Turner Workbook

8/3/2019 Turner Workbook

1/92

D. BRUCE TURNERAir Resources Field Research Office,

Environmental Science Services Administration

U. S. DEPARTMENT OF HEALTH, EDUCATION, AND WELFAREPublic Health Service

Environmental Health ServiceNational Air Pollution, Control Administration

Cincinnati, OhioRevised 1970


2/92

The ENVIRONMENTAL HEALTH SERIES of reports was established to re-port the results of scientific and engineering studies of man's environment: The com-munity, whether urban, suburban, or rural, where he lives, works, and plays; the air,water, and earth he uses and re-uses; and the wastes he produces and must dispose ofin a way that preserves these natural resources. This SERIES of reports provides forprofessional users a central source of information on the intramural research activitiesof the Centers in the Bureau of Disease Prevention and Environmental Control, andon their cooperative activities with state and local agencies, research institutions, andindustrial organizations. The general subject area of each report is indicated by theletters that appear in the publication number; the indicators are

AP Air PollutionRH Radiological HealthUIH Urban and Industrial Health

Triplicate tear-out abstract cards are provided with reports in the SERIES tofacilitate information retrieval. Space is provided on the cards for the user's accessionnumber and additional key words.Reports in the SERIES will be distributed to requesters, as supplies permit. Re-quests should be directed to the Center identified on the title page.

3rd printing May 1970

Public Health Service Publication No. 999-AP-26


3/92

PREFACEThis workbook presents some computational techniques currently used by scien-

tists working with atmospheric dispersion problems. Because the basic working equa-tions are general, their application to specific problems usually requires special careand judgment; such considerations are illustrated by 26 example problems. Thisworkbook is intended as an aid to meteorologists and air pollution scientists who arerequired to estimate atmospheric concentrations of contaminants from various typesof sources. It is not intended as a complete do-it-yourself manual for atmosphericdispersion estimates; all of the numerous complications that arise in making best esti-mates of dispersion cannot be so easily resolved. Awareness of the possible complex-ities can enable the user to appreciate the validity of his "first approximations" andto realize when the services of a professional air pollution meteorologist are required.

iii


4/92

ACKNOWLEDGMENTSThe author wishes to express his appreciation to Robert A. McCormick PaulA. Humphrey, and other members of the Field Research Office for their helpful dis-cussions and review; to Jean J. Schueneman, Chief, Criteria and Standards Develop-ment, National Center for Air Pollution Control, who suggested this workbook; to PhyllisHolland and Prank Schiermeier, who checked the problem solutions; to Ruth Umfleet51 w- o 7fn y for their aid; and to the Nati nal Center for Air Pollution Control,

public Health Service, and Air Resources Laboratory, Environmental Science ServicesAdministration, for their support.


5/92

CONTENTSABSTRACT viiChapter 1. INTRODUCTION 1Chapter 2. BACKGROUND 3Chapter 3. ESTIMATES OF ATMOSPHERIC DISPERSION 5

Coordinate System 5Diffusion Equations 5Effects of Stability 6Estimation of Vertical and Horizontal Dispersion 7Evaluation of Wind Speed 7Plots of Concentrations against Distance 7Accuracy of Estimates 7Graphs for Estimates of Diffusion 10Plotting Ground-Level Concentration Isopleths 10Areas Within Isopleths 17Calculation of Maximum Ground-Level Concentrations 17Review of Assumptions 17

Chapter 4. EFFECTIVE HEIGHT OF EMISSION 31General Considerations 31Effective Height of Emission and Maximum Concentration 31Estimates of Required Stack Heights 31Effect of Evaporative Cooling 32Effect of Aerodynamic Downwash , 32

Chapter 5. SPECIAL TOPICS 35Concentrations in an Inversion Break-up Fumigation 35Plume Trapping 36Concentrations at Ground Level Compared to Concentrationsat the Level of Effective Stack Height from Elevated Con-tinuous Sources 36Total Dosage from a Finite Release , 37Crosswind-Integrated Concentration 37Estimation of Concentrations for Sampling Times Longerthan a Few Minutes 37Estimation of Seasonal or Annual Average Concentrationsat a Receptor from a Single Pollutant Source 38Meteorological Conditions Associated with MaximumGround-Level Concentrations 38Concentrations at a Receptor Point from Several Sources 39Area Sources , 39Topography 40Line Sources ... , 40Instantaneous Sources ., 41

Chapter 6. RELATION TO OTHER DIFFUSION EQUATIONS 43Chapter 7. EXAMPLE PROBLEMS 45Appendices: , , 57

1 Abbreviations and Symbols 592 Characteristics of the Gaussian Distribution : 613 Solutions to Exponentials 654 Constants, Conversion Equations, Conversion Tables 69


6/92


7/92

ABSTRACTThis workbook presents methods of practical application of the binormal con-tinuous plume dispersion model to estimate concentrations of air pollutants. Estimates

of dispersion are those of Pasquill as restated by Gifford. Emphasis is on the estima-tion of concentrations from continuous sources for sampling times up:, to 1 hour.. Someof the topics discussed are determination of effective height of emission, extension ofconcentration estimates to longer sampling intervals, inversion break-up fumigationconcentrations, and concentrations from area, line, and multiple sources. Twenty-sixexample problems and their solutions are given. Some graphical aids to computationare included.

Vll


8/92


9/92

Chapter 1 INTRODUCTIONDuring recent years methods of estimating at-

mospheric dispersion have undergone considerablerevision, primarily due to results of experimentalmeasurements. In most dispersion problems therelevant atmospheric layer is that nearest theground, varying in thickness from several hundredto a few thousand meters. Variations in boththermal and mechanical turbulence and in windvelocity are greatest in the layer in contact withthe surface. Turbulence induced by buoyancy forcesin the atmosphere is closely related to the vertical

temperature structure. When temperature decreaseswith height at a rate higher than 5.4F per 1000 ft(1C per 100 meters), the atmosphere is in un-stable equilibrium and vertical motions are en-hanced. When temperature decreases at a lowerrate or increases with height (inversion), verticalmotions are damped or reduced. Examples of typ-ical variations in temperature and wind speed withheight for daytime and nighttime conditions areillustrated in Figure 1-1.

600

500

400

300

200

100

DAY

J k-10 1 234567TEMPERATURE, C

10 11 12 1 34567WIND SPEED, in/set

10 11

Figure 1-1. Examples of variation of temperature and wind speed with height (after Smith, 1963).

The transfer of momentum upward or down-ward in the atmosphere is also related to stability;when the atmosphere is unstable, usually in thedaytime, upward motions transfer the momentum"deficiency" due to eddy friction losses near theearth's surface through a relatively deep layer,causing the wind speed to increase more slowlywith height than at night (except in the lowest fewmeters). In addition to thermal turbulence, rough-ness elements on the ground engender mechanicalturbulence, which affects both the dispersion ofmaterial in the atmosphere and the wind profile(variation of wind with height). Examples of theseeffects on the resulting wind profile are shown inFigure 1-2.

As wind speed increases, the effluent from acontinuous source is introduced into a greater vol-ume of air per unit time interval. In addition tothis dilution by wind speed, the spreading of thematerial (normal to the mean direction of trans-port) by turbulence is a major factor in the dis-persion process.

The procedures presented here to estimate at-mospheric dispersion are applicablewhen mean windspeed and direction can be determined, but meas-urements of turbulence, such as the standard de-viation of wind direction fluctuations, are not avail-able. If such measurements are at hand, techniquessuch as those outlined by Pasquill (1961) are likelyto give more accurate results. The diffusion param-


10/92

eters presented here are most applicable to ground-level or low-level releases (from the surface to about20 meters), although they are commonly applied athigher elevations without full experimental valida-tion. It is assumed that stability is the samethroughout the diffusing layer, and no turbulenttransfer occurs through layers of dissimilar stabilitycharacteristics. Because mean values for wind direc-tions and speeds are required, neither the variationof wind speed nor the variation of wind directionwith height in the mixing layer are taken into ac-count. This usually is not a problem in neutral orunstable (e.g., daytime) situations, but can causeover-estimations of downwind concentrations instable conditions.

REFERENCESDavenport, A. G., 1963: The relationship of wind

structure to wind loading. Presented at Int.Conf. on The Wind Effects on Buildings andStructures, 26-28 June 63, Natl. Physical Lab-oratory, Teddington, Middlesex, Eng.

Pasquill, P., 1961: The estimation of the dispersionof wind borne material. Meteorol. Mag. 90,1063, 33-49.

Smith, M. E., 1963: The use and misuse of the at-mosphere, 15 pp., Brookhaven Lecture Series,No. 24, 13 Feb 63, BNL 784 (T-298) Brook-haven National Laboratory.

600r URBAN AREAGRADIENT WIND

SUBURBS LEVEL COUNTRY

GRADIENT WIND

&amples of variation of

ATMOSPHERIC DISPERSION ESTIMATES


11/92

Chapter 2 BACKGROUNDFor a number of years estimates of concentra-tions were calculated either from the equations ofSutton (1932) with the atmospheric dispersionparameters Cy , C, and n, or from the equations of

Bosanquet (1936) with the dispersion parametersp and q.Hay and Pasquill (1957) have presented experi-mental evidence that the vertical distribution of

spreading particles from an elevated point is re-lated to the standard deviation of the wind eleva-tion angle,


12/92


13/92

Chapter 3 ESTIMATES OF ATMOSPHERIC DISPERSIONis chapter outlines the basic procedures tosd in making dispersion estimates as sug-by Paaquill (1961) and modified by GiffordDINATE SYSTEMthe system considered here the origin is atI level at or beneath the point of emission,ie x-axis extending horizontally in the direc-1 the mean wind. The y-axis is in the hori-plane perpendicular to the x-axis, and theextends vertically. The plume travels alongillel to the x-axis. Figure 3-1 illustrates thelate system.SIGN EQUATIONS3 concentration, x, of gas or aerosols (parti-is than about 20 microns diameter) at x,y,zcontinuous source with an effective emissionH, is given by equation 3.1. The notationo depict this concentration is x (x,y,z;H).he height of the plume centerline when it

becomes essentially level, and is the sum of thephysical stack height, h, and the plume rise, AH.The following assumptions are made: the plumespread has a Gaussian distribution (see Appendix2) in both the horizontal and vertical planes, withstandard deviations of plume concentration distri-bution in the horizontal and vertical of o-y ^and azsrespectively; the mean wind speed affecting theplume is u; the uniform emission rate of pollutantsis Q; and total reflection of the plume takes placeat the earth's surface, i.e., there is no depositionor reaction at the surface (see problem 9).X (x,y,z;H)

exp

z+H

Q exp'z-H

a

1+ exp 11* 12(3.1)

'Note: exp a/b = e-n/>> where e Is the base of natural logarithmsand is approximately equal to 2.7183.

x,-y,Z)

(x,-y,o)

Figure 3-1. Coordinate system showing Gaussian distributions in the horizontal and vertical.

tcs


14/92

Any consistent set of units may be used. The mostcommon is;\ (g m" 1 ) or, for radioactivity (curies m~3 )Q (gsec~ l ) or (curies sec' 1 )u (m sec~ ! )IT,, att H,x,y, and z (m)

This equation is the same as equation (8.35) p. 293of Sutton (1953) when u's are substituted for But-ton's parameters through equations like (8.27) p.286. For evaluations of the exponentials found inEq. (3.1) and those that follow, see Appendix 3.x is a mean over the same time interval as the timeinterval for which the a's and u are representative.The values of both ay and trt are evaluated in termsof the downwind distance, x.

Eq. (3.1) is valid where diffusion in the direc-tion of the plume travel can be neglected, that is,no diffusion in the x direction.This may be assumed if the release is continuousor if the duration of release is equal to or greaterthan the travel time (x/u) from the source to thelocation of interest.

For concentrations calculated at ground level,i.e., z = 0, (see problem 3) the equation simplifiesto:

X (x,y,0;H) = Q exp(3.2)

Where the concentration is to be calculatedalong the centerline of the plume (y = 0), (seeproblem 2) further simplification results:X


15/92

Some preliminary results of a dispersion experi-ment in St. Louis (Pooler, 1965) showed that thedispersion over the city during the daytime behavedsomewhat like types B and C; for one night, experi-ment o-j. varied with distance between types D and E.ESTIMATION OF VERTICAL ANDHORIZONTAL DISPERSION

Having determined the stability class fromTable 3-1, one can evaluate the estimates of o-,. and


16/92

1 0'

DISTANCE DOWNWIND, km

Figure 3-2. Horizontal dispersion coefficient as a function of downwind distance from the source.



17/92

1,000

1 10DISTANCE DOWNWIND, km

100

Figure 3-3. Vertical dispersion coefficient as a function of downwind distance from the source.

Estimates338-901 O - BO - 2


18/92

12345 6*10~5CONC.580meters

Figure 3-4. Variations in concentration in the vertical beneath a more stable layer.three cases (where ^ can be expected to be withina factor of 2) should be correct within a factor of 3including errors in Vy and u. The relative confidencein the ,s (m decreasing order) is indicated by theheavy lines and dashed lines in Figures 3-2 and 3-3.

Estimates of H, the effective height of the plume,may he in error because of uncertainties in the esti-mation of AH the plume rise. Also, for problemsthat require estimates of concentration at a specificpoint the difficulty of determining the mean"wind" time interval d consequently theX'aXiS Can un-

PLOTTING GROUND-LEVELCONCENTRATION ISOPLETHSOften one wishes to determine the locatioiiHwhere concentrations equal or exceed a given mag-nitude. First, the axial position of the plume mustbe determined by the mean wind direction Forplotting isopleths of ground-level concentrationsthe relationship between ground-level centorlinoconcentrations and ground-level off-axis concentra-tions can be used:

.x (*,y,0;H)x (x,0,0;H)

GRAPHS FOR ESTIMATES OF DIFFUSION J!J oor?ina fe f a particular isopleth from the' A-axis can be dprpvmmoi-i ^v- nn i. .i_.(A avo.id p* titious comPutations, Figure 3-5P

- ' -evconcen-times wind speed (v u/Q) aeainst downwind distances for various effective heifhts of *ml"sion and limits to the vertical mixing foi eachT4bihty class (1 figure for each stability) Compu ations were made from Eq. (3.3), (3.4) andTa SEstimates of actual concentrat ons may be dete 'mined by multiplying ordinate values by Q/u

concentration at this3

] __JLfeyiiH)

S^TlO1^ = '345

2.9 x 10~:1 g m-a .exP I ~

10ATMOSPHERIC DISPERSION ESTIMATES


19/92

CISTAKCE.km

Figure 3-5A. xu/Q with distance for various heights of emission (H) and limits to vertical dispersion (L), A stability.

Estimates 11


20/92

10

DISTANCE, km

3-5B. ,vu/Q with distance for various heights of emission (H) and limits to vertical dispersion (L), B stability.



21/92

DISTANCE, km

Figure 3-5C. xu/Q with distance for various heights of emission (H) and limits to vertical dispersion (L), C stability.

Estimates 13


22/92

DISTANCE, km

Figure 3-5D. xu/Q with distance for various heights of emission (H) and limits to vertical dispersion (L), D stability.

14 ATMOSPHERIC DISPERSION ESTIMATES


23/92

10

10

DISTANCE, km

Figure 3-5E. xii/Q with distance for various heights of emission (H) and limits to vertical dispersion (U, E stability.

Estimates 15


24/92

100DISTANCE, km

igure 3-5F. xu/Q with distance for various heights of emission (H) and limits to vertical dispersion (L), F stabifity.

L6 ATMOSPHERIC DISPERSION ESTIMATES


25/92

From Table A-l (Appendix 3) when exp"= 0-346, y/ 4, 2, 91-92.

Estimates 17


26/92

CL>

gjm...

C-OCOOJ

"I '(*) 33NV1SIO flN!MSSO3



27/92

CO

oc/>

"oi

txO

X

Q.ODQCO

tao

3DNV1SIO

Estimates 19


28/92

ro-4_jc/i

C-3i=3

-c

XjOiCZIu

toCOOJ

33NV1SIQ



29/92

Qaool/>~o>>"OoTOOXHoOLOCOaupooCDi ,

3'3HV1S1Q

Estimates 21


30/92

03

o

CO

33HV1SIQ



31/92


32/92

caCQ

a>CJ

car^-TOQJ

'1 '(



33/92

CJ3_cf

CD-4 'CD

CDCD

X

q>o.oCJICOCD

33NV1SIQ

Estimates 25339-001 O - 69 - 3


34/92

COto

Xto-!=:H *OJ

CL>So

3DNV1SIQ QNIMSSO3



35/92

_opIc:CD*-'OJ

COo

ooCD

'(*}

Estimates 27


36/92

Xu m"

Figure 3-8. Area within isopleths for a ground-level source (from Hilsmeier and Gifford).

Jilsmeier, W. F., and F, A. Gifford, 1962: Graphsfor estimating atmospheric diffusion. ORO-545,Oak Ridge, Tenn. Atomic Energy Commission,10 pp.List, R, J., 1951: Smithsonian Meteorological

Tables, Sixth Revised Edition, 497-505, Wash-ington, D. C., Smithsonian Institution, 527 pp.

Martin, D, 0., 1965: Personal communication.Pasquill, F., 1961: The estimation of the dispersion

of windborne material. Meteorol. Mag 001063, 33-49.

Pooler, F., 1965: Personal communication.Button, 0. G., 1953: Micrometeorology, New YorkMcGraw-Hill. 333 pp.Turner, D. B., 1961: Relationships between 24-hour mean air quality measurements and mete-

orological factors in Nashville, Tennessee. J.Air Poll. Cont. Assoc., 77, 483-489.



37/92

EQJ(/OOi,I_JOJEOJ_dtD5"-4'O(D

XEr=E

crcao'*_jTO

='xO ^4.CD 5= JOCO =1ca -BCTJCOCD=3KxO

iatcs


38/92


39/92

Chapter 4 EFFECTIVE HEIGHT OF EMISSIONGENERAL CONSIDERATIONS

In most problems one must estimate the effec-tive stack height, H, at which the plume becomesessentially level. Rarely will this height correspondto the physical height of the stack, h. If the plumeis caught in the turbulent wake of the stack or ofbuildings in the vicinity of the stack, the effluentwill be mixed rapidly downward toward the ground(aerodynamic downwash). If the plume is emittedfree of these turbulent zones, a number of emissionfactors and meteorological factors influence the riseof the plume. The emission factors are: velocityof the effluent at the top of the stack, VH ; tempera-ture of the effluent at the top of the stack, TH ; anddiameter of the stack opening, d. The meteorolog-ical factors influencing plume rise are wind speed,u; temperature of the air, T,,; shear of the windspeed with height, du/dz; and atmospheric sta-bility. No theory on plume rise takes into accountall of these variables; even if such a theory wereavailable, measurements of all of the parameterswould seldom be available. Most of the equationsthat have been formulated for computing the ef-fective height of emission are semi-empirical. For arecent review of equations for effective height ofemission see Moses, Strom, and Carson (1964).

Moses and Strom (1961), having compared ac-tual and calculated plume heights by means of sixplume rise equations, report "There is no one for-mula which is outstanding in all respects." Theformulas of Davidson-Bryant (1949), Holland(1953), Bosanquet-Carey-Halton (1950), and Bo-saiiquet (1957) all give generally satisfactory re-sults in the test situations. The experiments con-ducted by Moses and Strom involved plume risefrom a stack of less than 0.5 meter diameter, stackgas exit velocities less than 15 m sec" 1 , and effluenttemperature not more than 35C higher than thatof the ambient air.

The equation of Holland was developed withexperimental data from larger sources than thoseof Moses and Strom (stack diameters from 1.7 to4,3 meters and stack temperatures from 82 to204 C); Holland's equation is used in the solutionof the problems given in this workbook. This equa-tion frequently underestimates the effective heightof emission; therefore its use often provides a slight"safety" factor.

Holland's equation is;

uwhere;

AH = the rise of the plume above the stack, m

VH = stack gas exit velocity, m sec ld = the inside stack diameter, mu = wind speed, m sec' 1p = atmospheric pressure, mbTH = stack gas temperature, KTa = air temperature, K

and 2.68 x 10~-! is a constant having units of mb"Jm-1 .Holland (1953) suggests that a value between

1.1 and 1.2 times the AH from the equation shouldbe used for unstable conditions; a value between0.8 and 0.9 times the AH from the equation shouldbe used for stable conditions.

Since the plume rise from a stack occurs oversome distance downwind, Eq. (4.1) should not beapplied within the first few hundred meters of thestack.EFFECTIVE HEIGHT OF EMISSION ANDMAXIMUM CONCENTRATION

If the effective heights of emission were thesame under all atmospheric conditions, the highestground-level concentrations from a given sourcewould occur with the lightest winds. Generally,however, emission conditions are such that the ef-fective stack height is an inverse function of windspeed as indicated in Eq. (4.1). The maximumground-level concentration occurs at some inter-mediate wind speed, at which a balance is reachedbetween the dilution due to wind speed and theeffect of height of emission. This critical wind speedwill vary with stability. In order to determine thecritical wind speed, the effective stack height as afunction of wind speed should first be determined.The maximum concentration for each wind speedand stability can then be calculated from Figure3-9 as a function of effective height of emissionand stability. When the maximum concentrationas a function of wind speed is plotted on log-loggraph paper, curves can be drawn for each stabilityclass; the critical wind speed corresponds to thepoint of highest maximum concentration on thecurve (see problem 14).ESTIMATES OF REQUIRED STACK HEIGHTS

Estimates of the stack height required to pro-duce concentrations below a given value may bemade through the use of Figure 3-9 by obtainingsolutions for various wind speeds. Use of this figureconsiders maximum concentrations at any distancefrom the source.

In some situations high concentrations upon theproperty of the emitter are of little concern, but

Effective Height31


40/92

maximum concentrations beyond the property lineare of the utmost importance. For first approxima-tions it can be assumed that the maximum concen-tration occurs where \/TcrB = H and that at thisdistance the IT'S are related to the maximum con-centration by:

(r v a., ---= Q 0.117 Qu e (4.2)Knowing the source strength, Q, and the concen-tration not to be exceeded xmnw one can determinethe necessary a-y


41/92

Diilanca Downwind, km

Figure 4-1. The product of


42/92

the height. Values other than 4.3 and 2.15 can beused. When these values are used 97 % of the dis-tribution is included within these limits. Virtualdistances xy and X K can be found such that at x-v ,ffy IT.,.,, and at x a , ax , == fr7n . These x's will differwith stability. Equations applicable to point sourcescan then he used, determining


43/92

Chapter 5 - SPECIAL TOPICSCONCENTRATIONS IN AN INVERSIONBREAK-UP FUMIGATION

A surface-based inversion may be eliminated bythe upward transfer of sensible heat from theground surface when that surface is warmer thanthe overlying air. This situation occurs when theground is being warmed by solar radiation or whenair flows from a cold to a relatively warm surface.In either situation pollutants previously emittedabove the surface into the stable layer will be mixedvertically when they are reached by the thermaleddies, and ground-level concentrations can increase.This process, called "fumigation" was described byHewson and Gill (1944) and Hewson (1945). Equa-tions for estimating concentrations with these con-ditions have been given by Holland (1953), Hew-son (1955), Gilford (1960a), Bierly and Hewson(1962), and Pooler (1965).

To estimate ground-level concentrations underinversion break-up fumigations, one assumes thatthe plume was initially emitted into a stable layer.Therefore,


44/92

wind in the stable layer and t rii is the time requiredto eliminate the inversion from h, the physicalheight of the stack to h f (Eq. 5.3).

t,,, is dependent upon both the strength of theinversion and the rate of heating at the surface.Pooler (1965) has derived an expression for esti-mating this time:

p:i SOR (hi h) h, (5.5)where tm time required for the mixing layer to

develop from the top of the stack to thetop of the plume, sec

p a = ambient air density, g m~3Cp = specific heat of air at constant pressure,

cal g- 1 "K-1R =-- net rate of sensible heating of an aircolumn by solar radiation, cal rn~2 sec" 1so vertical potential temperature gradient,

"Km- 1rate) Sz

h r (the adiabatic lapse

hi = height of base of the inversion sufficientto be above the plume, m

h = physical height of the stack, mNote that hi h is the thickness of the layer to beheated and f -1 1 is the average height of thelayer. Although R depends on season, and cloudcover and varies continuously with time, Pooler hasused a value of 67 cal m~2 sec" 1 as an average forfumigation.

Hewson (1945) also suggested a method of esti-mating the time required to eliminate an inversionto a height z by use of an equation of Taylor's(1915, p. 8):

u ~ 4 Kwhere: t = time required to eliminate the inver-

sion to height z, secz = height to which the inversion has been

eliminated, mK = eddy diffusivity for heat, m2 sec"1Rewriting to compare with Eq. (5.5),V h2

4 K (5.7)Hewson (1945) has suggested a value of 3 m3 sec"1for K.PLUME TRAPPING

Plume trapping occurs when the plume istrapped between the ground surface and a stable

layer aloft. Bierly and Hewson (1962) have sug-gested the use of an equation that accounts for themultiple eddy reflections from both the ground andthe stable layer:

/ n _.TT\ ^t2?r U

exp

-f exp

H

where L is the height of the stable layer and J = 3or 4 is sufficient to include the important reflec-tions. A good approximation of this lengthy equa-tion can be made by assuming no effect of the stablelayer until


45/92

these is at the distance of maximum concentrationat the ground. As a rough approximation the maxi-mum ground-level concentration occurs at the dis-

1tance where H. This approximation is

much better for unstable conditions than for stableconditions. With this approximation, the ratio ofconcentration at plume centerline to that at theground is:

, 0,H)x(x,0,0)

1 QQl.ouThis calculation indicates that at the distance

of maximum ground-level concentration the concen-tration at plume centerline is greater by aboutone-third.

It is also of interest to determine the relation-ship between


46/92

Table 5-1 VARIATION OF CALCULATED CONCENTRATIONWITH SAMPLING TIME

Ratio ofCalculated Concentration

2 Q

This table indicates a power relation with time:X (probablyibout 10 minutes); and p should be between 0.17md 0.2. Eq. (5.12) probably would be appliednost appropriately to sampling times less than 2lours (see problem 19).ESTIMATION OF SEASONAL OR ANNUALAVERAGE CONCENTRATIONS AT ARECEPTOR FROM A SINGLE POLLUTANTSOURCE

For a source that emits at a constant rate fromlour to hour and day to day, estimates of seasonaljr annual average concentrations can be made forany distance in any direction if stability wind "rose"data are available for the period under study. Awind rose gives the frequency of occurrence foreach wind direction (usually to 16 points) and windspeed class (9 classes in standard Weather Bureauuse) for the period under consideration (from 1month to 10 years) . A stability wind rose gives thesame type of information for each stability class.

If the wind directions are taken to 16 points andit is assumed that the wind directions within eachsector are distributed randomly over a period of amonth or a season, it can further be assumed thatthe effluent is uniformly distributed in the hori-zontal within the sector (Holland, 1953, p. 540).The appropriate equation for average concentrationis then either:

\/27T CTjs Uexp H

2.03QaK UX OVV\ I ._.exp I H (5.13)

orQ

Lu 162.55 QLux

(5.14)

depending upon whether a stable layer aloft is af-fecting the distribution.

The estimation of x for a particular directionand downwind distance can be accomplished bychoosing a representative wind speed for each speedclass and solving the appropriate equation (5.13 or5.14) for all wind speed classes and stabilities. Notothat a SSW wind affects a receptor to the NNEof a source. One obtains the average concentrationfor a given direction and distance by summing allthe concentrations and weighting each one accord-ing to its frequency for the particular stability andwind speed class. If desired, a different effectivoheight of emission can be used for various windspeeds. The average concentration can be expressedby:

2 Q f (G,S,N)(x,G)

exp

S NH,,


47/92

2. For elevated sources maximum "instantaneous"concentrations occur with unstable conditionswhen portions of the plume that have undergonelittle dispersion are brought to the ground.These occur close to the point of emission (onthe order of 1 to 3 stack heights) . These con-centrations are usually of little general interestbecause of their very short duration; they can-not be estimated from the material presented inthis workbook.

3. For elevated sources maximum concentrationsfor time periods of a few minutes occur withunstable conditions; although the concentra-tions fluctuate considerably under these condi-tions, the concentrations averaged over a fewminutes are still high compared to those foundunder other conditions. The distance of thismaximum concentration occurs near the stack(from 1 to 5 stack heights downwind) and theconcentration drops off rapidly downwind withincreasing distance,

4. For elevated sources maximum concentrationsfor time periods of about half an hour can occurwith fumigation conditions when an unstablelayer increases vertically to mix downward aplume previously discharged within a stablelayer. With small AH, the fumigation can occurclose to the source but will be of relatively shortduration. For large AH, the fumigation willoccur some distance from the stack (perhaps 30to 40 km), but can persist for a longer timeinterval. Concentrations considerably lower thanthose associated with fumigations, but of sig-nificance can occur with neutral or unstableconditions when the dispersion upward is se-verely limited by the existence of a more stablelayer above the plume, for example, an inversion.

5. Under stable conditions the maximum concen-trations at ground-level from elevated sourcesare less than those occurring under unstableconditions and occur at greater distances fromthe source. However, the difference betweenmaximum ground-level concentrations for stableand unstable conditions is only a factor of 2for effective heights of 25 meters and a factorof 6 for H of 75 m. Because the maximumoccurs at greater distances, concentrations thatare below the maximum but still significant canoccur over large areas. This becomes increas-ingly significant if emissions are coming frommore than one source.

CONCENTRATIONS AT A RECEPTOR POINTFROM SEVERAL SOURCESSometimes, especially for multiple sources, it isconvenient to consider the receptor as being at the

origin of the diffusion coordinate system. The

source-receptor geometry can then be worked outmerely by drawing or visualizing an x-axis orientedupwind from the receptor and determining thecrosswind distances of each source in relation to thisx-axis. As pointed out by GifEord (1959), the con-centration at (0, 0, 0) from a source at (x, y, H)on a coordinate system with the x-axis oriented up-wind is the same as the concentration at (x, y, 0)from a source at (0, 0, H) on a coordinate systemwith the x-axis downwind (Figure 5-2), The totalconcentration is then given by summing the indi-vidual contributions from each source {see problem20).

SOURCEUPWIND

RECEPTOR(0,0,0)

DOWNWEND

Figure 5-2. Comparison of source-oriented and receptor-oriented coordinate systems.

It is often difficult to determine the atmos-pheric conditions of wind direction, wind speed, andstability that will result in the maximum combinedconcentrations from two or more sources; drawingisopleths of concentration for various wind speedsand stabilities and orienting these according towind direction is one approach.AREA SOURCES

In dealing with diffusion of air pollutants inareas having large numbers of sources, e.g., as inurban areas, there may be too many sources of mostatmospheric contaminants to consider each source

Special Topics 39


48/92

individually. Often an approximation can be madeby combining all of the emissions in a given areaand treating this area as a source having an initialhorizontal standard deviation, trvoi A virtual dis-tance, xy , can then be found that will give thisstandard deviation. This is just the distance thatwill yield the appropriate value for ay from Figure3-2. Values of x, will vary with stability. Thenequations for point sources may be used, determin-ing ffy as a function of x -{- x y , a slight variation ofthe suggestion by Holland {1953). This proceduretreats the area source as a cross-wind line sourcewith a normal distribution, a fairly good approxi-mation for the distribution across an area source.The initial standard deviation for a square areasource can be approximated by


49/92

When estimating concentrations from finite linesources, one must account for "edge effects" causedby the end of the line source. These effects will ofcourse extend to greater cross-wind distances asthe distance from the source increases. For concen-trations from a finite line source oriented cross-wind, define the x-axis in the direction of the meanwind and passing through the receptor of interest.The limits of the line source can be defined as ex-tending from y, to y, where y, is less than y a . Theequation for concentration (from Button's (1932)equation (11), p. 154), is:(x,0,0;H)

(5.20)

The value of the integral can be determined fromtabulations given in most statistical tables (for ex-ample, see Burrington (1953), pp. 273-276; also seeproblem 24).INSTANTANEOUS SOURCES

Thus far we have considered only sources thatwere emitting continuously or for time periods equalto or greater than the travel times from the sourceto the point of interest. Cases of instantaneous re-lease, as from an explosion, or short-term releaseson the order of seconds, are often of practical con-cern. To determine concentrations at any positiondownwind, one must consider the time intervalafter the time of release and diffusion in the down-wind direction as well as lateral and vertical diffu-sion. Of considerable importance, but very difficult,is the determination of the path or trajectory otthe "puff." This is most important if concentra-tions are to be determined at specific points. Deter-mining tbe trajectory is of less importance if knowl-edge of the magnitude of the concentrations torparticular downwind distances or travel times isrequired without the need to know exactly at whatpoints these concentrations occur. Rewriting

tout-ton's (1932) equation (13), p. 155, results in anequation that may be used for estimates of concen-tration downwind from a release from height, n.

. . 2 QT r 1

6XP 2\ i ( y Ylexp I o-l-r- JL ^ \ y ' J

(The numerical value of (M*** is l5 -75 ->

Special Topics

(5.21)

The symbols have the usual meaning, with theimportant exceptions that QT represents the totalmass of the release and the u's are not those eval-uated with respect to the dispersion of a continuoussource at a fixed point in space.

In Eq. (5.21) the


50/92

Gifford, F. A., 1959: Computation of pollutionfrom several sources. Int. J, Air Poll., 2, 109-110.

Gifford, F. A,, 1960a: Atmospheric dispersion cal-culations using the generalized Gaussian plumemodel. Nuclear Safety, 2, 2, 56-59, 67-68.Gifford, F. A., 196Qb: Peak to average concentra-tion ratios according to a fluctuating plume dis-

persion model Int. J. Air Poll., 3, 4, 253-260.Hewson, E. W., and G. C. Gill, 1944: Meteorolog-ical investigations in Columbia River Valleynear Trail, B. C., pp 23-223 in Report submittedto the Trail Smelter Arbitral Tribunal by R. S.Dean and R. E. Swain, Bur. of Mines Bull 453,Washington, Govt. Print. Off., 304 pp.Hewson, E. W., 1945: The meteorological controlof atmospheric pollution by heavy industry.Quart. J. R. MeteoroL Soc., 71, 266-282.Hewson, E. W., 1955: Stack heights required tominimize ground concentrations. Trans. ASME

77, 1163-1172.Holland, J. Z,, 1953: A meteorological survey ofthe Oak Ridge area, p. 540. Atomic EnergyComm., Report ORO-99, Washington, D. C.,584 pp.

Nonhebel, G. f 1960: Recommendations on heightsfor new industrial chimneys. J. Inst. Fuel, 33,479-513.

Pooler, F., 1965: Potential dispersion of plumesfrom large power plants. PHS Publ. No. 999-AP-16, 1965. 13 pp.

Singer, I. A., 1961: The relation between peak andmean concentrations. J. Air Poll. Cont. Assoc.,11, 336-341.

Singer, I. A., K. Imai, and R. G. Del Campos, 1963:Peak to mean pollutant concentration ratios forvarious terrain and vegetation cover. J. Air Poll.Cont. Assoc., 13, 40-42.Slade, D. H., 1965: Dispersion estimates from pol-lutant releases of a few seconds to 8 hours in

duration. Unpublished Weather Bureau Report.Aug. 1965.Stewart, N. G., H. J. Gale, and R. N. Crooks, 1958:The atmospheric diffusion of gases dischargedfrom the chimney of the Harwell Reactor BEPG.

Int. J. Air Poll., 1, 87-102.Sutton, O. G., 1932: A theory of eddy diffusion inthe atmosphere. Proc. Roy. Soc. London, A,

135, 143-165.Taylor, G. I., 1915: Eddy motion in the atmos-

phere. Phil. Trans. Roy. Soc., A, 215, 1-26,



51/92

Chapter 6 RELATION TO OTHER DIFFUSION EQUATIONSMost other widely used diffusion equations are

variant forms of the ones presented here. With re-spect to ground-level concentrations from an ele-vated source (Eq. 3.2):

(x,y,0;H) = Qexp

IT


52/92


53/92

Chapter 7 EXAMPLE PROBLEMSThe following 26 example problems and their

solutions illustrate the application of most of thetechniques and equations presented in this work-book.PROBLEM 1: It is estimated that a burningdump emits 3 g sec" 1 of oxides of nitrogen.What is the concentration of oxides of nitrogen,

averaged over approximately 10 minutes, fromthis source directly downwind at a distance of3 km on an overcast night with wind speed ^ of7 m sec" 1? Assume this dump to be a pointground-level source with no effective rise.

SOLUTION: Overcast conditions with a windspeed of 7 m sec"1 indicate that stability class Dis most applicable (Statement, bottom of Table3-1). For x 3 km and stability D, o> = 190 mfrom Figure 3-2 and


54/92

level concentration occur and what is this con-centration on an overcast day with wind speed4 m sec" 1 ?

SOLUTION: On an overcast day the stabilityclass would be D. From Figure 3-9 for D sta-bility and H of 150 m, the distance to the pointof maximum ground-level concentration is 5.6km, and the maximum xu/Q is 3.0 x 1Q~U .

3.0 x lET* x 151

= 1.1 x ID-1 g m"3PROBLEM 6: For the conditions given in prob-

lem 4, draw a graph of ground-level centerlinesulfur dioxide concentration with distance from100 meters to 100 km. Use log-log graph paper.

SOLUTION: The frontal inversion limits the mix-ing to L = 1500 meters. The distance at whicha, = Q.47 L = 705 m is XL = 5.6 km. At dis-tances less than this, Eq. (3.3) is used to calcu-late concentrations:

x (x,0,0;H) = Q expAt distance equal to or greater than 2 XL, whichis 11 km, Eq, (3.5) is used:

(x,0,0;H) = Q2?r CTV L USolutions for the equations are given in Table7-1. The values of concentration are plottedagainst distance in Figure 7-1.

DOWNWIND DISTANCI, km

Figure 7-1. Concentration as a lunction of downwinddistance (Problem 6).

Table 7-1 CALCULATION OF CONCENTRATIONS FORVARIOUS DISTANCES (PROBLEM 6)

PROBLEM 7: For the conditions given in prob-lem 4, draw a graph of ground-level concentra-tion versus crosswind distance at a downwinddistance of 1 km.

SOLUTION: From problem 4 the ground-lovclcenterline concentration at 1 km is 2.8 x 10'"*g m~3 . To determine the concentrations at dis-tances y from the x-axis, the ground-level con-terline concentration must be multiplied by thofactor expo-y = 157 meters at x = 1 km. Values for thiscomputation are given in Table 7-2.

Table 7-2 DETERMINATION OF CROSSWINDCONCENTRATIONS (PROBLEM 7)

These concentrations are plotted in Figure 7-2.

PROBLEM 8: For the conditions given in prob-lem 4, determine the position of the 10"fl m"*ground level isopleth, and determine its urea,SOLUTION: From the solution to problem 6, thegraph (Figure 7-1) shows that the 1Q-B g irr 3isopleth intersects the x-axis at approximatelyx = 350 meters and x =- 8.6 kilometers.



55/92

-400 -200 +200CROSSWIND DISTANCE ly), m

400

Figure 7-2. Concentration as a function of crosswinddistance (Problem 7).

The values necessary to determine the isoplethhalf widths, y, are given in Table 7-3.Table 7-3 DETERMINATION OF ISOPLETH WIDTHS

(PROBLEM 8)

The orientation of the x~axis will be toward225 close to the 'source, curving more toward210 to 215 azimuth at greater distances be-cause of the change of wind direction withheight. The isopleth is shown in Figure 7-3.Since the isopleth approximates an ellipse, thearea may be estimated by * ab where a is thesemimajor axis and b is the semiminor axis.

a 86QO-350_ _ 4125 m2A (m2 ) = TT (4125) (902)

-=11.7xlOm 11or A = 11.7 km-

SOUftCE

Figure 7-3. Location of the 10"a g m" 3 ground-level iso-

pleth (Problem 8).

PROBLEM 9: For the conditions given in problem4, determine the profile of concentration withheight from ground level to z = 450 meters atx = 1 km, y meters, and draw a graph ofconcentration against height above ground.

SOLUTION: Eq, (3.1) is used to solve this prob-lem. The exponential involving y is equal to 1.At x = 1 km, try = 157 m, ^ = 110 m. (Fromproblem 4) .

Q 151(110) 4 3.5

x 10" g n

Values for the estimation of x(z) are given inTable 7-4.

PROBLEM 10: For the conditions given in prob-lem 4, determine the distance at which theground-level centerline concentration equals thecenterline concentration at 150 meters aboveground. Verify by computation of x (x>0 30)and* (x,0,150).

SOLUTION: The distance at which concentra-tions at the ground and at plume height areequal should occur where


56/92

Table 7-4 DETERMINATION OF CONCENTRATIONS FORVARIOUS HEIGHTS (PROBLEM 9)

d. f.

]z+Hf 1 / z+H Vl"M ) j is a function

Values of the parameters and of x al'e given inTable 7-9.

Table 7-9 DETERMINATION OF CONCENTRATION AS AFUNCTION OF DISTANCE (PfiOBLEM 26)

These values of x are graphed as a function of xin Figure 7-7. The downwind concentrationdrops below the critical value of 2.5 x 10~- at adistance of 6.5 km.100

10SCo

,-IU

Nx

0.1 1

DISTANCE, Vm10

Figure 7-7. Concentration of UDMH as a function of down-wind distance (Problem 26).Calculated widths within a given isopleth aresummarized in Table 7-10.The maximum width of the area encompassedby an isopleth is about 140 meters from thedownwind position. Since the wind direction isexpected to be from 310itl5 , the sector at anazimuth of 115 to 145 plus a 140-meter rectan-gle on either side should be evacuated.See Figure 7-8,

Example Problems 55


64/92

Table 7-10 DETERMINATION OF WIDTHS WITHINISOPLETHS (PROBLEM 26)

SCALE, km

Figure 7-8. Possible positions of the 2.5 x 10~a g m'isopleth and the evacuation area (Problem 26).



65/92

APPENDICES


66/92


67/92

Appendix 1: ABBREVIATIONS AND SYMBOLSAbbreviationscal calorieg gramK degrees Kelvinni meterrnb millibarsec second

Syml)ola ratio of horizontal eddy velocity to vertical

eddy velocityc,, specific heat at constant pressureC y Sutton horizontal dispersion parameterCE Sutton vertical dispersion parameterd inside stack diameter at stack topDT (x,y,0;H) Total dosagee 2.7183, the base of natural logarithmsf (0,S,N)hh,H

KL

frequency of wind direction for a givenstability and wind speed class

physical stack heightheight of the base of an inversioneffective height of emissioneffective height of emission for a particularwind speedvon Karman's constant, approximately equalto 0.4eddy diffusivitytwo uses: 1. the height of an air layer that is

relatively stable compared to thelayer beneath it; a lid

2. the half-life of a radioactivematerial

Sutton's exponentan index for wind speed classthree uses: 1. Bosanquet's horizontal disper-

sion parameter2. atmospheric pressure3. a dummy variable in the equa-

tion for a Gaussian distribution.q two uses: 1. Bosanquet's vertical dispersionparameter

2. emission rate per length of a linesource

emission rate of a sourcetotal emission during an entire releasenet rate of sensible heating of an air columnby solar radiationthe length of the edge of a square area sourcean index for stabilitya short time period

t,,,

TT,uUsv'vv*w'X

x*

yzz, tSOSz"AHn

"XL

time required for the mixing layer to developfrom the top of the stack to the top of theplumea time periodambient air temperaturestack gas temperature at stack topwind speeda mean wind speed for the wind speed class N.horizontal eddy velocitystack gas velocity at the stack topa velocity used by Caldervertical eddy velocitydistance downwind in the direction of themean winddesign distance, a particular downwind dis-tance used for design purposesthe distance at which er = 0.47La virtual distance so that a* (xx ) equals the ini-tial standard deviation, vxoa virtual distance so that o> (xr ) equals the ini-tial standard deviation, o>a virtual distance so that aK (xa) equals the ini-tial standard deviation,


68/92

the angle between the wind direction and aline sourceconcentration

wi crosswind-integrated concentrationa ground-level concentration for design pur-posesinversion break-up fumigation concentrationconcentration measured over a sampling time,tk

(S maximum ground-level centerline concentra-tion with respect to downwind distance

XK concentration measured over a sampling timetay~ relative concentrationy

relative concentration normalized for windspeedX (x,y,z;H) concentration at the point (x, y, z)from an elevated source with effectiveheight, H.X (x,o) the long-term average concentration atdistance x, for a direction from a source.



69/92

Appendix 2: CHARACTERISTICS OF THEGAUSSIAN DISTRIBUTIONThe Gaussian or normal distribution can be de-

picted by the bellshaped curve shown in Figure A-l.The equation for the ordinate value of this curve is:exp (A.1)

Figure A-2 gives the ordinate value at any distancefrom the center of the distribution (which occursat x) This information is also given in Table A-l.Figure A-3 gives the area under the Gaussian curvefrom ^ to a particular value of p where p =

This area is found from Eq. (A.2):

Area ( x to p) =exp ( 0.5 p'

J) dp (A.2)

Figure A-4 gives the area under the Gaussiancurve from p to -fp. This can be found from Eq.(A.3):

Area ( p to -}-p)

exp ( 0.5 p 2 ) dp (A.3)

-3

Figure A-l. The Gaussian distribution curve.

Appendix 261


70/92

0.01

2 :

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1,3 2.0 2.2 2.4 2.6 2.6 3.0 3.2 3.4 3.6 3.6 4.0

Figure A-2. Ordinate values of the Gaussian distribution.



71/92

0.01 0.1 0.5 1 Z 5 10 20 40--hp

80 90 95 98 99 99.8 99.99

U BXp (-0.5 p) dpr+J -

Figure A-3. Area under the Gaussian distribution curve from to p.

Appendix


72/92

0.01 0.5 1 2 5 10 20 30 40 50 60 70 80 90 95 98 99+p =- axp (-0.5 p2 ) dpP

99.8 99.99

Figure A-4. Area under the Gaussian distribution curve between p and +p.



73/92

Appendix 3: SOLUTIONS TO EXPONENTIALSExpressions of the form exp [-0.5 A8 ] whereA is H/a, or y/tfv frequently must be evaluated.

Table A-T'JvesB as a function of A where B - plo.5 A"]- The sign and digits to the right of theE are to be considered as an exponent

o 10. Forexample, if A is 3.51, B is given as 2.11E - Odwhich means 2.11 x 10 *

Appendix 3


74/92

o o o o o (MIMIMMCM (MCMIMCMM (OflflOCl



75/92

cocotococc, coojcomco

ppendix 3


76/92


77/92

Appendix 4: CONSTANTS, CONVERSIONEQUATIONS, CONVERSION TABLES

Constants

e = 2.7183 -J_ = 0.3679= 3.1416 L- = 0.3183T

27r = 6.2832 i = 0.15922?r

57= 2.5066 -= = 0.3989V27T^r = 0.7979

(Sir) 3/'-= 15.75Conversion Equations and Tables

T(C) =5/9


78/92


79/92

J >-l|O O >^BO tn JS *U1 -01 -UJ -UJ -UJ -UJ UI -UJ *UJ , Zw *Z M UJvrn ^1 * O O f1- * *O O1 VJ 3Em S r-. ^ fO -J- OJ - CO 00 -O W * * m .- I in m -i m ra zo< Oi "UJ UJ UJ UJ " Ul *U1 *UJ UJ UJ -J Za: U3 ô ^< H *** * f~ m ^* *o

z u tj .O UJ .1*** *" 13 w1/10:0 r- co * o* o 0*0 o ^t^=.Minuj oo -ON r--* r-rj o>o o--i o*m OCM ^* -i^3-3ro_ oo -00 rô mo mo -a o -*o MO moui** o *oi P- i -l IA rj (Mi m o soa -bJ -uj -iii -tij .uj -uj -UJ -uj .UJ ouj|V3 ^î(xjr4r--inM- KOCnS !^"* ZiU D < UlU. O rf Hui m ^-3-o"-u z a > z a > a >tt^Si B S ^ S 2u,| S ^S a & S " ^S ^ S"I > " 1- ^ a m^ *S -^ â SA U oS^sSS555^ Ul QCZ > IUO - B-*J U IUX

oo *cOO 1*lLloo mOo UJ

O


81/92

a -** r-PO O-* iUJIXJ

r- or-J 1

LU-*O CMCO O

mon.CLOof.o

LUX

OO Oo> oa

OOu_

Xu

Oi/l

osO -ftt> OUJ

OO Oift O

oo *o ooa UJ

OO

o Oo -o UJ

oB>LU

o mr- o1Ui

OO *-tin om iUJ

OOo oo

oo -*--to

oOo UJ

c** o10

i Iill!

o00o UJ

oo rst** LU

Oooo oo UJ

oo oooo UJo-o-o *in o

* oo UJ

o oo LU

h- r-aa O

in^r o-^ oo LU4-

O O

o?- *oo ow-t LU

Oo t~o* oo LUtn

in,m er(M Om LUin

in-j- otn -H

ffl

UJ

ZLU> DC>-H UJCJ 3OuJ axi- xX>- I_lO, LUo

^ mn zo LULU 1OCm xLU iO UJ

OmOo o(M BLUO-

o on iLU or>J i

(O-i --i*CO BLUCO

OO *Oo> o1A IUIM

m o4- UJ

mzz> a:UJZ I-LU LU> H

in

VJo ooou.oin oin

LUOftj

aZUJ

to -


82/92

UJI14_J

Oc oo ocUJ

oI

' LUo

' UJm oa- iLU

n Dm o - uo

fITO

co oc co Uj Y! C1

t) I

inm rvio in mcc. or- iLu E; aOLU

u. t-U U,' I

OLJ

QLU

=3kJ

GL

U.!-J O '=J_J Iu,in

o-jZ LUamu D

74 ATMOSPHERIC DISPERSION ESTIIVL


83/92

aaUJuz

OIM Itil(M

f-IM Oin t

-o*OCM LUf\l

f- 1-1(M O

oj- mo o

f- *M O

oo oOo UJ(M

o *fy LUtn

oo mJtM UJ(M

O* d-co am LU

CO J-N OJ- 1LU

in eooo o

DO fMm oJ 1*tuD

OO OOo IU

oo oo oo

OO -to oUJ

Z1IU

LUx

PPOS

-* oin UJm in*in iLJ

CMm st*ma UJoo r-O* UJ

DCD r->o oin UJOO OOo LU

Din CMf~m LU

oo mo oo LUf-

CM r-* O f *-*to IHitr-

(M **00 t* LUa*

o1LUDO >-4M O0* 1LUno

oooo oo LU

inr- vdr-l Oo UJ

O tMr- o* 1UJa

Kl QCO UJfJ

o-in OJrt O OLUcc ex.

CONVE

LULU-1< LU

s: zZ UJomu DZ

idix 4 75


84/92



85/92

Appendix 4 77


86/92

ZUlo

oarmtt UlUl Q.CL Z15J MOas:m a:uuiLU CL

CL.

Oftx.LU

LUa. LUa:CD uoaaraaiiuLU a.CLIMIL.Oa o

< a: a:| LU LUtn D-Q.

a x:oKO

oLU a.a. u

tn o4- ILUUJm

om oCM oLUm

* oUl

oo oo oo Ul

CD fMifi *Ocr Ul

m oaa ui

inCM enCJ O

oo oo oo*LU

OCM CM>- O

O Oin iUl in oo Ul

-i CMen oIM BUJ

mr-M* oUJ

oo oo oo LU

r*i -J~iv oO Ia UJrn

oO *~to oCM Ul

CDO CMPJ OU)

* O4- O

oo oo ooA UI

mtno o*> UJo

r- CMCM O

Ul

o ot- oo Ul

oo oo oo UJ

oO r-l* o-* BUl

ca -CO Otr\ UJ

mO> flr- oO BUlin

CMm o(M OUl*

oO r-lm otn iUl

Ul

Ul

or-aUlICOUJ-1

zUl .i-t LU10 Xoui aX- XX>- If-ICLUIDO-OI- I*Hz mDZOldU13EDCm xLU BOUI

o aro:a LUUJ CLCLu-

Or-. Ot~ as:- inm o:o ocuia. UJO.LU a.Q X

Oo mo oo Ul

oo oo oo

oo oo oo LU

oo mo oO Bexo

zotna:LUZo

\*r

oLUa:LU

Oo *o oo

oO --Io oo III

*M rvo oin UIm

o om

m oo

inH (Ntirvoo ui

o CMCM O si-^ ttf-r- oooO i

O r-*MO

Ul

Oooin o

t-uizo

U) r-lZ< nouioca:u.-zZUJODDVJoz

78 ATMOSPHERIC DISPERSION ESTIMAT


87/92

m

2;Ul

oruOfUl

Ula:

om CM\f\ o

UlM

O r-lO Oirt iUJr~

om -4a\ oOf Ul

OCMO Oino HIOO (MO ONO Ult-

om m(ft Oo- a

oo -*o oin aui

ONtn --4Q^ O00 UlMi

in CMm-o

oNO OCO OooUI oBUl

oo oo oo Ul

oo oo oo UJ

oo -* oUJCM

Ifl

UlX

oa.n.oUO

UlXott

aina:UJOL

Otnui az ui>- a.QUlo:UJXatno

O (Min o* iUl

O CO.H OO IUJ

oO 10o oo UJ

IM*O OOO IUlO

*O r-m o*o ui

r-0* o-H OO tu

oo -oo ooa Ul

IMO* *-*O O00 >Ulo*

O OJ-aUl

fMCO OfOOo

oo oo oo Ul

*OtfXin o

-4 oO I

oO Oo oo Ul

oo aUlo

mrg r-iCM! O

oo oo oo Ul

o otn ui

OO r->r- o

ao oo oo

J-O tMto oO 9Ul

*f CMO O00 BUl

fO fMCO O0> BUl

mo* rom om Bui

CM(O fOCO Om ui

i oCO Iui

irvH r-4r-4 O(J, B

Ul

CMm CMin oNT rutm

-**c *^00 OfO Ul

IM CM* Om iUii*>

zUlMUIV> 3COut a.Xr- XX>- BLUI

Ot-or) za uia:O XUt B

UittninuiDCa.

ino:oF-uu.

mauizo

oO Oo oO Iui

oo oo ooUJ

oo oo oo Ul

oo mo ooui

C"l O-4 Oo Ul

r-l OoUl

oC-1 *Oo oO IUl

oo*nOOO BUJ

oOO00 IUlo-NOO No o

o oO) BUl

o-o00Ul

IMfl F>m ofO IUl

CMCO OfO OCO*U1

O CMCO Oro IUlm

n oUl10

O Xr- Ulz o

O Ulat amUt UJzz>aatnUJa

uioc

a.inoVJa M QCa a uOi

att ecui m tuto a. ma.

ctaua:ui

-i


88/92

inr

O Zm !3fg * o o .-4 Q >o N orgh- o m *m m ~4 t- ~* o - o>-4 NO oo arct -ico o _jom * oro* w - Kz a i-


89/92

Appendix 4 81


90/92

-Jr-CD

z^UJ. | "3*-,!.^, ZUJZ > yj V i o tQo Z" 1 3 3 S S^ ^ U U fcH



91/92

zrIU

IUXUl

o(Laoaot-uLUX

if) 3E ^-U1U ^o m in m f- f- o w 3f~> mo mo mo OM oo oD: mo no mo oo oo ui CLin ui r-* --< *o o xCQ CL LU LU LU *LU LU I- X< *


92/92

Vl

THE

moa.a.r ou*- Of.t- a a^ *~4 tf m ^) i^ o ^ _jH- t~ UI UJ BUI UI *UI "UJ LU a z zl/l -t LUs: > o:Q >-4 UJujoc m in in * o m co ID 3Q.UI i-rn oo *** m *~* oa. -* o coo coo in o oo * o coo UJ n.r> (Mi* .o inio OÎPJ xt h- U) BUI 'Ul Ul "UJ UJ wtU H- X(QU.(vi tn m CM >- -o m xa > j *tn < Q.IU

7 a: i- 1-LU UIQi OOOOMmm _1QQ.UI oo om ow oo r-M mî ** noa. -*o ^-o *to oo oo ~lLl *U1 *ILJ UJ I_J *0 ^H ^ vD (M rH ^ d Uit a z tf Û3 m -. ^.* O 1< Of >_ |_UJ Df o o o * fn m i/\-a.uj om oo oo -t* tn ** ** m^ i LU*H a. oo oo oo 'to -to wo mo M*-z_j or o o o-i r-> coi ^- zo13 *- ^ w -* OM o.*n -10O a. oo jjo *o mo wo ^-o oooa--* o * * - m .* i m s;a< SI LU UJ LU >LU LJ LU .fcj oujI U i-* -f P4 c-4 4- m fy

Date post:	06-Apr-2018
Category:	Documents
Upload:	alon-mandel
View:	213 times
Download:	0 times

Turner Workbook

Documents