Integrated Risk and Vulnerability Management Assisted by Decision Support Systems: Relevance and Impact on Governance (Topics in Safety, Risk, Reliability and Quality, 8) 1402034512, 9781402034510

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INTEGRATED RISK AND VULNERABILITY MANAGEMENT ASSISTED BY DECISION SUPPORT SYSTEMS

TOPICS IN SAFETY, RISK, RELIABILITY AND QUALITY VOLUME 8 Editor Adrian V. Gheorghe Swiss Federal Institute of Technology, Zürich, Switzerland Editorial Advisory Board P. Sander, Technical University of Eindhoven, The Netherlands D.C. Barrie, Lakehead University, Ontario, Canada R. Leitch, Royal Military College of Science (Cranfield), Shriverham, U.K. Aims and Scope. Fundamental questions which are being asked these days of all products, processes and services with ever increasing frequency are: What is the risk? How safe is it? How reliable is it? How good is the quality? How much does it cost? This is particularly true as the government, industry, public, customers and society become increasingly informed and articulate. In practice none of the three topics can be considered in isolation as they all interact and interrelate in very complex and subtle ways and require a range of disciplines for their description and application; they encompass the social, engineering and physical sciences and quantitative disciplines including mathematics, probability theory and statistics. The major objective of the series is to provide a series of authoritative texts suitable for academic taught courses, reference purposes, post graduate and other research and practitioners generally working or strongly associated with areas such as: Safety Assessment and Management Emergency Planning Risk Management Reliability Analysis and Assessment Vulnerability Assessment and Management Quality Assurance and Management Special emphasis is placed on texts with regard to readability, relevance, clarity, applicability, rigour and generally sound quantitative content.

The titles published in this series are listed at the end of this volume.

Integrated Risk and Vulnerability Management Assisted by Decision Support Systems Relevance and Impact on Governance

Edited by Adrian V. GHEORGHE Swiss Federal Institute of Technology, Zürich, Switzerland

A C.I.P. Catalogue record for this book is available from the Library of Congress.

ISBN-10 ISBN-13 ISBN-10 ISBN-13

1-4020-3451-2 (HB) 978-1-4020-3451-0 (HB) 1-4020-3721-X (e-book) 978-1-4020-3721-4 (e-book)

Published by Springer, P.O. Box 17, 3300 AA Dordrecht, The Netherlands. www.springeronline.com

Printed on acid-free paper

All Rights Reserved © 2005 Springer No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Printed in the Netherlands.

Motto: “In companies today, only 10% to 20% of users access DSS tools. To reach the remaining 90% to 80%, companies are going to need to embed analytics into core solutions.” - PricewaterhouseCoopers Consulting -

Contents

PREFACE ACKNOWLEDGEMENTS

xv xxiii

I.

DISASTER RISK AND VULNERABILITY MANAGEMENT FROM AWARENESS TO PRACTICE (ADRIAN GHEORGHE, DAN VAMANU)

1

INTRODUCTION

1

1.

TOOLS FOR AN EDUCATED AWARENESS 1.1 The GIS manager 1.2 A risk-oriented database 1.3 Chemical risk assessment tools 1.3.1 Chemical risk cadaster 1.3.2 Chemical accident source terms 1.3.3 Chemical accident consequence assessment tool 1.3.4 Physical and health effects of spills 1.3.5 Atmospheric dispersion in complex terrain 1.3.6 Environmental monitoring network-assisted toxicological assessment 1.4 Nuclear Risk Assessment 1.4.1 Nuclear risk cadaster

9 11 13 15 15 18 20 22 24 28 31 31

viii

Contents 1.4.2 Nuclear accident source terms 1.4.3 Nuclear accident consequence assessment 1.4.4 Environmental monitoring network-assisted radiological assessment 1.5 Transportation Risk Tools 1.5.1 Routing dangerous rail/road cargoes comparative risk assessment 1.5.2 Routing dangerous rail/road cargoes hot spot identification 1.5.3 Tunnel fire assessment 1.5.4 The Risko’Meter 1.6 Risks in Water Management 1.6.1 Pollution dispersion in surface waters 1.6.2 Pollution dispersion in ground waters 1.7 Near-Earth Objects 1.7.1 Asteroids/comets terminal monitoring and Torino-scale assessment 1.7.2 Satellite motion and re-entry monitoring 1.7.3 Ballistic missile threat 1.8 Multiattribute risk assessment tools 1.8.1 The Risk Matrix a case of chemical risk acceptability assessment 1.9 An introduction to Quantitative Vulnerability Assessment 1.9.1 System vulnerability generic assessment 1.9.2 Territorial vulnerability assessment 1.9.3 Structural vulnerability assessment

2. FOUNDATIONS - SELECTED TOPICS 2.1 Atmospheric dispersion 2.1.1 The advection-diffusion equation 2.1.2 Atmospheric transport in complex terrain 2.2 Physical background of chemical source term models 2.2.1 The Critical Parameters 2.2.2 The Molar Volumes V1 , V3 . 2.2.3 Maxwell’s Rule for Andrews Isotherms 2.2.4 Shapes, volumes and heights 2.2.5 Adiabatic gas outflows 2.3 Operative models of chemical accident phenomenology 2.3.1 BLEVE 2.3.2 Pool fire 2.3.3 Flare 2.3.4 Explosion 2.3.5 Intoxication

34 36 39 42 42 45 48 50 52 52 55 58 58 60 62 64 64 67 67 69 71 73 73 73 82 99 99 100 100 101 101 112 112 117 121 126 134

Contents 2.4 Integrated dispersion and dose-effect models 2.5 Water pollution assessment recipes 2.5.1 Surface water 2.5.1.1 Near-field models 2.5.1.2 Far-field models 2.5.2 Ground water 2.5.2.1 The assessment concept 2.5.2.2 The model inputs 2.5.2.3 Spot assessment: concentration in, and ingestion from tap water wells 2.5.2.4 Spot assessment: discharge excursion in rivers/lakes 2.5.2.5 Spot Assessment: concentration excursion at table-top level 2.5.2.6 Area Assessment: the primarily exposed areas 2.6 A special case: fire in tunnels 2.6.1 Model scope 2.6.2 Model outline 2.6.3 Fire assessment: the near source zone 2.6.3.1 Problem setting 2.6.3.2 The algorithm 2.6.4 The initial conditions of the axial flow problem 2.6.4.1 Problem setting 2.6.4.2 The algorithm 2.6.5 Fire assessment: the far-zone axial flow problem 2.6.5.1 The approach 2.6.5.2 The algorithm 2.6.5.3 The critical ventilation velocity and the fire range 2.6.6 Fire assessment: the dose, and dose-effect models 2.6.6.1 Fire radiation effects 2.6.6.2 Toxic effects 2.6.7 The input 2.6.7.1 Initial data 2.6.7.2 First-instance derived data 2.6.7.3 Run-time empirical parameters 2.6.7.4 Option-relating inputs 2.6.7.5 Input style 2.7 Modeling system vulnerability – a generic approach to stability in multicomponent systems 3. STEPS TOWARDS PRACTICE: VIRTUAL CASE STUDIES 3.1 A pre-application environmental statement to decommissioning nuclear power plant X.

ix 139 145 145 146 152 157 157 159 162 164 167 172 175 176 177 177 177 179 181 181 183 185 185 185 193 195 195 199 202 202 203 204 205 206 206 212 214

x

Contents 3.1.1 Introduction 3.1.2 A pre-application documentation strategy 3.1.3 The Theater of Action 3.1.4 A Decommissioning Scenario 3.1.4.1 The primary sources and paths leading to health and environmental hazards 3.1.5 Space and Time Scales 3.1.6 Situation Maps 3.1.7 Radioactive inventories 3.1.7.1 Fission product inventories 3.1.7.2 Activation inventories 3.1.7.3 Reactor coolant inventory 3.1.8 Source Terms 3.1.9 Meteo Scenarios 3.1.10 Potential Impacts of Acute (Accidental) Releases 3.1.11 Potential Impacts of Long-Term Releases 3.1.12 Potential Doses from Direct Exposure 3.1.13 Potential Effects from Contaminated Fluids Discharged into the Ground Water Table 3.1.14 The Data Base 3.2 Routing a HAZM AT cargo 3.2.1 The case study format 3.2.2 The executive summary

215 216 218 219 220 221 223 231 231 235 237 238 246 250 274 278 282 288 292 294 296

4. CONCLUSION

307

REFERENCES

309

QUANTITATIVE AREA RISK ANALYSIS: AVAILABLE TOOLS AND OPEN PROBLEMS (VALERIO COZZANI, SEVERINO ZANELLI)

321

INTRODUCTION

322

1. QUANTITATIVE ASSESSMENT OF DOMINO HAZARDS IN QUARA 1.1 Propagation and escalation of accidents 1.2 Types of domino effect 1.3 Identification and assessment of accidental scenarios caused by the first type of domino events 1.4 Identification and assessment of accidental scenarios caused by the second type of domino effects

324 324 324

II.

325 326

xi

Contents 1.5 Possibility and probability of propagation 1.6 Software tools for domino hazard assessment

328 331

2. ASSESSMENT OF HAZARDS DUE TO THE FORMATION OF HAZARDOUS SUBSTANCES 333

IN THE LOSS OF CONTROL OF INDUSTRIAL CHEMICAL PROCESSES

2.1 Unforeseen formation of hazardous substances in industrial accidents 2.2 EUCLIDE database 2.3 Lumping approach to the description of chemical systems 2.4 Procedures for hazard assessment 2.5 Production of experimental data on products formed in “out of control” conditions

333 335 335 337 338

3. QARA CASE STUDIES 3.1 The QARA studies 3.2 Formation of hazardous substances in industrial accidents

339 339 341

4. CONCLUSIONS

344

REFERENCES

345

III.

ARIPAR-GIS, TRAT, OPTIPATH, EHHRA-GIS: FEATURES AND APPLICATIONS

OF

SOME TOOLS FOR ASSISTING DECISION-MAKERS IN RISK MANAGEMENT

(GIGLIOLA SPADONI, SARAH BOVINCINI)

349

INTRODUCTION

350

1. THE ARIPAR-GIS SOFTWARE

351

2. THE TRAT SOFTWARE

352

3. THE OPTIPATH PROCEDURE

354

4. THE EHHRA-GIS SOFTWARE

356

5. CONCLUSIONS

358

REFERENCES

359

IV.

RISK BASED DECISION MAKING: THREE EXAMPLES OF PRACTICAL APPLICATION TOOLS (MARCUS ABRAHAMSSON, HENRIK JOHANSSON, JERRY NILSSON, SVEN ERIK MAGNUSSON )

361

xii

Contents

INTRODUCTION

362

1. DECISION ANALYSIS INVOLVING EXTREME EVENTS

363

2. DEVELOPING A METHOD FOR ANALYSING MUNICIPAL VULNERABILITY 2.1 Background 2.2 Procedure 2.3 Theoretical and technical aspects 2.4 Model description 2.5 Preliminary conclusions

366 366 367 368 369 373

3. UNCERTAINTY IN QUANTITATIVE RISK ANALYSIS CHARACTERISATION AND METHODS OF TREATMENT

373

REFERENCES

380

V.

CATASTROPHE RISK MANAGEMENT. VULNERABILITY AND EQUITY (ANIELLO AMENDOLA, YURI ERMOLIEV, TATIANA ERMOLIEVA)

383

INTRODUCTION

384

1. INTEGRATED CATASTROPHE RISK MANAGEMENT: INSURABILITY OF EARTHQUAKE LOSSES

386

REFERENCES

399

VI. INTERACTIVE RISK MANAGEMENT

(BEATRICE CAPAUL )

403

INTRODUCTION

404

1. RISK MANAGEMENT

406

2. RISK LIFE CYCLE ANALYSIS AND PUBLIC SAFETY

406

3. INTERACTIVE RISK MANAGEMENT

413

VII.

PILOT PROJECT ON ENVIRONMENT AND HEALTH RAPID RISK ASSESSMENT IN SECONDARY RIVERS OF THE MEAN AND LOWER DANUBE BASIN. METHODOLOGY AND APPLICATION (BRUNO FRATTINI, NEIL MANNING )

417

Contents

xiii

INTRODUCTION

418

1. SCOPE 1.1 Target 1.2 Goals

420 420 420

2. BASIC STRUCTURE 2.1 Site Hazard Index (SHI) and Ranking 2.2 Environmental and Health Site Risk Index (SRI) and Ranking 2.3 Environment and Health Vulnerability Index 2.4 Risk and Vulnerability Ranking

421 423 427 429 430

3. BULGARIA IMPLEMENTATION 3.1 Industrial Site Selection for Test Cases 3.2 Results 3.3 Emergency and Prevention Measures

431 431 432 435

4. CONCLUSION S

438

5. REFERENCES

439

VIII.

FACING MODERN TIMES: CHALLENGES IN RISK ANALYSIS (RALF MOCK )

441

INTRODUCTION

442

1. RISK ANALYSIS METHODOLOGIES IN USE 1.1 Industrial Branches 1.2 Ratings of Risk Analysis Techniques

443 443 445

2. PROSPECTIVE IN RISK ANALYSIS METHODOLOGY

449

REFERENCES

453

IX.

A RESEARCH AND DEVELOPMENT STRATEGY ON ASSESSMENT AND MANAGEMENT OF TECHNOLOGICAL AND NATURAL RISKS (ALFREDO C. LUCIA)

457

INTRODUCTION

458

1. THE JOINT RESEARCH CENTRE AND THE SIXTH FRAMEWORK FOR RESEARCH AND DEVELOPMENT (2003 - 2006)

459

xiv

Contents

2. ROLE AND ACTIVITIES OF THE JRC IN THE FIELD OF RISK ASSESSMENT AND MANAGEMENT

459

3. THE MAJOR ACCIDENT HAZARDS BUREAU (MAHB)

461

4. NATURAL AND ENVIRONMENTAL DISASTER INFORMATION EXCHANGE S YSTEM (NEDIES)

463

5. MANAGEMENT OF NATURAL AND TECHNOLOGICAL HAZARDS IN CANDIDATE COUNTRIES

464

6. RISK COMPATIBILITY AND INTEGRATED RISK ASSESSMENT

465

7. OTHER RELEVANT ACTIVITIES

467

8. THE EUROPEAN COORDINATION CENTRE FOR AVIATION INCIDENTS REPORTING SYSTEMS (ECCAIRS)

468

9. THE PROJECT ON "INTEGRATED SAFETY ASSESSMENT AND RISK MANAGEMENT IN CIVIL AVIATION"

469

10. FORMAL COLLABORATIONS WITH INTERNATIONAL, NATIONAL OR LOCAL INSTITUTIONS

471

11. THE ROLE OF RESEARCH

471

REFERENCES

473

INDEX

475

PREFACE

Introduction This book includes terms of reference and offers an augmented volume of relevant work initiated within the comprehensive concept of “Knowledge Management and Risk Governance”. The latter stood for the initial title of an ad-hoc meeting held in Ascona, Switzerland, organized by the Technological Risk Management Unit of the Joint Research Centre of the European Commission (JRC) and the KOVERS Centre of Excellence in Risk and Safety Sciences of the Swiss Federal Institute of Technology, ETH Zurich. Background Risk governance, in addition to the continuous interest of researchers, has recently attracted the attention of policy-makers and the media and the concern of the public. New and emerging risks in various fields and a number of risk-related issues increased the public interest and prompted for a new framework in dealing with risks. The Conference on Science and Governance organized by the European Commission in October 2000 is one of the international forums addressing this issue. Other recent events such as the establishment of the International Risk Governance Council outline the importance of the governance concept in relation to that of risk management (see www.irgc.org). At the same time noticeable progress has been made in Information Technologies and Decision Support, passing from the process of information

PREFACE

xvi

to the process of knowledge. In this context new tools and methods became available, whose application in risk management may be beneficial. Moreover, it has been observed that tools and techniques in dealing with certain risk-related issues are more advanced in certain, specific fields, in some direct proportion to the technical, environmental and societal challenges involved. Therefore, there is an added value in understanding what tools are available for dealing with risks in various disciplines and explore their cross-applicability to other fields. Objectives The purpose of the present volume is to bridge the gap between risk sciences and decision support tools, in view of a better performance in governance. In particular, the main objectives are: • To define the knowledge management methods and tools applicable in risk governance; • To bring experience from the application of methods and tools available in various disciplines to other fields of risk governance; • To determine the present and future needs for knowledge management tools in risk governance; and • To promote the development and dissemination of such tools in a problem-solving context and for educational purposes. The work here assemblied addresses questions, and provides tentative answers to issues such as: • Do adequate tools for risk governance exist? • Are they available to decision-makers? • What are the needs of the various stakeholders (i.e. planners, regulators, industry, public) for an effective risk management? • What new tools have to be developed in order to cover these needs? What features should they have? The range of applications and associated decision support tools to address aspects of integrated risk and vulnerability management by use of decision support systems cover numerous disciplines and fields of application including process industry, transportation, natural disasters, emerging risks, critical infrastructures, insurance, national security related aspects. Problematique In the face of a turbulent and sometimes perplexing behavior of a world in transition, the Disaster Risk and Vulnerability Management (DRVM) tends to become a key buzzword in the business of governance. It naturally starts as an exasperated perception of an urgent need, gradually turning into an

PREFACE

xvii

articulated intellectual challenge awaiting sound solutions in terms of strategies, guidelines, implementation procedures, and practical tools to assist the ‘live’ management. Gheorghe and Vamanu in their paper “Disaster Risk and Vulnerability Management – from Awareness to Practice” introduce in detail theoretical and application-oriented work done to support assessment of risks and vulnerability in the context of modern governance oriented needs, including education and training. Starting from the existing reality, outstanding in the quest for a substantive and systematic commitment to responding the issue was the establishment, by the World Bank, of a Disaster Risk Management Institute (DRMI), based in Washington, D.C. The institute undertakes to, quote, 'enable people anticipate disasters and take action to protect life and property, and to ensure sustainable social and economic development'. Its activities include ‘supporting the pursuit of an optimal balance between disaster prevention, risk-sharing mechanisms and acceptance of residual risks in the face of limited resources’. It is believed that such an aim can be achieved 'by filling knowledge gaps, providing a clearing-house for information, building knowhow, mobilizing resources and forging partnerships with governments, private enterprises, international agencies and NGO's'. DRMI aims at offering a comprehensive and effective implementation to the concept of integral risk assessment, treating the vulnerability of the infrastructures, the probabilistic analysis of hazards and the risk evaluations in one smooth flow. Throughout the process, public perception considerations and stakeholders postures are believed to play an important part. Also, a satisfactory coverage of both natural disasters and technical hazards would involve in a balanced fashion the natural sciences and technical engineering offering the basic language to quantify risk, and the political and socio-economic science bringing in the geo-economic and geopolitical considerations, as well as the human dimension, that are indispensable in talking risk, carrying its messages, and properly responding to it. DRMI is geared towards 'developing tools for fast and efficient implementation; contracting of expertise; identifying expertise and know-how on defined risk issues; providing adequate quality control in project management, and for risk evaluation of large investments', etc. To manage risk, one has first to comprehend it. In turn, this means to mentally grasp, qualitatively perceive and define and, hopefully, objectively quantify the targeted systems' vulnerabilities; the system control variables which, when monitored, may indicate the imminence of a disaster about to strike; the foreseeable proportion of the disruptions; the likelihood of the latter; and, necessarily, the people's perception of the potential disaster's severity. Sizing the mitigating response in fair proportion to the disaster, and ensuring a proper preparedness to face mishaps is also a part of the risk management equation.

xviii

PREFACE

The number of variables involved may soar high - in the order of hundreds, or even thousands. And it is more to that: whenever risk management turns into emergency management, the time factor, and the manager's stress factor start to rank high in the overall performance. Doing disaster assessment near-real-time and reliably is an irreducible must. The natural manner to comply is - computer assistance. To this effect, ever since its inception DRMI has contemplated the development of capabilities to identify, evaluate, acquire, develop, custom-tailor, and dispatch computer-based tools. This line of action is evidently consistent with the ubiquity that the decision support systems (DSS) have gradually, gained ever since the advent of the ‘true’ mainframes, back in the 60s. Starting from the dictionary definition, ‘decision support systems are interactive computer-based systems and subsystems intended to help decision makers use communication technologies, data, documents, knowledge, and/or models to complete decision process tasks’, the approach taken by the authors include: Communication-driven DSS; Data-driven DSS; Document-driven DSS; Knowledge-driven DSS; Model-driven DSS. While a review of the currently expanding market of risk assessment–oriented DSS software is not on this book's agenda, a fair recognition and illustrative description of its typological profile may however be in order. The said profile can be discerned in terms of needs, and the means to have these served. Cozzani and Zanelli, outlining the Directive 96/82/EC (i.e. "Seveso-II" Directive) on the control of major hazards caused by dangerous substances report on relevant innovations in the safety requirements of process plants that have an impact on risk management. Among these are: the inclusion of substances likely to be formed in the loss of control of chemical processes in site inventory, the evaluation of domino accident hazard, and the requirement of land-use planning criteria. The development of land-use planning (LUP) criteria for the minimization of the industrial risk to which the population is exposed calls for the application of quantitative area risk analysis (QARA) techniques. QARA techniques currently available are mainly based on the modification of risk analysis techniques originally developed for the major accident risk assessment of single risk sources. Thus, these techniques show important limitations, mainly in the assessment of the effects on the global industrial risk due to the contemporary presence of different risk sources in a narrow area. The application of QARA techniques to land use planning - "Seveso-II" Directive requires the further development of procedures to assess specific problems as the presence of linear risk sources due to the transport of hazardous substances, the release of substances formed in the loss of control of chemical processes, domino accident hazards. This contribution addresses two of the open technological problems that arise in the application of QARA techniques to LUP. The

PREFACE

xix

methodologies available and the research needs in the quantitative assessment of domino hazards and of the hazards deriving from the release of dangerous substances formed in the loss of control of chemical processes are discussed. The potential impact on LUP of these hazards is also evidenced, discussing the results of two Italian case studies. Spadoni and Bonvicini discuss specialized decision support systems relating to a shared concern in all industrialized countries: the risks due to major accidents in the storage, production and transportation of dangerous chemicals. In Italy, it is argued, relevant work has been performed in the field of risk analysis. The chief aim of the research done over the past years has been the development of detailed techniques for the quantization of specific risks, implemented in user-friendly software codes. The main features of those tools are presented, particularly highlighting the application field for each of them and the support they can give to decision-makers in risk management. The paper by Abrahamsson, Johansson, Nilsson, and Magnusson discusses three ongoing, or recently finalised, projects carried out at the Lund University Centre for Risk Analysis and Management. The first section introduces decision making situations involving extreme or catastrophic events and the application of a newly developed decision analysis method. The second chapter discusses the framework and the methodological aspects of a computer based decision analysis tool for assessing and managing local or municipal vulnerability. The third part presents a comparative uncertainty analysis of risks from an ammonia storage facility employing a number of methods: Monte Carlo analysis, interval analysis, fuzzy arithmetic and probability bounds theory. In their paper, Amendola, Ermoliev, Ermolieva, address the issue of natural catastrophe risk management. The catastrophe risk management process has all the characteristics of a complex systems problem: multiple conflicting objectives and strategies, a diverse range of views on fairness, multiple stakeholders and interests, and many different policy variables. The purpose of research at the International Institute for Applied Systems Analysis in Laxenburg, Austria, is to develop and test an integrated systems approach that can potentially provide insights on the complex issues and trade-offs involved. The approach also includes development of tools. These are designed to take into account the complexities and spatial – temporal dependencies of catastrophic risks, and to investigate multiple policy options (i.e. interplay between investment in mitigation and risk-sharing measures). Case studies have been demonstrating how these tools can aid a decision process that involves the public and stakeholders from the very beginning. The apparent lack of transparency inherent to complex risk networks due to the increasing globalization and dynamics of risks calls for close co-

xx

PREFACE

operation among risk players in terms of the exchange of risk information, assessment procedures and methodologies as well as risk handling strategies. Building on this finding, the paper by Capaul argues that such a task requires another approach in risk management, called interactive risk management that takes into account not only the interdependency of risks but also the risk life cycle of risk-bearing systems, entities and situations as well as their interplay with the human element. Interactive risk management will help to lift the veil from hidden risk networks, thus facilitating an early warning system and a risk handling strategy to protect the public, the corporations involved and the environment from devastating incidents. Following the dramatic cyanide spill of Baia Mare (Romania) in January 2000, a project jointly supported by the Italian Ministry of the Environment and the World Health Organization, has been launched with the endorsement of the European Environment and Health Committee. The methodology presented by Frattini and Manning is grounded on the definition of an integrated environment and health risk assessment, directed to the development of homogeneous comparison between several countries. The tool is directed to national and local authorities in order to help making firstrecourse decisions in terms of emergency planning and risk reduction policies. The methodology was carried out with the involvement of international institutions (e.g. EC Joint Research Centre, the Hungarian National Institute for Environment and Health, the Florida State University, the Danish Toxicological Centre). For the sake of rapidity, the information necessary to run the model was reduced to the minimum set, capable to represent a complete (even if simplified) picture of the site risk. Suitable check lists have been printed for data gathering and a software tool has been developed for data management and results. A first test application was carried out in Bulgaria, with the help of the local Ministry of the Environment and Water. The application required training courses, site visits to selected industries and a final discussion on the results. Mock is addressing new challenges in the field of risk analysis in the context of advancements in the information technology. Risk analysts are currently faced with far-reaching changes in their professional field. The growing importance of complex systems, e.g. in telecommunication and transport pinpoints the limitations of established risk analysis techniques in the non-nuclear industries. These techniques are identified and rated according to their major goals, modernity, level of system sophistication, manageability, and user satisfaction. The challenging situation in risk analysis is characterized by updating the "lessons learned" from an early ETH Zurich Polyproject on what to do when dealing with integrated regional risk assessment and safety management.

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xxi

In his paper, Lucia introduces the mission of the EC - Joint Research Centre, aiming at the protection of the citizen and the environment, and some activities planned in the Framework Program 6 (2003 – 2006), particularly related to the assessment and management of technological and natural risks. The focus of these activities is on: • Development and maintenance of harmonized European monitoring and reporting systems; • Accident and disaster analysis and elaboration of lessons learnt, recommendations and guidelines; • Methodological development in the field of risk analysis, civil protection and emergency management, land use planning and strategic decision-making. Concluding remarks The advent of computers, decision support systems, Internet and new methods of calculation and assessment of risk and vulnerability of complex technical systems, up to integrated critical infrastructures, bring new dimensions to the overall governance issues of potentially hazardous technologies in their interaction with people and the environment. The risk governance concept has been recently established as an instrument of management, at the societal level, of new emerging risks, or in relation to critical infrastructure complexities. As recent realities show, the unexpected risks and vulnerabilities tend to exceed ‘design bases’, and even ‘plausibility’. A sad failure of imagination in relation to new potential attacks and manners of viewing infrastructures as a weapon has eventually left societies wide-open to events such as the U.S. 9-11 strike. And a sloppy emergency preparedness blatantly contradicting the standard red tape rhetoric has contributed to outrageous losses of lives and property, like with the December-2004 post-earthquake tsunami in South-East Asia. All of a sudden mankind found itself in a new era where, understanding how to protect infrastructures on the one hand, and the quality of life on the other hand, requires new instruments of assessing potential consequences of a large variety of situations from the explosion of a chemical plant, to the decommissioning of a nuclear facility, to loosing control on a satellite reentry, to the impact of a major near-Earth object, to an ill-advised regulation or political/military move. The present work is addressing characteristic risks and vulnerability situations in view of assisting governance related initiatives. It endeavors to stimulate the establishment of fresh platforms for risk dialogue and exchanges with stakeholders who rightfully demand to be better informed,

xxii

PREFACE

and look for some documented indications that the ongoing developments in science and technology would not negatively affect their business; their environment; their life. After all people has to have access to satisfactorily reliable and handy tools and computational instruments that would enable at least rough estimations on the risks and vulnerabilities they are currently facing. The advances in the IT & C and the ubiquity of their ways and means revive and bring to the forefront of scientist’s attention a plethora of on-theshelf concepts and methods in applied mathematics, physics, computer sciences, and systems engineering, from analytical models of phase transitions to correlation approaches such as the neural nets, the search for order in chaos, for predictiveness in time series, for complex behavior in simply-minded cellular automata. These, and others, are likely to be increasingly engaged into shaping new governance policies that would hopefully enjoy the participation of a new breed of informed stakeholders in complex, if sometimes controversial, decision making situations.

ACKNOWLEDGEMENTS The Editor wishes to express sincere gratitude to Professor Wolfgang Kröger, of the Swiss Federal Institute of Technology in Zürich, for his initiative and substantive support in the organization of an international workshop on the topics of the use of decision support systems and related technology in the field of research, education, consulting engineering and production-related management in various industries. Held in Ascona, Switzerland, late 2001, the workshop established and consolidated the framework, and brought specific technical contributions within the scope and format of this book. The book contributors are greatly indebted to all those who, through valuable suggestions for improvement, in various stages of the manuscript development, have enhanced the practical relevance of the work and helped finalizing the project. The following institutions and individuals are especially acknowledged: Prof. O. Kübler – President of the Swiss Federal Institute of Technology, Zürich Mr. David Wilkinson, Director, EC - Joint Research Center, Ispra Prof. A. Waldvogel – former Vice-president for Research, Swiss Federal Institute of Technology, Zürich Prof. U. Suter – Vice-president for Research, Swiss Federal Institute of Technology, Zürich Dr. S. Bieri – former Vice-president ETH – Rat Dr. H. Neukomm – Director for Research of the ETH – Rat Dr. J. Hammer – Co-Director, World Disaster Risk Management Institute, Alexandria, VA, USA Dr. F. Krimgold – Co-Director, World Disaster Risk Management Institute, Alexandria, VA, USA Dr. M. Christou – Unit Head, ISPC, EC – Joint Research Center, Ispra The Editor would like to express special consideration and appreciation to Mrs. Françoise Bordier for her constant support and encouragement in the finalization of the manuscript of this challenging work, in times when it seemed that the book would never make it to the press. In the preparation of the book for Springer, the Editor has been substantially assisted by Mr. Aurel Acasandrei, who skillfully and patiently prepared the final layout and the index.

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ACKNOWLEDGEMENTS

For the record, let it be said that the manuscript had a complicated history, due not only to the timing and style of the different authors, but also to the essentially emerging nature of the subject and to a shifting emphasis on a variety of issues in the field of decision support systems assisting the integrated risk and vulnerability assessment of complex technical and environmental systems.

DISASTER RISK AND VULNERABILITY MANAGEMENT FROM AWARENESS TO PRACTICE Adrian V. Gheorghe1), Dan V. Vamanu2) 1)

Swiss Federal Institute of Technology ETH-Zurich, Bucharest

2)

Institute of Atomic Physics IFA-

INTRODUCTION In the face of a turbulent and sometimes perplexing behavior of a world in transition, the Disaster Risk and Vulnerability Management (DRVM) tends to become a key buzzword in the business of governance. It naturally starts as an exasperated perception of an urgent need, gradually turning into an articulated intellectual challenge awaiting sound solutions in terms of strategies, guidelines, implementation procedures, and practical tools to assist the ‘live’ management. Outstanding in the quest for a substantive and systematic commitment to responding the issue was the establishment, by the World Bank, of a Disaster Risk Management Institute (DRMI), based in Washington, D.C. and currently making headway in the delicate business of counseling and technically-assisting risk policy-making in various regions, and especially in the disfavored ‘developing world’. The institute undertakes to, quote, ‘enable people anticipate disasters and take action to protect life and property, and to ensure sustainable social and economic development’. Its activities include ‘supporting the pursuit of an optimal balance between disaster prevention, risk-sharing mechanisms and acceptance of residual risks in the face of limited resources’. It is believed that such an aim can be achieved ‘by filling knowledge gaps, providing a clearing-house for information, building know-how, mobilizing resources and forging partnerships with governments, private enterprises, international agencies and NGO’s’. On these lines, DRMI aims at offering a comprehensive and effective implementation to the concept of integral risk assessment (Fig.1.1), treating the vulnerability of the infrastructures, the probabilistic analysis of hazards and the risk evaluations in one smooth flow. Throughout the process, public perception considerations and stakeholders postures are believed to play an important part. Also, a satisfactory coverage of both natural disasters and technical hazards would involve in a balanced fashion 1 A.V. Gheorghe (ed.), Integrated Risk and Vulnerability Management Assisted by Decision Support Systems, 1-320. © 2005 Springer. Printed in the Netherlands.

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INTRODUCTION

the natural sciences and technical engineering offering the basic language to quantify risk, and the political and socio-economic science bringing in the geo-economic and geopolitical considerations, as well as the human dimension, that are indispensable in talking risk, carrying its messages, and properly responding to it (Fig.1.2). In the end, DRMI is geared towards ‘developing tools for fast and efficient implementation; contracting of expertise; identifying expertise and know-how on defined risk issues; providing adequate quality control in project management, and for risk evaluation of large investments’, etc.

Fig.1.1. Integral risk management approach: the departments. The apparently all-purpose, all-azimuths ambitions of the DRMI evidence the unforgiving fact that, as a challenging ingredient of life, the risk features the inherent complexity of the life itself. To manage risk, one has first to comprehend it. In turn, this means to mentally grasp, qualitatively perceive and define and, hopefully, objectively quantify the targeted systems’ vulnerabilities; the system control variables which, when monitored, may indicate the imminence of a disaster about to strike; the foreseeable proportion of the disruptions; the likelihood of the latter; and, necessarily, the people’s perception of the potential disaster’s severity. Sizing the mitigating response in fair proportion to the disaster, and ensuring a proper preparedness to face mishaps is also a part of the risk

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management equation. The number of variables involved may soar high - in the order of hundreds, or even thousands. And it is more to that: whenever risk management turns into emergency management, the time factor, and the

Fig.1.2. Integral risk management approach: targets and actors. manager’s stress factor start to rank high in the overall performance. Doing disaster assessment near-real-time and reliably is an irreducible must. The natural manner to comply is - computer assistance. To this effect, ever since its inception DRMI has contemplated the development of capabilities to identify, evaluate, acquire, develop, custom-tailor, and dispatch computerbased tools. This line of action is evidently consistent with the ubiquity that the decision support systems (DSS) have gradually, if painstakingly, gained ever since the advent of the ‘true’ maiframes, back in the 60s. According to a popular web resource (v. DSS Resources.com), ‘decision support systems are interactive computer-based systems and subsystems intended to help decicion makers use communication technologies, data, documents, knowledge, and/or models to complete decision process tasks.’ More specifically, DSS would include:

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INTRODUCTION

Communication-driven DSS; Data-driven DSS; Document-driven DSS; Knowledge-driven DSS; Model-driven DSS

While a review of the currently expanding market of risk assessment– oriented DSS software is not on this book’s agenda, a fair recognition and illustrative description of its typological profile may however be in order. The said profile can be discerned in terms of needs, and the means to have these served (see also Fig.1.3): A DSS Generic Profile

The Need The Means (illustratively) _____________________________________________________________ Master the Theatre of Action

Have a GIS built-in capability, able to acquire electronically-published or paper maps of any region on Earth, and customize these for a variety of applications. Master the Phenomenology Keep software packages open-ended and modular in structure, capable of gradually acquiring models and codes covering potential disasters of various origins, and have these smoothly integrated into the overall logics and architecture of the decision assisting tool. Master the Data Include data libraries of various contents and origins (e.g. chemical data, nuclear data), relevant for the models employed and substantiating a sound and comprehensive knowledge base. Master the Tool Complexities Have a user interface as transparent and easy-going as feasible. Design it on rules of thumb such as ‘what the code runs is what you see’. Use simple, e.g. readable text-wise, typewriter-style input interfaces for cases when large numbers of

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Get Real...

articulated inputs are into play. Use graphics wherever appropriate to ease the understanding. Have the tool developed with the realworld conditions in mind. Key-words are: the availability of primary data - GIS and statistics; stakeholder proficiency with advanced tools, such as computers and software, and the academic knowledge behind these; tool affordability etc. Be prepared for scarcity of such resources, and make the decision support tools able to perform even under extreme conditions.

Fig.1.3. Archtypal structure of a DRVM decision support software.

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INTRODUCTION

A remarkable aspect that transpares from the thought-schemes above is that the desirable archtype of a risk-oriented DSS would blend in apropriate proportions all the five features listed in the summary categorization above. Indeed, while modeling makes undoubtedly the ‘heavy’ section of the system’s mechanics, a use of models without an educated mastering of the knowledge and knlowledge/information-bearing documents behind is simply unconceivable; likewise, at both the input and output ends of a modeling machine data libraries – both physical and geographic – secure (i) the machine’s feedstock, and (ii) the platform on which outputs can truly be turned to good account. If the structure described would normally satisfy a common sense rule of thumb, then what would be the substantive contents of a decision support (DS) toolkit that would observe the respective terms of reference? While the answer to such a query is inherently manyfold, the bulk of this paper focuses, in the sequel, on a working case these authors are familiar with, that has in addition the quality of having been developed under the World Bank’s Disaster Risk Management Institute’s aegis and, in a manner of speaking, the reign of its spirit. The respective open-ended, multi-modular DS is characteristically comprised of the following components: SUMMARY OF MODULES _____________________________________________________________ TYPE: database _________________ MODULE 1. THE GIS MANAGER MODULE 2. A RISK-ORIENTED DATA BASE TYPE: modeling, simulation and assessment __________________________________ MODULE 3. CHEMICAL RISKS 3.1. CHEMICAL RISK CADASTER 3.2. CHEMICAL ACCIDENT SOURCE TERMS 3.3. CHEMICAL ACCIDENT CONSEQUENCE ASSESSMENT 3.4. PHYSICAL AND HEALTH EFFECTS OF SPILLS 3.5. ATMOSPHERIC DISPERSION IN COMPLEX TERRAIN 3.6. ENVIRONMENTAL MONITORING NETWORK– ASSISTED TOXICOLOGICAL ASSESSMENT

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MODULE 4. NUCLEAR RISKS 4.1. NUCLEAR RISK CADASTER 4.2. NUCLEAR ACCIDENT SOURCE TERMS 4.3. NUCLEAR ACCIDENT CONSEQUENCE ASSESSMENT 4.4. ENVIRONMENTAL MONITORING NETWORK– SUPPORTED RADIOLOGICAL ASSESSMENT MODULE 5. TRANSPORTATION RISKS 5.1. ROUTING DANGEROUS RAIL/ROAD CARGOS – COMPARATIVE RISK ASSESSMENT 5.2. ROUTING DANGEROUS RAIL/ROAD CARGOS – HOT SPOTS IDENTIFICATION 5.3. TUNNEL FIRE ASSESSMENT 5.4 THE “RISKO’METER” MODULE 6. WATER RESOURCES RISKS 6.1. POLLUTION DISPERSION IN SURFACE WATERS 6.2. POLLUTION DISPERSION IN GROUND WATERS MODULE 7. NEAR-EARTH OBJECTS RISKS 7.1. ASTEROIDS/COMETS TERMINAL MONITORING, TORINO-SCALE ASSESSMENT 7.2. SATELLITE MOTION AND RE-ENTRY MONITORING 7.3. BALLISTIC MISSILE THREAT TYPE: regulatory assessment __________________________ MODULE 8. MULTIATTRIBUTE RISK ASSESSMENT TOOLS 8.1. THE RISK MATRIX - A CASE OF CHEMICAL RISK ACCEPTABILITY ASSESSMENT MODULE 9. AN INTRODUCTION TO QUANTITATIVE VULNERABILITY ASSESSMENT 9.1. SYSTEM VULNERABILITY GENERIC ASSESSMENT 9.2. TERRITORIAL VULNERABILITY ASSESSMENT 9.3. STRUCTURAL VULNERABILITY ASSESSMENT A caveat is immediately in order, on the line that illustrating a risk assessment-oriented DS by an apparently parochial case does in no way imply a product recommendation. I nstead, it only tables a clear case of a rear-end type approach – the one that targets enhancing the awareness of stakeholders on the topical variety and relative complexities of a subject that

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INTRODUCTION

is fashionable, often talked about as almost a matter of political correctness, yet seldom perceived in its grass-root details. The opposite, front-end approach would feature, on the other hand, the on-the-shelf and/or customtailored software packages offered on a rapidly emerging market, and aiming at a variety of clients from central and local governments to (re)insurers to major industries and services to the educational system, down to the pressure groups and the Armaghedon hobbyists.

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1.

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DRM TOOLS was developed by appointment of the World Bank’s Disaster Risk Management Institute to become an implicit substantive support for its founding manifesto. The platform introduced itself as ‘an open-ended, custom-tailor able software kit in the risk and vulnerability assessment business’.

In actual fact it eventually stood forth as a live illustration of an ‘ideology’ of risk assessment preparedness, propagated at different levels of stakeholder governance capability, from the grass-root entrepreneurs to statesmen and international organization boards. As expected, the TOOLS – and the ‘ideology’ behind - have stirred up mixed feelings. At one extreme, the exercise was dismissed along with any

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notion of risk governance, by the unavoidable skeptics who either (i) believe they know all about risk; or (ii) they know enough about risk; or – worse – (iii) believe that anything they do not know about risk, well, either does not exist, or is irrelevant anyway. At the other extreme the enthusiasm and expectations were soaring high, probably far beyond the original purpose and intent of the project, which was confined to a concept demonstration of the feasibility to tackle issues of wildly varying nature in the realm of natural and man-induced disasters, within a traded-off balance of accuracy versus technical complexity that, in the end, would make the respective issues intelligible at a layman stakeholder level. Within a time span of five years, these authors have lived enough to see that, eventually, even such a stark and stiff business as the reinsurance came to develop a genuine taste for the said ‘ideology’, and practical approaches. Similar expressions of interest that materialized in specific appointments were received from the finances, and defense, areas. Given such developments, it is believed that a briefing in retrospect, on the tools that made these possible, some of their theoretical foundations, and a few vivid examples of application would be worthwhile as a means of revealing how a bold and explicit approach of even sophisticated technicalities may in the end tease the intellect of down-to-earth stakeholders. In the sequel, most of the modules listed out at the end of the Introduction are shortly described in terms of intended mission; main features; and illustrated output samplings. For the generic category of readers known as ‘those who want to know more’, chapter 3 sketches the theoretical foundations of some frequently encountered concepts and methods, in risk assessment. Finally, chapter 4 illustrates how the tools as described can be put to good work. The briefing goes by module type, a short description, and features. Types are: (i) data base; (ii) modeling, simulation and assessment; and (iii) regulatory assessment. Types are not exclusive and, in fact, more often than not would diffuse into each other.

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1.1

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The GIS Manager

Type: data base

Description: The module is designed as a versatile and user-friendly interface allowing users to build up themselves comprehensive collections of work maps featuring links to GIS layers, to be used as either independent resources for risk representation, or in conjunction with the other modules in the DRM TOOLS SERIES – that would rely on, and require the respective map/GIS format.

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The product is intended designed in mind with a possible deficit of GIS resources on the user’s side, allowing the user to handle crisis situations, in any part of the world. Features: • Primary resources may be ordinary paper maps (atlas maps); aerial photos; satellite imagery; digital raster in multiband DEM (ESRI 1991) or similar formats; and vector resources, such as the open CIA data of the kind.

• On customer appointment, the development team may offer to convert any open primary resource having a sufficient format description, to the required internal code format. • The most popular computer graphics formats – BMP, JPEG, GIF are accepted at the input end. • The standard work maps (1024 x 1024 pixel 24-bit color BMPs) generated from the primary resources (I) can be used as plane maps for additional graphics representations and add-ons at user’s discretion; (ii) can be on-line integrated (be shared by) all the DRM TOOLS modules on the user’s system as GIS platform, source of inputs, and theater of output representation. • 3-D representation and fast animation are standard features with all DRM TOOLS modules. • Statistics on areas, population, land uses etc., of squared, elliptical (circular) or polygonal patches of territory can be performed either independently, or systematically – in relation to the territorial

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risk/consequences/impacts distributions produced by other modules in the series.

1.2

A Risk-Oriented Database

Type: data base

Description: Secure an user-friendly interface to the variety of data in the code bank that are required in chemical risk, and nuclear risk assessment operations. Create a shared platform for input data feed-in, for the DRM TOOLS software components.

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Features: ♦ The chemical section of the database gives access to 26 features, both quantitative and qualitative, for a default collection of substances totaling 701 entries. The primary data source is the Canadian Ministry of the Environment.

♦ The initial variety of substances can be user-enhanced, and all data can be updated at any time, at will.

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♦ The nuclear section covers 155 fission product nuclides, 47 features of these and a variety of supportive physical and procedural information of direct relevance in the management of / response planning for, radiological emergencies as well as health and environmental impact studies. The primary data source is the United States Nuclear Regulatory Commission.

♦ Numerical data on the radio nuclides on the record can be userupdated. ♦ Both the chemical and the nuclear section feature de minimis knowledge bases, at hand to recall elements of technical background as well as modeling and computational approximation assumptions that were employed in data computation.

1.3

Chemical Risk Assessment Tools

1.3.1 Chemical Risk Cadaster Type: modeling, simulation and assessment

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Description: The module endeavors to address two types of questions: (i) Assuming an accidental release of chemical pollutant, that has a finite duration, as opposed to an instantaneous discharge, how the healthand environmental consequence field around the source of release would look like, considering that, normally, the meteorology of the site would vary during the release.

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(ii) Assuming a routine operation of a fixed chemical facility, that entails a technologically-expected stationary release to the atmosphere of a polluting substance at a given rate (kg/s), how the health- and environmental consequence field around the source of release would look like.

A robust manner of modeling that answers the above relies on an analogy with a well-established method in the nuclear risk analysis (NRA), namely the evaluation of the Normalized Time-Integrated Air Concentration. The recommended reference is: Till J.E., Meyer H.R. (1983). Radiological Assessment, A Textbook on Environmental Dose Analysis. U.S. Nuclear Regulatory Commission, Washington D.C. NUREG/CR-3332 & ORNL5968. The analogy is permitted by the fact that both QCRA and NRA rest largely on the concept of dose (toxic dose vs. radiation dose).

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Features: ♦ Based on data on chemicals and the meteorology of a site, the code determines the areas where continuous releases to the atmosphere of hazardous chemicals pose health risks. Toxicity threats include concentration thresholds exceeding the Immediately Dangerous for Life and Health Limit (IDLH), the Threshold Limit Value (TLV), the Short Term Exposure Limit, as well as Expected Lethality Percentage. ♦ As such, the module applies to both normal releases, and protracted accidental releases relating to e.g. pipe breaks, or slowly-evaporating spills. ♦ When working on long-term meteorological statistics, the module may provide cadastral type of chemical risk information - a feature consolidated by code’s capability of generating, together with the workmaps visualizing the effect areas, statistics including data on exposed population, and land, that draw upon the GIS framework. ♦ The code is designed to primarily handle buoyant or neutral gases. 1.3.2 Chemical Accident Source Terms Type: modeling, simulation and assessment.

Description: Generates the release rate of a chemical from a tank storage facility as a function of time, and creates an appropriate file to keep it on record.

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Features: ♦ Direct access to the DRM TOOLS chemical data base. ♦ An input interface that allows preliminary calculations of several parameters of interest, including vapor and saturation pressures, specific and latent heats etc. ♦ Accommodates tanks of a variety of shapes, including cylinders, the sphere, and combinations (hemisphere-tipped cylinders etc.), in either vertical or horizontal position.

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♦ Has the chief capability of following the release process throughout its different phases, depending on the initial tank condition (pressure, temperature), the ambient conditions, the tank shape, and the hole position and size. The process may start as e.g. a liquefied gas discharge and continue as a vapor release, then as a supersonic, and/or subsonic gas flow and some hole sizes may entail two-phase flows also. ♦ While the current model employs a van der Waals model of the real gas, shorthand engineering approaches may also be implemented (see e.g. the TNO Netherlands methodology). ♦ The model theory is available to upgrade the source term facility to include pierced pipe releases. 1.3.3 Chemical Accident Consequence Assessment Tool Type: modeling, simulation and assessment.

Description: Based on data on chemicals and the meteorology at the time of an accidental release of hazardous chemicals to the atmosphere, this module determines areas of effect manifestation, such as fireballs, various kinds of explosion damage, and toxicity threats including lethality.

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Features: ♦ On-line access to the chemical database and GIS. ♦ Interactive input based on accident scenarios. ♦ GIS-linked, map overlaid outputs.

♦ Together with the work-maps visualizing the effect areas, statistics including data on the exposed population and land are also provided. ♦ Designed as a first-reaction tool, the module targets fast, conservative evaluations that integrate fire, explosion and toxicity in an

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overall consequence assessment file – input and output systematically archived. ♦ Terrain treated by selection from an appropriate variety of dispersion parameters according to roughness.

♦

Designed to primarily handle buoyant or neutral gases.

1.3.4 Physical and Health Effects of Spills Type: modeling, simulation and assessment.

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Description: Provide an electronic version of reference manuals in the field of physical and health effect calculations following releases of inflammable/ explosive/ toxic substances.

Features: ♦ User-friendly input interface, featuring on-line access to the DRM TOOLS databases, synoptic views on all inputs required, and on-line explanations on their technical meaning, ranges, limitations etc.

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♦ Transparent outputs in text listing and graphics form, including case archiving capabilities (input + output = case). ♦ Function buildup capability, providing for e.g. tables/graphics of time-dependence of physical quantities given by process equations. ♦ Fast response – abacus-wise, to motivate users find the tool attractive as a vademecum facility (laptops).

1.3.5 Atmospheric Dispersion in Complex Terrain Type: modeling, simulation and assessment.

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Description: Implements a model of atmospheric dispersion in terrains with a heavy orography that would be (i) comprehensive enough to fairly describe gradients of airborne pollutant concentrations in the field, as a result of mechanical distortions of air flows by obstacles, and thermal distortions by non-uniform slope heating; simple enough to provide for algorithms and codes that would be implementable on average PCs; and (iii) scientifically defendable.

Features: ♦ Under the KOVERS Project, a model has been developed, accepted in the peer-reviewed literature], and benchmarked against alternative models, to add supportive information on the atmospheric dispersion in terrains with a complex topography, including the urban areas. ♦ The model is based on a linearization and scaling of the NavierStokes equations for viscous flows;

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♦ It is designed to accept any terrain that can be digitized to serve as equations’ lower boundary condition, irrespective of the continuity class of the functions (distributions) describing the terrain. ♦ The implementation of the model offers, in essence, (a) the airborne concentration field (mg/m3 of polluted air) at ground level, over the territory exposed to the chemical cloud passage; and (b) the concentration excursion as a function of time, at any user-selected spot in the exposed territory; the latter set of data provides for the calculation of the time integral of the powered-concentration at a spot – a quantity known as ‘Toxic Dose’; a probit function technique then links toxic doses to lethality percentages.

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The model works (i) on an assumption of the results of the release’s nearfield mixing; and (ii) treating effectively and dynamically the atmospheric transport and far-field dispersion. The assumption on the near-field mixing is that the polluted air forms a vertical, regular shape (e.g. a cylinder) featuring an inner gaussian distribution of pollutant gas. The computer model distributes the substance in a number of ‘sub-puffs’ inside the near-field overall puff. The far-field dispersion governed by the model equations describes: (a) the trajectories assumed by the constituent sub-puffs in the near-field mixing volume, under the combined influence of the vertically-sheared dominant wind; the terrain shapes and obstacles; and the thermal distortion of the flows by the non-uniform Sun-heating of slopes and obstacle surfaces, around the clock and considering the cloud cover; and (b) the gaussian diffusion of each and every sub-puff, governed by time-dependent dispersion coefficients.

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1.3.6 Environmental Monitoring Network-Assisted Toxicological Assessment Type: modeling, simulation and assessment.

Description: Integrate on-line data acquisition from meteorological / radiological networks (national, regional) into the assessment of the health and environmental effects of releases from chemical and other industries dealing in potentially-airborne toxic substances.

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Features: The module assemblies a collection of functions offering: ♦ The capability to interactively define a grid of measurement sites on any given (mapped) territory. ♦ The capability to define lists of simultaneously measured, and periodically reported (telemetrically transmitted) physical quantities of interest.

♦ The mouse-driven scanning of the area covered by the monitoring grid thus defined, reporting the interpolated quantities at any given time. ♦ The mapping of the interpolation field, at any given time. ♦ The on-line, computer- or real time refreshing of the grid-acquired data, enabling a dynamic monitoring of ongoing processes fed with interpolated grid data.

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Based on these, the code is able to: ♦ Reconstruct the time-evolvement of release-covered areas for various sets of diffusion coefficients; ♦ List a collection of toxicological quantities including airborne activity concentrations, deposition, toxic doses and probit-computed expected lethality that can be linked to normative emergency and countermeasure levels - for source terms featuring various substances, release rates and heights, and emission durations.

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♦ Map areas of interest where the quantities above would exceed significant, law- enforced threshold levels, thus sizing emergency and response areas. The code operates on procedures and data recommended by, and in use with the American Institute of Chemists, Netherlands’s TNO, the Canadian Ministry of the Environment et al.

1.4

Nuclear Risk Assessment

1.4.1 Nuclear Risk Cadaster Type: Topical integration

Description: The module endeavors to address two types of questions: (i) Assuming an accidental radioactive release from a nuclear facility, that has a finite duration, as opposed to an instantaneous discharge, how the health- and environmental consequence field around the source of release would look like, considering that, normally, the meteorology of the site would vary during the release.

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(ii) Assuming a routine operation of a fixed nuclear installation, that entails a technologically-expected stationary radioactive release to the atmosphere, at a given rate (kg/s), how the health- and environmental consequence field around the source of release would look like.

A robust manner of modeling that answers the above is the evaluation of the Normalized Time-Integrated Air Concentration. The recommended reference is: Till J.E., Meyer H.R. (1983). Radiological Assessment, A Textbook on Environmental Dose Analysis. U.S. Nuclear Regulatory Commission, Washington D.C. NUREG/CR-3332 & ORNL-5968.

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Features: ♦ Based on data on fission products and other nuclides and the meteorology of a site, the code determines the areas where continuous releases to the atmosphere of radioactive airborne pollutants pose health risks.

♦ Radiation doses from exposure to radioactive cloud passages and ground shine are computed, on a variety of pathways leading to external and internal irradiation. ♦ As such, the module applies to normal releases, or protracted accidental releases relating to e.g. isolation failure of plant containments holding active gases and aerosols. ♦ When working on long-term meteorological statistics, the module may provide cadastral type of nuclear risk information - a feature consolidated by code’s capability of generating, together with the workmaps visualizing the effect areas, statistics including data on exposed population, and land that draw upon the GIS framework.

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1.4.2 Nuclear Accident Source Terms Type: modeling, simulation and assessment.

Description: Evaluates a nuclear accident source term (mix of radio nuclides in the release and rates of emission) based on plant status.

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Features: Three approaches are available: (i) A rule-based (parameter correlation-based) approach as per U.S. Nuclear Regulatory Commission ‘RTM – Response Technical Manual series. Key inputs are the specification of the natural and engineered containment reduction and escape factors; the time duration over which the reactor core has been uncovered; and the effective escape time, from containment.

An analytic approach modeling most of the essential depletion mechanisms in reactor containment, both natural and engineered, based on parametric studies done in the U.S. nuclear industry and endorsed/publicized by the U.S. regulations. Of special importance are the interconnectivity of the containment compartments; and the effective areas of retention by different mechanisms – from the containment walls to the ice crystals in ice condenser beds and to spray droplets. (iii) The box model retained by the EEC project STEPS (Source Term Estimation based on Plant Status, 1997-1998). Of essence is the interconnectivity of the plant volumes that are traveled by the release and the flow rates of mass exchange between these. (ii)

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The first method offers total releases over given times of escape. The other two also provide the time dependence of the release rates. 1.4.3 Nuclear Accident Consequence Assessment Type: modeling, simulation and assessment.

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Job description: This module implements model-derived computational rules to predict external and internal radiation doses that can be acquired following exposure to radioactive cloud passages and deposition consecutive to accidental releases from nuclear installations.

Features: The rules are compiled in the U.S. Nuclear Regulatory Commission’s series of ‘RTM - Response Technical Manuals’, including the ‘RTM-95 International Response Technical Manual’ that considers norms, procedures and practices agreed upon by the International Atomic Energy Agency (IAEA).

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Starting on (i) activity inventories summary evaluations, (ii) source term diagnoses based on plant status, and (iii) meteorological scenarios that all can be performed online at the user’s interface,

the code - Computes dose - to - distance functions and scans work maps at pixel level, for dose situation; and - Computes isodose and related curves and overlays results onto event’s work map. - Computes derived intervention levels (DIL) for countermeasures application. All computed quantities can be compared with a variety of health-effect and intervention-related normative levels, to assist emergency management.

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1.4.4 Environmental Monitoring Network-Assisted Radiological Assessment Type: modeling, simulation and assessment

Description: Integrate on-line data acquisition from meteorological / radiological networks (national, regional) into the assessment of the health and environmental effects of radioactive releases from nuclear installations.

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Features: The module assemblies a collection of functions offering: ♦ The capability to interactively define a grid of measurement sites in any (mapped) territory. ♦ The capability to define lists of simultaneously measured, and periodically reported (telemetrically transmitted) physical quantities of interest. ♦ The mouse-driven scanning of the area covered by the monitoring grid, reporting the interpolated quantities at any given time. ♦ The mapping of the interpolation field, at any given time.

♦ The on-line, computer- or real time refreshing of the grid-acquired data, enabling a dynamic monitoring of ongoing processes fed with interpolated grid data as inputs. Based on these, the code is able to: Reconstruct the time-evolvement of release-covered areas for various sets of diffusion coefficients;

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List a collection of radiological quantities including airborne activity concentrations, deposition, exposures, doses and concentration in food products, that can be linked to normative emergency and countermeasure levels - for source terms featuring various release rates and heights, emission durations, and isotopic mixes. Map areas of interest where the quantities above would exceed significant, law-enforced threshold levels, thus sizing emergency/response areas. The code operates on procedures recommended by, and in use with U.S. NRC, EPA, and DOE, and are referenced in the U.S. NRC’s ‘Response Technical Manuals’ series - including the ‘RTM-95 International Technical Response Manual’ that is also reflective of the IAEA methodology, as well as in the ‘FRMAC Assessment Manual – the Federal Manual for Assessing Environmental Data during a Radiological Emergency’.

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1.5

Transportation Risk Tools

1.5.1 Routing Dangerous Rail/Road Cargoes - Comparative Risk Assessment Type: modeling, simulation and assessment.

Description: Assists dangerous cargos managers to determine ‘the best route’ from the standpoint of a large number of assessment criteria, combined.

Features: The code offers the user the capabilities to:

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Design alternative routes taking a transport from an origin to a destination; ♦ Assess the routes according to a number of criteria that are sensitive to topometry (terrain relief); ♦

♦ Assess the routes according to a number of criteria that are sensitive to demography (population distribution) and land use. ♦ The assessment files thus generated may then be compared and scored against each other. The overall result is two-fold: (a) It provides a detailed knowledge of the risk-relating implications of choosing a route or another in the transportation of a hazardous substance; and

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(b) It produces the best-ranking route, from the combined standpoint of many criteria, simultaneously considered. The code is heavily GIS-intensive, combining topometric, demometric and land use-related criteria.

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1.5.2 Routing Dangerous Rail/Road Cargoes - Hot Spots Identification Type: modeling, simulation and assessment.

Description: Integrates the determination of train derailment and collision expected frequencies with the assessment of consequences of loss of containment in rail tanker events, with due consideration to the event site and environment, to identify and sort out ‘hot spots’, i.e. sites deserving special attention from a risk management standpoint.

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TOOLS FOR AN EDUCATED AWARENESS

Features: The module endeavors to demonstrate a natural, smooth and user-friendly integration of: (a) A probabilistic, ‘before-mishap’ assessment of the chances that the infrastructure of a railroad, plus the ‘payback engine’ that uses it, i.e. a cargo train, experience an accident - in this case a derailment, or a collision with another train or object crossing tracks, followed by the release of the cargoed hazardous substance; with

(b) A deterministic (scenario-based) assessment of the consequences of the accident - in this code version, limited to the release to the atmosphere of a fraction of the off-tanker-spilled substance, possibly ensuing a BLEVE fireball, an explosion, and the territorial dispersion of the airborne substance entailing toxic exposure; with (c) The assessment of the expectancy for lives lost, non-fatal casualties, cases requiring medical attention, areas and population exposed, over 24 varieties of land use; with

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47

A rough estimate of the accident costs relating to the affected persons, and the property lost, ecological reconstruction and reclamation, insurance, and Federal/Cantonal/ municipal assistance - if legally so provided; with (e) The core code platform’s database and GIS resources. (d)

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TOOLS FOR AN EDUCATED AWARENESS

1.5.3 Tunnel Fire Assessment Type: modeling, simulation and assessment.

Description: Implements a scientifically-defendable model accounting for the fire propagation in tunnels, capable of explaining fire extension, structure (gas fire density and temperature), and health effects by burns and toxicity.

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49

Features: ♦ Computes essential tunnel fire characteristics such as the fire plume height, linear extension, gas fire density and temperature as functions on the tunnel sizes and construction materials (walls and pavement), and on the accident source term involving several features of the ignited substance that eventually result in fire’s power (heat rate). ♦ Determines of the counter-plume ventilation rate that may arrest the fire progress into the tunnel, down to confining the fire near its very source as one major means of crisis response and consequence mitigation.

♦ Drawing upon the results above, evaluates the casualty risk to the persons exposed to fire radiation, in terms of expected 1st degree burns, 2nd degree burns, and fatal burns, percentages, as well as the expected fatality percentage following the inhalation of tunnel fire gases.

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TOOLS FOR AN EDUCATED AWARENESS

1.5.4 The Risko’Meter Type: modeling, simulation and assessment.

Description: Provides a ‘live’ perception of the fast-varying risk during transportation – crash consequences and probability included.

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51

Features: ♦ The code offers a ‘flyby’ facility, allowing the user to drive, or fly over, helicopter-style, on any route of his/her choice across the Swiss territory. ♦ The flyby machine takes the driver/flyer through the (simplified) 3-D perspective of the expected landscape, while the ‘headset’ displays the essential risk-related parameters as one goes. A count-bar on the headset Risk Scale keeps the driver informed on his/her risk-relating performance. Risk performance data are placed on record by a ‘Black Box’-like facility, to be subject to scrutiny and interpretation further on.

♦ Such simulations, that work much in a way of a ‘Road Risk Trainer’, are increasingly perceived as useful in the light of the obligation of the transporter companies to fully brief the cargo carriers on the risks likely to be encountered, or induced, on the route - which, in some countries, tends to become a legal norm.

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TOOLS FOR AN EDUCATED AWARENESS

1.6

Risks in Water Management

1.6.1 Pollution Dispersion in Surface Waters Type: modeling, simulation and assessment.

Description: Implement a sufficient set of low-to-moderate complexity models to account for the dispersion of pollutants following spills to surface waters.

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53

Features: The code is intended for the evaluation of the strength and extension of the dispersion of polluting liquid discharges into water bodies such as the rivers, lakes and ponds, estuaries, and the sea. The emphasis is on the use of models simple enough to fit the constraints of near-real time appraisal in an emergency, yet comprehensive enough to cover the variety of situations that may occur: surface or deep discharges, single-port or multiport diffusers, contact/no contact with banks etc.

- Algorithms based on the models adopted as reference by the U.S. Nuclear Regulatory Commission’s technical literature (v. ‘Radiological Assessment, a Textbook on Environmental Dose Analysis’ (NUREG/CR3332, ORNL-5968). The apparent dedication of the referenced source to nuclear matters does in no way affect, however, the generality of the models and their applicability to a variety of polluting releases, including chemical discharges. The chief caveat to the user would rather concern the appropriateness of the model-cases offered for any concrete case to be assessed, based on the circumstantial case input data (single- or multiport release, release depth, potential importance of shore effects, cross-currents etc.).

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TOOLS FOR AN EDUCATED AWARENESS

- Module designed as a ‘problem-solver’. Typically, it would use discharge input data to evaluate the initial mixing near-field phase, the output of which is then used as a source term for the assessment of the farfield dispersion.

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55

1.6.2 Pollution Dispersion in Ground Waters Type: modeling, simulation and assessment.

Description: Implements a sufficient set of low-to-moderate complexity models to account for the dispersion of pollutants following their ground penetration down to the water table level.

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TOOLS FOR AN EDUCATED AWARENESS

Features: The code is intended for the evaluation of the strength and extension of the dispersion of polluting liquid discharges into the underground water table, eventually affecting the water-tap wells, the surface waters in the area, and the bulk underground itself. The emphasis is on the use of models simple enough to fit the constraints of near-real time appraisal in an emergency, yet comprehensive enough to cover the variety of situations that may occur.

♦ Algorithms are based on models adopted in the U.S. Nuclear Regulatory Commission’s technical literature (v. ‘Radiological Assessment, a Textbook on Environmental Dose Analysis’ (NUREG/CR-3332, ORNL5968). ♦ The apparent dedication of the referenced source to nuclear matters does in no way affect the generality of the models and their applicability to a variety of polluting releases, including chemical discharges. The chief caveat to the user would rather concern the appropriateness of the model-cases offered for any concrete case to be assessed.

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57

♦ The module is designed as a ‘problem-solver’. Typically, it would use discharge input data to evaluate concentrations/dilutions down gradient from release sources, (a)

in water wells;

(b) in neighboring water bodies that drain the ground water table in the area; and (c) at arbitrary spots on top of the underground water table itself. Pointlike, line, and surface release sources are accommodated. Point-like, line, and surface release sources are accommodated.

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TOOLS FOR AN EDUCATED AWARENESS

1.7

Near-Earth Objects

1.7.1 Asteroids/Comets Terminal Monitoring and Torino-Scale Assessment Type: modeling, simulation and assessment.

Description: Implement a doable set of astronomical motions equations (no perturbations) to provide an indicative appraisal on the trajectory, chances of collision course and countdown to near-passage or impact, of Near-Earth Objects (NEO) such as asteroids and comets, based on a minimal knowledge of an initial vector, and object mass.

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59

Features: ♦ Allows the monitoring of a NEO fall, on knowing one object vector at the zenith of a given place on Earth. ♦ The inputs are: the First Observation Site (FOS) coordinates, object initial altitude, object vector angle with the FOS vertical, and the object orbit inclination in respect with the meridian plane of the FOS.

♦

Monitored are:

- The time since the passage at the 1st observation point; - The object’s Earth projection current geographic coordinates; - The current fall velocity; - The current fall height above ground. - The time into the fall, starting at FOS. ♦

The re-entry drag is duly accountable.

♦

The probability of collision and circular error are also accountable.

♦ The kinetic energy is monitored on-the-flight, including at nearpassage or impact.

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TOOLS FOR AN EDUCATED AWARENESS

♦ Collision probability and potential impact energy are used to place the event on the Torino Scale of NEO risk. 1.7.2 Satellite Motion and Re-entry Monitoring Type: modeling, simulation and assessment.

Description: Implement a doable set of orbital motions equations (no perturbations) to provide a means to monitor the trajectory, re-entry and fall,

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61

of satellites and space stations, based on a minimal knowledge of an initial vector, and object mass.

Features: ♦ Allows the monitoring of a satellite passage, on knowing satellite perihelion coordinates (geographic), the perihelion and aphelion heights above ground and the satellite orbit inclination in respect with the meridian plane of the perihelion. ♦ Monitored are: - The time since the passage at perihelion; - The satellite current coordinates (geographic); - The current flight velocity; - The current flight distance from perihelion; - The current flight height above ground. ♦ Re-entry drag accountable.

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TOOLS FOR AN EDUCATED AWARENESS

Note: illustrations – MIR Space Station Re-Entry simulation, April 2001. 1.7.3 Ballistic Missile Threat Type: Topical integration.

Description: Implement a doable set of orbital motion equations to provide a means to program the trajectory of a ballistic missile from a launch site to a destination and reconstruct the countdown to impact (mitigation time window).

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63

Features: ♦ Iterative trajectory programming to achieve operational CEP (circular errors probable);

♦ Computer time and real time drill runs; ♦ Effects assessment on the assumption of nuclear, chemical, or highexplosive, warheads. ♦ Re-entry drag accountable. ♦ 3-D suborbital flight reconstruction.

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TOOLS FOR AN EDUCATED AWARENESS

1.8

Multiattribute Risk Assessment Tools

1.8.1 The Risk Matrix - A Case of Chemical Risk Acceptability Assessment Type: regulatory assessment.

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65

Description: The ‘Risk Matrix’ approach is to see the risk, R, as the product of the consequence, C by a powered probability, P that the respective consequence occur: R=CxPq where q is an exponent reflective of the stakeholder’s (subjective) perception of the importance of the respective consequence.

Quantifying the risk requires to place various actual or virtual abnormal events on a scale of relative importance from the standpoint of event severity, and taking into account both the probability and the consequence dimension of the Risk Matrix. Features: Consistently, the code provides for: ♦ The design of relevant sets of physical indicators to characterize the severity of an abnormal industrial/transportation-related event;

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TOOLS FOR AN EDUCATED AWARENESS

♦ The inter-comparison of the physical indicators in terms of a shared relative scale of event severity; ♦ The interactive setting of the indicators on their respective physical, and relative, scales; ♦ The scaling of the abnormal event severity in terms of an Aggregated Consequence Indicator, derived on grounds of the Fuzzy Set Theory; ♦ The interactive definition of the event probability, various physical, economic and environmental factors considered; ♦ The interactive trading-off of abnormal event consequences against event probability, aimed at defining a region of risk acceptability within the Risk Matrix. ♦ The module is meant to demonstrate the feasibility of the notion of ‘cabling’ sets of technically sound and/or legally enforced rules to the benefit of a stakeholder-oriented risk analysis. Swiss Federal procedures implemented for demonstration. The indicator machine is, however, open-ended, allowing the insertion of fresh sets by customer appointment.

DISASTER RISK AND VULNERABILITY MANAGEMENT

1.9

67

An Introduction to Quantitative Vulnerability Assessment

1.9.1 System Vulnerability Generic Assessment Type: Methodological/ procedural.

Description: Identifies and implements a versatile and consistent method to quantify the vulnerability of critical infrastructures. Features: The proposed model provides, in essence: (i) a two-parameter description and the respective equation of state, for any multi-component, multi-indicator system featuring two states: ‘operable’ and inoperable’; (ii) a division of the two-parameter phase space of the system into ‘vulnerability basins’; and (iii) a 0-to-100 ‘Vulnerability Scale’, and the means to measure the respective ‘Vulnerability Index’, as an operational expression of a ‘Quantitative Vulnerability Assessment’ (QVA).

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TOOLS FOR AN EDUCATED AWARENESS

A method to diagnose the vulnerability of complex systems featuring large numbers of indicators, both internal and external, as well as to dynamically monitor the time-evolvement of the vulnerability as the indicators change is thus articulated and demonstrated. The method is generic and algorithmic, and is believed to having the potential to accommodate a virtually unlimited variety of applications. The notions are inspired by reference models in classical Statistical Physics such as the Bragg-Williams approximation to the Ising model, feed from the alternative interpretations by Thom and Zeeman, of the stability problem in Systems Theory, and are encouraged by similar approaches by Hacken, Weidlich and others. The apparently ‘heavy’ mathematical background of the method is amply compensated by the transparent implementation featuring a highly intuitive

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69

and mind-challenging modus operandi via a straightforward, interactive, user-friendly interface. 1.9.2 Territorial Vulnerability Assessment Type: modeling, simulation and assessment.

Description: Identify and implement a versatile and consistent method to quantify the vulnerability of critical infrastructures with specific application to a given territory.

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TOOLS FOR AN EDUCATED AWARENESS

Features: TERRITORIAL VULNERABILITY illustrates the application of the generic QVA method (see Module 9.1) to given areas featuring risks of various technical origins. To get the physical indicators required, the ‘Risk Classification and Prioritization 3rd generation van den Brand methodology is employed, as promoted by the International Atomic Energy Agency via its technical document IAEA-TECDOC-727 (Rev.1) dated November 1996. ‘Territorial Vulnerability’ borrows from the van den Brand approach the hazardous substance data base, which is linked to the local code’s data banks, as well as the shorthand method to evaluate effect-distances and areas from fire, explosions, and toxicity following environmental releases of such substances.

From this point on, the local code’s GIS is employed to determine people and property (land) affectations within the obtained areas and distances. Effect indicators are combined with indicators reflective of the managerial capability to mitigate risks, in order to fully enable the functioning of the generic QVA procedure.

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1.9.3 Structural Vulnerability Assessment Type: regulatory assessment.

Description: Adapt and apply the generic method of assessing complex system vulnerability to specific technical systems. Case: the nuclear reactor.

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TOOLS FOR AN EDUCATED AWARENESS

Features: ♦ Applies the generic QVA method to a physical installation, where the QVA-relevant indicators emerge from physical quantities that are monitor able by process gauges (or are derived from such quantities), and are articulated via the laws of Physics, instead of being freely defined by the analyst, and articulated via fuzzy logic canonic procedures. ♦ The working example is the nuclear reactor, modeled in the twotemperature zones, and adiabatic, approximation. A software assistant to understand textbook reactor transients is also provided.

For once - non-generic by virtue of the targeted system’s specificity the example is however believed to be telling as to the potential that the generic QVA concept may have in relation with other complex installations, or industrial compounds. ♦

DISASTER RISK AND VULNERABILITY MANAGEMENT

2.

FOUNDATIONS - SELECTED TOPICS

2.1

Atmospheric dispersion

73

2.1.1 The Advection-Diffusion Equation The general equation underlying the notion of atmospheric transport and dispersion links the physical measure Q (kg, mg, ppm, kg.m/s,Ci, MBq, etc., Q generically) of the quantity of interest (mass, momentum, activity) residing at time t (s) in a volume V (m3 ) of air, to the current ℑ (Q/s) of the respective quantity through the surface Σ (m ) that defines the boundary of the volume, also taking into the balance the source/sink contribution S (Q/s) inside the volume:

ℑ = −∂Q / ∂t + S (2.1.1) Introducing the respective densities for the quantities above, namely the density of current i (Q/(m⋅s)), the density of the quantity itself, ρ (Q /m3 ), and the density of the source (also known as the ‘source strength’) ἀ (Q/(m3 ⋅s), Eq.(2.1.1) reads

³ i ⋅ ds = −(∂ / ∂t )⋅ ³ ρdV + ³ αdV Σ

V

V

(2.1.2) Upon using the flux theorem, and in consideration of the fact that the result is valid for an arbitrary volume V one obtains the generic continuity equation

∇i + ∂ρ / ∂t = α (2.1.3) If the quantity Q is the mass of air, and recognizing that no sources/sinks are conceivable in this case (α = 0), one has

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FOUNDATIONS - SELECTED TOPICS

∂ρ 3 ∂ (ρvi ) = 0 +¦ ∂t i ∂xi (2.1.4) where vi are the cartesian components of the air velocity v (m/s) in the current of mass i = ρv. If the quantity Q is the momentum, then using the correspondence

ρ → ρvi, ij → vj⋅ρvi, and α = Fi (i, j = 1, 2, 3) for the generic density, the

density of current, and the density of force, respectively, then one gets the Navier-Stokes equations of motion

§ ∂vi

ρ ¨¨

© ∂t

3

+ ¦vj j

∂vi ∂x j

· ¸ = Fi ¸ ¹ (2.1.5)

∂ ∂ρ (ρvi ) = 0 +¦ ∂t i ∂xi 3

where the equation of air mass continuity was again duly accounted. The density of force can normally be split into a volume force contribution Fi,

Fi = − ρg ⋅ δ i 3 + ρ (Ω × v ) (2.1.6) featuring a gravity component (1st term), a Coriolis component (2nd term), and a surface force contribution Si

Si = −

∂p 3 ∂τ ij +¦ ∂xi j ∂x j (2.1.7) 2

featuring the contributions from the pressure field p (N/m ) and from the viscosity (friction, shear) – related forces represented by the divergence of the stress tensor τ. Finally, if Q refers to a diffusive quantity such as the activity or the mass of an airborne chemical, then an advection-diffusion (dispersion) equation is obtained under the following (common) assumptions: (i) The current i is made of a convective and a diffusive component:

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75

i = iconvective + idiffusive

(2.1.8)

with iconvective = ρv, and idiffusive = -D⋅∇ρ, where the diffusive component is taken as Fickian, with D (Dij) the tensor of the diffusion coefficients in the Boussinesq’s approximation (eddydiffusion). (ii) The customary time- and space-averaging and scaling of the mesoscale meteorology are performed so that the density ρ of activity/mass and the velocity in the equations that follow reflect such a processing; and (iii) The free term a in the equation (2.1.3) features a source, α(r,t), and a sink – i.e. a mechanism that removes diffusive substance from the accounting – taken (again generically) as proportional to the momentary density ρ(r,t):

α Ÿ α (r , t ) − δ ⋅ ρ (r , t ) (2.1.9) The overall result of the above is

∂2ρ ∂ρ 3 ∂ρ 3 − ¦ K i 2 + δρ = α , + ¦ vi ∂xi ∂xi ∂t i i

3

∂vi

i

i

¦ ∂x

=0 (2.1.10)

From among the many manners to solve Eq.(2.1.10), one that seems particularly fit for the contextual purposes of this book relies on the Green function of the linear differential operator in equation’s left-hand side, namely

L(r , t ) ≡

3 § ∂2 · ∂ρ ∂ − K j 2 ¸ +δ + ¦¨vj ¨ ∂x ∂x j ¸¹ ∂t j © j

(2.1.11) which leaves one with the following reciprocal relations:

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FOUNDATIONS - SELECTED TOPICS

L(r , t ) ⋅ ρ (r , t ) = α (r , t ) ⇔ ρ (r , t ) = L−1 (r , t ) ⋅α (r , t ) (2.1.12) Using now the trivial expansion of the source term a via Dirac’s delta ‘functions’ (distributions) +∞

α (r , t ) = ³ dt ′³ d 3 r ′α (r ′, t ′) ⋅ δ (r − r ′) ⋅ δ (t − t ′) −∞

∞

(2.1.13) the solution (2.1.12) can be rendered as +∞

ρ (r , t ) = ³ dt ′ ⋅ ³ d 3r ′ ⋅ α (r ′, t ′) ⋅G (r − r ′, t − t ′) −∞

∞

(2.1.14) introducing the Green function:

℘(r − r ′, t − t ′) = L−1 (r , t ) ⋅ [δ (r − r ′) ⋅ δ (t − t ′)]

(2.1.15)

The Fourier representations of the Dirac functions,

δ (r − r ′) =

1

d (2π ) ³ 3

3

⋅k ⋅e

ik ( r − r ′ )

δ (r − r ′) =

,

+∞

1

dt ⋅ e (2π ) ³ 3

iκ ( t − t ′ )

−∞

∞

when used in Eq.(2.1.15) would immediately give the following integral representation of the Green function (2.1.16):

℘(r − r ′, t − t ′) =

1

+∞

e ik (r − r ′ )+ iκ (t −t ′ )

−∞

κ − «− ¦ v j K j + i¨¨ ¦ K j k 2j + δ ¸¸»

3 ³ d k ³ dκ ⋅

(2π )4 i ∞

ª

3

§

3

«¬

j

©

j

·º

¹»¼ (2.1.16)

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77

Separating the variables in the integrals’ operand one identifies the following integral, that turns out to carry a physical meaning:

g (t − t ′) =

e iκ (t −t ′ )

+∞

1 ⋅ dκ 2πi −³∞

ª

3

§

3

·º

«¬

j

©

j

¹»¼

κ − «− ¦ v j k j + i¨¨ ¦ K j k 2j + δ ¸¸» (2.1.17)

Indeed, the integral can be performed by closing, in the complex plane 2 (χ1, χ2), and around the pole (-Σ̓vj kj , Σ̓Kj kj ), a contour comprising the real axis χ1 and a semicircle in the upper half-plane (the one that contains the pole) – which is feasible only if t > t’, so that the product in the exponent of the operand of (2.1.17) have a negative real part ensuring an exponential tending to zero as t →∞ (see figure, next):

i (κ 1 + iκ 2 )(t − t ′) ~ −κ 2 ⋅ (t − t ′),

κ 2 > 0 Ÿ (t − t ′) > 0 Ÿ G (t − t ′) ~ ϑ (t − t ′) ⋅ κ ⋅ (...)

(2.1.18) (2.1.19)

where h(t-t’) is Heaviside’s function (distribution), defined as:

­+ 1, if t ≥ t ′½ ¾ ¯0, if t < t ′ ¿

ϑ (t − t ′) = ®

Upon these, and using the Residues Theorem one obtains

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FOUNDATIONS - SELECTED TOPICS

g (t − t ′) = ϑ (t − t ′) ⋅ e

ª −i « « ¬

3

§

3

·º

j

©

j

¹¼

¦ v j k j −i ¨¨ ¦ K j k 2j +δ ¸¸ »» (t −t ′ ) (2.1.20)

Bringing the result (2.1.21) in Eq.(2.1.16) and re-arranging exponents one has

[x − x ′ −v (t −t′ )]

2

℘(r − r ′, t − t ′) =

3

+∞

j

−∞

× ∏ ³ dk j ⋅ e

ϑ (t − t ′) ⋅ e (2π )3 ∏j 3

−

j

j

j

4 K j (t − t ′ )

ª x j − x′j − v j (t −t ′ ) º » − « k j K j (t − t ′ ) − i «¬ 2 K j (t −t ′ ) »¼

⋅ e −δ (t −t ′ ) ×

2

(2.1.21)

evidencing the integrals: +∞

I j (t − t ′) = ³ dk j ⋅ e

ª x j − x′j − v j (t − t ′ ) º » − « k j K j (t − t ′ ) − i 2 K j (t −t ′ ) »¼ «¬

2

−∞

(2.1.22) The change of variable: 2

ª x − x′j − v j (t − t ′) º » , ξ j = − «k j K j (t − t ′) − i j 2 K j (t − t ′) »¼ «¬ gives

dk j =

dξ j

K j (t − t ′)

,

DISASTER RISK AND VULNERABILITY MANAGEMENT

I j (t − t ′) =

+∞

1 −ξ 2 ⋅ ³ dξ j ⋅ e j = K j (t − t ′) −∞

79

π

K j (t − t ′) (2.1.23)

here a Poisson integral was used. With these, Eq.(2.1.21) reads (2.1.24):

℘(r − r ′, t − t ′) =

ϑ (t − t ′) ⋅ e (2π )3 / 2 ∏j 3

−

[x j − x′j −v j (t −t ′ )]2 2σ 2j (t − t ′ )

⋅ e −δ (t −t ′ ) /σ j (t − t ′) (2.1.24)

where the gaussian standard deviations σ(t-t’) were defined as

σ j (t − t ′) = 2 K j (t − t ′) note difference between σj depending on (t-t’), and Kj multiplying (t-t’). Combining the results and considering the effect of the Heaviside function integrals’ limits, ultimately one has: t

ρ (r , t ) = ³ dt ′³ d 3 r ′ ⋅α (r ′, t ′) ⋅ G (r − r ′, t − t ′) ⋅ e −δ (t −t ′ ) −∞

∞

(2.1.25) with 3

G (r − r ′, t − t ′) = ∏ G j (x j − x′j , t − t ′) j

(2.1.26)

G j (r − r ′, t − t ′) =

1

2π ⋅ σ j (t − t ′)

⋅e

−

[x j − x′j −v j (t −t ′ )]2 2σ 2j (t −t ′ )

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FOUNDATIONS - SELECTED TOPICS

σ j (t − t ′) = 2 K j (t − t ′)

Equations (2.1.25,26) provide a solution to the advection-diffusion equation, in the form of the density ρ(r,t) of the quantity of interest at place r and time t, for a source α(r,t) of an arbitrary distribution in space, and time profile. A useful restriction on this result is obtained taking a point-source placed at xs, ys, H, and which starts releasing at time t = 0:

α (r ′, t ′) = Q(t ′) ⋅ ( x′ − xS ) ⋅ δ ( y − yS ) ⋅ [δ ( z′ − H ) + δ ( z + H )] (2.1.27)

Q(t ′) = 0 ⇐ t ′ ≤ 0 In Eqs.(2.1.27) it is implicitely assumed that the (virtual) source is placed at height H (m), and that a reflection takes place, rendered by a reflected source at –H (m). Introducing the source (2.1.27) into the solution (2.1.25,26), and noting that

xC (t , t ′) = xS + v x (t − t ′) (2.1.28)

yC (t , t ′) = y S + v y (t − t ′)

are the horizontal coordinates at time t, of centers of puffs released from the source at time t’, taking also v = ̣ v the velocity of the gravitational settling of the released pollutants, and making a distinction between a horizontal, isotropic diffusion and the vertical diffusion one obtains:

ρ (r , t ) =

t

1

dt ′

dt ′ ⋅ ⋅ Q(t ′) ⋅ e (2π ) ³ σ (t − t ′) ⋅ σ (t − t ′) 3/ 2

0

2 0

−δ (t −t ′ )

⋅

v

(2.1.29)

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81

Following a common practice, one generalizes the diffusion coefficients σh(t-t’) and σv(t-t’), substituting semi-empirical formulas for the original Eqs.(2.1.24). If, in addition, one represents now the source as a sum of discrete puffs

J = 1, 2, ... , INT(t ′), [s ]

Q(t ′) = ¦ Q j ⋅ δ (t ′ − J ), j

(2.1.30) then one has

ρ (r , t ) = ¦ ρ j (r , t ) = ¦ Q j ⋅ G (r − rj , t − J ) j

j

(2.1.31) with

[

G (r − r j , t − J ) =

1

(2π )3 / 2

] [

] [

]

­° x − x j (t ) 2 + y − y j (t ) 2 z − z j (t ) 2 ½° exp® − 2 ¾ 2σ 2j (t − t ′) 2σ v (t − J ) °¿ °¯ ⋅ σ h2 (t − J ) ⋅ σ v (t − J )

and r(t) = (x (t) , y (t) , z (t)) – the coordinates of the center of puff J at time t. While the solutions above cover satisfactorily the cases discussed in this book, a general solution of the advection-diffusion equation should comprise, beside the particular solution of the equation with source, the solution of the equation without source

L(r , t ) ⋅ ρ 0 (r , t ) = 0 (2.1.32) normally under the (initial) condition

ρ 0 (r ,0) = Ψ (R ) (2.1.33)

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Searching now ρ0 as a Fourier expansion

ρ 0 (r , t ) = ³ d 3k ⋅ ρ 0 (k , t ) ⋅ eik ⋅r ∞

(2.1.34) one can easily obtain the solution via the same Green function (2.1.24):

ρ 0 (r , t ) = ³ d 3r ′ ⋅ Ψ (r ′) ⋅ G (r − r ′, t ) (2.1.35) One can see that the sum of the solutions (2.1.29) and (2.1.35) would describe a polluting release in an already polluted environment. 2.1.2 Atmospheric transport in complex terrain Most of the atmospheric transport models would implicitly assume that the dynamics of the transported pollutant particles is tightly bound to the dynamics of the air flows. In contrast, ETH-NUKERISK would somehow relax the assumption on such a binding, and operate on a distinction between the motion of the air that carries polluting particles, and the motion of the airborne particles themselves. What makes the difference is particle’s different inertia and frictional properties. Not only is the fact well-known: it is also given proper consideration in at least two striking instances related to the context: (i) the contamination of the vegetation canopy, which recognizes an impaction phenomenon consisting in particle’s leaving the air path line near e.g. a leaf by virtue of centrifugal forces and heading straight onto leaf’s surface – which may stop the particle and take it out of the air flow and the jurisdiction of the respective continuity equation; and (ii) the CLB (Constant Level Baloons – ‘tetroons’) flight tracking, where it is recognizes that in a real atmosphere the vertical movement of the tetroon is not usually that of the surrounding air, thus various schemes being called to account for the differences. Combining these, the present model would take that an airborne solid particle is an entity different from both the particle in a vacuum and an air particle. Heated at source or subsequently, by solar irradiation, the solid particle may in turn heat the air in its close neighborhood inducing lift forces that would give the entity an apparent (efficient) density that may differ considerably from both the density of the solid material, and the air density. Intuitively, one also submits that the frictional properties of such ‘air-

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83

dressed’ solid particles would differ from those described by air’s GENERAL TRANSPORT EQUATION

ℑ=−

∂Q +S ∂t

______________________________________________________________________ CURRENTS

QUANTITIES

SOURCES

______________________________________________________________________

Q = ³ ρ ⋅ dV

ℑ = ³ i ⋅ dS

V

Σ

[i ] = [Q] / (s ⋅ m 2 )

S = ³ α ⋅ dV V

[α ] = [Q] / (s ⋅ m3 )

[ℑ] = [Q] / s

[ρ ] = [Q] / m3

[S ] = [Q] / s

______________________________________________________________________

∇i +

∂ρ =α ∂t

_______________________________________________________________________ MOMENTUM

ACTIVITY

_________________________

∂vi ∂v + ¦ v j i = ai ∂t ∂x j j

___________________________________

∂ρ ∂ρ ∂2ρ + ¦ vi − ¦ Ki 2 = α ∂t ∂xi ∂xi i i ∂vi

−

1

ρm

∂τ ¦ ∂x + (Ω × v ) ij

i

j

j

¦ ∂x i

i

=0

84

ai = − gδ i 3 −

FOUNDATIONS - SELECTED TOPICS

1

ρm

⋅

∂ρ − ∂xi

∂ρ m ∂ (ρ m vi ) = 0 + ∂t ∂xi

[ρ ] = Ci / m3 , [K i ] = m 2 / s

[ai ] = m / s 2 , [ρ m ] = kg / m3 viscosity, particle behavior being rather governed by the Stokesian concept

[ p] = Pa, [τ ji ] = Pa, [Ω] = s −1

[vi ] = m / s of drag. What the model attempts to describe are, therefore, flows of air-dressed 3 solid particles of an apparent density ρm (kg/m ), going with the air currents, but not always exactly as the air currents. In fact, one submits that in a flat and uniformly heated terrain particle flows would mainly follow the air flows, with the exception of their rise phase and small-turbulence fluctuations, whereas in any other, more complex, terrain the differences would pop up all along particle trajectories. On the other hand, since the leading factor is the air flow, it is natural to start inferring the particle equations of motion from the equations of motion of the air – that are essentially hydrodynamic in nature. The immediate consequence of the picture above is that particle flows are conserved as far as number of particles involved. A particle would follow an air path line at a given height above ground and distance from the upcoming obstacles as long as its inertia and friction would not require it to leave one path line for another. The latter may result in particle’s being stopped and fixed on the ground/obstacles, or being captured into hydrodynamic cavities or other large eddy systems of mechanical and/or thermal origin featuring the air circulation. Obviously such phenomena would determine over concentrations of particles at selected spots into the terrain – which is also a fact of life, thinking only of the snow heaps upfront and particularly in the wake downwind from obstacles in blizzards. In fact, the main thrust of the model is to heuristically provide for a mean to identify the places in the terrain that are prone to plume segments persistence and/or overconcentration through such effects as flow slowing-down, inversion, blocking, canyon squeezing, large eddies in front and/or in the wake of

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obstacles, forced impaction – including by rains etc. In turn, persistence and over-concentration are the key factors in sizing the contrasts in exposure/doses, time-integrated concentrations and deposition that the model is after, by virtue of the strategy described. According to the assumptions above one has taken as reference equation for the model the Navier-Stokes equations for the air as a standard viscous fluid:

∂V / ∂t + (V∇ )V = g − (1 / ρ m )∇p + νΔV + (1 / 3) ⋅ν ⋅ ∇(∇V ) (2.1.36)

∂ρ m / ∂t + ∇( ρ mV ) = 0 (2.1.37) with V(r(t),t) the Eulerian field, g – the (effective) gravity acceleration, ρm – the air density and ν - the air kinematic viscosity. Except for g that stands for the volume forces, all driving forces are contained in the pressure’s p(r(t),t) gradient field, while the frictional, dissipative forces are accounted for by equation’s viscosity-dependent terms. Heuristically, it is assumed now that the equations of motion of an ‘air – dressed’ solid particle will qualitatively copy the reference equation’s structure. It may read:

a = g − (1 / ρ m )∇Pw − (1 / ρ m )(Π D ∇Pt ) − F D w + (Coriolis...) (2.1.38) In Eq.(2.1.38), g preserves its meaning while ρm is now only a mass parameter with density dimensions. w is particle’s velocity. The frictional, dissipative contribution is parametrized via the 4th term – Stokesian in nature, with F a friction tensor in a scalar multiplication with w. A natural supposition is that F would reflect the quasi-geostrophic behavior of the atmosphere, in the sense of underlying some distinction between movements in a horizontal plane and the vertical movements. A ratio, gs, was introduced to this effect, between the vertical and horizontal components of F, while the shear was, for simplicity, scaled down to 0, so that the friction tensor would read:

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FOUNDATIONS - SELECTED TOPICS

§f ¨ F =¨0 ¨0 ©

0 f 0

0 · ¸ 0 ¸ g s ⋅ f ¸¹ (2.1.39)

Another assumption implicit above is that all true (non-inertial) driving forces acting upon the particle can be described by gradients of scalar fields that must have pressure dimensions. A distinction was made between a field Pw(r(t),t) accounting for the flat (horizontal) winds, and a field standing for origin of all terrain-sensitive movements of the particle, Pt(r(t),t). Gradients governing terrain-induced motions. Much of the model’s heuristics concentrate on the field Pt. To get a Pt reflective of terrain’s influence it was thought natural to have it depending on the relative altitude of the particle with respect to the terrain. Assume the terrain conceived as a solid surface T(u, v, z) = 0

(2.1.40)

or, alternatively, z = Z(u,v)

(2.1.41)

so that T(u, v, z) = z - Z(u,v)

(2.1.42)

is the relative altitude of the particle – sometimes known as the ‘generalized vertical coordinate’. One submits that the pressure field Pt may be the following function of T:

Pt (u , v, z ) = T (u , v, z ) ⋅ exp(− β ⋅ T (u , v, z )) + const (2.1.43) The way it was constructed, Pt would show a constant value at ground, and would exponentially decrease far off the ground. Strictly speaking, the gradient of Pt is

∇Pt = −(1 − βT ) ⋅ EXP(− βT ) ⋅ ∇Z (2.1.44)

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87

which would make perfect sense if Z would be an ordinary function, differentiable at least once. Yet this is not generally the case, for a complex terrain is an indeed complex reality showing more often than not discontinuities, both step-wise (fractures, buildings) and quasi-singular (stacks, poles, trees). An obvious precaution would therefore dictate to think Z in terms of a generalized function, or distribution. Mathematically, this boils down to see it as a possible mix of a true function with some parametric representations of the Heaviside and Dirac distributions, and also take the partial derivatives involved in the gradient of Z in a sense consistent with whatever choice made. To highlight this, the symbol δ was used in the sequel for differentiation, instead of the common d so that, for instance, the gradient of Pt in projection on the axes u, v, z would read:

(∇Pt ) |u = −(1 − βT ) ⋅ exp(− βT ) ⋅ (δZ / δu ), (2.1.45)

(∇Pt ) |v = −(1 − βT ) ⋅ exp(− βT ) ⋅ (δZ / δv ), (∇Pt ) |z = −(1 − βT ) ⋅ exp(− βT )

Equations above indicate that particle’s motions would respond to terrain’s shape via terrain’s however tortuous variations in slope, which holds a promise of accounting for the mechanical turbulence in particle flows. Wind-accounting gradients. As to the field generating the winds, it can be inferred by taking that it is structured so as to determine, in an uniformly heated terrain, at some stabilized height Hb above ground reached by the particle after its rise phase is consummated, the wind velocity that is prescribed by any available wind power laws. In a system of axes holding u to the South, v to the East and z upwards the latter assumption reads:

0 = −(1 / ρ )(∂Pw / ∂u ) | H b − f ⋅ w10 ⋅ (H / 10 )

p (c)

⋅ cos α (2.1.46)

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FOUNDATIONS - SELECTED TOPICS

0 = −(1 / ρ )(∂Pw / ∂v ) | H b − f ⋅ w10 ⋅ (H / 10)

p (c)

⋅ sin α

where w10 is the wind speed at 10 meters height and p(c) is the power law’s exponent that depends on the atmospheric stability. Up to a constant, the wind pressure field reads:

Pw (r (t ), t ) = ρ ⋅ f ⋅ (T (u, v, z ) / 10 )

p(c)

(w10 D r ), (2.1.47)

w = iu ⋅ w10 ⋅ cos α + iv ⋅ w10 ⋅ sin α + iz ⋅ 0, and

r (t ) = iu ⋅ u (t ) + iv ⋅ v(t ) + iz ⋅ z (t ), iu, iv, iz – unit vectors of axes The next step with model’s heuristics is to have the tensor Π that couples terrain-induced pressure gradients to particle accelerations absorbing, and thereby controlling, several other aspects of physical relevance. Parameterizing a heated terrain. By arguments similar to those that have guided the choice of structure for the friction tensor F , tensor Π will show differences between the horizontal and the vertical components. Pre-empting a deeper analysis, the same ratio, gs, may be used to mark this difference. Moreover, a necessary distinction will be made between a background, insolation-independent, and an essentially variable, insolation-dependent contribution. In addition, inversion- and small-scale turbulence – related features may be incorporated. With these combined, Π will read:

0 0 §(Πb + Πs ) ⋅ erf(η( z − Hi )) · ¨ ¸ (Πb + Πs )⋅ erf(η(z − Hi )) Π=¨ 0 0 ¸ ¨ 0 0 gs (Πb + Πs )¸¹ © (2.1.48) Πb is the background gradient that, in conjunction with parameter β above will get the emitted particle stabilized at height Hi over a non-

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insolated terrain, while the additional Πs would carry the Sun’s contribution. The error function affecting tensor’s horizontal components

erf (η ( z − H i )) = 2 / π ⋅

η (2− H i )

³ exp(− x )⋅ dx 2

0

(2.1.49) attempts to materializing an inversion layer – if any – , its effects being to reverse motion as the particle passes from below the level Hi to above this level. The intensity of this influence varies across a layer with indefinite boundaries, the ‘thickness’ of which would depend on the parameter η, to the extent that large η would give erf a behavior close to the sign-function SGN(η(z-Hi)), i.e. equal to -1 if z < Hi , 0 if z = Hi , and +1 if z > Hi . In this version, the model would take that the inversion lid would show a daily oscillation, from the ground level at midnight up to a maximum at the local noon, Him:

H i (t ) = H im ⋅ (1 − cos((t − t midnight )π / 12)) / 2 (2.1.50) Better assumptions are of course conceivable. A simple, if rough, manner to parameterize the solar contribution to the pressure gradients is to (i) scale down to zero all radiative effects, and (ii) assume ΠS to be proportional to the cosine of the angle that (parallel) solar rays make, at each time of the day and each day of the year, cloud cover and geographic coordinates considered, with the normal to the terrain’s surface. Within the terms already established, the normal to the terrain’s surface makes a vector field n(u,v), the projections of which are given by the appropriate Monge parameters:

(

2

(

2

)

nu = −(δZ / δu ) / (δZ / δu ) + (δZ / δv ) + 1 ,

2

)

nv = −(δZ / δv ) / (δZ / δu ) + (δZ / δv ) + 1 ,

(

2

2

1/ 2

)

nZ = 1 / (δZ / δu ) + (δZ / δv ) + 1 2

1/ 2

1/ 2

As to the Sun’s direction ns , it is given in the same axes by:

(2.1.51)

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FOUNDATIONS - SELECTED TOPICS

nsu = cos d ⋅ cos ϕ ⋅ sin λ − sin d ⋅ cos λ (2.1.52)

nsv = cos d ⋅ sin ϕ nsz = cos d ⋅ cos ϕ ⋅ cos λ − sin d ⋅ sin λ with d the solar declination at the time of observation, λ - the geographic latitude, and ϕ - the hour angle relating to the geographic longitude of the site. With these, the solar contribution to the pressure gradient is

Π S = S ⋅ (n D ns ) = S ⋅ (nu ⋅ nsu + nv ⋅ nsv + nz ⋅ nsz ) (2.1.53) Factor S would further filter this: it may vary from S = 1 on a sunny daytime to 0 at night or on a cloudy daytime weather. Also sensitive to terrain’s shape via n(u,v), the insolation contribution holds a promise to modulate the thermal turbulence of particle flows. Small-scale turbulence may induce erratic fluctuations in particle paths either uniformly or selectively, i.e. only below/above the inversion level (looping, lofting, fumigation, coning, fanning effects). A simple parameterization for this effect is to assume that the concurrent gradient factors Πb + Πs are modulated over a 24-hour day in a way that (i) no smallscale turbulence manifests from dusk to dawn, (ii) turbulence sets up at dawn and ceases at dusk with a maximal amplitude mid-time, and (iii) actual instantaneous deviations from the ideal path vary at random between the limits thus set. The modulating factor may in addition be filtered to vanish either above or below the inversion layer H. Some sensitivity to the stability category may also be introduced. Summing these up, the gradient factor may be written as:

(

Π b + Π s Ÿ Π = (Π b + Π s ) 1 + M (1 − 2 RND ) / c R

)

(2.1.54)

where 2 M = D((1 + erf(ε(Hi – z)) + exp(-ε (Hi – z)))/2,

(2.1.55)

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91

D = sin((t – tdawn)π/(tdusk – tdawn)) if tdawn < t < tdusk, and D=0

otherwise (2.1.56)

§1 if small turbulence above inversion level ¨ ε = ¨ 0 if small turbulence throughout ¨ - 1 if small turbulence below inversion layer © (2.1.57) RND - a random fraction between 0 and 1, as obtainable via computer’s random-numbers generator, and c – a stability factor, with c = 1 ... 6 for the stability categories A, B, C, D, E, F, and k an incidental exponent. Needless to say that, like the inversion, the small-scale turbulence can be parameterized using other appropriate functions, and/or modeled under more accurate assumptions. In actual fact, logical functions are sometimes used in the codes to simulate the analytical functions above. Finally, a set of assumptions was in order about how to treat the variations d/du, d/dv in taking the gradients of the pressure fields. Terrain as signal: sampling, smoothing, filtering. While an ideally-smooth terrain – one that may be represented by a true function such as a (3-D) Gaussian hill with moderate slopes – would not raise any particular query as to the differentiation by any common numerical method, attempts to apply the model to e.g. a parallelepiped building featuring vertical walls and sharp edges may produce odd results unless the differentiation is more critically examined, and the procedures adjusted. The difficulty comes with the fact that, in spite of the relative independence that particles may show with respect to the air flows – as emphasized in the model, the pattern of the particle motions is still hydrodynamic in nature, rather than mechanical as some equations would imply. In other words, particle dynamics is not exclusively governed by its local position, but also by the shape (differences in height and orientation) of the surrounding terrain within a certain distance from the particle that would depend on terrain’s rugosity and fluid’s dynamical properties (mass, friction). It was found that one convenient way to conceptualize this is to think the relation of particle to terrain in terms of a signal-detector relationship. This angle of approach has a tendency to recurrently occur in a variety of contexts

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where, however, standard tools of signal theory such as the Fourier analysis, convolution and filtering apply to the kinematic and dynamic variables that appear in the physical equations, rather than to more distant factors such as the terrain. The other way is to see the terrain as a signal Z(u(t),v(t)), and the flying particle as a detector, sensitive to the signal and its (generalized) derivatives as the particle travels across terrain. The signal Z may naturally accommodate continuous portions as well as stepwise jumps and deltoid singularities, as discussed in the preceding sections. On the other hand, the particle would ‘read’ the signal in a manner characteristic for all detectors, i.e. delivering an interpretation of Z that would typically reflect (i) a sampling, (ii) a smoothing and (iii) a filtering of the original signal. The present version of the model emphasizes the importance of a proper choice of detector’s ‘window’. The following arguments were found of prime consequence: - Particle behavior depends essentially on how much of the signal (surrounding terrain) is ‘felt’ (read) by the detecting particle at each flight moment. Intuitively, in a highly viscous environment upcoming obstacles, are ‘felt’ much earlier than in an environment of low viscosity, and the same should be true for sharp, high obstacles in comparison with the smooth, lower ones. - Terrain gridding should not be of essence in this context, for one may encounter cases when the terrain would be rigorously describable via true functions, either algebraic (a bare gaussian hill) or logical (e.g. a rectangular building on a flat terrain), that is – without necessarily a recourse to gridding. - Time-chopping would rather pertain to an accurate solving of the equations of motion (3). In principle, time-chopping should be as fine as feasible in terms of tolerable computer time, for otherwise numerical spurious effects on particle paths may occur, beyond those that are actually induced by particle inertia (particle’s leaving one air path line for another). In comparison, controlling detector’s (flying particle’s) reading (differentiation) window has more to do with the very setting of the problem. In summary: (i) The terrain is to be sampled according to a chosen grid, in cells commensurable with actual terrain rugosity (frequency, amplitude and slope of height deviations from reference levels). (ii) Terrain’s signal Z should be a smoothed interpretation of the sampling result, to be obtained by an appropriate interpolation. (iii) The Physics of the flying particle will be ascribed to the detector’s range (flying window), expressed via a characteristic length in the definition of the variations δ/δu, δ/δv that operate in the equations above, the characteristic length being in principle independent on the terrain gridding.

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Explicitly, if at a given moment t the particle is located at coordinates u, v, z, the immediate causes of particle’s changing position will be – apart from the flat winds, the differences (δZ/δu) = (Z(u + L,v) – Z(u – L,v))/(2L) (δZ/δv) = (Z(u,v + L) – Z(u,v – L))/(2L)

(2.1.58)

with L the characteristic length that, according to the numerical experiments done, may range from 1 m up to several tens of meters or more. Typically, it was found that in a hilly terrain of low-to-moderate slopes L may be lower, while the simulation of particle flows obstructed by e.g. a parallellipipedic building, or emerging from high stacks would rather require characteristic lengths comparable with, or higher than obstacle’s sizes. The evaluation of signal levels Z above was done by a four-point bivariate interpolation over the chosen, quadratic terrain grid of a step h. One has, for any given point (u,v):

Z (u , v ) = Z (i + 1, j + 1) ⋅ ru ⋅ rv + Z (i, j + 1) ⋅ ru ⋅ (1 − rv ) + + Z (i + 1, j ) ⋅ rv ⋅ (1 − ru ) + Z (i, j )(ru ⋅ rv − ru − rv + 1),

(2.1.59)

with i = INT(v/h), j = INT(u/h), (INT for lower-rounded integers), rv = v/h – i, ru = u/h – j. Numerical experiments have so far indicated that other, more sophisticated interpolation procedures – including the one based on the ideal signal-sampling functions of the form sin(kx)/x would not necessarily give better results in comparison with those yielded by the interpolation (24). The latter gives true heights in the grid knots and a minimal area-coverage inbetween, so that good approximations of terrain’s surface can be obtained without excessively stressing the need for small-cell grids – which in turn may save computer memory for vectorization. It is also noted that other solutions to evaluate the variations (d/du), (d/dv) were tested, patterned after alternative standard procedures to numerically express partial derivatives – with, insofar, only inconclusive improvements. However, the temptation to refine detector’s filter (the ‘flying’ differentiation window) to give it a better coverage of the terrain’s variations around the instantaneous position of the particle remains, in principle, justifiable and worth further trials.

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FOUNDATIONS - SELECTED TOPICS

Note that the particle acceleration in the left-hand side of Eqs.above is taken in a mechanical sense, no distinction being made between a lagrangian and an eulerian variation of velocity. This somehow sweeping assumption may find, in fact, a correspondence in the standard scaling of mesoscale equations, where the advective parts (VL)V are sometimes neglected. Also the Coriolis terms were not taken into account in the current version of the model, designed for short-to-medium space scales only. Taking at t = 0 the particle coordinates u, v, z at source, as well as the appropriate particle velocities w =0, w =0, w = 0 at the initial moment, Eqs.above detailed as explained will make a Cauchy problem that one can solve e.g. iteratively. Chopping the time in intervals of a duration t a simple iteration is Taylor’s, the first step of which gives: 2

u(t + τ) = u(t) + τ⋅wu(t) + (τ /2)⋅au(t) 2 v(t + τ) = v(t) + τ⋅wv(t) + (τ /2)⋅av(t) 2 z(t + τ) = z(t) + τ⋅wz(t) + (τ /2)⋅az(t), wu(t + τ) = wu(t) + τ⋅αu(t) wv(t + τ) = wv(t) + τ⋅av(t) wz(t + τ) = wz(t) + τ⋅az(t),

(2.1.60) (2.1.61)

with au, av, az, given by Eqs. (2.1.38). In the final analysis the flow model can be summarized as in the boxed outline below. Its basic control parameters are: SOURCE-RELATED: - Geographic coordinates: latitude, longitude; - Time of (first) emission: month, date, hour, minute; - Height of emission above terrain; METEO-RELATED: Stability category (A ... F) – affecting vertical wind profiles and intensity of small-scale turbulence; - Wind: speed (m/s) at 10m height, direction (degrees from N by E), ranges of random, gaussian-distributed fluctuations in direction and speed, or a prescribed history for these quantities; - Assumed maximal height of inversion layer at mid-day; - Assumed plume rises at midnight of the day, and at noon; -

MODEL-SPECIFIC: - Reference gradient coefficient Πb, and barometric exponent β – to determine plume ascension up to the observed stabilized height; commonly

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Πb = 1.4 Pa/m, β = 0.001 (1/m); both modulated by corrections from night to daylight regime, so as the plume rise vary between the prescribed limits at midnight and noon; - Solar factor, S, varying from 1 for a clear sky through 0 for full overcast; - Inversion layer exponent, η = 1 ... 0.85 m ; - Reference friction coefficient (horizontal) f = 0.1 (1/s), adjustable for accounting for oscillating vs. damped flows; - Geostrophic ratio gs = 10; - Reference mass factor r = 1.3 kg/c.m., modulated within a gaussian distribution if so deemed; - The terrain-and-particle related characteristic length L = 1...50 or more, lower in smooth terrain and higher in urban areas. FLOW MODEL OUTLINE

- Reference mass factor r = 1.3 kg/c.m., modulated within a gaussian distribution if so deemed; - The terrain-and-particle related characteristic length L = 1...50 or more, lower in smooth terrain and higher in urban areas. A routine was designed under rough assumptions (a straightforward Kepler problem for Earth’s yearly motions), to give Sun’s declination as

96

FOUNDATIONS - SELECTED TOPICS

well as noon/midnight and dawn/dusk times (true GMT and local), on a month-date-hour and fractions basis. Apsides were taken at Rmax = 1.52E+08 and Rmin = 1.47E+08 km, respectively, resulting in an eccentricity e = (Rmax - Rmin)/(Rmax + Rmin), an ex-centric anomaly (in radians) given by u – e⋅SIN u = 2⋅π(t0 – t)/8760, (t in hours) t0 = 8760(e⋅SIN u0 – u0 )/2π u = ASN((1 – 2⋅Rmin/(Rmax + Rmin))/e), a true anomaly

θ = 2⋅ATN(SQR((1 + e)/(1 – e))TAN(u/2)) and a declination d = – (23.45⋅π/180)⋅COS(θ + 11⋅π/180) o

(2.1.62) o

plying maxima at +23 27’ and an apsidal-to-solstice axes angle of 11 . The overall compactness of the model made it possible to have all timedependent variables, including declination, refreshed at each time step, while still securing a tolerable computer pace. As already indicated in section 2, no particle is lost from the mass balance once the particle is generated. Usually the model would monitor each particle as long as it falls within the view field of the respective geographical map (that may be placed at will in a 3D-perspective) provided by the codes, a proper scaling taking care of the field’s coverage of the territory of interest. On the other hand, the issue on how energy and momentum are conserved in the system as described deserves a note in its own right. In this respect two aspects are of essence: the fact that (i) particles permanently exchange momentum and energy with the pressure gradient fields, that in turn are mainly supplied by the Sun, and (ii) the system is dissipative, particles gaining and loosing kinetic energy not only on the account of changing height, but also on friction. It should be obvious by now that, in its own heuristic way, the model reflects several aspects that standard hydrodynamic models would describe via characteristic numbers such as Reynolds’ and Froude’s. Though it was recognized that a more transparent linking of model’s control parameters to such numbers may help its acceptance, no real attempt at that was yet made. Another remark is that the notion of substituting a heuristic construction for the exact (hydrodynamic) equations may recall one characteristic style of approach – the Multilayer Perceptron (MLP) of the neural networks. Both

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the pressure and drag matrices in the model would indeed function as sort of MLP ‘weight matrices’, whereas the various sigmoid functions governing inversion etc. may recall MLP’s non-linear ‘activation functions’. Choosing the right parameters in these to fit either a neat Navier-Stokes solution or an experimentally-observed flow pattern would amount to ‘training’ the system, and various ways and means are conceivable to have such a process automated. An MLP-based parallel-processing of the motions of a collection of particles/puffs would certainly make an attractive perspective. TEXTBOOK PARAMETERS IN ADVECTION-DIFFUSION MODELS 1. The Karlsruhe-Juelich gaussian standard deviations:

σ h = ph ⋅ x q

h

x and σh in meters

σ v = pv ⋅ x q

v

x and σv in meters

_________________________________________________________________ Category ph qh pv qv _________________________________________________________________ 50 m height -------------A B C D E F

1.503 .876 .659 .640 .801 1.294

.833 .823 .807 .784 .754 .718

.151 .127 .165 .215 .264 .241

1.219 1.108 .996 .885 .774 .662

100 m height -------------A B C D E

.179 .324 .466 .504 .411

1.296 1.025 .866 .818 .882

.051 .070 .137 .265 .487

1.317 1.151 .958 .818 .652

98

FOUNDATIONS - SELECTED TOPICS

F 180 m height --------------A B C D E F

.253

1.057

.717

.486

.671 .415 .232 .208 .245 .671

.903 .903 .903 .903 .903 .903

.025 .033 .104 .307 .546 .484

1.500 1.320 .997 .734 .557 .500

One interpolates between categories and heights, and extrapolates head segment down to 0m, and tail segment up to 2000m – for x < 200 km.

2. Doury’s Dispersion Coefficients.

σh = (Ah · t)kh,

t in seconds, σh in meters

σȞ = (AȞ · t)kȞ,

t in seconds, σv in meters ___________________________________________________________

t(s) Ah kh Av kv ___________________________________________________________ __ Class 1 (strong diffusion) 0 4.05E-01 2.4E+02 1.35E-01 3.28E+03 1.35E-01 9.70E+04 4.63E-01 5.08E+05 6.50 1.30E+06 2.00E+05

.859 1.130 1.130 1.000 .824 .500

.42 1.00 20.00 20.00 20.00 20.00

.814 .685 .500 .500 .500 .500

Class 2 (weak diffusion) 0 4.05E-01 2.4E+02 1.35E-01 3.28E+03 1.35E-01 9.70E+04 4.63E-01 5.08E+05 6.50 1.30E+06 2.00E+05

.859 1.130 1.130 1.000 .824 .500

.20 .20 .20 .20 .20 .20

.500 .500 .500 .500 .500 .500

DISASTER RISK AND VULNERABILITY MANAGEMENT

99

3. Wind Power Law Exponents. w(z) = w10 · (z/10)Pw ,

for z ≤ 200 m

w(z) = w(200),

for z > 200 m

________________________________ Category Pw Inversion lid (m) ________________________________ A

.07

1600

B

.13

1200

C D E F

.21 .34 .44 .44

800 600 300 200

2.2

Physical background of chemical source term models

2.2.1 The Critical Parameters Recalling the 3rd degree in volume V van der Waals equation

V 3 − (RT / p + b )V 2 + (a / p ) ⋅ V − (ab ) / p = 0 (2.2.1) the critical state of a substance corresponds to a triple, real root of this equation. In such a case, Viete’s formulas give:

100

FOUNDATIONS - SELECTED TOPICS

3 ⋅Vc = RTc / pc + b (2.2.2) 2 c

3 ⋅ V = a / pc Vc3 = ab / pc With Vc , pc , Tc – the critical parameters of the substance. Knowledge of any two of these is sufficient to determine van der Waals parameters a and b. 2.2.2 The Molar Volumes V1 , V3. Below the critical temperature Tc and in a certain range of temperatures, Eq.(2.1.1) has three distinct real solutions. If V1 < V2 < V3 are the said solutions, then V1 is known as the molar volume of the substance in a normally compressed liquid state, V3 is the molar volume of the substance in fully gaseous state, whereas V2 does not have a physical correspondence. To determine V1 and V3 module SOURCE.WRK in ETH-CHEMRISK makes use of a standard algebraic procedure based on Cartan’s formulas. Writing Eq.(2.2.1) as

V 3 + a1V 2 + a2V + a3 = 0 (2.2.3) with a1 = -(RT/p + b),

a2 = a/p,

a3 = -ab/p,

the change of variable V = X + c,

c = -a1 /3

(2.2.4)

brings Eq.(2.1.3) to the form 3

X + pX + q = 0

(2.2.5)

with 2

p = 3⋅c + 2⋅a1 c + a2 3 2 q = c + a1 c + a2 c + a3 = 0

(2.2.6)

DISASTER RISK AND VULNERABILITY MANAGEMENT

101

Table A.1 gives a systematics of the the possible solutions of Eq.(2.2.5). 2.2.3 Maxwell’s Rule for Andrews Isotherms Let it be reminded that the position on the pressure scale of the flat, horizontal segment of the experimentally obtained Andrews isotherms can be understood following the observation that a thermodynamic cycle closing upon the marks 1-2-3-4-2-5-1 on the van der Waals isotherm in Illustration 178 features a nil variation of entropy (Thermodynamics’ 2nd Law). Accordingly, one has

³ dS = ³

[

]

dQ 1 = ⋅ ³ dV + ³ ( p − pv )dV = 0 T T

or, furthermore, V3

³ ( p − p )dV = 0 v

V1

(2.2.7) since the internal energy integral over the cycle is obviously nil. Equation (2.2.7) is known as Maxwell’s rule. Using the van der Waals expression of the pressure p(V) = RT/(V – b) – a/V

2

(2.2.8)

the Maxwell integral in Eq.(2.2.7) yields the relation:

RT ⋅ ln

V3 − b + a(1 / V3 − 1 / V1 ) − pv (V3 − V1 ) = 0 V1 − b (2.2.9)

that was used with module SOURCE.WRK of ETH-CHEMRISK. 2.2.4 Shapes, volumes and heights As indicated, the outflow regime for a chemical escaping from a vessel

102

FOUNDATIONS - SELECTED TOPICS

depends on the relative position of the evacuation hole and the level of the liquid phase in the vessel – if any. Five situations have been selected in practice. The respective relations of liquid heights to liquid volumes in the vessels are summarized in Table A.2. 2.2.5 Adiabatic gas outflows A gas outflow from a vessel may be seen as being generally governed by the following equations:

1 1 1 ∂v / ∂t + ⋅ ∇v 2 − v × (∇ × v ) = ⋅ f + ⋅ σ 2 ρ ρ (2.2.10) γ

pV = K ⋅ e

s Cv

(2.2.11) Eq.(2.2.10) is the momentum equation for the fluid of velocity v, under volume forces of density f and surface tensions of density s (vector), while Eq.(2.2.11) is the equation of the thermodynamic state of the fluid, with γ = Cp/Cv the ratio of molar heat capacities (isentropic ratio), and s the entropy density. Assuming a permanent, irotational, force-free, and adiabatic motion of an ideal gas, the foregoing equations are brought, respectively, to the form:

1 2 dp v +³ =0 2 ρ (2.2.12) γ

p / ρ = const. where the integral in Eq.(2.2.12) is taken along a flow line starting invessel and ending outside. Cartan solutions for molar volumes. 3

X + pX + q = 0 (for notations, v. Eqs. (2.1.3 ... 6) V1 and V3 taken from among X1, X2, X3 so that V1 ≤ V3 Case

Solutions

DISASTER RISK AND VULNERABILITY MANAGEMENT

103

____________________________________________________ 1. q = 0, p = 0 X1 = X2 = X3 = c 2. q = 0, p > 0

X1 = c, X2 = X3- complex

3. q = 0, p < 0

X1 = c, X2 = c + (-p)1/2 X3 = c – (-p)1/2

4. q 0, p = 0

X1 = c + (-q)

5. p 0, q 0 5.1. p >0 d = -(q2/4 + p3/27) < 0 5.2. p < 0 AND 2 3 d = -(q /4 + p /27) = 0 5.3. p < 0 AND 2 3 d = -(q /4 + p /27)>0

1/3

, X2 = X3 - complex

1/2 1/3

α = [-q/2 + (-d) ] 1/2 1/3 β = [-q/2 – (-d) ] * X1 = α + β, X2 = X3 - complex 1/3 3 1/2 ρ = (-p /27) , R = ρ X1 = c + 2R X2 = X3 = c – R ρ = (-p3/27)1/2, θ = ATN(-2/q(d)1/2) 1/3 R = (ρ) cos(θ /3), 1/3 sin(θ /3), I = (ρ) X1 = c + 2R, 1/3 X2 = c – R – 3 I, 1/3 X3 = c – R + 3 I.

where the integral in Eq.(2.2.12) is taken along a flow line starting invessel and ending outside. Using Eq.(2.2.12) and remembering the sound velocity in the fluid

c = γp / ρ = γRT / μ , (p – the pressure, ρ – the density, T – the absolute temperature, μ – the molar mass, and R – the ideal gas constant), Eq.(2.2.11) can be transformed into either of the following:

1 2 c02 ª§ p · «¨ ¸ v + γ − 1 «¨© p0 ¸¹ 2 ¬

(γ −1) / γ

º − 1» = 0 »¼ (2.2.13)

104

FOUNDATIONS - SELECTED TOPICS

(γ −1) º 1 2 c02 ª§ ρ · «¨¨ ¸¸ v + − 1» = 0 γ − 1 «© ρ 0 ¹ 2 »¼ ¬

(2.2.13’) where

c0 = γp0 / ρ 0 = γRT0 / μ is the sound velocity in the initial state of the fluid (the in-vessel end of the flow line) featuring the parameters p0, ρ0, T0, and v = 0. Alternatively, one has:

§ γ −1 v2 · c 2 = c02 ¨¨1 − ⋅ ¸ 2 c02 ¸¹ ©

§

ρ 2 = ρ 02 ¨¨1 − ©

1 / (γ −1)

(2.2.14)

γ −1 v · 2

2

⋅

¸ c02 ¸¹ (2.2.14’)

§ γ −1 v2 · p = p ¨¨1 − ⋅ ¸ 2 c02 ¸¹ © 2

γ / (γ −1)

2 0

(2.2.14”) Liquid volumes and heights in vessels of different shapes/positions ___________________________________________________________ Tank Liquid volume – to – height relation ___________________________________________________________

DISASTER RISK AND VULNERABILITY MANAGEMENT

105

CYLINDER, VERTICAL V(h) = πR2h,

0≤h≤L

SPHERE

­ 2§ h· °πh ¨ R − 3 ¸, ° © ¹ V (h ) = ® ° 4π R 3 − π (2 R − h )2 §¨ R − 2 R − h ·¸, °¯ 3 3 ¹ ©

0≤h≤R R ≤ h ≤ 2R

CYLINDER, HORIZONTAL

­ ª º ° « » 2 1 ° LR 2 «§¨ h − 1·¸ 1 − §¨ h − 1·¸ + ATNC » − 1 2 ° «© R ¹ » ©R ¹ §h · ° « » ¨ − 1¸ ©R ¹ ° ¬« ¼» ° 0≤h≤R V (h ) = ® ° ª º ° « » 2 ° 2 1 § h· § h· « − 1» °LR π − ¨1 − ¸ 1 − ¨1 − ¸ − ATNC 2 « » R R © ¹ © ¹ § h· ° 1 − « » ¨ ¸ ° «¬ »¼ © R¹ ¯ R ≤ h ≤ 2R

106

FOUNDATIONS - SELECTED TOPICS

HEMISPHERE – TIPPED CYLINDER, HORIZONTAL

­ 2§ h· °πh ¨ R − 3 ¸ + ¹ ° © ° º ª ° » « 2 1 §h · ° 2 «§ h · − 1» 2 °LR «¨© R − 1¸¹ 1 − ¨© R − 1¸¹ + ATNC h » · § ° 1 − » « ¸ ¨ ° ©R ¹ ¼» ¬« ° V (h ) = ® 0≤h≤R ° 4π 2R − h · ° R 3 − π (2 R − h )2 §¨ R − ¸+ 3 ¹ ° 3 © ° ª º ° « » 2 ° 2 1 § h· § h· « − 1» °LR π − ¨1 − ¸ 1 − ¨1 − ¸ − ATNC 2 « » R R ¹ © ¹ © ° § h· − 1 « » ¸ ¨ ° «¬ »¼ © R¹ ¯ R ≤ h ≤ 2R HEMISPHERE – TIPPED CYLINDER VERTICAL

­ 2§ h· 0≤h≤R °πh ¨ R − ¸, 3¹ ° © ° 2π V (h ) = ® R 3 + πR 2 (h − R ), R ≤h ≤R+L 3 ° ° 2π 3 h−L−R· 2§ 2 ¸¸ ° R + πR L + π (h − 1 − R ) ¨¨ R − © ¹ ¯ 3 R + L ≤ h ≤ 2R + L

DISASTER RISK AND VULNERABILITY MANAGEMENT

107

1. A gas motion is said sonic, or critical, or chocked, if it evolves at a velocity v equaling the sound velocity c, in the respective conditions (p, T). The critical velocity, vcr , of the gas is obtained from Eq.(2.2.14) for v = c. One has:

vcr = c = c0 2 / (γ + 1) (2.2.15) to which the following critical pressure and critical density correspond (not to be mistaken for the critical pressure and density of the theory of phase transitions, also evoked in the context):

ρ = ρ0 [2/(γ + 1)1/ (γ-1)

(2.2.16)

p = p0 [2/(γ + 1)γ /(γ -1)

(2.2.16’)

In a chocked outflow the fluid’s mass rate, expressed via the mass current Jcr = rcr ⋅ vcr, is Q = - dm/dτ = Jcr A

(2.2.17)

with A the area of the exit cross section of the out flowing jet. Using in Eq.(2.1.17) the results (2.1.15,16) one gets

μγ § 2 · ¸ Q = − dm / dτ = − Ap ⋅¨ RT ¨© γ + 1 ¸¹

(γ +1) / (γ −1)

(2.2.18) or, since the process is assumed to be adiabatic, i.e. T = T0 (p/p0)(γ-1)/γ

(2.2.19)

one obtains for the chocked outflow rate the equation:

§ p· A Q = − dm / dτ = −γ ⋅ p ⋅ ¨¨ ¸¸ c0 © p0 ¹

γ −1 2γ

§ 2 · ¨¨ ¸¸ © γ +1¹

(γ +1) / (γ −1)

(2.2.20)

108

FOUNDATIONS - SELECTED TOPICS

that was used with the model adopted in code module SOURCE.WRK. If (p, T’, n) and (p - dp, T”, ν - dν) are two successive states of the fluid in a vessel of volume V0, then the following equations hold:

pV0 = νRT ′ (Clausius – Clapeyron)

(2.2.21)

( p − dp )V0 = (ν − dν )RT ′′ (Clausius – Clapeyron)

p − dp § T ′′ · =¨ ¸ p © T′ ¹

(2.2.21’)

γ (γ −1)

(adiabatic flow)

(2.2.21”)

By dividing Eqs.(21’) and (21) to each other, and knowing that fluid mass m can be written as m = νμ, one obtains 1− dν/ν = 1− dm/m = (1− dp/p)(T’/T”)

(2.2.22)

Since, on the other hand, Eq.(11”) gives T” / T’ = (1− dp/p)

(γ−1)/γ

(2.2.23)

then, in the 1st order of dp/p the result (12) reads:

1 − dm / m = (1 − dp / p )

1/ γ

1 dp ≅ 1− ⋅ γ p (2.2.24)

that is

dm =

1

γ

⋅m⋅

dp p (2.2.25)

Using now pV0 = (m/μ)RT’ T’/T0 = (p/p0)(γ -1)/γ

(Clausius – Clapeyron) (adiabatic flow)

DISASTER RISK AND VULNERABILITY MANAGEMENT

109

one brings Eq.(15) to the form

V § p· dm = 02 ¨¨ ¸¸ c0 © p0 ¹

(γ −1) / γ

dp (2.2.26)

Back now to Eq.(2.2.18), one may write dτ = − dm/Q which, after some algebra, reads

∇i + ∂ρ / ∂t = α (2.2.27) Eq.(2.2.27) plus the initial condition p(t)|t = 0 = 0 is the differential equation of the choked gas outflow. It can readily be integrated, to give

p (t ) =

p0

ª «1 + Ac0 ⋅ γ − 1 V0 2γ « ¬

§ 2 · ¸¸ ¨¨ © γ +1¹

(γ +1) / (γ −1)

º ⋅t» » ¼

2γ / (γ −1)

(2.2.28) with .

c0 = γRT0 / μ The choked outflow regime comes to an end as the pressure conditions in vessel are such that the respective critical pressure is diminished down to the ambient pressure. Assuming this happening at a time τ1, the duration of the choked phase is obtained from

110

§ 2 · ¸¸ p(τ 1 )¨¨ © γ +1¹

FOUNDATIONS - SELECTED TOPICS γ / (γ −1)

= pa , (2.2.29)

where pa is the ambient pressure. Using the result (2.2.18) taken at time τ1, from Eq.(2.2.19) one gets

V 2 § γ +1· τ1 = 0 ⋅ ⋅ ¨ ¸ Ac0 γ − 1 © 2 ¹

(γ +1) / (γ −1) ª

« « ¬

§ p0 · ¨¨ ¸¸ © pa ¹

(γ −1) / γ

º 2 ⋅ − 1» γ +1 » ¼ (2.2.30)

which is another result reproduced in the main text and used with the codes. 2. A subsonic, or subcritical, outflow may now continue, from time t on, starting with a pressure

§ γ +1· p (τ 1 ) = pa ¨ ¸ © 2 ¹

γ (γ −1)

(2.2.31) and ending, if left by itself, when the ever decreasing vessel pressure equals the ambient pressure p. Its flow rate is

Q = − dm / dτ = JA = ρ Av A (2.2.32) Using the result (2.1.13) which, being valid along a flow line starting at initial pressure p0 = p and ending at the ambient pressure pa reads (γ −1) / γ º 2 2 ª § pa · v = c «1 − ¨¨ ¸¸ » γ − 1 «¬ © p ¹ »¼ 2

(2.2.33) with

DISASTER RISK AND VULNERABILITY MANAGEMENT

c = γRT / μ = γR / μ ⋅ T0 ( p / p0 )

(γ −1) / γ

= c0

111

( p / p0 )(γ −1)/ γ (2.2.34)

(the adiabatic equation employed again), one gets

v = c0

§ pa · ¨¨ ¸¸ © p0 ¹

(γ −1) / γ

⋅

§p · 1 − ¨¨ a ¸¸ © p¹

(γ −1) / γ

2 ⋅ γ − 1 § pa ·(γ −1)/ (2γ ) ¨¨ ¸¸ © p ¹ (2.2.35)

In conjunction with Eq.(2.2.26) this result gives

V dm = 02 c0

§p · ⋅ ¨¨ 0 ¸¸ © pa ¹

(γ −1) / γ

§p · ⋅ ¨¨ a ¸¸ © p¹

(γ −1) / γ

⋅ dp (2.2.36)

On the other hand, the gas density in the evacuation section of area A, obtained from the adiabatic equation

p / p γ = pa / ρ γA

1/ γ

ρA =

μp § pa ·

¨ ¸ RT ¨© p ¸¹

γ

§p · = 2 pa ¨¨ 0 ¸¸ c0 © pa ¹

(γ −1) / γ

is (2.2.37) Upon using the results (2.2.25, 26, 27), equation (2.2.32) written as

dτ = − dm / ( ρ Av A ) (2.2.38) can be brought to the form

112

FOUNDATIONS - SELECTED TOPICS

V 1 γ − 1 § p0 · dτ = 0 ⋅ ⋅ ⋅¨ ¸ Ac0 γ 2 ¨© p ¸¹

(γ −1) / ( 2γ )

⋅

du

γ +3 1 − u (γ −1)/ γ u ⋅ 2γ

(2.2.39) which is the differential equation for the subsonic outflow. By integration, it can be brought to read:

V 2 § p0 · t − τ1 = 0 ⋅ ⋅¨ ¸ Ac0 γ − 1 ¨© pa ¸¹

(γ −1) / ( 2γ )

z2

⋅ ³ ( p(t )) ⋅ z1

(1 − z )

dz

2 (γ +1) / ( 2 (γ −1))

(2.2.40)

where the time-dependent pressure is implicit in the integration limit z1:

§ p · z1 = 1 − ¨¨ a ¸¸ © p(t ) ¹ z2 =

γ −1 γ

,

(γ − 1) / (γ + 1) (2.2.40’)

2.3

Operative Models of Chemical Accident Phenomenology

The models in this section were compiled and adapted for an algorithmic treatment from the references listed as [1]. 2.3.1 BLEVE The following is a summary presentation of the algorithm employed in assessing the risk from a Boiling Liquid Expansion Vapor Explosion (BLEVE) event. CONSTANTS Quantity Variable Unit Value ___________________________________________________________

DISASTER RISK AND VULNERABILITY MANAGEMENT

113

Gravity Acceleration: G m/s2 9.81 2 4 Stefan-Boltzmann Constant: sigmaB kW/(m .K ) 5.67E-11 Molar Mass, Air Mair kg/kmol 28.9467* Ideal Gas Constant Rgas l.Atm/K 0.082 Emittance Factor (emissivity) epsilon 1.0** Atmospheric Transmissivity tau 1.0** π (pi) pi 3.141593 ___________________________________________________________ *Computed as Mair = 28 x 0.7808 + 32 x 0.2095 + 39 x 0.0093 + 44 x 0.0004 in proportion with the molar masses of Nitrogen, Oxygen, Carbon Dioxide, and a reference inert gas. ** Admissible simplifying assumption. USER INPUTS Quantity Variable Unit ___________________________________________________ Substance Mass of Substance Ambient Temperature Ambient Pressure

chem$ mass tambient Pambient

kg C mm Hg

CODE-EXTRACTED DATA BASE INPUTS Quantity Variable Unit ___________________________________________________ Molar Mass of Substance Boiling Temperature Latent Heat, Vapors Specific Heat Combustion Heat

Mol tBoil hv cv hc

kg/kmol C kJ/kmol kJ/(kmol.K) kJ/kg

114

FOUNDATIONS - SELECTED TOPICS

STEPS TO STATIC OUTPUTS > Compute absolute temperatures: Tboil = tboil + 273.15 Tambient = tambient + 273.15 > Compute air density on given ambient conditions: roair = Mair x Pambient/(760 Rgas x Tambient) > Compute heating-up factor as follws: If Tboil >Tambient then Tfactor = cv (Tboil - Tambient) Otherwise Tfactor = 0. > Compute evaporation rate as: msecund = 0.001 hc/(hv + Tfactor) > With dp = 1 the emittance for a pool fire 1 m in diameter, compute: hfdf = 42 msecund/(roair (G dp)0.5))0.61 > On this, compute the emittance of the black radiator: Ez = 0.35 msecund hc/(1 + 4 hfdf) and the emittance of the flame: E = Ez epsilon which, for BLEVE should be doubled: E=2E > Now infer flame maximum temperature: Tmax = (E/sigmaB + Tambient4)1/4 >Also compute the maximum fireball radius:

DISASTER RISK AND VULNERABILITY MANAGEMENT

115

razaB = 3.24 mass0.325 and the exposure time: texpB = 0.852 mass0.26 SIGNIFICANT OUTPUTS so far obtained are: __________________________________________________________ Quantity Variable Unit ___________________________________________________ BLEVE Radius razaB m Exposure Time texpB s Radiation Emittance E kW/m2 Radiation Temperature Tmax K __________________________________________________________ STEPS TO RUNNIG OUTPUTS For a distance running from the outer limit of the fire ball out to the distance corresponding to a value of 1.0E-02 % for the percentage of exposed persons affected by 1st degree burns, in steps of 1 meter, compute the heat load on a person standing and facing the fire ball, and the consequent probits, and percentages, for lethal, 3rd degree burns, severe injuries by 2nd degree burns, and injury by 1st degree burns: If R is the running distance, then: > Compute the form factor for a vertical cylinder taken to model a standing person: Fmax = razaB razaB/R2 > Compute the thermal radiation level q = 1000 E Fmax tau > Compute the probit functions for 1st, 2nd, and 3rd degree burns, respectively:

116

FOUNDATIONS - SELECTED TOPICS

Probit1 = -39.83 + 3.0186 ln(texpB q4/3) Probit2 = -43.14 + 3.0186 ln(texpB q4/3) Probit3 = -36.38 + 2.5600 ln(texpB q4/3) > Now compute percentage of persons affected: Proc1 = 50 (1 + erf(arg1)), with arg1 = (Probit1 - 5)/20.5 Proc2 = 50 (1 + erf(arg2)), with arg2 = (Probit2 - 5)/20.5 Proc3 = 50 (1 + erf(arg3)), with arg3 = (Probit3 - 5)/20.5 where erf(x) is a polynomial approximation good to 1.0E-06, to the error function z erf(z) = (2/pi0.5) œexp(-t2) dt. 0 > Obtain the Complementary Cumulative Distribution Functions (CCDF) as measures of risk, as follows: - Interpret the percentage of affectation divided by 100 as the probability that a single exposed person be affected, at spot. Normalize all Proc3, Proc2, Proc1 quantities, obtained as functions of distance, to their sum-total, in order to obtain a (discrete) probability distribution function, f(R), with Rmax Ȉf(R) = 1 Rmin - Compute the Cumulative Distribution Function (CDF) as: R CDF(R) = ™f(R) Rmin - Compute the Complementary Cumulative Distribution Function (CCDF) as: CCDF(R) = 1 - CDF(R). The code will graphically represent Percentages vs. distance R, and lg(CCDF) vs. lg(R) - decimal logarithms implied.

DISASTER RISK AND VULNERABILITY MANAGEMENT

117

2.3.2 Pool Fire The following is a summary presentation of the algorithm employed in assessing the risk from a pool fire event. CONSTANTS Quantity Variable Unit Value ___________________________________________________________ Gravity Acceleration: G m/s2 9.81 Stefan-Boltzmann Constant: sigmaB kW/(m2.K4) 5.67E-11 Molar Mass,Air Mair kg/kmol 28.9467* Ideal Gas Constant Rgas l.Atm/K 0.082 Emittance Factor (emissivity) epsilon 1.0** Atmospheric Transmissivity tau 1.0** π (pi) pi 3.141593 ___________________________________________________________ * Computed as Mair = 28 x 0.7808 + 32 x 0.2095 + 39 x 0.0093 + 44 x 0.0004 in proportion with the molar masses of Nitrogen, Oxygen, Carbon Dioxide, and a reference inert gas. ** Admissible simplifying assumption. USER INPUTS Quantity Variable Unit ___________________________________________________ SUBSTANCE Mass of Substance Pool Radius Ambient Temperature Ambient Pressure

chem$ mass poolrad tambient Pambient

kg m C mm Hg

118

FOUNDATIONS - SELECTED TOPICS

CODE-EXTRACTED DATA BASE INPUTS Quantity Variable Unit ___________________________________________________ Molar Mass of Substance Boiling Temperature Latent Heat, Vapors Specific Heat Combustion Heat

Mol tBoil hv cv hc

kg/kmol C kJ/kmol kJ/(kmol.K) kJ/kg

STEPS TO STATIC OUTPUTS > Compute absolute temperatures: Tboil = tboil + 273.15 Tambient = tambient + 273.15 > Compute air density on given ambient conditions: roair = Mair Pambient/(760 Rgas Tambient) > Compute heating-up factor as follws: If Tboil >Tambient then Tfactor = cv (Tboil - Tambient) Otherwise Tfactor = 0. > Compute evaporation rate as: msecund = 0.001 hc/(hv + Tfactor) > With dp = 2 poolrad, compute: hfdf = 42 msecund/(roair (G dp)0.5)0.61 > On this, and taking - for the fire diameter df = dp, and - for the fire height hf = df hfdf compute the emittance of the black radiator: Ez = 0.35 x msecund hc/(1 + 4 hfdf)

DISASTER RISK AND VULNERABILITY MANAGEMENT

119

and the emittance of the flame: E = Ez epsilon . > Now infer flame maximum temperature: Tmax = (E/sigmaB + Tambient4)1/4 >Also compute the exposure time: texpB = mass/(msecund Apool), where Apool = pi poolrad2 is the pool area. SIGNIFICANT OUTPUTS so far obtained are: _______________________________________________ Quantity Variable Unit _______________________________________________ Fire Diameter df m Fire Height hf m Exposure Time texpB s Radiation Emittance E kW/m2 Radiation Temperature Tmax K __________________________________________________________ STEPS TO RUNNIG OUTPUTS For a distance running from the fire radius (equaling the pool radius) out to the distance corresponding to a value of 1.0E-02 % for the percentage of exposed persons affected by 1st degree burns, in steps of 1 meter, compute the heat load on a person standing and facing the fire ball, and the consequent probits, and percentages, for lethal, 3rd degree burns, severe injuries by 2nd degree burns, and injury by 1st degree burns: If R is the running distance, then: > Compute the maximum form factor for a vertical cylinder taken to model a standing person, as follows:

120

FOUNDATIONS - SELECTED TOPICS

hr = hf/poolrad Xr = R/poolrad A = (Xr + 1)2 + hr2 B = (Xr - 1)2 + hr2 Fh = [atn(((Xr + 1)/(Xr - 1))0.5 - ((Xr2 - 1 + hr2)/((A x B)0.5) atn(((xr-1) A/((Xr+1) B))0.5)]/pi Fv = [(1/Xr) atn(hr/((Xr2-1)0.5)) + (hr (A - 2 Xr)/(Xr (A B)0.5)) atn(((Xr - 1) A/((Xr + 1) B))0.5) - (hr/Xr) atn(((Xr - 1)/(Xr + 1))0.5)]/pi Fmx = (Fh2 + Fv2)0.5 > Compute the thermal radiation level q = 1000 E Fmax tau > Compute the probit functions for 1st, 2nd, and 3rd degree burns, respectively: Probit1 = -39.83 + 3.0186 ln(texpB q4/3) Probit2 = -43.14 + 3.0186 ln(texpB q4/3) Probit3 = -36.38 + 2.5600 ln(texpB q4/3) > Now compute percentage of persons affected: Proc1 = 50 (1 + erf(arg1)), with arg1 = (Probit1 - 5)/20.5 Proc2 = 50 (1 + erf(arg2)), with arg2 = (Probit2 - 5)/20.5 Proc3 = 50 (1 + erf(arg3)), with arg3 = (Probit3 - 5)/20.5 where erf(x) is a polynomial approximation good to 1.0E-06, to the error function z erf(z) = (2/pi0.5) œ exp(-t2) dt. 0 - Obtain the Complementary Cumulative Distribution Functions (CCDF), as follows: - Interpret the percentage of affectation divided by 100 as the probability that a single exposed person be affected, at spot. Normalize all Proc3, Proc2, Proc1 quantities, obtained as functions of distance, to their sum-total, in order to obtain a

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(discrete) probability distribution function, f®, with Rmax ™f® = 1 Rmin -

Compute the Cumulative Distribution Function (CDF) as:

R CDF® = ™ f® Rmin -

Compute the Complementary Cumulative Distribution Function : CCDF® = 1 – CDF®.

The code will graphically represent Percentages vs. distance R, and lg(CCDF) vs. lg® – decimal logarithms implied. 2.3.3 Flare The following is a summary presentation of the algorithm employed in assessing the risk from a pool fire event. CONSTANTS Quantity Variable Unit Value ___________________________________________________________ Gravity Acceleration: G Stefan-Boltzmann Constant: sigmaB Molar Mass, Air Mair Ideal Gas Constant Rgas Emittance Factor (emissivity) epsilon Atmospheric Transmissivity tau π (pi) pi

m/s2 kW/(m2.K4) kg/kmol l.Atm/K

9.81 5.67E-11 28.9467* 0.082 1.0** 1.0** 3.141593

Saturation Pressure Constants***: -------------------------------------------K1 = (22.92 + 21.18 + 21.86 + 21.36 + 21.60 + 21.86 + 26.92 + 21.51) / 8 K2 = (2.71 + 1.63 + 2.82 + 2.265 + 2.70 + 2.82 + 4.90 + 2.37) / 8 K3 = (0.0289 + 0.0209 + 0.0214 + 0.0174 + 0.0166 + 0.0186 + 0.0168 + 0.0114 + 0.0065) / 9

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K4 = (0.725 + 0.783 + 0.776 + 0.843 + 0.831 + 0.809 + 0.857 + 0.761 + 0.850) / 9 _____________________________________________________________ * Computed as Mair = 28 x 0.7808 + 32 x 0.2095 + 39 x 0.0093 + 44 x 0.0004 in proportion with the molar masses of Nitrogen, Oxygen, Carbon Dioxide, and a reference inert gas. ** Admissible simplifying assumption. *** Computed as averages of the respective values for NH3, C2H4, C2H6,C3H8, 1-3 butadiene, n-butane, SO2, Cl2. USER INPUTS Quantity Variable Unit ___________________________________________________ Substance chem$ Hole diameter du m Ambient Temperature tambient C Ambient Pressure Pambient mm Hg Exposure Time texpB s Stoichiometric Volume Ratio jst 4* ___________________________________________________ * Propane taken as reference. CODE-EXTRACTED DATA BASE INPUTS Quantity Variable Unit ___________________________________________________ Molar Mass of Substance Mol Boiling Temperature tBoil Saturation Pressure at 20 C pv20 Density relative to Air at 4 C: roa Latent Heat, Vapors hv Specific Heat cv Combustion Heat hc

kg/kmol C mm Hg kJ/kmol kJ/(kmol.K) kJ/kg

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STEPS TO STATIC OUTPUTS > Compute absolute temperatures: Tboil = tboil + 273.15 Tambient = tambient + 273.15 > Compute air density on given ambient conditions: roair = Mair x Pambient/(760 x Rgas x Tambient) > Compute saturation pressure at ambient temperature: pv = pv20 exp(1000 x K2 x (1/293.15 - 1/Tambient)) x 1.013E5 x pv/760 > Compute the evaporation rate through the sequence: pratio = Mol x pv/(8314 x Tambient) rou = pratio/(1 - K3 x pratioK4) rou = rou/roair b2 = 23 + 41 x roa b1 = 50.5 + 48.2 x roa - 9.95 x roa2 Ka1 = 0.32 x roa/(rou^0.5) x (b1/(b1+b2)) x jst hf = du/Ka1 df = du/(2 Ka1 (b20.5)) hfdf = hf/df poolrad = df/2 msecund = roair ((G x df) 0.5) (hf/(42 x df))1/0.61 > On this, compute the emittance of the black radiator: Ez = 0.35 msecund hc/(1 + 4 x hfdf) and the emittance of the flame: E = Ez * epsilon . > Now infer flame maximum temperature: Tmax = (E/sigmaB + Tambient4)1/4

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SIGNIFICANT OUTPUTS so far obtained are: ___________________________________________________________ Quantity Variable Unit _______________________________________________________ Saturation Vapor Pressure pvsat mm Hg Relative Vapor Density at Hole Center rou Fire Diameter df m Fire Height hf m Exposure Time texpB s Radiation Emittance E kW/m2 Radiation Temperature Tmax K ___________________________________________________________ STEPS TO RUNNIG OUTPUTS For a distance running from the fire radius (equaling the pool radius) out to the distance corresponding to a value of 1.0E-02 % for the percentage of exposed persons affected by 1st degree burns, in steps of 1 meter, compute the heat load on a person standing and facing the fire ball, and the consequent probits, and percentages, for lethal, 3rd degree burns, severe injuries by 2nd degree burns, and injury by 1st degree burns: If R is the running distance, then: > Compute the maximum form factor for a vertical cylinder taken to model a standing person, as follows: hr = hf/poolrad Xr = R/poolrad A = (Xr + 1)2 + hr2 B = (Xr - 1)2 + hr2 Fh =[ atn(((Xr + 1)/(Xr - 1))0.5) - ((Xr2 - 1 + hr2)/((A x B)0.5)) atn(((Xr-1) A/((Xr+1) B))0.5)]/pi Fv = [(1/Xr) atn(hr/((Xr2-1)0.5)) + (hr (A - 2 Xr)/(Xr (A B)0.5)) atn(((Xr - 1) A/((Xr + 1) B))0.5) - (hr/Xr) atn(((Xr - 1)/(Xr + 1))0.5)]/pi

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125

Fmx = (Fh2 + Fv2)0.5 > Compute the thermal radiation level q = 1000 E Fmax tau > Compute the probit functions for 1st, 2nd, and 3rd degree burns, respectively: Probit1 = -39.83 + 3.0186 ln(texpB x q4/3) Probit2 = -43.14 + 3.0186 ln(texpB x q4/3) Probit3 = -36.38 + 2.5600 ln(texpB x q4/3) > Now compute percentage of persons affected: Proc1 = 50 (1 + erf(arg1)), with arg1 = (Probit1 - 5)/20.5 Proc2 = 50 (1 + erf(arg2)), with arg2 = (Probit2 - 5)/20.5 Proc3 = 50 (1 + erf(arg3)), with arg3 = (Probit3 - 5)/20.5 where erf(x) is a polynomial approximation, good to 1.0E-06, to the error function z 0.5 erf(z) = (2/pi )œ exp(-t2) dt. 0 > Obtain the Complementary Cumulative Distribution Functions (CCDF) as measures of risk, as follows: - Interpret the percentage of affectation divided by 100 as the probability that a single exposed person be affected, at spot. Normalize all Proc3, Proc2, Proc1 quantities, obtained as functions of distance, to their sum-total, in order to obtain a (discrete) probability distribution function, f(R), with Rmax Ȉf(R) = 1 Rmin - Compute the Cumulative Distribution Function (CDF) as: R CDF® = Ȉf® Rmin

126

-

FOUNDATIONS - SELECTED TOPICS

Compute the Complementary Cumulative Distribution Function: CCDF® = 1 – CDF®.

The code will graphically represent Percentages vs. distance R, and lg(CCDF) vs. lg® – decimal logarithms implied. 2.3.4 EXPLOSION The following is a summary presentation of the algorithm employed in assessing the risk from the shock wave deflagration of a given quantity of explosive material. CONSTANTS Quantity Variable Unit Value ___________________________________________________________ Gravity Acceleration: G m/s2 9.81 2 4 Stefan-Boltzmann Constant: sigmaB kW/(m .K ) 5.67E-11 Molar Mass,Air Mair kg/kmol 28.9467* Ideal Gas Constant Rgas l.Atm/K 0.082 Emittance Factor (emissivity) epsilon 1.0** Atmospheric Transmissivity tau 1.0** The ‘kiloton’ constant kiloton J/kt 4.182E9 The ‘psi-to-Pa’ constant*** psitopa psi/Pa 1.45E-4 ___________________________________________________________ * Computed as Mair = 28 x 0.7808 + 32 x 0.2095 + 39 x 0.0093 + 44 x 0.0004 in proportion with the molar masses of Nitrogen, Oxygen, Carbon Dioxide, and a reference inert gas. ** Admissible simplifying assumption. *** psi - pounds per square inch. USER INPUTS Quantity Variable Unit ___________________________________________________ SUBSTANCE Mass of Substance Blast Yield Fraction

chem$ mass yieldproc

kg

DISASTER RISK AND VULNERABILITY MANAGEMENT

Positive Phase Duration Ambient Temperature Ambient Pressure Subject Position Typical Fragment/Debris Fragment/Debris Shape Fragment Cross-Sectional Area Glass Pane Width Glass Pane Height Glass Pane Thickness Glass Elasticity Modulus Glass Density Glass Poisson Coefficient

127

texpB tambient Pambient subject position mfragment fshape$ Af aglass bglass dglass Eglass roglass nuePoisson

s C mm Hg kg m2 m m m Pa kg/m3

CODE-EXTRACTED DATA BASE INPUTS Quantity Variable Unit ___________________________________________________ Molar Mass of Substance Boiling Temperature Latent Heat, Vapors Specific Heat Combustion Heat

Mol tBoil hv cv hc

kg/kmol C kJ/kmol kJ/(kmol.K) kJ/kg

STEPS TO STATIC OUTPUTS > Select a reference mass for the exposed human body. Use the following correspondence: Variable subject$ Variable mbody (kg) ____________________________________________ “Adult-Man” 75 “Adult-Women” 55 “Child” 25 “Baby” 5 ____________________________________________ > Compute the Dynamic Load Factor (DLF) for a freely mounted glass pane, as follows: - The moment of inertia of the pane, as plate:

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FOUNDATIONS - SELECTED TOPICS

Inertia = roglass x dglass x aglass x bglass x (aglass3+bglass3)/6 - The lowest natural frequency of the pane: fglass = (pi/2) (1/aglass2 + 1/bglass2) (Eglass Inertia/(roglass dglass (1-nuePoisson2)))0.5 - The period of the pane oscillations: Tglass = 1/fglass - A scaled variable to determine DLF: ttoT = texpB/Tglass Use the following correspondence: ttoT DLF _________________________________________________ 0.3 and < 1.0 1+ (ttot - 0.3) (8/15)/(1 - 0.3) > 1 and < 2 1+ 8/15 + (ttot - 1) (4/15)/(2 - 1) > 2 and < 3 1+ 12/15 + (ttot - 2) (1/15)/(3 - 2) > 3 and =4 1+ 13.5/15 _________________________________________________ > Compute the static load on a window pane, as follows: (i)

Glass window pane area: Aglass = aglass bglass

(ii)

The critical value of the deflection to thickness ratio: deltatodcr = 6 (bglass/aglass)1.5

(iii)

The 0-iteration static load: Pst=2.0e6 dglass2/(Aglass0.18 dglass0.7 0.225 aglass2)

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(iv)

129

Compute actual deflection to thickness ratio: deltatod = 706E-15 Pst aglass3 bglass/dglass4

(v)

If deltatod < deltatodcr then - Compute eta = 1 + (1/9) (deltatodcr - deltatod), - Assign Pst/eta to Pst, and - Go to Step IV

> Get ambient pressure in Pascal and ambient temperature in Kelvin: Pa = pambient 1.013E5/760 Tambient = tambient + 273.15 > Compute air density under ambient conditions: roair = Mair pambient/(760 Rgas Tambient) > Compute the kiloton expression of the explosion yield: Yield = yieldproc 1000 hc mass/kiloton Special clause: if substance is TNT, then Yield=mass/1000000 > Compute quantities RB1, RB3, RB5, RB10, RB20 for the correspondence: Expected Effect

Overpressure Radius (psi) (m) ___________________________________________________________ X1. Window glass shatters. Light injuries from fragments.

1

RB1

X2. Residential structures collapse. Serious injuries common. Fatalities may occur.

3

RB3

X3. Most buildings collapse. Injuries universal.

5

RB5

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FOUNDATIONS - SELECTED TOPICS

Fatalities widespread. X4. Reinforced concrete buildings severely damaged or demolished. Most people killed.

10

RB10

X5. Heavily-built concrete buildings severely damaged or demolished. Fatalities approach 100%.

20

RB20

as follows: RB1 = 1000 Yield0.33 2.20 RB3 = 1000 Yield0.33 1.00 RB5 = 1000 Yield0.33 0.71 RB10 = 1000 Yield0.33 0.45 RB20 = 1000 Yield0.33 0.28 > Use Lagrange polynomials to interpolate and get P1 in the correspondence: X6. Extrapolation towards explosion center. Total demolition and” kill area.”

P1

as follows: y1 = 1, X1 = RB1 y2 = 3, X2 = RB3 y3 = 5, X3 = RB5 y4 = 10, X4 = RB10 y5 = 20, X5 = RB20 X=1 Lag1 = (X-X2)(X-X3)(X-X4)(X-X5)/((X1-X2)(X1-X3)(X1-X4)(X1-X5)) Lag2 = (X-X3)(X-X4)(X-X5)(X-X1)/((X2-X3)(X2-X4)(X2-X5)(X2-X1)) Lag3 = (X-X4)(X-X5)(X-X1)(X-X2)/((X3-X4)(X3-X5)(X3-X1)(X3-X2)) Lag4 = (X-X5)(X-X1)(X-X2)(X-X3)/((X4-X5)(X4-X1)(X4-X2)(X4-X3)) Lag5 = (X-X1)(X-X2)(X-X3)(X-X4)/((X5-X1)(X5-X2)(X5-X3)(X5-X4)) P1 = y1 Lag1 + y2 Lag2 + y3 Lag3 + y4 Lag4 + y5 Lag5

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STEPS TO RUNNIG OUTPUTS For a distance running from 1 metre from the explosion centre to RB1, compute the appropriate probits, and percentages, as follws: > Interpolate overpressure for current distance: Distance X Overpressure Psw (m) (psi) ___________________________________________________________ X < RB20 X >= RB20 and X < RB10

Psw = P1 + (X - 1)(20 - P1)/(RB20 - 1) Psw = 20 + (X - RB20)(10 - 20)/(RB10RB20) X >= RB10 and X < RB5 Psw = 10 + (X - RB10)(5 - 10)/(RB5 RB10) X >= RB5 and X < RB3 Psw = 5 + (X - RB5)(3 - 5)/(RB3 - RB5) X >= RB3 and X Compute scaled overpressure and impulse: Pscaled = Ps/Pa is = Ps x texpB/2 iscaled = is/(Pa1/2 mbody1/3) > Based on the scaled overpressure and impulse above, compute:

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-

Lethality Probit and Percentage through Lung Injury: S = 4.2/Pscaled + 1.3/iscaled ProbitLung = 5.0 - 5.74 ln(S) arg = (ProbitLung - 5)/20.5 ProcLung = 50 (1 + erf(arg))

-

Lethality Probit and Percentage through Head Injury: S = 2.43E3/Ps + 4.0E8/(Ps is) ProbitHead = 5.0 - 8.49 ln(S) arg = (ProbitHead - 5)/20.5 ProcHead = 50 (1 + erf(arg))

-

Lethality Probit and Percentage through Whole Body Injury: S = 7.38E3/Ps + 1.3E9/(Ps is) ProbitWhole = 5.0 - 2.44 ln(S) arg = (ProbitWhole - 5)/20.5 ProcWhole = 50 (1 + erf(arg))

> Based on the Dynamic Load Factor on window glass panes, DLF, and the static load above, compute: -

Lethality Probit and Percentage through Lung Injury: S = DLF Ps/Pst ProbitGlass = 2.67 + 5.62 x ln(S) arg = (ProbitGlass - 5)/20.5 ProcGlass = 50 (1 + erf(arg))

> To evaluate lethality through impact of fragments/debris, do: -

Compute projectile drag coefficient:

Variable shape$ Drag Coefficient, Cd ___________________________________________________________

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“Side-Exposed-Cylinder” 1.20 “Base-Exposed-Cylinder” 0.82 “Sphere” 0.47 “Disc” 1.17 “Face-Exposed-Quadratic-Slab” 1.17 “Face-Exposed-Cube” 1.05 “Edge-Exposed-Cube” 0.80 “Side-Exposed-Oblong Box” 2.05 “Edge-Exposed-Oblong Box” 1.55 “Face-Exposed-Strip” 1.98 ___________________________________________________________ > Compute Lethal Speed Vo (average, based on fragment at rest initially; object hit immediately), as: rol = (7 Pa + 6 Ps) roair/(7 Pa + Ps) ul = Ps (5/(roair (7 Pa + Ps)))0.5 accfo = Cd Af rol ul2/(2 mfragment) Vo = accfo texpB/2 > Upon the above, compute the probit in consideration of the projectile (fragment/debris) mass: Variable mfragment Variable ProbitFrag ___________________________________________________________ >4.5 ProbitFrag = -13.9 + 10.54 ln(Vo) >=0.1 and Obtain the Complementary Cumulative Distribution Functions (CCDF) as measures of risk, as follows: - Interpret the percentage of affectation divided by 100 as the probability that a single exposed person be affected, at spot. Normalize ProcFrag quantities, obtained as functions of distance, to their sum-total, in order to obtain a (discrete) probability distribution function, f(X), with

Xmax Ȉf(R) = 1 1 -

Compute the Cumulative Distribution Function (CDF) as:

X CDF(X) = Ȉf(X) 1 - Compute the Complementary Cumulative Distribution Function (CCDF) as: CCDF(X) = 1 - CDF(X). The code will graphically represent Percentages vs. distance X, and lg(CCDF) vs. lg(X) - decimal logarithms implied. 2.3.5 Intoxication The following is a summary presentation of the algorithm employed in assessing the risk from the atmospheric dispersion of a toxic release. CONSTANTS Quantity Variable Unit Value ___________________________________________________________ Gravity Acceleration: G m/s2 9.81 Molar Mass,Air Mair kg/kmol 28.9467* Ideal Gas Constant Rgas l.Atm/K 0.082 ___________________________________________________________ * Computed as

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135

Mair = 28 x 0.7808 + 32 x 0.2095 + 39 x 0.0093 + 44 x 0.0004 in proportion with the molar masses of Nitrogen, Oxygen, Carbon Dioxide, and a reference inert gas. ** Admissible simplifying assumption. USER INPUTS Quantity Variable Unit ___________________________________________________ Substance Mass of Substance Ambient Temperature Ambient Pressure Doury Stability Class Wind Speed

chem$ mass tambient Pambient K$ W$

kg C mm Hg m/s at ground

CODE-EXTRACTED DATA BASE INPUTS Quantity Variable Unit ___________________________________________________ Molar Mass of Substance Mol kg/kmol Boiling Temperature tBoil C Immdiately Dangerous for Life and Health Limit IDLH mg/m3 Threshold Limit Value TLV mg/m3 Short Term Exposure Limit STEL mg/m3 Emergency Response Planning Guidelines 1 ERPG1 mg/m3 Emergency Response Planning Guidelines 2 ERPG2 mg/m3 Emergency Response Planning Guidelines 3 ERPG3 mg/m3 Probit Function Coefficient A Aprob Probit Function Coefficient B Bprob Probit Function Exponent N Nprob ___________________________________________________________ STEPS TO STATIC OUTPUTS > Compute absolute temperatures:

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Tboil = tboil + 273.15 Tambient = tambient + 273.15 > Compute air density on given ambient conditions: roair = Mair x Pambient/(760 Rgas Tambient) STEPS TO RUNNIG OUTPUTS > Compute effect radii for IDLH, TLV, STEL, ERPG1, ERPG2, ERPG3 as follows: I. Start looping at time t =1 s II. Compute the dispersion coefficients at time t. These are of the form sigh = (Ah t)Kh sigv = (Av t)Kv with Ah, Av, Kh, Kv obtained by interpolation from the Doury table offered at the user interface: Time Ah Kh Av Kv ________________________________________________ Atmospheric Stability Class 1 (strong diffusion) ________________________________________________ 0 2.40E2 3.28E3 9.70E4 5.08E5 1.30E6

4.05E-1 1.35E-1 1.35E-1 4.63E-1 6.50E0 2.00E5

0.859 0.42 1.130 1.00 1.130 20.00 1.000 20.00 0.824 20.00 0.500 20.00

0.814 0.685 0.500 0.500 0.500 0.500

Atmospheric Stability Class 2 (weak diffusion) ________________________________________________ 0 2.40E2 3.28E3 9.70E4 5.08E5 1.30E6

4.05E-1 1.35E-1 1.35E-1 4.63E-1 6.50E0 2.00E5

0.859 0.20 1.130 0.20 1.130 0.20 1.000 0.20 0.824 0.20 0.500 0.20

0.500 0.500 0.500 0.500 0.500 0.500

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________________________________________________ III. Find the effect radius as follows: q = 2 M/(fpi sigh sigh sigv Rcon), with fpi = (2 pi)1.5 If q > 0 then r = 2 x ln(q), or else r = 0. If r > 0 then r = sigh x r0.5, or else r = 0. If r = 0 then the process is complete, and go to step (iv). Otherwise The relevant distance is made of the radius of the puff, r, and the path W t, (W - the wind speed) walked by the puff center over time duration t: rwind = W t + r If rwind > RRad then memorize rwind as RRad. Make a time-step forward: t=t+1 Go to step (III). IV. The effect radius is obtained as the integer part of RRad, and the exposure time, or effect duration, as Tmax = the integer part of t. A time step of 0.005 from Tmax is then adopted, and the process is remade with the results now displayed, which results in the tables having as headers: ____________________________________ Time Puff Radius Coverage Radius (s) (m) (m) ____________________________________ > The radii corresponding to different lethality percentages are computed in a loop that, essentially, performs the following: -

For each percentage, Perc, solve for Probit the equation: Perc = 50 (1 + erf((Probit - 5)/20.5)

where erf(x) is a polynomial approximation, good to 1.0E-06, to the error function

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z erf(z) = (2/pi0.5) œ exp(-t2) dt. 0 The equation is solved iteratively, seeking an accuracy of 0.005 in testing the left-to-right hand side equality. - Adopt as exposure time, tEXP, in minutes, the maximum of the effect times determined at the preceding step into the algorithm. - Determine the concentration that should be consistent with the exposure time, tEXP, and the Probit as found:

ln(TICn) = (Probit - Aprob)/Bprob TICn = exp(ln(TICn)) If TICn>0 then CON = (TICn/tEXP)1/Nprob, or else CON = 0. -

Convert to mg/m3:

CON = CON/mgtoppm, with mgtoppm = Rgas Ta 760/(Mol pambient). - Once the relevant concetration, CON, is obtained, a full set of data can be reported, for a running radius, according to the table header: _____________________________________________________

Radius Concentration Exposure Time Death Percentage (%) (m) (mg/m3) (s) () _____________________________________________________ > Obtain the Complementary Cumulative Distribution Functions (CCDF) as measures of risk, as follows: - Interpret the percentage of affectation divided by 100 as the probability that a single exposed person be affected, at spot. Normalize all Proc quantities, obtained as functions of distance, to their sum-total, in order to obtain a (discrete) probability distribution function, f(R), with Rmax Ȉf(R) = 1 Rmin -

Compute the Cumulative Distribution Function (CDF) as: R CDF(R) = Ȉ f(R) Rmin

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139

- Compute the Complementary Cumulative Distribution Function (CCDF) as:

CCDF(R) = 1 - CDF(R). The code will graphically represent Percentages vs. distance R, and lg(CCDF) vs. lg(R) - decimal logarithms implied.

2.4

Integrated Dispersion and Dose-Effect Models

The current module endeavors to address two types of questions: 1. Assuming an accidental release of radioactive pollutant, that has a finite duration, as opposed to an instantaneous discharge, how the healthand environmental consequence field around the source of release would look like, considering that, normally, the meteorology of the site would vary during the release. And 2. Assuming a routine operation of a nuclear/chemical facility, that entails a technologically-expected stationary release to the atmosphere of gases and/or aerosols at a given rate (Ci/s, mg/s), how the health- and environmental consequence field around the source of release would look like, again considering that, normally, the meteorology of the site would vary with time. The ‘health- and environmental consequence field’ means, in the context, the area around the source where: χ/Q - the long term dispersion factor, or DilFac, exceeds a normative threshold; - radiation doses (equivalent) acquired by various paths - external, inhalation, ingestion - would exceed a level that is considered normative by national/international regulations and practices (ingestion and several latephase doses not covered in this code version); - the airborne concentration of pollutant at, e.g., the ground level would exceed a level that is considered normative by the procedures of the Quantitative Chemical Risk Analysis (QCRA), such as the Immediately Dangerous for Life and Health Limit (IDLH), the Threshold Limit Value (TLV), and the Short Term Exposure Limit (STEL); the expected lethality percentage following acute chemical intoxication resulting from the release exceeds given levels. A robust manner of modeling the above relies on a well-established method in the nuclear risk analysis (NRA), namely the evaluation of the Normalized Time-Integrated Air Concentration. The recommended reference is Till and Meyer [2].

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FOUNDATIONS - SELECTED TOPICS

As a rule, the dose is directly proportional to the time-integral of the concentration, being calculated over the entire period of exposure: t

Hα ³ Ψ ( x, y,0)dt 0

(2.4.1) In case of accidental releases the exposure periods of interest are hours, or days, and an average value of the release rate may be used as a simplifying assumption. In the case of routine releases, the exposure periods are days, weeks, months, or years, and the release rate is normally provided by the installation design. Basically, the calculation of the time-integrated concentration χ is straightforward. However, it poses initial problems insofar as the prerequisite of stationary turbulence required for the computation does not apply to the entire duration of release. For this reason, the release duration is broken into individual duration intervals Δt, in which the stationary condition is fulfilled. Then, the contribution of the individual duration intervals are superimposed to obtain the total contribution. By additional identification of each state of turbulence in the duration interval Δtν by means of the wind direction φ, wind velocity k, and diffusion category j, which is sufficiently accurate for practical calculations, the time-integrated concentration in a given wind direction may be calculated as follows:

χ φ = ³ Ψdt ≈ ¦ Ψφjk 0

Δtφ ν ⋅ Δt ¦ Ψφ ⋅ ¦ ν ⋅ ¦ Δtφ ν ≈ ν ¦ Δtφ ν φ ν jk

t jk

jk

jk

jk

jk

jk

≈ ¦ pφjk ⋅ Ψφjk ⋅ Δt ≈ Ψ φ ⋅ Δt jk

(2.4.2) in which pφjk is the frequency of the joint occurrence of a certain combination jk in the direction φ related to all of the combination jk. For easier application, the wind rose is divided into n sectors of equal size. If the wind direction φ denotes the direction of the angle-bisecting line of a sector i, and if it is assumed that all effluent plumes falling into this

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141

sector coincide with the direction of the bisector, the following equation applies:

χ i = Ψ i Δt (2.4.3) where

Ψ i = ¦ pijk jk

+∞

n Ψφjk ( x, y,0)dy 2πx −³∞

(2.4.4)

In connection with the relative frequency p and based on the assumptions made before, the direction φ has been replaced by the index of the dispersion sector i. Note that

¦p

ijk

=1

ijk

Taking into account the basic equation for the airborne concentration (Gauss plume)

Ψ=

§ y 2 · ª § ( z − H )2 · § ( z + H )2 ·º Q ¸ ¨− ¸» × exp¨ − 2 ¸ «exp¨¨ − + exp 2 2 ¸ ¨ ¸ ¨ 2σ ¸ « 2 σ 2 σ 2π uσ yσ z y z z ¹ © ¹»¼ © ¹¬ © (2.4.5)

where

Q = release rate (mass/time), and

H = effective release height the following is now obtained for the time-integrated activity concentration:

χ i ( x,0) = Q Δt ¦ pijk jk

n

(2π )

3 1/ 2

u jk x

⋅

[

(

)]

exp − H 2 / 2σ zj2 ( x )

σ zj ( x)

(2.4.6)

For convenience, both sides of Eq.(2.4.6) are sometimes divided by

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Q = Qǻt. This leads to the so-called Ȥ/Q - value,

exp[− H / (2σ zj ( x ))] χi n = ¦ pijk ⋅ 1 / 2 Q σ zj ( x) jk (2π 3 ) u jk x 2

2

(2.4.7)

which is commonly termed long-term dispersion factor (DilFac). This factor is usually applied to evaluate the inhalation due to routine releases. The quantities pijk are delivered by three-dimensional dispersion meteorological statistics for the simultaneous occurrence of wind in direction i, atmospheric stability in class j, and wind speed in class k. For n = 16, and a particular sector i, where pikj ≡ n jk / N , and u k being the representative wind speed in class k, (the wind velocity ‘class’ equals the wind speed in knots), Eq. (2.4.7) can be expressed in the form used, e.g., by the U.S. Nuclear Regulatory Commission in Regulatory Guide 1.111:

χ Q

= 2.032¦ jk

[xu σ ] N

n jk

−1

k

zj

ª H2 º exp «− 2 » ¬« 2σ zj ¼» (2.4.8)

In this equation, n jk is the length of time (in hours) of the simultaneous occurrence of a particular wind direction, wind speed class k, and atmospheric stability class j, and N is equal to the total monitoring hours. Once the code determines the long term dilution factor field around the release source following the procedure described, the appropriate equations are used to determine doses. Depending on the nature of the pollutant, models were developed for the radiation doses, and the chemical doses, respectively.

Radiation Doses ___________________________________________________________ Abbreviations: EDE - Effective Dose Equivalent CEDE50 - Committed Effective Dose Equivalent, 50 years ___________________________________________________________ DOSE (mrem) Equation ___________________________________________________________ Air submersion external EDE Ha = Σ(Teff_air,i x Qi x DF x DCFa,i) i

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143

DaB = Σ(Teff_air,i x Qi x DF x DCFaB,i) i Air submersion inhalation acute lung DaL = ΣҞTeff_air,i x Qi x DF x DCFaL,i) i Air submersion inhalation thyroid DaT = ΣҞTeff_air,i x Qi x DF x DCFaT,i) i Air submersion inhalation CEDE50 DCEDE = ΣҞTeff_air,i x QixDFxDCFaCEDE,i) i Shared Dimensional Equation: mrem = s x μCi/s x s/m3 x (mrem/s)/(μCi/m3) ___________________________________________________________________ Air submersion inhalation acute bone

DEPg = ΣҞQTi x DDF x DCFEPg,i x Teff_gnd,i) i Dimensional Equation mrem = μCi x (μCi/m2)/μCi x (mrem/s)/(μCi/m2) x s ___________________________________________________________________ Ground external EDE

Total Acute Bone Dose Equivalent TABD = Ha + DaB + DEPg Total Acute Lung Dose Equivalent TALD = Hai + DaL + DEPg Total Effective Dose Equivalent

TEDE = Hai+DCEDE+DEPg

Dimensional Equation mrem = mrem + mrem + mrem ___________________________________________________________________ Quantities in the equations above are: Teff-air,i

s

Effective Exposure Time to Cloudshine, i-nuclide:

Teff_air,i = 1.44 x T1/2,i x (1 - 0.5^(Texp_air/T1/2)) Teff-gnd,i

s

Effective Exposure Time to Groundshine, i-nuclide:

Teff_gnd,i = 1.44 x T1/2,i x (1 - 0.5^(Texp_gnd/T1/2)) with Texp_air Texp_gnd T1/2, i

s s s

The actual exposure time to cloudshine, max. 4 hrs The actual exposure time to groundshine Nuclide i halflife

Qi QTi

μCi/s μCi

Release rate of nuclide i in the mix, average Total release of nuclide i in the mix

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DF DDF DCF., i

s/m3 (μCi/m2)/μCi varia

Long term dilution factor Deposition factor Dose Conversion Factors

(see dimensional equations) The physical meaning of the quantities is detailed in, e.g. McKenna et al. [3], wherefrom the dose model is derived. It is on this basis that the code maps the ‘health- and environmental consequence field’ in the sense given above, thus providing a ‘cadastral’ presentation of the impacts that nuclear installations may present. Chemical Doses The chemical pollutant concentration is obtained, at each point, as Con = DilFac * Qr kg/m3 = (s/m3).(kg/s)

(2.4.9)

where Qr (kg/s) is the average release rate. The concentration expressed in kg/m3 is then brought to ppm/m3 units, on the knowledge of an average temperature and pressure over the exposure time: Conppm = Con Rgas Ta 760 1000000 / (Mol Pa)

(2.4.10)

where Rgas is the ideal gas constant, Ta (K) is the absolute temperature, Pa (mm Hg) is the ambient pressure and Mol is the molar mass of the substance. Upon these, the toxic dose, ToxDose, field results from the equation ToxDose = (Conppm Nprob) tEXP

(2.4.11)

with Nprob - the probit exponent referred to above, and tEXP the exposure duration, in minutes. The calculation of the respective expected lethality percentage proceeds via the evaluation of the probit function, Probit Probit = Aprob + Bprob ln(ToxDose)

(2.4.12)

where Aprob and Bprob are the database-supplied probit coefficients and

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145

ln indicates the natural logarithm. In the end, the expected lethality percentage, LPercentage is obtained as: LPercentage = 100 * {1 + erf [(Probit - 5)/(20.5)]} / 2

(2.4.13)

where erf denotes the error function x erf(x) = (2/π ) * œ exp(-t 2) dt 0 .0.5

It is on this basis that dedicated software can conveniently map the ‘health- and environmental consequence field’ in the sense given above, thus providing a ‘cadastral’ presentation of the impacts that fixed chemical installations may present.

2.5

Water Pollution Assessment Recipes

2.5.1 Surface Water Tools were also developed, for the assessment of the strength and extension of the dispersion of polluting liquid discharges into water bodies such as the rivers, lakes and ponds, estuaries, and the sea. The emphasis was on the use of models simple enough to fit the constraints of near-real time evaluations in an emergency, yet comprehensive enough to cover the variety of situations that may occur. Given their association to longer-term risks, the sediment effects were not taken into account in this version. In response to the assumed limitations above, the algorithms were again based on the models summarized by Jirka G.H., Findikakis A.N., Onishi Y., and Ryan P.J. in reference [4]. The apparent dedication of the referenced source to nuclear matters does in no way affect, however, the generality of the models and their applicability to a variety of polluting releases, including chemical discharges. The chief caveat to the user would rather concern the appropriateness of the model-cases offered for any concrete case to be assessed, based on the circumstantial case input data (single- or multiport release, release depth, potential importance of shore effects, cross-currents etc.). The module is designed as a ‘problem-solver’. Typically, it would use discharge input data to evaluate the INITIAL MIXING NEAR-FIELD PHASE, the output of which is then used as a SOURCE TERM for the

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FOUNDATIONS - SELECTED TOPICS

assessment of the FAR-FIELD DISPERSION. Results are in terms of volumetric concentrations of pollutant (kg/m3). 2.5.1.1

Near-Field Models

The Surface Point Discharge Problem: A single port of cross-sectional area Ao (m2) discharges a liquid pollutant of density DENS (kg/m3) at a volumetric flow rate Qo (m3/s) at, or close to, the surface of a water body of depth H (m), density DENSo (kg/m3), and featuring a cross-current of speed Ua (m/s). Constants: The Gravity Acceleration g = 9.81 m/s2. The π (pi) number, pi = 3.141593. STEP 1: Determine Discharge Type: 3.1 If DENS < DENSo, then one has a BUOYANT JET. Determine Characteristic Quantities: - The Density Deficit DELTADENS = DENSo - DENS (kg/m3); - The Characteristic Length lo = (Ao/2)^(0.5) (m); - The Ejection Velocity Uo = Qo/Ao (m/s); - The Densimetric Froude Number Fo = Uo/((DELTADENS/DENSo) g lo)^(0.5); - The Maximum Vertical Penetration of the Surface Jet Hmax = 0.42 lo Fo (m); -

The Relative Crossflow Velocity R = Ua/Uo; The Critical Relative Crossflow Velocity

Rcrt = (0.05/(Hmax/H))^(0.75). 3.1.1 If BUOYANT JET and R =0.75 then one has a SHALLOW DISCHARHE. 3.1.2 If BUOYANT JET and R > Rcrt then the jet is ATTACHED to shoreline.

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3.2 If DENS = DENSo, then one has a NEUTRAL JET. 3.3 If DENS > DENSo, then one has a NEGATIVE-BUOYANCY JET. Refer the case to Submerged Point Discharges. 4. STEP 2: Compute Characteristic Outputs (Near-Field Source Term), namely: 4.1 The Dilution, DIL = CONo/CON, where CONo (kg/m3) is the initial pollutant concentration at the discharge mouth, and CON is pollutant concentration at a point of interest. Actually compute an average, or BULK dillution, DILs, taken as featuring the near-field zone; and 4.2 The Extent of the Near-Field Zone: NFext = Xt, or min(Xt,Xc) (m), where Xt (m) is the Transition Distance, and Xc (m) is the cross-current deflection length scale, as follows: 4.3 Deep Unattached Buoyant Jets: DILs = 1.4Fo, NFext = Xt = 15 lo Fo (m). 4.4 Shallow Unattached Buoyant Jets: DILs =1.4 Fo (0.75/(Hmax/H))^(.75), NFext = Xt = 15 lo Fo. 4.5 Attached Buoyant Jets: DILs = 0.70 Fo (0.75/(Hmax/H))^(0.75), NFext = min(Xt,Xc) (m), where Xt = 15 lo Fo, Xc = 2 lo/R. 4.6 Neutral Jets: DILs = 0.32 X/D, where X (m) is the distance of interest downflow from the discharge mouth; D = (4 Ao/pi)^(0.5) (m) is the equivalent diameter of the release mouth. 4.7 Negative-Buoyancy Jets: see 3.3. The submerged Point Discharge 1. Problem: A single port of cross-sectional area Ao (m2) discharges a liquid pollutant of density DENS (kg/m3) at a volumetric flow rate Qo (m3/s), under an angle THETA (deg. of angle) from the horizontal, deep below the surface of a water body of depth H (m) and density DENSo (kg/m3), 2. Constants: The Gravity Acceleration g = 9.81 m/s2; The π (pi) number, pi = 3.141593. 3. STEP 1: Determine Discharge Type: 3.1 If DENS < DENSo, then one has a BUOYANT JET. Determine Characteristic Quantities: - The Density Deficit DELTADENS = DENSo - DENS (kg/m3);

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-

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The Effective Diameter of Release Mouth (m) D = (4Ao/pi)^(0.5) The Characteristic Length lo = (pi D^2/8) (m); The Ejection Velocity Uo = Qo/Ao (m/s); The ‘Deep’ Densimetric Froude Number

Fd = Uo/((DELTADENS/DENSo) g D)^(0.5); -

The ‘Shallow’ Densimetric Froude Number

Fs = Uo/((DELTADENS/DENSo) g lo)^(0.5); If BUOYANT JET and H/D >0 .22 Fd then Case is DEEP RECEIVING WATER. 3.1.1.1 If BUOYANT JET in DEEP RECEIVING WATER and THETA = 90 deg., then one has a DEEP VERTICAL JET. 3.1.1.2 If BUOYANT JET in DEEP RECEIVING WATER and THETA = 0 deg., then one has a DEEP HORIZONTAL JET. 3.1.2 If BUOYANT JET and H/D = DENSo, then one has a NEUTRAL/NEGATIVEBUOYANCY JET. 4. STEP 2: Compute Characteristic Outputs (Near-Field Source Term), namely: 4.1 The Dilution, DIL = CONo/CON, where CONo (kg/m3) is the initial pollutant concentration at the discharge mouth, and CON is pollutant concentration at a depth of interest. Actually one computes (i) a CENTERLINE DILUTION, DILc, and (ii) a BULK DILLUTION, DIL - to be taken as representative for the Near-Field Mixing Zone. 4.2 One takes that the effect of cross-flows on deep discharges may, for almost all practrical purposes, be neglected. The Maximum Vertical Mixing Distance, Zmix = 0.8 H (m). Dilutions are computed as follows: 4.3 Vertical Deep Buoyant Jet in Deep-Receiving Water, 4.3.1. Centerline Dilution as a function of the vertical distance z (m) from nozzle: DILc = 0.11 (z/D)^(5/3)/Fd^(2/3)

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149

4.3.2. Bulk Dilution DIL = 1.4 DILc. 4.4 Horizontal Deep Buoyant Jet in Deep-Receiving Water, 4.4.1. Centerline Dilution at the Maximum Vertical Mixing Distance from nozzle, Zmix = 0.8 H (m) from nondimensional graph by Roberts P.J. – see Fig.2.5.1, giving DILc/Fd = f(z/(D Fd)), to be applied for z = Zmix. 4.4.2. Bulk Dilution DIL = 1.4 DILc.

Fig.2.5.1. Centerline dilution of a submerged, horizontal, round, buoyant jet in a stagnant, uniform fluid. Source: Roberts P.J.W. (1977). Dispersion of Buoyant Wastewater Discharged from Outfall Diffusers of Finite Length, KH-R-35, W.M.Keck Lab, California Institute of Technology, Pasadena, CA, U.S.A.

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FOUNDATIONS - SELECTED TOPICS

4.5 Vertical Deep Buoyant Jet in Shallow-Receiving Water, 4.5.1. Bulk Dilution DIL =0 .9 (H/D)^(5/3)/Fd^(2/3) 4.6 Horizontal Deep Buoyant Jet in Shallow-Receiving Water, 4.3.1. Bulk Dilution DIL = 1.4 Fs (0.75/(Hmax/H))^(0.75), with Hmax = 0.42 lo Fs. 4.7 Deep Neutral/Negative Buoyancy Jets: treated as a Horizontal Deep Buoyant Jet in Deep-Receiving Water (see 4.4). The Submerged Multiport Discharge 1. Problem: A multiple port of length Ld (m), consisting of n identical ports, spaced l meters from each other, each port d meters in diameter, discharges a liquid pollutant of density DENS (kg/m3) at a volumetric flow rate Qo (m3/s), under an angle THETA (deg. of angle) from the horizontal, deep below the surface of an ambient water of density DENSo (kg/m3), depth H (m), crossflow velocity Ua (m/s), Lr cross-length, and flow rate Qr (m3/s). Multiport system should be amenable to one of three engineered archetypes: unidirectional; staged; or alternating. 2. Constants: The Gravity Acceleration g = 9.81 m/s2; The π (pi) number, pi = 3.141593. 3. STEP 1: Determine Discharge Type: 3.1 If DENS < DENSo, then one has a DEEP MULTIPORT BUOYANT JET. Determine Characteristic Quantities: - The Density Deficit DELTADENS = DENSo - DENS (kg/m3); - The Characteristic Port Length B = (pi D^2)/(4 l) (m); - The Total Area of the Release Mouth (m2) Ao = n (pi d^2/4) - The Ejection Velocity Uo = Qo/Ao (m/s); - The Densimetric Froude Number Fs = Uo/(((DELTADENS/DENSo) g B)^(0.5)); - The Critical Length Ratio LRcrt = 1.84 Fs^(4/3) (the assumptions on a vertical ejection is considered to hold in all cases - see reference). 3.1.1 If DEEP MULTIPORT BUOYANT JET and H/B>LRcrt then Case is DEEP RECEIVING WATER. 3.1.1.1 If Ua=0 then DEEP MULTIPORT BUOYANT JET in DEEP RECEIVING WATER and NO CROSSFLOW 3.1.1.2 If Ua