest in the lower (coastal) reach of the basin. The Standardized Precipitation Index was used as an indicator of drought. IMERG provided the most accurate estimates of the Index in the upper reach, while CMORPH performed best for the middle and lower reaches. Overall, for all products, the errors in drought estimates were highest for the upper reach compared to the middle and lower reaches. Six satellite-based precipitation products with high spatial and temporal resolution (TRMM 3B42RT, TRMM 3B42V7, PERSIANN, PERSIANN CDR, CMORPH RAW and CRORPH CRT) were evaluated for their ability to capture the characteristics of extreme precipitation from over the Wei River basin, a semi-arid to semi-humid climate transition area in China.84 The reference dataset was the China gauge-based daily precipitation analysis for 2009 to 2014, derived using about 2400 gauge stations across mainland China and an optimal interpolation method. Twelve extreme precipitation indices (Table 2.1) were used for the evaluation. Overall, TRMM 3B42V7 was found to be the most reliable product for capturing extreme precipitation characteristics in the Wei River basin, including the spatial patterns. It was followed by CMORPH CRT. All products were more accurate in the plain areas of the basin than in the mountainous areas.

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35

extreme precipitation and drought estimates derived from several satellite-based precipitation products. Reanalysis products In both atmospheric and oceanic contexts, reanalysis uses a single, consistent and up-todate atmospheric or coupled atmosphereeocean model, combined with a data assimilation system, to process historical data spanning an extended period. Using a single and consistent system helps avoid the temporal discontinuities that occur over time in routine operational analyses, but this does not remove discontinuities caused by substantial changes in observing systems. While reanalysis is now a routinely used tool in atmospheric studies, application of global ocean models to the reanalysis of ocean observations is at an earlier stage of development. Reanalyses using a coupled oceaneatmosphere modelling system are becoming increasingly common.85 Reanalyses are different to hindcasts. The latter provide similar model-based results, but without data assimilation (this Chapter, Historical Simulations using Global Climate Models). The main use of reanalysis is to produce long-term homogeneous records of weather, climate and ocean signals. Historical reanalyses have been found to be generally suitable for studying past extreme events.86 Typically, reanalysis involves using a fixed version of an operational numerical weather forecasting model to transform observed data from multiple sources into a dynamically coherent dataset.87 The observed data are also used to constrain the model boundary conditions, for determining the uncertainty of other observations, and for evaluating the resulting reanalysis data products.88 As opposed to simple methods of interpolation and extrapolation, reanalysis reflects the physical and dynamical processes when extending observations at a point to adjacent locations. This results in a dynamical and coherent characterisation of the climate and/or ocean system at global, regional or national scales. Regional and larger scale reanalyses can provide additional insights on extremes, through the use of higher resolution model simulations made practical by the reduced areal coverage. The accuracy of these reanalyses is greater relative to global reanalyses, since they are often applied over regions where there is a high density of in situ data that can be assimilated into the model. Reanalyses can be used to investigate changes in climate extremes, thereby complementing the findings from analyses of in situ and satellite-derived data. In this way, reanalysis can, for example, improve on precipitation estimates based solely on satellite estimates of temperature and humidity. The majority of reanalysis products cover the more recent decades, and many are updated in real time. However, some extend back to the start of the 20th century and even to the mid-19th century.5 The fact that reanalyses can provide spatially complete coverage for physically consistent data means they are often upheld as the optimal source of data for studying changes in climate over recent decades. But in reality, and largely due to changes in the underpinning observational data, reanalyses are also subject to inhomogeneities.89 These are primarily the result of discontinuities in observed data used in the reanalysis, for example, the use of radiosonde data from 1958, and satellite data from 1979. However, the more recent data assimilation schemes cope with changes in observing systems by reconciling observations with different biases using variational and other methods. Some

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discontinuities can only be detected by incorporating multiple data sources in the reanalysis. Thus, even though there have been increasingly rapid and complex changes in observing systems in recent decades, modern reanalyses provide the most accurate and homogeneous observation-constrained datasets available.90 A new generation reanalysis data product, the Global Land Data Assimilation System, has been used to develop a higher resolution (0.25
 0.25
) open-access global land-based gridded dataset91 of 71 annual and, in some cases monthly, extreme indices. It covers the period 1970 to 2016 for all land north of 60
S latitude. It is based on sub-daily temperature and precipitation data. The 71 indices include the original 27 Expert Team indices (Table 2.1) as well as additional indices mainly designed for assessing sectoral impacts.92 A further three indices, cooling and heating degree days, and a humidity-moderated variant of the former, are available in a separate, but largely comparable, dataset.93 Monthly and annual values are available for the period 1970 to 2018. In addition, ERA5 is the fifth generation of reanalysis products released by the European Centre for Medium-Range Weather Forecasts.94 It is based on a fixed version of an operational and robust medium-range forecasting system. This, and the assimilation of a large number of reprocessed datasets, has resulted in improved quality of the reanalysis product. It has global coverage at 0.3
 0.3
(31 km horizontal resolution), for hourly values of global atmosphere, land surface and ocean wave data from 1950 onwards. ERA5. and two other reanalysis products (ERA5-LAND and NARR), were assessed against in situ observations for their ability to identify days on which extreme heat and cold temperatures occurred over the period 1979e2016 at 230 locations in the United States and Canada.95 Cold events had a better match than did warm events, with ERA5 having the best match with station data overall. Agreement was greatest in mid-latitude, continental locations, while performance was reduced in coastal areas and in the Arctic. Because of its improved resolution and processes relative to earlier versions, temperature and precipitation data in ERA5 have the potential to provide more accurate estimates of extreme river flows.96 An overview of ocean reanalyses97 lists around 20 products. These support analysis of marine extremes such as wind-driven waves, including their influence on extreme sea levels. The homogeneity of time series of surface waves observed using buoys are often compromised by changes in the observing platform. As an alternative, reanalysis and hindcast products are being used increasingly in global and regional studies of changes in wind-driven waves, and in extreme sea levels. But these methods can also be impacted by changes in assimilated data. For example, 20th century reanalyses show spurious trends in near surface wind speed and significant wave height.98 This reflects the increasing number of observations, as well as changes in the quality of the assimilated data. The effects are greatest in the North Atlantic and Pacific Oceans, in the Tasman Sea, and in the South Atlantic region east of South America. While the DINAS-COAST Extreme Sea Levels dataset applies a static approximation to estimate extreme sea levels, the Global Tide and Surge Reanalysis provides a more recent, dynamically-derived dataset for the period 1979e2017 as well as projections from 2040 to 2100.99 The differences between the two datasets are generally larger than the confidence intervals of the latter reanalysis product. Its extremes are generally lower than observed extremes, particularly in the tropics. However, the spatial patterns of extreme sea levels are in qualitative agreement.100

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Five different atmospheric reanalysis products have been used to simulate daily maximum surge values at 882 tide gauge locations across the globe.101 The longest reanalysis product extended back to 1836. A statistical reconstruction approach used predictors, such as wind speed and mean sea level pressure obtained from remote sensing and climate reanalysis, to predict daily maximum storm surge.102 Estimates were validated using independent tide gauge observations and storm surge reanalyses. The models simulated daily maximum surge better in extratropical and sub-tropical regions than in the tropics. Predictions were less robust for extreme storm surge events. Models forced with remotely sensed data showed a slightly improved performance over those forced with predictors from reanalysis products. The models showed a significant improvement over Global Tide and Surge Reanalysis estimates. A dynamics-based approach, in which large-scale processes derived from oceanic reanalysis are combined with storm surge simulations using a barotropic numerical model, has also been used to estimate extreme storm surges.103 Hourly storm surge simulations adjusted using monthly reanalysis data were found to be consistent with tide gauge observations, resulting in improved long-term extreme water level estimates for the west coast of Canada, where many parts of the coastline are at a large distance from tide gauge stations with long records. Historical simulations using global climate models Use of global climate models to assess the changing characteristics of extremes over recent decades is a significant challenge, and especially so for precipitation extremes. This is due, in part, to limitations in model resolution and physics, as well as to the previously discussed lack of consistency in the gridded observations often used to evaluate their performance. The extent to which such models are able to represent the known occurrences of current and past extremes is an important indicator of their ability to simulate future changes in these conditions. Recently, Phase 6 of the Coupled Model Intercomparison Project produced simulations from 32 new generation global climate models. These have improvements in terms of both physical processes and higher spatial resolution. One focus of Phase 6 has been to assess changes in climate extremes for the past and future periods, using two approaches to defining and analysing climate extremes. The first approach uses the climate extremes indices defined by the Expert Team (Table 2.1). These represent relatively frequent extreme events in a given year or month. The other approach has been to analyse changes in more extreme event statistics, based on extreme value theory. This typically involves a Generalized Extreme Value distribution analysis to fit annual extremes, and subsequently examining changes in rare events, such as 50-year return values. Several recent studies have used these approaches to inter-compare Phase 5 and 6 models, and to also evaluate their performances against observations- and reanalysis-based reference datasets. Overall, the skill of Phase 6 models was found to be similar to those of Phase 5 models, indicating limited general improvement in the ability to simulate extremes. The studies also reveal that no single Phase 5 or 6 model stands out as being distinctly superior across either temperature or precipitation extremes. For example, the findings of a recent study were based on comparisons with a gridded observations-based, extreme indices dataset (HadEX3), and with four reanalysis datasets.104 The evaluation was also conducted for selected rare extremes, calculated using Generalized Extreme Value analysis. Similar to Phase 5 models, the Phase 6 models replicated the overall

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observed climatological pattern of extreme temperature indices. But the latter tended to simulate reduced warm biases over mid-latitude Asia and also South America. Cold biases in the cold extreme indices over high latitude regions persisted in the Phase 6 models, though with stronger amplitudes than those in the Phase 5 models. However, the same study did find that the higher spatial resolution and additional physical complexity of the new generation models resulted in improved skill globally with respect to extreme precipitation intensity, including reduced dry biases over the tropical and subtropical rain band regions. But in common with Phase 5 models, not all Phase 6 models were able to successfully simulate the key characteristics of extreme precipitation-related circulation patterns in northeast United States.105 This helps explain why these models continue to vary in their ability to simulate precipitation extremes. In general, the higher-resolution models scored better in terms of their ability to simulate the synoptic patterns associated with extreme precipitation. The two generations of global climate models have also been compared in terms of their ability to provide estimates of relatively rare temperature and precipitation extremes, as indicated by 20-year return values.106 The estimates were also compared with similar quantities calculated from gridded land-based daily observations. No notable differences were found between the two generations of models in terms of their ability to simulate the more extreme daily temperatures and precipitation. In addition, model performance in simulating the rarer extremes was in general substantially reduced relative to the simulation of less rare extremes. This has been confirmed in another global study.107 It showed that, while intense precipitation (the 90th percentile) is simulated reasonably well by both Phase 5 and 6 models, two of six Phase 6 models greatly overestimated the 99th percentile of the precipitation distribution, especially in the tropics. Another recent study108 assessed the ability of 16 of the new generation Phase 6 models to represent present-day wet and dry precipitation extremes on a daily time scale over the continental United States. The study also used nine extreme precipitation indices identified by the Expert Team (Table 2.1), facilitating an assessment of the frequency, intensity and spatial structure of extreme precipitation. Three gridded gauge- and satellite-based datasets for 1997 to 2014 provided a basis for comparison. These reference datasets showed significant differences in area-average intensity distributions, and in spatial patterns of precipitation extremes over the United States. This highlights a significant constraint in assessing the validity of observation- and model-based estimates of extremes. In general, the multi-model mean was better at capturing the extreme precipitation indices than most individual models, especially in comparison to gauge-based data. Model resolution, which varied from w0.7 degrees to w2.8 degrees, was not a good indicator of model performance. Model-based representation of the extreme precipitation indices improved in the summer, relative to the winter. Overall, the results revealed continuing biases in global climate models, and highlighted that no single model was consistently the most reliable across all indices. The findings of a recent assessment109 of the ability of Phase 6 models to simulate bivariate compound extreme events are highly relevant, given that such events often have major social, economic and environmental consequences. The study validated the models for the cooccurrence of heat waves and meteorological drought, and for heavy rain and strong wind. Observations and a reanalysis dataset for the period 1980 to 2014 were used to validate the models over Europe, Eurasia, Australia and North America. Some models performed well over all regions except Australia. This was particularly the case for heavy rain and strong

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wind over northern Australia, suggesting limits in the ability of the models to simulate tropical and extratropical cyclones, mesoscale convective systems and local convection. Higher model resolution did not improve performance over any region. Based on climate extreme indices calculated from a high-resolution daily observational dataset for China from 1961 to 2005, Phase 6 models showed improvements over Phase 5 models in the simulation of extreme climate indices over China.110 This was especially the case for extreme precipitation indices, for both the climatological pattern and the interannual variation. One exception was for consecutive dry days. The Phase 6 multi-model ensemble mean had difficulty reproducing the cold nights and warm days indices, and had large cold biases over the Tibetan Plateau. Phase 6 model performance when simulating extreme precipitation indices was generally lower than when simulating temperature indices. Extratropical storm track representation in the Phase 6 historical ensemble for 1979 to 2014 has been compared with that in the Phase 5 models, and in three global reanalysis products.111 The main biases found in the Phase 5 models persisted in the Phase 6 simulations, albeit to a lesser extent. Low-resolution models tended to underestimate the frequency of high-intensity cyclones. Explosively developing cyclones were underestimated across all ocean basins in both hemispheres. In the Northern Hemisphere, the Phase 6 models exhibited an overall improvement compared to the Phase 5 models, largely as a result of increased horizontal resolution. For the Southern Hemisphere, the improvement was likely as a result of improved model physics. A recent study112 found that Phase 6 models, forced with the historical and the future SSP5-8.5 scenario, severely underestimated the intensification in mid-latitude storm tracks that has occurred in recent decades. Significantly, the intensification assessed using reanalyses has already reached the model-projected end-of-the-century intensification. HiFLOR, a new high-resolution coupled model designed to investigate the potential skill in simulating tropical cyclone activity, was found to provide more realistic simulations of the structure, global distribution and seasonal and interannual variations of tropical cyclones, relative to its lower resolution predecessor.113 It was also able to simulate extremely intense tropical cyclones compared to observations, as well as their interannual variations. The study represented the first time a global coupled model was able to simulate such extreme cyclones in a multi-century simulation. Global atmosphereewave model ensemble forecasts have been shown to produce reliable estimates of global wind speed and wave height return periods, when compared with extreme value analyses performed on ERA, a commonly used reanalysis dataset.114 The findings highlight the potential use of ensemble probabilistic forecasts in statistical analyses of significant wave height and ocean wind speed extremes at the global scale. Gridding Data generated by climate models, as well as satellites, radar and other sensors, are mapped on different grids, while in situ observations have irregular spatial coverage. Quantitative evaluation and analysis of these data requires that they be interpolated to a common grid. In situ observations are often gridded by converting them from point observations to values on a latitudeelongitude grid. Alternatively, climate model outputs and the like are often downscaled, which involves data values for observation sites being inferred from gridded values. Gridded data may represent values for regularly spaced, point locations, or an area average.

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There is a fundamental mismatch between the spatial representativeness of in situ observations made at particular sites (points), and that of gridded atmospheric and oceanic data which represent area mean values.115 This represents an ‘issue of scale’ when comparing the observed and gridded datasets.7 It especially affects phenomena such as precipitation, whose spatial features are discontinuous, or extremes calculated from daily or sub-daily data. The situation is exacerbated when the spatial resolution of the gridded data cannot capture the spatial details at local and regional levels. But the scaling issue also affected Australian heatwave trends, which were found to be significantly different amongst gridded and in situ datasets.116 When observations are interpolated to generate gridded datasets, the data are smoothed, affecting the long-term trends. This is especially problematic in regions with a low density of observations. Conversion from in situ observations to gridded data skews the probability distribution towards more frequent low-magnitude events, and less frequent high-magnitude events. This procedure is generally considered to be a much larger source of uncertainty than subsequently re-gridding the data to successively larger grid sizes. The relatively high-spatial heterogeneity of precipitation extremes means that the processes of gridding, and of increasing the grid size, often result in significantly lower localised maxima. But the sensitivity varies with the type of extreme index. For example, the smoothing effects as a result of increasing the grid size are substantially larger for precipitation indices further into the tail of the probability distribution, ultimately limiting detection of these extremes at coarser resolutions. To address the issue of general underestimation of long-period return values for extreme precipitation when using gridded daily datasets, a spatial statistical approach involving second-order nonstationary Gaussian processes was used to infer the underlying climatology over a fine grid via kriging.117 This technique produced gridded estimates that do not smooth extreme daily precipitation measurements, and are thus consistent with statistics from the original station data, while increasing the resulting signal-to-noise ratio. Merging of data from different observation sources and other products using a common grid requires the use of interpolation techniques which reproduce the spatial continuity of field represented by the discrete observations. These techniques generally involve estimating a representative value at each grid point, based on weighted values of adjacent observations. Then, the challenge is to determine the weights used in the interpolation. The procedure can involve either deterministic or stochastic (also known as geostatistical) approaches, depending on the mathematical principles being applied.118 The former approaches include inverse distance weighting, polynomial interpolation, spline interpolation and moving window regression. These create continuous surfaces from measured points, by using mathematical formulae that determine either the extent of similarity, or the degree of smoothing. Methods in the latter category utilise statistical models that quantify the spatial autocorrelation and the statistical relationships between measurement points. They have the advantage of providing some measures of the certainty and accuracy of the predicted values. Examples include kriging and optimal interpolation. Since the latter is optimal in the sense that it is the best linear, unbiased estimator of a field, it is also referred to as ‘statistical interpolation’. There is no general guideline as to which method should be preferred. The optimal technique will vary with the specific application, influenced by data characteristics such as measurement errors, spatial bias, inhomogeneities, temporal resolution

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and station density. The last tends to be the greatest contributor to uncertainties. In general, these are small for temperature, but considerably larger for precipitation as well as for indices such those related to drought.119 An extreme index can be calculated using the in situ or high-resolution gridded data and then interpolated to the grid resolution. Or the index can be calculated after gridding. The order can have a significant effect on the final gridded values. For example, indices related to the more extreme tails of the probability distribution resolution, such as the monthly maximum one-day precipitation, are substantially altered when the order of operation is changed, and also when the data are re-gridded to larger grid sizes. Once again, indices based on lesser extremes, such as the number of days with precipitation 10 mm, are relatively insensitive to resolution choice, and the order of operation has no noticeable effect. Importantly, the choice of order of operation depends on the intended use of the resultant dataset.120 For example, evaluating model estimates requires the best estimate of the spatial average. In such instances, interpolating the in situ data to the desired grid resolution should take place prior to calculating the extreme indices. On the other hand, when it is desirable that the gridded dataset best reflect the values of each grid coordinate, such as in monitoring applications, the alternate order of operation should be used. Generally, the more extreme a precipitation index, the more sensitive it is to the order of operation and resolution choices. But when extreme indices are calculated prior to interpolating to a larger grid size, resolution sensitivity is largely eliminated. Depending on the application, this may be, or may not be, desirable. These general points are in some instances confirmed, but at other times contradicted, in the findings of a study that examined eight downscaled datasets of gridded daily weather data for recent decades across the conterminous United States.121 The datasets were compared amongst themselves, and with in situ daily precipitation and temperature observations made at 3855 locations. Comparisons used 27 extreme indices identified by the Expert Team (Table 2.1). The considerable differences among the downscaled datasets highlighted the influence of interpolation methods, even for local comparisons with nearby weather stations located inside a grid cell. Differences between downscaled and in situ data were greater for precipitation than for temperature, while longer-term climate averages varied less than the shorter-term weather extremes. The performance of downscaled datasets was not influenced systematically by spatial resolution, but did vary regionally, being poorest in regions with complex terrain. Overall, the above findings highlight the need for careful selection of downscaled datasets, based on uncertainties in the variables of interest, in the regional performance and in relation to their resolution. Since there is no basis for selecting the ‘best’ dataset, using ensembles of datasets may provide the optimal choice. Furthermore, understanding the sources and levels of uncertainty might well be advanced by the use of a recently developed rain gauge-based product that uses a probabilistic interpolation method.122 The resulting ensemble of multiple grids provides uncertainty information arising from the gridding process.

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Blending Blending, or merging, is the process of combining two or more datasets to create a single, new dataset which has the collective advantages of the individual datasets, and often much more.123 For example, as highlighted in Box 2.3, satellite observations include nonnegligible random errors and biases. These are largely a result of the indirect nature of the relationship between the observations and precipitation, inadequate spatial resolution and temporal sampling and deficiencies in the algorithms which ultimately involve adjustments based on rain gauge data.40 In an attempt to overcome these problems, other sources of information, such as gauge and radar data, are often merged with the satellite data. This takes advantage of the individual strengths of the various information sources, improving both spatial and temporal resolutions as well the accuracy of the estimates. It is usual to assume the gauge observations are bias-free.124 An optimal interpolation objective analysis technique is commonly used to generate regular gridded fields. The benefits of blending datasets are particularly pertinent for information-sparse countries such as most of those in Africa.125 Because of these benefits, there are many datasets that combine in situ, satellite, reanalysis and other data. However, few of these datasets directly address the specific need to quantify changes in extreme events over time. CHIRTSmax is one such dataset.126 It combines high-resolution (0.05 degrees), cloudscreened archives of geostationary satellite thermal infrared observations with a dense set of around 15,000 in situ observations for 1983 to 2016. The dataset addressed the lack of a near-surface, monthly mean maximum air temperature archive with global coverage. Another example is dOISST.v2,127 a daily sea surface temperature dataset on a 0.25 degrees spatial grid, covering the period from September 1981 to the present. The temperature field is generated using optimum interpolation to blend in situ buoy and ship observations, and the Advanced Very High Resolution Radiometer satellite data. The CHIRPS dataset128 is particularly suited to analysis of longer-term precipitation extremes such as drought. It combines station data, and high resolution, satellite-based precipitation estimates, to represent sparsely gauged locations. The archive is quasi-global (50
Se 50
N) and high resolution (0.05
), with daily, pentadal and monthly precipitation covering the period from 1981 onwards. A novel blending procedure incorporating the spatial correlation structure of precipitation estimates is used to assign interpolation weights.129 Relative merits of instrumental era datasets The preceding sections have highlighted the substantial uncertainties that can occur when characterising past precipitation, temperature and other extremes. The uncertainties are influenced by the origins and nature of the data, the estimation procedures for indirect observations and by the corrections and other quality control processes.130,131 Datasets based on in situ observations are often assumed to provide the ‘truth’, against which other satellite, reanalysis and other products can be validated. The most accurate weather, climate and ocean data do indeed originate from measurements taken at well-maintained and qualitycontrolled weather stations. Importantly, in situ observations also possess uncertainties.132 Nevertheless, many gridded products of extreme indices have been compared with the same indices derived from high-quality observing networks. But there is increasing

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recognition of uncertainties in the in situ data, and datasets not being fully independent due to the use of the same in situ data to reduce uncertainties in satellite, reanalysis and other products. This has resulted in a focus on intercomparisons of datasets, and on examining ensemble uncertainties, rather than on identifying the best-performing gridded dataset.133 Intercomparisons for a range of spatial and temporal scales and coverage provide useful guidance to those who use the data, as well as to those who apply the subsequent findings. Thus, a robust understanding of how extremes are changing should be proceeded by both comparative validations and sensitivity analyses of the more widely used datasets. It is desirable that these provide daily rather than more aggregated data. Ideally the comparisons and sensitivity analyses will focus not only on the statistical moments of the distribution of the daily data, such as mean, variance and skewness, but also explicitly on the tails of the distribution by using extreme value theory or examining the relevant percentiles. Using this combination of approaches can help address the uncertainties that arise due to assessing datasets considering only the tails of the distribution. An example134 of this more comprehensive approach involved an examination of gridded datasets of daily temperature anomalies based on in situ data (HadGHCND), as well as several reanalysis products. These were used to determine the sensitivity of assessing global and regional temperature extremes over 1980e2014, for both the entire distribution as well as its tails. The study found that assessments of temperature extremes are sensitive to dataset choice, with instances of substantial differences in the magnitude of given extremes between datasets. The differences between datasets were greatest in the cold tails of the distribution, and for daily minimum temperature anomalies. They were also generally largest for regions that are more data sparse, such as southeastern South America and southern Africa. There was better agreement for regions that are rich in higher-quality data, such as North America. This study, and those summarised in Box 2.5, generally find that no best-performing dataset can be identified, leading to the recommendation that users understand the origins of each dataset and use this information to select the extreme precipitation product that is most fit for purpose. Satellite-derived extreme precipitation datasets must be analysed with care if they are to provide useful information on long-term trends. This is especially the case for regions where gauge densities are low. Blending multisource data enhances the spatiotemporal accuracy of satellite precipitation products. Additional pertinent summary comments arose from a study133 which compared the characterisation of precipitation extremes in several widely used daily gridded products derived from in situ data, satellite retrieval, reanalysis and model simulations for the conterminous United States. The strength of correspondence between datasets, as indicated by correlation and extremal dependence, was found to be ordered by observation type e rain gauge, satellite, reanalysis and simulation. This was in line with uncertainty increasing for extremes identified by a high-quality rain gauge network, by remote sensing and by numerical simulation. The spread in extremal dependence across the product groups led to questions about sources of uncertainty and about where and when certain products should and should not be used. Caution is needed when employing gridded products for extremal analysis, particularly on daily timescales and especially in the absence of a high-quality rain gauge network. Over all, validation findings have two important implications. Since it is generally impossible to demonstrate that one product is more accurate than another, multiple observationsbased products should be used when evaluating model-based estimates of extremes.

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BOX 2.5

Examples of studies validating instrumental era datasets A comparison of five gridded precipitation products derived from gauge and remotely sensed data120 demonstrated that the measurement of extreme precipitation can be subject to substantial product and resolution biases, at both quasi-global and regional scales. ‘Extreme extremes’, such as the monthly maximum one-day precipitation, were found to be more sensitive to resolution and product choice than ‘moderate extremes’, such as the number of heavy rain days in a month. For the former index, the standard deviation between five products as a percentage of the multiproduct mean at 0.25
 0.25
resolution was 28%, compared to only 6% for the latter index. Generally, the more extreme a precipitation index is, the more sensitive it is to product and resolution choice. Uncertainties in representations of one of the Expert Team’s extreme precipitation indices, annual daily precipitation maxima, were assessed using a high-resolution in situ validation dataset.135 This was made up of 13 observational datasets from the FROGS database.129 These comprise both in situ- and satellite-based archives. The latter included datasets with and without corrections using in situ data. The analysis was conducted for three sub-regions e Japan, India and Southeast Asia, in the archipelagic area between the Indian and Pacific Oceans e in order to assess the influence of station density, orography and coastal complexity. Satellite products corrected using in situ data showed better general agreement, and less interproduct spread, when compared to the

uncorrected products, especially in areas with a high density of in situ observations. Spatial and temporal patterns showed high consistency for Japan, which has a dense station network, while large inter-product variation was found for India and the Southeast Asia region. There station density is sparser. In such areas, the length of record for each station also influenced the benefits of adjusting the satellite estimates. Extreme temperature and precipitation indices derived from two century-long reanalyses and atmospheric model simulations have been compared with gridded extremes from the HadEX2 dataset for the period 1901e2010.136 Changes in temperature extremes from about 1980 on, as indicated by reanalyses, were most consistent with gridded observational data, while larger differences occurred for the pre-satellite era. Lower agreement was generally found for temporal changes in precipitation extremes, although temporal and spatial correlations with observations were mostly significant. Temperature and precipitation extremes identified in century-long reanalyses were in general agreement with observations after about 1950, especially in regions with good observing networks. The reanalysis products often indicated changes in the first half of the 20th century that were inconsistent with the in situ data. Daily precipitation 90th percentiles have been used to investigate the differences between extreme precipitation estimated by six gauge-based, nine satellite-derived and seven reanalysis products.40 Differences were larger for arid regions than for humid regions, and

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BOX 2.5 (cont'd) for lower latitudes than at higher latitudes. Overall, the satellite-derived and gaugebased products produced higher estimates of extreme precipitation over Africa, southern Asia and South America, when compared to all but one of the reanalysis products. Space-based estimates of precipitation have been shown to be generally severely challenged in arid and mountainous areas.137 A comparative evaluation of three satellite precipitation products (TMPA, CHIRPS and PERSIANN-CDR) was conducted for such an area in China, for the period from 2000 to 2015. The three products were able to capture the general features of the interannual variations in two extreme rainfall intensity indices, but TMPA and PERSIANN-CDR failed to reproduce the temporal trends of consecutive dry- and wet-day indices (Table 2.1). While CHIRPS performed best at capturing the rainfall extremes detected by gauges, that product still contained relatively large errors at the daily time scale. Five gridded precipitation satellite products were evaluated against rain gauge data for 41 locations in Malaysia.138 While all products replicated the intensity of heavy rainfall (20e50 mm/day) with reasonable accuracy, they tended to underestimate the intensity for days with little rain (rain 50 mm/day). The largest consistent database of daily gridded annual precipitation indices and extremes for land areas has been used to assess the relative merits of in situ, space-based and reanalysis products.139 The database used a common daily 1o x 1o latitude/longitude grid extending from 50o S to 50o N. It comprised

10 annual indices representing the frequency, duration and intensity dimensions of extreme precipitation (Table 2.1). While acknowledging important differences, the analysis assumed that the indices calculated from each product could be directly compared. In reality, satellites return instantaneous rain rates while in situ products generally measure accumulations over 24 h. There is also a mismatch between station-based products, which convert point data to grids, and areal average precipitation estimates such as are produced by reanalyses. The assessment found that the three categories of products generated similar spatial patterns, but the climatologies based on a common 13-year period (2001e13) showed substantial differences. In situ products were found to have the greatest similarities, while reanalysis products had the largest variations. However, reanalyses showed better agreement with in situ observations over extra-tropical land areas compared to the satellite products. Daily precipitation intensity varied least between products while the number of days with more than 20 mm precipitation varied the most. Representation of annual maxima of daily precipitation in 22 state-of-the-art products (station-based in situ (5), satellite observations with (8) or without (4) a correction using rain gauges, and reanalyses (5)) gridded at 1
1
resolution for the terrestrial regions of a quasi-global domain was assessed in terms of inter- and intra-product spread.140 The latter provided a measure of observational uncertainty. Extreme precipitation in satellite products compared relatively well with in situ data. Gauge-corrected satellite (Continued)

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BOX 2.5 products agreed more closely with in situ observations, and had less intra-product spread relative to the uncorrected products. Reanalyses provided a heterogeneous representation of extreme rainfall, particularly over the tropics, and had the highest intraproduct spread. The analysis results showed that none of the datasets could be thought of as providing the best estimate overall. They also led to the recommendation that

(cont'd) reanalyses not be considered as reliable sources of extreme precipitation data, but to use an ensemble of in situ and (preferably corrected) satellite data when estimating precipitation extremes, and observational uncertainties, regionally and globally and their observational uncertainties. Clearly, these recommendations are not applicable for other precipitation indices, grid resolutions and time scales.

Secondly, until recently, the spatial resolutions used in most model-based precipitation products do not result in substantial product sensitivity. For example, at a 2.5
 2.5
resolution, there is little inter-product variation for either extreme or moderate extreme indices. But model resolutions are increasing rapidly, with many new generation global climate models now having an average resolution of approximately 1
 1
. At this resolution, the uncertainty between observational products is substantial. Robust evaluations of the more extreme precipitation indices in the newer, higher-resolution climate models will be conditional on significant reductions in the uncertainties of observations-based products.

Change and extreme event detection A suite of methods is required to detect temporal changes in extremes. This section summarises the procedures designed to help ensure data used in detection studies is of sufficient quality. It also summarises relevant statistical and other analytical methods. Chapter 8 will describe additional methods used to attribute causes to past and future changes in extremes, as well as to the occurrence of individual and compound extreme events. In general, confidence in detected changes in extremes depends on the temporal duration and spatial extent of the extreme events, data quality and quantity, the methods used to determine the nature of any changes, the choice of reference periods (especially for detecting changes in the magnitude of extremes) and on the availability of relevant studies.6,141 The time scale over which the extreme occurs dictates the temporal resolution requirements. For example, longer time resolution data (e.g. monthly, seasonal and annual values) can be used in studies of multi-year drought and abnormally wet periods. Analysis of changes in extremes occurring on short time scales typically requires the use of high-temporal resolution data, such as daily or sub-daily observations. Systematic changes in extremes may be difficult to detect if there is a large amount of natural interannual variability in the time series.

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Furthermore, a valid analysis of extremes in the tails of the distribution requires long time series to obtain reasonable estimates of the intensity and frequency of rare events. The rarer the event, the more difficult it is to identify long-term changes, simply because there are fewer cases to evaluate. For example, analysis of temporal changes in extreme rainfall between 1839 and 2017 for three Australian cities was hampered by potential differences in the variance and mean of the historical and modern data, as well as by the possibility of unrecognised inhomogeneities in the data.142 Observational records suggest that two of the cities may have experienced several extreme rainfall events between 1840 and 1860. These are more extreme than those found in the modern record, resulting in significant statistical differences between the historical and modern data. Comprehensive guidance on the detection of change in extremes is widely available.41,36,143,144 It covers topics such as preparation of data series for the analysis of extremes, the use of descriptive indices and extreme value theory to evaluate extremes, trend calculation and other statistical approaches for detecting changes in extremes, and assessment of observed and modelled changes in extremes. The following sections provide a summary of these and related topics.

Data preparation Preparing datasets for detecting temporal changes in extremes involves a thorough process of quality control, gap filling of missing values, and homogenisation. Quality control of meteorological and oceanographic data aims to identify and rectify the many shortcomings of measurement, logging and archiving systems, including mechanical and recording errors. Tests include consistency checks against other observations, and range and constraint checks against reasonable climatological norms and the station record. Errors, such as those arising from instrument malfunctions and human mistakes, are unlikely to be duplicated across observing networks. As a result, they are more readily detected by comparison with observations made at nearby locations. Such approaches are more successful when the correlation decay distance is large. This is usually the case for temperature. But it is less so for precipitation and wind, for example, and especially in summer for the former.145 The results of extremes analyses can also be influenced by the completeness of the serial data. An extreme event might cause the observing system to fail and not be captured in the data record. This negatively biases the extreme event indicators. Or a data outlier associated with an extreme event can be erroneously flagged and therefore deleted from a dataset.146 A completeness criterion frequently used for daily data requires that there be no more than three missing days in any month, and less than 15 missing days in a year.36 A variety of methods can be used to interpolate missing data. An assessment of five interpolation methods147 found that their reliability varied with the relative amount of missing data, the degree of coherence with data from neighbouring stations and whether data were missing at random or more systematically. A major constraint on determining whether extremes are changing is the need for longterm homogeneity of the time series. Weather, climate and ocean data are considered to be homogenous when all trends and variations in the data are inherent to the climate system.

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Data inhomogeneity can arise from changes in siting, instrumentation and/or observing practices. These may lead to artificial jumps or trends, which can hinder detection of any genuine longer-term changes in extremes. A common approach to identifying and reducing inhomogeneities in an observed data series is to compare it with those for neighbouring reference stations. Four challenges related to this process have been identified,41 namely: (i) most experience relates to the homogenisation of temperature observations from dense networks; (ii) the ability to remove biases rapidly diminishes for sparse networks (the norm early in the instrumental era) and where the correlation decay distance is low, such as for precipitation, wind and humidity; (iii) homogenised data still contains random errors arising from the effects of the homogenisation procedure e these relate to both the break signal and the noise signal, and to the efficacy of the homogenisation method; and (iv) homogenisation of daily variability around the mean is more difficult than it is for monthly and annual data, even when specific homogenisation methods are used. This reflects the fact that inhomogeneities for daily data are less well understood. As a result of these challenges, availability and access to homogeneous datasets is a significant barrier to detecting changes in extremes. The global database of meteorological drought events during the period 1951e2016 is publicly available through the European Commission’s Global Drought Observatory.51 It is an excellent example of good practice.

Change detection methods Detection is the identification of a statistically significant change in the extreme values of a climate variable over a given period of time. The past two decades have seen a considerable improvement in the ability to detect trends and other temporal changes in the likelihood of given extremes. This achievement reflects the growing realisation that many of the early and greatest consequences of global warming will arise from extreme weather, climate and ocean events. Hence, determining if there have been changes in these events over time is of high importance. Analyses of weather, climate and ocean data tend to focus on the lower order moments of the probability distribution, and less on the tails of the distribution (Box 2.2). They also tend to assume the data follow a normal (i.e. Gaussian) distribution, with its exponentially decaying tails. In this case, the probability of samples from such a population occurring beyond three standard deviations is exceedingly small. However, the probability distributions of many atmospheric and oceanic variables, such as precipitation and wave heights, have tails that decline more slowly. The dataset will include observations that are many standard deviations from the mean. In these instances, occurrence of a new extreme event could have a substantial influence on the likelihood of the same extreme reoccurring. Thus, an accurate characterisation of the tail of the distribution is necessary in order for estimates of the return period of a high magnitude, but very rare extreme to be reliable. Analysis of extremes There are two basic approaches to defining extremes, and thence to the analysis of temporal changes.36 Both approaches analyse events in the tails of probability distributions. The first e the non-parametric approach e is more suited to events with shorter return periods,

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such as those occurring as often as 5% or 10% of the time. Most commonly, descriptive indices of extremes are used, such as those developed by the Expert Team (Table 2.1). As already noted, these descriptive indices, such as exceedances above the 90th percentile threshold, do not define real extremes. But they do have the advantage of producing a large number of observations exceeding the threshold, thereby allowing more robust statistical analyses. However, comparison of three different percentile indices in common use produced very different results,148 highlighting the need for care in interpreting changes in extremes using such indices. A complementary approach e the parametric approach based on Extreme Value Theory e provides a statistical framework specifically relevant to the study of the more significant extremes. It evaluates the intensity and frequency of extremely rare events, such as those occurring less than 1% to 5% of the time. Engineering and similar applications may call for estimates of the magnitude of events that occur once in a 100 or 1000 years. These may well be absent from the observed record.149 Extreme Value Theory fits theoretical distributions to the extremes in a time series of data. Such theoretical distributions make it possible to describe the behaviour of extremes using a few key parameters. This approach has three major advantages: (i) even though the extremes may not be observed in the available time series, the properties of the population, including infrequent, large-magnitude extremes, can be estimated from the theoretical distributions based on Extreme Value Theory; (ii) trends in the extremes and/or the dependence of extreme events on other factors can be taken into account, by using non-stationary parameters for the Extreme Value Theory distribution150; and (iii) Extreme Value Theory distributions can accommodate right-skewed distributions characterised by large magnitude events and outliers. Extreme Value Theory defines two types of theoretical distributions fitting extreme values. The peaks over threshold method estimates the parameters of the Generalized Pareto distribution, based on events that exceed a high threshold. While this approach generally requires more interventions by the user, it can result in potentially more accurate estimates of extreme quantiles than the second, more commonly used method. This is the block maximum approach, in which the parameters of the Generalized Extreme Value distribution are estimated using the maximum (or in some cases, the minimum) values of consecutive blocks (e.g. years) of a time series. The Generalized Extreme Value distribution characterises the block maxima when blocks are sufficiently large, for example, 365 daily observations in a one-year block. The Generalized Extreme Value distribution combines the Gumbel, Fréchet and Weibull distributions into a single family, thus allowing a continuous range of possible shapes. But these distributions do not always fit the observed extremes. For example, fitting a Gumbel distribution to annual maximum sea levels may lead to an overestimation of extreme sea levels, especially those with lower probabilities.99 The general form of the Generalized Extreme Value distribution is described by three parameters e location, scale and shape. These can be estimated using three approaches: (i) the method of maximum likelihood; (ii) the method of L-moments or probability weighted moments; or (iii) the ordinary method of moments. The maximum likelihood method is most appropriate when samples of extremes are sufficiently large, and when the climate may be non-stationary. In such instances, covariates can be used to take into account the nonstationarity.151 When samples are small, the method of L-moments is usually preferred.

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The ordinary method of moments is generally not recommended as it tends to underestimate long-period return values. Practical guidance and software for the application of Extreme Value Theory, including worked examples, is available.36,144,152,153 It covers topics such as testing the goodness-offit of the fitted distribution, testing and adjusting for non-stationarity and interpretation of the estimated return periods. Trend detection Detection of a change in extremes over time is often based on the presence of a statistically significant trend in the time series. But detecting such a trend is not a straightforward exercise. For example, there is no standard definition of trend. The various statistical and other techniques for detecting trends vary in their applicability. Different temporal aggregations of the data also affect the findings. Moreover, an assumption of stationarity may not be valid, and time series may be of insufficient length and homogeneity to distinguish the trend from natural and other sources of variability. In addition, both temporal and spatial correlations should be taken into account. Significant correlations are frequently present in extremes data. This is often a result of the large-scale and long-duration meteorological patterns that are related to the occurrence of extreme events. In common usage, a trend is a generally consistent change in a given variable. In the present context, ‘trend’ refers to a progressive change in a time series, over a time scale which is longer than the dominant time scales of variability. However, in the climate system, variability occurs at all time scales. This can make it difficult to distinguish a trend from lowfrequency variability. In other instances, such as in the terminology of the United Nations Framework Convention on Climate Change, trend and variability relate to the same time scale, but their causes differ (Chapter 1, Terminology and Definitions). In that terminology, a trend describes the component of climate change that can be directly or indirectly attributed to human activities, while variability describes the component of climate change at the same time scale that is attributable to natural causes. Thus, in such usage, trends can be detected only in conjunction with methods designed to determine the extent to which changes can be attributed to anthropogenic influences on the climate system (Chapters 8 through 10). A pragmatic approach to detecting trends involves calculating trends over a specified period, regardless of cause. Simple linear trend estimates can be made using the least squares method, and estimating the uncertainty in the fitted trend as a result of sampling variability. But standard linear regression is usually not the preferred method to determine trends because in most cases the metrics of extremes are not normally distributed. In some cases, least squares trends may be sensitive to individual values. For example, a single outlier occurring near the beginning or end of the observational time series will have excessive influence on the calculated trend. In such instances, the data typically are not normally distributed, making a non-parametric method for estimating a trend more statistically robust. An example of such a method is Kendall’s tau-based slope estimator. This measures the relative ordering of all possible pairs of extremes data points, with time being the independent variable. The magnitude of the trend is estimated by the median of all non-zero pairwise trends. Once again it is important to assess the statistical significance of the fitted trend, in this case by determining the sum of the signs of the differences of all possible pairs of data points.154 Many publications elaborate on these points and provide illustrative examples.36 Extreme Value Theory, as described above, can also be used to detect systematic changes in the occurrence of the more rare extremes. The extreme quantiles can be calculated for time I. Changes

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slices if the observed record is short enough to assume stationarity. Alternatively, temporal changes in extremes can be assessed using more advanced methods in which the parameters in the statistical distributions vary over time.155 A recently developed method156 provides estimates for the extremes that are considerably improved on those obtained using more common methods of extreme value analysis, particularly for shorter-term datasets. This includes improved prediction of the highest and smallest values in the dataset and of extreme events extrapolated to smaller probabilities than covered by the data. An additional advantage is that the method requires no subjective methodological interventions by the user. A method based on combining machine learning and biased simulations157 also has the potential to characterise the properties of very rare extremes.

Event detection methods Extreme weather, climate and ocean events can be defined in many different ways, depending on the purposes of the analyses. This leads to the use of various analytical techniques, all of which differ in their ability to identify changes between individual events. The results of studies of extreme events are strongly influenced by the choice of method as well as by the extremeness of the event. The occurrence of an extreme event at a specific location can be confirmed by using the techniques discussed in the previous section (Change Detection Methods). This includes comparing the observed value with a fixed threshold or with a threshold based on the quantiles (e.g. 99%) for the empirical distribution of the observations for that location. An alternative approach is to determine the return period for the event, based on the statistical distribution of extreme values observed at the location. All extreme events have a spatial extent that goes beyond an individual observation point. They may even encompass many observing sites. The areal extent often increases with the extremeness of an event. Data for a single observation point are typically a poor indicator of the extent of an event, as well as of the duration of the event itself. Thus, methods for characterising extreme events must consider not only the extremeness of the event, as indicated by the observed data at a given location, but also the temporal duration and spatial extent. It is also important to highlight that the extremeness of conditions will vary during the event as well as over the affected area. Extremeness will also vary with the space- and timeintegration scales being considered. These complexities of extreme events are accommodated in the Weather Extremity Index.158 The Index is based on an evaluation of extremeness which is ‘event-adjusted’. That is, it is based on the optimisation of both the identified area and time duration for every event. The Index is determined in three steps: (i) return periods for various integration times are estimated using data from individual sites; (ii) these return periods are interpolated to a grid; and (iii) determining the area and time period for which extremeness was maximised. The Index is defined by the maximum product of the common logarithm of the spatial geometric mean of the return periods, multiplied by the radius of a circle of the same area as the one over which the geometric mean is calculated. The Weather Extremity Index has been used to identify extreme precipitation events occurring in central Europe between 1961 and 2013.159,160 By taking into account not only the return periods of the precipitation totals, but also the event duration and spatial extent, the Index was used to identify extreme precipitation events at three spatial scales: central Europe, individual basins and their sub-catchments. I. Changes

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Projecting future changes in extremes Overview The outputs of numerical models are the only source of robust information on the future characteristics of weather, climate and ocean extremes. This is in stark contrast to the numerous sources of information on past extremes, as described earlier in this chapter. Nevertheless, there is still ample variety, as many different modelling approaches and inputs are used to simulate possible future changes in atmospheric and ocean conditions, including extremes. The ability of models to simulate the frequency, intensity and spatial location and areal extent of weather, climate and ocean extremes varies greatly, depending on the configuration of the model, the inputs used and on the complexity and spatiotemporal scales of the extreme events. The first realistic modelling of the global climate, taking into account the increasing atmospheric concentrations of greenhouse gases, was undertaken in the mid-1970s. That model had a limited computational domain, used simplified topography and fixed cloudiness, and made no allowance for either energy transport by the oceans or the seasonal and diurnal cycles. Despite this, the model identified many changes that are now being observed, including increased precipitation intensity.161 Today’s models represent atmosphere and ocean dynamics using mathematical formulations of the natural laws that govern the evolution of the component systems: atmosphere, ocean, cryosphere, land and biosphere. The laws include the fundamental laws of physics (e.g. NaviereStokes equations which describe motion in liquids and gases) as well as the fundamental conservation laws related to energy, mass, linear momentum and angular momentum. These are often described by empirical relationships. Atmospheric models also include parameterisations of physical processes and phenomena, such as radiation, clouds, turbulence, convection, gravity waves and chemical reactions that are not represented by grid-scale dynamics. The advantage of using a fully coupled atmosphereeocean model, as opposed to an atmosphere-only model with prescribed sea surface temperatures, is illustrated by comparing changes in the probability of temperature extremes at 1.5
C of global warming.162 Particularly over the tropics and Australia, estimated changes in the likelihood of given annual temperature extremes can be 5 to 10 times higher for the latter model configuration. Global atmosphereeocean general circulation models represent atmosphere, ocean, sea ice and land processes, while Earth system models additionally include representations of various biogeochemical cycles such as the carbon and sulphur cycles, as well as ozone formation and destruction. Earth system models are thus the most complex category of model used to assess future changes in climate. Unlike the deterministic or probabilistic nature of seasonal and most decadal climate predictions, simulations of possible climate futures on timescales ranging from decades to millennia are conditional on the respective scenario of future socioeconomic, technological and political developments. Specifically, the models are normally forced with estimates of future changes in natural solar and volcanic forcings as well as future anthropogenic forcings due to changes in greenhouse gas and aerosol concentrations, and in land-use and land management.

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The evolution of variables describing the state of the ocean and atmosphere is computed numerically on discrete grids, using high-performance computers. The horizontal and vertical resolutions of the grids are an important determinant of the ability of a model to simulate the evolution of the variables and the associated atmospheric and oceanic features. The chaotic nature of the climate system means that small differences in the initial conditions at the start of the simulation give rise to a range of climate trajectories over time. For the atmosphere, very small differences can escalate rapidly, leading to dissimilar states after just a few weeks. Within a decade, the ocean, as well as ice and land cover, also evolve differently. This is again a result of internal variability in the atmosphereeocean system. Hence, differences in simulations are a result of internal variability as well as variations in the model formulations. Metrics from a large ensemble of simulations performed using the same model, and the same external forcing but different initial conditions, can provide a robust estimate of the climate change signal. The spread among the simulations describes internal variability, rather than differences in forcing and model formulation. In general, current climate models are capable of projecting changes in extremes. But the accuracy and uncertainties very much depend on the model, its implementation and on the specific extreme. The outputs of all climate models contain uncertainties of various kinds, reflecting uncertainties in the initial conditions, in the dynamic and physical formulation and parameterisations and in the scenarios such as future changes in atmospheric greenhouse gas concentrations. At climate timescales, the last two sources of uncertainty tend to dominate. Globally, coordination of climate modelling activities, such as the Coupled Model Intercomparison Project, now in its sixth phase,163 has contributed significantly to the increased understanding of sources and levels of uncertainty. It helped develop a consensus on modelling and information sharing protocols, and also on key inputs. These include the data used to define initial conditions and scenarios that characterise the evolution of key forcings such as greenhouse gas concentrations and volcanic aerosols. Such initiatives have led to major achievements in simulating future changes in atmosphere and ocean conditions, including extremes.

Scenario-based forcing The most widely used scenarios are the Representative Concentration Pathways and Shared Socioeconomic Pathways. The former provide time series of emissions and concentrations of the full range of greenhouse gases, aerosols and chemically active gases, as well as land use and land cover. They are labelled by the approximate radiative forcing reached by 2100, going from 2.6, 4.5, 6.0 to 8.5 W m2, and spanning the range from approximately under 2
C warming to high (>4
C) best estimates of warming by the end of the 21st century. Initially, Shared Socioeconomic Pathways described only the socioeconomic development scenarios. But they are now more widely used to reflect the wide range of future emission and atmospheric concentration scenarios that result from possible socioeconomic changes, including assumptions about mitigating greenhouse gas emissions. An integrative pathway framework is now widely used, with climate projections for the given representative concentration pathways being analysed relative to the Shared Socioeconomic Pathways.164 SSP1 through SSP5 denote the five socioeconomic scenario families: sustainable pathways,

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middle-of-the-road, regional rivalry, inequality and fossil fuelerich development, respectively. A second number (e.g. SSP1-1.9, SSP1-2.6 and SSP5-8.5) represents the approximate global effective radiative forcing levels (e.g. 1.9, 2.6 and 8.5 W m2 by 2100), for newly developed emissions scenarios.163 The choice of scenario is particularly relevant for medium- to long-term projections, including those covering the mid to end of the 21st century. By then the scenarios, and the consequential changes in atmospheric and oceanic conditions, start to appreciably deviate from each other. The newer Shared Socioeconomic Pathways provide unprecedented inputs for climate modelling and projections. They include harmonised historical and future gridded emissions of major greenhouse gases (CO2 and CH4), of reactive species such as CO, SOx, CH4, NOx, volatile organic compounds and aerosols, as well as land use and land cover and natural forcings including solar forcing and volcanic aerosols. Extended Concentration Pathways supplement the Representative Concentration Pathways scenarios of climate forcing, by taking them beyond 2100 to 2300.165 The longer timescale means these pathways are based less on realistic socioeconomic storylines, and more on simplifying assumptions about future changes in climate forcing. The extensions to the Representative Concentration Pathways are based on harmonised emissions projected by four Integrated Assessment Models for 2005e2100. These projections involve a mix of constant emissions, constant concentrations or simplified changes to emissions. Thus, ECP3 extends RCP2.6 with constant emissions after 2100. ECP4.5 and ECP6 extend RCP4.5 and RCP6, respectively, with a smooth transition towards concentration stabilisation after 2150. ECP8.5 extends RCP8.5 with constant emissions after 2100, followed by a smooth transition from 2150 to stabilised concentrations after 2250. A Supplementary Extension (SCP6to4.5) adjusts RCP6 emissions after 2100 to reach RCP4.5 concentration levels by 2250 and thereafter. A key distinction between anthropogenic and natural drivers of global change is that global changes by natural drivers are unpredictable and cannot be managed. Therefore, they can only be described and studied with reference to past events. In contrast, anthropogenic global change can, by definition, be managed through the modulation of human pressures. It is also predictable, albeit with largeuncertainties.166

Model resolution and the spatial scales of extremes The relatively low spatial resolution of early climate models meant it was difficult to make confident statements about changes in extremes, even if the projected changes in the mean climate were assumed to be reliable. Today, the nominal horizontal resolution in global climate models is typically around 100 km, resulting in an effective resolution of 200 to over 600 km.167 This is suitable for simulating future climates at continental to global scales. Such models have also been used to study future changes in regional climates. Coupled atmosphere ocean global climate and Earth system models are usually able to represent extremes, such as unusually hot or cold seasons, as well as some features of heatwaves and cold spells. But these models are not capable of resolving local details, thereby limiting their usefulness for studying future changes in most weather, climate and ocean extremes, including heavy precipitation and droughts. However, recent developments mean that

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some global models now run at resolutions as high as 10 to 25 km.168 Global climate models with variable resolution is another significant development e the spatial resolution is locally enhanced in areas such as where there is complex terrain or intense land use169, or where tropical cyclones are generated.170 Modelling at resolutions more consistent with smaller-scale extreme weather events, such as heavy precipitation, tropical cyclones and tornadoes, has also been achieved by either dynamic or statistical downscaling. The former approach typically involves the use of a higherresolution regional model to simulate meteorological conditions within a limited-area, higher-resolution subdomain of a global model. But the more common approach is to use a regional climate model. These dynamical models are similar to global climate models and include convection-permitting high-resolution climate models. They can provide realistic simulations of sub-daily extreme precipitation events. The models are run over a limited area (domain), with a higher resolution. At the domain boundaries, regional climate models take their values from a driving dataset, such as provided by a global climate model. Such highresolution model simulations are capable of providing more realistic representations of weather, climate and ocean extremes, including those related to convective storms and tropical cyclones. Some extremes are also affected by local or regional feedbacks, which can be better represented in regional climate models. Examples are the high-resolution ensemble projection of extreme precipitation over China171 and the use of statistical and dynamical downscaling techniques, including convection-permitting simulations, when modelling daily extreme precipitation events in southeastern South America.172 An almost global analysis of the impact of global warming on various indices of extreme events was recently undertaken using an ensemble of two regional climate models at w25 km resolution, driven by three global climate models for low and high emissions scenarios.173 The performance of this ensemble was compared with projections using Phase 5 and as well as some Phase 6 models, and with coarser resolution (w50 km) regional climate model projections. All projections were validated against both global and regional observation datasets. The higher-resolution regional climate model ensemble showed a better performance in several regions and for several indices, in terms of both intensity and spatial patterns. Statistical downscaling uses empirical relationships between predictor variables, which are outputs of global climate models, and dependent variables such as the extreme indices listed in Table 2.1. Stochastic weather generators174 are a computationally inexpensive way to downscale the output from global climate models, and generate multi-year time series with high temporal and spatial resolutions. The generator’s parameters are calibrated using observed or modelled historic weather data for a site, and subsequently adjusted using projected changes in climatic conditions based on the global climate model output. A major drawback of weather generators was the inability to replicate the spatial coherence of the downscaled data.175 But this and other constraints have recently been overcome.176 Thirteen weather generators have been analysed using extreme event indices associated with large precipitation events, as well as return periods based on the Generalized Extreme Value distribution.177 Three-parameter and semi-parametric weather generators were found to be more consistent with observations for all indices, with first-order Markov chain models performing as well as second or third order models. Evaluations using return periods produced similar results.

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The impact on estimates of annual extremes of daily precipitation over global land areas due to increasing the spatial resolution in six new generation global climate models was assessed by comparisons with in situ and satellite observations.178 Model performance at the regional scale was also assessed, using four extreme precipitation indices. All models simulated more intense precipitation extremes at higher resolution. Levels of uncertainty in the observations as large as inter-model differences made quantitative evaluation of model performance difficult. However, consistently across all four precipitation extremes, the models showed lower skill at higher resolution in comparison to the corresponding lower resolution version. This highlighted that simply increasing the spatial resolution may not result in a systematic improvement in the simulation of precipitation extremes. Other enhancements, such as improved physics, and tuning related to model biases,179 may also be required. Tropical cyclones present a particularly significant challenge to modellers, including in terms of both simulating the features themselves and assessing their influence on extremes of wind-driven waves and sea level. Tropical cyclones are relatively small-scale features, dictating high model resolution. In addition, their relative infrequency and large variability, necessitate the use of model ensembles and long simulations. Moreover, their sensitivity to large-scale atmospheric and oceanic conditions demands minimal model biases. Several recent developments with higher resolution, tropical cyclone-permitting global and regional climate simulations provide new opportunities to assess how these extreme circulation features are likely to respond to anthropogenic forcing. Many global studies of future changes in tropical cyclones have used a high-resolution atmosphere general circulation model, with sea surface temperature boundary conditions generated using a coarse-resolution coupled Earth system model. Others have been based on coupled models. These include relatively coarse-resolution ocean models, with w100 km horizontal resolution. However, evidence suggests that tropical cyclone sensitivity in such coupled models depends on the horizontal resolution, highlighting the need to use high-resolution models for both atmosphere and ocean simulations. This is because mesoscale oceanic features influence tropical cyclone sensitivity. Strong and slowly propagating cyclones enhance vertical ocean mixing, bringing colder subsurface water to the surface and mixing warm surface water down to several hundred meters. A 3 km resolution in cyclone-active regions would effectively negate the need for convective parameterisation. This would enable far more realistic simulations of tropical cyclone activity and extratropical transitions. Neither the suite of models in Phase 6 of the Coupled Model Intercomparison Project, nor their downscaled products, can provide robust projections of how weak tropical cyclones will respond to global warming. On the other hand, there is improved detection of more intense cyclones in the higher resolution versions of these models, as they can simulate the full intensity spectrum. This may explain why both global and downscaled models are in more agreement on projected changes in intense (Category 4 and 5) tropical cyclones.170 In order to resolve such mesoscale process, both in the atmosphere and ocean, one of the highestresolution coupled climate change experiments conducted to date used an atmospheric model with a horizontal resolution of 25 km and a coupled ocean model with a nominal resolution of 10 km.180

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The High Resolution Model Intercomparison Project181 is a response to many of these challenges. It has provided an important opportunity to undertake a more systematic assessment of the influence of horizontal resolution in the simulation of global tropical cyclones. One study used simulations generated by six models for the period 1950 to 2014. Model resolutions ranged between around 25 and 200 km. A resolution of 25 km typically resulted in the identification of more frequent and stronger tropical cyclones, together with a more accurate spatial distribution and storm structure. The same six models from the High Resolution Model Intercomparison Project, plus three additional models, have been used to assess projected changes in tropical cyclone properties for 2015e50, assuming a high-emissions scenario.182 To help compensate for the increased computational expense resulting from the higher model resolutions, the simulations were limited to these 35 years. Plus, the number of ensemble members was reduced for most models, and coupled models used a short multidecadal spin-up. Two complementary tracking algorithms were used to identify the tropical cyclones within the six hourly model output data. Three metrics were used in the study, namely number of cyclones per year, accumulated cyclone energy throughout the warm core phase of each model storm, and wind speed as an indicator of intensity. The models showed a wide variety of behaviours. Some of the higher resolution (20e50 km) models represented tropical cyclone frequency, spatial distribution and intensities comparable to the observed track information. As noted above, the relative rarity and large variability of tropical cyclones necessitate the use of model ensembles and long simulations in order to assess the statistical change in very rare events, such as the occurrence of intense tropical cyclones. Recent improvements in computational power have made it possible to generate 5000 year scale ensemble simulations using an atmospheric general circulation model that realistically simulated tropical cyclone activity, mainly because of its 60 km resolution.183 But the analysis was based on only one model performing simulations for 60 years, with a constant 4
C surface warming condition and constant sea surface temperatures consistent with the warming patterns projected by six coupled global climate models. The same simulation design was used to examine changes in tropical cyclone motion.184 The so-called resolution challenge has also been tackled by downscaling the outputs of nine Phase 6 coupled global climate models using a very high, variable-resolution but simplified coupled atmosphereeocean tropical cyclone model.170 Use of an angular momentum radial coordinate system, which results in increasing spatial resolution of the storm core as its intensity increases, has been shown to produce skilful real-time intensity forecasts. The simplified model included random seeding to initiate storms. The seeding rate, which was held constant globally, seasonally, interannually and over time, did not appear to influence the simulated level of tropical cyclone activity. The vast majority of seeded disturbances dissipated quickly, owing to being placed in unfavourable environments. The few disturbances that persisted were all in favourable environments. However, unlike for dynamic downscaling, the approach made no allowance for the simulated cyclones to influence their environment. Thus, there was no cooling of the ocean, due to ‘cold wake’ and other interactions, and also no drying of the atmosphere. Both of these processes are known to inhibit cyclogenesis. As a result, the extratropical transition of a simulated storm is negatively impacted. An alternative approach has used the atmospheric component only of a coupled global climate model.185 Resolution was 15 km throughout the Northern Hemisphere, increasing

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to 60 km in the Southern Hemisphere. The simulations utilised high-resolution sea surface temperature fields, as well as daily sea ice conditions derived from an ensemble of Phase 5 general circulation models forced by a high-emissions scenario.

Projecting extremes Climate projections aim to quantify the response of the climate system to hypothetical though plausible scenarios of external factors that ‘force’ future changes in the climate. These will also reflect climate feedbacks that can amplify or moderate changes, as well as the role of natural variability compared to the ‘forced’ changes. Various methods are used to model how extremes will change in a warming world. These include transient and equilibrium simulations, and time-slice experiments. Transient simulations are designed to represent the evolving climate state of the Earth system as the climate system responds to gradual changes in radiative forcing. This allows the time-dependent response of a climate model to be analysed. Global transient climate simulations may be downscaled using either dynamical or statistical approaches. In contrast, in an equilibrium simulation, the model fully adjusts to a change in radiative forcing, thereby providing information on the difference between the initial and final states of the Earth system, but not on the time-dependent responses. Time-slice experiments represent only a short, specific period of time, typically a few decades. These experiments have the advantage of being computationally cheaper, allowing for a higher number of ensemble members and/or higher resolution. Fig. 2.5 illustrates the application of the time-slice technique to equilibrium and transient simulations. Medium emissions simulations extended (to 2300) (ECP4.5) and short-term (to 2100) high-emissions simulations (RCP8.5) from the CMIP5 multi-model ensemble were used in the experiment.186 The former is in reality a quasi-equilibrium ensemble, since even by the 23rd century the climate is not in full equilibrium. Projections of extreme temperatures differ substantially between transient and quasiequilibrium climate states.186 For example, globally there are broad regions where the probability ratio of moderate heat extremes, such as one-in-ten hot seasons, are twice as likely in the transient climate (i.e. a one-in-five year event), compared with a quasi-equilibrium climate state. A similar situation was found for cold extremes, with far fewer cold seasons (below the 10th percentile) for the quasi-equilibrium climate state than for the transient climate state. The frequency of hot summers in a situation where the global-average temperature passes rapidly through a given global warming level, compared to the global average temperature equilibrating at that level, is substantially greater in much of Eurasia, in the Middle East, and North America and northern Africa. Thus, assessments of future extremes for transient 1.5
C and 2
C warmer worlds are likely to substantially overestimate changes in the frequency of heat extremes relative to equilibrium 1.5
C and 2
C climates. Since the consequences of a given level of global warming vary depending on the transience of the climate state, it is important to be clear when defining global warming temperature targets, such as 1.5
C. In contrast to these large differences in the frequency and magnitude of extremes in transient and equilibrium worlds for the same level of global warming, regional climate sensitivity for selected climate extremes is very similar for model ensembles in both Phases 5

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FIGURE 2.5

Comparison of transient RCP8.5 and quasi-equilibrium EP4.5 simulations and time-slice experiments. The time-slices are for the same model average of global warming for the two simulation ensembles, 2050 to 2075, and the 23rd century, respectively. The vertical grey bars show the years extracted, with the depth of grey indicating the number of simulations extracted for that year. Reprinted by permission from Springer Nature. From King AD, Lane TP, Henley BJ, Brown JR. Global and regional impacts differ between transient and equilibrium warmer worlds. Nat Clim Chang. 2020;10(1):42e47. https://doi.org/10.1038/s41558-019-0658-7.

and 6 of the Coupled Model Intercomparison Project.187 This is likely due to land processes, such as soil moisture and snow feedbacks, more strongly affecting regional mean temperatures. Global mean temperature, in comparison, is more strongly influenced by oceane climate interactions, and hence by anthropogenically forced ocean warming. Natural climate variability can obscure changes in climate extremes. This is particularly the case in the near-term, say the next 10 to 20 years, when differences in radiative forcing and hence in warming levels are largely independent of the socioeconomic and emissions scenarios. It is thus challenging to distinguish between the effect of natural variability, and the thermodynamically driven changes in climate extremes, when investigating changes for relatively small increases in global mean surface temperature. On the other hand, changes in temperature and precipitation extremes between a global warming of 1.5
C and 2
C are highly dependent on the pathways of emissions scenarios, including both the differing

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greenhouse gas concentrations and forcing compositions.188 This was demonstrated using ensemble simulations for an Earth system model with three scenarios e RCP8.5, RCP4.5 and RCP8.5 with emissions of aerosols and atmospheric oxidants fixed at year 2005 levels. The simulation results showed that the chemical compositions of emissions scenarios, rather than just the resulting level of global warming, must be considered. The scenario dependence of the changes in precipitation extremes is larger than for temperature extremes, with the former extremes having different regional patterns under the three scenarios. The preceding findings are consistent with those of the Half a Degree Additional Warming, Prognosis and Projected Impacts project.189 It applied a framework for assessing how extreme events might differ in worlds that are 1.5
C and 2
C warmer than the preindustrial and current (2006e15) climates. Specifically, the project endeavoured to distinguish between the consequences of an additional half degree of warming on the one hand and, on the other hand, the uncertainty in climate model responses and internal climate variability that dominate in simulations under low emissions scenarios. Large ensembles of decadelong time-slice simulations were prepared for both the present day, and for temperatures stabilised at the higher warming levels. These were used to examine how changes in the 99th percentile values of monthly maximum temperatures, and the first percentile of the monthly minimum temperatures, scaled with global mean warming.190 The scaling of increasing extremes with global mean temperatures was found to be regionally variable. ‘Hotspots’ were identified where the tail of the temperature distribution (above 99th percentile) warmed at a faster rate than the rest of the temperature distribution. Since the study used atmosphereonly models, forced by prescribed sea surface temperatures and sea ice concentrations, the regional differences resulting from small changes in global warming levels may not be reliable. This is especially the case for precipitation extremes as these can be highly variable relative to regional-scale changes over time.3 Recently, this challenge to accurately project future rainfall extremes has resulted in exploring the possible benefits of applying the emergent constraint technique.191 This exploits the statistical relationships between the current observed climate, and the future changes projected by climate models. The approach provides a way to both reduce uncertainties and improve projections.192 A recent study193 used the technique to substantially reduce model uncertainties, as well as improve extreme rainfall projections globally. Forty eight Phases 5 and 6 global climate models were used to simulate changes in the frequency of daily extreme rainfall events (99th percentile) in the recent past (1980e2017) and in projections for 2080 to 2100. Changes were also assessed using several multi-decadal observational precipitation datasets, in order to evaluate model performance and also provide a constraint on the precipitation projections. The analysis identified a robust relationship between simulated historical and projected changes in precipitation extremes, applicable both globally and regionally. This justifies observations of recent changes being used along with the model-derived relationships to constrain future changes in the frequency of precipitation extremes, thereby reducing uncertainty. This was indicated by reductions in inter-model spread of between 20 and 40%. The constraint indicates that, under a medium emissions scenario, precipitation extremes could occur around 32  8% more often by the end of the 21st century relative to the present day.

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Projecting marine extremes Numerical modelling of Earth systems initially focussed on the atmosphere. It was not until the 1960s that early work was undertaken on models of the ocean. Even then, the focus was on the uptake of heat and CO2 by the oceans, and the implications for the long-term changes in the mean state of ocean temperatures and sea levels. Despite this later start, numerical modelling of ocean systems has today reached a level of intellectual and technical maturity comparable to that for atmospheric modelling.85 Ocean models are now an equal and integral part of current ocean and atmospheric research. Recent advances in high-resolution ocean modelling provide both opportunities and challenges for simulating the ocean and wider Earth systems. Since the 1970s, much of the focus of global ocean circulation modelling has been on understanding, representing and parameterising mesoscale eddies (Figure 1.3). This emphasis continues today. But sub-mesoscale variability is now routinely resolved in process models, and simulated in a small number of global models, while sub-mesoscale effects are parameterised in most global models.194 These and related developments are aided by the recent increase in the availability of observations to support parameterisation of the effects of mesoscale and sub-mesoscale eddies, as well as for use in validation of model results. However, most coupled climate models still handle sea ice and the ocean as distinct components that only exchange interacting fields using a coupler. This has the advantage of permitting the separate development of coupler, ocean and sea-ice model code.195 Estimating future changes in marine extremes is especially challenging. The time scales of interest are months to millennia, but the models must represent or parameterise processes whose time scales are minutes to hours. Moreover, while the most energetic spatial scales for the ocean relate to mesoscale eddies ranging in size from 100 km in the tropics to less than 10 km near the poles and on continental shelves, the modelling domain is essentially global. Thus, although atmosphereeocean general circulation models and Earth system models are able to simulate future changes in sea surface temperatures, their relatively coarse ocean resolution (typically about 100 km) limits their ability to simulate extremes in sea surface temperature, including marine heatwaves. For example, 26 models in the Community Model Intercomparison Project Phase 5 archive and 30 simulations from the National Center for Atmospheric Research Large Ensemble Community Project were used to assess changes in monthly sea surface temperature extremes.196 The models were forced by observed greenhouse gas concentrations for 1976e2005, and by a high emissions scenario for greenhouse gases through the remainder of the 21st century. The findings highlighted the need to use higher resolution models, and daily sea surface temperatures. Compared to heatwaves over land, much less is known about the location, frequency and intensity of marine heatwaves, including how these characteristics evolve over time. Frequently used metrics for marine heatwaves include (i) the annual mean probability ratio (the fractional change in the number of days per year a marine heatwave was detected); (ii) the relative change in the annual average area of an individual heatwave; (iii) the maximum annual intensity above a given temperature threshold (typically the local 99th percentile); (iv) the annual mean duration above the temperature threshold; and (v) the annual cumulative mean intensity, given by the product of the duration and the mean intensity of exceedance.

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A study197 which investigated the nearshore and offshore co-occurrence of marine heatwaves and cold spells detected in two different ocean temperature datasets found significant differences between the datasets in terms of the counts, durations, intensities and timing of these events. Two more recent studies198,199 have shed light on the significant impact of spatial and temporal resolution on the ability to simulate future occurrences of marine heatwaves. The first study compared the duration, intensity and frequency of marine heatwave events simulated in a global oceanesea ice model running at coarse (100 km), eddypermitting (25 km) and eddy-rich (10 km) resolutions. The same metrics were also derived from a global, daily, high-resolution (25 km) gridded product based on sea surface temperatures observed between January 1985 and December 2017. For all three configurations, the simulated marine heatwaves were weaker, longer-lasting and less frequent than in observations, but the highest resolution configuration performed best, both globally and regionally. In general, Earth system models are able to capture the broad features of marine heatwaves, but the relatively coarse resolution of the ocean components of standard Community Model Intercomparison Project Phase 6 models tends to bias the projections towards weaker and longer events. A second study compared the historical and projected marine heatwaves simulated by a 10 km dynamically downscaled near-global (75
Se75
N) ocean circulation model with those identified using (i) a global daily gridded sea surface temperature dataset for 1982 to 2018; and (ii) 23 coarser-resolution, Phase 5 climate models under a high-emissions scenario. For each grid point, marine heatwaves were identified using the same definition as the previous study. But in the second study, the metrics used were the number of heatwave days per year, and the mean heatwave intensity. The latter was defined as the mean temperature anomaly during all heatwaves in each year, relative to the seasonal climatology. The coarse-resolution models generated less intense marine heatwaves over the historical period, but greater intensification in coming decades. When simulating past and future marine heatwaves in the regions of the western boundary currents, coarse-resolution models showed greatest disagreement relative to both the observations and the higher-resolution simulations, as well as among themselves. Significantly, in these regions, a substantial fraction of marine heatwaves is generated by internal variability related to local forcing and mesoscale processes, rather than to large-scale climate processes. Most coupled atmosphereeocean general circulation models do not provide realistic simulations of local wind-generated waves. This has impeded the ability to produce comprehensive global projections of wind-wave extremes. Recently,200 10 ensemble global datasets of 21st century global wind-wave climate projections were compiled. These are based on 79 coupled atmosphereeocean general circulation models simulations with dynamical or statistical wave downscaling, typically for a six-hourly timescale and for medium and highemissions scenarios. The resulting 148 global ocean wave climate projections for 2081e2100 are on a 100 km resolution spatial grid. They provide readily accessible extreme statistics of significant wave height and other global ocean wave metrics, at monthly, seasonal and annual time scales. The global climate model forced wave simulations for 1979e2004 in each of the ensemble datasets were validated at both the global and regional scales, using waverider buoy observations, wave hindcasts/reanalysis and satellite altimetry data. Overall, both dynamical and statistically based simulations exhibited good agreement relative to satellite measurements and reanalysis products, but with relatively less model skill at the regional scale. Notably, the simulations exhibited good agreement for data from near-coast buoys, even within I. Changes

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semi-enclosed coastlines and under extreme wave conditions. The model skill found for nearcoast buoys is comparable to that indicated using offshore buoy data as well as highresolution coastal wave hindcasts.201 However, extreme statistics of significant wave height are highly dependent on model resolution in tropical cyclone regions, and are sensitive to sampling. Analyses for these regions suggest a resolution of at least 25 km is required for reliable global projections of extreme waves.202 A parallel initiative involving a comprehensive global analysis of future changes in local wind-generated wave extremes203 used an innovative approach to examine the extent to which the magnitude of a 100-year significant wave height will be affected by anthropogenic forcing. Ocean surface winds simulated by an ensemble of selected Phase 5 global climate models provided at least six-hourly data, rather than the more commonly generated monthly statistics. However, the resolution of the models meant they were not able to resolve localised extreme wind events, such as those associated with intense tropical and extra-tropical storms. The model outputs for medium- and high-emissions scenarios were used to force seven runs of a global wave model, and generate a dataset of storm wave conditions. This was used to investigate changes in global 100-year return period significant wave heights over the 21st century. The extreme value analysis for each grid point used a modified point over threshold approach (this Chapter, Analysis of Extremes). Pooling the highest extreme ocean wave conditions from the ensemble of global wave model runs resulted in the identified extremes collectively representing a 140-year time period, rather than the 20 years (2081e2100) of the projection. As a result, no extrapolation of the empirical probability distribution function fitted to the data was required. This reduced the intrinsic uncertainties inherent in the use of standard extreme value analyses and made it possible to identify statistically significant changes in extreme significant wave height on a global basis (Chapter 6, Extreme Windwaves and Open Ocean Swells). Modelling of future sea level extremes has made similar progress, as evidenced by the use of downscaled projections nested in global simulations for 2040 to 2100.99 The downscaling involved regional climate simulations and dynamically simulated tides, storm surges and projected changes in mean sea level. Importantly, the resulting three-hourly fields include physically-based interactions between these determinants of sea level extremes. As such a dynamic approach is computationally intensive, the current dataset was based on only one global model driven by medium- and high-emissions scenarios. Another major advance was the unprecedented high resolution along the coast, with a grid size of 2.5 km globally, and 1.25 km in Europe. The latter reflects the 250 m resolution for bathymetry in Europe, compared to 30 km resolution for the rest of the globe. Despite this marked increase in resolution, return periods for extreme sea level events in regions prone to tropical cyclones may still be underestimated by this dataset. This is an important focus for future research, as revealed by the findings of a recent study which developed ensemble projections of extreme storm surge events for historical and future climate conditions over a 5000 year period.204 This first attempt to quantify future changes in such events for a timeframe greater than 100 years considered changes in tropical cyclone frequencies, intensities and tracks. These were based on dynamic climate projections using a single 60 km horizontal resolution Phase 5 atmospheric-ocean general circulation model, with downscaling to a 20-km resolution using a non-hydrostatic regional climate model. Storm surges were projected using two different empirical models e a calibrated, local storm surge model, and a statistical storm surge model. Using the approach described above for local wind-generated wave extremes, the 90 ensemble projections of storm surge for 2051 to I. Changes

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2110 represented 5400 years of data, enabling 100-to-1000-year storm surge return periods to be estimated without statistical extrapolation. Even more recently, a statistical model driven by an ensemble of four high-resolution climate models was used to generate 10000 years of synthetic tropical clyclones in recent and future climates.205 The outputs were used to generate high-resolution (10 km) wind speed return period maps up to 1000 years, in order to assess local-scale changes in extreme wind speed probabilities. The ‘mean sea level offset approach’ to estimating future sea level extremes is an alternative to the ‘dynamic approach’ described above.206 It assumes that statistical distributions of the tidal, storm surge and wave components remain unchanged, and do not interact. As a result of these assumptions, a future increase in mean relative sea level is the only oceanographic factor driving future changes in extreme sea level. This allows statistical extreme value models to be used to parametrise observed or modelled historic extreme sea levels, taking into account past increases in mean relative sea level. Subsequently, the modelled distribution is shifted, in line with relative sea level projections.207 But even with the methodological and related advances described above, significant uncertainties in future sea level extremes remain, hampering adaptation planning in coastal areas.208 Importantly, despite the recent progress in climate change and sea level science, estimates of long-term future changes in mean and extreme sea levels under different emissions scenarios continue to be highly uncertain. This is mainly due to the large uncertainty in estimates of future mass loss from the Greenland and Antarctic ice sheets.33 These large uncertainties of ice sheet melting processes give rise to a range of unlikely e but not impossible e high-end sea level scenarios. Approaches to estimate such scenarios use various lines of evidence. The most common approach is a probabilistic framework. Probabilistic sea level projections provide probability density functions that are conditional upon emissions scenarios. They selfconsistently project not only likely values of mean sea level rise, but also the likelihood of high-risk, low-probability conditions. These include futures associated with rapid loss of the Antarctic or Greenland ice mass, despite these processes being physically poorly understood.209 The high-end projections combine upper quantile estimates from simulations of the individual components of sea level change, and assumptions regarding contributions from processes that have not been taken into account in the physical modelling of future sea level changes. This includes the possibility of marine ice-cliff instabilities in ice-sheet contributions. In such cases of recognised ignorance, expert elicitation evidence has been used.210 A number of bio-physical and human processes, including potential changes in extreme water levels due to possible future changes in storminess, are typically not included in probabilistic sea level projections. Despite such limitations, the resulting regional high-end sea level scenarios can be used by risk-averse coastal planners and managers to determine adaptation pathways over the 21st century and beyond. Maximum regional high-end scenarios occur at low-to-mid latitudes, and are substantially higher than changes in global mean sea level. It is important to note that, even in these locations, and over the next few decades, coastal subsidence in some localities can cause relative sea level changes that exceed the high-end sea level scenarios by at least one order of magnitude. Moreover, probabilistic projections are subject to large uncertainties, with mean values sometimes differing by at least a metre. Such large differences in probabilistic assessments have tended to prevent users from substituting conventional sea level scenarios with state-of-the-art probabilistic sea level projections.

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Uncertainties: types, sources, evaluations, corrections and implications Confidence in projections provided by a climate model is based on how well the model represents our physical understanding of the climate system, and on the ability of the model to represent atmospheric processes and climate conditions for a range of spatial and temporal scales. Confidence is increased if the model is also able to simulate past variations in climate. Confidence is further increased when simulations provided by multiple independent models are clear and consistent in the direction and magnitude of projected changes. Uncertainties in projected changes in extremes in a future warmer climate are influenced by the ability of models to simulate the contemporary climate as well as their ability to represent the known physical mechanisms affected by climate change. There are three main categories of uncertainty for climate projections, namely those related to the scenarios which define the drivers of change, to model uncertainty which manifest as model biases and model spread, and to uncertainty due to internal variability. The intrinsic uncertainty due to internal climate variability can be estimated probabilistically, using large initial-condition ensembles. A given model produces multiple simulations with identical forcing. Internal variability can be estimated by analysing the consequences of small changes in the initial conditions, or by sampling different time-slices of a pre-industrial control run. Importantly, the uncertainties in local to regional projections of climate extremes that are a result of internal variability are irreducible, even if climate models improve significantly. However, other sources of uncertainty can be reduced, at least in principle. But they cannot be treated as probabilistic. For longer-term, model-based climate projections, it is possible to estimate the relative contributions of these other sources of uncertainty, including uncertainties resulting from differences in spatial resolution. An ensemble of different climate models can be used to estimate model response uncertainty, while a range of forcing scenarios can be used to estimate future forcing uncertainty. Uncertainties in model-based projections vary across the globe, including the existence of uncertainty hotspots. These spatial patterns have been described for projected changes in extreme precipitation changes, including for both climate model and internal variability uncertainties.211 Climate model uncertainty exceeded internal variability uncertainty for all seasons and precipitation intensities. The largest differences were found in tropical regions, where model uncertainty was three times as large as internal variability uncertainty in the June to August season, and twice as large in the other seasons. Tropical and subtropical regions were identified as the global uncertainty hotspots. The large uncertainty in these regions is primarily due to the predominance of convective rainstorms. These cannot be adequately represented in lower-resolution climate models. In addition, the sparse observation networks in parts of these regions hamper bias corrections as well as efforts to improve model performance. The Sahara Desert and the southern part of the Middle East appeared as local hotspots. It is extremely challenging to identify long-term changes in atmospheric and oceanic extremes in the presence of internal climate variability. This is especially so when the extreme event of interest is truly rare, occurs at small spatial scales, and the response to external forcing is weak relative to internal variability. The challenges are further exacerbated by data records that are short and compromised in other ways.212

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As approximations of the climate system, climate models also display systematic errors (bias). This is most often caused by the imperfect representations of atmospheric, ocean and land physics, by incorrect initialisation of the model, and by errors in the process parameterisation chain. For example, while climate models project an increase in heat extreme events, the future changes vary greatly between models, even for the same mean warming.213 Climate models were found to underestimate the frequency of unusually hot days for many tropical and subtropical regions in the future. This uncertainty has been linked to differences in landeatmosphere feedback across models, including those related to land surface humidity processes. Thus, a significant constraint for future projections is the ability of climate models to accurately simulate the present day variability of daily surface maximum temperature. To overcome such limitations, the outputs of global and regional climate models are often corrected by improving their alignment with observations. However, the resulting corrections typically reduce the advantages of climate models by modifying spatio-temporal field consistency, by altering relations between variables, and by violating conservation principles. Bias correction does increase agreement of climate model output with observations in reanalyses, thereby narrowing the uncertainty range of simulations and projections. But it does so, without any satisfactory physical rationale. This obscures rather than reduces uncertainty, which may have detrimental consequences for the findings of attribution and impact studies that use the bias-corrected data.214 Also, in essence, bias correction involves a statistical calibration that will perform well when applied and tested on the same data, but not necessarily in the period of the intended application such as later in the 21st century. In these instances, no data exist for calibration, or for validation. Several specific methods have been developed to correct for biases that impact on the simulation of extremes, with these usually focussing on correcting the shapes of the model-simulated distributions. Recently, the effectiveness of one of these methods e the purely statistical quantile-based bias correction scheme e was compared with an innovative method based on subset selection.215 Since the biases in the shape of distributions tend to persist through time, correcting for shape bias may be appropriate when the focus is on characterising changes in the past and future distributions. But, typically, correcting for shape bias does not improve comparisons based on the ratio of the probabilities of extremes between two periods. This is due to the systematic errors persisting in the long-term trend. In contrast, the novel subset-selection method optimises for the whole distribution shape. This is achieved by optimally choosing ensemble members that, when pooled, produce a distribution which is closest to the observations, or to a benchmark simulation. Thus, the bias correction does not violate the models’ physics or multivariate relationships. It therefore has wider potential applicability, in that it may not degrade impact studies or multivariate analyses. A recent study has demonstrated the considerable benefit of making climate projections conditional on historical observations.216 This involves using methods such as those described above. Uncertainties in the drivers of future changes can be accommodated by performing simulations for a range of scenarios that prescribe possible future evolutions of the climate forcings under different trajectories of technological, political and societal development over the remainder of the present century, and often beyond. A common approach to assessing this source of uncertainty in global climate models is to evaluate differences in the outputs of

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an ensemble of models for a range of scenarios.217 These reflect uncertainties in the simulations due to differences in the ways the models represent the dynamic and physical responses to different forcings. But erroneous estimates of uncertainties will occur if the models are not independent, or if they share errors and omissions in the ways processes are represented. This can lead to unrepresentative estimates of uncertainty. For these reasons, analyses of climate extremes are often based on ensembles of simulations produced by ‘independent’ global climate models. Multi-model ensembles expedite assessment of the robustness, reproducibility and uncertainty of the simulations. The Coupled Model Intercomparison Project, now in Phase 6, facilitates such multi-model ensemble analysis. This involves assembling coordinated model simulations undertaken by various national and international climate modelling centres. The simulations cover past and present climates, as well as future, scenario-based climates. Multimodel-based assessments must consider which models to include, and how to combine them.218 Choices range from including all available models, with a one-modelone-vote approach, to selecting a single or very few better-performing models. This begs the question e what procedures and criteria should be used when deciding on what constitutes better performing? The process is explicit in model selection, and implicit in model weighting. It relies on value-laden choices of metrics, as is also the case when using a constrained ensemble of emulators for future projections.219 Since characterising uncertainties in model projections requires running the model many times over, uncertainty assessment is more feasible using models that demand less computer processor time. Such models are generally simpler in the sense of being more idealised, or less realistic. Hence, there is an important trade-off between model realism and uncertainty quantification.220 However, the required trade-offs can be reduced. For example, the technique of spatial pooling of data in neighbouring grid cells can, to some extent, reduce the ensemble size needed for projecting climate variables with weak spatial dependence, such as precipitation extremes.212 This has also been demonstrated in the previous section in the context of extreme ocean wave conditions. Model evaluations are an integral part of increasing confidence in climate change projections. The direct approach to model evaluation compares climate model output with observations. For example, general circulation models show increasing, but spatially varying trends in heatwave properties across the conterminous United States. Evaluation of 32 Phase 5 models, and the ensemble median, involved assessing their ability to simulate historical heatwaves between 1950 and 2005, using a set of heatwave indices.221 In addition, differences in simulation results can be better understood by comparing the roles of processes such as cloud formation and ocean currents in isolation, and in fully coupled models. Another approach is called ‘instrument simulator’. This involves calculating what a satellite would detect if it was observing the Earth’s features, as simulated by the model. Finally, and as described above, ensemble methods are used to characterise the uncertainty in climate model simulations that result from model internal variability, boundary conditions, model structure and differences in model formulations. These, and other more

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recently developed tools, enable more rapid and comprehensive evaluation of model simulations, including projections of extremes.222 When projections of extremes are framed in terms of specific global warming targets (e.g. 1.5
C or 2
C above pre-industrial temperatures), the levels of uncertainty are reduced relative to projections for specific emissions scenarios and time intervals.223 The former framing does not eliminate the large uncertainty due to model structural uncertainty, but simply transfers it to uncertainty in the time when a given target will be reached. Thus, when the projections are framed in terms of global warming targets, the latest two generations of climate models (Phases 5 and 6 of the Coupled Model Intercomparison Project) do not substantially differ in their simulation quality and target projections of extreme temperature and precipitation.

Conclusions This chapter has documented the impressive progress made in the ability to characterise past changes in extremes, as well as to describe their future changes. The chapter also provides a summary of the methods used in the studies which provide the evidence base for the following four chapters. These cover past and future changes in weather, climate and ocean extremes. The progress has been at numerous levels. This includes improved clarity in the definition of these extremes, as well as in the associated metrics. Another significant advance has been the creation and regular updating of many comprehensive, quality-controlled datasets that are fit for purpose with respect to detecting and interpreting past changes in extremes. These national, regional and global archives cover both land and ocean areas, and are based on in situ observations and remotely sensed data, as well as on derived data products such as atmospheric and oceanic reanalyses. The quality of the datasets has improved markedly as a result of using advanced calibration techniques, and the assimilation of data and blending of datasets. There is now greater understanding of the impacts of interpolating in situ observations and other data to a common grid, including the order in which the operations are carried out. There is no one pre-eminent dataset. Studies that use an ensemble of datasets, and undertake both comparative evaluations and sensitivity analyses, can often deliver more optimal results. Despite improved access to national weather records that have hitherto been unavailable, spatial coverage of in situ observations continues to be highly uneven. Large gaps remain in parts of Africa and South America, for example. There is also a relative dearth of data that can be used in the analysis of ocean extremes. The availability and reliability of information on extremes in the pre-instrumental era have also improved tremendously, in terms of both the quantity and quality of proxy archives. The resulting palaeoclimate reconstructions have contributed to a marked improvement in palaeoclimate modelling, including increased spatial and temporal resolutions that facilitate rigorous analyses of longer-term and larger-scale climate extremes. Studies of changes and variability in extremes prior to any anthropogenic forcing can now be based on physically consistent reconstructions, rather than relying totally on statistical techniques. The findings provide an important context for assessing the more recent and future variations. Phase 6 of the Coupled Model Intercomparison Project has resulted in simulations of past and future climates using 32 new generation global climate models. Recent developments include improvements in the representation of physical processes, and higher spatial I. Changes

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resolutions. Higher resolution models show significant improvement in skill over Phase 5 models in the simulation of precipitation extremes. But overall, no Phase 6 model stands out as being distinctly superior. Hence, there has been increasing emphasis on the use of multi-model ensemble simulations. Multi-model ensembles facilitate assessment of the robustness, reproducibility and uncertainty of model simulations. Advances in both dynamic and statistical downscaling have also led to improvements in modelling at resolutions more consistent with smaller-scale atmospheric and oceanic events, including heavy precipitation, tropical cyclones, heatwaves and extreme wave heights and sea levels. Ensemble probabilistic forecasts also show potential for use in statistical analyses of significant wave height and ocean wind speed extremes. Similarly, multi-member ensembles of model simulations can provide a probabilistic assessment of uncertainties. The outputs of numerical models are the only source of robust information on the future characteristics of weather, climate and ocean extremes. The level of skill is highly dependent on the model, its implementation and on the specific extreme of interest. The Coupled Model Intercomparison Project has had a major influence on understanding and reducing sources and levels of uncertainty. This includes facilitating a consensus on the data used to define initial conditions and also on the scenarios that characterise the evolution of key forcings, such as greenhouse gas concentrations and volcanic aerosols. Such initiatives have led to major achievements in simulating future changes in atmosphere and ocean conditions, including extremes. Probabilistic projections of atmospheric and oceanic extremes are especially relevant when there is high uncertainty in future trajectories of extreme events, such as in the case of sea level extremes. Extreme Value Theory is used to support projections of events which have a wide range of likelihoods, including low-likelihood, high-impact events. The results of studies of extreme events are strongly influenced by the choice of methods used, as well as by the extremeness of the event. A suite of methods should be used when investigating temporal changes in extremes. These include the initial steps of data quality control, gap filling of missing values and homogenisation. Two basic approaches can used in the subsequent analysis of temporal changes in events in the tails of probability distributions. The non-parametric approach is more suited to those events with shorter return periods. The descriptive indices for these more common extremes produce a relatively large number of observations exceeding the threshold, facilitating the use of more robust statistical analyses. But the results can be sensitive to the choice of index. The complementary, parametric approach is based on Extreme Value Theory. It provides a sound statistical framework which is more applicable to the study of very rare extremes. Detection of changes in extremes over time is often based on identifying the presence of a statistically significant trend in the time series of interest. The methods summarised in this chapter underpin our understanding of past and future changes in extremes, as described in the following four chapters. But, as is shown in Chapters 8 through 10, these same methods are also relevant when attributing these changes to specific causes. These include anthropogenic forcing, which represents the direct influence of human activities on the atmosphereeocean system.

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130. Zumwald M, Knüsel B, Baumberger C, Hirsch Hadorn G, Bresch DN, Knutti R. Understanding and assessing uncertainty of observational climate datasets for model evaluation using ensembles. WIREs Clim Chang. 2020;11(5). https://doi.org/10.1002/wcc.654. 131. Kennedy JJ. A review of uncertainty in in situ measurements and data sets of sea surface temperature. Rev Geophys. 2014;52(1):1e32. https://doi.org/10.1002/2013RG000434. 132. Matthews JL, Mannshardt E, Gremaud P. Uncertainty quantification for climate observations. Bull Am Meteorol Soc. 2013;94(3):ES21eES25. https://doi.org/10.1175/BAMS-D-12-00042.1. 133. Timmermans B, Wehner M, Cooley D, O’Brien T, Krishnan H. An evaluation of the consistency of extremes in gridded precipitation data sets. Clim Dynam. 2019;52(11):6651e6670. https://doi.org/10.1007/s00382-018-45370. 134. Gross MH, Donat MG, Alexander LV, Sisson SA. The sensitivity of daily temperature variability and extremes to dataset choice. J Clim. 2018;31(4):1337e1359. https://doi.org/10.1175/JCLI-D-17-0243.1. 135. Nguyen P-L, Bador M, Alexander LV, Lane TP, Funk CC. On the robustness of annual daily precipitation maxima estimates over monsoon Asia. Front Clim. 2020;2(October):1e19. https://doi.org/10.3389/ fclim.2020.578785. 136. Donat MG, Alexander LV, Herold N, Dittus AJ. Temperature and precipitation extremes in century-long gridded observations, reanalyses, and atmospheric model simulations. J Geophys Res Atmos. 2016;121(19):11174e11189. https://doi.org/10.1002/2016JD025480. 137. Chen C, Li Z, Song Y, et al. Performance of multiple satellite precipitation estimates over a typical arid mountainous area of China: spatiotemporal patterns and extremes. J Hydrometeorol. 2020;21(3):533e550. https:// doi.org/10.1175/JHM-D-19-0167.1. 138. Ayoub AB, Tangang F, Juneng L, Tan ML, Chung JX. Evaluation of gridded precipitation datasets in Malaysia. Rem Sens. 2020;12(4):613. https://doi.org/10.3390/rs12040613. 139. Alexander LV, Bador M, Roca R, Contractor S, Donat MG, Nguyen PL. Intercomparison of annual precipitation indices and extremes over global land areas from in situ, space-based and reanalysis products. Environ Res Lett. 2020;15(5):055002. https://doi.org/10.1088/1748-9326/ab79e2. 140. Bador M, Alexander LV, Contractor S, Roca R. Diverse estimates of annual maxima daily precipitation in 22 state-of-the-art quasi-global land observation datasets. Environ Res Lett. 2020;15(3):035005. https://doi.org/ 10.1088/1748-9326/ab6a22. 141. Hunziker S, Brönnimann S, Calle J, et al. Effects of undetected data quality issues on climatological analyses. Clim Past. 2018;14(1):1e20. https://doi.org/10.5194/cp-14-1-2018. 142. Ashcroft L, Karoly DJ, Dowdy AJ. Historical extreme rainfall events in southeastern Australia. Weather Clim Extrem. 2019;25(January):100210. https://doi.org/10.1016/j.wace.2019.100210. 143. AghaKouchak A, Easterling D, Hsu K, Schubert S, Sorooshian S. In: Extremes in a Changing Climate: Detection, Analysis and Uncertainty. Singh VP, ed. Water Science and Technology Library; Vol 65. 144. Mudelsee M. Statistical Analysis of Climate Extremes. Cambridge University Press; 2020. https://doi.org/ 10.1007/978-94-007-4479-0. 145. WMO. Guidelines on the Defintion and Monitoring of Extreme Weather and Climate Events. World Meteorological Organization; 2018:74. http://www.wmo.int/pages/prog/wcp/ccl/documents/GUIDELINESONTHE DEFINTIONANDMONITORINGOFEXTREMEWEATHERANDCLIMATEEVENTS_09032018.pdf. 146. You J, Hubbard KG. Quality control of weather data during extreme events. J Atmos Ocean Technol. 2006;23(2):184e197. https://doi.org/10.1175/JTECH1851.1. 147. Aieb A, Madani K, Scarpa M, Bonaccorso B, Lefsih K. A new approach for processing climate missing databases applied to daily rainfall data in Soummam watershed, Algeria. Heliyon. 2019;5(2):e01247. https://doi.org/ 10.1016/j.heliyon.2019.e01247. 148. Schär C, Ban N, Fischer EM, et al. Percentile indices for assessing changes in heavy precipitation events. Clim Change. 2016;137(1e2):201e216. https://doi.org/10.1007/s10584-016-1669-2. 149. Huang WK, Stein ML, McInerney DJ, Sun S, Moyer EJ. Estimating changes in temperature extremes from millennial-scale climate simulations using generalized extreme value (GEV) distributions. Adv Stat Climatol Meteorol Oceanogr. 2016;2(1):79e103. https://doi.org/10.5194/ascmo-2-79-2016.

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C global warming. Sci Rep. 2017;7(1):46432. https://doi.org/10.1038/srep46432. 189. Mitchell D, AchutaRao K, Allen M, et al. Half a degree additional warming, prognosis and projected impacts (HAPPI): background and experimental design. Geosci Model Dev (GMD). 2017;10(2):571e583. https://doi.org/ 10.5194/gmd-10-571-2017. 190. Lewis SC, King AD, Perkins-Kirkpatrick SE, Mitchell DM. Regional hotspots of temperature extremes under 1.5
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194. Fox-Kemper B, Adcroft A, Böning CW, et al. Challenges and prospects in ocean circulation models. Front Mar Sci. 2019;6(FEB):1e29. https://doi.org/10.3389/fmars.2019.00065. 195. Harris C. Coupled atmosphere-ocean modelling. In: New Frontiers in Operational Oceanography. GODAE OceanView; 2018. https://doi.org/10.17125/gov2018.ch16. 196. Alexander MA, Scott JD, Friedland KD, et al. Projected sea surface temperatures over the 21st century: changes in the mean, variability and extremes for large marine ecosystem regions of Northern Oceans. Elem Sci Anthr. 2018;6. https://doi.org/10.1525/elementa.191. 197. Schlegel RW, Oliver ECJ, Wernberg T, Smit AJ. Nearshore and offshore co-occurrence of marine heatwaves and cold-spells. Prog Oceanogr. 2017;151:189e205. https://doi.org/10.1016/j.pocean.2017.01.004. 198. Pilo GS, Holbrook NJ, Kiss AE, Hogg AM. Sensitivity of marine heatwave metrics to ocean model resolution. Geophys Res Lett. 2019;46(24):14604e14612. https://doi.org/10.1029/2019GL084928. 199. Hayashida H, Matear RJ, Strutton PG, Zhang X. Insights into projected changes in marine heatwaves from a high-resolution ocean circulation model. Nat Commun. 2020;11(1):4352. https://doi.org/10.1038/s41467-02018241-x. 200. Morim J, Trenham C, Hemer M, et al. A global ensemble of ocean wave climate projections from CMIP5-driven models. Sci Data. 2020;7(1):105. https://doi.org/10.1038/s41597-020-0446-2. 201. Morim J, Hemer M, Wang XL, et al. Robustness and uncertainties in global multivariate wind-wave climate projections. Nat Clim Change. 2019;9(9):711e718. https://doi.org/10.1038/s41558-019-0542-5. 202. Timmermans B, Stone D, Wehner M, Krishnan H. Impact of tropical cyclones on modeled extreme wind-wave climate. Geophys Res Lett. 2017;44(3):1393e1401. https://doi.org/10.1002/2016GL071681. 203. Meucci A, Young IR, Hemer M, Kirezci E, Ranasinghe R. Projected 21st century changes in extreme wind-wave events. Sci Adv. 2020;6(24):1e10. https://doi.org/10.1126/sciadv.aaz7295. 204. Mori N, Shimura T, Yoshida K, et al. Future changes in extreme storm surges based on mega-ensemble projection using 60-km resolution atmospheric global circulation model. Coast Eng J. 2019;61(3):295e307. https:// doi.org/10.1080/21664250.2019.1586290. 205. Bloemendaal N, de Moel H, Martinez AB, et al. A globally consistent local-scale assessment of future tropical cyclone risk. Sci Adv. 2022;8(17):1e14. https://doi.org/10.1126/sciadv.abm8438. 206. Wahl T. Sea-level rise and storm surges, relationship status: complicated!. Environ Res Lett. 2017;12(11):111001. https://doi.org/10.1088/1748-9326/aa8eba. 207. Kirezci E, Young IR, Ranasinghe R, et al. Projections of global-scale extreme sea levels and resulting episodic coastal flooding over the 21st century. Sci Rep. 2020;10(1):1e12. https://doi.org/10.1038/s41598-020-67736-6. 208. van de Wal RSW, Zhang X, Minobe S, et al. Uncertainties in long-term twenty-first century process-based coastal sea-level projections. Surv Geophys. 2019;40(6):1655e1671. https://doi.org/10.1007/s10712-019-09575-3. 209. Jevrejeva S, Frederikse T, Kopp RE, Le Cozannet G, Jackson LP, van de Wal RSW. Probabilistic sea level projections at the coast by 2100. Surv Geophys. 2019;40(6):1673e1696. https://doi.org/10.1007/s10712-019-09550-y. 210. Dayan H, Le Cozannet G, Speich S, Thiéblemont R. High-end scenarios of sea-level rise for coastal risk-averse stakeholders. Front Mar Sci. 2021;8(May):1e16. https://doi.org/10.3389/fmars.2021.569992. 211. Tabari H, Hosseinzadehtalaei P, AghaKouchak A, Willems P. Latitudinal heterogeneity and hotspots of uncertainty in projected extreme precipitation. Environ Res Lett. 2019;14(12):124032. https://doi.org/10.1088/17489326/ab55fd. 212. Li C, Zwiers F, Zhang X, Li G, Sun Y, Wehner M. Changes in annual extremes of daily temperature and precipitation in CMIP6 models. J Clim. 2021;34(9):3441e3460. https://doi.org/10.1175/JCLI-D-19-1013.1. 213. Freychet N, Hegerl G, Mitchell D, Collins M. Future changes in the frequency of temperature extremes may be underestimated in tropical and subtropical regions. Commun Earth Environ. 2021;2(1):28. https://doi.org/ 10.1038/s43247-021-00094-x. 214. Ehret U, Zehe E, Wulfmeyer V, Warrach-Sagi K, Liebert J. Should we apply bias correction to global and regional climate model data? Hydrol Earth Syst Sci. 2012;16(9):3391e3404. https://doi.org/10.5194/hess-163391-2012. 215. Herger N, Angélil O, Abramowitz G, Donat M, Stone D, Lehmann K. Calibrating climate model ensembles for assessing extremes in a changing climate. J Geophys Res Atmos. 2018;123(11):5988e6004. https://doi.org/ 10.1029/2018JD028549. 216. Ribes A, Qasmi S, Gillett NP. Making climate projections conditional on historical observations. Sci Adv. 2021;7(4):1e10. https://doi.org/10.1126/sciadv.abc0671.

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217. Fyfe JC, Kharin VV, Santer BD, Cole JNS, Gillett NP. Significant impact of forcing uncertainty in a large ensemble of climate model simulations. Proc Natl Acad Sci USA. 2021;118(23). https://doi.org/10.1073/ pnas.2016549118. e2016549118. 218. Lee JY, Marotzke J, Bala G, et al. Future global climate: scenario-based projections and near-term information. In: Masson-Delmotte V, Zhai P, Pirani A, et al., eds. Climate Change 2021: The Physical Science Basis. Contribution of Working Group I to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change (IPCC). Cambridge University Press; 2021. doi:10.1017/9781009157896.006. 219. Pulkkinen K, Undorf S, Bender F, et al. The value of values in climate science. Nat Clim Change. 2022;12(1):4e6. https://doi.org/10.1038/s41558-021-01238-9. 220. Helgeson C, Srikrishnan V, Keller K, Tuana N. Why simpler computer simulation models can be epistemically better for informing decisions. Philos Sci. 2021;88(2):213e233. https://doi.org/10.1086/711501. 221. Shafiei Shiva J, Chandler DG. Projection of future heat waves in the United States. Part I: selecting a climate model subset. Atmosphere. 2020;11(6):587. https://doi.org/10.3390/atmos11060587. 222. Eyring V, Cox PM, Flato GM, et al. Taking climate model evaluation to the next level. Nat Clim Change. 2019;9(2):102e110. https://doi.org/10.1038/s41558-018-0355-y. 223. Wehner MF. Characterization of long period return values of extreme daily temperature and precipitation in the CMIP6 models: Part 2, projections of future change. Weather Clim Extrem. 2020;30(June):100284. https:// doi.org/10.1016/j.wace.2020.100284.

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Have atmospheric extremes changed in the past? For the scientific community focusing on impacts of climate change and variability, historical observations of extreme indicators can facilitate a better understanding of the role of extreme events and sectoral implications. (Mistry, 2019).1

Introduction Chapter 1 highlighted that formal interest in changes in weather and climate extremes over time is relatively recent. Changes in these extremes during the pre-instrumental era, and more recently, provide both a baseline and understanding for contemplating what changes might occur in the more immediate future and beyond. Information from the preinstrumental era provides a longer-term context for changes in the more recent instrumental record. Variations in climate observed over the last two millennia are likely to be representative of the Earth’s climate in the present century had anthropogenic forcing of the climate system not occurred.2 This chapter therefore considers changes in atmospheric extremes over both the preinstrumental and instrumental periods, but with a greater focus on the 1950s onward. This is when reliable observations became more generally available (Chapter 2, Instrumental Era Data). Emphasis will be on temperature and precipitation extremes, but other extremes will be considered where relevant evidence exists. This, and the following chapter describe how extremes have changed over time. The underlying causes of the detected changes, and formal attribution, will be discussed in Chapters 7 and 9, respectively.

Atmospheric extremes in the pre-instrumental era The aim of this section is to compare the occurrence of palaeo-extremes with those occurring in more recent times. The focus is on extremes that have occurred in the last 2000 years (the Common Era, CE). There is generally higher confidence in proxy evidence from this period relative to earlier times. Even then, only longer-duration and larger spatial-scale

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extremes are usually identifiable (Chapter 2, Pre-instrumental Era Data and Related Considerations). There is low confidence in detecting overall changes in extremes using palaeo-archives.3 This is because of limited studies, incomplete global coverage, regional variability and also dating and other uncertainties. But for specific extremes and regions, recent detailed and better-calibrated studies increase the confidence in identifying changes. Thus, there is generally high confidence assessing high-magnitude flood events, as well as for prolonged and widespread droughts lasting several decades or longer e so-called ‘mega-droughts’. The long history of Chinese civilisation has resulted in many, well-dated documentary records of weather and climatic conditions. These, in combination with numerous natural proxies, enable high-resolution paleoclimatic reconstruction of extreme events over the last 2000 years.4 Extreme droughts and flood events in China occurred frequently between 1551 and 1600. The severity of the winters of 1654, 1670, 1690, 1861, 1892 and 1929 exceeded those of the coldest winters since 1951. Nineteen extreme summer heatwaves have occurred in China during the last 1000 years, including the northern China heat wave in the summer of 1743. This was the greatest in terms of intensity, injuries, area of coverage and duration. Millennial ensemble reconstructions of annually resolved temperature variations have identified a globally coherent extended cold period between 1594 and 1677 (the Little Ice Age). This is unique within the past millennium. But no similarly coherent warm phase occurred during the pre-industrial (1000e1850) era.5 The current (post-1974) warm phase is the only period of the past millennium where both hemispheres are known to have experienced contemporaneous warm extremes. For Europe as a whole, recent summer temperatures have been anomalously high. There is no evidence of any period in the last 2000 years being as warm.6 However, in 1540, maximum temperatures in Central Europe were higher than in the summer of 2003, the warmest Central European summer in the observational record up to that time.7 The paleoclimate record provides unequivocal evidence of droughts that far exceed those occurring in more recent times, in terms of both magnitude and longevity.8 For example, while the 20th century dust bowl in the United States may stand out as the most extreme summer drought of recent centuries, extended drought reconstructions suggest that the spatial extent and magnitude of this event was exceeded by a 16th century ‘mega-drought’ over the United States, western Canada and northwestern Mexico.2,9,10 Another study used paleoclimatic evidence to conclude that the drought conditions in western North America in the mid-12th century far exceeded the severity, duration and extent of all subsequent droughts.11 However, two paleoclimate reconstructions of drought and precipitation for Central and Southern California indicated that the drought conditions experienced in California from 2012 to 2014 were the most severe in the last 1200 years. Precipitation during the drought was anomalously low, but not outside the range of natural variability.12 More recently, hydrological modelling and new 1200-year tree-ring reconstructions of summer soil moisture showed that the driest period in southwestern North America since 800 CE occurred in the late 16th century. The drought that persisted in the same region from 2000 was found to be the second driest 19-year period since 800 CE. A reconstruction of the central European summer hydroclimate from 75 BCE to 2018 CE revealed that droughts around 40, 590, 950 and 1510 CE were part of a multi-millennial drying trend, while the sequence of European summer droughts since 2015 CE is unprecedented

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in the past 2110 years.13 A separate study14 found that central Europe experienced longer and more severe droughts during the 15th century, and again between around 1770 to 1840 CE, relative to those observed early in the 21st century. These include the droughts in 2003, 2015 and 2018. They are within the historical variability. Flood events more extreme than those recorded since the start of the 20th century have likely occurred in the past 500 years in northern and central Europe, the western Mediterranean and eastern Asia.15 There is also robust evidence that floods during the CE exceeded current probable maximum flood levels in the Upper Colorado River of the United States,16 while flooding in the upper Yellow River basin around 1000 BCE has no more recent equivalents.17 On the other hand, the frequency of widespread severe droughts and extreme pluvials for continental South America south of 12
S since the 1960s do not have precedents in reconstructions dating back to 1400 CE.18 Based on an annually and spatially resolved proxy (tree-rings and corals) reconstruction of hydroclimate variability, periods of multi-decadal drought across eastern Australia in the 1500s were more persistent than any event in the historical record, including the intense drought experienced in Eastern Australia between 2003 and 2009.19 This event was followed by record-breaking rainfall and flooding in the austral summer of 2010e2011. These extreme conditions are not evident in a record dating back to 1500 CE. The comparatively new field of research called paleotempestology extends the relatively short observational record (10 million) cities for the same periods. © 2017 The Authors. Reprinted with permission. Source: Papalexiou, S. M., AghaKouchak, A., Trenberth, K. E., and Foufoula-Georgiou, E. (2018). Global, Regional, and Megacity Trends in the Highest Temperature of the Year: Diagnostics and Evidence for Accelerating Trends, Earth’s Future, 6, 71e79, https://doi.org/10.1002/2017EF000709

Due to larger differences between datasets for the early 20th century, confidence in earlier changes is lower. Confidence is also lower for Africa and South America, due to insufficient data, or inconsistency in the trends.45 There are also strong spatial and seasonal differences in how local temperature extremes are changing. But both observations and reanalyses show that, generally, cold extremes are warming at a faster rate than warm extremes. Consequently, the extreme temperature range has decreased substantially since the 1950s.40 Such changes are more rapid over land areas than the oceans.46,47 The magnitudes of the changes and trends described above vary with the metric used, the analytical methods, the location and the spatial and temporal coverage. For example, similar spatial shifts for temperature extremes and the corresponding arithmetical mean or median temperature have occurred over Europe.48 This apparently paradoxical finding is due to equating the shifts to changes in the high and low quantiles, or standard deviations, between separate time periods, as opposed to determining them with reference to a historical baseline. There are some other notable exceptions to the general changes and trends described above. A much-studied example relates to a region in the eastern United States where

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observations show a general decline in both maximum and minimum temperature extremes, despite a general warming of the Earth. The regional cooling trend began in the late 1950s. Explanations for this so-called ‘warming hole’ have been confounded by both technical and scientific considerations. The former include the choice and analysis of temperature indices, characterising the spatial extent of the ‘hole’, marked seasonal differences and climate model simulations indicating an increasing rather than decreasing frequency and intensity of hot extremes. There are likely to be multiple causes for this phenomenon, including variability in large-scale ocean and atmospheric patterns and changes in external forcings such as changing land use, aerosol emissions and associated indirect effects on temperature from precipitation, cloud cover, soil moisture and evapotranspiration.49 The ‘hole’ now appears to be reducing.50 Another example relates to the geographic differences in the occurrence of late-spring frosts. These affect the performance of plants and animals across the world’s temperate and boreal zones. Between 1959 and 2017, these frosts decreased in North America but increased across most parts of Europe and Asia. Interestingly, the most notable increase in late-spring frosts has occurred in regions where the risk of such frosts used to be low, such as the coastal and eastern parts of Europe and East Asia.51 It is informative to know when and where changes in temperature extremes have consistently emerged, or will emerge, from the background ‘noise’ of climate variability. Observational evidence shows that such changes have already occurred over large parts of the Earth. This is much earlier, and over larger areas, than predicted by models.52 The delayed emergence in modelled data reflects a combination of the simulated changes being weaker than observed, while simulated variability is greater than observed.

Heatwaves There is no standard definition of a ‘heatwave’, either in scientific research or in the policy community.53 As for other extremes, the definition must cover the key characteristics of intensity, frequency, duration, timing and spatial extent. In the case of heatwaves, it should also be founded on the premise of prolonged periods of excessive heat. In this regard, there has been progress from the use of rigid, duration-only indices and simply counting days above a given temperature threshold. Now multi-definition and characteristic frameworks are often used. These include metrics that combine multiple heatwave attributes.54 The record-breaking heat wave experienced in western North America in June 2021 was outside the distribution of temperatures previously observed in that region. The relative intensity of the event was over four standard deviations from the mean. Globally, since 1960, only five other heat waves have been more extreme.55 The first comprehensive global and regional analysis of observed heatwave changes56 found that since 1950 increases in heatwave frequency, duration and cumulative heat e the extra heat experienced during a heatwave e have been accelerating. Trend magnitudes were mainly significant, but not globally uniform. In almost all regions, heatwave frequency has undergone the most rapid and significant change. Detailed analysis of changes in cumulative heat revealed substantial increases, both globally and regionally. The changes have been largely driven by increases in the overall number of heatwave days. But in some regions, small increases in average intensity also played a role. An analysis of trends in concurrent

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heatwaves occurring between May and September in the mid- to high-latitudes of the Northern Hemisphere found an almost 50% increase in their mean spatial extent between 1979 and 2019. Over the same period, their maximum intensity increased by almost 20%, along with a sixfold increase in their frequency.57 While longer, slightly warmer heatwaves may result in a similar change in cumulative heat as shorter, more intense events, different management interventions will likely be required in sectors such as public health and energy supply. Based on a heatwave index that takes into account both heat wave duration and intensity, the percentage of global land area affected by heatwaves tripled between the 1980s and 2002e12.58 Many of the general changes in heatwaves described above have also been found at the regional scale. Studies at that scale can provide further insights into the complex atmosphere, ocean and land interactions driving the occurrence of heatwaves in different parts of the world (Chapter 8). For example, between 1961 and 2010, the majority of observing stations in northern, north-western, central and the east coast of India experienced significant increasing trends in the number of heatwave days. However, three stations on the east coast and two stations from North India showed significant decreasing trends.59 Another informative example is provided by a study of heatwave trends and interannual variability across Southern California from 1950 to 2020.60 Inland urban areas were more impacted by heatwaves than were coastal urban and rural areas, with significant rising trends in frequency, duration, intensity and season length. These metrics were strongly correlated with an increase in night-time mean warming. A heatwave metric based exclusively on night-time temperatures showed the strongest trends for all metrics, with the frequency trend of 1.4 events per decade being almost three times greater than metrics based on day-time temperatures and the Excess Heat Factor.61 Heatwaves in the urban areas of Southern California are starting earlier and ending later in the year, with the season now extending from March to September, compared to May to August in the mid-20th century.60 In the United Kingdom, the lengths of heat waves lasting over 10 days have declined from the mid-1970s to at least 2016, whereas the lengths of heat waves lasting up to 10 days increased slightly over a similar period.62 Between 1980 and 2015, most of the capitals of countries in the European Union experienced significant positive trends of the majority of heatwave indices, and especially between 1998 and 2015. However, small decreases occurred in several northern and especially southwestern cities.63 Between 1951 and 2015, Guangzhou, China, experienced consistent positive trends in the frequency, duration and intensity of heat waves.64 For over two decades, the relatively large increase in the frequency of day- and night-time extremes in low-income countries worldwide has contributed to a greater increase in the number of heatwave days compared to high-income countries.65 In this context, an analysis of the magnitude and the spatial extent of the most extreme heat waves experienced in Africa between 1979 and 2015 showed that, in the more recent years, Africa experienced hotter, longer and spatially more extensive heat waves than in the last two decades of the 20th century.66 But despite such findings, databases of extreme heatwave impacts suggest the opposite to be true.67

Cold waves There has been recent speculation, largely though not entirely media-based,68 that cold waves in the northern midlatitudes are becoming more severe as well as more frequent.

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The evidence is to the contrary e cold waves in the northern midlatitudes are becoming less severe.69 Specifically, analysis of over 1000 globally distributed stations with at least 50 years of in situ observations revealed a strong warming in cold waves everywhere in the northern midlatitudes. The rate was between three to five times the rate of increase in global mean temperature between 1900 and 2018. Since 1950, all these land areas experienced a strong decrease in the area affected by cold waves. Despite the use of a different metric e a threshold based on the 10th quantile winter daily minimum temperature, as opposed to the annual minimum of the daily minimum temperature e similar results were found for 22 locations in South Korea. All experienced a decrease in cold spells between 1976 and 2015.70 However, in the most recent 10 years, the trend reversed for nine of the 22 stations. The trends were significant despite the short record. Somewhat similar findings have been reported for India.59 A comparison of data for 1971e80 and 1991e2000 showed an overall decrease in the average number of cold wave days, with systematic decreases over north, north-west and north-east India, and a slight increase over some southern parts of central India. However, between 2001 and 2010 there was a slight increase in the frequency and spatial extent of cold wave days relative to the previous decade. Between 1960 and 2016, there was a decreasing trend in annual cold spell duration and cold wave frequency in South Africa.71 Similarly, between 1962 and 2006, there was a decrease in the number of cold wave days across 209 cities in the United States.72 Chapter 8 (Low Temperature Extremes, including Atmospheric and Marine Cold Waves) provides insights into why the frequency of cold waves is declining in the Northern Hemisphere, despite some claims to the contrary.

Heavy precipitation One expected consequence of a warming world is intensification of the global hydrological cycle due, at least in part, to increasing water vapour content in a warmer atmosphere.73 This is already occurring (Fig. 3.4). The change should result in an increase in both total and heavy precipitation. In keeping with this theory, annual, summer and winter single-day to monthly precipitation maxima for Central Europe have increased between 1901 and 2013. These changes scale positively with the increase in Northern Hemisphere temperature, though the scaling factors vary considerably between seasons and subregions. In general, they are close to the theoretical, thermodynamical ClausiuseClapeyron scaling of approximately 6%e8%oC-1.74 But observed hourly extreme rainfalletemperature scaling relationships vary, from negative in the tropics and sub-tropics, to in excess of ClausiuseClapeyron scaling in mid-latitudes. In order to provide further insights to the scaling with temperature, Australia-wide average changes in the magnitude and frequency of extreme hourly and daily rainfall observations between 1990e2013 and 1966e89 were calculated.75 These were compared with the expected changes from ClausiuseClapeyron scaling as a result of the change in global mean surface temperature. While the increases in daily rainfall extremes were found to be consistent with ClausiuseClapeyron scaling, they were within the range of natural variability. In contrast, changes in the magnitude of hourly rainfall extremes were close to, or exceeded, twice the expected ClausiuseClapeyron scaling, and exceeding three times ClausiuseClapeyron scaling in

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FIGURE 3.4 Annual average precipitable water above land and ocean areas of the Northern Hemisphere for 1979 to 2020, expressed as anomalies from the 1981 to 2010 average. NCEP/NCAR Reanalysis I data provided by the NOAA-ESRL Physical Sciences Laboratory, Boulder Colorado from their Web site at https://psl.noaa.gov/.

the tropical region north of 23
S. These results highlight that ClausiuseClapeyron scaling on temperature leads to a substantial underestimate of observed changes in hourly rainfall extremes, at least in Australia. Despite precipitation extremes being more spatially heterogeneous than is the case for changes in temperature extremes,76 recent research has confirmed the anticipated intensification of precipitation extremes. This includes evidence of an intensification on average globally over the past century.43 However, regional extreme precipitation changes over the same time period were not as robust. Generally, there was little agreement between the various global datasets as to whether precipitation extremes at the regional scale have intensified or weakened. For most land areas, and since 1950, there has been an increase in the number of days exceeding the 95th percentile of daily precipitation.40 The trend is more apparent from the 1970s on. But over the same period, adjoining land areas have experienced positive and negative changes in days with heavy rainfall (10 mm), resulting in little change globally. However, consistent though albeit moderate increases have occurred over North America and in the high latitudes of Eurasia. There have been even larger increases in south-east Asia and central Australia. On the other hand, there have been decreases in the number of heavy precipitation days around the Mediterranean and extending into the Middle East. There are

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indications of a slight increase in the number of heavy precipitation days globally in recent decades. Maximum one-day precipitation has increased globally since the beginning of the 20th century and more so in recent decades. Since the 1950s, there have been substantial increases in Europe and in the eastern half of North America, as well as the eastern portions of southern South America, and some of India and China. An updated analysis of observed changes in extreme precipitation using several additional years of high-quality station data (up to 2018) has provided further insights into whether the signal in extreme precipitation has strengthened in recent years.77 The analyses were conducted for two time periods: for 1950e2018 when spatial coverage was greater, and over 1900e2018 when the benefits of longer station records are offset by much more limited spatial coverage. The analysis showed that extreme precipitation has increased at about two-thirds of stations, with significantly increasing trends for the globe, for the continents including Asia, Europe and North America, and for regions including central North America, eastern North America, northern Central America, northern Europe, the Russian Far East, eastern central Asia and East Asia. The percentage of stations with significantly decreasing trends was not different from that expected by chance. A comparison of trends in observations ending in 2018 with those from data ending in 2000e2009 showed a consistent median rate of increase, but a larger percentage of stations with statistically significant increasing trends. This indicated a recent increase in the ability to detect an intensification in extreme precipitation, likely due to the availability of longer records. As is the case for the preceding two studies, analyses of heavy precipitation have typically used fixed-time periods, such as a day or five days. But such extreme events often persist for many days. An analysis of observed (1961e2010) heavy precipitation78 revealed that the global mean annual-maximum precipitation calculated using complete events of variable duration was significantly greater than when calculated using daily extremes. This is because single day extremes will often divide a multi-day precipitation event into several separate one-day precipitation events. Importantly, between 1961 and 2010, the relative rates of increase in globally averaged persistent precipitation extremes were found to be lower than for daily extremes, especially for the Southern Hemisphere, but also for large expanses between the equator and 45
N. A global analysis of 8730 high-quality, daily precipitation records investigated changes in the frequency and magnitude of extremes during the 1964e2013 period.79 Globally, the ratio of positive to negative trends in heavy precipitation was 1:5. This increased to 2:8 in Eurasia. The ratios of significant-positive to significant-negative trends were much higher, at 2:4 and 7:0, respectively. There was strong spatial coherence in the regional pattern of frequency changes, but less so for magnitude changes, with increasing trends in magnitude being only slightly more frequent than decreasing trends. All of the preceding studies highlighted that spatial heterogeneity is a major challenge when characterising changes in precipitation extremes. This is demonstrated at the national scale by a comparison of changes in extreme precipitation between 1930e70 and 1971e2017 in India. A systematic increase in extreme precipitation was concentrated in southern India, while areas showing a decrease in extreme precipitation were concentrated in central, north and north-eastern India.80 Similarly, contrasting trends were found across the State of Rio de Janeiro, Brazil.81 Seasonal variations also confound extreme precipitation analyses. This was found in an analysis of gridded estimates of the relative and absolute changes in the 20-yr

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return value for daily precipitation for each season between 1950 and 2017 for the conterminous United States.82 Of added interest is the fact that these estimates were derived using a spatial statistical approach that did not smooth the extreme precipitation measurements, thereby avoiding a general underestimation of the return values (Chapter 2, Gridding). The results showed that the largest spatially-coherent changes in return values between 1950 and 2017 occurred between September and February, with the dominant changes being positive, although large regions with negative changes also occurred in each of these seasons. But overall, for the conterminous United States, there has been a significant increase in the area where extreme one-day precipitation events have made an above average contribution to the annual precipitation total (Fig. 3.5). Nine of the top 10 years have occurred since 1996. The escalating rate of change in most extremes is highlighted in a recent analysis which showed that just one decade of additional warming of the Earth has resulted in significant increases in the frequency of heat and rainfall extremes.83 For example, between the first and second decades of the 21st century, the land area affected by temperature extremes that might be expected about 0.1% of the time (three-sigma extremes) increased from around 5% to around 9% (Fig. 3.6a). While the four-sigma extremes were still nearly extremely rare in the first decade of the 21st century, they affected about 3% of the land area during the next decade, representing an approximate 1000-fold increase from the 1951e1980 baseline. Moreover, the number of observed record-breaking monthly temperatures has increased eightfold relative to a climate without anthropogenic forcing (Fig. 3.6b).

FIGURE 3.5 Percent of the land area of the conterminous United States with a much greater than normal proportion of precipitation derived from extreme (90th percentile) one-day precipitation events. Data source: https://www. ncdc.noaa.gov/extremes/cei/graph I. Changes

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FIGURE 3.6 Accelerating trends in temperature and rainfall extremes. (a) Annual averages of the percent of the global land area with monthly temperatures above given sigma-thresholds in any calendar month. (b) Global annual mean of the observed local monthly temperature records on land as a percentage of those expected in the absence of anthropogenic forcing. The thick black line shows the data with 10-year smoothing. The magenta line and shading show the median and 90% confidence interval determined with a statistical model with anthropogenic forcing and Gaussian noise. (c) Global land area mean of the ratio of the observed number of local daily rainfall records aggregated over the year as a percentage of those expected in a stationary climate. The thick black line shows the data with 10-year smoothing. The blue shading shows the 90% confidence interval for a stationary climate. Reproduced under the Creative Commons Attribution 4.0 International License, http://creativecommons.org/licenses/by/4.0/. Robinson A, Lehmann J, Barriopedro D, Rahmstorf S, Coumou D. Increasing heat and rainfall extremes now far outside the historical climate. npj Clim Atmos Sci. 2021;4(1):45. https://doi.org/10.1038/s41612-021-00202-w

The comparable increase in the number of rainfall records has now reached around þ30% (Fig. 3.6c). Tropical regions have experienced the largest increases in the frequency of hot and wet extremes. They now also experience unprecedented events that would have been virtually impossible without anthropogenic forcing. While the increased number of local daily rainfall records may be related to natural multi-decadal variability over the period from 1901 to 1980, the subsequent observed increase in record-breaking rainfall events is consistent with rising global temperatures.84 While theory suggests a general increase in heavy precipitation, an important question is whether such increases are also influenced by water availability. A study85 based on both observations and model simulations revealed robust increases in precipitation extremes over 1951e2010 in both the dry and wet regions of the world. However, while observed data analysed in a more recent study86 also showed increases in humid regions since 1950, no significant changes were identified in the more arid regions. In these latter regions, the signal-to-noise ratio was generally small, at least in part due to the large variability of precipitation and sparse observational coverage. This highlights the need to improve access to longterm high-quality observations of daily precipitation to fill data gaps, particularly for Africa and South America (Chapter 2, In Situ Land-surface Data). Sparse gauge networks, such as in Sub-Saharan Africa, for example, can be complemented by satellite and satellite-gauge precipitation products.87 Collectively, these precipitation products for this region show a positive trend in extreme precipitation events, particularly in wet areas. The effect of atmospheric warming on snowfall is a complex balance between the competing effects of increased temperature and increased precipitation.88 This interplay is reflected in changes in snowfall from 1988 to 2013 in the Australian Alps in southeastern

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Australia.89 A significant decreasing trend was observed for the total number of light snow days, while the total number of heavy snow occurrences remained constant. The temporal changes in snow cover over as many as 104 winter seasons at 60 locations in Poland exhibit less complex patterns.90 The number of days with snow cover in each of 68 winter seasons declined throughout Poland, by at least four days each 10 years. Over the same period, the maximum depth of snow cover also declined in most areas of Poland, with a positive but statistically insignificant trend being limited to northeastern Poland. No statistically significant trend in the occurrence of either high or low snowfall years between 1900e2001 and 2006e2007 was found when using area-weighted data for the conterminous United States. But regional trends were identified.91 Large decreases in the frequency of low-extreme snowfall years occurred in the west north-central and east north-central regions of the United States, while large increases occurred in the northeast, southeast and northwest regions. Trends between 1950e1951 and 2006e2007 were found to be much more consistent, with the entire United States and the central and northwest regions experiencing significant declines in high-extreme snowfall years. In contrast, the northeast, southeast, south and northwest regions experienced significant increases in the frequency of low-extreme snowfall years. But snowstorm records dating to the late 1800s show that most of the biggest snowstorms in eastern United States have occurred since 1990.92 Data back to 1900 for the southern six states of the United States show no significant trend in the areal extent of snowstorms of at least Category 1, as defined by the Regional Snowfall Index93 (Fig. 3.7). But the frequency of such storms has increased in the more recent decades.

Drought The existence of long-term trends in historic drought frequency and severity continues to be highly uncertain. This is due, in part, to the lack and brevity of observations, but also to large internal variability and to multiple definitions and indicators of drought.94 The latter include snow droughts and flash droughts (Box 3.1). Notwithstanding these challenges and limitations, a catalogue of meteorological drought events between 1951 and 2016 has been compiled,107 based on separate applications of the Standardized Precipitation-Evapotranspiration Index and the Standardized Precipitation Index. Trends in drought frequency were identified using both indicators at a 12-month accumulation scale. This is usually an indicator of hydrological droughts. Increasing trends were identified for the United States East Coast, Amazonia and north-eastern Brazil, Patagonia, the Mediterranean region, most of Africa and for north-eastern China. Decreases in drought frequency occurred in northern Argentina, Uruguay and northern Europe. Compared to 1951e80, during 1981e2016, both indicators showed that meteorological droughts were more severe over the north-western United States, parts of Patagonia and southern Chile, the Sahel, the Congo River basin, southern Europe, north-eastern China and south-eastern Australia. On the other hand, the eastern United States, south-eastern Brazil, northern Europe and central-northern Australia experienced less severe droughts. The areal extent of drought increased in southern South America, the Mediterranean region, central and eastern Asia and for all of sub-Sahara Africa.

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FIGURE 3.7 Areal extent of snowstorms in the southern six states of the United States that are of at least Category 1, as defined by the Regional Snowfall Index. Data source: https://www.ncdc.noaa.gov/snow-and-ice/rsi/overview

Another recent global study108 was based only on the Palmer Drought Severity Index. But in addition to observations, it used climate models and reconstructions to provide a longerterm, global perspective on changes in drought occurrence. The study identified three distinct periods of change globally between 1900 and 2017 e an increase from 1900 to 1949, a decrease from 1950 to 1975 and then another increase subsequently. For the first half of the 20th century, positive trends in drought occurrence were detected in all regions except for Mexico and Monsoon Asia. Negative trends during the mid-20th century were identified for Mexico, North America, Europe and the Mediterranean region. More recently, positive trends occurred in most regions. These findings are consistent with those based on an analysis of largely independent observations-based global datasets covering 1901e2010. None of these indicated systematic, long-term global changes in dry extremes.43 An analysis of exceptional drought events in Europe between 1766 and 2020 showed that the 2018e2020 drought event had an unprecedented intensity that persisted for more than two years.55 Southwestern North America has been anomalously dry and warm in the 21st century, relative to the 20th century.10,109 An analysis of daily meteorological observations from 1976 to 2019 for 337 long-term weather stations distributed across the western United States identified widespread warming (0.2
C per decade for the daily maximum temperature) across most of the region.110 It also found a reduction in annual precipitation of 2.3 mm per decade, along with increasing interannual variability of precipitation. Importantly, the

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BOX 3.1

Historic changes in flash droughts and snow droughts Flash drought is a designation and concept that has gained increasing attention in the research literature and media. The term was first used in the United States in the early 2000s, to describe droughts that are characterised by sudden onset and rapid intensification, usually resulting in severe impacts.95,96 Four global reanalysis datasets covering the period 1980 to 2015 were used to estimate the occurrence of flash drought, using a validated methodology based on anomalies in evaporative stress and the standardised evaporative stress ratio.97 A statistically significant increase in flash drought occurred in six of the fifteen regions, while three had a significant decreasing trend. It is possible to distinguish between two types of flash droughts e heat wave flash drought and precipitation deficit flash drought. Between 1979e88 and 2009e18, the conterminous United States experienced an increase in the area impacted by both types of droughts, but the frequency of rapidly intensifying flash droughts did not change significantly over the same period. Trends in precipitation deficit flash drought were positive for almost all regions, with the trends being statistically significant for about half of the regions. Trends in heat wave flash drought were also positive in almost all regions, with the majority being statistically significant. Trends in both categories of droughts were also positive and significant for the conterminous United States as a whole. The positive trends in both indicators can be attributed, at least in part, to the fact that both directly depend on air temperature,

which has increased over recent decades. Trends in flash droughts are not evident when using indicators that depend only on soil moisture or evaporative stress.98 This explains, at least in part, why a separate study99 using a soil moisture-based indicator of heat wave flash drought in the conterminous United States from 1916 to 2013 found a decreasing frequency over the 20th and early 21st centuries. The occurrence of heat wave flash drought was highest in the 1920s through 1940s, but reached a minimum between 1965 and 1972. The frequency increased slightly in the 1980s, but decreased again from 1990 to 2009. Of the 15 flash droughts that occurred in India between 1951 and 2016, the most severe happened in 1979.100 China experienced a significant increase in the frequency of flash drought events between 1961 and 2005.101 Between 1960 and 2015, heat wave flash droughts dominated in the Pearl River basin. They underwent a significant increase, while precipitation deficit flash droughts showed only a slight increase.102 These latter results are consistent with the finding of significant trends in flash drought frequency for China between 1979 and 2010, with heat wave flash droughts increasing by 129% while precipitation deficit flash droughts increased by only 59%.103 Similarly, flash droughts increased over South Africa by 220% from 1961 to 2016.104 In contrast, the northern regions of Spain, where flash droughts are more common than in other parts of the country, showed negative trends in the frequency of flash drought for the period 1961e2018.105 But the central and southern

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BOX 3.1 (cont'd) regions of Spain, which experience fewer flash drought events, showed generally positive trends. Overall, 40% of all droughts occurring in Spain can be characterised by rapid development. Worldwide changes in the duration and intensity of snow droughts, as indicated by snow water equivalent deficits, were assessed for the period from 1980 to 2018.106 During this time, snow droughts became more prevalent, intense and longer for the western

United States, with that region and Europe and Eastern Russia experiencing 28%, 16% and 2% longer snow drought durations, respectively. The probability of a snow drought exceeding the average intensity increased by 15%, 4% and 3%, respectively. On the other hand, in the Hindu Kush and Central Asia, extratropical Andes, greater Himalayas and Patagonia, the average snow drought duration decreased over the same period, by 4%, 7%, 8% and 16%, respectively.

daily observations showed that extreme-duration drought increased in terms of both the mean and longest dry interval between precipitation events (0.6 and 2.4 days per decade, respectively). There was increased interannual variability in these dry intervals (Fig. 3.8).111 The benefits of using multiple indices when studying drought were identified in an assessment of changes in drought between 1982 and 2015 in the Yarlung Zangbo River basin in southwestern China.112 It allowed the evaluation of drought characteristics from the perspectives of meteorology, hydrology and agriculture. Since the beginning of the 21st century, meteorological drought in the basin has changed from moderate wet to moderate dry, while the agricultural drought transitioned from severe to moderate dry.

Extreme storms, including tropical cyclones Extreme storms include tropical cyclones, atmospheric rivers and severe extratropical cyclones and convective storms such as tornadoes. Their relative rarity, short duration and often small scale, as well as the associated high degree of multidecadal internal variability, means that it is extremely challenging to detect systematic changes in the frequency, intensity and spatial behaviour of extreme storms. The challenge is compounded by the heterogeneous nature of the observational records, including ‘best-track’ data. A study113 which used a reanalysis dataset and a satellite-based precipitation product for 2001 to 2010 found that in most of the oceanic regions where they are active, tropical and extratropical cyclones made greater contributions to extreme hourly precipitation than to annual precipitation. Over 80% of hourly and daily precipitation extremes (greater than the 99.99th percentile) were associated with either extratropical cyclones or fronts over midlatitude oceanic regions. They are also associated with a smaller, but still very substantial proportion of these systems over midlatitude land areas. Coexisting tropical cyclones and fronts made significant contributions (22% and 19%, respectively) to extreme 24 h precipitation

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FIGURE 3.8 Trends in the occurrence of flash drought. The black lines show the annual mean of the spatial extent of flash drought for the indicated regions, determined using four reanalysis datasets for 1980 to 2015. The green shaded area depicts the variability between the four reanalyses as described by the standard deviation, while the trend in the spatial extent of flash drought is shown by the blue line. P-values highlighted in red are statistically significant trends at the 90% confidence level using the ManneKendall test. Reproduced under the Creative Commons Attribution 4.0 International License, http://creativecommons.org/licenses/by/4.0/. Christian JI, Basara JB, Hunt ED et al. Global distribution, trends, and drivers of flash drought occurrence. Nat Commun. 2021;12(1):6330. https://doi.org/10.1038/ s41467-021-26692-z

related to tropical cyclones in East Asia and eastern North America. Such large contributions were rarely found in other land areas. Fronts remote from the centres of extratropical cyclones were shown to contribute to extreme precipitation as much as the centres of extratropical cyclones.113 Tropical cyclones Theoretical studies undertaken over 30 years ago predicted that anthropogenic forcing would result in an increase in the thermodynamic upper bound for tropical cyclone winds, and thereby lead to a higher frequency of intense storms. But the rarity of these intense cyclones, combined with the limitations of the observational record, has made it difficult to determine if there are trends in the tropical cyclone record consistent with the theoretical predictions.114

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Importantly, the quality of tropical cyclone intensity and related data has improved from the 1980s on, as a result of satellites providing global coverage at appropriate spatial and temporal resolutions. There is evidence that this satellite-based record is now of sufficient length to detect any statistically significant trend in global tropical cyclone intensity.115 Indeed, a homogenised global tropical cyclone intensity record for 1979 to 2017 revealed statistically significant positive trends in the probability of these events exceeding hurricane intensity (65 kt), as well as in the proportion of higher tropical cyclone intensities. The probability of major tropical cyclones (intensity >100 kt) has increased by about 8% per decade. Between 1982 and 2018, the global mean lifetime maximum intensity of major tropical cyclones (lifetime maximum intensity >96 kt e Categories three to five in SaffireSimpson Hurricane Wind Scale) showed a statistically significant increase of 3 kt per decade.116 These findings are consistent not only with with the theoretical interpretations described above, but with experimental understanding based on model simulations.117 All ocean basins other than the northern Indian Ocean contributed to the positive global trend, with the greatest increases occurring in the North Atlantic.115 There, the probability of major tropical cyclone exceedance increased by 49% per decade, while the proportion of major tropical cyclone intensities increased by 42% per decade. Two observational datasets have shown that the proportion of 24-h tropical cyclone intensification rates greater than 30 kt significantly increased in the Atlantic Basin between 1982 and 2009.118 But only one of the two datasets showed a significant increase for data averaged over all ocean basins. However, the large natural variability of tropical cyclone frequency limits the usefulness of only a few decades of satellite-era observational data when quantifying long-term historical trends in tropical cyclone characteristics.119 This constraint has been addressed by very recent improvements in the application of reanalysis products, resulting in a reconstructed longterm proxy of annual tropical cyclone numbers.120 The record extends back to the mid 19th century. When used together with high-resolution climate model experiments, it allows an objective assessment of changes in global- and regional-scale tropical cyclone numbers since 1850. The reanalysis dataset assimilated only sea-level pressure fields, rather than all available troposheric observations. This made it less sensitive to temporal inhomogeneities in the observations. Importantly, the resulting analysis identified robust negative trends in the annual number of tropical cyclones at both global and regional scales during the 20th century. While annual tropical cyclone numbers at the basin scale exhibit considerable variability, since 1850 statistically significant negative trends occurred in every basin except the South Indian Ocean. There the downward trend becomes apparent only during the 20th century. Overall, the trends are consistent with the weakening of the Hadley and Walker circulations in the 20th century. This makes conditions for tropical cyclone formation less favourable. Recently, longer-term perspectives on temporal changes in tropical cyclone frequency have also been provided for the North Atlantic basin. A study121 analysed an homogenised database of records covering the period from 1851 to 2019. It showed that the basin-wide increases in both tropical cyclone and major tropical cyclone activity since the 1970s are not part of a century-scale increase, but rather a rebound from a deep minimum which occurred from the 1960s to the 1980s. This was likely due to internal multi-decadal and other climate variability as well as to aerosol effects. Both masked century-scale greenhouse gas forcing. The second study was based on dynamical downscaling of three climate reanalysis products

I. Changes

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3. Have atmospheric extremes changed in the past?

that span more than a century.122 They are based mostly on sea surface temperature and surface pressure data. The downscaled tropical cyclone metrics showed consistent and substantial increases in tropical cyclone activity through the period covered by the reanalyses, but again a prominent reduction in frequency in the 1970 and 1980s. The recent positive trends in the Atlantic Basin have continued, as highlighted by the extremely active 2020 and 2021 Atlantic tropical cyclone seasons (Box 3.2).

BOX 3.2

The record breaking 2020 Atlantic tropical cyclone season The 2020 Atlantic tropical cyclone season comprised a record-equalling (with 2005) 30 named tropical storms. This is more than double the long-term average. The season included 14 tropical cyclones, and seven major tropical cyclones. The latter was also record equalling with 2005.123e125 The season marked the fifth consecutive year with an above-normal Atlantic tropical cyclone season. It started early and at a rapid pace, including being the record sixth consecutive year with named storm forming before the ‘official’ June 1 start of the North Atlantic season. A record nine named storms occurred through to July. Ten storms formed in the month of September, the most in any single month on record. By midSeptember, the World Meteorological Organisation’s rotating list of 21 names for tropical cyclones in the Atlantic was fully expended, for only the second time in history. The Greek alphabet was used for the remainder of the season. Twelve separate storms made landfall in the conterminous United States, exceeding the previous record of nine set in 1916. Five of the 12 landfalls occurred in the state of Louisiana, setting

another record for most landfalls in a single state in a season. The 2020 season was also notable for the large number of storms that intensified rapidly e 10 of the 13 tropical cyclones that formed underwent rapid intensification. A few of these underwent explosive intensification. This tied the previous record number of rapidly intensifying storms set in 1995. Consistent with a trend towards slowermoving tropical cyclones over the United States,126 in the 2020 season, two tropical cyclones stalled their forward motion as they were making landfall. Subtropical storm Alpha, which formed over the northeastern Atlantic in mid-September 2020 and made landfall on the Iberian Peninsula with an estimated intensity of 45 kt, was the first known subtropical or tropical cyclone to make landfall in mainland Portugal.127 For the second successive year, the North Atlantic also had a very active season in 2021, with 21 named storms, making it the thirdmost active Atlantic tropical cyclone season on record. It is also the second in a row, and third overall, in which the designated 21name list of storm names was fully expended.

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Significantly, since the 1960s, there has been a substantial decrease in the number of tropical cyclones occurring annually in the Australian region, as well as for each of its three ocean basins.128 The average number of landfalling tropical cyclones also declined. But consistent with the above findings, over the same period, there was a large increase in the proportion of severe tropical cyclones. However, it is important to highlight that tropical cyclone intensity data prior to the 1980s are considered to be inconsistent with those for later years. Recently, several metrics in addition to frequency and intensity have been used to assess temporal changes in tropical cyclone behaviour. These are thought to be relatively less sensitive to data constraints.21 One of the metrics, tropical cyclone translation speed, is the speed at which tropical cyclones move across the Earth’s surface. It is a useful metric, since slower translation speeds are usually associated with greater local rainfall, increased structural wind damage and more hazardous coastal storm surges.129 The global slowdown in the best-track translation speeds detected between 1949 and 2016130 has recently been attributed, at least in part, to data heterogeneity. This is largely due to the reliance on satellite data in the latter half of the period.131,132 But this interpretation has itself been questioned.133 The substantial differences between ocean basins, for both the occurrence frequency and translation speeds of tropical cyclones, may also confound global trends in translation speed. A recent study focussed exclusively on the western North Pacific, which accounts for some 30% of the total global tropical cyclones.134 Tropical cyclone translation speed showed a significant decrease between 1949 and 2017, and especially before 1981. The translation speed was almost unchanged after 1981, when the best-track data became more reliable. The 5.9% changes in translation speed over the ocean contributed mostly to the overall trend. While the translation speed over land also decreased from 1949 to 1981, there was no significant trend over the entire observational period. For the same period, the translation speed of the weaker tropical depressions showed no significant trend. The translation speed was also shown to change with latitude and intensity. When tropical cyclones moved north from the tropical ocean, changes in their translation speeds were highly consistent with the changes in the latitude. The translation speed also increased with the maximum wind, when the wind speed was less than 64 kt. Consistent with this, a statistically significant increase in translation speed over the South China Sea between 1998 and 2017 has been linked to an observed increase in tropical cyclone intensity over the same time period.135 Historical, large-ensemble model simulations have indicated that the decreases in the global or hemispheric translation speeds of tropical cyclones between 1951 and 2011 were not statistically significant.136 In the pre-satellite era, the translation speed based on the observations was higher than that derived from the simulations. There was close agreement subsequently, suggesting that the slowing trend detected in the observations is a result of data inhomogeneities. However, observations over the period 1961 to 2017 did show a significant 11% decrease in the translation speed of tropical cyclones over the coast of China.129 The comparable value for multi-model ensemble simulations was 10%. A 118-year record of tropical cyclone translation speed over the conterminous United States from 1900 to 2017 also showed a 17% decrease. The trend was significant when the effects of multi-decadal variability were removed while data artefacts and discontinuities were not.133 An analysis that focused exclusively on 36 years of best track data for the post-satellite era found that the global-mean tropical cyclone translation speed increased by 5.9% in the major tropical cyclone passage regions.137 This observed change between 1982 and 2017 was

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3. Have atmospheric extremes changed in the past?

attributed, in part, to an increase in the number of tropical cyclone position points in the North Atlantic region, where translation speeds are typically fastest. It was also attributed to a poleward migration of tropical cyclones from the tropics to the extra-tropics, given that the speed of the ambient wind in which tropical cyclones are embedded increases with latitude. The frequencies of both extreme slow- and fast-translation events of Atlantic tropical cyclones displayed a significant positive trend between 1980 and 2019.138 The latter were primarily located in northern areas of the North Atlantic, while the extreme slowtranslation events were located further equatorward. The slow-translation events showed a significant positive trend over the ocean, but not over land. However, the significant increases in the frequency of extreme fast-translation events occurred over both ocean and land. The underlying reasons for the apparent inconsistencies in findings related to changes in translation speed will be further explored in Chapter 7, including the impact of additional global warming on translation speed. A second metric receiving increasing attention is the mean latitude of the lifetime maximum intensity of tropical cyclones. An analysis of this metric for all ocean basins was conducted using data from 1982 to 2012. This is a period when global best-track data are considered most complete and of highest quality, and storm positions were reliably monitored globally using geostationary satellites.139 The data revealed statistically significant poleward trends in the mean latitude of around 0.5o and 0.6o per decade in the Northern and Southern Hemispheres, respectively. There were large inter-basin differences in the rates of change, and in their statistical significance. The largest contribution to the Northern Hemisphere trend was from the western North Pacific Ocean, the basin with the highest annual frequency of tropical cyclones. In contrast, the North Indian Ocean has the lowest mean annual frequency. The small equatorward trend for that basin had relatively little effect on the hemispheric trend. The North Atlantic Ocean and eastern North Pacific showed small poleward trends, and also contributed little to the hemispheric trend. Both the South Pacific and the South Indian Oceans made substantial contributions to the poleward trend in the Southern Hemisphere. Consistent with the foregoing findings, in the western North Pacific Basin, the average latitude of maximum tropical cyclone intensity shifted north by a statistically significant 0.8o per decade when data for 1977 to 1998 and 1999 to 2013 were compared.140 This rate is higher than the statistically significant poleward trend in the latitude of maximum intensity of 0.24
per decade for a longer period from 1961 to 2016.141 But it is comparable to the 0.21
latitude per decade change for 1945 to 2013. This included an adjustment for the effects of inter-annual variability.142 The latter two studies reveal that the increase in the latitude of maximum intensity is not uniform over time.143 For example, no significant trend was detected before 1980.141 The trend was only 0.03
latitude per decade between 1961 and 1979, but increased substantially to 0.51
latitude per decade from 1980 to 2016. This is similar to the rate for all tropical cyclones (0.58
latitude per decade, also for 1980 to 2016). The rates were 0.94
and 0.29
latitude per decade for weak and intense tropical cyclones, respectively.144 A global rate of 0.15
latitude per decade between 1982 to 1999 and 2000 to 2018 has also been reported.145 The foregoing evidence of poleward migration in the mean latitude of lifetime maximum intensity is consistent with the observed increases in the sea surface temperatures over tropical ocean basins in recent decades, and the resulting expansion of the tropics.146 But

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according to multiple studies,143 in recent decades, tropical cyclone tracks have migrated equatorward in the Atlantic Basin, as has the average latitude of lifetime maximum tropical cyclone intensity. This apparently anomalous behaviour is thought to reflect the influence of the Atlantic Multi-decadal Oscillation, a coherent mode of internal variability occurring in the North Atlantic Ocean. There is a strong relationship between the Atlantic Multi-decadal Oscillation and the annual mean latitude of lifetime maximum intensity of tropical cyclones in the Atlantic. The warm phase of the Oscillation, which has persisted since the mid-1970s, correlates with an equatorward migration of the latitude of maximum intensity. When the Oscillation signal is removed from the 1944 to 2016 time series of the annual-mean latitude of peak intensity, the migration rate is essentially zero.143 Interestingly, a recent study shows that multi-decadal oscillations were forced by bursts of volcanic activity during the preindustrial era, rather than being a coherent mode of internal variability in the climate system.147 Another migration of tropical cyclones has also been observed, adding further to tropical cyclone risk. A westward migration, both globally and for the two hemispheres, was evident in an analysis of changes in the annual mean longitude of lifetime maximum intensity. The configuration of the ocean basins means that such a migration enhances the rate at which the distance between the location of lifetime maximum intensity and the land is reducing. Globally between 1982 and 2018, and for all tropical cyclones with a lifetime maximum intensity reaching at least 34 knots, this distance decreased by about 30 km per decade. The annual frequency of global tropical cyclones coming within 200 km of land increased by about two additional cyclones per decade, while the fraction of their annual mean lifetime that tropical cyclones spent this close to the coast increased by around 2% per decade globally. The increase in the number of tropical cyclones globally making landfall (þ1  2 cyclones per decade) was not significant.145 Consistent with the preceding findings, between 1967 and 2018, the rate of decay of North Atlantic landfalling tropical cyclones slowed.148 This is indicated by a 94% increase in the decay timescale. The larger the decay timescale, the slower the decay, and the stronger the tropical cyclone. While in the late 1960s, a typical landfalling Atlantic tropical cyclone lost about 75% of its intensity in the first day post landfall, by the late 2010 the corresponding decay was only about 50%. Thus, the destructive power of tropical cyclones has extended progressively farther inland.149 While there are inter-basin differences in the preceding three metrics, they are consistent for the two hemispheres. But the North Atlantic is a notable exception. The equatorward migration of the mean latitude of lifetime maximum intensity also results in the maximum intensity locations of the strongest storms migrating away from landfall, at a rate of nearly 100 km per year.150 The characteristics of the intensity life cycle of a tropical cyclone e from genesis through intensification and maturity to weakening e are important determinants of its destructive potential. Consequently, there is considerable interest in understanding how key features of the life cycle have changed over time. The time between genesis and reaching lifetime maximum intensity is determined by the intensification rate. The duration of the weakening phase subsequent to achieving maximum intensity is much less studied. This is despite it lasting for a similar length of time and also being more likely to occur near and over land.116 Between 1980 and 2014, a robust and systematic reduction of tropical cyclone genesis occurred in the lowest latitudes for cyclone formation (latitudes w5e12
), along with a coherent poleward shift in the preferred genesis regions over most ocean basins.146 Between

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3. Have atmospheric extremes changed in the past?

1982 and 2018, the global mean duration of major tropical cyclones shortened by about one day, due to both faster intensification and weakening e approximately 3 and 4 h per decade, respectively. However, global mean accumulated cyclone energy, which is dependent on both intensity and duration, did not show a significant change, with reductions in duration being offset by increases in intensity. There was also no change in the time spent as a major tropical cyclone.116 The most intense tropical cyclones are those which have undergone rapid intensification. Around 80% of major tropical cyclones occurring globally are classed as rapid intensification storms, while only 6% of the storms that do not undergo rapid intensification become major storms.151 The relatively high frequency and forecast errors of these storms, as well as their destructive potential, have led to new research into whether the frequency of rapid intensification events is changing, including as a result of anthropogenic forcing (Chapters 7 and 9). Only one of the two most reliable long-term observational records used to calculate tropical cyclone intensity changes showed a significant increase in intensification rates greater than 30 knots in 24 h between 1982 and 2009. However, both datasets showed significant increases in the Atlantic Basin.118 From 1979 to 2018, there was a significant increase in the occurrence of strong rapid intensification events over the western North Pacific, with these being defined as 24 h intensity increases of at least 50 kt.152 A related study identified an increase in the frequency of tropical cyclones undergoing rapid intensification over the South China Sea.153 Overall, the identified changes in the metrics discussed here have major implications for tropical cyclone risk.154 Atmospheric rivers The term ‘atmospheric river’ first appeared in the scientific literature in the early 1990s, followed by an exponential growth in technical publications, and attention in the media. There was an unusual level of debate before a formal definition was published.155 That definition characterises an atmospheric river as a long, narrow and transient conduit of strong horizontal water vapour transport. It generally occurs in a low-level jet stream ahead of the cold front of an extratropical cyclone. A quantitative, global characterisation of the life cycles of atmospheric rivers, based on two reanalysis products for 1979/80 to 2017, provided information on their spatial distribution, temporal evolution and seasonal dependence.156 Atmospheric rivers frequently result in heavy precipitation when they are forced to rise, such as when passing over a mountain range. On landfall, atmospheric rivers typically bring heavy rain, strong winds and low pressures to the coastal area, often resulting in storm surge and flooding.157 On average, four or five atmospheric rivers are present in each hemisphere at any one time. They play an important role in the poleward transport of heat, and in the global water cycle. Atmospheric rivers are responsible for more than 90% of all poleward water vapour transport in the extra-tropics, making them the largest flows of fresh water on Earth e the water volume transported by a single atmospheric river far exceeds that carried by land rivers. They transport more than double the flow of the Amazon River on average and 27 times the average discharge of the Mississippi River. Atmospheric river-associated precipitation accounts for up to 40%e60% of the total precipitation over the extratropical oceans. Atmospheric rivers deliver 20%e30% of annual precipitation in western Europe and the western United States, and 14%e44% of warm-season total precipitation in East Asia.158,159

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The influence of atmospheric rivers is largely confined to the western coastlines of South America, North America, South Africa, Europe and New Zealand, and to the eastern coastline of Japan. Their influence is also felt over continental regions, including Central and Eastern United States. Recent studies have also identified atmospheric river-like features over the western Mediterranean, and polar and the Middle East and North Africa regions.160 Atmospheric rivers occur on the order of 40 days per year over western North America, northern Europe, southern South America and New Zealand.161 Depending on the season, between 50% and 98% of extreme rainfall events (exceeding the 90th percentile values) in New Zealand between 1979 and 2018 were associated with atmospheric river conditions on the western side of mountainous regions and for northern areas. The highest values for stations in these areas occur in summer.162 Atmospheric rivers account for up to 78% of total precipitation and up to 94% of extreme precipitation on the western coast of the South Island of New Zealand,163 and also strongly contribute to extreme ablation and snowfall, and hence to mass balance overall.164 A scale characterising atmospheric river strength and impacts uses the intensity of vertically integrated water vapour transport and the duration of the atmospheric river. It provides a framework for differentiating between the primarily beneficial impacts of the majority of events (e.g. contributing to reservoir storage, snowpack and drought relief) (Category 1) and the relatively few occurrences that are primarily hazardous (e.g. dam overtopping, flooding and excessive erosion) (Category 5).165 Since atmospheric rivers are directly associated with many extreme precipitation and flood occurrences in the midlatitudes, improved forecasts of atmospheric rivers and their impacts would increase preparedness.166,167 The short duration of satellite records, and the lack of observations over regions where atmospheric rivers occur, impedes the detection of long-term temporal changes in their behaviour. As a result, information on historic changes is relatively limited, especially in areas other than the western coast of North America (Box 3.3). Severe extratropical cyclones Fifteen commonly used detection and tracking algorithms for extratropical cyclones were applied to a reanalysis dataset to assess trends in seasonal hemispheric cyclone centre counts between 1989 and 2009.173 The results showed consistent but mostly insignificant decreases in the number of deep cyclone centres (core pressure 980 hPa) in the Northern Hemisphere, for both summer and winter. There was a weak, mostly insignificant increase in the number of deep cyclone centres in the Southern Hemisphere austral summer. Consistent with these findings, multiple reanalysis datasets revealed that between 1979 and 2014, the number of strong cyclones (amplitude  -15 hPa) in the Northern Hemisphere in summer decreased at a rate of 4% per decade.174 Two reanalysis datasets for the periods 1871 to 2009 and 1901 to 2008 were used to examine trends in extreme cyclone events (minimum core pressure below 970 hPa).175 In contrast to the above findings, both datasets showed an increasing trend in these events, from the 1960s in the Northern Hemisphere and from the 1920s in the Southern Hemisphere. This is consistent with the statistically significant positive trend in stronger cyclones (central pressure 18 m/s) by 10 and 5%, respectively. For tropical cyclone strength storms (>33 m/s), extreme 3-hourly rainfall rates and extreme 3-day accumulated rainfall amounts increase by 11 and 8%, respectively. An alternative approach was used to attribute the extremely active 2015 tropical cyclone season in the western North Pacific Ocean. It included a particularly high frequency of Category four and five cyclones. Accumulated cyclone energy was used as an indicator of seasonal tropical cyclone activity. Based on a Fraction of Attributable Risk equalling 0.81, anthropogenic forcing substantially increased the likelihood of having a season at least as extreme as that in 2015.138 Other extreme events In recent years, a wide variety of other types of extreme atmospheric events have been the focus of attribution studies. Table 9.1 summarises the findings for a selection of events which occurred between 2015 and 2022. Many of the findings were reported in the annual Special Supplements to the Bulletin of the American Meteorological Society. The table provides a highly simplified binary categorisation of the findings. Important information, such as the size of the attributed signal, and confidence levels, can be found in the referenced publications. Most findings are consistent with those presented earlier in this chapter. The vast majority of studies report an attribution to anthropogenic forcing. However, this should not be considered indicative of the findings had the extreme events been randomly selected and reported. For example, events that become less extreme will be underrepresented in a set of extreme event attribution statements.166 Questions on the influence of

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Attribution findings for specific extreme events

TABLE 9.1

Attribution of anthropogenic forcing for changes in selected extreme events, 2015 to 2022.

Event

Forcing attributed

2018 European Winter Wind Storms139

No Yes e events less likely

140

Severe cold outbreaks in 2019 in the Eastern United States

Yes e event less likely

141

Cold 2017/18 winter in North America

Yes e event less likely

142,143

Record cold event in 2016 in eastern China

January 2021 cold air outbreak over eastern China

Yes e event less likely

April 2020 exceptional cold spell over Northeast China187

Yes e event less likely

Early growing period frost in central France in 2021144

Yes e event more likely

Severe frosts in western Australia in September 2016145

Yes e events less likely

January 2016 mid-Atlantic snowstorm146

No e high uncertainty

2014/15 snowpack drought in Washington state, United States147

Yes e event more likely

Extreme cold start to 2018 spring in the United Kingdom148

Yes e event less likely

30-day high rainfall in 2019 over Ontario and Quebec, Canada149

Yes e event more likely

Intense precipitation event, November 2021, British Columbia, Canada189

Yes e event more likely

188

Increased amount e yes; Rain days e No

150

Extended rainy 2018/19 Winter, Yangtze Valley, China

Yes e event less likely

2019 Extremely Wet Rainy Season in Southern China151 152

Extreme JanuaryeSeptember 2018 precipitation, mid-Atlantic United States Extremely wet March 2017 in Peru

Yes e event more likely Yes e event more likely

153 154

Heavy precipitation in AprileMay 2017 over the Uruguay River Basin 155

Yes e event more likely No

Record wet 2016 winter in southeast Australia

Yes e event more likely

175

Record-breaking winter precipitation over Beijing in February 2020 2020 JuneeJuly heavy Meiyu rainfall in the Yangtze River Basin

Yes e event less likely

Heavy rainfall associaed with tropical cyclones hitting Madagascar, Mozambique and Malawi191

Yes - events more likely and intense

Late onset of the 2015 wet season in Nigeria156

No

179,194,177,192

Yes e event more likely

180

Record Low North American Monsoon Rainfall in 2020

Yes e event more likely

181

2020 extreme dry-wet contrast over South China

Yes e event more likely

182

2020 summer successive hot-wet extremes in South Korea

183

Yes e event more likely

157

MayeJune 2019 severe low precipitation event in southwestern China

Yes e event more likely

Southern African 2015/16 flash drought

Yes e event more likely

Record-breaking Warm and Wet Winter 2019/20 in Northwest Russia

158

(Continued)

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354 TABLE 9.1

9. Atmospheric extremes: attribution of changes and events

Attribution of anthropogenic forcing for changes in selected extreme events, 2015 to 2022.dcont’d

Event

Forcing attributed 159

Record low sunshine JanuaryeFebruary 2019, Yangtze Valley, China

Yes e event more likely Yes e event more likely

160

Record low sunshine over Japan during August 2017

Yes e event more likely

161

Record sunshine of winter 2014/15 in the United Kingdom

Yes e event more likely

162

2017 earliest summer onset in South Korea

Yes e event more likely

163,164

Extreme 2015/16 El Niño

165

Persistent anticyclone over northwestern Europe in December 2016

Inconclusive e model dependent

anthropogenic forcing are posed most often when a positive connection is suspected.167 Thus overall, even though each event attribution study endeavours to give an unbiased estimate of the influence of anthropogenic forcing on the extreme event, a set of event attribution studies does not give an unbiased estimate of the influence on extreme events in general. Hence, while cataloguing extreme event analyses is useful, summarising results across event attribution studies is problematic.168 Compound extreme events A recently developed compound event attribution framework184 has been applied to two compound extreme events. The first considered the hot and dry conditions that prevailed in the Western Cape region of South Africa from 2015 to 2017 and again in 2019. Consistent with the precipitation-based drought attributions discussed above, the Fraction of Attributable Risk for precipitation ranged between 0.3 and 0.9, indicating anthropogenic forcing had a moderate influence on the dry conditions. For each of the four years, the Fraction of Attributable Risk was close to 1.0, with narrow uncertainty ranges, indicating that such forcing strongly contributed to the recent hot years in the region. The values for the Fraction of Attributable Risk based on both temperature and precipitation were usually in between those for temperature and precipitation, as were the uncertainty ranges. This supported the conclusion that anthropogenic forcing contributed at least 70% to the concurrent hot and dry conditions in 2015 and 2016, and at least 40% in 2017 and 2019. The second application of the new framework related to spatially compounding events when drought affected both Lesotho and South Africa in 2007 and in 1992. These events resulted in crop failures in both countries, as well as severe food insecurity in the former. Attribution was hampered by large variability across models and by the large uncertainty ranges. However, for two of the three models used, best estimates of the Fraction of Attributable Risk were above 0.5 for each country, as well as in combination. Significantly, values tended to be highest for the latter, leading to the conclusion that anthropogenic forcing contributed to the extreme droughts in 1992 and 2007 in both Lesotho and South Africa, and especially to their co-occurrence. The results for 2007 were generally consistent with an earlier study for 2007.185

II. Causes

Summary and conclusions

355

In a global analysis, a pattern-based detection and attribution approach using multivariate analysis44 identified the large-scale covariance relationships between observations, fingerprints and internal variability. These revealed the underlying causes of regional aridification. The first fingerprint explained 93.6% of the total spaceetime variance between temperature, precipitation and the Climate Moisture Index, an aridity indicator based on precipitation and atmospheric evaporative demand. It was characterised by global-scale warming and the intensification of global wetedry patterns. Both were largely driven by multi-decadal increases in greenhouse gas forcing. The second fingerprint captured marked interhemispheric temperature contrast-associated meridional shifts in the intertropical convergence zone. That fingerprint revealed non-linear changes between 1950 and 2014. These were related to the intertropical convergence zone moving southwards before 1975, in response to increases in hemispherically asymmetric sulphate aerosol emissions. It shifted northwards after 1975, due to reduced sulphur dioxide emissions and the greenhouse gaseinduced warming of Northern Hemisphere landmasses. A conditional attribution approach, with circulation fixed to the observations using flow analogues, was used to assess the contribution of atmospheric circulation and anthropogenic forcing to the record-breaking precipitation event in the middle and lower reaches of the Yangtze River, and the concurrent record-breaking hot event in South China between June and July 2020. Anthropogenic forcing was shown to have resulted in a fivefold increase the occurrence risk of events similar to the precipitation event, with the Fraction of Attributable Risk reaching 0.80. The Fraction of Attributable Risk for the hot event was 0.99. Thus, under similar atmospheric circulation conditions, the compound event was exacerbated by anthropogenic forcing, with the temperature extreme being the more strongly affected.169 In spring to early summer of 2019, Yunnan province in southwestern China was dominated by persistent hot and dry weather, especially during May. A probabilistic attribution using multi-model simulations, with and without anthropogenic forcings, showed that the likelihood of a temperature at least as high as that observed in Yunnan in 2019 increased by between 123% and 157% due to anthropogenic forcing. The likelihood of the extremely low precipitation increased by between 13% and 23%. Anthropogenic forcing resulted in the likelihood of the compound hot and dry extreme event increasing by 43%.170 The above findings are consistent with the bivariate-based Fraction of Attributable Risk being similar in magnitude, or smaller, than that for the equivalent univariate value so long as the trend in the second variable is comparatively small and the dependence between the two variables is moderate or high. This is a typical situation for temporally co-occurring hot and dry extremes. On the other hand, if both variables have large trends, or the dependence between them is weak, the bivariate-based Fraction of Attributable Risk is usually larger, and likely to provide a more adequate quantification of the anthropogenic influence.184

Summary and conclusions Both a 2018 review167 and a more recent assessment by the Intergovernmental Panel on Climate Change2 have highlighted the rapid growth in evidence of increasing human influence on both the trends in extremes and the changes in the frequency and intensity of extreme events. This is particularly the case for temperature and precipitation extremes, droughts and

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356

9. Atmospheric extremes: attribution of changes and events

tropical cyclones, as well as for compound extremes such as dry/hot events and fire weather. The growth in robust evidence reflects not only the recent methodological advances described in Chapter 8, but also the growing realisation of the importance of attribution findings to developing policies and plans for managing the impacts of extremes in the coming years and decades.186,171 Despite the ongoing discussions about the evolution of attribution science, the use of diverse approaches and the limitations of both observations and models, the majority of the attribution studies discussed above reach a consistent conclusion e most of the significant long-term changes in the observational record of extreme weather and climate occurrences can be attributed to anthropogenic forcing, at least to some extent. The same applies to significant changes in the frequency and intensity of extreme events. The findings of a recent study172 are therefore hardly surprising. It involved an analysis of a large randomised sample of 88,125 climate-related papers published between 2012 and 2020. The resulting broadly defined scientific consensus, far exceeding 99%, was that anthropogenic greenhouse gas emissions have played a role in recent changes in the world’s climate. An earlier study of the literature between 1991 and 2012 reported a 97% consensus. Despite the impressive progress in attribution studies, over just a few decades, their geographical coverage continues to be very patchy. Many of the relatively neglected areas are highly vulnerable to weather and climate extremes. Also, the types of extremes which have been assessed is insufficiently diverse. There have been calls, so far unanswered, for a set of objective and pre-determined extreme event selection and definition criteria. These would not only help minimise selection bias, but also contribute to methodological improvements.

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Marine extremes: attribution of changes and events .. major progress in probabilistic event attribution research over the last few years allow us to tackle the question whether and to what extent external climate drivers such as human-induced climate change alter the likelihood of ocean extreme events. (Frölicher and Laufkötter, 2018).1

Introduction Chapter 7 discussed the drivers of marine extremes such as marine heatwaves and extreme wind-wave events, open ocean swells and sea levels. The extensive literature which underpinned the discussion shows that the above quotation is indeed generally valid. But that is not the case for formal attribution of temporal changes in the frequency or magnitude of marine extremes or of extreme ocean events. This chapter will show that there are relatively few such studies. The need for more of these analyses goes well beyond fulfilling scientific curiosity. Attribution studies play an important role in informing the development of ocean and coastal policies and plans.2 They can show how anthropogenic forcing influences ocean extremes, which in turn impact on marine species and ecosystems, with subsequent ecological, economic and social consequences.3 Improving our understanding of these causal linkages can greatly enhance the robustness of policy-relevant findings on the benefits of mitigation efforts designed to reduce the magnitude and increasing rate of climate change impacts.4 This includes being able to specify the relationship between greenhouse gas emissions reduction scenarios and decreases in the proportion of the global ocean with marine ecosystems exposed to stresses induced by anthropogenic forcing. Any reductions also allow additional time for both autonomous and planned adaptation.5 This chapter first presents the findings of the very small number of formal attributions of temporal changes in marine extremes. It then goes on to consider the slightly more numerous attributions of extreme oceanic events. Tellingly, all of these relate to marine heatwaves.

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Attribution findings for past and projected changes The Northeast Pacific is characterised by a long-term warming pool e the sea surface temperature increased by around 2 C between 1996 and 2020 e and by the frequent and increasing occurrence of marine heatwaves. The concurrent increase in sea level pressure and other long-term changes in the large-scale atmospheric patterns in the warming pool region have been larger than expected from internal variability alone. The patterns suppress the transfer of heat from the ocean to the atmosphere due to a decline in cold air advection over the region. This has resulted in a reversal from cooling, to a significant warming over the late 20th and early 21st centuries. The changes have been attributed primarily to increased greenhouse gas concentrations, with anthropogenic aerosols playing a secondary role. As a consequence of the increased heating, up to 60% of the marine heatwave events which occurred between 2010 and 2020 were more intense and longer lasting than could be solely attributed to climate variability. Rather, greenhouse gas forcing was found to be a necessary, though not sufficient causation for the more intense and persistent marine heatwave events in the current climate. In the coming decades, this forcing is likely to become a sufficient cause for marine heatwave events with magnitudes and durations at least as large as those experienced in the early decades of the 21st century.6 A recent study7 of the temporal variations in the global wave climate, driven by changes in atmospheric circulation patterns, did not investigate extreme wave conditions explicitly. Nevertheless, the findings can still inform coastal hazard and planning strategies since long-term shifts in the overall wave climate also imply changes in wave extremes. The study investigated the roles of both natural variability and anthropogenic forcing in the net, longterm variations and trends of each wave climate type between 1985 and 2018. This involved analysing the variability and trends in wave climate types driven by atmospheric circulation patterns which generated waves with similar directions and power. An anthropogenic forcing signal was detected for the wave climate types in the Indian Ocean, as well as in the tropical wave climate types of the Atlantic and Pacific Oceans. In contrast, the monsoon, extra-tropical, sub-tropical and polar wave climate types of the Pacific and North Atlantic Oceans were dominated by natural variability. These findings are consistent with those of a study8 which concluded that the present wave climate in the North Atlantic, the equatorial Pacific and the Southern Oceans is already affected by anthropogenic forcing, for both significant wave and swell heights. Importantly, ongoing anthropogenic forcing acts not only to increase significant wave and swell heights, but to also significantly decrease them regionally, as in parts of the North Atlantic and South Pacific. The likely influence of changes in Arctic sea ice extent on the occurrence of weather and climate extremes has been highlighted previously (Chapter 7, Low Temperature Extremes, including Atmospheric and Marine Coldwaves). A detection and attribution analysis9 showed that the observed trends in the anomalies of annual and September Arctic sea ice extent were consistent with multi-model, large-ensemble simulations that included anthropogenic forcings, but were highly unlikely to have occurred under the combined influence of natural forcings and internal variability alone. Given the downward trend in Arctic sea ice extent, and that the record-setting low sea ice cover in 2007 and 2012 was extremely unlikely to occur under natural forcings alone, the attribution study concluded that future September

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minimum events more extreme than that in 2012 will be attributable to anthropogenic forcing, with high certainty.

Extreme event attribution findings Attribution of extreme ocean events is dominated by studies of marine heatwaves. In this regard, there are two informative overviews.1,10 Each highlighted findings that are consistent with 87% of marine heatwaves being attributable to anthropogenic forcing in the current climate.11 Furthermore, the simulated Fraction of Attributable Risk has been shown to approach unity (0.94e0.97) at 2 C of global warming (Fig. 10.1). A more detailed understanding of the consequences of anthropogenic forcing comes from a recent comprehensive assessment which calculated the occurrence probabilities of marine heatwaves, as opposed to the probabilities of extreme seasonal mean sea surface temperatures. This made it possible to attribute the duration, intensity and cumulative intensity of each heatwave. Out of over 30,000 distinct, spatio-temporally contiguous marine heatwaves that occurred globally between 1981 and 2017, the study12 focussed on seven marine heatwaves that covered at least one million km2 of ocean and had a major documented impact in the region in which they occurred. The occurrence probabilities of their duration, intensity and cumulative intensity were found to have increased more than 20-fold as a result of anthropogenic forcing. The 2015/16 marine heatwave in the Tasman Sea was the longest and most intense event on record for that region. An event attribution analysis using seven coupled global climate

FIGURE 10.1 Simulated changes in the Fraction of Attributable Risk for different levels of global warming for marine heatwaves exceeding the 99th preindustrial percentile. The simulated changes in Fraction of Attributable Risk are plotted against simulated global mean atmospheric surface temperature changes since 1861e80. The thinner lines represent individual model projections, while the thicker lines represent multi-model averages for the representative concentration pathways (RCPs) of 8.5 and 2.6. The time series are smoothed with a 20-year running mean, and the year labels represent the central year of two decades. Reprinted by permission from Springer Nature Customer Service Centre GmbH: Springer Nature, Copyright 2018. Frölicher TL, Fischer EM, Gruber N. Marine heatwaves under global warming. Nature. 2018;560(7718):360e364. https://doi.org/10.1038/s41586-018-0383-9.

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models found that anthropogenic forcing resulted in the duration and intensity of such an event being at least 330 times and 6.8 times as likely, respectively.13 The 2016 marine heat waves which occurred to the north of Australia and in the Bering Sea and Gulf of Alaska extended over broad areas of the ocean. The former event was the most intense and the second longest on record for that region. It was virtually certain to be at least 8.5 times as likely in 2006e2020 as a result of anthropogenic forcing, with its duration virtually certain to be at least 53 times more likely. The event in the Bering Sea and Gulf of Alaska was virtually certain to be at least 7.3 times more likely, with its duration virtually certain to be at least 7.4 times more likely. Both anthropogenic forcing and internal variability likely contributed to the occurrence of these two marine heatwaves. But given that anthropogenic forcing reduced their return periods by a factor of up to 200, it was extremely unlikely that natural variability alone contributed to the two events.14 A study which assessed the contribution of anthropogenic forcing to the 2015 recordbreaking high sea surface temperatures observed in the central equatorial Pacific and tropical Indian Ocean also concluded that the excessive warming in both regions was well beyond the range of natural variability. Simulated annual values of the Fraction of Attributable Risk reached at least 0.86, indicating robust attribution to the increase in the concentration of atmospheric greenhouse gases.15

Conclusions Given the ecological and wider consequences of ocean extremes, the unequivocal findings of the few attribution studies that have been undertaken to date highlight the urgent need to increase the attribution effort. This is especially the case for attribution of extreme ocean events, where studies have been limited to marine heatwaves. Other extreme marine events, including those related to winds, ocean waves, swells and sea level, either in isolation or combination, can generate equally significant impacts, albeit more often at a local scale. Regardless, the impacts of these extreme events need to be managed in a proactive manner. This requires a clear understanding of whether and how these hazards will change in the future, including as a result of ongoing emissions of greenhouse gases. The preceding chapters have shown that the science of attribution is sufficiently mature to provide credible attribution findings for all marine extremes. This includes the analysis of observed data which is fit for purpose and the production of robust model-based simulations for both the factual and counterfactual worlds. Use of the findings to inform ocean and coastal policies will greatly reduce risks and enhance ecosystem productivity.

References 1. Frölicher TL, Laufkötter C. Emerging risks from marine heat waves. Nat Commun. 2018;9(1):650. https:// doi.org/10.1038/s41467-018-03163-6. 2. Webb RS, Werner FE. Explaining extreme ocean conditions impacting living marine resources. Bull Am Meteorol Soc. 2018;99(1):S7eS10. https://doi.org/10.1175/BAMS-D-17-0265.1. 3. Poloczanska ES, Burrows MT, Brown CJ, et al. Responses of marine organisms to climate change across oceans. Front Mar Sci. 2016;3(MAY):1e21. https://doi.org/10.3389/fmars.2016.00062. 4. Guo X, Gao Y, Zhang S, et al. Threat by marine heatwaves to adaptive large marine ecosystems in an eddyresolving model. Nat Clim Change. 2022;12(2):179e186. https://doi.org/10.1038/s41558-021-01266-5.

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5. Henson SA, Beaulieu C, Ilyina T, et al. Rapid emergence of climate change in environmental drivers of marine ecosystems. Nat Commun. 2017;8(1):14682. https://doi.org/10.1038/ncomms14682. 6. Barkhordarian A, Nielsen DM, Baehr J, Barkhordarian A, Nielsen DM, Baehr J. Greenhouse gas forcing a necessary causation for marine heatwaves over the Northeast Pacific warming pool. Res Sq. 2022. https://doi.org/ 10.21203/rs.3.rs-1068304/v1. Published online. 7. Odériz I, Silva R, Mortlock TR, et al. Natural variability and warming signals in global ocean wave climates. Geophys Res Lett. 2021;48(11):1e12. https://doi.org/10.1029/2021GL093622. 8. Dobrynin M, Murawski J, Baehr J, Ilyina T. Detection and attribution of climate change signal in ocean wind waves. J Clim. 2015;28(4):1578e1591. https://doi.org/10.1175/JCLI-D-13-00664.1. 9. Kirchmeier-Young MC, Zwiers FW, Gillett NP. Attribution of extreme events in Arctic sea ice extent. J Clim. 2017;30(2):553e571. https://doi.org/10.1175/JCLI-D-16-0412.1. 10. Wernberg T, Smale DA, Frölicher TL, Smith AJP. Climate change increases marine heatwaves harming marine ecosystems. In: Liss P, Le Quéré C, Forster P, eds. Critical Issues in Climate Change Science. 2021:4. https:// doi.org/10.5281/zenodo.5596820. 11. Frölicher TL, Fischer EM, Gruber N. Marine heatwaves under global warming. Nature. 2018;560(7718):360e364. https://doi.org/10.1038/s41586-018-0383-9. 12. Laufkötter C, Zscheischler J, Frölicher TL. High-impact marine heatwaves attributable to human-induced global warming. Science. 2020;369(6511):1621e1625. https://doi.org/10.1126/science.aba0690. 13. Oliver ECJ, Benthuysen JA, Bindoff NL, et al. The unprecedented 2015/16 Tasman Sea marine heatwave. Nat Commun. 2017;8(1):16101. https://doi.org/10.1038/ncomms16101. 14. Oliver ECJ, Perkins-Kirkpatrick SE, Holbrook NJ, Bindoff NL. Anthropogenic and natural influences on record 2016 marine heat waves. Bull Am Meteorol Soc. 2018;99(1):S44eS48. https://doi.org/10.1175/BAMS-D-17-0093.1. 15. Park I-H, Min S-K, Yeh S-W, Weller E, Kim ST. Attribution of the 2015 record high sea surface temperatures over the central equatorial Pacific and tropical Indian Ocean. Environ Res Lett. 2017;12(4):044024. https://doi.org/ 10.1088/1748-9326/aa678f.

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C H A P T E R

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Hindsights, insights and foresights In the area of climate change, the long-term nature of the projected changes and impacts, and the transformative character of solutions gives foresight a prominent role in policy development. (Leitner et al., 2019).1

Introduction The preceding chapters covered the science of weather, climate and ocean extremes under the two key themes of changes and causes. The first considered past and future changes in the extremes. Where the evidence allowed, changes over the last two millennia were considered, as well as projections for the remainder of the 21st century, and well beyond in some cases. Methodological and related developments were also reviewed under the theme of change. In recent decades, there have been major advances in both characterising past changes in extremes, as well as in projecting their future evolution. The causes of these changes in extremes, and especially those that are apparent in the instrumental record, were examined by considering their proximate and broader drivers. The influence of the initial state, as well as the roles of natural variability and feedbacks, were also examined. This laid the foundation for a more detailed analysis of the influence of anthropogenic forcing on past and future changes in weather, climate and ocean extremes. The analysis involved the application of various attribution frameworks, approaches and methods, once again benefitting from the major recent advances in attribution science. As before, there was a twofold focus, the first being on attribution of the temporal changes in the extremes, as detected in observations, model-based simulations and reanalysis products. The second focus was on the attribution of a specific extreme event, or class of comparable events. This present chapter reflects on the learning related to these changes and causes, by applying a hindsighteinsighteforesight framework to the science of weather, climate and ocean extremes (Fig. 11.1).

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Here, the framework is not used in a formal technical sense, as it might be in the case of foresighting, for example.2,3 Rather, it is applied in order to structure, summarise and extend the information presented in Chapters 2e10.

Hindsights e reflecting on the evidence of change A key question highlighted in Fig. 11.1 e how have weather, climate and ocean extremes changed in the past, and how might these extremes change in the future? e has been answered in detail in Chapters 3e6. These document the abundant evidence which shows that systematic temporal increases in the frequency and intensity of most of these extremes have occurred, relative to pre-industrial times. The exceptions are noteworthy, and mostly expected, as in the case of cold extremes. Numerous studies also reveal that the rates of change have often accelerated in the more recent decades, though not for all locations or extremes. Several locations have recently experienced extreme events which are not replicated in the post-industrial records, some of which span at least two centuries.

FIGURE 11.1 Hindsights, insights and foresights related to the science of weather, climate and ocean extremes.

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Insights e identifying and attributing the drivers of changes in extremes

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All of the atmospheric and oceanic extremes examined in Chapters 5 and 6 are projected to undergo changes in their frequency and intensity, especially for medium and high emissions scenarios. The durations of some extremes, such as atmospheric and marine heatwaves, are also anticipated to increase. The projected temporal trends for most extremes are consistent with those detected in post-industrial records, but with the rate of change sometimes accelerating further, at least through to the end of the 21st century. Studies which project atmospheric extremes heavily outnumber those which investigate how marine extremes will change in the future. Given that the oceans cover 71% of the Earth’s surface, and provide about 50% of global primary production, this large imbalance is in urgent need of rectification.

Insights e identifying and attributing the drivers of changes in extremes The preceding findings lead to a second key question e what drives the past and projected changes and, specifically, what role does anthropogenic forcing play? It is even more difficult to provide robust answers to this question, as the challenge is to separate the roles of internal variability as well as the many external forcings. The former is natural, unforced and chaotic, while the latter can have either natural or anthropogenic origins. Detailed answers to the question are provided in Chapters 7e10. These have benefitted from the recent progress in attribution science. This involves determining whether, and by how much, a given forcing may be responsible for specific extreme events or for a change in the frequency and other characteristics of the extreme over time. While internal variability can play a significant role in the occurrence of a specific extreme event, external forcings are the main drivers of both past and future systematic changes in atmospheric and marine extremes, at least at global and continental scales. Enhanced radiative forcing, largely due to changes in the atmospheric concentrations of greenhouse gases and reflective aerosols, causes surface temperatures to increase. This is a response by the atmosphereeocean system, as it attempts to restore a radiative balance. The resulting global warming not only increases the water-holding capacity of the atmosphere, but also alters atmospheric stability and meridional temperature gradients, affecting climate and ocean dynamics. The consequential changes include those related to weather, climate and ocean extremes. The changes in extremes that are driven by global-scale thermodynamic processes, and the longer-term warming of the atmosphere and ocean and associated increases in atmospheric water vapour content, are relatively well understood. On the other hand, the changes driven by dynamic processes are far less understood. In addition, changes in extremes at regional and local scales are strongly influenced by regional feedback mechanisms, as well as by forcings such as changes in regional land cover and land use, and in anthropogenic aerosols. The complex interplays between these forcings and feedbacks, and the associated uncertainties, are the reasons why identification and attribution of drivers is so challenging. The relative importance of the changes caused by anthropogenic forcing and natural variability varies between the types of extremes. So too does the time of emergence. This is when

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the influence of external forcing on the probability or intensity of an extreme emerges from the noise of year-to-year variability. For example, for most regions globally, the annual maximum daily maximum temperature signal emerges at less than 0.5 C of global warming. Emergence of maximum temperature extremes was also found to be widespread and early, with 96% to 99% of the globe emerging by 1 C of warming. Changes in minimum temperature extremes generally emerge at lower levels of global warming. Globally for annual maximum one-day precipitation, emergence occurs after at least 0.6 C of warming, with warming exceeding 2 C being needed in some regions. There has thus been a rapid growth in the evidence of increasing human influence on both the trends in extremes, and the changes in the frequency and intensity of individual extreme events. This is particularly the case for temperature and precipitation extremes, droughts, wildfires and tropical cyclones, as well as for compound extremes such as dry/hot events. Unsurprisingly, therefore, the majority of the attribution studies undertaken to date reach a consistent conclusion - most of the significant long-term changes in the observational record of extreme weather, climate and ocean events can be attributed to anthropogenic forcing, at least to some extent. The same applies to significant temporal changes in the frequency and intensity of extreme events. But the geographical coverage of attribution studies is very patchy. The same is the case for the types of extremes which have been assessed. For most of these extremes, the observed changes in frequency and intensity generally scale with the increase in greenhouse gas concentrations, and hence with global mean temperature. So too do the projected changes through to the end of the 21st century. However, the relationships are often non-linear, and are not always positive. The latter is especially the case for cold and snowfall extremes, and also for the frequency of tropical cyclones.

Foresights e the implications for policies and actions Collectively, the preceding evidence-based hindsights and insights reveal that most weather, climate and ocean extremes are increasing in terms of their frequency, intensity and other relevant metrics. Moreover, to varying degrees, these changes can be attributed to human activities, and especially those which result in the emission of greenhouse gases. These changes also have consequences, such as droughts, floods and disruptions to marine ecosystems. When, and preferably before, these consequences become intolerable, interventions will be required. This is especially the case if the consequences are to be kept within acceptable limits. These actions are generally described as mitigation (i.e. emissions reduction), adaptation and disaster risk reduction.4 It is a significant challenge to decide when a specific response is required, as well as the nature and intensity of the effort. This is largely because the answers can be highly location-specific. The evidence generally required to support such decisions typically comprises information on the hazard level and the consequential impacts. This can be illustrated at global scale (Fig. 11.2). The figure presents a global-level assessment of risk thresholds for extreme events and aggregated impacts, as a function of global mean surface temperature increase relative to pre-industrial levels. The most recent assessments of the risk thresholds are shown in the right of each diagram. For the aggregated

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FIGURE 11.2

Comparison of risk thresholds across four assessments undertaken by the Intergovernmental Panel on Climate Change. The two left-most diagrams link the global mean surface temperature increase to estimates of risk associated with: (left) extreme weather, climate and ocean events; and (centre) aggregate impacts. For the left- to right-hand columns, the levels of risk are as assessed in the Third, Fourth and Fifth Assessment Reports and in the Special Report on Global Warming of 1.5 Degrees. Grey areas at the top of each column correspond to temperatures above the assessed range in the corresponding report. Dashed lines connect the midpoints between undetectable and moderate risk, and between moderate and high risk. Reprinted by permission from Springer Nature Customer Service Centre GmbH: Springer Nature, copyright 2020. Adapted from: Zommers Z, Marbaix P, Fischlin A, et al. Burning embers: towards more transparent and robust climate-change risk assessments. Nat Rev Earth Environ 2020;1(10):516e529. https://doi.org/10.1038/s43017-020-0088-0.

impacts, the risks transitions have shifted towards lower temperatures, likely reflecting improvements in the science, including detection and attribution, as well as the increasing scope of the evidence base.5 On the other hand, for extreme events, a given risk level is associated with somewhat higher rates of global warming in the later assessments. Multiple factors may have contributed to this change, including refinement of the assessment framework, with clearer criteria for judging risk and more precision in assigning the temperature levels associated with risks. For example, the third of the four assessments refined the definition for the transition between undetectable and moderate risks. This involved adding the requirement that impacts had to be detectable and attributable to anthropogenic forcing, with at least medium confidence. Of course, other critical requirements are to establish the level of risk that triggers action, either proactively or retroactively,6 and identify acceptable levels of residual risk.7

Is this the end of the story? As mentioned in Chapter 1, this book tells a story which not only describes the major advances in our understanding of the science of weather, climate and ocean extremes, but also encourages further efforts to increase our knowledge of these hazards and their associated risks. Importantly, application of the hindsighteinsighteforesight framework has

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highlighted the growing number of significant opportunities to apply the science of weather, climate and ocean extremes. These include not only the increasing ability to clarify the consequences of the current and anticipated changes in these extremes but also to identify and apply the responses which can reduce the unacceptable risks, as well as exploit the relatively few benefits of such changes. Thus, the story is continued in a sequel to this current book e Managing the Consequences of Weather, Climate and Ocean Extremes in Our Warming World.4

References 1. Leitner M, Bentz J, Lourenço TC, et al. Foresight Promotion Report for Policy & Decision-Makers; 2019. https://www. placard-network.eu/wp-content/uploads/Foresight-report-2019.pdf. 2. Wiebe K, Zurek M, Lord S, et al. Scenario development and foresight analysis: exploring options to inform choices. Annu Rev Environ Resour. 2018;43(1):545e570. https://doi.org/10.1146/annurev-environ-102017-030109. 3. Government Office for Science [Government of the United Kingdom of Great Britain and Northern Ireland]. A Brief Guide to Futures Thinking and Foresight; 2021. https://assets.publishing.service.gov.uk/government/uploads/system/ uploads/attachment_data/file/964195/A_brief_guide_to_futures_thinking_and_foresight.pdf. 4. Hay JE. Managing the Consequences of Weather, Climate and Ocean Extremes in Our Warming World. United Kingdom: Elsevier and the Royal Meteorological Society; 2023. 5. Zommers Z, Marbaix P, Fischlin A, et al. Burning embers: towards more transparent and robust climate-change risk assessments. Nat Rev Earth Environ. 2020;1(10):516e529. https://doi.org/10.1038/s43017-020-0088-0. 6. Brown K, DiMauro M, Johns D, et al. Turning risk assessment and adaptation policy priorities into meaningful interventions and governance processes. Philos Trans R Soc A Math Phys Eng Sci. 2018;376(2121):20170303. https://doi.org/10.1098/rsta.2017.0303. 7. Adger WN, Brown I, Surminski S. Advances in risk assessment for climate change adaptation policy. Philos Trans R Soc A Math Phys Eng Sci. 2018;376(2121):20180106. https://doi.org/10.1098/rsta.2018.0106.

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Index Note: ‘Page numbers followed by “t” indicate tables, “f” indicate figures and “b” indicate boxes.’ A Absorbing aerosols, 216 Accumulated Winter Season Severity Index, 222 Actuaries Climate Index, 30 Adaptation, 376 Additional correction, 304 Advective heat waves and warm spells, 203 Aerosols, 216, 228, 237 American Meteorological Society, 270 Angular momentum radial coordinate system, 57 Anthropogenic aerosols, 368, 375 Anthropogenic forcing, 201, 328, 332, 368 Arctic amplification, 210e211 Atlantic Meridional Overturning Circulation, 227e228 Atlantic Multi-decadal Oscillation, 104e105, 223 Atlantic tropical cyclone season (2020), 102b Atmosphereeocean general circulation models, 61 Atmosphereeocean system, 127, 197, 375 Atmospheric aerosols, 216 Atmospheric blocks, 248e249 Atmospheric cold waves, 209e213 Atmospheric extremes, 18, 81, 327, 375. See also Marine extremes attribution findings for past and projected changes in extremes, 328e336 specific extreme events, 336e355 changes in atmospheric extremes in instrumental era, 86e115 future changes in, 145e172 cold waves, 149e152 compound extremes, 169e172 daily and short-term temperature extremes, 146e148 drought, 155e157 extreme storms and convection, 157e169 heatwaves, 148e149 heavy precipitation, 152e155 in pre-instrumental era, 81e86 Atmospheric heatwaves, futures of, 150b Atmospheric models, 52

Atmospheric rivers, 84e86, 106e107, 108b, 161e163, 334, 348 drivers of, 219e221 Atmospheric simulations, 200e201 Atmospheric warming on snowfall, 95e96 Attributable risk, fraction of, 369 Attribution, 373 of heatwaves, 338b methods, 269 evaluating progress in extreme event attribution, 315e317 extreme event attribution methods, 285e315 innovations in, 283b of long-term observed and projected changes, 273e285 science, 270, 270f, 327 studies, 270, 272e273 Attribution findings for past and projected changes in extremes, 328e336 attribution findings for temporal changes in specific extremes, 329e336 overview, 328e329 for specific extreme events, 336e355

B BarentseKara Sea region, 212e213 Bayesian approaches, 277, 282e285 Bayesian inference, 277 Biases, 66 Biogeochemistry, 181 Black carbon, 216 Blending, 42 Block maximum approach, 49 Blocking anticyclones, 206e207 Boulder approach, 294b

C Causal counterfactual theory, 283b Central England Temperature, 87 Change detection, 46e51 data preparation, 47e48

379

380 Change detection (Continued ) methods, 48e51 analysis of extremes, 48e50 trend detection, 50e51 CHIRPS dataset, 42 CHIRTSmax, 42 ClausiuseClapeyron relation, 213e214 ClausiuseClapeyron scaling, 91, 165, 221 Climate, 374 modelling uncertainty, 282 models, 145e146 simulations, 19, 273 projections, 58 Climate Extremes Index, 30 Cold extremes, 332 Cold spells, 212e213 Cold waves, 90e91, 149e152 Colorado extreme precipitation event, 342b Common Era (CE), 20 Compound extremes, 3e4, 30, 112e115, 139e140, 169e172, 188e189, 248e253, 336 events, 354e355 Conditional attribution approach, 355 Conditioning, 287, 293 Confidence, 7, 10, 18e19, 36, 46, 65, 67, 81e82, 86, 88, 133, 159, 184, 269, 272e277, 282, 288, 300, 309f, 310, 330, 335e336, 347, 377 Consequences, 376 Convection-permitting model, 153e154 Convective inhibition, 234e236 Convective storms severe, 109e112, 234e240 mesoscale convective systems, 234e236 severe hailstorms, 236e238 tornadoes, 238e240 and severe turbulence, 165e167 Coupled Model Intercomparison Project, 28, 37, 53, 56, 58e59, 145e146 Coupled model simulations, 232 Coupling effects, 250e251 Cryosphere-dominated system, 189 Cumulative cyclone presence, 232e233 Cyclones, 227 cyclone-induced extreme, 185 cyclone-related precipitation, 232e233

D Detection, 48 Diaries, 20 DINAS-COAST, 32 Disaster risk reduction, 376 Discriminant analysis, 285 Drivers of past and future changes in weather, climate and ocean extremes, 195, 198e253, 373 compound extremes, 248e253 drivers of atmospheric rivers, 219e221

Index

droughts, 222e227 extreme sea levels, 244e248 extreme snowstorms, 222 extreme storms, 227e240 extreme wind speeds, 240e242 extreme wind wave events and open ocean swells, 242e244 high-temperature extremes, 198e209 low-temperature extremes, 209e213 precipitation extremes, 213e219 soil moistureeatmosphere feedbacks, 200f Droughts, 21, 96e99, 155e157, 222e227, 334e335, 348e350 Dynamical models, 55 Dynamics-based approach, 37

E Earth system models, 52, 61, 161, 181, 189 Earth’s energy imbalance, 1 Ecclesiastical documents, 20 Ecosystems, 367 El NiñoeSouthern Oscillation, 195e196, 204e205, 207e209, 220, 223, 230, 235, 237, 239, 275 Emergence time of, 148, 173, 182, 255, 375e376 from natural variability, 148, 154e155, 157, 182e183, 183f, 189, 204, 207, 254 Emissions reduction, 376 Ensemble approach, 279 Eocene, 160 ERA5, 36 European heat wave (2003), 204 EUSTACE, 28b Event attribution, 269 Event detection methods, 51 Evidence-based interventions, 181 Explosive cyclones, 109 External forcing, 195e196 Extra-tropical cyclones, severe, 107e109, 163e165, 232e234 Extreme event attribution methods, 285e315, 294b attribution question and methodology, 293e300 attribution synthesis, 310 attribution trigger, 288e290 communicating findings, 312e315 evaluating progress in, 315e317 event, 290e293 contextualise, 300e301 observational records and climate modelling system, 301e305 observations-and/or model-based attribution analysis, 306e310 Extreme storms, 99e112, 227e240, 335e336 and convection, 157e169 atmospheric rivers, 161e163 convective storms and severe turbulence, 165e167

Index

extreme wind gusts, 168e169 severe extra-tropical cyclones, 163e165 tropical cyclones, 158e161 severe convective storms, 234e240 severe extratropical cyclones, 232e234 tropical cyclones, 227e232 Extreme Value Theory, 49e51 Extremes, 17 change and extreme event detection, 46e51 detecting past changes in, 18e46 instrumental era data, 21e46 pre-instrumental era data, 20e21 events, 352e354 evidence, 374e375 framework for multiple sources of information and methods, 18f future of extreme snowfall events, 156b hindsighteinsighteforesight framework, 374e377 hot events, 337e340 identifying and attributing drivers of changes in extremes, 375e376 implications for policies and actions, 376e377 precipitation, 332e333 events, 341e355 projecting future changes in, 52e64 projecting marine extremes, 61e64 sea levels, 135e139, 186e188, 244e248 snowstorms, 222 temperatures, 128e132 and precipitation indices, 25te26t terminology, 27b uncertainties, 65e68 wave heights, 133e135 weather, climate and oceanic events, 2e4 wind waves events, 242e244 and open ocean swells, 184e186 wind gusts, 168e169 speeds, 112, 132e133, 184, 240e242

F Farming, 20 Feedback processes, 215e216 Fingerprint, 279 fingerprint-based approaches, 280e282 Fire-induced thunderstorms, 236 Flash droughts, 98b, 335 Flood events, 83 Flowering dates, 20 Framing, 287, 293 Fréchet distribution, 49

381

Frequentist approaches, 277, 279e280 Fronts, 227

G Generalized Extreme Value distribution, 49e50 Generalized Pareto distribution, 49 Geostatistical approaches, 40 GESLA-2 dataset, 32 Global climate models, 186 historical simulations using, 37e39 Global gridded land-based datasets, 28, 28b Global Land Data Assimilation System, 36 Global Ocean, 127e128 Global Precipitation Climatology Centre’s Full Data Product, 30 Global warming, 196e197, 213e214, 375 hiatus, 198 or slowdown, 86 Granger causality, 283b Greenhouse gas, 181, 228, 367, 376 concentrations, 182 emissions, 1e2 forcing, 198, 209 Gridded precipitation datasets, 30 Gridding, 39e41 Gulf of Alaska, 370 Gumbel distribution, 49

H HadEX, 28b HadEX3, 37e38 HadGHCND, 43 Hailstorms, severe, 236e238 Heatwaves, 30, 89e90, 148e149, 198e209 Heavy precipitation, 55, 91e96, 152e155 High Resolution Model Intercomparison Project, 57 High-resolution global climate model simulations, 216e217 modelling, 167 and observations, 215 High-temperature extremes, 198e209 drivers of heatwaves over land, 201e204 drivers of marine heatwaves, 204e209 Hindcast attribution, 351 Hot extremes, 330e332 Hurricane Harvey, 231, 351 Hurricane Michael landfall, 252

I ICOADS Release 3.0, 32 In situ land surface data, 21e30 ocean data, 31e32

382 Indirect ‘proxy’ measures, 19 Informative metric of change, 148 Ingredient-based approach, 294b Instrument simulator, 67e68 Instrumental era changes in atmospheric extremes in, 86e115 cold waves, 90e91 compound extremes, 112e115 daily and other short-term temperature extremes, 86e89 drought, 96e99 extreme storms, 99e112 heatwaves, 89e90 heavy precipitation, 91e96 data, 21e46 blending, 42 gridding, 39e41 historical simulations using global climate models, 37e39 reanalysis products, 35e37 relative merits of instrumental era datasets, 42e46 remotely observed data, 32e35 in situ land surface data, 21e30 in situ ocean data, 31e32 studies, 44b marine extremes in, 128e140 extreme sea levels, 135e139 extreme temperatures, 128e132 extreme wave heights and open ocean swells, 133e135 extreme wind speeds, 132e133 Interdecadal Pacific Oscillation, 207e208, 229e230 Intergovernmental Panel on Climate Change (IPCC), 2e3, 9 Internal climate variability, 224, 270 Internal variability, 375 Inverse distance weighting, 40e41

J Joint Expert Team, 24e27

L L-moments or probability weighted moment method, 49e50 La Niña, 231, 237 Lake heatwaves, 149 Landeatmospheric feedbacks, 249 Landfalling droughts, 225 drivers of, 225b Last Glacial Maximum, 84e86 Leeuwin Current, 213 Local processes, 204e205 Logbooks, 20

Index

Long-term observed and projected changes, methods for attribution of, 273e285 attribution using combination of observations and climate modelling, 276e285 attribution using observations, 274e276 Loop Current, 237 Low-frequency component analysis, 275 Low-temperature extremes, 209e213

M MaddeneJulian Oscillation event, 207e208, 220 Marine cold spells, 131e132 Marine cold waves, 209e213, 214b Marine extremes, 182, 375. See also Oceans, extremes attribution findings for past and projected changes, 368e369 compound extremes, 188e189 extreme event attribution findings, 369e370 simulated changes in fraction of attributable risk, 369f extreme sea levels, 186e188 extreme temperatures, including marine heatwaves, 182e184 annual time series, 183f extreme wind speeds, 184 extreme wind waves and open ocean swells, 184e186 future changes in, 182e189 in instrumental era, 128e140 in pre-instrumental era, 127e128 Marine heatwaves, 129b drivers of, 204e209 Marine surprises, 128e131 Maximum likelihood method, 49e50 Mean sea-level offset approach, 64 Mega-droughts, 82 100-member Max Planck Institute Grand Ensemble, 147, 198e199 Merging. See Blending Mesoscale convective systems, 109e110, 165e166, 234e236 Meteorological droughts in South Africa, 224 Mistral, 241e242 Mitigation, 376 Model resolution, 54e58 Moderate extremes, 27b Moving window regression, 40e41 Multi-model, 146, 213 approach, 185e186 multimodel-based assessments, 67 simulations, 330 Multivariate analysis, 277

Index

N Natural forcing, 195e196 Natural variability, 10, 189 NaviereStokes equations, 52 Necessary causality, 294b Newspapers, 20 Non-parametric approach, 48e49 Non-stationarity of climate system, 272 Normal distribution, 281 North Atlantic Oscillation, 243e244, 275 North Pacific High, 209

O Observational records and climate modelling system, 301e305 Observations-and/or model-based attribution analysis, 306e310 Observations-only attribution studies, 276 Oceanic extremes, 18, 127 Oceans, 127 buoys, 132e133 compound extremes, 139e140 extremes, 367, 374. See also Marine extremes marine extremes in instrumental era, 128e140 pre-instrumental era, 127e128 system models, 189 Oklahoma/Texas heatwave and drought (2011), 204 Open ocean swells, 133e135, 242e244 Optimal fingerprinting, 281 analyses, 330 Ordinary method of moments, 49e50

P Pacific coast heatwave (2021), 302b Pacific Decadal Oscillation, 220, 223, 329 PAGES2k initiative, 20e21 Paintings, 20 Pakistan flood and Russian heat wave/fires (2010), 204 Palaeoclimate modelling, 21 Paleoclimate reconstruction method, 22b Palmer Drought Severity Index, 97, 157 Parametric approach, 49 Past changes, 111, 373 Pattern correlation statistics, 281e282 Phenological records, 20 Pliocene, 160 Polar-orbiting satellites, 32e33 Polynomial interpolation, 40e41 Pre-instrumental era atmospheric extremes in, 81e86 data, 20e21

383

marine extremes in, 127e128 Precipitation, 40, 82, 84 extremes, 213e219 Probabilistic framework, 64 Projected changes, 375 Projected wave extremes, 185 Proxy-based climate reconstructions, 86

Q Quasi-resonant amplification, 204

R Radiative forcing, 196e197 Radiative heatwaves and warm spells, 203 Re-emergence mechanism, 205e206 Reanalysis products, 35e37 Regional extreme events, 30 Regional Hadley circulation, 228e229 Regional multidecadal variability, 227e228 Regression-based approaches, 280e282 Remotely observed data, 32e35 Representative Concentration Pathways, 53 Risk Ratio, 308 Risk-based approach, 287e288, 293 Rossby waves, 203 Rotated empirical orthogonal function analysis, 275

S Sampling, 277 Satellite-based estimates of extremes, 33 Satellite-based precipitation products, 34b Scaling factor, 280 Scattering aerosols, 216 Scenario-based forcing, 53e54 Sea ice variability, 212e213 Sea surface temperatures, 223 Semi-parametric weather generators, 55 Shared Socioeconomic Pathways, 53e54 Signal detection theory, 312 Single polar-orbiting satellites, 32e33 Skew surge, 137 Snow droughts, 98b Solar forcings, 272 Southern Annular Mode, 243 Southern Blob, 206e207 Sparse gauge networks, 95 Spatial heterogeneity, 93e94 Spatial scales of extremes, 54e58 Spline interpolation, 40e41 Standardized Precipitation Index, 96 Standardized Precipitation-Evapotranspiration Index, 96, 157 Stationary high-pressure systems, 248e249

384 Statistical downscaling, 55 Statistical interpolation, 40e41 Statistical techniques, 277 Statisticaledynamical downscaling technique, 158e159 Stochastic weather generators, 55 Storm surges, 244e246 Storyline approach, 293, 294b Sufficient causality, 294b Sulphate, 216 SupplyeDemand Drought Index, 155 Surface atmospheric pressure, 135

T Temperature, 82 Temporal optimal detection, 282 Three-parameter weather generators, 55 Thunderstorms, 227, 234 Tibetan Plateau, 238 Tides, 244e246 Time-based fingerprints, 281 Tipping year, 155 Tornadoes, 55, 238e240 Trend detection, 50e51 Tropical cyclones, 55e56, 100e106, 158e161, 227e232, 328, 350e352. See also Convective storms tracks, 160 translation speed, 103

Index

U Uncertainty, 10, 65e68 Unconditional attribution, 291 Urbanisation, 199

V Validation criteria, 304 Vertical wind shear, 234 Volcanic eruptions, 228

W Warming hole, 88e89 Wave power, 134e135, 243e244 Wave setup, 247 Wave swash, 247e248 Wave transformations in surf zone, 135 Weather, 374 forecast model, 199 Weather Extremity Index, 51 Weibull distribution, 49 Western Hemisphere Warm Pool, 219e220 Winds, 86, 106 sea, 133e134 set-up, 135 World Climate Research Programme project on Climate Variability and Predictability, 24 World Meteorological Organization’s Commission for Climatology, 24 World Weather Attribution, 288