Concentration Fluctuations and Averaging Time

in Vapor Clouds

DAVID J. WILSON Department of Mechanical Engineering

University of Alberta Edmonton, Alberta, Canada T6G 2G8

CENTER FOR CHEMICAL PROCESS SAFETY of the

American Institute of Chemical Engineers 345 East 47th Street 0 New York, NY 10017

dcd-wgC1.jpg

This Page Intentionally Left Blank

Concentration Fluctuations and Averaging Time

in Vapor Clouds

Selected Publications Available from the Center for Chemical Process Safety

American Institute of Chemlcal Engineers of the

Guidelines for Technical Management of Chemical Process Safety Plant Guidelines for Technical Management of Chemical Process Safety Guidelines for Implementing Process Safety Management Systems Guidelines for Auditing Process Safety Management Systems Guidelines for Investigating Chemical Process Incidents Guidelines for Chemical Process Documentation Guidelines for Hazard Evaluation Procedures, 2nd Edition with Worked Examples Guidelines for Chemical Process Quantitative Risk Analysis Guidelines for Process Equipment Reliability Data with Data Tables Guidelines for Chemical Transport Risk Analysis Tools for Making Acute Risk Decisions Guidelines for Use of Vapor Cloud Dispersion Models Workbook of Test Cases for Vapor Cloud Source Dispersion Models Guidelines for Evaluating the Characteristics of Vapor Cloud Explosions, Flash Fires,

Guidelines for Engineering Design for Process Safety Guidelines for Safe Automation of Chemical Processes Guidelines for Vapor Release Mitigation Guidelines for Storage and Handling of High Toxic Hazard Materials Guidelines for Storage and Handling of Reactive Materials Guidelines for Preventing Human Error in Process Safety Guidelines for Process Safety Fundamentals for General Plant Operations Guidelines for Safe Operations and Maintenance Proceedings of the International Conference and Workshop on Modeling and

and BLEVEs

Mitigating the Consequences of Accidental Releases of Hazardous Materials, 1995

1994 Proceedings of the International Symposium on Safe Chemical Process Automation,

Proceedings of the International Process Safety Management Conference, 1993 Proceedings of the International Symposium on Hazard Identification and Risk

Analysis, Human Factors and Human Reliability in Process Safety, 1992 Proceedings of the International Symposium on Runaway Reactions, 1989 Proceedings on the International Conference on Vapor Cloud Modeling, 1987 Proceedings of the International Symposium on Preventing Major Chemical

Accidents, 1987

Concentration Fluctuations and Averaging Time

in Vapor Clouds

DAVID J. WILSON Department of Mechanical Engineering

University of Alberta Edmonton, Alberta, Canada T6G 2G8

CENTER FOR CHEMICAL PROCESS SAFETY of the

American Institute of Chemical Engineers 345 East 47th Street 0 New York, NY 10017

0 Copyright 1995 American Institute of Chemical Engineers 345 East 47th Street New York, New York 10017

All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior permission of the copyright owner.

For more information, a free catalog, or to place an order, call 1-800-242-4363, fax 212-705-8400, or write to AIChExpress Service Center American Institute of Chemical Engineers, 345 East 47th Street, New York, NY 10017.

ISBN 0-81 69-0679-3

PRINTED IN THE UNITED STATES OF AMERICA

DISCLAIMER: It is sincerely hoped that the information presented in this document will lead to an even more impressive safety record for the entire industry; however, the American Institute of Chemical Engineers, its consultants, CCPS subcommittee members, their employers, theiremployers' officers and directors, and the author, David J. Wilson disclaim making or giving any warranties or representations, express or implied, including with respect to fitness, intended purpose, use or merchantability andlor correctness or accuracy of the content of the information presented in this document. As between ( I ) the American Institute of Chemical Engineers, its consultants, CCPS subcommittee members, theiremployers, theiremployers' officers and directors, and the author, David J. Wilson and (2) the user of this document, the user accepts any legal liability or responsibility whatsoever for the consequence of its use or misuse.

PREFACE ix

ACKNOWLEDGMENTS xvii

1. Background and Objectives 1

2. Sampling and Averaging Time Definitions

Calculating Mass-Weighted Sampling Time Effective Sampling Time &,a for Block Time Averages

5 8

12

3. Effect of Averaging Time on Mean Calculations 15

Ensemble Averaging and Zero Sample Time Meandering 17 Field Data for Sampling and Averaging Time Effects 19 Plume Spread Sampling Time Effects Deduced from Velocity Fluctuation Statistics 20 Measurement of Crosswind-Velocity Sampling Time Exponent pv 23 Averaging Time Effects on Plume Spread oy 24 Random Force Model for Sampling Time Effects on Crosswind Spread 28 Comparing the Random Force Model to CONDORS Data 30 Comparing the Random Force Model with o, - rF2 31

4. Concentration Fluctuation Modeling 37

Overview 37 Types of Concentration Fluctuation Models 38 Conditional Statistics for Fluctuation Calculations 39 Wind Tunnel Simulation versus Field Testing for Model Validation 42

V

vi

5.

6.

7.

8.

9.

10.

Probability Distributions

Exponential Probability Distribution Clipped-Normal Probability Distribution Log-Normal Probability Distribution Gamma Probability Distribution Recommended Probability Distribution and Conditional Intensity Functions

Release Height and Source Size Effects on Fluctuation Intensity

Internal Fluctuations in Jets and Plumes with No Meandering Fluctuation Intensity in Meandering Plumes from Ground Level Releases Meandering Plume Models for Source Size Effects on Elevated Releases Comparison with Chatwin and Sullivan’s Similarity Model Release Momentum Effects on Source Size Fluctuations Near the Ground: Dissipation by Wind Shear Terrain Roughness, Atmospheric Stability, and Compatibility

with Existing Hazard Assessment Models

Source Density Effects on Fluctuations

Dense Plumes Buoyant Plumes

Buildings and Obstacles

Modeling Concentration Fluctuations in Building Wakes

Threshold Crossing and Peak Levels

Time Sequence versus Ensemble Repeat Averages

Framework for an Operational Model

Adjusting Mean Concentration for Averaging Time Concentration Fluctuation Statistics

Concentration Fluctuation Intensity Fraction of Time Threshold Concentration Is Exceeded Once-per-Event Peak Concentration

Summary

Contents

45

45 45 47 48 48

53

55 56 62 68 70 71

73

75

75 80

83

88

89

89

98 99 99

101 103 104

Concentration Fluctuations and Averaging Time in Vapor Clouds vii

Appendix A Averaging and Sampling Time Effects on Plume Spread Velocity and Concentration Fluctuations

Inertialess Fluctuation Spxtrum Concentration Fluctuations

Effect of Averaging Time on Concentration Variance Power Law Exponent qc for Averaging Time Effect of Sampling Time on Concentration Variance Power Law Exponent pc for Increased Sampling Time

Sampling Time Effects on Crosswind Velocity Variance Sampling Time Effects for the Transverse Isotropic Spectrum

Velocity Fluctuations

Averaging Time Effects for Finite Sampling Time Gifford’s Random Force Model for 0, Wilson’s Power Law Approximation to Gifford’s Random Force Model Relative “Instantaneous” Spread vs. Fixed Axis Zero Sample Time Spread General Power-Law Plume Spread Equation

Appendix B Peak Values and Threshold Crossing Probability

Hazard Probability of Exceeding a Threshold for a Random Starting Time

Probability of G,(t) of First Crossing Threshold c* Hazard Rate h, for a Steady Release Rate Quasi-Steady Approximation for Time-Varying Release Peak-to-Mean Concentrations Rice’s Theory for Threshold Upcrossing Rate N+ Threshold Crossing N‘ Using In-Plume Statistics Exponential pdf for Derivatives Markov Spectrum for Derivatives Von Karman Spectrum for Derivatives Cutoff Frequency for Concentration Derivative Spectrum Estimating In-Plume Derivative for Threshold Crossing Rate Dependence of Peak Concentration on Averaging and Sampling Times Summary of Working Equations for Threshold Crossing

in an Established Steady Release

Appendix C Eulerian and Lagrangian Turbulence Scales Crosswind Velocity Time Scale Vertical Velocity Time Scale Recommendation

107

107 108 108 109 110 111 112 112 114 117

120 123 126 126

129

129 131 133 134 135 136 138 140 143 144 145 147 148 150

153

153 154 155

viii

REFERENCES

NOMENCLATURE

INDEX

Contents

157

169

177

Including concentration fluctuations in hazard assessment models provides a rational way of dealing with the high variability associated with atmospheric dispersion, where the mean concentration can vary by a factor of two or more over an ensemble of identical releases.

Engineers are usually very uncomfortable with natural processes that have a high degree of variability. Hanna (1993) discussing uncertainties in air quality model predictions noted that factors of f50% root mean square uncertainty in mean concentration are not unusual, and that "this fundamental level of model uncertainty is likely to exist due to data input errors and stochastic fluctuations no matter how sophisticated a model becomes." The peak concentration observed during any one release event can vary by a factor of 10 among the members of an ensemble of identical releases into the same atmospheric conditions, see Hanna, Chang and Shimaitis (1993), and Hanna and Chang (1993) for some specific examples.

The objectives of this review are:

To develop clear, unambiguous definitions of statistical terms such as "plume sampling time", "concentration averaging time", "receptor exposure time", "peak concentration during an event" and other fluctuation-related variables that are often confused with each other, or incorrectly specified in hazard assessments. To identify areas where further information is required to define concentration variability statistics. To formulate an operational model for predicting concentration fluctuations based on the current state of knowledge of dispersion processes, and to identify the components that are derived from a strong theoretical or experimental basis, and those for which more arbitrary assumptions are required.

ix

X Preface

. To identify and quantify the situations for which there is adequate knowledge to predict concentration fluctuations in the near-field, close to sources, and far downwind where dispersion is dominated by atmospheric turbulence.

The current state of knowledge is discussed and quantified for the following topics related to concentration fluctuations in vapor clouds.

Averaging Time

With increased averaging time (i.e. increased event duration for an accidental release) the plume from a point source meanders back and forth over a fixed receptor. As the high concentration in an instantaneous "snapshot" plume flaps back and forth, the time-averaged concentration will decrease on the plume centerline, and increase in the outer fringes of the plume. At the same time, meandering will increase the intensity of concentration fluctuations everywhere across the plume, and produce longer periods of zero concentration intermittency near the plume centerline. To estimate the probability of exceeding toxic or flammable concentration thresholds these averaging time effects must be accurately predicted.

Results: A new theoretically-based model is proposed for the effect of averaging time. Time averaging effects are accounted for by increasing the crosswind plume spread (with atmospheric sampling time equal to averaging time), and using this increased crosswind spread to calculate the reduced centerline mean concentration. This model properly accounts for the effects of source size and plume travel time on averaging time. In effect, the travel time correction takes into account that if a plume has travelled for only 1.0 minute from source to receptor, an additional 10 minutes of sampling time at the receptor will significantly increase the timeexposure averaged plume width. In contrast, for a plume that has travelled for 100 minutes from source to receptor, an additional 10 minutes of sampling time will have much less effect on plume spread. The widely-accepted 0.2 power law for averaging time fails to account for this and should be replaced.

Unresolved Issues: There is little experimental data available to validate the model. Also, the new averaging time model requires a user-specified time scale of velocity fluctuations following a puff downwind (the Lagrangian timescale TLv). Estimates of this time scale range from 1000 to 15,000 seconds, with some of the variability caused by variation in the sampling time over which TLv is calculated from measurements. Further review is required before specific values can be recommended with confidence.

Concentration Fluctuations and Averaging Time in Vapor Clouds xi

Probability Distributions

Operational models are limited to predicting the mean and standard deviation of concentration for fluctuating plumes. The probability of ignition, or of receiving a dangerous toxic load must be estimated from assumed probability distributions for concentration fluctuations. Several pdf candidates, such as exponential, log-normal and clipped-normal distributions have been proposed, and produce significantly different results for the probability of exceeding a user-defined hazard threshold level. These pdf functions are reviewed to find a compromise between accuracy and ease of calculating the frequency distribution of time-varying concentrations.

Results: The log-normal probability distribution is recommended for estimating concentration extreme values for fraction of events over a threshold. This distribution function is not only the most convenient from a computational standpoint for calculating the non-linear toxic load L = c"t, where a = 1.5 to 4.0 but is also one ,of the best at predicting peak values. The use of a log-normal distribution requires a user-specified input for the intermittency factor (i.e. fraction of non-zero readings that will occur in a sample.) A simple empirical model for intermittency that can be used with the log-normal pdf is recommended.

Unresolved Issues: The log-normal pdf does not do as well at predicting low concentrations, that are less than 20% of the conditional mean Cp. Experimental data suggests that the shape of the pdf evolves with travel time, and using a single function such as the log-normal is only an approximation.

Intermittency

All real plumes produce significant periods of near zero concentration interspersed with non-zero fluctuating concentration. For hazard assessments of toxic and flammable releases it is essential to predict the fraction of time that zero concentrations will occur.

Results: A simple empirical equation is recommended for estimating the fraction of non-zero concentrations that will occur in the sample. This empirical equation directly relates the total fluctuation intensity i including zero readings to the in-plume conditional intensity $, of non-zero concentrations. Knowing these two intensities exactly determines the zero concentration intermittency. The recommended equation is compared with both wind tunnel and field-trial data to demonstrate its accuracy.

Preface xii

Unresolved Issues: Measured intermittency factors are quite sensitive to the noise threshold below which the concentration is taken to be zero. The empirical model relies on measurements, and so has some instrument response built in. This is equivalent to spatially averaging the concentration over a sample volume with diameter of order 1 to 10 m.

Threshold Crossing Probability

The few operational models that predict concentration fluctuations have a pollution control orientation, with the key variable being the fraction of concentrations that exceed a specified threshold for an infinitely long steady release. In industrial hazard assessment a more relevant variable is the probability of surviving an event of fmed duration without crossing a toxic or flammable threshold limit. Models for this survival probability are reviewed and new quantitative methods are recommended for estimating this probability.

Estimating the probability of surviving an event without having crossed a specified flammability, toxicity or regulatory threshold requires complicated statistical analysis because concentration fluctuations are timecorrelated. This requires a knowledge of how events in the past are correlated with the current level of concentration in order to predict the probability of the concentration crossing the threshold level in the next instant.

Results: A new practical model for estimating survival probability and peak values during an event is derived. A simplified version of this model is suggested for predicting the effect of averaging time on once-per-event peak concentrations. The model is compared to experimental data, and shows a high level of skill in predicting the ratio of peak values that would occur at two different averaging times.

Unresolved Issues: The theory (developed in Appendix B) for predicting the probability of surviving an event without crossing a specified threshold has not been tested on multiple repeats of an identical release event. This is an ideal candidate for testing using wind tunnel or water channel data with large numbers of repeats to determine if the probability of surviving an event without crossing a threshold (such as flammability) can be accurately estimated.

Source Size

The ratio of instantaneous plume spread to meandering spread is critically dependent on the relative size of the source to the scale of the eddies that dominate the dispersion process. This plume meandering influences concentration fluctuation intensity and averaging time corrections for both mean concentration.

Concentration Fluctuations and Averaging Time in Vapor Clouds xiii

Results: A modified meandering plume model is proposed for calculating the effect of turbulence scale (release height) and source diameter on centerline fluctuation intensity in a plume. The recommended constants in the model are set by comparison with a set of wind tunnel experiments on varying source sizes. This meandering plume model accurately predicts fluctuation intensities over a wide range of downwind distances and source sizes.

Unresolved Issues: Source size corrections apply only to release from an isokinetic coflowing source (a jet with the same velocity as the local wind speed). This is not a realistic representation of a real source from a vessel rupture or an evaporating pool. (see section on Jet Momentum). Wind tunnel or water channel simulation of real sources is needed to test the correction function that accounts for momentum and buoyancy on effective source size.

Source Density

A buoyant source rises to produce a plume that has a larger effective source size due to self-induced entrainment. A dense plume sinks to the ground, spreads laterally, and suppresses both vertical mixing and horizontal plume meandering. The available information on concentration fluctuations in dense and buoyant plumes is reviewed.

Results: Experimental data shows that the internal (non-meandering) fluctuations in a dense plume have the same magnitude and vertical mean concentration and fluctuation intensity profile shapes as a passive plume. It is recommended that fluctuation intensities from a wide (line) dense source can be estimated using the same equations as a passive source. The available data on concentration fluctuations in buoyant plumes suggests that buoyancy increases intermittency close to the source.

Unresolved Issues: Dense plumes meander from side to side because they entrain ambient air with crosswind velocity fluctuations. The crosswind concentration profile in a dense plume is much flatter than the profile across a passive plume, and this may lead to smaller meander-induced concentration fluctuations on the plume centerline, and larger fluctuations at the edges when a dense plume meanders. There is no model available for meandering of non- Gaussian plume profiles, and one should be developed.

Jet Momentum

A release begins to meander only after it has entrained enough air to be moving downwind at a velocity close to the local wind speed. Momentum jets

xiv Preface

cause rapid entrainment of ambient a3 near the source and produce a large effective source size that reduces meandering effects. Models capable of accounting for jet momentum are reviewed and corrections for momentum effects proposed.

Results: Based on physical arguments simple operational equations are recommended for the effective source size that will influence a meandering plume. These recommendations use the momentum in a horizontal jet, or the rise of a buoyant jet to increase the size of the source so that meandering begins after the jet or plume has slowed down and entrained some ambient air.

Unresolved Issues: There is no information as to whether this method works, except an appeal to common sense. Wind tunnel or water channel simulation with varying jet momentum and direction (eg. upwind, vertical, downwind) are needed to refine this model. Large effective source sizes reduce peak concentrations by reducing plume meandering. Effective source size is an important topic to optimize the design of pressure relief systems to minimize hazard zones.

Terrain Roughness and Atmospheric Stability

These factors change the instantaneous plume dispersion and so alter the effect of plume meandering. Methods of accounting for generalized distributed terrain roughness are reviewed.

Results: No direct corrections for roughness or atmospheric stability are required. Field measurements and wind tunnel data both indicate that terrain roughness and atmospheric stability affect only concentration fluctuations above the roughness elements through their influence on vertical and crosswind plume spread. Mean concentration dispersion models that account for the effect of terrain roughness on plume spread automatically produce the correct effect on concentration fluctuations. With this in mind, all operational fluctuation models recommended are expressed in terms of plume spread rather than downwind distance.

Unresolved Issues: Concentration fluctuations within an array of roughness elements close to the surface, or inside an industrial plant facility, are probably strongly affected by the distribution and size of these roughness elements relative to the size of the plume. There is no information available on fluctuations within the roughness elements. This in-roughness dispersion is a situation of great practical importance, and some wind tunnel or water channel simulations should be carried out to quantify this case. Enhanced mixing within the roughness may reduce concentration fluctuation hazards, by decreasing peak' values.

Concentration Fluctuations and Averaging Time in Vapor Clouds xv

Buildings and Obstacles

Obstacles upwind from the source strongly affect mixing and dilution close to a source. Upwind obstacles increase plume spread, decreasing mean concentration. The intensity of fluctuations (ratio of standard deviation to mean) is increased in the near wake of a building, and decreased far downwind. Obstacles downwind from the source also increase mixing and dilution if they are smaller than the plume width and height. In contrast, downwind obstacles that are larger than the plume can increase concentrations by restricting plume growth in regions of converging streamlines, trapping plumes in vortices and channeling flow through the gaps between obstacles. Little is known about concentration fluctuations in these flow channeling conditions.

Results: Available information suggests that ground-level sources near buildings are strongly affected by the presence of the building for about five building heights. Neglecting the effect of nearby buildings is likely to overestimate the mean concentration, and underestimate the intensity of fluctuations. The behaviour of wind tunnel measurements is consistent with the no-building plume adjusted for the changing turbulent scale in the near-wake of the building. In the absence of further data, the no-building case should produce a reasonable estimate of peak values, but may underestimate the area over which they occur.

Unresolved Issues: Specifk methods need to be developed to adjust turbulence scale so that the meandering plume model can be applied to near-wakes behind buildings. Some further laboratory simulations may be required to provide the necessary data base for these adjustments.

Vertical Wind Shear

The strong variation of wind speed with height above ground causes dispersing puffs to be stretched and diffused as the top of a puff moves faster than the material close to the ground. In addition to reducing the mean concentration by along-wind dispersion, at the head and tail of a transient short-duration release, along-wind stretching also reduces concentration fluctuations in plumes close to ground level.

Results: The recommended operational model accounts for wind-shear effects on fluctuations using an along-wind shear distortion parameter with an empirical constant. With this shear-induced dissipation the meandering plume model fits wind tunnel data well.

xvi Preface

Unresolved Issues: Concentration fluctuation levels decrease dramatically close to the ground, and fluctuate with a longer time scale (at slower frequencies). If receptors such as ignition sources are located very close to the ground the recommended fluctuation model probably overestimates the fluctuation intensity and may greatly overestimate the probability of exceeding a specified threshold. Some high-resolution experimental measurements close to the surface should be made in a wind tunnel or water channel simulation to determine what credit can be given for reduced risk from receptors located very close to ground level.

Compatibility with Mean Concentration Models

An operational model for concentration fluctuations should be compatible with models used to calculate mean concentrations. The way in which various concentration fluctuation models deal with mean concentration, and the degree of compatibility with dispersion models for mean concentration, is discussed.

Resulfs: AU the models recommended in this review are expressed in terms of plume spread rather than downwind distance. This allows them to be used as add-ons to existing mean concentration models that produce plume spread as one of their outputs. All the parameters needed for calculating fractions of concentrations over a threshold, peak values, and probability of surviving an event without crossing a threshold are completely specified by self-contained equations that need only the mean concentration, plume spread, and plume rise from standard hazard assessment models.

Unresolved Issues: The recommended concentration fluctuation model assumes Gaussian profiles in both the vertical and crosswind directions. Some mean concentration models use non-Gaussian vertical profiles, and modification of the meandering plume fluctuation model may be needed to accommodate these differences.

Acknowledgments

The author gratefully acknowledges numerous contributions by the CCPS Vapor Cloud Subcommittee to the structure and organization of this report. The subcommittee members are: Ronald Lantzy, Chair @ohm and Haas), Gib Jersey, Vice-Chair (Mobil Research & Development), Donald Connolley (AKZO Nobel Chemicals), Gene Lee (Air Products & Chemicals), William Hague (Allied Signal), Doug Blewitt (Amoco), David Fontaine (Chevron Research and Technology), David Winegardner (Dow chemical), Seshu Dharmavaram (E.I. DuPont), David Guinnup (US EPA), Ebrahim Esmaili (Exxon Research and Engineering), Malcolm Preston (ICI Engineering), Sanford Bloom (Martin Marietta Energy Systems), Jerry Schroy (Monsanto Chemical), George DeVaull (Shell Oil), David McCready (Union Carbide).

Steven Hanna (Sigma Research) and Rex Britter (Cambridge University) made many technical suggestions during the project, and provided a critical review of a fnst draft of the manuscript. Several other reviewers made useful comments that contributed to the final version.

Bob G. Perry, director, and William J. Minges, staff, CCPS, provided financial and logistical support for the project.

Gail Anderson typed the manuscript and the revisions to several drafts, and Trevor Hilderman prepared the index. Shuming Du made several helpful suggestions on mean return time in Appendix B.

The author’s research on concentration fluctuations has been supported by the Natural Sciences and Engineering Research Council of Canada. The material on threshold crossing probability is from research funded jointly by NSERC, Alberta Occupational Health and Safety and the Canadian Gas Processors Association to David J. Wilson, Mechanical Engineering, University of Alberta, Edmonton, Alberta, Canada T6G2G8.

xvii

This Page Intentionally Left Blank

Background and Objectives

Most plume dispersion models used in hazard assessments are based on environment protection models developed by regulatory agencies for predicting the long-term impact of pollution sources. These regulatory-based models focus on estimating hour to hour variations for typical annual distributions of meteorological variables. For example, R.B. Wilson’s (1993) review of the EPA models CRSTER and MPTER describes the direct simulation method for estimating concentration variability by running these regulatory models for each hour over a year. These models ignore short term concentration fluctuations, and use the hour-to-hour mean values as a measure of mean concentration variability. For intervals less than an hour, averaging time effects are ignored, and plume spread parameters typical of three to ten minute averaging times are used for the one hour averaging periods. In the terminology used in the present study, these regulatory models predict concentration fluctuation statistics for a total sampling time t, of one year, with sequential block averaging times t, of one hour. These direct simulation methods also account for hour-to-hour changes in mean wind direction, an important factor in reducing long term mean concentration at a fixed receptor.

The present study will focus on the variability of mean and fluctuating concentrations observed for sampling times ranging from a few seconds to a few hours. Most hazard assessment models require estimates of peak concentrations that occur over intervals of a few seconds during a time-varying release that itseIf may only last for minutes. Clearly, something must be done to modify hourly averages from regulatory models to estimate these brief peak concentrations. There are two approaches currently being used to estimate concentration peaks:

The dispersion equations that predict long-term ensemble-averaged mean concentrations are assumed to apply to short term peaks. The vertical and horizontal plume spreads by and 0, are adjusted empirically to match the equations to measured peak values from a few field experiments.

1