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DOE/TIC-11223 (DE 82002045) Handbook on ATMOSPHERIC DIFFUSION Steven R. Hanna Gary A. Briggs Rayford P. Hosker, Jr. Atmospheric Turbulence and Diffusion Laboratory National Oceanic and Atmospheric Administration . . Prepared for the Office of Healtli and Environmental Research Ofilce of Energy Research U. S. Department of Ener,q\ 1982 Jean S. Smith, Publication Editor Editing, composition, proofreading, book design, illustrations, and page makeup for this publication were performed by staff members of the Technical Information Center. This documait is Published by TECH N 1C A L IN F 0R M A TI 0 N CENTER U. S. DEPARTMENT OF ENERGY DISCLAIMER This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency Thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof. DISCLAIMER Portions of this document may be illegible in electronic image products. Images are produced from the best available original document. NOTICE International Cop>-right. 0 1:. S. Department of Energy. 1982, under the provision, of rlic lInn,vr\al Copyright Convenrion. United States copyright is nor ,i\xrted iindrr rhc llnircd Sratrs Copyright Law. 'I'irle 17, Unired- States Cock. Library of Congress Cataloging in Publication Data Hanna, Steven R. Handbook on atmospheric diffusion. Includes bibliographical references and index. "DOE/TIC-1 1223." 1. Atmospheric diffusion-Handbooks, manuals, etc. 2. Smoke plumes-Handbccks, manuals, etc. 3. Cooling towers-Climatic factors-Handbooks, manuals, etc. I. Briggs, Gary A. , II. Hosker, Rayford P. Ill. United States. Dept. of Energy. Office of Energy Research. IV. United States. Dept of Energy. Office of Health and Environmental Research. V. Title. QC8 80.4.044H 36 551.5'153 81 -1 51 49 ISBN 0-87079-127-3 AACR2 Available as DE82002045 (DOE/TIC-11223) for $10.75 from National Technical Information Service U. S. Department of Commerce Springfield, Virginia 22161 DOE Distribution Category UC-11 Printed in the United States of America 1982 With the Clean Air Acts and increased environmental Basic meteorological concepts are covered first consciousness, many engineers, consulting companies, and then plume rise, source effects, and diffusion planners, and meteorologists find themselves pro- models. Chapters on cooling tower plumes and urban pelled into the work of calculating atmospheric diffusion are included. Suggestions are made for diffusion. Many of these people are not interested in calculating diffusion in special situations, such as for knowing the detailed theoretical derivation of a instantaneous releases (puffs), over complex terrain, formula and its complete set of references. All they over long distances (10 km to global scales), and want to know are the best current formulas for their during times when chemical reactions or dry or wet problems plus a simple physical description of the deposition are important. principles of analysis. This book should be helpful to This work was performed under an agreement those who must make such problem-solving calcula- between the U. S. Department of Energy and the tions of atmospheric diffusion. National Oceanic and Atmospheric Administration. The book can be used also a textbook for a as one-quarter course at either the upper undergraduate or the graduate level. In fact, the basic outline [Editor’s Note: Dr. Steven Hanna and Dr. Gary evolved from a graduate course on atmospheric Briggs were with National Oceanic: and Atmospheric diffusion taught in the Environmental Engineering Administration, Atmospheric Turbulence and Diffu- Department at the University of Tennessee. sion Laboratory, Oak Ridge, Tenn., during the The number of pages was purposely limited to preparation of this book; at present Dr. Hanna is with make the book more usable. A detailed index permits Environmental Research and Technology, Lexington, quick location of subject areas, and a few problems Mass., and Dr. Briggs is with Environmental Pro- are provided after each chapter. tection Agency, Research Triangle Park, N.C.] Steven R. Hanna Atmospheric Turbulence and Diffusion Laboratory September 1981 iii ... Preface . . . . . . . . . . . . . . . . 111 2-8 Multiple Sources . . . . . . . . 17 Problems . . . . . . . . . . . . . 17 1 Meteorology . . . . . . . . . . . . 1 1-1 Introduction . . . . . . . . . . 1 3 Source Effects . . . . . . . . . . . 19 1-2 General Circulation . . . . . . . 1 3-1 Overview . . . . . . . . . . . 19 1-3 Vertical Temperature Structure 3-2 Stack Aerodynamic Effect . . . . 19 and Stability . . . . . . . . . . 2 3-3 Structure of Flow Around 1-3.1 Adiabatic Temperature Gradient 2 Buildings . . . . . . . . . . . 19 1-3.2 Stability . . . . . . . . . 3 3-4 Diffusion Calculations 1-4 Structure of the Planetary Around Buildings . . . . . . . . 21 Boundary Layer . . . . . . . . 4 3-4.1 Isolated Sources Upwind 1-4.1 Turbulence Fluxes . . . . . 4 of Buildings . . . . . . . 22 1-42 Ekman Spiral . . . . . . . 5 3-4.2 Sources Close to Buildings . . 22 1-4.3 Similarity Theory Gives Wind Problems . . . . . . . . . . . . . 24 and Temperature Profiles in Surface Layer . . . . . . . 6 4 Gaussian Plume Model for Continuous 1-4.4 Turbulence Parameters . . . 7 Sources . . . . . . . . . . . . . . 25 1-5 Use of Spectra to Estimate 41 Why Use theGaussianModel? . . . . 25 Turbulence Parameters . . . . . . 8 4 2 Formof theGauss.i.an Mode1 . . . . 25 1-6 Lagrangian Turbulence . . . . . . 9 4-3 Stability Classification Schemes . . 27 Problems . . . . . . . . . . . . . 10 44 Choice of oYa nd . . . . . . . 27 44.1 Stability ClassMethod . . . 27 2 PlumeRise . . . . . . . . . . . . . 11 4-4.2 Theoe ando. Method . . . 30 2-1 Introduction . . . . . . . . . . 11 45 Wind-Speed Variation with Height . 31 2-2 Top-Hat-ModelEquations . . . . . 11 46 Maximum Ground Concentration 2-2.1 Definitions . . . . . . . . 11 and Fumigation . . . . . . . . . 32 2-2.2 Set of Equations for 47 Averaging Times and Peak-to-Mean Vertical Plume . . . . . . 12 Concentration Ratios . . . . . . 33 2-2.3 Set of Equations for 4-8 Sector Model for Long Sampling Bent-Over Plume . . . . . 13 Times . . . . . . . . . . . . 34 2-3 Plume Trajectory Near Source . . . 13 Problems . . . . . . . . . . . . . 35 2-3.1 Vertical Plumes . . . . . . 13 2-3.2 Bent-Over Plumes . . . . . 13 5 Statistical Models of Diffusion from 2-4 Plume Rise Limited by Ambient Sources . . . . . . . 36 Continuous-Point Stability . . . . . . . . . . . 14 5-1 Introduction . . . . . . . . . . 36 24.1 Vertical Plumes . . . . . . 14 5-2 Taylor’s Theorem . . . . . . . . 36 2-4.2 Bent-Over Plumes . . . . . 14 5-3 InfluenceofEddy Sizeono . . . . 38 2-5 Plume Penetration of Elevated 5-4 Lagrangian-Eulerian Relations . . . 39 Inversion . . . . . . . . . . . 14 5-5 Monte Carlo Particle Trajectory 2-6 Plume Rise Determined by Models of Diffusion . . . . . . . 40 Ambient Turbulence . . . . . . 15 Problems . . . . . . . . . . . . . 40 2-6.1 Nearly Neutral Conditions . 16 2-6.2 Convective Conditions . . 16 6 Puff Diffusion . . . . . . . . . . . 41 2-7 Maximum Ground Concentration 6-1 Introduction . . . . . . . . . . 41 withBreakupMode1 . . . . . . . 17 6-2 Statistical Approach . . . . . . . 41 V -.-- vi 6-3 Similarity Approach . . . . . . . 42 9-5.2 Trajectory Models . . . . . 62 6-4 Applications . . . . . . . . . . 44 9-5.3 Grid Models with Winds Problems . . . . . . . . . . . . . 44 Prescribed . . . . . . . . 62 9-6 Environmental Protection Agency 7 Similarity Modelsof Diffusion . . . . . 46 Models . . . . . . . . . . . . 62 7-1 Introduction . . . . . . . . . . 46 9-7 Model Evaluation . . . . . . . . 63 7-2 Diffusion of Continuous Plumes Problems . . . . . . . . . . . . . 66 in the Surface Layer . . . . . . . 46 7-2.1 Neutral Conditions . . . . . 46 7-2.2 Nonneutral or Adiabatic 10 Removal Mechanisms . . . . . . . . 67 Conditions . . . . . . . . 47 10-1 Introduction . . . . . . . . . 67 7-3 Diffusion in the Full Depth of 10-2 Dry Deposition . . . . . . . . 67 the Daytime Planetary 10-2.1 Gravitational Settling . . . 67 Boundary Layer . . . . . . . . 48 10-2.2 Deposition of Gases and of Problems . . . . . . . . . . . . . 49 Particles with Radii Less Than About 10pm . . . . 68 8 Gradient Transport(K) Models . . . . . 50 10-3 Wet Deposition . . . . . . . . 71 8-1 The Basic Gradient Transport . 10-4 Chemical Removal . . . . . . . 72 Model . . . . . . . . . . . . 50 10-5 Removal Processes in the Box 8-2 Analytical Solutions . . . . . . . 50 Model . . . . . . . . . . . . 73 8-2.1 One-Dimensional Equation. Problems . . . . . . . . . . . . . 73 Time.Dependent. Constant K. No Wind. Instantaneous Area Source . . . . . . . 50 11 Cooling Tower Plumes and Drift Deposition . . . . . . . . . . . . . 74 8-2.2 Three Dimensions. Time- Dependent. Constant K. 11-1 Introduction . . . . . . . . . 74 No Wind. Instantaneous 11-2 Plume Rise from Cooling Point Source . . . . . . . 51 Towers . . . . . . . . . . . 74 11-2.1 Visible Plume 8-2.3 Two.Dimensiona1. Time- Dimensions . . . . . . . 76 Independent. Variable u and K. Continuous 11-2.2 Numerical Approach for Ground-Level Line Source . . 51 Deep Visible Plumes . . . . 77 11-3 Drift Deposition . . . . . . . . 78 8-2.4 Three.Dimensional. Time- Problems . . . . . . . . . . . . . 80 Independent. Constant u and K. Continuous-Point Sourceat GroundLevel . . . 52 12 Air-Pollution Meteorology in Complex 8-3 Numerical Solutions of the Terrain . . . . . . . . . . . . . . 81 Diffusion Equation . . . . . . . 53 12-1 Introduction . . . . . . . . . 81 8-3.1 Numerical Instabilities . . . . 53 12-2 Meteorology . . . . . . . . . 81 8-3.2 Specifying the Vertical 12-3 Diffusion Calculations . . . . . . 84 Diffusivity . . . . . . . . 54 Problems . . . . . . . . . . . . . 86 . . . . . . . 8-4 Higher Order Closure 55 Problems . . . . . . . . . . . . . 56 13 Long-Range Transport and 9 Urban Diffusion Models . . . . . . . 57 Diffusion . . . . . . . . . . . . . 87 9-1 Importanceof Emissions . . . . . 57 13-1 Introduction . . . . . . . . . 87 9-2 Box Model . . . . . . . . . . . 57 13-2 Modeling Concepts . . . . . . . 87 9-3 The Atmospheric Turbulence and 13-3 Application to an Inert Tracer . . . 89 Diffusion Laboratory Model . . . . 59 Problems . . . . . . . . . . . . . 90 9-4 Street Canyon and Highway Submodels . . . . . . . . . . . . 6 1 9-5 Computerized K Models for References . . . . . . . . . . . . . . 91 Urban Diffusion . . . . . . . . 62 9-5.1 An Urban Diffusion Author Index . . . . . . . . . . . . . 98 Model That Also Predicts Windsand Temperatures . . 62 Subject Index . . . . . . . . . . . . . .1 00 Meteorology 1-1 INTRODUCTION North of 30" N latitude, the direct Hadley sell breaks down, and energy is transported by traveling high and low pressure systems moving from west to To set the stage for the remainder of the east. Warm southerly winds and cold northerly winds handbook, in this chapter we must briefly review help accomplish the energy transport. Even more several aspects of meteorology, including the general energy is transported by latent heat processes, where, circulation, vertical stability, and surface-layer struc- for example, Gulf of Mexico water is evaporated, tiire. Most students are eager to begin immediately transported northeastward, and condensed. again as the study of applications of the Gaussian plume precipitation. For each gram of water involved in this model; however, even the application of the Gaussian process, 540 cal is transported toward the north. plume model requires a knowledge of wind roses and Between 60" N and the pole is another wind belt with stability and an appreciation of the influence of wind an easterly component at the surface, but this shear on the range of usefulness of the model. Also, circulation is not well defined. the latest developments in plume-rise theories require Upper-level winds strongly influence winds near the ability to understand and estimate vertical pro- the surface, where most diffusion problems occur. In files of eddy dissipation rate. Therefore this chapter general, the speed of the upper-level winds is propor- will be a useful reference for the remainder of this tional to the slope of surface of constant pressure. handbook. The atmospheric pressure -(p) typically varies by no more than about 5% at sea level over the earth's surface. However, the temperature (T) could be 1-2 GENERAL CIRCULATION 300°K at the equator and 240°K at the poles. The equation of state for the atmosphere, The sun is the source of nearly all energy received by the earth's atmosphere, and the spherical shape of the earth is responsible for the unequal absorption of this energy by the earth's surface and the atmosphere. where R is the gas constant (0.287 x lo' ergs g-' Without the transport of heat by the atmosphere and OK-'), tells us that the density (p) must be less at the the oceans from the equator to the poles, tempera- equator than at the poles. The hydrostatic equation, tures would be several tens of degrees colder at the poles and warmer at the equator. However, the fact is that there is a strong poleward transport of heat that is accomplished by direct Hadley cells, traveling high and low pressure systems, and major perturbations, such as hurricanes. In the northern hemisphere where.2 is the height and g is the acceleration of Hadley cell, air rises over the equator (causing much gravity (980 cm/sec2), then suggests that the pressure rainfall), moves at high elevations toward the north, decreases with height faster at the poles than at the descends at about 30" N latitude (causing dry desert equator. It follows that, if pressure p is constant (say regions), and then moves as the Northeast (NE) trade 1000 mb, or lo6 dynes/cm2) at sea level, then any winds near the surface from 30" N toward the other constant pressure surface aloft (say 500 mb, or equator. The NE trades are known as the most 0.5 x lo6 dynes/cm2) will slope downward from the persistent general wind system on earth. equator to the pole, as in Fig. 1.1. 1 2 ATMOSPHERIC DIFFUSION p = 0.5 x lo6 dynes/cm2 /LOW TEMPERATURE\ HIGH DENSITY FORCE . Fig. 1.1 Cross section of the earth’s atmosphere, showing how sloping pressure surfaces result at mid-atmosphere. Westerly winds are caused by a balance between pressure and Coriolis forces. forces The equation of motion says that air will first be Other hydrodynamic forces, which are beyond the accelerated toward the poles along the upper constant scope of this chapter, frequently cause the westerly pressure surface in the figure: flow to be compressed into narrow belts, called jet streams, with speeds up to 200 km/hr. Meteorological data are gathered from many stations across the globe and are stored at the National Climatic Center, National Oceanic and where u = easterly component of wind speed Atmospheric Administration (NOM), Asheville, N.C. v = northerly component of wind speed Many statistical operations (e.g., annual wind roses or y = n.ort-he rly coordinate axis frequency distributions of wind direction and speed) subscript p = constant pressure surface have already been carried out and can be obtained f = Coriolis parameter, which is equd to from the National Climatic Center at very reasonable two times the earth’s rotation rate times prices. Surface weather summaries at larger National the sine of the latitude Weather Service stations are collected into reports called “Local Climatological Data,” which are mailed The parameter f is of the order of sec-’ . The to subscribers monthly. The Climate Atlas of the apparent Coriolis force arises as a result of the earth’s United Stutes (U. S. Department of Commerce, 1968) rotation, which constantly displaces a Cartesian co- contains many data useful for diffusion calculations. ordinate system fixed to the surface. An analogy is given by rolling a marble from the edge of a rotating 1-3 VERTICAL TEMPERATURE record turntable toward the center. The marble will STRUCTURE AND STABILITY encounter regions with less angular momentum than it has. To an observer fixed to the turntable, the marble will always curve toward the right if the 1-3.1 Adiabatic Temperature Gradient turntable is rotating counterclockwise. SiSlarly, in the northern hemisphere the Coriolis force is to the right, and in the southern hemisphere it is to the left. If a parcel of dry air is moved vertically without The poleward pressure force is thus balanced by a exchanging heat with its environment (i.e., adiabati- Coriolis force toward the equator in both hemi- cally), the first law of thermodynamics becomes spheres, which causes general westerly flow at mid- levels in the atmosphere at mid-latitudes. The magni- 1 tude of the resulting “geostrophic” wind speed is 0 = cp dT - -dp P given by setting du/dt = 0 in Eq. 1.3, which yields the formula where cp is the specific heat of air at constant pressure (lo’ ergs g-’ “K-l) and T must be in degrees Kelvin (or absolute). Substituting from the