Radiological Assessment: Predicting the Transport, Bioaccumulation and Uptake by Man of Radionuclides Released to the Environment (N C R P Report 1984) 9780913392669, 0913392669, 9781435629448

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NCRP Report No. 76

RADIOLOGICAL ASSESSMENT: PREDICTING THE TRANSPORT, BIOACCUMULATION, A N D UPTAKE BY M A N OF RADIONUCLIDES RELEASED TO THE ENVIRONMENT Recommendations of the NATIONAL COUNCIL O N RADIATION PROTECTION AND MEASUREMENTS

Issued March 15, 1984 National Council on Radiation Protection and Measurement 7910 WOODMONT AVENUE

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BETHESDA, MD. 20814

LEGAL NOTICE This report was prepared by the National Council on Radiation Protection and Measurements (NCRP). The Council strives to provide accurate, complete and useful information in its reports. However, neither the NCRP, the members of NCRP, other persons contributing to or assisting in the preparation of this report, nor any person acting on the behalf of any of these parties (a) makes any warranty or representation, express or implied, with respect to the accuracy, completeness or usefulness of the information contained in this report, or that the use of any information, method or process disclosed in this report may not infringe on privately owned rights, or (b) assumes any liability with respect to the use of, or for damages resulting from the use of, any information, method or process disclosed in this report.

Library of Congress Cataloging in Publication Data National Council on Radiation Protection and Measurements. Radiological assessment. (NCRP report, ISSN 0083-209X ; no. 76) "Issued December 1, 1983." Bibliography: p. Includes index. 1. Radioisotopes-Physiological effect. 2. Radioisotopes-Migration. 3. Radioisotopes-Migration-Mathematical models. 4. Ionizing radiation-Measurement-Mathematical models. 5. Radioactive pollution. 6. Environmental health. I. Title. 11. Series. RA1231.R2N26 1983 628.5 84-4773 ISBN 0-913392-66-9

Copyright O National Council on Radiation Protection and Measurements 1984 All rights reserved. This publication is protected by copyright. No part of this publication may be reproduced in any form or by any means, including photocopying, or utilized by any information storage and retrieval system without written permission from the copyright owner, except for brief quotation in critical articles or reviews.

Preface T h e management and treatment of radioactive effluents has resulted in controlling exposure of the public to low levels which can be difficult and expensive to verify by environmental monitoring. Accompanying these lower levels of exposure has been an increased knowledge of environmental processes (especially bioaccumulation) which can result in additional exposure which may be greater than that arising from the intake of the environmental radioactivity in air and water alone. In the case of potential groundwater contamination, the exposure to the radioactivity may not even occur for time periods extending to thousands of years and beyond. As a result, the assessment of the potential consequences of the release of radioactive materials to the environment has required the use of mathematical models. Since the ultimate goal of radiological assessment is t o develop relationships between the source term or input of radionuclides to the environment and potential health effects in man, environmental transport models can be very important in some situations. These mathematical models quantitatively describe the air, water, and ground pathways, including the movement of the radioactivity through food pathways. Mathematical models can be used for a variety of purposes, including evaluation of (1) proposed discharges of radionuclides, (2) the routine operational release of radioactivity, and (3) the accidental release of radioactivity to the environment. The use of environmental transport models for radionuclides has been widely accepted with the result that computerized mathematical models (codes) have proliferated. Considerable variation exists in sophistication among models, the types of parameters needed for the models, and the degree t o which the models have been validated. T h e purpose of this report is to review the current status of the application of radionuclide transport models from the point of discharge to the environment to the point of intake by man. Models are reviewed that describe the transport of radionuclides through the atmosphere, surface and ground waters, deposition on terrestrial surfaces and in sediments, and accumulation in food products. Usage factors are considered that determine the intake of radionuclides by ...

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humans due to dietary habits, physiological parameters, and living customs. Evaluation of the prediction capabilities of the various models is important in determining their limitations in meeting current and future requirements for radiological assessment. This report includes an in-depth analysis of the data base accompanying these models in order to examine potential uncertainties inherent in the choice of model input parameters. Where available, model validation experimental results are included. Although the report is written as a reference document for the more technically sophisticated user of environmental transport models, it should be useful to others because of the information provided on important factors that influence environmental transport. The Council has noted the adoption by the 15th General Conference of Weights and Measures of special names for some units of the SysGme International d'UnitCls (SI) used in the field of ionizing radiation. The gray (symbol Gy) has been adopted as the special name for the SI unit of absorbed dose, absorbed dose index, kerma, and specific energy imparted. The becquerel (symbol Bq) has been adopted as the special name for the SI unit of activity (of a radionuclide). One gray equals one joule per kilogram; and one becquerel is equal to one second to the power of minus one. Since the transition from the special units current employed-rad and curie-to the new special names is expected to take some time, the Council has determined to continue, for the time being, the use of rad and curie. To convert from one set of units to the other, the following relationships pertain: 1 rad = 0.01 J kg-'= 0.01 Gy 1curie = 3.7 x 10'' S-' = 3.7 X 10'' Bq (exactly). The present report was prepared by the Council's Task Group 2 and 3 of Scientific Committee 64. Serving on the Task Group were: William L. Templeton, Chirrnan. Task Cmup 2 Battelle, Pacific Northwest Laboratory Richland, Washington

John E.Till, Chairman, Task Croup 3 Radiological Assessment Corp. Neeses, South Carolina

Members David A. B a k e r Battelle, Pacific Northwest Laboratory Richland, Washington B. Gordon Blayloek Oak Ridge National Laboratory Oak Ridge, Tennessee Richard B. Codell U.S. Nuclear Regulatory Commission Washington, D.C. David N. Edgington University of Wisconsin Center for Great Lakes Studies Milwaukee, Wisconsin F r a n k A. Gifford Atmospheric Environmental Research Oak Ridge, Tennessee F. Owen Hoffman Oak Ridge National Laboratory Oak Ridge, Tennessee

Yook Ng Lawrence Radiation Laboratory Livermore, California William L. Robison Lawrence Livermore Laboratory Livermore, California J a m e s 0. Duguid Battelle Memorial Institute Columbus, Ohio David A. Waite Battelle Memorial Institute Columbus, Ohio J o h n P. Witherspoon Oak Ridge National Laboratory Oak Ridge, Tennessee

Consultants

George G. Killough Oak Ridge National Laboratory Oak Ridge, Tennessee Gunther Scbwarz Brinck System Planning Aechen, Federal Republic of Germany Yasuo Onishi Battelle, Pacific Northwest Laboratory Richland, Washington

J a m e s G. Droppo Battelle, Pacific Northwest Laboratory Richland, Washington Charles W. Miller Oak Ridge National Laboratory Oak Ridge, Tennessee

Serving on the Scientific Committee were: Richard Foster, Chairman (1979-1981) Sunriver, Oregon

Melvin W. Carter, Chairman (1981-present) Georgia Institute of Technology Atlanta, Georgia

Merril Eisenbud

William A. Milla

New York University Tuxedo, New York John W. Healy Los Alamos National Laboratory Los Alamos, New Mexico William E. Kreger Bainbridge Island, Washington

Nuclear Regulatory Commission Washington, D.C. J. Newel1 Stannard University of Calif., San Diego La Jolla, California

McDonald E. Wrenn University of Utah Salt Lake City, Utah

NCRP Secretariat-E. Ivan White

The Council wishes to express its appreciation to the members and consultants for the time and effort devoted to the preparation of this report. Warren K. Sinclair President, NCRP Bethesda, Maryland April 30, 1984

Contents Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Assessment of Radionuclides Released to the Atmosphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Atmospheric Transport Models . . . . . . . . . . . . . . . . . . 2.1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.2 Theories of Atmospheric Diffusion . . . . . . . . . . . . 2.1.3 Types of Atmospheric Models . . . . . . . . . . . . . . . . 2.1.4 Parameters of Atmospheric Models and Their Variability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.5 Variability of Concentration Estimates . . . . . . . . . 2.2 Radionuclide Deposition and Resuspension . . . . . . . . . . . 2.2.1 Deposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.2 Resuspension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Terrestrial Transport and Bioaccumulation in TerrestrialFoodProducts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1 Transfer to Vegetation . . . . . . . . . . . . . . . . . . . . . . 2.3.2 Transfer to Animal Products . . . . . . . . . . . . . . . . . 2.4 Data Base for Terrestrial Transport Bioaccumulation Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.1 Transfer to Vegetation . . . . . . . . . . . . . . . . . . . . . . 2.4.2 Transfer to Animal Products 2.5 Special Case Radionuclides (Tritium. Carbon-14) . . . . . 2.5.1 Tritium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5.2 Carbon-14 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. Assessment of Radionuclides Released to Surface Waters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Surface Water Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.2 Model Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.3 Evaluation of Parameters and Data Bases . . . . . . 3.1.4 Distribution Coefficients (KD). . . . . . . . . . . . . . . . 3.1.5 Verification of Models . . . . . . . . . . . . . . . . . . . . . . . 3.1.6 Validation and Data Sets . . . . . . . . . . . . . . . . . . . .

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3.2 Bioaccumulation Factors (BF) . . . . . . . . . . . . . . . . . . . . . . 3.2.1 Bioaccumulation Factors for Cesium. Cobalt. and

Strontium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Factors for Iodine and Ruthenium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.3 Bioaccumulation Factors for Plutonium. Uranium and Radium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.4 Bioaccurnulation Factors for Carbon and Tritium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.5 Factors Influencing the Variability of Reported Bioaccumulation Factors . . . . . . . . . . . . . . . . . . . 3.2.6 Uncertainties Associated with . Bioaccumulation factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Assessment of Radionuclides Released to Groundwater . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.1 Types of Groundwater Assessments Needed . . . . 4.2 Types of Groundwater Models . . . . . . . . . . . . . . . . . . . . . . 4.2.1 Groundwater Models for Low-Level Waste . . . . . 4.2.2 Groundwater Models for High-Level Waste Repositories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.3 Performance Assessment for Mill Tailing Waste Migration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Equations for Groundwater Flow and Radionuclide Transport . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.1 Groundwater Flow . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.2 Mass Transport . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.3 Chain Decay of Radionuclides . . . . . . . . . . . . . . . . 4.3.4 Percolation of Water into the Ground . . . . . . . . . 4.4 Parameters for Transport and Flow Equations . . . . . . . . 4.4.1 Dispersion and Diffusion in Porous Media . . . . . . 4.4.2 Porosity and Effective Porosity . . . . . . . . . . . . . . . 4.4.3 Hydraulic Conductivity for Saturated Flow . . . . . 4.4.4 Adsorption and Retardation Coefficients . . . . . . . 4.5 Methods of Solution for Groundwater Movement and Solute Transport . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5.2 Numerical Methods . . . . . . . . . . . . . . . . . . . . . . . . . 4.6 Model Validation. Use and Misuse . . . . . . . . . . . . . . . . . . 4.6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6.2 Model Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6.3 Examples of Validation . . . . . . . . . . . . . . . . . . . . . . 4.6.4 Use of Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.2 Bioaccurnulation

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4.6.5 Misuse of Models . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Usage Factors for Predicting Exposure to Man . . . . . . . 5.1 Dietary Pathway Usage Factors . . . . . . . . . . . . . . . . . . . . . 6.1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1.2 Generic Usage Factors . . . . . . . . . . . . . . . . . . . . . . . 5.1.3 Usage Factors for Terrestrial Foods . . . . . . . . . . . 5.1.4 Usage Factors of Aquatic Foods . . . . . . . . . . . . . . . 5.1.5 Usage Rates for Water and Other Beverages . . . . 5.2 Inhalation Pathway Usage Factors . . . . . . . . . . . . . . . . . . 5.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.2 Minute Volumes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.3 Significant Factors Affecting Minute Volumes for Radionuclide Intake via Inhalation . . . . . . . . . . 5.2.4 Average Time Spent at Rest and a t Light to Moderate Activity . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.5 Summary and Discussion . . . . . . . . . . . . . . . . . . . . 6.3 Reduction in External Exposure from Shielding Due to Buildings. Homes. and Vehicles . . . . . . . . . . . . . . . . . . . 6 Identification of Uncertainties Associated with Model Predictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Sources of Model Uncertainties . . . . . . . . . . . . . . . . . . . . . 6.3 Determination of Model Uncertainties . . . . . . . . . . . . . . . 6.3.1 Model Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.2 Parameter Inprecision Analyses . . . . . . . . . . . . . . . 6.3.3 The Effect of Bias in the Selection of Parameter Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4 Uncertainties Among Various Types of Models . . . . . . . 6.4.1 Atmospheric Transport Models . . . . . . . . . . . . . . . 6.4.2 Terrestrial Food Chain Transport Models . . . . . . 6.4.3 Specific Activity Models for % and I'"C . . . . . . . . 6.4.4 Surface Water Transport Models . . . . . . . . . . . . . 6.4.5 Aquatic Food Chain Transport Models . . . . . . . . . 6.4.6 Groundwater Transport Models . . . . . . . . . . . . . . . 6.4.7 Human Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 The Application of Models for Environmental Assessments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1 Classes of Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1.1 Environmental Assessment Models . . . . . . . . . . . . 7.1.2 Research Models . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2 Application of Environmental Assessment Models for Screening . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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196 198 198 198 199 200 204 208 208 208 210

214 216 216 217 219 219 220 220 220 221 225 225 227 228 229 230 230 231 231 232 233 233 233 234 235

7.3 Improvement of Radiological Assesment Models . . . . . . 7.3.1 Reduce Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . 7.3.2 Model Simplification . . . . . . . . . . . . . . . . . . . . . . . . 8 Conclusions and Recommendations . . . . . . . . . . . . . . . . . . 8.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2 Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . APPENDIX A: Applicability of Models for Routine Releases to the Accident Situation . . . . . . . APPENDIX B: Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The NCRP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . NCRP Publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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1. Introduction The development of nuclear material for national defense, of nuclear energy for the generation of electricity, and the applications of radionuclides in medicine, industry, and consumer products result in the release of radioactive material into the environment. Assessment of the radiological impact or consequences of the release of these materials into air and water, or their disposal in the ground, is a quantitative procedure. Fig. 1.1 shows the major steps in this assessment process and the pathways between the source and released material (source term) and the intake by individuals. T o describe these pathways quantitatively requires the use of mathematical models which incorporate the many factors that cause or affect the movement of radionuclides from one compartment to another. In Fig. 1.1 the arrows indicate the links between compartments where the application of mathematical models is useful. These models predict the transport, bioaccumulation, and intake by humans of radionuclides released to the environment. With this knowledge of the amounts of radioactive material released to the environment and ultimately ingested or inhaled, radiation dose may be calculated directly using conversion factors that relate the quantity of the energy absorbed in human tissues to external or internal sources. The ultimate goal of radiological assessment is to develop relationships between the source term or input of radionuclides t o the environment and resulting health effect upon man. A basic tenet for radiation protection of public health is to maintain exposures as low as reasonably achievable (ALARA), taking economic and social considerations into account, within the overall constraint of dose limits. This philosophy requires that models provide reasonable assurance that routine exposure of the public will be in accordance with regulatory guidelines, and also necessitates the use of models in the development of an optimum cost-benefit design for effluent treatment techniques. Mathematical models can be used to fulfill a variety of objectives. They are used for the preoperational evaluation of discharges of radionuclides to determine dominant pathways of exposure, key radionuclides in the source term, and the critical exposure groups or 1

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1. INTRODUCTION

SURFACE WATER TRANSPORT

DEPOSITION TERRESTRIAL

BIOACCUMULATIO IN FOOD PRODUCT

Fig. 1.1 Major steps considered in evaluating the effects of radionuclides released to the environment. (Crosshatched boxes indicate areas not addressed in this report.)

INTRODUCTION

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individuals. During periods of actual emissions, models are relied upon to guide operation of effluent treatment systems, environmental surveillance, predict concentrations in the biosphere which are below detectable limits, and convert measured values of radionuclide intake and exposure, into estimates of radiological dose. The use of environmental transport models for radionuclides has been widely accepted, and this methodology will be helpful to future understanding of the transport of many non-radioactive substances whose chemical behavior is similar to specific radionuclides. Considerable variation exists in sophistication among models, the availability of parameter values, and the degree to which models have been validated. The purpose of this report is to review the current status of the application of radionuclide transport models from the point of discharge to the environment to the point of intake by man. This process, called radiological assessment, is illustrated in Fig. 1.1and begins by defining the quantity of radionuclides that are released and enter the environment. Uncertainties in the measurements or estimates of the source term are passed on to the assessment calculations. This report does not specifically address the development of source terns; however, it should be borne in mind that important information about source terms must be available in order to determine which radionuclide transport models to use in an assessment. This information should incorporate the proximity of different points of release, the time distribution of release, the quantity and species of radionuclides released, and the chemical and physical form of the radionuclides. In the description of the models that follow, sufficient information is presented to allow the user to determine which of the source term conditions listed above should be considered. Models are reviewed that describe the transport of radionuclides through the atmosphere, surface waters, and ground waters, deposition on terrestrial surfaces and in sediments, and accumulation in food products. Uptake of radionuclides by humans is determined with usage factors that describe dietary habits, physiological parameters, and living customs of the receptors. The final steps in the assessment process are estimating dose and health effects from exposure to the radionuclides. Because these last two areas are under study by other committees of the NCRP, dose rate factors and health effects are not included in this report. Radionuclides may be released under a controlled situation in which the point of release, the quantity of radionuclides, and the duration of release are predetermined and monitored. This is commonly referred to as a routine or chronic release and most models assume that an equilibrium condition exists between the source term and concentra-

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1.

INTRODUCTION

tions in model compartments. On the other hand, radionuclides may also be released in an uncontrolled situation such as during an accident in which a pulse of radioactivity escapes for a brief period. This report focuses on models that deal with routine releases although the applicability of equilibrium models to the accident situation is addressed in Appendix A. The report also focuses on methods for assessing exposure to individuals (i.e., critical groups) rather than the collective exposure to large populations, i.e. the methods provide assessments applicable to critical groups representative of individuals in a specific location having specific dietary habits and not all persons within a large geographical area. The latter would involve summations over large distances and long time periods, factors which greatly increase the uncertainty of the assessment. As previously stated, evaluation of the predictive capabilities of the various models is important in defining the limitations in use of the models in meeting current standards and for guiding future decisions on degree of protection desired and achievable. For the models to be useful, it is essential to know their uncertainties and their potential to over- or under-predict dose. This report includes an in-depth analysis of the data base accompanying these models in order to examine potential uncertainties inherent within the choice of values for selected model parameters. Also, where available, the results of model validation experiments which compare model predictions with field observations are included. For those models and parameters that are dependent on specific elements, the discussion is limited to those of most concern for the uranium fuel cycle; these are cobalt, strontium, ruthenium, iodine, cesium, radium, uranium, and plutonium. The specific radionuclides, tritium and carbon-14, are given individual consideration and treated as tracers in the hydrologic and carbon cycles, respectively. The report is written as a reference document for users having a considerable range of technical knowledge of environmental transport. For example, Sections 2, 3, and 4 contain details of mathematical models for atmospheric, surface water, and groundwater transport which are likely to be fully understood only by those with expertise in these areas. However, others are expected to find these sections useful because they provide information on the important factors that qualitatively influence environmental transport. A glossary of terms is included in Appendix B. The remaining sections are expected to be of equal interest to all who must deal with radiological assessment. Because of the interdisciplinary nature of the study, each section is preceded by a concise summary of the environmental transport processes being discussed and how the information relates to the overall assessment scheme shown in Fig. 1.1.

2. Assessment of Radionuclides Released to the Atmosphere Radionuclides released to air are transported away from the point of release and dispersed through atmospheric mechanisms. The objective of atmospheric transport models is to predict the concentration of radionuclides at specific locations surrounding the source. I n order to do this, one must first know the release rate of each nuclide (Ci s-I), physical characteristics of the source (such as stack height), and meteorological data in the vicinity of the point of release. The concentration i n air (Ci m-3) is the input data used to calculate rate of intake by inhalation; deposition (Ci m-2) on soil and water for external exposure rates; intake rate from consumption of growing crops either as a result of direct deposition or resuspension from soil; rate of intake as a result of accumulation by food crops from soil; and exposure due to immersion in a radioactive cloud. Radionuclides may also enter the soil-crop pathway as a result of irrigation with contaminated water. The ultimate goal of terrestrial transport and bioaccumulation models is to determine the quantity of radionuclides reaching man through the food chain. Once the concentration in food or on land surfaces has been calculated, the radiological exposure to individuals may be estimated with appropriate usage and dose rate factors. Tritium and carbon-14 are two radionuclides treated o n a special case basis because of their ubiquitous nature and because of their association with water and carbon dioxide respectively, in the environment.

2.1 Atmospheric Transport Models 2.1.1 Introduction Radionuclides entering the atmosphere from natural and manmade sources are transported and diluted by atmospheric processes. In this 5

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2. ASSESSMENT OF RADIONUCLIDES

section atmospheric transport and diffusion models that are available to describe this phenomenon are discussed briefly and their properties evaluated. Emphasis, however, is given to the most widely used approach, the Gaussian plume model. Our interest is in models that can be used to simulate plumes of material emitted from point sources such as containment leaks, for time periods of a few tens of minutes or more, and for distances up to approximately 100 km from source, within which it is convenient to distinguish between short-range, localscale (0-10 km) models and longer-range, regional-scale (>lo km) models. Airborne radionuclides, like other atmospheric contaminants, are transported by such large, essentially horizontal and two-dimensional motions of atmospheric wind systems as the weather map's "highs and lows." These transport winds are ordinarily treated as given input quantities, and atmospheric models attempt to account for the effect of turbulent diffusion. Turbulent diffusion in the atmosphere occurs a t widely varying rates. It may proceed a t nearly the slow rate of molecular diffusion on a calm, clear night; but most of the time, atmospheric diffusion is much faster. Consequently, the correct specification of turbulent diffusion is a crucial element of atmospheric models. The motion of large-scale winds over the surface of the earth sets up a turbulent boundary layer, or mixed layer, whose highly variable depth and diffusive properties are controlled by two distinct but interrelated turbulence effects; (1) Intense mechanical mixing is caused by turbulence in the shear zone created by the drag of the ground surface on the lower layers of the atmosphere. This effect is stronger the higher the wind speed is in the free atmosphere over the mixed layer, and the rougher the underlying surface. The length scale of the resulting turbulence is related to the size of the surface roughness elements (grains of dirt, vegetation, buildings, forest cover, water waves, city streets, canyons, etc.). (2) Solar heating of the earth's surface creates buoyant thermals, i.e., large, rising "bubbles" of warm air, which result in an upward heat flux. These thermally-driven eddies are much larger than the mechanically-produced eddies and are more vigorous the more intense the upward heat flux a t ground level. The mixed layer is deep, on the order of a kilometer or more, and diffusion is rapid, when thermal and mechanical turbulence effects are strong. When they are weak, as on a calm, clear night, the boundary layer can be only a few meters thick and turbulent diffusion above it is virtually absent. Fig. 2.1 illustrates the daytime portion of this characteristic diurnal sequence of mixed-layer depth changes, as measured simultaneously by vertically-oriented acoustic radar, and pulsed-laser instruments

2.1 ATMOSPHERIC TRANSPORT MODELS

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2.

ASSESSMENT OF RADIONUCLIDES

(Johnson and Ruff, 1975). The essence of the problem of atmospheric modeling is to incorporate relevant physical details of this highly variable, turbulent-flow process into reasonable computer algorithms capable of simulating atmospheric diffusion. Detailed discussions of the physics of the atmospheric boundary layer can be found in the monograph by Lumley and Panofsky (1964), and in two American Meteorological Society workshop volumes (Haugen, 1973; Wyngaard, 1980).

2.1.2

Theories of Atmospheric Diffusion

The mean value of air concentration, x , of a radionuclide (or any other airborne material) is a function of position and time, x = x (x, y, z, t). The object of an atmospheric transport and diffusion model is to specify x and its frequency distribution a t any point in space. Three principal theoretical approaches are available, the so-called statistical, gradient-transport, and similarity theories. G.I. Taylor's (1921) statistical theory assumes a stationary, homogeneous turbulence field and derives x in terms of the mean square displacement of an air "particle" from its average position. Gradient-transport theory, or K-theory, assumes that the material flux, I",, is proportional to the local concentration gradient in the 4-direction and from this derives a diffusion equation based on mass continuity:

where I", = material flux in the xi direction (g s-'m-' or Ci s-'m-'1, Kij = the (i, j) - th component of the diffusion tensor (m2s-I), i, j = 1, 2, 3, x = concentration (g m-3 or Ci m-3), q = coordinate (m) (in what follows, x, y, and z are sometimes substituted for xl, x2, and x3, respectively).

The nine components of Kij form the eddy diffusivity tensor. It cannot in general be assumed that they are constants. In the simplest case, when the off-diagonal (i # j) terms equal zero and the diagonal terms (i = j) are constant, the classical Fickian form of the diffusion equation results, for which many solutions are known. The eddy diffusivity is very much larger than (lo8 to 10'' times) its molecular counterpart. This situation is obtained in the atmosphere only a t very large scales, approaching the global limit. At the smaller scales of

2.1 ATMOSPHERIC TRANSPORT MODELS

1

9

interest to us, the K's are in general functions of x and z, and the offdiagonal components Kx,and K,, are important because of wind shear. Monin and Yaglom (1971), Yaglom (1975), and Pasquill (1974) have published reviews of the few known analytic solutions of Eq. (2-1) for atmospheric boundary layer flows; these solutions tend to be quite complicated mathematically. Similarity theory attempts to overcome the restriction to turbulence homogeneity of statistical theory, and the great complexity of realistic K-theory solutions except in the simplest asymptotic cases, by analyzing the problem dimensionally. But boundary layer turbulent flow in the atmosphere is governed by a large number of physical variables, in addition to space and time coordinates, including surface heat flux, surface roughness, ambient wind speed, air viscosity, source height, and many other less well-defined factors. Consequently, a large number of characteristic dimensionless groups arise, and similarity solutions have been found only for a few limited problems such as the mean, steady-state, axial concentration distribution x (x, 0, 0) in the near-surface layer, which is roughly the lowest 10% of the boundary layer. For more detailed understanding, summaries of all three of these theories from the standpoint of atmospheric pollution applications can be found in Pasquill (1974, 1975) and Gifford (1968, 1975). A fourth class of diffusion theory, called second- or, more generally, higher-order closure theory has recently been applied to atmospheric diffusion modeling, although applications to turbulent flows were first made more than 40 years ago. This theory is based on the principle that knowledge of all the moments of the distribution of a quantity is fully equivalent to knowing its distribution. Expressions for the moments, i.e. the mean, variance, skewness, and so on, of the turbulent velocity field can be obtained from the equations of motion, and similarly for the related field of concentration. However, it develops that the resulting hierarchy of moment equations is infinite; moments of any order turn out to depend on those of the next higher order. Gradient-transport theory can be viewed from this perspective as a first-order truncation of the equation system, in which the flow is characterized in terms of the gradient of the mean concentration. Second-order closure methodology bounds the system by means of assumptions relating higher-order moments to the second-order moment. Atmospheric modeling applications are mathematically complicated and require significant amounts of large-computer time (Donaldson, 1973; Lewallen and Teske, 1976). The best use of this methodology appears to be as a powerful research tool for simulating boundary-layer diffusion in typical, representative situations, rather than as a means of attacking particular operational problems.

10

2.1.3

/

2. ASSESSMENT OF RADIONUCLIDES

Types of Atmospheric Models

The above few interrelated theories of atmospheric diffusion have been applied to the problem of estimating concentration patterns of airborne radionuclides, in order to satisfy various regulatory requirements, in a much larger number of atmospheric diffusion models. The literature describing these applications is vast and growing and has produced a number of critical surveys and reviews, aimed a t the needs of various classes of users. The following recent reviews of this heterogeneous and rapidly expanding body of applications are especially relevant to this report: Barr and Clements (1983); Hanna, et al. (1982); Drake, et al. (1979); Johnson, et al. (1976); Liu (1980); USEPA (1978); Turner (1979); Eliassen (1980); Hoffman, et al. (1977); Crawford (1978); and Hanna (1983). There is a t the moment no particularly standardized scheme for classifying diffusion model types. Models have been grouped in the above reviews in terms of the diffusion theories involved, according to the complexity of the numerical modeling required, by source configuration, by the distance of material transport, and by their relation to particular regulatory requirements. Table 2.1 is a summary of atmospheric model types and characteristics, condensed from tables given by Drake et al. (1979) and Hosker (1983). The classification is a composite in that it reflects regulatory requirements, source types, numerical aspects, and distance scales; but its description of model characteristics is widely understood and accepted by the modeling profession. For present purposes, it provides a useful, operational classification of models. The following brief description of these models, mostly abstracted from Hosker's (1983) review, conveys only their essential features in qualitative terms. The reader requiring details of mathematical structure and input parameter requirements of models should consult the survey by Liu (1980), who has outlined the details of a large number of atmospheric models of various types in convenient tabular form. Gaussian plume and puff models The most widely used model of diffusion is the continuous pointsource Gaussian plume formula: x ( x , Y, z ) / Q = (2*a,aZu)-' exp(-3/2d) (2-2) [exp(-(z - he)'/2a,2) + exp(-(z + h#/2d)]

TABLE 2.1-Characteristics of tranmort and dis~ersionmodels" Model Type

GeorC8p:ical

Steady-State

or Time-Dependent

Frame of Reference

Reaction Mechanisms

Removal Mechanisms

Treatment of Turbulence

Topography Treated

Gaussian plume and puff

Local

Steady-state or Timedependent

Eulerian or Lagrangian

Nonreactive or reactive

Dry and wet

Diffusion coefficients

Homogeneous to simple terrain

Regional trajectory

Regional or National

Time-dependent

Lagrangian, or mixed Lagrangian and Eulerian

Nonreactive or reactive

Dry and wet

Difhion coefficients or eddy diffusivities

Nonhomogeneous to complex terrain

Box and multi-box

Local or Regional

Steady-state or Timedependent

Eulerian or Lagrangian

Nonreactive, reactive, or gas-to-particle

Dry and wet

Well-mixed, or eddy diffusivities

Homogeneous to simple terrain

Grid

Local or Regional

Steady-state or Timedependent

Eulerian

Nonreactive, reactive, or gas-to-particle

Dry and wet

Eddy diffusivities, or complex formulation

All terrain

Particle

Local or Regional

Time-dependent

Mixed La-

Nonreactive, reactive, or gas-to-particle

Dry and wet

Eddy diffusivities

All terrain

grangian and Eulerian

Cm

( I ,

TABLE 2.2-Continued Model Type

Geographical Scale

Steady-State or Time-Dependent

Frame of Reference

Reaction Mechanisms

Removal Mechanisms

Treatment of Turbulence

Topography Treated

Global

Global

Time-dependent

Eulerian

Nonreactive or reactive

Dry and wet

Eddy diffusivities

All terrain

Physical

Local

Time-dc-

Mixed Lagangian and Eulerian

Nonreactive

None

Not applicable

All terrain

pendent

"Modified from Drake rt aL. 1979, and Hosker, 1983.

i 4

8

?

z2 C

E

t]

$'4

where

x

(x, y, z ) = steady-state concentration a t a point (x, y, z ) , (g mV3or Ci m-3), Q = continuous release strength (g s-' or Ci s-'), u = mean (horizontal) transport wind speed in x-direction (m s-'), a,, a, = horizontal and vertical standard deviation of concentration distribution (m), and he = effective source height (m).

The double exponential term in z accounts for a conventionally assumed "reflectionn of the plume by the underlying surface. The dispersion lengths a, and a, are empirically-based functions of downwind distance, x, atmospheric stability conditions, source height, and surface roughness. The various series of diffusion field trials that provide values of a, and a, were made mostly a t atomic energy laboratories and field sites during the past 25 years or so. These experimental series have been reviewed in detail by Islitzer and Slade (1968) and Draxler (1979). The Gaussian plume model is illustrated in Fig. 2.2(a). Eq. (2-2) is an exact solution to the diffusion equation under certain conditions. For a stationary, homogeneous turbulent flow (i.e., for which statistical properties do not vary in time or space) it describes the near-field of diffusion exactly, based on statistical theory [see, e.g., Hinze (1959)l. Also, it is a solution to the Fickian or constant-K diffusion equation which makes it useful for global diffusion problems. For emissions not significantly affected by strong surface layer shears the theoretical credentials of the Gaussian-plume formula allow its strict application very near the source (out to a few hundred meters), and very far away ( 2 1000 km). Extension to regional-scales, i.e. distances from a source on the order of a few tens to hundreds of km, is accomplished by using the empirical a,- and a,-curves, which will be described below. Gaussian puff models assume that a plume element in the form of a three-dimensional Gaussian function is moved horizontally by the mean transport wind field u(x, y), i.e., the weather-map wind field, which is determined by standard principles of meteorological analysis and prediction. This kind of model can account for complicated wind transport paths, a situation illustrated schematically in Fig. 2.2(b), since it is not restricted to a constant value of u; and consequently it has been widely applied a t regional scales. There is comparatively little experimental diffusion data available a t these distances, so specifying any a-value is speculative. There is an important difference between puff models and the plume

6

14

/

2.

ASSESSMENT OF RADIONUCLIDES

Fig. 2.2(a) Coordinate system of the Gaussian plume model, showing distribution of concentration in the horizontal and vertical (after Twner, 1969).

yw

RELEASE POINT

Fig. 2.2(b) Schematic illustration of a "Puff" model (after Hanna et al., 1982).

model specified by Eq. (2-2). Models based on Eq. (2-2) attempt to simulate the time-average field of concentration, usually for an averaging time of the order of a few tens of minutes. In contrast, the socalled-puff models try to simulate the instantaneous plume spreading about its axial centroid, in the form of a sequence of overlapping puffs, resulting in a kind of "snapshot" of the plume. Fig. 2.3(a) and (b)

2.1 ATMOSPHERIC TRANSPORT MODELS

1

17

illustrate this conceptual difference by means.of actual instantaneous and time-exposure photographs of wind-tunnel generated smoke plumes. Because puff models portray the instantaneous plume concentration field, they are appropriate for estimating the maximum (shortterm) concentration a t a point. When combined with trajectory models, they also are useful in the important case of accidental releases, because releases may then vary in time or occur in brief bursts, such that a steady release cannot be assumed. Trajectory Models

At regional or greater travel distance, where an adequate empirical basis is lacking, trajectory models are frequently used. In these models, material transport is driven by the observed wind field, for instance that of a weather map, or by the output of a predictive or forecast wind-field model, as illustrated in Fig. 2.2(b) for the puff model. Diffusion is accounted for by moving-box, growing-puff, or small airparticle elements for which atmospheric diffusivity is specified according to one of the principles outlined in section 2.1.2 above, most often by some form of K-theory. Statistical-sampling, or "Monte-Carlo" forms of puff-trajectory models have also been proposed (Hanna, 1983). Trajectory models are quite flexible and can, in principle, account for wet- and dry-removal processes (washout and fallout), chemical transformations, and time-varying wind and stability conditions. Disadvantages of trajectory models arise from their sensitivity to errors in selecting values for the driving wind field, and from uncertainties associated with modeling time-variable diffusion and removal processes along the trajectory. To these should be added the problem that, although many trajectory models are in use, few have yet been adequately evaluated.

Grid Models Grid models are finite-difference approximations to the equation of motion, continuity, diffusion, and species conservation and removal. A region is covered by a grid of points at which solutions to the governing equation system are generated using standard finite-differencing techniques. There are several problems with the use of grid models. Computational instabilities, which can make nonsense of a solution in a few time steps, must be carefully controlled by proper choice of space and time grid intervals. To avoid this type of finite-

18

/

2. ASSESSMENT OF RADIONUCLIDES

differencing error, as well as to increase computational efficiency and reduce computer running time, pseudo-spectral models have been introduced. In these grid models, finite Fourier Transforms of the concentrations field are used to define derivatives in the diffusion equation. Christensen and Prahm (1976) discuss the computational advantages of the technique; and Prahm and Christensen (1977), and Mills and Hirata (1978) describe applications to long-range diffusion problems. Practical limitations are imposed on grid spacing in all such models by available computer capacity. Resulting grids are generally incapable of resolving important initial and boundary conditions in adequate detail, such as point sources or any but the largest of terrain features. This severely restricts the applicability of grid models to a large class of transport problems. Consider the fact that plumes from point sources (chimneys, tall stacks, etc.) are commonly observed to be as a rule 10 to 20 times as long as they are wide. (Otherwise they would not be commonly known as "plumes.") Typical grid-model spacings may be 0.5 to 5 km horizontally, often nearer the latter figure. Thus, a grid cannot resolve diffusion from a point-source plume until the plume has traveled many kilometers downwind. This puts quite real practical limits on what is in principle a modeling approach of great generality. Drake et al. (1979), Liu (1980), and Hanna (1983) have summarized existing grid models and their properties.

Particle-in-cell models attempt to overcome the numerical instabilities that affect grid models by calculating a "pseudo-velocityn field, which is composed of the actual velocity field plus a "diffusion velocity" (Lange, 1978). The wind field is assumed to be non-divergent, V . u = 0. The diffusion velocity, u ~ is , defined from gradient transport theory as UD = (Kij . Vxlx) where K is the diffusion tensor. From these definitions and thediffusion equation of K-theory, an equation for the concentration field can be written in terms of the pseudovelocity up: where u = the (vector) wind field (m s-'1,

uD = a diffusion velocity (m s-'),

2.1 ATMOSPHERIC TRANSPORT MODELS L C ~=

/

19

a pseudo-velocity, up = u + UD (m s-'1,

t = time (sec), and

x

= the concentration field a t a point ( x , y, z ) , (g m-3 or

Ci m-3). This equation is evaluated over a three-dimensional grid covering the region of interest. An initial distribution of a large number (on the order of lo4) of particles is specified over the grid; this might, for instance, be in the form of a Gaussian plume. These points are assumed to be transported to new cell locations each time step by u, according to Eq. (2-3). Then a new u~ is computed from the resulting concentration field and the process is iterated. This type of model readily accommodates processes such as a particle settling and deposition, washout, and radioactive decay. As with grid models, the ability of particle-in-cell diffusion models to resolve point-source plumes is constrained by the grid-cell size. In addition, the outer limit of material travel time that can be modeled is restricted by the larger number of points that must be followed to assure adequate definition of concentration gradients at great downwind distances. Finally, the basic theoretical limitations of K-theories, mentioned earlier, are equally applicable to these models.

BOXModels and Global Models Box models are based on mass conservation in a specified volume, in which the materials are assumed to be well mixed. This volume may range in size from a small portion of the boundary layer of a region, through that of the region itself, e.g., the Los Angeles basin (Friedlander and Seinfeld, 1969), to the entire atmosphere, in the example of global dispersion of nuclear weapons debris or COz (Machta, 1973). It is clearly essential in such a model that the time of turbulent mixing through the box be either much shorter or much longer than any time scales associated with removal or chemical transformation processes; otherwise the assumption of uniform mixing will be invalid. The generalization can perhaps be risked that the degree to which a class of models has been validated tends to be inversely proportional to model complexity. Box models, being inherently simple but physically sound, have been widely validated and in general found to perform well. The basic principles of box models have been discussed in the papers by Lettau (1970) and Tennekes (1976).

20

/

2. ASSESSMENT OF RADIONUCLIDES

Global models are not, strictly speaking, a distinct model class but rather are the global asymptotic limits of several of the above model classes. Global circulation models, originally aimed a t weather prediction, have been applied to the problem of climate change caused by anthropogenic increases in atmospheric COz (Smagorinsky, 1974; Manabe and Weatherald, 1967). Global reservoir-type box models have been applied to the climate change problem as has been mentioned; and the Gaussian plume model in a trajectory version has also been applied to material transport at large distances (Heffter and Ferber, 1975). Similar models have been used for many years to estimate long-range transport of radioactive clouds. Despite the fact that a penalty must be paid in terms of computer storage and running time to model the global atmosphere, a major theoretical simplification results from the fact that a constant K for diffusion can be assumed.

Physical Models By appropriate scaling of relevant dimensionless flow parameters, chiefly the Reynolds number for momentum, and Froude number for heat transport, so that laboratory wind- and water-tunnel flows corredly simulate the atmosphere, a large class of complicated flow and diffusion patterns can be studied in detail. Where this procedure applies, it is a much simpler and more economical way to model diffusion in complicated situations, such as in flow over rough terrain and flow in the wakes of buildings and other obstacles. Physical models are used mostly a t the local, short-range scales of diffusion, up to a few kilometers. This is because atmospheric turbulence and diffusion at larger scales are strongly influenced by accelerations arising from the earth's rotation. Abbey (1976) has summarized wind tunnel and related atmospheric modeling of wakes, and Hosker (1983) has provided a detailed discussion of the entire subject of physical modeling of atmospheric flows and diffusion. Particularly for wake and rough terrain flows, physical modeling seems under-utilized in comparison with purely numerical modeling studies. Indeed, for these intricate flows it may provide the main possibility of generating data adequate to validate numerical diffusion models.

2.1.4 Parameters of Atmospheric Models and Their Variability Any of the models so briefly described above could be used to simulate radioactive cloud transport and diffusion. However, the Gaus-

2.1 ATMOSPHERIC TRANSPORT MODELS

1

21

sian plume model has been by far the most widely applied. Hoffman et al. (1977), reviewing 83 computer codes for environmental radionuclide releases, remark that "Nearly all the codes dealing with atmospheric transport are based on the Gaussian plume dispersion model," Similar statements occur in many of the above-mentioned reviews. Turner's (1979) survey of atmospheric models contains 192 references, most of them to models described by some form of Eq. (2-2). The 18 "kinematic models" reviewed in detail by Liu (1980) make explicit use of the Gaussian distribution assumption. There are several reasons for this widespread use, among them the conservatism inherent in the regulatory process. The Gaussian model has been adopted as a standard method in regulating both radioactive (USNRC, 1977a; IAEA, 1980) and other (USEPA, 1978) airborne species. But more importantly, Gaussian models are firmly rooted in available experimental data, have a good if not perfect theoretical basis, and are simple enough to be easily adaptable to a wide variety of air pollution problems. Gaussian models also are the most extensively validated class of diffusion models, and their behavior, including their shortcomings, is comparatively well known. The following discussion of the parameters of atmospheric diffusion models accordingly centers on those of the Gaussian model; but the information applies equally to parameters of the other model types, since it is based on essentially all the available atmospheric diffusion data. Gaussian models have been developed to cope with a variety of pollution situations and regulatory requirements. Some of the factors that different models have addressed include: averaging period; source configuration; average concentration or maximum values vs frequency distribution; receptor configuration; and terrain type. Table 2.2, based on three of Liu's (1980) tables, summarizes the objectives, space- and time-scales, and documentation for the Gaussian models he surveyed. Each of these models contains modules (algorithms) designed to calculate the parameters appearing, explicity or implicitly, in Eq. (2-2) as applied to a particular kind of problem. These parameters might be classified as either basic, derived, or lumped. Basic parameters include: (1) basic fluid properties like viscosity, specific heat, and density-the kind of atmospheric properties normally available in tables; (2) field parameters, including gravitation and the rotational (Coriolis) parameter; and (3) basic measured or well-determined atmospheric quantities like wind-speed, direction, and gradient; temperature and its vertical gradient; humidity; surface heat flux. Derived parameters include: all the diffusivities and diffusion lengths, K,j, ay, a,; the parameters that characterize the stability of the atmosphere with respect to vertical turbulent motions, i.e., Richardson's number,

22 / 2. ASSESSMENT OF RADIONUCLIDES

Busse and Zimmerman (1973)

Busse, A.D. and J.R. Zimmerman, "User's Guide for the Climatological Dispersion Model," Publication No. EPA-RA-73-024 (NTISP B 227346/AS). Environmental Protection Agency, Research Triangle Park, North Carolina 27711, December 1973. Bmbaker, K.L., P. Brown and R.R Cirillo. "Addendum t o User's Guide for Climatological Dispersion Model," Publication No. EPA-460/3-77-105, Environmental Protection Agency, Research Triangle Park, North Carolina 27711, May 1977.

Long-term (monthly, seasonal, or annual) climatological average concentration a t any ground-level receptor from multiple point and area sources in urban areas. CDMQC estimates short-term (hourly or daily) average concentration a t any ground-level receptor from multiple point and area sources in urban areas.

Implicit, up to 100 km

10-month up to 1-year for CDMQC

1-hr up to 24hours

N

'

B% ~d

x

m

p, 0

5! Z

m

'a 0 P

r3

5 E

TALE 2.2-Properties Models

Developers

Reference

of selected goussian modelsa Objectives

tQ

A

Spatial Scales

Temporal Scales

Implicit, up to 100 km

1-hour u p to 1year

\

CRSTER

EPA (1977)

Environmental Protection Agency, "User's Manual for Single Source (CRSTER) Model," Publication No. EPA-450/2-77-013 NTIS PB 271360, Office of Air Quality Planning and Standards, Research Triangle Park, North Carolina 27711, July 1977.

Atmospheric conditions that lead to high ground-level concentration for a given set of emission characteristics over moderately complex terrain. Short-term (hourly or daily) and long-term (monthly or annual) arithmetic average concentration a t any ground-level receptor from single point source. Maximum short-term concentration (hourly or daily) a t any ground-level receptor. Frequency distribution for various concentration levels over different averaging periods.

h,

% E

CI) CI)

?i

Z 4

%

FE 0 2

C

0

5R

GEM

Fabrick et al. (1977)

Fabrick, A., R S . Sklarow and T. Wilson, 'Point Source Model Evaluation and Development Study", Science Application, Inc.. West Village. California. March 1977.

T o estimate short-term (hourly) average concentration a t any ground-level receptor.

ISC

Bowers et al. (1979)

Bowers, J.F., J.R. Bjorklund, and C.S. Chiney, "Industrial Source Complex (ISC) Dispersion Model User'e Guide," H.E.Cramer Company, Inc., Salt Lake City, Utah, January 1977.

Short-term (hourly, up to daily) and longterm (up to 1year) arithmetic average concentration at any ground-level receptor from point, area, and volume sources. Long-term (monthly, seasonal, or annual) climatological average concentration a t any ground-level receptors from point, area, and volume 80urces.

From 100 m up to 100 km

1-hour to 24hours, 1month to 1year

F CL

4

?i

%

tQ

TABLE 2.2-Properties of selected gaussian models' Models

Developers

Reference

Objectives

Pierce, T.E.and D.B.Turner, "Users Guide for MPTEFt," Publication No. EPA-6001 8-80-016, Environmental Protection Agency, Research Triangle Park, North Carolina, 1980.

Short-term (hourly), concentration a t ground-level receptor from multiple point sources.

Q,

Spatial Scales

Temporal Scales

Implicit, up to 100 km

1-hour to 1-day

\

MPTER

EPA (1980)

F)

% rn !2

Xz

Up to one-day arithmetic average concentration a t any ground-level receptor from multiple point sources. MSDM

MESO PLUME

Ermak and Nyholm (1978)

EPA (1979)

4

%

B

0

2

Ermak, D.L. and R.A. Nyholm, 'Multiple Source Dispersion Models," U.C. Lawrence Livermore Lab., Livermore, California, 1972.

T o estimate short-term (hourly) average concentration a t each grid cell within the modeling region.

Up to 100 km

Benkley, C.W.and A. Bass, "Users Guide to MESOPLUME (Mesoscale Plume Segment) Model," Publication No. EPA-60017-80057, Environmental Protection Agency, Washington, D.C.. 1979.

Short-term (hourly, up to several days) arithmetic average concentration a t each grid cell within the modeling region.

Up to several hundred kilometers

1-hour

2

E

U

E? 1-hour to several days

EPA (1979)

Benkley, C.W. and A. Bass, "Users Guide to MESOPUFF (Mesoscale Puff) Model," Publication No. EPA-600/7-80-058, Environmental Protection Agency, Washington, D.C.,

Short-term (hourly to several days) arithmetic average concentration a t each grid cell within the modeling region.

Up to several hundred kilometers

l-hour to several days

Short-term (hourly) concentration a t given ground-level receptor from multiple point sources, line sources, and area sources.

Implicit, up to 100 km

l-hour to l-day

1979.

PAL

Petersen (1979)

Petersen, W.B., "User's Guide for PAL: A Gaussian Plume Algorithm for Point, Area, and Line Sources," Publication No. EPA-600/ 4-78-013, Environmental Protection Agency, Research Triangle Park, North Carolina, February 1978.

Up to one day arithmetic average concentration at any ground-level receptor from multiple point sources, line sources, and area sources.

*

r

h)

TABLE 2.2-Properties of selected gaussian modeIsa Models

Developers

Reference

Objectives

OD

Spatial Scales

Temporal Scales \

PTDIS PTMAX PTMP

PTMAX

EPA (1973)

Turner, D.B.and A.D. Bussee, "User's Guide to the Interactive Versions of Three Point Source Dispersion Programs: PTMAX, PTDIS,and PTMTP," Meteorology Laboratory, EPA, Research Triangle Park, North Carolina, June 1973.

Short-term (hourly) centerline groundlevel concentration downwind from a point source a t distance specified.

See above.

Short-term (hourly) maximum groundlevel concentration under each combination of atmospheric stability and wind speed, conditions from a single point source. Downwind distance of maximum concentration for each combination of atmospheric stability and wind speed cond i t i o n ~from a single point source.

Implicit, up to 100 km

1-hour FJ

*

CI)

8

V)

X

z

4

2 Implicit, up to tens of kilometers

1-hour

See above.

RAM

Turner and Novak (1978)

Turner, D.B. and J.H. Novak, "User's Guide for RAM," Environmental Protection Agency, Research Triangle Park, North Carolina, 1978.

Short-term (hourly) concentration a t any ground-level receptor downwind from multiple point sources. Arithmetic average concentration (up to one day) a t any ground-level receptor downwind from multiple point sources. Short-term (hourly) concentration and up to 24-hour arithmetic average concentration a t any ground-level receptor from multiple point and area sources in urban areas.

Implicit, up to 100 km

1-hour to 24hour

b'

>

2 A

CO

3 z! 0

fi (I)

co

0

3

5u

TABLE 2.2-Properties of selected gaussian modelsa Models

Developers

Reference

Objectives

Spatial Scales

Temporal Scales

Koch and Stadsklev (1974)

Koch, RC. and G.H. Stadsklev, 'A User's Manual for the Sampled Chronological Input Model (SCIM)" GEOMET Report No. 3261, prepared for U.S. EPA under Contract No. 68-020281, December 1974.

Short-term (hourly) concentration and long-term (monthly) arithmetic average concentration a t any ground-level receptor from multiple point and area sources in urban mas. Maximum short-term concentration (hourly) at any ground-level receptor. Frequency distribution for various shortterm concentration levels.

Implicit, up to 100 km

1-hour to 1-year

u 0

SCIM

TCM

Christiansen and Porter (1976)

Christiansen, J.H. and R A . Porter, "User's Guide to the Texas Climatological Model," Texas Air Control Board, Austin. Texas, May 1976.

Long-term (monthly, seasonal, or annual) climatological average concentrations a t each ground-level grid cell from multiple point and area sources in urban areas. Identify high contributors to concentration a t each grid cell.

\

P

% rn !2

B

z

t-3

FE z

2r U

!2

2.1 ATMOSPHERIC TRANSPORT MODELS

32

/

2. ASSESSMENT OF RADIONUCLIDES

Ri, the Monin-Obukhov stability length, L, and the Pasquill class; and various other buoyancy and mechanical turbulence parameters. All these share the characteristic that they can be described by means of theoretically-deduced equations involving the basic parameters. Lumped parameters include quantities like deposition and resuspension velocities, washout coefficients, building-wake corrections, and entrainment velocities. Values of these parameters are more or less well known through experiment but may lack complete theoretical specification in the form of basic, defining equations, because of complexity. Details of how parameters are specified in Gaussian models are summarized in Liu's (1980) review. Although measurement of basic parameters in the field may present problems, and their representativeness must be carefully considered in relation to various model properties such as grid-point locations and spacing, the basic parameters are not usually major contributors to model output variability. T h e uncertainties attributable to the derived and lumped parameters of atmospheric models, particularly the diffusion lengths, stability class, and wet and dry deposition velocities, are usually the most significant factors. 2.1.4.1 Atmospheric Diffusion Categories

Pasquill (1961) proposed dividing all atmospheric turbulence conditions in terms of boundary layer stability into six approximately equally represented classes ranging from class A, very unstable, through class F, very stable. He based values of the diffusion lengths for these classes on existing experiments and theory. Pasquill's diffusion lengths are limited to diffusion from surface-level sources, to downwind distances of about a kilometer over uniform, level, fairly smooth vegetation, and to averages over a few minutes. Near-calm wind, very stable conditions, specifically excluded from Pasquill's original classes, are now sometimes called class G conditions. These classes have been widely applied in atmospheric modeling, in the form of curves of a, and a, vs downwind distance suggested by Gifford (1961), and are sometimes called Pasquill-Gifford (PG) curves. Several alternatives for determining the stability class a t any given time and place are in use. Pasquill's original proposal, a classification scheme based on insolation, cloud cover, and wind speed conditions experienced in the U.K., was modified by Turner (1964) for use with standard U.S. National Weather Service airport observations; this is conveniently expressed in the widely-used STAR code (Holzworth, 1976). Various researchers have proposed classifying stability condi-

2.1 ATMOSPHERIC TRANSPORT MODELS

/

33

tions on the basis of us, the standard deviation of the horizontal wind direction, as measured by a windvane sensitive to turbulent fluctuations. Vertical temperature gradient, as measured between standard heights of 10 and 60 meters, is the method recommended in the U.S. Nuclear Regulatory Commission's Regulatory Guide 1.23 (USNRC, 1972). Stability classification based on the fundamental physical parameters known to characterize atmospheric boundary layer turbulence, i.e. Richardson's number Ri, the Monin-Obukhov stability length L, and convective scaling parameters, is recommended for instance in the report of an American Meteorological Society workshop (Hanna et al., 1977). The remarkable expansion of environmental concerns in the past decade imposes problem conditions far exceeding the inherent limitations to horizontally homogeneous terrain, short distances, steadystate, etc., of the above scheme. Applications are required for great horizontal distances, elevated sources, averaging times up to a year, near-calm, stable conditions, time-variable sources, terrain ranging in type from somewhat irregular to mountainous, and from forests and coast lines to cities. Few of these extensions are supported by really adequate experimental data of the quality and amount that was available to develop the original diffusion categories. Reviews by Gifford (1976), Draxler (1983), and Pasquill (1978) address the basic theoretical issues involved in such diffusion parameterization schemes. Draxler (1979) has summarized important recent atmospheric diffusion experiments aimed at selecting the appropriate diffusion lengths, a, and a,, in all of the above non-ideal situations. Horst, et a1. (1979) and Briggs (1983), among others, have re-examined both the classical and more recent experimental diffusion data sets in detail from the standpoint of contemporary boundary layer theory, in efforts to provide optimum a-parameterizations. Interim practical recommendations are summarized in the workshop proceedings reported by Hanna et a1. (1977) and Crawford (1978). 2.1.4.2

Variability of a, and a,

Residual Scatter The following examples from current literature indicate the residual scatter of u-parameters that can be expected, given optimum specification of atmospheric turbulence type. Figure 2.4 is a plot of measured vs predicted a, values based on three independent series of diffusion

34

/ 2. ASSESSMENT OF RADIONUCLIDES

2.1 ATMOSPHERIC TRANSPORT MODELS

/

35

experiments re-analyzed by Horst, et al (1979). These observations cover a reasonably full range of stability conditions, sampling distances to about 3 km but to 25 km in some cases, and flat prairie or desert terrain. Stability class in this particular example was determined according to the NRC guidelines (USNRC, 1972) by the vertical temperature gradient (AT/Az) method. The predicted a,-values can be seen to be scattered about observed values to within a factor of approximately 2. This scatter is appreciably reduced, to a factor of perhaps 1.6, if account is taken of the effect of the dimensionless quantity S = a,/(xe), which is a complicated, empirically determined function of concentration-averaging time and boundary layer turbulence (i.e., stability properties). Specification of a,

Correct specification of a, proves to be a difficult problem because of the marked stability variation and vertical inhomogeneity of turbulence in the boundary layer. Briggs and McDonald (1978) have reanalyzed the Prairie Grass series of diffusion data (on which the original PG-curves were largely based) on the basis of similarity theory. An example of their results for vertical dispersion is illustrated in Figure 2.5. The quantity u, is the friction-velocity of boundary-layer theory, and h is a scale height for diffusion, defined in terms of the crosswind-integrated ground-level concentration; h e Q (Jxdy)-'. In terms of an equivalent Gaussian distribution, a, = 0.8h, so the scatter of those points reflects the scatter of a,. The logarithmic standard deviation in this case indicates a scatter of a factor of 1.2 to 1.4. This is slightly smaller than the previous result for a,, and probably represents the best that can be achieved with this kind of research-grade experimental data.

Variation of a, and a, with Source Height

The diffusion lengths uy and a, were originally based on empirical concentration data from plumes released near the surface at a height of one meter. Later experiments, for example those discussed by Vogt (1977), and Nickola (1979), indicate a dependence of a, on release height. Hanna (1980) estimates that during the day a, varies only slightly with release height but that a, increases by a factor of about two as source height increases from the surface to several hundred meters.

36

/

2.

ASSESSMENT OF RADIONUCLIDES

Fig. 2.6 Example of resulta from Briggs and McDonald's (1978) analysis of Prairie Grass diffusion data. The curves show vertical dispersion, h, as a function of downwind distance, x; circles are stable values (positive values of stability length, L)and dots are unstable values (negative L-values). Curves illustrate theoretical results from similarity theory (after Brigge and McDonald, 1978).

Effect of Non-Ideal Experimental Conditions An example of diffusion data scatter in non-ideal experimental conditions is shown in Fig. 2.6. These are a,-values, computed by Draxler (1979) using a u8-stability method, from the rough-terrain, Mt. Iron diffusion data series (Hinds and Nickola, 1967). For these data, the scatter of the computed values is about a factor of 2 relative to the observations. For other non-ideal situations, i.e., diffusion at shoreline sites, in complex forests, over cities, at extremely low wind speeds, and at long ranges, data are generally too sparse to support a reliable estimate of scatter (Draxler, 1979). Most studies report only a few experimental values, measured over a range of stability classes. Scatter of diffusion-length estimates will almost certainly exceed a factor of 2 in these cases, and will probably lie somewhere in the range of 2 to 5.

The source height, k,in Eq. (2-2) is termed an effective source height to account for the initial buoyancy and momentum created by

2.1 ATMOSPHERIC TRANSPORT MODELS

/

37

or OBSERVED (Y)

Fig. 2.6 Predictions of a, for Mt. Iron aeries of diffusion experiments, based on wind direction fluctuation, vs observed values (after Draxler, 1979).

the emission of radioactive gases a t high temperatures or under high pressure (Briggs, 1969,1975;Briggs and McDonald, 1978). If the plume is sufficiently radioactive, its buoyancy will be continually augmented by the resulting "self-heating" (Gifford, 1967). Initial plume buoyancy is usually the dominant effect because of the small radioactivity content of most releases. The Gaussian Model accommodates the buoyancy effect by defining an effective source height, h, = h, + Ah, as the sum of the actual source height, k , and the buoyant plume rise, Ah. The practical importance of Ah in concentration calculations can be appreciated from the fact that most large, coal-fired power plants could not meet currently allowable ambient SOn standards without taking credit for Ah. Plume rise in these plants roughly doubles the effective stack height, greatly reducing surface-level concentrations. For radioactive sources, such as operating nuclear power plants, the buoyancy effect is smaller, and is in many cases, negligible. In buoyant rise, the heated plume is moving relative to the surrounding air flow. Small-scale wind shear occurs at the plume's edge (the resulting eddies can often be seen at the edges of power-plant or cooling-tower plumes). This is assumed to result in an entrainment of cooler ambient air into the plume, gradually reducing its buoyancy. The actual rise of the plume, relative to the ambient flow, tends to be a regular phenomenon because it is controlled by the velocity of

entrainment. The plume is a t the same time carried along and deformed by the turbulence in the boundary layer. Thus, the resulting estimates of Ah, and of downwind concentration where the plume reaches the ground, exhibit scatter. Some idea of its magnitude can be gained from Fig. 2.7(a) and (b) (Briggs and McDonald, 1978). Nondimensionalized values of maxium downwind ground concentration, 0.0010

I

" , .c

0

\ R

-

-n LL

?

. .. . A

0

m

0.004

-

0 x

-

E

0

X

0.002 1

2

.v

4

U

e

+( ~ ~ / h , ) h

Fig. 2.7(a) Maximum ground concentration, x,,, sionalized (after Briggs and McDonald, 1978).

0

88. qv

-

v

10

vs wind speed, u, nondimen-

STABLE V

UNSTABLE 0 NORTHFLEET V TILBURY

Fig. 2.7(b) Effective stack height, he,vs wind speed, u, nondiiensionalized (after Briggs and McDonald. 1978).

2.1 ATMOSPHERIC TRANSPORT MODELS

/

39

X,,, and he are plotted as functions of wind speed; h, is source height and Fb is the total plume buoyancy flux at the source. These data are for stable and unstable ambient conditions a t the Northfleet and Tilbury (U.K.) power plants, and are further identified and described in the reference. The actual data scatter in Fig. 2.7(b) is quite small, and the fit of the observations to the various theoretical estimates is good. The scatter of these particular data points is no more than a factor of 1.2. On the other hand, the figure represents a highly optimized level of analysis, not all of which is at present reflected in the usual model parameterizations of he.This is in part because the derived parameter he depends on basic parameters that are not all routinely observed. In particular, the surface heat flux, H, which is especially significant in the unstable, low-wind speed cases, could, for these data, only be estimated to be somewhere between 25 and 75 ~m'sec-~, implying an uncertainty in he of a factor of about 1.4, according to Briggs.

Deposition Velocity The amount of radionuclide deposition on various kinds of vegetation, food crops, and other surfaces is taken into account in models by defining a "deposition velocity," ud, such that the (dry) deposition flux, F D , of airborne material to the surface is given by, F D = ud ( X A - XR). The latter two terms are the bulk air concentration and that at the receptor surface, respectively. Wet removal, or precipitation scavenging, can be treated in a similar way in the case of gases. Precipitation scavenging of particles (as well as highly reactive gases) is treated as a n exponential removal process, not unlike radioactivity decay. Thus, wet removal involves both wet-deposition velocities, u,, and scavenging rates, A. Deposited material can also be picked up and carried aloft from the surface by the wind. The aerodynamics of this phenomenon is handled in a way analogous to the above handling of deposition, by defining a "resuspension rate." Typical values of all these parameters, and further details of the many, complicated physical effects involved, are presented in Section 2.2.

2.1.5

Variability of Concentration Estimates

Many evaluations of the output of particular atmospheric models, especially the ground-level concentration values, x ( x , y, 0), have been made over the years. However, the points of view and objectives of

40

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2. ASSESSMENT OF RADIONUCLDES

such comparisons have been as diverse as the models themselves. Some model developers have been content with qualitative comparisons with experimental data, such as time series plots, isopleth analyses, and scatter diagrams. Others have used a variety of statistical measures of quality of agreement, such as mean absolute deviation, standard deviation, standard error of estimate, correlation coefficients, and so on. Bornstein and Anderson (1979) have surveyed these various statistics as applied in model validations. Several authors have performed sensitivity analyses and some of these studies have been summarized by Rote (1980). A workshop jointly sponsored by the Environmental Protection Agency and the American Meteorological Society emphasizes the desirability of using non-parametric statistical specifications of concentration distributions (Fox, 1981). An American Meteorological Society committee has also evaluated the technical aspects of air quality models (AMS, 1981). As a general comment on these and related studies it can be said that analysis of the error properties of atmospheric models in realworld applications (as opposed to sensitivity analyses, where no comparisons with observed data are involved) is a t a very rudimentary stage. After a decade of intensive model buildmg, atmospheric scientists have only recently begun to consider such questions as "What is the best statistical measure of model output validity?" The more fundamental question, "How does the structure of a given model affect the propagation of parameter errors and errors in the model output," has, rather surprisingly, not yet been raised in the considerations of this group. For this reason it is at present possible to discuss the error properties of atmospheric model outputs only in fairly general terms. Considering observed input parameter variabilities similar to those in the examples of the previous section, Pasquill (1974) gave estimates of the uncertainty of diffusion predictions based on Eq. (2-2). This question was subsequently considered further by the American Meteorological Society's 1977 Committee on Atmospheric Turbulence and Diffusion, which issued a position paper, and more recently a t the workshop reported by Crawford (1978). The conclusions of the workshop are summarized in Table 2.3, and these agree with the earlier estimates of model uncertainty. Little and Miller (1979) also surveyed a number of validations of specific atmospheric models. These include Gaussian model results for short-period and short-range concentration estimates, monthly to annual averages, long-range values (to 140 km), complex terrain, and low wind-speed conditions, and three non-Gaussian examples. Tables 2.4, 2.5, and 2.6 were adapted from Little and Miller (1979) and summarize the results of this survey. Although, as these authors are

2.1 ATMOSPHERIC TRANSPORT MODELS

TABLE 2.3-An -- .----. .- . .- -

/

41

estimate of the uncertuinty associated with concentration predictions made by the Gaussian plume modeP Range of the Ratio Predicted Observed

Conditions

0.8-1.2 Highly instrumented flat-field site; ground-level centerline concentration within 10 km continuous point source 0.1-10 Specific hour and receptor point; flat terrain, steady meteorological conditions; within 10 km of release point 0.5-2 Ensemble average for a specific point, flat terrain, within 10 km of release point (such as monthly, seasonal, or annual average) b Complex terrain or meteorology (e.g., sea breeze regimes) "After Crawford, 1978. b T h e group that assembled these estimates did not feel there was enough information available to make even a "scientific judgement" estimate under these conditions. -

TABLE2.4-Some

-

ualidation results for ensemble auerages predicted by the Gaussian plume mo&P Conditions

Range of the Ratio Observations Predictions

Annual average SO2concentrations for b a n e County, Tennessee; both point and area source emissions included

0.5-2.0

Continuous gamma-ray measurements 0.04-6.8 km downwind of a boiling water reactor

0.56-3.0

Gamma-ray doses downwide of Humboldt Bay Nuclear Power Plant

0.5-2.0

Monthly gamma-ray doses for four stations downwind of a nuclear power plant a t a n inland site

0.21-3.3 individual stations 0.65. mean of all data

Short term surface level releases of fluorescein particles under thermally stable atmospheric conditions a t Hanford, Washington

0.2-5.0.72% of samples

Short term SF6 releases from a 36-m high stack under stability categories B through F at the Rocky Mountain Arsenal, Denver, Colorado

0.33-3.0.8976 of samples 0.1-10,100% of 'samples

"From Little and Miller, 1979.

careful to point out, "not enough model validation studies have been performed to allow for a reliable statistical analysis," their results are important for several reasons. The data assembled, although sparse, represent the current state of the art. Moreover, these results generally

42

/

2. ASSESSMENT OF RADIONUCLIDES

TABLE 2.5-Validation results for Gaussian plume model predictions at distances to 140 km' Ran of the Ratio ~%ervations Predictions

Conditions

=Kr measurements 30-140 km downwind of the Savannah River Plant Weekly and annual averages Seasonal averages: Spring

0.25-4 0.25-0.5, 69% of samples 0.1-0.5, 100% of samples

Summer

0.25-2,46% of samples 0.1-2,85% of samples

Fall

0.25-2,31% of samples 0.1-2,85% of samples

Winter

0.25-0.5,69% of samples 0.1-0.5,92% of samples

Annual average

0.25-1, 77% of aamples 0.1-10,79-95% of samples

10-hour averages, six variations of the model

0.5-2.4245% of samples 0.1-10,79-95% of samples

" From Little and Miller. 1979. TABLE 2.6-Some validation results for Gaussian plume model predictions in both complex terrain and also under low wind speed inversion conditiod Conditions

Ran of the Ratio ~T~ervations

Predictions

Review of a number of experiments conducted in complex terrain for plume centerline concentrations

0.003-100, individual measurements close to the source 0.50-2, ~ 2 - 1 5krn downwind of source

Review of a number of experiments conducted under low wind speed, inversion conditions Smooth desert-like terrain Wooded flat terrain Wooded hilly terrain

'From Little and Miller, 1979.

Stability Category F G E 0.1-0.43 0.08-0.77 0.05-0.28 0.04-0.05 0.03-0.05 0.0334.05 0.003-0.02 0.002-0.003

2.2 RADIONUCLIDE DEPOSITION AND RESUSPENSION

1

43

agree with the earlier uncertainty estimates, which were largely based on the judgement of experts. Table 2.4 shows that the variability of short-term, short-range Gaussian model predictions ranges from factors of approximately 3 to 10, depending on sample percentage but that this decreases to factors of 2 to 4 for averaged data. Estimated average values of the predicted/ observed ratios for these cases indicate little or no model bias. For the long-range (Savannah River) experiments of Table 2.5, the variability of the Gaussian model output ranges from factors to 1.4 to 4 for various averaging periods, except that 10-hour averages for six different versions of the model show scatter by factors of from 2 to 10. Averaged ratios for seasonal concentrations in this table reveal a consistent bias, the reason for which is not well understood. Table 2.6 shows that, except for complex-terrain applications very close to the source, the variability of the remaining Gaussian model applications ranges between factors of 1 and 3. This is particularly interesting in the case of the light-wind, stable experiments, all of which have large biases that seem to increase sharply with terrain irregularity and slightly with increasing stability. The trajectory, particle, and grid models exhibit about the same amount of scatter as the Gaussian models when applied to the same (Savannah River) data, and are similarly unbiased, as Crawford (1978) has previously noted. 2.2 2.2.1

Radionuclide Deposition and Resuspension

Deposition

Dry Deposition Models

The dry deposition velocity, ud, relates the concentration, x , at some specified height (usually 1 meter) above the surface to the dry deposition flux, Fd, to the surface.

The dry deposition velocity includes effects of both atmospheric and surface processes between the reference height and the depositional surface. Current models for dry deposition fall short of a complete inclusion of all major recognized factors. Although specific mechanisms may

44

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2. ASSESSMENT OF RADIONUCLIDES

differ, the overall processes for dry deposition of gases and particles are similar enough to allow generic discussion. Ideally, input to a dry deposition model should be situation specific; controlling properties such as particle size distribution, solubility, roughness length, and displacement height should be used to predict the removal rate, rather than an invariant deposition velocity. Based on review of current models, there are two aspects of dry removal computation that may be improved in consequence models. These involve inclusion of the effect of the deposition-developed vertical concentration profile and a consistent definition of the magnitude and reference height of normalized dry deposition parameters. Dry deposition processes are conveniently separated into atmospheric and surface processes. This approach in different formats has been suggested by a number of authors. Actual dry deposition consists of a continuum of processes between the atmosphere and surface; division is accomplished by definition of a reference height. T h e specification of a reference height is basic to any proposed model. Atmospheric processes involve the delivery of material to the surface by the movements of the atmosphere. Surface processes such as impaction and sorption control the dry removal a t the receptors. Depending on ambient conditions and the characteristics of the depositing material, either the atmospheric or surface processes may be limiting. The modeling of these processes as resistances to dry deposition is a powerful alternative approach to the deposition velocity approach. The atmospheric resistance, r,, plus the surface resistance, r,, are equal to the total resistance, r,:

The deposition velocity is the inverse of the total resistance a t any reference height. The resistance approach is useful in understanding the processes controlling dry deposition. The question of the proper height for division of atmospheric and surface resistance is not a trivial problem. Failure to account for variation of these resistances as a function of height can lead to errors in dry deposition computations. The depth of the depleted plume will vary from case to case. The surface sink for a material results in the development of a vertical concentration profile with progressively lower concentrations near the surface. This directly influences the dry deposition computation and makes the consistent choice of heights and dry removal rates necessary. Literature data for dry deposition have been generally reported as deposition velocities relative to a one-meter reference height. As such,

2.2 RADIONUCLIDE DEPOSITION AND RESUSPENSION

/

45

these data contain information on both the atmospheric and surface processes under the reference height, but do not include information on atmospheric processes above the reference height. The current Nuclear Regulatory Commission (NRC) consequence model (USNRC, 1977a) allows for the mass of material removed by dry deposition by decreasing the total mass,in the plume a t progressive downwind distances. Since the reference height is defined as the division between surface and atmospheric resistances, the logical approach is to use a height near the surface. The wind profile can be used to define the height for which wind speed effectively is zero. This height, the roughness length, Zo (or displacement height for higher tree canopies), provides a consistent basis for separation of surface and atmospheric dry deposition processes based on an assumption of similarity of wind and airborne material profiles. It is beyond the scope of this report to define models for specific particles or gases (except for iodine which is presented below). Each should be considered on a case-by-case basis. The relative importance of atmospheric and surface processes defines the configuration and detail for a specific substance. For example, for materials that have a relatively low dry deposition rate, the atmospheric terms will be much less important than for a material with a higher deposition rate. Horst (1977) has developed a model for correction of the Gaussian plume model for the surface depletion of nonsettling particles. Although perhaps the most precise approach, this model requires considerable computation and applications are restrictively expensive. To overcome this problem, a hybrid source depletion model has been derived that allows for the surface depletion effects (Horst, 1978). This source depletion model compares quite well with the surface depletion model and has computationally reasonable algorithms. This simpler model reduces the source strength in the Gaussian model as a function of downwind distance to account for both the loss of airborne material and to account for the change in vertical profiles. The hybrid source depletion model may be applied in two ways. Either the approximation equation given by Horst (1978) is evaluated for each site, or a set of nomograms may be developed for generic application. The inclusion of the profile effects will significantly improve the estimates of surface flux, particularly for the more rapidly depositing materials. The model allows separate input of atmospheric and surface effects. Horst's profile approximation is the atmospheric resistance term. This model of the atmospheric processes includes both the ambient atmospheric and local surface characteristics. The procedure for defining a surface deposition velocity (given in

46

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2.

ASSESSMENT OF RADIONUCLIDES

Horst's paper) requires the definition of a deposition velocity a t a known height. The estimation of appropriate surface dry deposition velocities is an area where considerable improvement may be made. Sehmel's wind-tunnel study of particle deposition rates over various surfaces is one example of data for estimating surface deposition velocities. Gaseous, as opposed to particulate, dry deposition appears to depend on factors such as surface area, surface moisture, stoma openings, etc. Sehmel (1980) lists over 50 possible factors that enter into the determination of dry deposition velocity. These various factors need to be considered on a site-specific basis. From the wind-tunnel tests, Sehmel and Hodgson (1976, 1979) derived a generalized technique for estimating dry deposition of particles, which is only dependent on particle diameter, particle density, stable atmospheric roughness height and friction velocity, u* (see Section 2.1). This model describes particle motion in the atmosphere by a multidimensional, nonsteady-state continuity equation which can be represented by a three-box deposition model as a function of height above the surface. The first box represents the airborne vertical movement of the particles, which is described by standard meteorological diffusion equations. The second box represents the region just above the vegetative canopy or surface elements in a region where atmospheric transfer processes are modified by the canopy or surfaces. The third and final box is a t and within the deposition surface canopy. In the model, mass transfer resistances are calculated to describe the particle flux through the boxes from the reference concentration height (1meter) to the surface. The concentrations and fluxes are conserved a t the boundaries between the boxes (see Fig. 2.8). The results of the model computations are presented as graphs of deposition velocity a t one meter above the surface versus particle diameter (Sehmel, 1980). A typical graph is presented in Figure 2.9 for a particle density of 2.5 g cmP3,a friction velocity of 30 cm s-' and roughness heights from 0.001 to 10 cm. Sets of curves dependent on other particle densities and friction velocities from 10 to 200 cm s-' are given in Sehmel(1980). Table 2.7, adapted from the cited reference, gives surface roughness heights and friction velocities for various surfaces. Note the wide variation of surface roughness height with the type of surface. An alternate model for estimation of dry deposition of reactive gases onto a plant canopy has been presented by Heinemann and Vogt (1980). They define the deposition velocity of iodine by the semiempirical equation: vd =

ADu,F

(cm s-l)

(2-6)

2.2 RADIONUCLIDE DEPOSITION AND RESUSPENSION

/

47

Fig. 2.8 Conceptual three box model. (From Sehmel and Hodgson, 1976.)

where A = a quality factor (cm2 g-') representing a change in the plant canopy during its growing season which also incorporates a proportionality factor, D = areal density of the plant canopy in dry mass per unit ground surface area (g-dry cm-'), u, = the friction velocity (cm s-I), and F = the relative humidity (unitless).

From data derived in a series of experiments on grass and clover a t the Jiilich Nuclear Research Center, the above cited investigators were able to estimate an average u, = 26 cm s-' and A = 5.6 cm2 g-'. Other experiments in Germany gave D = 0.017 g cm-2 and F = 0.79 for Julich. The resulting product of these values gives a v d of 2 cm s-' for iodine vapor deposition on dry grass during the grazing period. Correcting for periods of high moisture on the grass such as early morning or during the night, a value for ud was obtained of 3 cm s-'. Preliminary investigations of the value of u d for elemental iodine attached to particles gives a value of 0.1 cm s-'. The above model concerns elemental iodine and not organic iodine compounds which may have a deposition velocity orders of magnitude less.

48

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2. ASSESSMENT OF RADIONUCLIDES

-

I

I

l

l

I

l

l

I

l

l

I

-

STABLE ATMOSPHERE WITH

20 (cm) 10

-

-

-

-

-

-

-

I

10-3 10-2

I

I

I

I

l

lo-'

l

I

l

l

I

1 o2

10

1 PARTICLE DIAMETER (pm)

Fig. 2.9 Predicted deposition velocities at 1 m for u, = 30 cm s-' and particlz -~ from Sehmel, 1980). density of 2.5 g ~ r n (adapted

TABLE 2.7-Aerodynamic surface roughness heights, z., and friction velocities, u - , for wind speeds, y of I and 5 m s-I at 2~metersabove the surface' Surface z.(cm) u,,(m 8-'1 Fnr

For

Smooth mud flata, ice Smooth snow or short grass

0.005

0.038

0.19

Smooth sea

0.02

0.043

0.22

Level desert

0.03

0.045

0.23

0.15

0.73

Mown grass 1.5 cm 3 cm 6 cm

60 cm

Long grass 60-70 cm Fully grown root crops

'From Sehmel, 1980.

14

/

2.2 RADIONUCLIDE DEPOSITION AND RESUSPENSION

49

Table 2.8 shows the wide range in experimental determinations of dry deposition velocities onto various media during varied atmospheric conditions for the various elements discussed in this report. Along with the ranges the values typically used in radiological assessments are listed. Note the exceedingly wide range of values reported for plutonium particles and for iodine in gaseous form-over three orders of magnitude. The wide ranges in deposition velocity are due to measurement technique as well as normal variation.

Wet Deposition The washout of particles and gasses from the atmosphere may, in some cases, be a significant contributor to ground deposition of the materials. Washout is defined as the scavenging of particles and gases by precipitation from a cloud. The deposition resulting from this process can be described by a "wet deposition velocity," v,, analogous to the dry deposition velocity discussed above. For particulate and gaseous material:

where

W = wet flux (pCi m-2s-'), and level air concentration of radioactive material (pCi m-3).

xo = surface

TABLE 2.8-Dry deposition velocities for selected elements in cm S-' Element

Cobalt Strontium Ruthenium Iodine Cesium Plutonium Uranium Radium

Fom

Particle Particle Particle Gas Particle Particle Particle Particle

Range

0.3-1.9" 0.002-0.01" 0.02-2.3' 0.02-26' 0.04-0.6' 0.0026-0.0 1 8 ~

. 0

Value

Typically Used 0.1' 0.1'.~ 0.1' lC 0.1' 0.1' 0.1' 0.1'

" Sehmel (1980) Craig et af. (1976) Soldat et al. (1974) Note that although the high value of the range for strontium is only 0.01 cm 8-l, the generic value for particle deposition velocity of 0.1 cm s-' is generally used in assessments " Range not available

50

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2. ASSESSMENT

OF RADIONUCLIDES

The wet flux may be estimated from two parameters: scavenging rate coefficient, $,, and washout ratio, w, (Slinn, 1978). The scavenging rate coefficient is usually defined as:

where

k = rate of removal of material from the air per unit volume (pCi m-3s-1), and

x = local air concentration of material (pCi m-3). The scavenging rate can be looked upon as analogous to the radioactive decay rate. It may be calculated from the collection efficiency of the precipitation (Slinn, 1978; Dana, 1980) or, alternately, derived from experimentally determined rain spectra (Dana and Hales 1976). The latter approach is more suitable for the accident case, because the parameters used to determine $, are measured during specific precipitation occurrences and not from averages over many days. A more suitable model for estimating wet deposition of long-term chronic releases of radionuclides is the washout ratio, w,. The washout (or scavenging) ratio is defined as the ratio of precipitation phase to air concentration of contaminant, with the concentrations normally evaluated a t the surface (Dana, 1980). For radioactive materials: xr w, = -

(unitless)

xo

where X, = concentration

of radionuclide in precipitation a t the surface (pCi mc3), and xo is as defined above.

The washout ratio is much more easily measured than the parameters of the scavenging rate coefficient. In essence, the washout ratio represents an integral of the scavenging rate and associated space dependent parameters over height z:

where x(z) = atmospheric air concentration as a function of height (pCi m-3), and

2.2 RADIONUCLIDE DEPOSITION AND RESUSPENSION

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51

po= precipitation rate (rainwater equivalent) at the surface (m

s-I). The wet flux, W, may be given in terms of the washout ratio, w,: Then from Equations (2-7) and (2-11) the wet deposition velocity is: The wet removal of reactive gases (non-noble gases) depends on their chemical properties including solubility and gas and liquid transfer rates in addition to the rainfall rate and raindrop spectra. For gases that form simple solutions in water and are at equilibrium, the washout ratio is just the reciprocal of Henry's law constant, H. Washout ratios of particles and reactive gases may be obtained from values given in the literature (Slinn, 1978; Englemann, 1968; Dana, 1980). Table 2.9 shows the ranges of long-term average washout ratios for some representative materials. The washout ratio method, when used for long-term chronic type releases, is generally accurate to a factor of 2 using site-specific annual average data (Slinn, 1978). By the use of Eq. (2-12), and using an annual average PO,the wet deposition velocity may be approximated for washout on an annual basis. As an example, consider a site with an annual precipitation rate of 100 cm y-' (typical of the midwestern United States). Find the wet deposition velocity for iodine gas which has a washout ratio of 1000 (Table 2.9).

Thus, on an annual basis, u, is two orders of magnitude less than the typically used dry deposition velocity for iodine gas of 1.0 cm s-' (Table 2.8), so can, in general, be ignored in any radiological assessTABLE 2.9-Measured washout ratios for selected materials Material

had Iron Sodium Fallout Iodine Gas Calcium Manganese Chlorine

W.

Reference

Slinn, 1978 Slinn, 1978 Slinn, 1978 Slinn. 1978 Slinn, 1978 Dana, 1980 Dana, 1980 Dana. 1980

52

/

2. ASSESSMENT OF RADIONUCLLDES

ment. However, for short time periods during a rainfall, the wet deposition may indeed be greater than the average deposition rate. 2.2.2

Resupension

When a relatively insoluble material such as a long-lived radionuclide has been deposited on the ground, it may again in time be "resuspended" into the air and thus become a significant contributor to the inhalation or food chain pathway doses to persons long after the source term has ceased to exist. In addition, contaminated areas such as tailings piles, may erode through wind and water action thus spreading material over a large area, later to be resuspended. This resuspension process may be carried on by various mechanisms such as rainfall, winds, human and animal activity. The amount of material resuspended will depend on a great many parameters, as does the deposition process. Among the primary parameters are the nature of the surface, the age and chemical properties of deposited material and the magnitude and duration of wind, rain and other physical disturbances. Various models describing resuspension processes have been proposed. The earliest of these dealt more with the physics of particle interactions and forces between them. See the review article by Slinn (1978) for a summary of the complexities involved. Because of the uncertainty of these micro scale mechanisms over wide areas, more empirical models have been developed. Today two models are generally used: mass loading and resuspension factor. However, a third model, still under development, resuspension rate, may potentially be more useful (Healy, 1980).

Mass Loading In this model the amount of resuspended material in the air is estimated by measuring its concentration in the soil and the mass loading (concentration) of soil particles in the air above. Hence, the air concentration of the material of interest x, is given by: where

C, = concentration of the material of interest in soil (pCi pg-I), and C, = concentration of particulate matter in air (pg m-3).

2.2 RADIONUCLIDE

DEPOSITION AND RESUSPENSION

/

53

This mass loading method is primarily applicable to those instances in which the material of interest is mixed uniformly within the top 1 cm or more of soil. For instance, many years after the deposition of radioactivity, measured values of C, have been reported for various locations of the United States. They range from 9 to 79 pg m-3 (NAPCA, 1968). However, a value for C, of 100 pg m-3 has been recommended as a generic value for predictive purposes (Anspaugh et al.,1974). Although the above method has been used effectively for sites with aged deposits of material which have been mixed into the soil, it has not given realistic results when used to predict resuspension from relatively fresh layers of contaminant on the soil surface. Another deficiency of the mass loading method is that the implicit assumption that soil and contaminant are resuspended equally may be invalid in many instances (Linsley, 1978).

Resuspension Factor This model has been developed from studies of soil and air contamination after nuclear bomb testing in the southwestern United States. The resuspension factor K(t) is defined as a function of time after a contaminant was deposited on the soil surface.

where = air

concentration of resuspended activity at time t after the deposition has been completed (pCi m-3), and = surface deposition per unit area (pCi m-*). A simple exponential decay model was first proposed by Langham (1969,1971) and Kathren (1968): (m-'1 (2-15) K(t) = K(0) exp(-ln 2 t / k ) where K(0) = initial resuspension factor at time t = O'(m-'), t, = weathering half-time (d), and t = time after initial deposition (d). Stewart (1964) and Mishima (1964) have compiled measured values to of K(0) from various experiments and found a range of from m-'. m-'. However, only a few values were greater than Sehmel (1980), in a review of the literature has found mechanically-

54

/

2. ASSESSMENT OF RADIONUCLIDES

m-' and wind-caused factors caused factors ranging from lo-'' to ranging from to m-'. Weathering half-times of from 35 to 70 days have been measured from experiments lasting several weeks after deposition.' After long times, up to about 20 years after deposition, Eq. (2-15) drastically underestimates the resuspension factor. This phenomenon led Anspaugh et al. (1975) to develop a variation of this equation. From empirical data Anspaugh approximated the resuspension factor as: where X = a n empirical factor of 0.15 d-I/'. The second term was added based on the assumption that there would be no further decrease in the resuspension factor after 17 years. This period is the longest time after deposition for which measurements have been reported according to Anspaugh et al. (1975). This long-term component i: derived from limited experimental observations of resuspension of plutonium from undisturbed surfaces at nuclear weapons test sites in semi-arid conditions (Anspaugh, et al., 1975). The model used in the "Reactor Safety Study" (USNRC, 1975) is similar to Eq. (2-16), but with modifications to the time dependent term.

K(t)=10-5exp(-ln2t/0.977)+10-9 ( m ) (2-17) Here t is in years. The environmental half-time used is 0.977 y or about 50 weeks. However, K(0) has been lowered an order of magnitude from Anspaugh's formulation (Eq. 2-16). Another variation of this basic model has been used in the Liquid Metal Breeder Reactor Final Environmental Statement (USAEC, 1974) and the NRC UDAD code (Momeni et al., 1979). In this model K ( t ) is calculated for two periods: K(t)

=

loe5 exp(-ln 2 tlt,)

(m-I)

for t 6 664 d

and K(t) = lo-'

m

)

for t > 664 d

(2-18)

In Eq. (2-18), t, is taken to be 50 days, which is about midway between the two extreme values of 35 and 70 days. For a critical examination of these two models also see Lassey (1980).

'

These weathering half times derived from experimental measurements appear to some investigators as questionable (Sehmel, 1980); however, it appears that it is reasonable to expect that the resuspension source availability will decrease in some manner with time.

2.2 RADIONUCLIDE DEPOSITION AND RESUSPENSION I

I

I

I

I

1

/ I

55

-

-

-

REACTOR SAFETY STUDY (Eq. 2-17)

\

-

-

'4

-L/ UDAD (Eq. 2-18) -

-

/\

ANSPAUGH

-

et

-

al. (Eq. 2-16)

-

18

696 795

542 606

261 306

17

25

31

41

7 4 34 3

38 41 39 18

66 69 52 27

86 76 70 26

-

6

0.49 4.33 0.93 49

0.84 7.23 1.45 67

1.48 10.68 3.59 69

2 12 12 50

20 7 22 58

30 7 28 82

50 8 25 99

23 112 3 21

74 112 2 87

93 116 1 113

99 87 1 97

g d-'

Eggsb Meats Beef Pork Other and Mixtures Poultry Fish' Freshwater fin Saltwater fin Shellfish (all) Potatoes Vegetablesd Leafy, mixturesd Deep yellow, mixturesP Legumes, mixtures Other, mixtures Fruit Citrus, tomatoes Other, mixtures Dried Grain (flour equivalent)

-

"Adapted from Rupp (1980). An average egg weighs 48 g (Blanchard, 1978). The egg group includes egg salads, creamed eggs, omelets, and mixtures which are primarily eggs. ' National Marine Fisheries Service Survey, 1973-1974 raw data. Blanchard, 1978. 'These quantities are considered by the U.S.D.A. to be relatively low compared to previous surveys.

5.1 DIETARY PATHWAY USAGE FACTORS

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201

TABLE 5.4-Relative frequency of types of milk consumed by infants of various Age (Months)

Feeding

Otol l t o 2 2 t o 3 3 t o 4 4to5 5 t o 6 6 t o 9

Relative Percent

Breast-fed Milk-based formulac Milk-free formulac Evaporated milk formula Evaporated milk and water Fresh cow's milk

20 64 10 4 2

15 65 10 4

6

12 59 10 3 2 14

10 49 10 2 29

8 41 8

5 29 6 2 2 41 58

2

3 2 1 92

0

lnspiratory reaene volume (complementary air)

m P

rnU

Normal inspiration

>

.-

P

-

->u 3.-

3 I;; En U ria.4.

J

L

Collapsed lung

Fig. 5.4 Lung capacities and volumes.

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USAGE FACTORS FOR PREDICTING EXPOSURE TO MAN

Several terms are frequently used to describe the volumes and capacities of the lungs and data are presented in a variety of ways. Therefore, brief definitions of the terms for lung volumes, capacities, and rates are given in the glossary (Appendix B) and are schematically displayed in Fig. 5.4. Data are frequently expressed in terms of vital capacity, tidal volume ventilation or minute volume and daily or annual inhalation rate. The dynamic volumes-those volumes comprising the vital capacity-vary considerably with the physical exertion of an individual and with size, age, sex, altitude and health status. The critical parameter for estimating the quantity of inhaled radionuclide is the minute volume for an individual a t the time of exposure. Ventilation rate and minute volume, expressed as L/min, are both used in the published literature. In this report we only refer to minute volume.

5.2.2 Minute Volumes A report by Thompson and Robison (1983) summarizes the minute volumes by sex, age, physical exertion, etc; a summary of some of the findings is given in Table 5.10.

Infants - Newborn (1 week or younger)

The International Commission on Radiological Protection (ICRP, 1975) lists a minute volume of 0.5 L min-' for a resting newborn and TABLE 5.10-Summary of ventilation rates (minute volumes) at normal body temperature and pressure, saturated in L min-'--and in m3 d-'' Subject

Age

Newborn Infants Infants Children Children Teenage Boys Teenage Girls Adult Men Adult Women

1 hr. to 1 wk. 2 wk. to 1 mo. 1 to 12 mo. 1t04y

5 to 12 y 13 to 19 y 13 to 19 y 20 Y 20 Y

Resting 0.7 ( 1 . 0 ) ~ 0.9 (1.3) 1.5 (2.2) 3.3 (4.8) 7.1 (10) 7.6 (11) 5.6 (8.1) 8.8 (13) 6.4 (9.2)

Active 2.1' (3.0) 2.7' (3.9) 4.5' (6.5) 10' (14) 20 (36) 30 (43) 25 (36) 30 (43) 25 (36)

Maximum work

-

-

63 (91) 130 (187) 89 (128) 132 (189) 98 (141)

'Average ventilation rates based on studies reviewed by Thompson and Robison (1983). Numbers in parentheses are the equivalent breathing rates in m3 d-'. ' Bawd on three times the resting minute ventilation (Deming and Washburn, 1935).

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5.2 INHALATION PATHWAY USAGE FACTORS

TABLE5.11-Currently adopted minute volumes (L min-') for the r e s t i s state Newborn

ICRP (1975) USNRC (1977b3

Infant

1.5 (4.2) 2.7

0.5 (1.5)" -

Child

4.8 (13) 7.0

"Minute volumes for nonresting, light activity conditions are shown in parentheses.

TABLE5.12-Currently proposed daily ventilation rates in m3 d-' Source

Newborn

Infant

Child

Teen

ICRP (1975) USNRC (1977b3

0.8 -

3.8 3.8

15 10

22

Men Adult &

23

21 22

1.5 L min-' for an active newborn (Table 5.11). They assume that the 0.5 L.min-' rate applies 23 hours per day and the 1.5 L min-' for 1 h for a total daily volume of approximately 0.8 m3 (Table 5.12). From the studies of Bolton and Herman (1974), Hathorn (1974, 1978), and Brady et al. (1964) it would appear that an average value for resting newborn infants would be more in the range of 0.6 to 0.8 L min-I with a mean of 0.7 L min-'. This is a 40% increase over the ICRP value (ICRP, 1975). In view of the fact that the general assessments of the inhalation pathway for newborns assume that the breathing rate for the resting condition applies 23 hours per day, it would seem a higher average breathing rate for the resting condition should be used for newborn infants. Deming and Washburn (1935) have reported that the average minute volume for infants who are awake but quiet is about 22% greater than in the sleep state; they also provide data which indicates that the minute volume during crying is 3 to 3.5 times that observed in the sleep state. Thus the minute volumes for a crying active state would be 2 L min-'. The distribution is log-normal with an arithmetic mean of 0.63 L min-l, a geometric mean of 0.60 L min-' and a geometric standard deviation of 1.35. Infants - 1 week to 1 month

Data on minute volumes for infants and children more than just a few days old are very limited. Most of the literature addresses newborns or children over 5 years of age. Data from Deming and Washburn (1935) indicate that the average resting minute volume for infants 2 to 4 weeks (1month) of age is 0.9 L min-' with a range from 0.88 to 0.92 L min-'. Insufficient individual data are available to determine the distribution. If one assumes that

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USAGE FACTORS FOR PREDICTING EXPOSURE TO MAN

the minute volume in the active state is 3 times that in the resting state (Deming and Washburn, 1935), then the active minute volume is about 2.7 L min-'.

Infants - 2 to 12 months Deming and Washburn (1935) reported data from which it was calculated that the resting minute volume for infants age 1to 3 months and infants 4 to 12 months is 1.6 L min-'. The average for 2 to 12 months was 1.3 L min-'. It is clear from both Deming and Washburn's (1935) and Krieger's (1963) studies that the minute volume increases rapidly with age during infancy. Therefore, a reasonable average resting minute volume for the 2- to 12-month age group would be about 1.5 L mine'. The active state minute volume would be about 4.5 L min-' assuming, again, that the active state minute volume is three times that for the resting state (Deming and Washburn, 1935). The distributions for the data from Deming and Washburn's study are log-normal with an arithmetic mean of 1.4 L min-', the geometric mean of 1.33 L min-' and the geometric standard deviation of 1.44.

Children - Ages 1 to 4 y Few data are available on the minute volumes either at rest or at maximum exercise for children between 1 and 4 years of age. The data of Kattan et al. (1978) and Krieger (1963) would suggest that 3.3 L min-' is the average resting volume for this age group and if it is assumed that the active minute volume is three times the resting rate (Deming and Washburn, 1935), then the average active minute volume would be about 10 L min-'. Insufficient individual data were available to assess the distribution of minute volumes in this age group.

Children - Ages 5 to 12 y Resting minute volumes for boys between the ages of 5 and 12 were found to be about 7.1 L min-' by both Orzalesi et al. (1965) and Eriksson (1972). Onalesi et al. (1965) also found that girls in this age range had similar volumes of 7.1 L min-I; this rate is based on only four subjects and is a bit higher than the average for teenage girls and adult women.

5.2

INHALATION PATHWAY USAGE FACTORS

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213

For maximum exercise in this age group, average minute volumes, derived from the studies reviewed by Thompson and Robison (1983) are 61 and 63 L min-' for boys and girls, respectively. Average minute volumes for routine play and activity would be less than these values. Assuming that the minute volume during average childhood play and exertion would be about 3 times the resting rate, then 20 L min-' would be a reasonable estimate, which is consistent with results reported by Gadhoke and Jones (1969). Insufficient individual data were available to determine the distribution of minute volume in this age group.

Teenage - Ages 13 to 19 y The average minute volumes derived from the studies reviewed by Thompson and Robison (1983) are 7.6 L min-' for boys and 5.6 L min-' for girls for the resting state and 130 L min-' and 89 L min-' respectively for the maximum work state. Gadhoke and Jones (1969) report sub-maximal work minute volumes ranging from 25 to 49 L min-'. The minute volumes under submaximum and maximum work are very similar to the comparable same-sex values for adults. Very few minute volume data are available for teenagers for submaximal work conditions; however, because teenagers tend to approach adult minute volumes under maximum work conditions, it can be assumed that under light-to-moderate activity the rates would be similar. These distributions are log-normal with an arithmetic mean, and geometric mean of 8.3 and 8.2, respectively, and a geometric standard deviation of 1.3.

Adults Average values for the minute volume for adult men and women for both resting and maximum work conditions have been reviewed by Thompson and Robison (1983). The minute volumes for the resting, submaximum work, and maximum work conditions are summarized in Table 5.10. Several studies have been directed toward evaluating the minute volumes as a function of work and exercise. Studies reviewed by Thompson and Robison (1983) report results for men in light-tomoderate exercise on treadmills, ergometers, and controlled exercise, and the results all fall between 17 and 45 L min-'. At higher work

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USAGE FACTORS FOR PREDICTING EXPOSURE T O MAN

loads, the minute volume begins to increase and approach the average maximum work load values of about 130 L min-'. Studies t o determine the minute volume a t submaximal work load for women indicate a range from about 12 to 36 L min-'. Skubic and Hodgkins (1966) and Michael and Horvath (1965) both report results within this range. The distribution of minute volumes for males over the age of 20 for the resting state is log-normal, has an arithmetic mean of 8.8 L min-', a geometric mean of 8.5 L min-', and a geometric standard deviation of 1.28. The minute volume distributions for males for age groups 20 to 30, 31 to 40, 41 to 50, and older are all log-normal with geometric standard deviations ranging from 1.22 to 1.45. T h e distribution of minute volume for men over the age of 20 for maximal work conditions appears to be log-normal with an arithmetic mean of 127 L min-', a geometric mean of 125 L min-', and a geometric standard deviation of 1.22. Resting minute volumes for adult women between, 20 and 60 are log-normally distributed. The arithmetic mean, geometric mean and geometric standard deviation are 7.3 L min-', 7 L min-' and 1.34, respectively. The limited number of data points for maximum-work minute volumes for women make the distribution uncertain. However, because minute volume distributions for the resting conditions for women, men, and infants all appear to be log-normal, we assume these have the same distribution, with a geometric standard deviation of 1.42 L min-' and an arithmetic and geometric mean of 109 and 104 L min-', respectively. The age ranges selected for analysis above were arbitrary; however, they do show how the minute volume changes with age. Although these rates can be used in assessment for the particular age group, the minute volumes do vary within a group. For example, the volumes for 18- and 19-year-old subjects is generally a bit higher than those for the 13- and 14-year-old subjects and, therefore, slightly higher than the listed average for the entire age group. Similarly, the 11- and 12year-old children have slightly higher minute volumes than do the 5and 6-year-old children.

5.2.3

Significant Factors Affecting Minute Volumesfor Radionucltde Intake via Inhalation

Age Distribution The data in Table 5.10 indicate a range of average resting minute volumes from 0.7 L min-' for newborn infants to 8.8 L min-' for adult

5.2 INHALATION PATHWAY USAGE FACTORS

I

215

males. Therefore, it is necessary to have some idea of the age distribution of the population because the difference in range of average minute volumes between infants and adults is about a factor of 13, while the difference between young children and adults is less than a factor of 3. For both sexes, the resting ventilation rates are not greatly different as a function of age after about 13 or 14 years of age. However, maximum minute volumes do tend to decrease with age (Dill et al., 1963). Sex Resting minute volumes are not very different between sexes through about 12 years of age. From teenage on through adulthood, however, the males have resting volumes that are about 40 to 50% higher than females. Men also have 35 to 40% higher volume under maximum work conditions than women. Therefore, the sex ratio in a population will make some difference in an inhalation assessment. State of Physical Activity The most significant parameter that needs to be determined is the state of activity of the population during a period of radionuclide inhalation. For example, differences in resting minute volumes between sexes and among ages is not large, the greatest being that between young children and adults, about a factor of 3. However, minute volumes under maximum work are about 15 times those a t rest for both sexes and all ages greater than 5 years (Table 5.10). The minute volumes observed under average working or activity conditions are four to eight times those observed a t rest. Thus, it is clear that the state of exercise or level of activity is very important in determining the quantity of radionuclide inhaled over periods of a few hours or days. For continuous chronic exposure, average values for the percentage of time spent in the resting and active states may be used with the appropriate minute volumes for developing general assessments. Other Variables Other variables that can alter the minute volume for both the resting and submaximal work state have been reviewed by Thompson and Robison (1983). These include temperature (hot vs cold environment);

216

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USAGE FACTORS FOR PREDICTING EXPOSURE T O MAN

altitude; weight; height; smoking and general health state-especially pulmonary-related diseases. Many papers discuss the effects of these and other variables on minute volumes. However, they are perturbations of the basic results already discussed for the various age groups and sexes, and of lesser magnitude than the evaluation of whether resting- or active-state minute volumes should be applied to a given situation. 6.2.4 Average Time Spent at Rest and Light-to-Moderate Activity The most common assumptions for the average number of hours spent at rest and at work or in light-to-moderate exercise is 8 hours per day at rest, 8 hours per day at work, and 8 hours per day at personal light-to-moderate activity (ICRP 1975); and for a large population, this is generally adequate. To be more precise would require a detailed knowledge of the daily habits of the exposed population. These habits, even for an individual, will vary depending on the time of year, climatic conditions, time of day, etc. If such details were available, it might be possible to also determine the percentage of time that a small portion of the population would be at maximum ventilation rates. Unless such data are available, so that the distribution and standard deviations of the time spent at rest or at various stages of exertion can be determined, it is necessary to use the general approach with specific fractions of time allocated for each state of minute ventilation. 6.2.6 Summary and Discussion Data are available to evaluate infants and adult men and women for both the resting and maximum activity states; however, limited data are available for evaluating the distribution of the minute volumes for children 1 through 12 years of age and for teenagers. The distributions of the available data are log-normal with geometric standard deviations in the range 1.3 to 1.5. Therefore, it can be assumed that minute volumes in the other age groups will also be log-normally distributed with similar standard deviations. Observed, average minute volumes, a log-normal distribution, and a geometric standard deviation of 1.4 will provide an estimate of the distributions of inhaled radionuclide for the children and teenagers. Because the distributions are lognormal, use of the arithmetic mean includes more than 50% of the population. For example, for infants the mean value of 0.7 L min-'

5.3 REDUCTION IN EXTERNAL EXPOSURE

/

217

falls a t about the 62"* percentile of the distribution. For the resting state of adult males, the mean falls a t about the 60thpercentile. For the resting state of women and the maximum activity state of men and women, the mean minute volume falls a t the 60th, 67th,and percentiles, respectively. The arithmetic mean value of the minute volumes for resting and active states for the selected age groups are listed in Table 5.10. These data, when used in conjunction with the assumptions that the data are distributed log-normally with geometric standard deviations of about 1.4, can be incorporated in stochastic models for the distribution of inhaled radionuclides in a population. 5.3

Reduction in External Exposure from Shielding Due to Buildings, Homes, and Vehicles

On the average, people in the U.S. are reported to spend 95% of their time indoors either a t home or in large buildings for work or pleasure (Oakley, 1972). This estimate is based upon a large scale international study reported by Szalai (1972) in which the U.S. portion was conducted by Robinson and Converse (1966). These data have been summarized in a report for the Environmental Protection Agency by Moeller and Underhill (1976). Some occupations obviously require that more time be spent outdoors. Farmers, ranchers, road and building construction crews, linemen for telephone and electric companies, etc. are examples. Assuming an &hour work day, it is reasonable to assume that 70 to 75% of such a person's wake time may be spent outdoors. However, for people who spend considerable time in their cars for occupational purposes, this time is considered to be time indoors since vehicles provide a similar degree of protection from external radiation as do houses. To predict the amount of time an individual in a population spends indoors requires a detailed knowledge of that person's occupation and habits. However, to determine an average distribution of time individuals might be expected to spend indoors, it is probably reasonable to assume that the general distribution is uniform within an estimated range of 70 to 95%. There will be only a small percentage of the population at each end of the spectrum that will spend on average 100% of their time indoors or less than 70% of their time indoors. If such a significant fraction of a person's time is spent indoors, then it may be necessary to know the reduction in absorbed dose relative to open air exposure which would occur from the shielding afforded by the buildings and vehicles. A report by Burson and Profio

218

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USAGE FACTORS FOR PREDICTING EXPOSURE TO MAN

(1975) provides original data, as well as a summary of several other studies, on shielding provided by structures such as homes, office and industrial buildings and vehicles. Shielding factors vary for a structure depending on whether the source of radiation exposure is ground deposited or is a cloud. The reported reduction factors (ratio of the exposure rate in the structure to the exposure rate in open air) for radionuclides deposited on the ground range from an average of about 0.27 for single story wooden houses to 0.06 for reinforced concrete and brick homes. Basements provide more protection than other areas of the house and average reduction factors range from 0.003 to 0.08. Large office buildings provide more shielding, and, therefore, lower reduction factors than homes (other than basements). For example, average reduction factors in one- and two-story office buildings range from 0.01 to 0.12. Vehicles provide reduction factors in the range observed for onestory houses. The range for cars, pickups, buses, trucks and trains is 0.15 to 0.6. The range for trucks and trains is encompassed within the observed range for automobiles, pickups and buses. In the case of cloud sources, only average reduction factors are available for buildings and vehicles. These values are probably representative of the upper range for a particular structure. If i t is assumed that a range similar to that observed for ground deposits applies, then reduction factors might be as follows; wood frame homes, 0.6 to 0.9; masonry houses and masonry houses with basements, 0.3 to 0.6 and 0.2 to 0.4 respectively; and large office buildings, 0.05 to 0.2. The distribution between these ranges for both ground deposited and cloud sources could be considered to be uniform because there is likely to be a continuous range of values due to difference in materials and architecture. A precise analysis of reduction' factors for individuals in a specific area would require information on the percentage of the different type dwellings in the area. Data on the numbers of one- and two-story single family dwellings in different regions of the United States are given for 1970 by Moeller and Underhill (1976). For individuals, it is also necessary to determine how much time is spent at home (in one- or two-story wood or masonry dwellings) and how much time is spent in large office or industrial buildings; a general range of 6 to 10 hours per day or 30 to 50 hours per week can be assumed. Seventy to 95% of a person's time spent indoors is the equivalent of 118to 160 hours per week, of which 30 to 60 hours would be in office or industrial buildings. These time distributions and ranges can be used in.conjunction with the range of reduction factors of Burson and Profio (1975) to estimate the range of effective reduction factors expected for individuals.

6. Identification of Uncertainties Associated with Model Predictions The models and parameters described i n Sections 2-5 are only mathematical approximations of real environmental situations and processes. Furthermore, the parameters used i n these mo&ls are highly variable. Therefore, it is important to conszder the level of uncertainty associated with model calculations. Only a few specific quantitative examples of model uhcertainty can be given because of the limited extent to which environmental transport models have been validated i n the field or evaluated through statistical studies. 6.1 Introduction Few efforts have been directed toward the analysis of the uncertainty associated with environmental radiological assessment models. The necessary amounts of detailed data have rarely been available, and a need for such efforts has not always been apparent, since dose predictions for routine operation of nuclear facilities generally have been well below applicable standards. The models as applied were generally biased to produce results intended to overestimate actual doses. This "conservative" bias was often embodied in the assumptions.underlying the design of the model as well as in the choice of values for the independent variables, or model parameters. With increasing emphasis on restricting release and dose to levels considered "as low as reasonably achievable" (the ALARA concept), concurrent importance is being placed on decreasing the amount of deliberate conservatism in assessment calculations. However, removal of conservative assumptions from assessment models may increase the possibility of underestimating actual dose unless the magnitude of uncertainty in model predictions is taken into account. Quantifying the uncertainty associated with dose assessment models is, therefore, receiving growing attention. 219

220

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6. IDENTIFICATION OF MODEL PREDICTIONS

6.2 Sources of Model Uncertainties Uncertainties exist in environmental transport and exposure models because they are mathematical approximations of the real world (Schwarz, 1980; Shaeffer, 1980; ICRP, 1979). Model uncertainties may lead to improper extrapolations due to either incorrect formulation of the mathematical equations and/or selection of incorrect parameter values. Incorrect extrapolations are most likely to occur when models are used to predict the transport of radionuclides among different geographical locations and over periods of time that are different from the conditions for which the models and data bases were initially developed. For example, models used to evaluate the geological disposal of high-level wastes may be especially subject to incorrect extrapolation because predictions are made far into the future using data bases derived from short-term experiments (Section 4). Much uncertainty is due to a lack of relevant data or large variability in the available data for quantifying model parameters. Parameter variability is especially significant in present environmental radiological assessment models which are "deterministic" rather than "stochastic." Deterministic models use single values for each parameter to produce a predicted quantity. This ~redictedquantity cannot reflect the influence of parameter variability. Stochastic models, on the other hand, can produce a range or dstribution of predicted values as a function of parameters which are defined as random variables. In stochastic models, parameter variability can be considered explicitly. Most models used for environmental radiological assessments are, however, deterministic. In deterministic models, parameter values may be selected from the upper end of the reported range to reduce the probability of underestimation. This procedure introduces a strong bias in model predictions resulting in substantial overestimation of actual events. More often, however, values are selected based on a n average of data reported in the literature (see Sections 2.3 and 3.2). This is also a source of bias, because such average values may be significantly different from values best representing a specific situation.

6 . 3 Determination of Model Uncertainties 6.3.1 Model Validation The best method to determine model uncertainty is through testing the model against accurately measured, independent sets of field or

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221

laboratory observations made over the range of conditions for which application of the model is intended. This procedure is referred to as "model validation." As discussed in preceding sections, only limited validation studies have been performed on radiological assessment models. Furthermore, model validation experiments are not always feasible. For example, low-level environmental concentrations of radionuclides and radiation exposures resulting from routine operations of nuclear fuel cycle facilities are often extremely difficult to measure. Even when detection of low-level concentrations of radionuclides is possible, the high costs encountered usually limit the extent of validation to only a few situations.

6.3.2 Parameter Imprecision Analyses In situations where validation information is not readily available or sufficiently complete, a procedure referred to as a "parameter imprecision analysis" can be used to evaluate model predictions (Schwarz, 1980). This procedure involves estimating the variability (or imprecision) associated with each model parameter to ascertain the influence on the model output of the combined variability of all model parameters (Fig. 6.1). This requires transforming a deterministic model into a stochastic model. The term "imprecision" is used because the analysis only provides an evaluation of the model's uncertainty due to uncertainties in parameter estimation. It does not provide an evaluation of uncertainty due to the use of an inappropriate equation or set of equations. T o provide a reasonable indication of predictive uncertainty, the mathematical structure of the model must be an appropriate representation of the real world and estimates of parameter variability must be unbiased. Scientific judgment must be used to ensure that the model and its parameter estimates satisfy these criteria. Analytical error propagation formulae can be used to perform parameter imprecision analyses on relatively simple models (Shaeffer, 1980; Collee et al., 1980; Schubert et al., 1967). For more complex models, numerical techniques employing the use of a computer may be more convenient than complex analytical solutions (Rubinstein, 1981; Iman et al., 1980,1981a, b; Schwarz and Hoffman, 1981; O'Neill, 1979; McKay et al., 1979). Most work using parameter imprecision analysis for radiological assessments has focused on the air-pasture-cow-milk-child pathway for 13'1 (Stocum, 1970; Shaeffer and Hoffman, 1979; Hoffman and

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6. IDENTIFICATION OF MODEL PREDICTIONS (1) Descrlbe uncertain model parameters as random variables

:kikg Parameter x

Parameter y

C 3

Parameter z

3

w

B

LL

E'

LL

LL

Values of y

Values of x

\

Values of z

/ (2) Distributions of parameter values are then used as input to a model I

1

MODEL

1

I (3) The model produces a distribution of dose estimates

Values of Dose

Fig. 6.1 Parameter imprecision analysis.

Baes, 1979; Schwarz and Hoffman, 1981), and the transport of 13'Cs and in aquatic and terrestrial systems (Schubert et al., 1967; Matthies et al., 1981; Hoffman et al., 1982). For the 1311 air-pasturecow-milk-child pathway simple analytical procedures have been used (Hoffman and Baes, 1979; Schaeffer and Hoffman, 1979). Table 6.1 shows the results obtained using a simple analytical approach. This approach reduces the model to a linear multiplicative chain of independent parameters.

Table 6.1-Results of an analytical approach to a parameter imprecision anolysis for the and Baes 1979) Parameter

Biomass normalized deposition parameter for Iz Effective mean residence time on pasture vegetation Total dry matter intake by a dairy cow Fraction of dairy feed composed of fresh forage Milk transfer coefficient Fraction of time during a year a cow receives fresh forage Annual milk consumption of children (ages 0.5-2 yrs.) Fraction of ingested iodine that deposits in the thyroid gland Fkciprocal of the thyroid mass Effective mean residence time of la'I in the thyroid Dose to air concentration ratio Distribution of dose to air concentration ratioc D/x (mrem m3 pCi-' y-')

Symbol

Geometric Mean (units)

I3'I2

air-pasture-COW-infant pathway (after Hoffman Percent Contribution to Total Imprecisionc

II

VD

0.12 (m3 kg-Is-')

l/xvem

6.1 (d)

QT

15 (kg d-') 0.42 (-)

FP

0.01 (d L-') 0.37 (-)

UM

300 (L y-')

FTh

0.30 (-)

l/m l/h?i

0.57 (g-') 6.5 (d)

D/x

5100 (mrem m3 pCi-' y-')

8.53d

1.09'

Mode Median Mean

1700 5100 8700

XM"

14000 28000 57000

F, Fm

-2.1

0.002

0.18

0.02

1.8

2.7 -0.87

0.014 0.058

1.3 5.3

-4.6 -1.0

0.3 0.17

27.6 15.6

0.04

3.7

-1.2

0.W

7.7

-0.56 1.86

0.25 0.15

23.0 13.8

1.8

5.7

z m U 4

m

Z

S

54

3

0 z

g E t-

d

xw xm

100

" p , mean of logarithms of parameter values. All values are accurate to only two significant figures. 2, variance of logarithms of parameter values. 'These values are based on assumption that all parameters are statistically independent; changes are expected with future quantification of parameter covariance. Calculated by adding ln(897 millirem g s pCi-' d-') to 1.77, the sum of the means of logarithms of values for each parameter. "Xu,X95,2& are the upper 84th, 95th and 99th percentiles, respectively, of the predicted distribution of the D/x ratio.

3 3 2 4

C(

m

c/i

\

N

N

w

224

/

6. IDENTIFICATION OF MODEL PREDICTIONS

where

D/x

K

= the thyroid dose resulting from a given concentration of 13'Iz in air ( x )and the subsequent transport over the pasture-cowmilk pathway prior to ingestion of 13'1 in milk by children within the age group 0.5-2 y. is a constant (897 mrem g sec pCi-' day-'), with all other parameters being described in Table 6.1.

Assuming that the variability of parameter values is reasonably approximated by a log-normal distribution, log-transformation permits simple analytical propagation of errors using normal statistics. In this example, the sum of the means of log transformed parameter values, pp, equals the mean of the log transformed dose, PD,

The sum of the variances of the independently distributed log transformed parameter values, a:, equals the variance of the log transformed dose VD,

If covariance exists between model parameters, additi6nal terms would be required, affecting the results in Table 6.1. Covariance between many of these parameters, especially UM,FTh, m, and AT;, is suspected but experimental quantification is not documented (Dunning and Schwarz, 1981). In this example, the geometric mean or median (X,) of the distribution of dose predictions is: The mode (X,), arithmetic mean, (X),84th (XS4), 95th (X95), and 99th (X*) percentiles of the distribution of dose predictions is:

6.3 DETERMINATION OF MODEL UNCERTAMTIES

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225

The contribution of parameter variability to the total predictive imprecision is estimated by dividing the variance of the log transformed parameter values, u2,, by the variance of the log transformed distribution of dose predictions, a;. The results in Table 6.1 indicate that the 99th percentile (5.7 x lo4 mrem y-' per pCi m-3) of the estimated distribution of thyroid dose incurred from a given air concentration of 13'12is about one order of magnitude greater than the median value (5100 mrem y-l per pCi mP3) of the predicted dose. Most of the imprecision involves the parameters (F,, m, As!) for which site-specific information will be most difficult to obtain. The results of other studies are presented in Table 6.2 for a variety of exposure pathways and radionuclides. Table 6.2 indicates that parameter imprecision may contribute to a range of about one to two orders of magnitude about the geometric mean.

6.3.3 The Effect of Bias in the Selection of Parameter Values Bias (i.e., the tendency to over- or underestimate) in the predictions of deterministic models can be evaluated by comparing their results with the distribution of predicted doses produced through parameter imprecision analyses (Fig. 6.2). As mentioned previously, substantial overestimation is expected when conservatism is applied in the selection of each parameter in a deterministic model. For example, in a model composed of ten or more multiplicative parameters (where each parameter contributed equally to the total model uncertainty), the selection of only the 84th percentile for each model parameter results in a predicted value that exceeds the 99.9th percentile of the distribution of model output (Hoffman and Baes, 1979). Thus, bias in the selection of parameter values may have a pronounced effect on the total conservatism in the final model prediction.

6.4 Uncertainties Among Various Types of Models The examples of parameter imprecision analysis (Tables 6.1 and 6.2) demonstrate the potential for considerable discrepancies between a single deterministic estimate produced by a model and the actual value or range of values which are possible for a given situation. Among the models reviewed in this report, the largest uncertainties are expected to be associated with the prediction of deposition, sedi-

TABLE 6.2-A summary of results for parameter uncertainty analysis performed on a variety of environmental exposure pathway models. Valuespresented are the 5th percentile (La), geometric mean (X,), and upper 95th (XW) percentile of the predicted distributions of model results. Radionuclide

2aDh 2JOPu 131~2

"Sr "Sr

'"Cs '"Cs 137Cs

Exposure Pathway

Soil-air-inhalation-lung" (mrad y-I per pCi g-' soil) Soil-vegetation-ingestion-bonew (mrad y-' per pCi g-I soil) Air-pasture-milk-ingestion-thyroidd* (rem y-' per pCi m-3 air)

Water-fmh-ingestion-bone-surfacek (mrem) y-I per pCi L-'water) Deposition-multiple terrestrial food pathways-bone surfacebd (mrem y-' per p c i m-2 d-1 1 Deposition-soil-pasture-milkd.' (pCi L-I per Ci km-') Water-fish-ingestion-total bodyb (mrem y-' per pCi L-'water) Deposition-multiple terrestrial food pathways-total bodyb-d(mrem y-' per pCi m-2 d-I)

& 2.5 x 4.1 x

lo4

\

x, 9.4 x 1.1x

X,

Reference

lo-'

Garten (1980)

3 x 10-1

Garten (1980)

23

Schwan and Hoffman (1981) Hoffinan e t al. (1982) Hoffman et al. (1982)

3.5 x

lo-2

M

p

Z

0.66

9.6

3.9

0.26

6.5

10

50

220

0.28

1.2

5.1

0.67

4.8

X

9.3 x 1.2 X

10"

lo-'

4.4 x

lo-'

"Estimated dose rate a t age 70 from a lifetime exposure. Estimated dose rate to age 70 years as the result of a continuous exposure beginning at age 20. ' Simple analytical procedures used to propagate parameter error. Monte Carlo computer techniques used to propagate paramater error. "Estimated thyroid dose rate for children of the age group 0.5 to 2.0 years. 'Values approximated from published figures using lognormal statistics.

0.16

Matthies et al. (1981) Hoffman e t al. (1982) Hoffman et al. (1982)

=!

z

C,

3-

3Z

8

z

0 0

r M

E~j

2 5 5

6.4 UNCERTAINTIES AMONG VARIOUS TYPES OF MODELS

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227

VALUES OF PREDICTED DOSE (D,)

Fig. 6.2 A frequency distribution of predicted doses (D,), produced through parameter imprecision analyses, compared with a deterministic model prediction of dose (Dd). The probability of the deterministic prediction being underconservative is indicated by y. The expression 1 - y indicates the probability of the deterministic model prediction being conservatively biased.

mentation, resuspension, food chain bioaccumulation, and ground water transport. These uncertainties are predominantly due to the use of generic or default values for model parameters that depend, to a large extent, on the characteristics of the site and the biogeochemical behavior of the various physico-chemical forms of the radionuclides. Improved estimates for these parameters are difficult, requiring a considerable investment in site-specific research. Less uncertainty is expected for predictions of atmospheric and surface water dispersion of prolonged (or chronic) releases of radionuclides. These calculations are dependent on known physical parameters whose variability is reduced by the effects of temporal and spatial averaging. Although some models may have larger uncertainties than others, the importance of these uncertainties will vary depending on the amount and composition of the released radionuclides, the magnitude of the dose received by members of the general public, and the relative contribution to the dose by each exposure pathway. 6.4.1 Atmospheric Transport Models

Gaussian plume models appear to be relatively accurate (within a factor of 2 to 4) for predicting long-term average air concentrations over flat terrain (Section 2.1), especially when site-specific meterological data are used for values of model parameters and the location of the predicted concentration is relatively close to the point of release (within 10 km). There is less certainty for short-term predictions under complex conditions of meterology and terrain. Under these conditions, uncertainties of one to two orders of magnitude may be encountered (Miller and Little, 1982). The major sources of uncer-

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tainty are related to the specifications of wind patterns at sites with complex terrain and complex meterological characteristics, the classification of atmospheric stability, the values selected for the dispersion parameters a, and a,, and the values selected for wet and dry deposition. The prediction of the rate a t which radionuclides are transferred from the atmosphere to the terrestrial system is influenced by values assumed for parameters that determine wet and dry deposition. These calculations can be associated with one to three orders of magnitude uncertainty for gases and particulates when predictions are made for short-term releases. Less uncertainty is expected for deposition calculations of prolonged releases because of the effects of time averaging (Section 2.2). Although the parameters involved with the calculation of resuspension also span several orders of magnitude, this exposure pathway is usually of secondary importance, with the exception of those circumstances where the ground surface is the primary source of contaminated material. 6.4.2

Terrestrial Food Chain Transport Modek;

Validation of terrestrial food chain models has generally been restricted to isolated testing of a few model parameters. Some attempts have been made to test the aggregation of models which consider all variables from source term to concentrations in air, water and foods. These tests have only met with partial success, because contamination from atmospheric weapons testing interferes with measurements of the amounts of radionuclides, and because actual releases of radionuclides from nuclear facilities are intermittent rather than constant. For radioiodine releases, partial validation information indicates that the assumption of dry deposition parameters for iodine in elemental form (I2) tends to overpredict concentrations of 13'1 in milk (Weiss and Keller, 1977; Weiss et al., 1975; Riedel and Von Gadow, 1976; Erb, 1979; Golden et al., 1982; Voilleque et al., 1981). This tendency is expected because 13'1 released in chemical forms other than elemental iodine are associated with substantially lower rates of atmospheric deposition (see Sections 2.2 and 2.3, and Hoffman, 1977). Most of the uncertainty associated with terrestrial food chain models is due to bias in the selection of parameter values and the lack of data for transfer coefficients for specific foods (Section 2.3). The variability of values for parameters used to predict the transfer of radionuclides into major food categories (milk, meat, and vegetables) is large. Therefore, discrepancies between field measurements of concentrations in foods and predicted concentrations of "deterministic" models are

6.4

UNCERTAINTIES AMONG VARIOUS TYPES OF MODELS

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229

expected. The use of conservative assumptions in the absence of sitespecific data should, however, result in predictions that tend to overestimate the concentration in terrestrial foods. Although site-specific data can be readily obtained for agricultural parameters such as vegetation biomass and its later consumption by animals, uncertainty still remains in the selection of appropriate food chain transfer factors for specific radionuclides (Section 2.3). Derivation of isotope-specific transfer factors on a site-specific basis through empirical measurements or through correlation with readily available environmental factors such as soil characteristics, climate, vegetation species, animal type, etc., should help reduce a substantial amount of the uncertainty inherent in terrestrial food chain models. More complete validation studies, however, will be necessary to document the overall uncertainty associated with these models. 6.4.3 Specific Activity Models for 3H and 14C

If dose assessments of 3H and 14C are performed using the specific activity approach, reasonable confidence can be placed in the dose estimate being equivalent to an upper limit when the specific activity (i.e., the ratio of the mass of the radioisotope to the mass of its related naturally occurring stable element) in environmental media is assumed to be equal to the specific activity within the human body a t the point of interest (Section 2.5). This assumption ignores the likely dilution of the body content of 3H and 14Cthrough intake of less contaminated sources of hydrogen and carbon. Sources of error which could offset this maximum conservatism are related to: (a) the estimated release rate, (b) the estimated physical dispersion from the point of release, (c) the concentration of stable hydrogen and carbon in air and water at the location of assumed exposure, and (d) the estimated fraction of the receptor that is hydrogen and carbon. Accounting for dilution in the body and intake of less contaminated sources of stable hydrogen and carbon (Section 2.5) reduces the conservatism provided by the specific activity approach, but also increases the probability of underpredicting the dose, given that sources of hydrogen and carbon may be highly variable for any specific individual. Additional uncertainty will also be encountered if the specific activity approach is only used .to estimate the concentration of 3H and 14C in air, water, and food. Dose calculations will then be a function of intake rates (ingestion and inhalation), conversion factors relating dose to a unit intake of 3H and 14C, and estimates of the fractions of food and beverages composed of hydrogen and carbon.

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6. IDENTlFICATION OF MODEL PREDICTIONS

Such an approach includes sources of uncertainty due to variability in diet and physiology, including the effects of age-dependen~e.~ These sources of uncertainty are not encountered when the specific activity within the human body is related directly to the maximum specific activity in the environment, with no account given for dilution from intake of relatively uncontaminated sources of stable hydrogen and carbon. 6.4.4

Surface Water Transport Models

For surface water transport models, accuracies to within a factor of two are likely (Section 3.1, Little and Miller, 1979). Although few validation studies have been conducted, the prediction of physical dispersion in surface waters is reasonably well known. This is because, for most situations, boundary conditions are well defined and the impact of time averaging of discontinuous releases is small. For most assessment situations, simple box models are adequate. A major source of uncertainty is the amount of interface between the soluble fraction and suspended and deposited sediment. The usefulness of highly variable distribution coefficients (Kd), for predicting the behavior of radionuclides in natural aquatic systems is tenuous. Values of Kd are frequently determined under laboratory conditions for specific sediment types and chemical elements. Usually, the impact from contamination of sediments is small enough to offset concerns about gross uncertainty in model predictions. However, for some radionuclides, the potential for sediments to act as a secondary source of input into aquatic food chains needs to be evaluated. 6.4.5

Aquatic Food Chain Transport Models

For aquatic food chain models, the largest uncertainty is in estimating the coefficient for the transfer of radionuclides from water to edible

,

'Although this report has not specifically addressed the issue of uncertainties associated with the external and internal dose factors, much of the total uncertainty in assessing radiological impacts on humans may be due to these factors. Dose factors are used to convert exposure rates to contaminated air, water, foods and surfaces into values of dose equivalents. In the example of the imprecision analyses for the transport and dose of 13'Iz over the pasture-cow-milk-child-thyroid pathway, more than 40% of the total variability in the model prediction was due to the variability in the biological parameters used to estimate the internal dose factor, assuming statistical independency among the parameters of the internal dose factor (see Table 6.1). The importance of this source of variability is especially noteworthy because, although site-specific investigations may be used to reduce the uncertainty in the environmental transport models, it is not likely that such investigations will modify the estimate of the internal dose factors.

6.4

UNCERTAINTIES AMONG VARIOUS T Y P E S OF MODELS

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231

aquatic organisms, i.e., the bioaccumulation factor (Section 3.2). The variability in values of the bioaccumulation factor may span several orders of magnitude. Generic values for bioaccumulation factors currently used in assessment models ignore dependence on measurement technique, species of organism, water quality and water chemistry. Usually, these generic values have been derived from fallout contamination or from stable element concentrations. Their use in deterministic assessment models generally leads to overestimates of the concentration of radionuclides in aquatic foods; however, overprediction for all aquatic environments cannot be assumed a priori. Estimation of bioaccumulation factors can be improved substantially by establishing correlations with environmental factors such as water concentration of the related stable element, water concentration of an analogue element, suspended matter, nutrient levels, etc. 6.4.6 Groundwater Transport Models

For the most part, models which predict groundwater flow and pressure have been used and tested for several decades and have been shown to provide reliable predictions over time periods of 20 to 30 years. Hydrologists also believe that these models will provide reliable estimates of porous flow in simple geologic settings over the longer time period needed for assessing waste disposal systems (i.e., more than 1000 years). However, in situations of unsaturated flow and transport, and fracture flow and transport, the models are not as reliable and validation is extremely difficult to achieve (Section 4). Uncertainties in describing boundary conditions, and in characterizing environmental conditions over geological time scales are particularly troublesome. Few other pathways require predictions extending so far into the future, and few include components, that, like host rock, are difficult to test nondestructively. Major efforts, however, are currently underway to address the issue of predictive uncertainty in ground water transport models as a function of parameter imprecision (Kocher, 1982; Cranwell and Helton, 1982).

6.4.7 Human Factors The exposure to environmental radioactivity is greatly influenced by human dietary habits, inhalation rates, and occupancy rates. Although the types of foods and intake rates assumed in model calculations are based upon reference members of critical groups of the

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6. IDENTIFICATION OF MODEL PREDICTIONS

population, site-specific habits for any given individual may differ substantially from reference values (Section 5). In the past, attempts have been made to offset large uncertainties associated with food chain transfer factors by postulating conservative (i.e., tending to maximize dose) usage factors for the critical population group. More recently, attempts to increase the realism of model predictions have eliminated conservative usage factors and have replaced them with averaged values derived from site-specific or regional surveys. In view of the large uncertainty associated with generic food chain transfer factors, the intended realism associated with these new estimates of human usage factors may be misleading. This is especially apparent in cases where the selection of default values for other model parameters has not been conservative. Unlike human usage factors, many parameters currently used in environmental radiological assessment models cannot be readily determined on a site-specific basis (Sections 2, 3, and 4). With the exception of data on infant and child milk consumption, the variability of values for dietary habits is difficult to assess because literature data frequently 'are derived from daily recall surveys and have not attempted to follow individual usage patterns over extended time periods (Section 5). These data can be expected to overestimate the variability associated with annual average factors for actual individual members of population groups. In general, more variability in dietary habits, and occupancy factors are expected for adult members of the population than for younger age groups, with the least variability expected to occur among infants.

6.5 Conclusion The overall uncertainty in the calculation of dose is recognized as an issue requiring continued attention. Concentrations of radionuclides in the terrestrial and aquatic environment may be determined through measurements rather than model calculations but estimates of dose from radionuclides deposited in the body will depend on the continued use of internal dosimetry models. Therefore, the accuracy attainable by environmental radiological assessment models likely will be limited by the uncertainties inherent within the calculation of dose conversion factors for internally deposited radionuclides.

7. The Application of Models for Environmental Assessments Models developed for assessment purposes are distinctly different from those intended to serve as research tools. Usually, the best model for a given assessment is the easiest one to use that produces results within a n acceptable degree of accuracy. Simple screening models are useful for identifying potentially important radionuclides and pathways. Research model. are typically more complex and attempt to explicitly simulate individuul mechanisms and processes involved with enuironmental transport; however, their accuracy is not necessarily improved by increased complexity. The utility of assessment models is optimized when the uncertainty in the results is reduced while mathematical simplicity is maximized.

7.1 Classes of Models Although various classifications of the models reviewed in this study are possible, two basic categories are recognized here: models specifically developed for use in assessments (environmental assessment models) and models developed as tools for research (research models).

7.1.1 Environmental Assessment Models The purpose of radiological assessment models is to predict concentrations of radionuclides in various environmental media (i.e., air, water, sediment, soil, and terrestrial and aquatic foodstuffs). To be useful, the predictions made by assessment models must be defensible. T o be defensible, they must be sufficiently complete in that all important exposure pathways are included and the range of uncertainty in the results has been confirmed through validation tests. Ideally, parameter values and model predictions should be capable of being tested 233

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ENVIRONMENTAL ASSESSMENTS

through field validation. Untested assessment models should be given an intentional and clearly stated degree of conservative bias to reduce the probability of underestimation.

7.1.2 Research Models In contrast to models specifically developed for assessment purposes is the class of models developed as research tools. Research models differ from assessment models in their objectives. Emphasis is placed on their ability to explicitly simulate the processes and mechanisms affecting the behavior of radionuclides in the environment. Because these models are usually developed to identify all distinct physical processes and biological mechanisms, they are mathematically more complex than is typical of assessment models. However, the ability to field test the parameters and predictions of research models is not important as a constraint for their development. Intentionally conservative bias is also absent because of the desire to describe environmental transport mechanisms realistically, and to understand them. Furthermore, unlike radiological assessment models, the development of research models is not constrained by the limitations set by potential users. Although research models are often adapted for assessment purposes, their use is usually restricted t o situations where either an assessment model does not exist or where there are insufficient data to quantify critical parameters. Caution should be exercised before considering adaptation of a research model for a given assessment problem. In Section 4, the application of complex research-level models for geological waste isolation is described as model "overkill." For complex dynamic models, the experimental determination of many coefficients describing the transfer of a given material between compartments may be impractical. Research models often are dependent on parameters that cannot be readily measured in the field without significantly perturbing of the ecosystem. Also, without specification of parameter covariances, increasing model complexity increases the sensitivity of predictions to parameter error propagation (O'Neill et al., 1980; Gardner et al., 1980). Examples of complex research models are illustrated in Fig. 3.1 and 3.4 of Section 3.1 for aquatic systems. In contrast to these complex models is the use of the simple "bioaccumulation factor" in Section 3.2 to describe the multiple processes of radionuclide transport directly from water to fish.

7.3 IMPROVEMENT OF RADIOLOGICAL ASSESSMENT MODELS

I

235

7.2 Application of Environmental Assessment Models for Screening

\

Realizing that quantitative predictions are based on simplifying assumptions and generalizations of complex real-world behavior, a useful application of assessment models is to screen for the more important radionuclides and exposure pathways. Typically screening involves comparison of conservatively biased model predictions (predictions expected to be on the high side) with established limits. A radionuclide and exposure pathway can be considered insignificant when predicted concentrations are less than a small fraction of the protection limit (Hoffman and Kaye, 1976). On the other hand, radionuclides and pathways predicted by screening models to result in concentrations that approach or exceed limiting values indicate the need for further analysis. The amount and type of conservatism applied for screening will depend on the level of understanding of the radionuclides behavior in the environment, the amount and quality of available data, and the history of model validation. Many environmental models used for assessment and research purposes can be adapted for screening calculations. Usually, however, calculation procedures are not extensive and the data base includes generic default parameter values for use in the absence of site-specific information. Sometimes research models are proposed for screening calculations. Research models are often implemented incorrectly when the actual behavior of the radionuclide in food chains is not well understood or when relevant parameter values and model validation results are lacking. However, unless available data can justify the need, increased mathematical complexity for screening purposes is likely to be unwarranted (Hoffman et al., 1978; Kaye et al., 1982).

7.3 Improvement of Radiological Assessment Models 7.3.1 Reduce Uncertainties Improvements in environmental models are needed to reduce the uncertainties of their predictions. The use of screening models can facilitate these improvements by identifying those radionuclides and pathways requiring better data. Once the important radionuclides and pathways are identified, field validation tests can quantify the degree

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ENVIRONMENTAL ASSESSMENTS

of the uncertainty. Further improvements may be made through better estimation of parameters, adjustments in model structure, and calibration of model predictions against data sets obtained from validation tests. Additional field validation tests can confirm these improvements. Reduction in predictive uncertainty can also be accomplished by using site-specific parameters whose values may be readily determined for a specific site, such as standing vegetation biomass, the bulk density of surface soil, and some aspects of cattle management practices (Section 2.3). However, radionuclide-specific environmental transfer factors or rate constants such as deposition velocity, distribution coefficients, weathering rates, and food chain transfer coefficients cannot be determined for a specific site without extensive monitoring or experimental investigation (Kaye et al, 1982). Matching these model parameters with easily measurable environmental variables such as temperature, pH, soil type, and specific food products should improve the accuracy of model predictions.

7.3.2

Model Simplification

Perhaps the most effective improvements in environmental assessment models can be made in achieving an optimum level of model simplification. As mentioned in many of the previous sections, the "best" model for a given assessment will be the model that is easiest to use and which produces results within an acceptable degree of accuracy. Thus, relatively simple model formulations have prevailed in environmental radiological assessments despite the availability of models described in the previous chapters which are substantially more complex but not necessarily more accurate. Simple models consisting of few parameters for important radionuclides and pathways should be more amenable to field validation than more complex models because of reduced demands on simultaneous parameter measurement. Thus, an optimum level of complexity can be envisioned when all parameters are readily measurable and the possibility of predictive error due to unforseen correlations among the parameters is small. However, an optimum level of simplification will be determined by the amount of predictive uncertainty accepted by the user and the ease of model implementation.

8. Conclusions and Recommendations 8.1 Conclusions The objective of this report has been to analyze the current status of the application of models used for radiological assessments. Several conclusions are drawn based upon our evaluation of the models and their use. Because of the general nature of these conclusions, they are not explicitly mentioned within the body of the report and are summarized in the following statements. The order in which they appear does not reflect any order of their importance. (1) Models are available to address all significant pathways of potential importance to the radiological exposure of humans in the vicinity of the release of radionuclides. The models utilize a broad data base derived from studies of stable elements and radioactive tracers performed over several decades. (2) Radiological assessment models are essential for a priori evaluation of the acceptability of planned and unplanned releases of radioactivity to the environment. In addition, they are the only mechanism available to estimate the impact of releases that are below detectable levels in the environment. (3) Further development of radiological assessment models and improvements in the data base should be pursued selectively by considering the radionuclides, pathways, and exposure groups that are of most importance in terms of the final estimated dose. As a part of this selection process, emphasis must be given to improving the data that a t present introduce the greatest uncertainty in dose. (4) It is recognized that models and data bases for some environmental transport mechanisms are more complete than others (e.g., the state-of-the-art for atmospheric transport models is more advanced than those for groundwater transport, etc.); however, this disparity is a normal scientific response' to fulfilling the most immediate needs first, as development of the nuclear industry progressed. This is not to imply that future

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research should automatically focus on radiological assessment models and data bases that are less developed, rather, the emphasis in the future for research must be based upon the criteria previously stated in item (3), pathways, radionuclides, and exposure groups contributing the most to total estimated dose. (5) Additional work is needed to improve our confidence in the results of model calculations and make them more defensible. Also, more emphasis must be given to better documentation of models and making models and data bases more useable by individuals involved in day-to-day calculations. This report is unique in that it attempts to show the interrelationship of each of the major pathways of exposure in the assessment process, the strengths and weaknesses of the models, and uncertainty associated with the data base. Additional work is needed to provide a complete manual or handbook that covers the entire spectrum of radiological assessment from source term to analysis of health effects.

8.2 Recommendations In order to enhance the use of radiological assessment models and better understand their capabilities, it is recommended that future research emphasize two vital areas, model validation and model simplification. Justification for these two recommendations is elaborated below.

Model Valufation This study indicates that there is a high degree of uncertainty in the accuracy and precision of methods used for environmental radiation assessments. One factor contributing to this high degree of uncertainty is that few concerted efforts have been made to validate with field data the transport models or basic environmental parameters used in the models. The technique of radiological assessment has now reached the point where model development has greatly exceeded the efforts to validate the models. Although validation research would be extremely beneficial in terms of derived benefits, this research has typically been given low priority because of anticipated high costs, and the long times normally required to accumulate statistically valid results. It is recommended that priority for future research be given to the

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validation of radiological assessment models. It is also recommended that this validation effort be carefully planned and carried out as a unified effort includng all agencies and groups involved in the development and application of radiological assessment models. Therefore, a comprehensive long-range plan for validation is needed to determine priorities for validation research and the projected cost vs. anticipated benefits. Priorities need to be carefully established, because validation experiments will require considerable commitment of time and financial resources. Model Simplification In recent years, the trend has been toward more complex models; however, the increased complexity has not necessarily improved the accuracy of estimates of dose and, in certain cases, has had the opposite effect. It is recommended that future model development be directed toward the simplest model that will adequately address each assessment situation. Currently, there is no comprehensive set of simple screening models that would provide a preliminary estimate of dose. Screening models should be developed for use in the preliminary evaluation of radionuclide releases. To be effective, screening models should have a predetermined level of uncertainty and should be the only model required if the resulting dose is less than a prescribed level.

APPENDIX A

Applicability of Models for Routine Releases to the Accident Situation The majority of models that predict the behavior of radionuclides in the environment are based upon concepts that simulate steadystate conditions. The source term for assessing routine releases is generally assumed to be uninterrupted and without significant perturbations for a long period of time such that near-equilibrium conditions exist for the duration of the release. Accidental releases, on the other hand, involve injection of a pulse of radioactivity that results in a high concentration in environmental media which may be rapidly eliminated from some compartments and persist in others for many years. Therefore, it is important to consider the applicability and limitations of the models discussed in this report to the accident situation in which equilibrium conditions may not exist. Methods for evaluating accidental releases of radionuclides are needed to predict the severity of accidents before they occur and to assist in determining protective action and health implications during and after a contaminating event. The evaluation of postulated accidents is also of considerable interest both in the assessment of risk from commercial nuclear plants (USAEC, 1975) and in establishing criterion for siting nuclear facilities (CFR, 19711). In any accident analysis, it is reasonable to assume that pathways of exposure to man would be limited by constraints placed upon individuals to restrict the amount of time spent in the area and to minimize the consumption of contaminated food products. I t is our opinion that for generic accident analyses, the models discussed in this report could be used for initial estimation of the total integrated dose, provided that conditions expected to prevail during the time of the accident are taken into account. For example, models developed for routine releases (perhaps with minor modifications) could be useful in identifying potentially important pathways of ex240

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posure, areas where interdiction of land use might be necessary, and sites which should be evacuated. In the case of the actual event, we recommend that emphasis be placed on a comprehensive environmental monitoring program as an integrated part of the emergency response plan. This program should not preclude the use of models discussed in this report to assist in identifying and prioritizing pathways of exposure to monitor during or following the accidental release. Therefore, for analysis of accidental releases, emphasis should be given to developing realistic source terms and providing immediately available meteorological and demographic data rather than creating new models specifically for the accident case.

APPENDIX B

Glossary

'

I

absolute humidity: Vapor content of water in air expressed as g m-3. A key parameter in the calculation of dose from tritium released to the atmosphere. acceptable degree of accuracy: The amount of error or uncertainty in model predictions tolerated for any given assessment situation. Usually, a greater degree of accuracy is required for potential outcomes involving high risks and/or economic costs. accuracy: As applied to environmental assessment models, accuracy implies agreement between the model prediction and actual events. An "accurate" model should be precise and unbiased. algorithm: An explicit step by step procedure for producing a solution to a given problem. In a computer model, an algorithm may be any statement or set of statements expressing the functional operation of a model which enables a set of input data to produce a given output. anisotropy: Referring to the character of a medium in which, at any point, the properties are different in different directions. aquifer: A formation or group of formations, or part of a formation that contains sufficient saturated permeable material to yield significant quantities of water to wells and springs. aquitard (confining bed): A body of impermeable material stratigraphically located adjacent to one or more aquifers, which tends to isolate the water in a permeable portion of the aquifer from another portion. benthos: Aquatic bottom-dwelling organisms (benthic organisms). bias: The tendency for an estimate to deviate from an actual or real event. Bias may be the tendency for a model to over- or underpredict. bioaccumulation factor (BF):The ratio of radionuclide concentration in an organism or tissue to that in water or food products. boundary layer: That portion of a moving fluid in which turbulent diffusion is taking place. This turbulence may be due to mechanical effects, thermal effects, or some combination of both. ?A2

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box model: A pollutant transport model based on mass conservation of the pollutant in a specified volume. Such models are inherently simple but physically sound. concentration factor: See bioaccumulation factor. conservative bias: A tendency to overestimte rather than underestimate. default value: A value prescribed for a model parameter in the absence of data directly relevant to the assessment situation. deterministic model: A model whose output is predetermined by the mathematical form of its equations and the selection of a single value for each input parameter. diffusion: The spreading out of a material in a fluid due to thermal or mechanical agitation. dispersion coefficient: A measure of the spreading of a flowing substance due to the nature of the porous medium. dispersivity: A geometric property of a porous medium which determines the dispersion characteristics of the medium by relating the components of pore velocity to the dispersion coefficient. distribution coefficient: The quantity of the radionuclide sorbed by the solid per unit weight of solid divided by the quantity of radionuclide dissolved in the water per unit volume of water. environmental assessment model: A type of model specifically designed to address questions formulated in the context of an environmental assessment. Environmental assessment models are usually less complex mathematically than are models used as tools in research. e r r o r propagation: The translation of input errors into estimates associated with modeling art; in this context, statistical and numerical error propagation techniques are the fundamental methods used to combine parameter uncertainties into an estimate of the overall uncertainty in model pAdictions. This process is referred to in this report as a "parameter imprecision analysis." eutrophic: Waters with good supply of nutrients and hence a rich organic production. extrapolation: The projection of model calculations to situations outside the realm of past experience or known data. Model calculations performed within the realm of experience and pertinent data are considered to be interpolations unless verified by measurement. flux (specific discharge, darcy velocity): The volume of discharge from a given cross-sectional area per unit time divided by the area of the cross section. fracture flow: Groundwater flow through a fractured medium. The

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APPENDIX

medium itself may be porous and permeable, but the flow would be dominated by fractures, cracks or solution cavities. Gaussian model: A pollutant diffusion model based on an assumption of stationary, homogeneous turbulent flow. The distribution of material in the plume or puff is assumed to be gaussian in shape. gradient-transport theory: A theory of pollutant transport which assumes that the pollutant flux is proportional to the local concentration gradient in the direction of the mean fluid flow and from this derives a diffusion equation based on mass continuity. grid model: A pollutant transport model that is a finite-difference approximation to the equation of motion, continuity, diffusion, and species conservation and removal. Grid models are severely restricted in their applicability to a large class of pollutant problems. high-level waste: High-level radioactive waste is defined by 10 CFR 60 (May 1983) as: "(1) irradiated reactor fuel, (2) liquid waste resulting from the operation of the first cycle solvent extraction system, or equivalent, and the concentrated waste from subsequent extraction cycles, or equivalent, in a facility for reprocessing irradiated reactor fuel, and (3) solids into which such liquids have been converted." higher-order closure theory: A theory of pollutant diffusion which is based on the principle that knowledge of all the moments of the distribution of a quantity is fully equivalent to knowing its distribution. homogeneity: The properties, or conditions of isotropy or anisotropy are constant from point to point in the groundwater medium. hydraulic conductivity (permeability): The volume of water that will move per unit time in the aquifer under a unit gradient through a unit cross sectional area perpendicular to the direction of flow. intrinsic permeability: The measure of the ability of a rock or soil to transmit fluid under a fluid potential gradient (see definition of hydraulic conductivity). isotropy: As applied to groundwater, referring to the character of a groundwater medium in which the properties a t any point within the medium are the same in all directions. K-theory: See gradient-transport theory. leaky aquifer: An aquifer which consists of a t least two permeable units separated by a less permeable layer which partially separates the water in each unit, but allows for a certain amount of leakage between units. low-level waste: Low-level waste is defined by 10 CFR 61 (December 1982) as ".. . radioactive waste not classified as high-level radioac-

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tive waste, transuranic waste, spent nuclear fuel or byproduct material (uranium or thorium tailings and waste) . . . . ." macrophyte: Plants that can be seen with the unaided eye. minute volume or ventilation rate: The volume of air expired per minute. It is the product of the tidal volume and the breathing frequency. mixed layer: See boundary layer. model: A mathematical abstraction of an ecological or biological system, sometimes including specific numerical values for the parameters of the system. model overkill: The inappropriate applications of complex models for problems that can be adequately addressed using simpler approaches. model prediction: The result or dependent variable produced by a model calculation. model structure: The conceptual design, mathematical equations and set of algorithms that control the results or predictions produced from a given set of input data or assumptions. model validation: Documentation of the discrepancy (or agreement) between model predictions and actual events through comparison of predicted values with accurately measured field data obtained over the range of conditions representing the extent of intended application of the model. moisture content: The volumetric fraction of the groundwater medium "occupied by liquid water." molecular diffusion: The spreading out of molecules or ions in a fluid, in a direction tending to result in uniform concentrations in all portions of the system. oligotrophic: Waters deficient in nutrients. omnivorous: Feeding on both plants and animals. parameters: Any one of a set of independent variables in a model whose values determine the characteristics or behavior of the model. parameter imprecision analysis: An analysis of uncertainty using error propagation techniques to produce a stochastically variable prediction as a function of stochastically variable parameters. percolation (infiltration): The process of downward movement of water from the surface into underlying materials. periphyton: The aquatic community of diatoms and other algae, bacteria, fungus and protozoa, which is attached to substrates. phytoplankton: T h e plant organisms of plankton. piscivorous: Feeding on fish. plankton: Aquatic organisms, usually microscopic, which float pas-

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APPENDIX

sively or exhibit limited locomotor activity. pore velocity, seepage velocity: The average rate -of flow in the pores of a given groundwater medium. This is approximated by dividing the flux by the effective porosity. porosity: The property of containing interstices. Total porosity is expressed as the ratio of the volume of interstices to total volume. Effective porosity refers t o the porosity through which flow occurs. porous flow: Goundwater flow which is predominantly through pores in the medium, or through the interstitial spaces between small grains of material (as opposed t o fracture flow, defined previously). pressure head: The height above a standard datum of the surface of a column of water that can be supported by the pressure a t a given point. The gradient of the pressure head is usually the driving force for ground water flow. probabilistic model: See stochastic model. research model: Any model developed to fulfill research objectives. Usually research models are developed to provide insight into explicit processes and mechanisms and thus are mathematically more complex than assessment models. retardation coefficient: The measure of the capability of the porous medium to impede by sorption the movement of a particular radionuclide being carried by the fluid. saturated zone: T h e portion of the porous medium in which only fluid occupies (fills) all of the interconnecting interstices (void space or pores) which can interact with other portions of the medium. screening: The process of rapidly identifying potentially important radionuclides and exposure pathways by eliminating those of known lesser significance. screening models: Simple models employing conservative assumptions for the expressed purpose of screening out radionuclides and exposure pathways of negligible importance. sensitivity analysis: Analysis of the mathematical sensitivity of the model predictions to selected perturbations of model parameters. similarity theory: A theory of pollutant diffusion based on dimensional analysis of the physical variables that control boundary layer turbulent flow. site-specific data: Data used in radiological assessment models which are obtained to describe the particular location for which the assessment is being performed. W.hen site-specific data are not available, default values must be used. soil-to-plant concentration ratio: Bi,, the ratio of the concentration of a radionuclide (i) in fresh vegetation to that in dry soil. CRi, the

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ratio of the concentration of a radionuclide (i) in dry vegetation to that in dry soil. sorption: All mechanisms, including ion exchange, that remove ions from the fluid phase and concentrate them on the solid phase of the medium. specific activity method: A model which estimates dose from a radionuclide by assuming the specific activity in food or water is equal to or a fraction of the specific activity in air for a given location. This approach bypasses the steps normally used in radionuclide transport models; however, it is primarily applicable to radionuclides that have a n abundant stable carrier in nature such as water for tritium and carbon dioxide for carbon-14. specific retention: The ratio of the volume of water which the rocks or soil, after being saturated, will retain against the pull of gravity to the unit volume of rock or soil. specific storage: The volume of water released from or taken into storage per unit volume of the porous medium per unit change in head. specific yield: The ratio of (1) the volume of water which the rock or soil, after being saturated, will yield by gravity, t o (2) the volume of the rock or soil (sometimes referred to as "effective porosity"). stability class: A measure of the state of atmospheric turbulence conditions. statistical theory: A theory of diffusion in a fluid which assumes a stationary, homogenous turbulence field and derives the pollutant concentration in terms of the mean-square displacement of a fluid "particle" from its average position. stochastic model: Any model whose input and output are expressed as random variables. Contrast with deterministic model. stratification: The phenomenon occurring when a body of water becomes divided into distinguishable layers. tidal volume: The volume of air breathed in and out under any condition. trajectory model: Atmospheric transport model which is driven by an observed or predicted wind field, generally for distances beyond 10 km. Diffusion is accounted for using a moving-box, growing puff, or small air-particle elements. transfer coefficient to milk (Fi,): The fraction of element (i) ingested daily by a cow that is secreted in milk at steady-state or equilibrium. transfer coefficient to other animal product (e.g., meat, eggs) (Fir):The fraction of element (i) ingested daily by a herbivore that

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APPENDIX

can be measured in 1 kg of animal product a t steady-state or equilibrium. transmissivity: The rate a t which water is transmitted through a unit width of the aquifer under a unit hydraulic gradient. transport:The movement .of a material within a single environmental medium, e.g., dispersion in the atmosphere. uncertainty: The lack of sureness or confidence in the predictions of models. uncertainty analysis: Analysis of the uncertainty in model predictions. unsaturated zone: The portion of a porous medium where the interconnecting interstices are only partially filled with fluid. utilized area factor (U): The effective area of pasture grazed daily by a herbivore. ventilation rate: See minute volume. water table: The surface in an unconfined groundwater body at which the water pressure is atmospheric (e.g., the level reached in dug wells). zooplankton: The animals of plankton.

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THOMPSON,S. E., BURTON,C. A., QUINN,D. J. A N D NG, Y . C. (1972). Concentration Factors of Chemical Elements i n Edible Aquatic Organisms, Report No. UCRL-50564, Rev. 1 (Lawrence Livermore Laboratory, Livermore, California). THOMPSON, S. E. A N D ROBISON,W. A. (1983). A Summary of Ventilation Rates as a Function of Age, Sex, Physical Activity, Climatic Conditions and General Health State, Report No. UCRL 89037 (Lawrence Livermore National Laboratory, Livermore, California). THORNTHWAITE, C. W. A N D MATHER,J. (1957). Instructions and Table for Computing Potential Evapotranspiration and the Water Balance, Publications in Climatology, Laboratory of Climatology, Centerton, New Jersey 10,3. TILL, J. E. A N D MEYER,H. R. Eds. (1983). Radiological Assessment (U.S. Nuclear Regulatory Commission, Washington, D.C.). TILL,J. E., MEYER,H. R., ETNIER,E. L., BOMER,E. S., GENTRY,R. D., KILLOUGH, G. G., ROHWER,P. S., TENNEY, V. J. A N D TRAVIS,C. C. (1980). Tritium-An Analysis of Key Environmental and Dosimetric Questions, Report No. ORNL/TM-6990 (Oak Ridge National Laboratory, Oak Ridge, Tennessee). TITAEVA, N. A. (1967). "On the character of radium and uranium bond in peat," Goekhimya 12, 1943. TURNER, D. B. (1964). "A diffusion model for an urban area," J. Appl. Meteor. 8,83. TURNER, D. B. (1969). Workbook of Atmospheric Dispersion Estimates, Pub. No. 995-AP-26 (U.S. Department of Health, Education and Welfare, Washington, D.C.). TURNER,D. B. (1.979). "Atmospheric dispersion modeling, a critical review," J. Air Poll. Control Assoc. 29, 502. USAEC (1974). U.S. Atomic Energy Commission, Proposed Final Environmental Statement, Liquid Metal Fast Breeder Reactor Program, Vol. 11, Part 11, '2-19, Report No. Wash-1535 (U.S. Atomic Energy Commission, Washington, D.C.). USAEC (1975). U.S. Atomic Energy Commission, Reactor Safety Study-An Assessment of Accident Risks in U.S. Commercial Nuclear Power Plants. Report No. Wash-1400 (U.S. Atomic Energy Commission, Washington, D.C.). USEPA (1978). U.S. Environmental Protection Agency, Guidelines on Air Quality Models, Report Nos. EPA-450/2-78-027, OAQPS No. 1.2-080 (U.S. Environmental Protection Agency, Research Triangle Park, North Carolina). USNRC (1972). U.S. Nuclear Regulatory Commission, On-site Meteorological Programs, Regulatory Guide 1.23 (U.S. Nuclear Regulatory Commission, Washington, D.C.). USNRC (1975). U.S. Nuclear Regulatory Commission, Reactor Safety Study, A n Assessment of Accident Risks in U.S. Commercial Nuclear Power Plants, Report No. WASH-1400 (U.S. Nuclear Regulatory Commission, Washington, D.C.).

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USNRC (1976). U.S. Nuclear Regulatory Commission, Regulatory Gulde 1.113, Estimating Aquatic Dispersion of Effluents from Accidental and Routine Reactor Releases for the Purpose of Implementing Appendix I. (Office of Standards Development, U.S. Nuclear Regulatory Commission, Washington, D.C.). USNRC (1977a). U.S. Nuclear Regulatory Commission, Regulatory Guide 1.111, Methods for Estimating Atmospheric Transport and Dispersion of Gaseous Effluents in Routine Releases from Light- Water-Cooled Reactors, Revision 1 . (Office of Standards Development, U.S. Nuclear Regulatory Commission, Washington, D.C.). USNRC (1977b). U.S. Nuclear Regulatory Commission, Regulatory Guide 1.109 Revision 1, Calculation of Annual Doses to Man from Routine Releases of Reactor Effluents for the Purpose of Evaluating Compliances with 10 CFR Part 50, Appendix I. (Office of Standards Development, U.S. Nuclear Regulatory Commission, Washington, D.C.). USNRC (1978). U.S. Nuclear Regulatory Commission, Liquid Pathway Generic Study, Report No. NUREG-0440 (U.S. Nuclear Regulatory Commission, Washington, D.C.). USNRC (1979). U.S. Nuclear Regulatory Commission, Draft Generic Environmental Impact Statement on Uranium Milling, Report No. NUREG-0511, Vol. 1 & 2 ( U S . Nuclear Regulatory Commission, Washington, D.C.). VANDERPLOEG, H. A., PARZYCK, D. C., WILCOX,W. H., KERCHER, J. R. AND KAYE,S. V. (1975). Bioaccumulation Factors for Radionuclides in Freshwater Biota, Report No. ORNL-5002 (Oak Ridge National Laboratory, Oak Ridge, Tennessee). H. A., BOOTH,R. S. A N D CLARK,F. H. (1976). "A Specific VANDERPLOEG, activity and concentration model applied to Cesium-137 movement in a eutrophic lake," page 164 in Radioecology and Energy Resources, Cushing, C. E. Jr., Ed. (Dowden, Hutcheson & Ross, Stroudsburg, Pennsylvania). VOGT,K. J. (1979). "Models for the assessment of the environmental exposure by tritium released from nuclear installations," page 521 in Symposium on the Behavior of Tritium in the Environment, Report No. IAEA-STI/PUB/ 498 (International Atomic Energy Agency, Vienna). VOGT, K. J . (1977). "Empirical investigations of the diffusion of waste air plumes in the atmosphere," Nuc. Tech. 34,43. D. M., VOILLEQUE',P. G., KAHN,B., KRIEGER,H. L., MONTGOMERY, KELLER,J. H. AND WEISS,B. H. (1981). Evaluation of the Air-VegetationMilk Pathway for '"I at the Q d Cities Nuclear Power Plant Station, Report No. NUREG/CR-1600 (U.S. Nuclear Regulatory Commission, Washington, D.C.). WADDEL, W. W., COLE,C. R. A N D BACA,R. G. (1974). A Water Quality Model for the South Platte River basin-Documentation Report, prepared for the U.S. Environmental Protection Agency (Battelle, Pacific Northwest Laboratories, Richland, Washington). J. S. A N D FISHMAN,M. J. (1962). Adsorption of Cs on Clay WAHLBERG, Miner&, USGS Bulletin 1140-A (U.S. Geological Survey, Washington, D.C.).

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WAHLGREN, M. A. AND MARSHALL, J . S. (1975). "The behavior of plutonium and other long-lived radionuclides in Lake Michigan," page 227 in Impacts of Nuclear Releases into the Aquatic Environment, Report No. IAEA-STI/ PUB/406 (International Atomic Energy Agency, Vienna). M. A,, ALBERTS,J . J., NELSON,D. M. A N D ORLANDINI, K. A. WAHLGREN, (1976). "Study of the behavior of transuranics and possible chemical homologues in Lake Michigan water and biota," page 9 in Transuranium Nuclides in the Environment, Report No. IAEA-STI/PUB/410 (International Atomic Energy Agency, Vienna). J. A. AND EDGINGTON, D. N. (1980). "Plutonium WAHLGREN, M. A., ROBBINS, in the Great Lakes," page 659 in Tramuranic Elements in the Erwironment, Hanson, W. Ed., Report No. DOE/TIC-22800 (National Technical Information Service, Springfield, Virginia). WAHLGREN, M. A. A N D ORLANDINI, K. A. (1982). "Comparison of the geochemical behavior of plutonium, thorium and uranium in selected North American lakes," page 757 in Enoironmental Migration of Long-lived Radionuclides, Report No. IAEA-STI/PUB/597 (International Atomic Energy Agency, Vienna). WALKER, J . S., MARGOLIS, F. J. A N D TEATE,H. L. JR. (1963). "Water intake of normal children," Science 140, 890. J. E. (1965). "The Cesium-137 content of beef WARD,G. M. A N D JOHNSON, from dairy and feed-lot cattle," Health Phys. 11, 95. J. E. A N D WILSON,D. W. (1967). Fifth Annual WARD,G. M., JOHNSON, Report to the U.S. Atomic Energy Commission of the Project Food Chain Transfer of Cesium-137 from Troposphere to Man (Colorado State University, Fort Collins, Colorado). WATTERS,R. A., EDGINGTON, D. N., HAKONSON, T. E., HANSEN,W. C., F. W. A N D WILDUNG, R. E. (1980). "Synthesis of SMITH,M. H., WHICKER, the research literature," page 1in Tramuranic Elements in the Environment, Hanson, W. C. Ed., Report No. DOE/TIC-22800 (National Technical Information Service, Springfield, Virginia). WEISS, N. H. A N D KELLER,J. H. (1977). "Enhancement of radioiodine concentration in milk due to wet processes in the environment," paper 184 presented at the 1977 annual meeting of the International Radiological Protection Association, Paris, France (International Radiological Protection Association, Fontenay-aux-Roses, France). VOILLEQUE, P. G., KELLER,J . H., KAHN,B., KRIEGER, H. L., WEISS,B. H., MARTIN,A. AND PHILLIPS,C. R. (1975). Detailed Measurement of I3'I in Air, Vegetation and Milk around Three Operating Reactor Sites, Report No. NUREG-75/021 (U.S. Nuclear Regulatory Commission, Washington, D.C.) WILDUNG, R. E., ROUTSON, R. C., SERNE,R. 1. A N D GARLAND, T. R. (1975). Pertechnetate, Iodide and Methyl Iodide Retention by Surface Soils. Report No. BNWL-1950, Pt. 2 (Battelle Pacific Northwest Laboratory, Richland, Washington). WILSON,J. L. A N D MILLER,P. J. (1978). "Two dimensional p ~ u m ein uniform ground-water flow," J. Hydraulics Division, ASCE 104, 503.

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WINOGRADE, I. J. A N D PEARSON, F. J. (1976). "Major carbon-14 anomaly in a regional carbonate aquifer: Possible evidence of megascale channelling, South Central Great Plains," Water Resources Research 1 2 , 1125. J. P. A N D TAYLOR,F. G. (1969). "Retention of a fallout WITHERSPOON, simulant containing '"Cs by pine and oak trees," Health Phys. 17,825. WOODHEAD, D. S. (1972). "Levels of radioactivity in the marine environment and the dose commitment to marine organisms," page 31 in Symposium on the Interaction of Radioactive Contaminants with the Constituents of the Marine Environment, Report No. IAEA-STI/PUB/313 (International Atomic Energy Agency, Vienna). WYNGAARD, J. C. Ed. (1980). Workshop on the Planetary Boundary Layer (American Meteorological Society, Boston, Massachusetts). YAGLOM, A. M. (1975). "Equations with time dependent coefficients describing diffusion in a stationary atmospheric surface," Layer. Atmos. and Ocean. Phys. 1 1 , l l . YAGUCHI, E. M., NELSON,D. M. A N D MARSHALL, J. S. (1973). "Plutonium and other radionuclides in biota near the Big Rock Nuclear Plant," page 32 in Radiological and Environmental Research Division Annual Report (Argonne National Laboratory, Argonne, Illinois). YOTSUKURA, N. AND SAYRE,W. W. (1976). "Transverse mixing in natural channels," Wat. Resources Res. 12,695. YOUSEF,Y. A., KUDO,A. AND GLOYNA, E. I?. (1970). Radioactivity Transport in Water: Summary Report, Report No. ORO-490-20 (Oak Ridge National Laboratory, Oak Ridge, Tennessee).

The NCRP The National Council on Radiation Protection and Measurements is a nonprofit corporation chartered by Congress in 1964 to: 1. Collect, analyze, develop, and disseminate in the public interest information and recommendations about (a) protection against radiation and (b) radiation measurements, quantities, and units, particularly those concerned with radiation protection; 2. Provide a means by which organizations concerned with the scientific and related aspects of radiation protection and of radiation quantities, units, and measurements may cooperate for effective utilization of their combined resources, and to stimulate the work of such organizations; 3. Develop basic concepts about radiation quantities, units, and measurements, about the application of these concepts, and about radiation protection; 4. Cooperate with the International Commission on Radiological Protection, the International Commission on Radiation Units and Measurements, and other national and international organizations, governmental and private, concerned with radiation quantities, units, and measurements and with radiation protection. The Council is the successor to the unineorporated association of scientists known as the National Committee on Radiation Protection and Measurements and was formed to carry on the work begun by the Committee. The Council is made up of the members and the participants who serve on the eighty-one Scientific Committees of the Council. The Scientific Committees, composed of experts having detailed knowledge and competence in the particular area of the Committee's interest, draft proposed recommendations. These are then submitted to the full membership of the Council for careful review and approval before being published. The following comprise the current officers and membership of the Council: 284

THENCRP Officers President Vice President Secretary and Treasurer Assistant Secretary Assistant Treasurer

WARRENK. SINCLAIR S. JAMES ADELSTEIN W. ROGERNEY EUGENE R. FIDELL JAMES F. BERG

Members GEORGER. LEOPOLD THOMASA. LINCOLN RAYD. LLOYD ARTHURC. LUCAS CHARLES W. MAYS ROGER0.MCCLELLAN JAMESMCLAUGHLIN BARBARA J. MCNEIL F. MEANEY THOMAS CHARLES B. MEINHOLD MORTIMERL. MENDELSOHN WILLIAME. MILLS DADEW. MOELLER A. ALANMOGHISSI ROBERTD. MOSELEY,JR. JAMES V. NEEL WESLEYNYBORG MARYE. O'CONNOR FRANKPARKER ANDREWK. POZNANSKI NORMAN C. RASMUSSEN WILLIAMC. REINIG CHESTERR. RICHMOND JAMES T. ROBERTSON ROBERTE. ROWLAND LEONARD A. SAGAN J. SCHULL WILLIAM GLENNE. SHELINE ROYE. SHORE WARRENK. SINCLAIR LEWISV. SPENCER J O H NB. STORER ROYC. THOMPSON JOHNE. TILL ARTHURC. UPTON GEORGEL. VOELZ EDWARD W. WEBSTER GEORGEM. WILKENING H. RODNEY WITHERS

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THENCRP Honorary Members LAURISTON S. TAYLOR, Hommty President

Currently, the following subgroups are actively engaged in formulating recommendations:

SC-48: SC-52: SC-53: SC-54: SC-55: SC-57:

Basic Radiation Protection Criteria Medical X-Ray, Electron Beam and Gamma-Ray Protection for Energies Up to 50 MeV (Equipment Performance and Use) X-Ray Protection in Dental Offices Standards and Measurements of Radioactivity for Radiological Use Waste Disposal Task Group on Krypton-85 Task Group on Carbon-14 Task Group on Disposal of Accident Generated Waste Water Task Group on Disposal of Low-Level Waste Task Group on the Actinides Task Group on Xenon Biological Aspects of Radiation Protection Criteria Task Group on Atomic Bomb Survivor Dosimetry Subgroup on Biological Aspects of Dosimetry of Atomic Bomb Survivors Industrial Applications of X Rays and Sealed Sources Radiation Associated with Medical Examinations Radiation Received by Radiation Employees Operational Radiation Safety Task Group 1on Warning and Personnel Security Systems Task Group 2 on Uranium Mining and Milling-Radiation Safety Programs Task Group 3 on ALARA for Occupationally Exposed Individuals in Clinical Radiology Task Group 4 on Calibration of Instrumentation Instrumentation for the Determination of Dose Equivalent Apportionment of Radiation Exposure Conce~tualBasis of Calculations of Dose Distributions ~iolo'ical Effects and Exposure Criteria for Radiofrequency Electromagnetic Radiation Bioassay for Assessment of Control of Intake of Radionuclides Experimental Verification of Internal Dosimetry Calculations Internal Emitter Standards Task Group 2 on Respiratory Tract Model

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Task Group 3 on General Metabolic Models Task Group 4 on Radon and Daughters Task Group 6 on Bone Problems Task Group 7 on Thyroid Cancer Risk Task Group 8 on Leukemia Risk Task Group 9 on Lung Cancer Risk Task Croup 10 on Liver Cancer Risk Task Group 11 on Genetic Risk Task Group 12 on Strontium Task Group 13 on Neptunium SC-59: Human Radiation Exposure Experience SC-60: Dosimetry of Neutrons from Medical Accelerators SC-61: Radon Measurements SC-62: Priorities for Dose Reduction Efforts SC-63: Control of Exposure to Ionizing Radiation from Accident or Attack SC-64: Radionculides in the Environment Task Croup 5 on Public Exposure to Nuclear Power Task Group 6 on Screening Models SC-65: Quality Assurance and Accuracy in Radiation Protection Measurements SC-67: Biological Effects of magnetic Fields SC-68: Microprocessors in Dosimetry SC-69: Efficacy Studies SC-70: Quality Assurance and Measurement in Diagnostic Radiology SC-71: Radiation Exposure and Potentially Related Injury SC-72: Radiation Protection in Mammography SC-74: Radiation Received in the Decontamination of Nuclear Facilities SC-75: Guidance on Radiation Received in Space Activities SC-76: Effects of Radiation on the Embryo-Fetus SC-77: Guidance on Occupational and Public Exposure Resulting from Diagnostic Nuclear Medicine Procedures SC-78: Practical Guidance on the Evaluation of Human Exposures to Radiofrequency Radiation SC-79: Extremely Low-Frequency Electric and Magnetic Fields SC-80: Radiation Biology of the Skin (Beta-Ray Dosimetry) SC-81: Assessment of Exposure from Therapy Committee on Public Education Committee on Public Relations Ad Hoc Committee on Policy in Regard to the International System of Units Ad Hoc Committee on Comparison of Radiation Exposures Study Group on Acceptable Risk (Nuclear Waste) Study Group on Comparative Risk Task Group on Comparative Carcinogenicity of Pollutant Chemicals Task Force on Occupational Exposure Levels

In recognition of its responsibility to facilitate and stimulate cooperation among organizations concerned with the scientific and related aspects of radiation protection and measurement, the Council has created a category of NCRP Collaborating Organizations. Organizations or groups of organizations that are national or international in

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scope and are concerned with scientific problems involving radiation quantities, units, measurements, and effects, or radiation protection may be admitted to collaborating status by the Council. The present Collaborating Organizations with which the NCRP maintains liaison are as follows: American Academy of Dermatology American Association of Physicists in Medicine American College of Radiology American Dental Association American Industrial Hygiene Association American Institute of Ultrasound in Medicine American Insurance Association American Medical Association American Nuclear Society American Occupational Medical Association American Podiatry Association American Public Health Association American Radium Society American Roentgen Ray Society American Society of Radiologic Technologists American Society of Therapeutic Radiologists Association of University Radiologists Atomic Industrial Forum Bioelectromagnetics Society College of American Pathologists Federal Emergency Management Agency Genetics Society of America Health Physics Society National Bureau of Standards National Electrical Manufacturers Association Radiation Research Society Radiological Society of North America Society of Nuclear Medicine United States Air Force United States Army United States Department of Energy United States Department of Labor United States Environmental Protection Agency United States Navy United States Nuclear Regulatory Commission United States Public Health Service

The NCRP has found its relationships with these organizations to be extremely valuable t o continued progress in its program. Another aspect of the cooperative efforts of the NCRP relates to the special liaison relationships established with various governmental organizations that have an interest in radiation protection and meas-

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urements. This liaison relationship provides: (1) an opportunity for participating organizations to designate an individual to provide liaison between the organization and the NCRP; (2) that the individual designated will receive copies of draft NCRP reports (at the time that these are submitted to the members of the Council) with an invitation to comment, but not vote; and (3) that new NCRP efforts might be discussed with liaison individuals as appropriate, so that they might have an opportunity to make suggestions on new studies and related matters. The following organizations participate in the special liaison program: Defense Nuclear Agency Federal Emergency Management Agency National Bureau of Standards Office of Science and Technology Policy Office of Technology Assessment United States Air Force United States Army United States Coast Guard United States Department of Energy United States Department of Health and Human Services United States Department of Labor United States Department of Transportation United States Environmental Protection Agency United States Navy United States Nuclear Regulatory Commission

The NCRP values highly the participation of these organizations in the liaison program. The Council's activities are made possible by the voluntary contribution of time and effort by its members and participants and the generous support of the following organizations: Alfred P. Sloan Foundation Alliance of American Insurers American Academy of Dental Radiology American Academy of Dermatology American Association of Physicists in Medicine American College of Radiology American college of Radiology Foundation American Dental Association American Industrial Hygiene Association American Insurance Association American Medical Association American Nuclear Society American Occupational Medical Association

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American Osteopathic College of Radiology American Podiatry Association American Public Health Association American Radium Society American Roentgen Ray Society American Society of Radiologic Technologists American Society of Therapeutic Radiologists American Veterinary Medical Association American Veterinary Radiology Society Association of University Radiologists Atomic Industrial Forum Battelle Memorial Institute Bureau of Radiological Health College of American Pathologists Commonwealth of Pennsylvania Defense Nuclear Agency Edison Electric Institute Edward Mallinckrodt, Jr. Foundation Electric Power Research Institute Federal Emergency Management Agency Florida Institute of Phosphate Research Genetics Society of America Health Physics Society James Picker Foundation National Association of Photographic Manufacturers National Bureau of Standards National Cancer Institute National Electrical Manufacturers Association Radiation Research Society Radiological Society of North America Society of Nuclear Medicine United States Department of Energy United States Department of Labor United States Environmental Protection Agency United States Navy United States Nuclear Regulatory Commission

To all these organizations the Council expresses its profound appreciation for their support. Initial funds for publication of NCRP reports were provided by a grant from the James Picker Foundation and for this the Council wishes to express its deep appreciation. The NCRP seeks to promulgate information and recommendations based on leading scientific judgment on matters of radiation protection and measurement and to foster cooperation among organizations concerned with these matters. These efforts are intended to serve the public interest and the Council welcomes comments and suggestions on its reports or activities from those interested in its work.

NCRP Publications NCRP publications are distributed by the NCRP Publications' office. Information on prices and how to order may be obtained by directing an inquiry to: NCRP Publications 7910 Woodmont Ave, Suite 1016 Bethesda, Md. 20814 The currently available publications are listed below.

Proceedings of the Annual Meeting No. 1 2

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Title Perceptions of Risk, Proceedings of the Fifteenth Annual Meeting, Held on March 14-15, 1979 (Including Taylor Lecture No. 3) (1980) Quantitative Risk in Standards Setting, Proceedings of the Sixteenth Annual Meeting Held on April 2-3, 1980 (Including Taylor Lecture No. 4) (1981) Critical Issues in Setting Radiation Dose Limits, Proceedings of the Seventeenth Annual Meeting, Held on April 8-9, 1981 (Including Taylor Lecture No. 5) (1982) Radiation Protection and New Medical Diagnostic Procedures, Proceedings of the Eighteenth Annual Meeting, Held on April 6-7, 1982 (Including Taylor Lecture No. 6) (1983) Environmental Radioactivity, Proceedings of the Nineteenth Annual Meeting, held on April 6-7, 1983 (Including Taylor Lecture No. 7) (1984)

Symposium Proceedings

The Control of Exposure of the Public to Ionizing Radiation in the Event of Accident or Attack, Proceedings of a Symposium held April 27-29, 1981 (1982) 291

NCRP PUBLICATIONS

Lauriston S. Taylor Lectures No. 1

Title and Author The Squares of the Natural Numbers in Radiation Protection by Herbert M . Parker (1977) Why be Quantitative About Radiation Risk Estimates? by Sir Edward Pochin (1978) Radiation Protection-Concepts and Trade Offsby Hymer L. Friedell (1979) [Available also in Perceptions of Risk, see above] From "Quantity of Radiation" and "Dose" to ''Exposure" and "Absorbed Dose"-An Historical Review by Harold 0.Wyckoff (1980) [Available also in Quantitative Risks in Standurds Setting, see above] How Well Can W e Assess Genetic Risk? Not Very by James F. Crow (1981) [Available also in Critical Issues in Setting Radiation Dose Limits, see above] Ethics, Trade-offs and Medical Radiation by Eugene L. Saenger (1982) [Available also in Radiation Protection and New Medical Diagnostic Approaches, see above.] The Human Environment-Past, Present and Future by Merril Eisenbud (1983) [Available also in Environmental Radioactivity, see above.]

NCRP Reports No. 8

Title Control and Removal of Radioactive Contamination in Laboratories (1951) Recommendations for Waste Disposal of Phosphorus-32 and Iodine-131 for Medical Users (1951) Recommendations for the Disposal of Carbon-14 Wastes (1953) Radioactive Waste Disposal in the Ocean (1954) Maximum Permissible Body Burdens and Maximum Permissible Concentrations of Radionuclides in Air and in Water for Occupational Exposure (1959) [Includes Addendum 1issued in August 19631 Measurement of Neutron Flux and Spectra for Physical and Biological Applications (1960) Measurement of Absorbed Dose of Neutrons and Mixtures of Neutrons and Gamma Rays (1961) Stopping Powers for Use with Cavity Chambers (1961)

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Safe Handling of Radioactive Materials (1964) Radiation Protection in Educational Institutions (1966) Medical X-Ray and Gamma-Ray Protection for Energies Up to 10 MeV-Equipment Design and Use (1968) Dental X-Ray Protection (1970) Radiation Protection in Veterinary Medicine (1970) Precautions in the Management of Patients W h o Have Received Therapeutic Amounts of Radionuclldes (1970) Protection against Neutron Radiation (1971) Basic Radiation Protection Criteria (1971) Protection Against Radiation from Brachytherapy Sources (1972)

Specification of Gamma-Ray Brachytherapy Sources (1974) Radiological Factors Affecting Decision-Making in a N u clear Attack (1974) Review of the Current State of Radiation Protection Philosophy (1975) Krypton-85 in the Atmosphere-Accumulation, Biological Significance, and Control Technology (1975) Natural Background Radiation in the United States (1975) Alpha-Emitting Particles in Lungs (1975) Tritium Measurement Techniques (1976) Radiation Protection for Medical and Allied Health Personnel (1976) Structural Shielding Design and Evaluation for Medical Use of X-Rays and Gamma-Rays of Energies U p to 10 MeV (1976) Environmental Radiation Measurements (1976) Radiation Protection Design Guidelines for 0.1-1 00 MeV Particle Accelerator Facilities (1977) Cesium-137 From the Environment to Man: Metabolism and Dose (1977) Review of NCRP Radiation Dose Limit for Embryo and Fetus in Occuptionally Exposed Women (1977) Medical Radiation Exposure of Pregnant and Potentially Pregnant Women (1977) Protection of the Thyroid Gland in the Event of Releases of Radioiodine (1977) Radiation Exposure From Consumer Products and Miscellaneous Sources (1977) Instrumentation and Monitoring Methods for Radiation Protection (1978) A Handbook of Radioactivity Measurements Procedures (1978)

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NCRP PUBLICATIONS

Operational Radiation Safety Program (1978) Physical, Chemical, and Biological Properties of Radiocerium Relevant to Radiation Protection Guidelines (1978) Radiation Safety Training Criteria for Industrial Radiography (1978) Tritium in the Environment (1979) Tritium and Other Radionuclide Labeled Organic Compounds Incorporated in Genetic Material (1979) Influence of Dose and Its Distribution in Time on DoseResponse Relationships for Low-LET Radiations (1980) Management of Persons Accidentally Contaminated with Radionuclides (1980) Mammography (1980) Radiofrequency Electromagnetic Fields-Properties, Quantities and Units, Biophysical Interaction, and Measurements (1981) Radiation Protection in Pedintric Radiology (1981) Dosimetry of X-Ray and Gamma-Ray Beams for Radiation Therapy in the Energy Range 10 keV to 50 MeV (1981) Nuclear Medicine-Factors Influencing the Choice and Use of Radionuclides i n Diagnosis and Therapy (1982) Operational Radiation Safety-Training (1983) Radiation Protection and Measurement for Low Voltage Neutron Generators (1983) Protection in Nuclear Medicine and Ultrasound Diagnostic Procedures in Children (1983) Biological Effects of Ultrasound: Mechanisms and Clinical Applications (1983) Iodine-129: Evaluation of Releases from Nuclear Power Generation (1983) Radiological Assessment: Predicting the Transport, Bioaccumulation, and Uptake by Man of Radio-nuclides Released to the Environment (1984) Exposures from the Uranium Series with Emphasis on Radon and its Daughters (1984) Evaluation of Occupational and Environmental Exposures to Radon and Radon Daughters in the United States (1984)

Binders for NCRP Reports are available. Two sizes make it possible to collect into small binders the "old series" of reports (NCRP Reports Nos. 8-31) and into large binders the more recent publications (NCRP Reports Nos. 32-71). Each binder will accommodate from five to seven reports. The binders carry the identification " N C W Reports" and

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come with label holders which permit the user to attach labels showing the reports contained in each binder. The following bound sets of NCRP Reports are also available: Volume I. NCRP Reports Nos. 8, 9, 12, 16, 22 Volume 11. NCRP Reports Nos. 23, 25, 27, 30 Volume 111. NCRP Reports Nos. 32, 33, 35, 36, 37 Volume IV. NCRP Reports Nos. 38,39,40,41 Volume V. NCRP Reports Nos. 42,43,44,45, 46 Volume VI. NCRP Reports Nos. 47,48,49,50,51 Volume VII. NCRP Reports Nos. 52, 53, 54, 55, 56, 57 Volume VIII. NCRP Report No. 58 Volume IX. NCRP Reports Nos. 59, 60,61,62,63 Volume X, NCRP Reports Nos. 64,65,66, 67 (Titles of the individual reports contained in each volume are given above). The following NCRP Reports are now superseded and/or out of print: No. 1

Title X-Ray Protection (1931). [Superseded by NCRP Report No. 31 Radium Protection (1934). [Superseded by NCRP Report No. 41 X-Ray Protection (1936). [Superseded by NCRP Report No. 61 Radium Protection (1938). [Superseded by NCRP Report No. 131 Safe Handling of Radioactive Luminous Compounds (1941). [Out of Print] Medical X-Ray Protection U p to Two Million Volts (1949). [Superseded by NCRP Report No. 181 Safe Handling of Radioactive Isotopes (1949). [Superseded by NCRP Report No. 301 Radiological Monitoring Methods and Instruments (1952). [Superseded by NCRP Report No. 571 Maximum Permissible Amounts of Radioisotopes in the Human Body and Maximum Permissible Concentrations i n Air and Water (1953). [Superseded by NCRP Report No. 221

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Protection Against Radiations from Radium, Cobalt-60 and Cesium-137 (1954). [Superseded by NCRP Report No. 241 Protection Against Betatron-Synchrotron Radiations U p to 100 Million Electron Volts (1954). [Superseded by NCRP Report No. 511 Safe Handling of Cadavers Containing Radioactive Isotopes (1953). [Superseded by NCRP Report No. 211 Permissible Dose from External Sources of Ionizing Radiation (1954) including Maximum Permissible Exposure to Man, Addendum to National Bureau of Standards Handbook 59 (1958). [Superseded by NCRP Report No. 391 X-Ray Protection (1955). [Superseded by NCRP Report No. 26 Regulation of Radiation Exposure by Legislative Means (1955). [Out of print] Protection Against Neutron Radiation U p to 30 Million Electron Volts (1957). [Superseded by NCRP Report No. 381 Safe Handling of Bodies Containing Radioactive Isotopes (1958). [Superseded by NCRP Report No. 371 Protection Against Radiations from Sealed Gamma Sources (1960). [Superseded by NCRP Report Nos. 33, 34, and 401 Medical X-Ray Protection Up to Three Million Volts (1961). [Superseded by NCRP Report Nos. 33, 34, 35, and 361 A Manual of Radioactivity Procedures (1961). [Superseded by NCRP Report No. 581 Exposure to Radiation in an Emergency (1962). [Superseded by NCRP Report No. 421 Shielding for High Energy Ebctron Accelerator Installations (1964). [Superseded by NCRP Report No. 5111 Medical X-Ray and Gamma-Ray Protection for Energies Up to 10 MeV-Structural Shielding Design and Eualuation (1970). [Superseded by NCRP Report No. 491

Other Documents The following documents of the NCRP were published outside of the NCRP Reports series: "Blood Counts, Statement of the National Committee on Radiation Protection," Radiology 63, 428 (1954)

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"Statements on Maximum Permissible Dose from Television Receivers and Maximum Permissible Dose to the Skin of the Whole Body," Am. J. Roentgenol., Radium Ther. and Nucl. Med. 84, 152 (1960) and Radiology 75, 122 (1960) X-Ray Protection Standards for Home Television Receivers, Interim Statement of the National Council on Radiation Protection and Measurements (National Council on Radiation Protection and Measurements, Washington, 1968) Specification of Units of Natural Uranium and Natural Thorium (National Council on Radiation Protection and Measurements, Washington, 1973) NCRP Statement on Dose Limit for Neutrons (National Council on Radiation Protection and Measurements, Washington, 1980) Krypton-85 in the Atmosphere- With Specific Reference to the Public Health Significance of the Proposed Controlled Release at Three Mile Island (National Council on Radiation Protection and Measurements, Washington, 1980) Preliminary Evaluation of Criteria For the Disposal of Tmnsuranic Contaminated Waste (National Council on Radiation Protection and Measurements, Bethesda, Md, 1982)

Copies of the statements published in journals may be consulted in libraries. A limited number of copies of the remaining documents listed above are available for distribution by NCRP Publications.

Index Adsorption/desorption properties of sedi- Data sets, terrestrial, 67 ments, 99, 101,106, 112, 115, 117 concentration ratios, 73, 75, 81, 85, 89, Adsorption/retardation properties of soils, 95 182 transfer coefficients, 78,81, 85,89, 95 Advection, 99, 103, 113 Data sets, usage factors, 199 Advective-diffusion, 101, 102, 103, 108, aquatic, 204 112 external exposure, 217 with decay and source/sink terms, 102 generic, 199 without decay and source/sink terms, inhalation, 208 103 terrestrial, 200 Applications of models, 233 water consumption, 208 environmental, assessment, 233 Deposition from atmospheric, 43 research, 234 dry, 43 screening, 235 reactive gases, 46 Aquatic pathways, 204 wet, 49 bioaccumulation factors, 136 velocity of. 49 usage factors, 204 Diffusion models, atmospheric, 5 uncertainties in, 230 basic parameters for, 21 UAslow as reasonably achievable" higher closure theory, 9 (ALARA), 99 k-theory, 8 Atmospheric transport models, 5 lumped parameters for, 32 wet, 39, 49 velocity, 18 Bioaccumulation factors, aquatic, 96,136 Distribution coefficients (Kd), 96,115,121, factors influencing variability, 148 182 uncertainties associated with, 153,230 validation, 153 External exposure. usage factors, 217 Bioaccumulation, terrestrial, 57 Food consumption rates, see Usage factors

Concentration ratios, terrestrial, 73 Consumption rates, see Usage factors Data sets, atmospheric, 34 Data sets, groundwater, 177 dispersion, 177 182 distribution coefficient (L), hydraulic conductivity, 180 porosity, 178, 180 Data sets, surface waters, 125 bioaccumulation factors, 136 distribution coefficients (Kd), 118, 126, 128, 132,134 298

Gaussian plume models, 6 properties of, 22 Global models, 17 Grid models. 17 Groundwater assessments, need for, 158 geological isolation of high level waste (HLW), 158 nuclear power plant accidents, 160 shallow land burial, 159 uranium milling and mining, 160 Groundwater flow and radionuclide transport, 166

INDEX Groundwater flow (Continued) groundwater flow, 166 mass transport, 170 decay of radionuclides, 172 Groundwater models, 157 data sets, 177 uncertainties in, 231 percolation, 173 Hydraulic, conductivity, 180 properties of lakes and estuaries, 115 Imprecision analyses, parameters, 221 Improvement of models, 235 Inhalation pathway, usage factors, 208

Kd, (distribution coefficient), 96,125,182 Models, atmospheric transport, 10 box, 19 data sets, 34 deposition and resuspension, 43 diffusion, 5 eddy diffusivity in, 8 effective source height for, 36 friction velocity in, 46 Gaussian plume and puff, 10 global, 19 grid, 17 Monin-Obukhor stability length, 33 parameters for, 20 particle in cell, 18 Pasquill-Gifford (PG) curves, 32 physical, 20 plume reflection, 13 precipitation scavenging, 39 pseudo-spectral, 18 Richardson's number, 33 types of, 10-20 uncertainties in, 227 variability of concentration estimates in, 39 validation of, 39 Models, groundwater, 161 data sets, 177 decay of radionuclides, 172 groundwater flow, 166 high level waste, 162 low level waste, 161 mass transport, 170 mill tailing waste, 166

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299

Models, groundwater (Continued) misuse of, 196 parameters for, 173 percolation, 173 uncertainties in, 231 validation of, 188 Models, screening, 239 Models, simplification of, 239 Models, surface waters, 98 advection, 113 advection-diffusion with decay and source/sink terms, 102 advection-diffusion without decay and source/sink terms, 103 advective diffusion, 101,108 CHNSED, sediment transport, 114 complete mixing, 105 contaminant transport, 98 data sets, 125 diffusion-dispersion, 112 diffusion with or without decay and source/sink terms, 108 EXAMS, contaminant transport, 98 FETRA, sediment transport, 114 FLESCOT, three-dimensional, 99,114, 117 geochemical, 98 liquid pathway, 103 Lagrangian routing with decay and source/sink terms, 15 MINTEQ,geochemical, 98 Monte Carlo, 108 one-dimensional estuary, 103 particle scavenging, 108 plug flow, 105 SERATRA, sediment transport, 114, 117 sediment transport, 98 three dimensional, 99 time concentration, 100,105 transport and fate, 98 transformation, 100 TODAM, sediment transport, 114 uncertainties in, 230 validation of, 124 verification of, 121 water quality, 98 well mixed compartment, 106 Models, terrestrial, 57 air-vegetation. 57 data sets, 67

300

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INDEX

Models, terrestrial (Continued) direct deposition, 59 harvest loss, 63 simple equilibrium, 59 soil-vegetation, 59, 62 steady-state, 59 TERMOD, pathway, 58 transient, 57 two-compartment, 64 uncertainties in, 228 vegetation-animal, 66 weathering half-life, 61 XOQDOQ, deposition/retention, 60 year-2000, radiation dose, 59 Model uncertainties, 219 among model types, 225 bias, 219 determination of, 220 sources of, 220 Models, validation of, 238 Pathways, 5-56, 57, 136 aquatic, 136 atmospheric, 5 dietary, 57-95 groundwater, 157 imprecision analyses, 221 surface waters, 96 to animal products, 66 to vegetation, 57 uncertainty analysis, 225 Radionuclides, special cases, 87 carbon-l4,92 tritium, 88 Reactive gases, 46 wet removal of, 51 Resuspension, 52 mass loading, 52 factor, 53 rate of. 56 Scavenging, atmospheric, 39 rate coefficient for, 50 Sediments, 96 adsorptionldesorption properties, 106, 115,117 data sets, 118, 126,128,132,134 CHNSED model, 114 deposition and resuspension, 115 FETRA model, 114 FLESCOT model, 114, 117

Sediments (Continued) particle cohesiveness, 113 particle size, 113 precipitation/dissolution values, 117 resuspension and transport, 113, 119 SERATA model, 114, 117 suspended, 119 TODAM model, 114 transport, 103 water interface, 98 Specific activity approach, 87 uncertainties in, 229 Surface water models, 96 Terrestrial pathways, 57 models, 57-96 transfer coefficients, 78 usage factors, 200 uncertainties in, 228 Transfer coefficients, terrestrial, 78 Uncertainties in models and parameters, 153, 219

aquatic food chains, 230 atmospheric transport, 227 bioaccumulation factors, 153 groundwater transport, 231 human factors, 231 specific activity approach, 229 surface water transport, 230 terrestrial food chains, 228 Usage factors, 198 aquatic, 204 external exposure, 217 generic, 199 inhalation, 208 terrestrial, 200 water and other beverages, 208 Validation of atmospheric transport models, 39 Validation of models. 124, 220 Variability, factors influencing parameters, 74, 148, 202 bioaccumulation factors, 148 concentration ratios, 74 transfer coefficients, 78 usage factors, 202 Variability of atmospheric concentration estimates, 39 Verification of surface water models, 121 Water quality models, 98