AIRPOLLUTION 491 tration, the direct radiative effect of increasingCO2 aloneis not sufficient to explain currenttrends that showan increasein nighttime temperaturesbut not an increasein daytime highs.45The input sourcesof greenhousegases and their sinks are not yet well described.The measurementof temperatureon a global basisis not sufficiently uniform in technique and separatedfrom local influence to separatethe "noise" of local variability from true trends. Natural changessuch as increasesin cloud cover may not have been accuratelydepicted in existing models of climate change. In general, projections of global warming have been based on assumptions regardingthe growth of greenhousegases. If it is assumedthat they will continue to grow exponentially, by the year 2040 the change in atmosphericconcentration of greenhousegases would be the equivalentof doubling of the CO2 concentrationfrom its preindustrial level. It is this doubling that leads the National ResearchCouncil to estimatea temperaturerise of 10to 5°C.46In anotherprojection of emissionsby the IntergovernmentalPanel on Climate Change,global temperaturesare expected to rise between0.80 and 3.5°C by 2100.47Obviously, there is still considerabledis- agreementabout the potential for global warming. On the other hand, the conse- quencesof ignoring thesetrends are sufficiently dramatic that intensive researchwill continue in the nextdecade. Even without the risks of climate change,improvements in energy efficiency to reduce CO2 emissionsand to eliminate CFCs are justified. The expectationof damagesfrom climate changeprovides a rationale for pursuing theseprograms vigorously.
6-7 AIR POLLUTION METEOROLOGY The AtmosphericEngine The atmosphereis somewhatlike an engine. It is continually expandingand com- pressinggases, exchangingheat, and generally raising chaos. The driving energy for this unwieldy machine comesfrom the sun. The difference in heat input between the equatorand the poles provides the initial overall circulation of the earth's atmo- sphere.The rotation of the earth coupled with the different heatconductivities of the oceansand land produce weather.
Highs and lows. Becauseair hasmass, it alsoexerts pressure on things underit. Like water, which we intuitively understandto exert greaterpressures at greaterdepths, the atmosphereexerts more pressureat the surfacethan it does at higher elevations.The highs and lows depicted on weathermaps are simply areasof greaterand lesserpres- sure. The elliptical lines shown on more detailed weathermaps are lines of constant pressure,or isobars. A two-dimensionalplot of pressureand distancethrough a high- or low-pressuresystem would appearas shownin Figure 6-11.
4SG.Kukla and T. R. Karl, "Nighttime Warming and Ihe GreenhouseEffect," Environmental Science and Technology,27, pp. 1468-1474, 1993. 46L. B. Lave and H. Dow1atabadi,"Climate Change: The Effects of Personal Beliefs and Scientific Uncertainty," Environmental Science and Technology,27, pp. 1962-1972, 1993. 47C&ENews. p. 20, August 28,1995. 492 INTRODUCTIONTOENVIRONMENTAL ENGINEERING I Y r .-t A A
I X I p -""~=~~~"--O 2.8 102.4 102.0kPa A A X (a)
Y
("E~~\,~~~~=~~~ t B
X
P B~:::::~~~~7fO1.2 k Pa B 100.8 100.4
X FIGURE 6.11 (b) High and low pressuresystems.
The wind flows from the higher pressureareas to the lower pressureareas. On a nonrotatingplanet, the wind direction would be perpendicularto the isobars(Fig- ure 6-12a). However, since the earth rotates, an angular thrust called the Coriolis effect is added to this motion. The resultant wind direction in the northern hemi- sphereis as shown in Figure 6-12b. The technical namesgiven to thesesystems are anticyclonesfor highs and cyclonesfor lows. Anticyclones are associatedwith good weather.Cyclones are associatedwith foul weather.Tornadoes and hurricanes are the foulest of the cyclones. Wind speedis in part a function of the steepnessof the pressuresurface. When the isobarsare closetogether, the pressuregradient (slope)is said to be steepand the wind speedrelatively high. If the isobarsare well spreadout, the winds are light or nonexistent. AIRPOLLUTION 493 I
r
--<~~~~~~~),,'" If t \ ,. .~ '" (a) Anticyclonewithout Coriolis effect
---<:::::~~~~~~\.:,I"'/.,1,,/J
---"'.,1.,1 FIGURE 6-12 (b) Anticyclone with Coriolis effect Wind flow due to pressuregradient.
Thrbulence Mechanical turbulence. In its simplest terms, we may considerturbulence to be the addition of randomfluctuations of wind velocity (that is, speedand direction) to . the overall averagewind velocity. Thesefluctuations are caused,in part, by the fact that the atmosphereis being sheared.The shearingresults from the fact that the wind speedis zero at the ground surfaceand rises with elevationto nearthe speedimposed by the pressuregradient. The shearingresults in a tumbling, tearing motion as the massjust abovethe surfacefalls over the slower moving air at the surface.The swirls thus formed are called eddies.These small eddies feed larger ones. As you might expect, the greater the mean wind speed,the greater the mechanical turbulence. The more mechanicalturbulence, the easierit is to disperseand spreadatmospheric pollutants. Thermal turbulence. Like all otherthings in nature,the rather complex interaction that produces mechanical turbulence is confounded and further complicated by a 494 INTRODUCTIONTO ENVIRONMENTALENGINEERING third party. Heating of the ground surfacecauses turbulence in the samefashion that heatingthe bottom of a beakerfull of water causesturbulence. At somepoint below boiling, you can see density currents rising off the bottom. Likewise, if the earth's I surface is heated strongly and in turn heatsthe air aboveit, thermal turbulence will be generated.Indeed, the "thermals" soughtby glider pilots and hot air balloonists are thesethermal currents rising on what otherwise would be a calm day. The conversesituation can arise during clear nights when the ground radiates its heat away to the cold night sky. The cold ground, in turn, cools the air aboveit, causinga sinking density current.
Stability The tendency of the atmosphereto resist or enhancevertical motion is termed sta- bility. It is related to both wind speedand the changeof air temperaturewith height (lapse rate). For our purpose,we may use the lapse rate alone as an indicator of the stability condition of the atmosphere. There are three stability categories.When the atmosphereis classified as un- stable,mechanical turbulence is enhancedby the thermal structure. A neutral atmo- sphereis one in which the thermal structure neitherenhances nor resistsmechanical turbulence. When the thermal structure inhibits mechanical turbulence, the atmo- sphereis said to be stable. Cyclones are associatedwith unstable air. Anticyclones are associatedwith stable air.
Neutral stability. The lapse rate for a neutral atmosphereis defined by the rate of temperatureincrease (or decrease)experienced by a parcel of air that expands (or contracts) adiabatically (without the addition or loss of heat) as it is raised through the atmosphere.This rate of temperaturedecrease (dT/dz) is called the dry adia- batic lapse rate. It is designatedby the Greek letter gamma (f). It has a value of approximately -1.00°C/100 m. (Note that this is not a slope in the normal sense, that is, it is not dy/dx.) In Figure 6-13a, the dry adiabatic lapse rate of a parcel of air is shownas a dashedline and the temperatureof the atmosphere(ambient lapse rate) is shown as a solid line. Since the ambient lapse rate is the same as f, the atmosphereis said to have a neutral stability.
Unstable atmosphere. If the temperatureof the atmospherefalls at a rate greater than f (for example, -1.01°C/100 m), the lapse rate is said to be superadiabatic, and the atmosphereis unstable. Using Figure 6-13b, we can see that this is so. The actual lapse rate is shown by the solid line. If we capture a balloon full of polluted air at elevation A and adiabatically displace it 100 m vertically to elevation B, the temperature of the air inside the balloon will decreasefrom 21.15° to 20.15°C. At a lapse rate of -1.25°C/100 m, the temperatureof the air outside the balloon will decreasefrom 21.15° to 19.90°C. The air inside the balloon will be warmer than the air outside; this temperaturedifference gives the balloon buoyancy. It will behave as a hot gas and continue to rise without any further mechanical effort. Thus, me- chanical turbulence is enhancedand the atmosphereis unstable.If we adiabatically displace the balloon downward to elevation C, the temperatureinside the balloon AIRPOLLUTION 495
Volume at Rest T = 20.15 Same Temperature as Surroundings 400 ,/Dry Adiabat = r '" Displaced " 100 m e 300 ~ ~1;1t, i I Displaced co A b. t rd 100 m ~.-mIen 200 Lapse Rate Ambient cccR)", Volume at Rest 1 00 C/l00 T = 22.15 'c"'Z~',. SameTemper.ature 100 -AI-~Z' = - . m ,"cc" as Surroundmgs ~n 19 20 21 22 Temperature (OC) (0)
500 V I C 0 ume onhnues. Warmer ./ to Rise 400 ',#" Dry Adiabat = r Ambient i'}~'~c,,::i,'~ -B', T = 19.90 "i:-.~'}'_B :g 300 ~':::L"""'~, "" ""c ".., ,i.~', , 19 20 21 22 Temperature (OC) (b) 500 Ambient Volume Displaced T = 20.65 Upward 100 m 400 B'" -', , " \ ---v Volume ~ " v ":c"v Cooler Restored .E 300 -A I ~ A-i~t.itSCcC to Original -DAd' b t -r ~ ' " ccCCCc Warmer Leve I and ~ ry la a-", " !!J!i"~;,,'-:-- Temperature :I: 200 " C!;"C;CCC7~'!"'... -C / " :ii:::i;c~:1t~;;}!C A b' ,Ambient'" m lent T = 21.65 Volume Displaced 100 Lapse Rate Downward 100 m -£2~T = -0,5 "CIl00 m I~. Jl )~ ( 19 20 21 22 Temperature (OC) Icl FIGURE 6-13 Lapse rateand displacedair volume. (Source:Atomic Energy Commission, Meteorologyand Atomic Energy,Washington, DC: U.S. GovernmentPrinting Office, 1955.) AIRPOLLUTION 497 Plume types. The smoke trail or plume from a tall stacklocated on flat terrain has beenfound to exhibit a characteristicshape that is dependenton the stability of the atmosphere.The six classical plumes are shown in Figure 6-14, along with the cor- respondingtemperature profiles. In eachcase, r is given as a broken line to allow Wind ,..' . t\ ';:'::t,.i..;.'..'~.;.;~:.~i-.;,:.,.,.."',.! 1: ,',;."".'.."(,.".:..:.,.i..':':..'::.':.;.:( ."..::::':.:::,.'..,' Z ~r' ".:"!'(~i;~~';~;.'~';;~i;:l:::'\::;:.',:::~::'~~..,,::.,'i' T --Strong Lapse Condition (Looping) t;l ". ,.,.' '.' ,..,' ,..,.,;' ".' ,:":,,, .,',",.', :..: . t \ ""',,',.,",,: ' ,. .' . Z r' "'."":""::'::'::::..::"':'::"',:..:::,;:..':.::',:..:::::.~,..::.::':'..- T -Weak Lapse Condition (Coning) Zt ~ \ / [~~.""'._."'.,..., ..'. ". ',..' .."'".."...' ..., ..,..." T -Inversion Condition (Fanning) t ~ \ \.::"::..:.;.:.~;:::~:;;~::.' Z~ " ,' '.' T -Inversion Below, Lapse Aloft (Lofting) t ~,( "" .,.. .,. .'" .."..." '.,..' '..., "". Z~ ..::'~.:.:':;~:'::.:...'. T -Lapse Below, Inversion Aloft (Fumigation) t \ ...'.' ...' '..'.,".' ".,.,:.;,;,.~.,.:".:'."".:"'.""...',;"'. .,., ...' ..'" " Z ~r' , : ::..:: ::..;:.::..:::: T --Weak Lapse Below, Inversion Aloft (Trapping) FIGURE 6-14 Six typesof plumebehavior. (Source: P. E. Church,"Dilution of WasteStack Gases in the Atmosphere,"lndustrialEngineering Chemistry, vol. 41,pp. 3753-3756,1949.) 498 INTRODUCTIONTO ENVIRONMENTALENGINEERING comparisonwith the actual lapse rate, which is given as a solid line. In the bottom three cases,particular attentionshould be given to the location of the inflection point with respectto the top of the stack. Terrain Effects Heat islands. A heat island results from a mass of material, either natural or an- thropogenic, that absorbsand reradiatesheat at a greaterrate than the surrounding area. This causesmoderate to strongvertical convectioncurrents abovethe heat is- land. The effect is superimposedon the prevailing meteorologicalconditions. It is nullified by strong winds. Large industrial complexes and small to large cities are examplesof places that would have a heatisland. Becauseof the heatisland effect, atmosphericstability will be less over a city than it is over the surroundingcountryside. Depending upon the location of the pol- lutant sources,this can be either good news or bad news. First, the good news: For ground level sourcessuch as automobiles,the bowl of unstable air that forms will allow a greaterair volume for dilution of the pollutants. Now the bad news: Under stable conditions, plumes from tall stackswould be carried out over the countryside without increasing ground level pollutant concentrations.Unfortunately, the insta- bility causedby the heatisland mixes theseplumes to the ground level. Land/sea breezes. Under a stagnatinganticyclone, a stronglocal circulation pattern may develop acrossthe shoreline of large water bodies. During the night, the land coolsmore rapidly than the water.The relatively coolerair overthe land flows toward the water (a land breeze,Figure 6-15). During the morning the land heatsfaster than water. The air over the land becomesrelatively warm and begins to rise. The rising air is replaced by air from over the water body (a sea or lake breeze,Figure 6-16). FIGURE 6-15 Land breezeduring the night. AIRPOLLUTION 499 ~--,.. '" 1/ / -0- WamIAir overLand \ / I '" " Rises\ ) Air -A LakeBreeze WamI ~- '.":-'~ ~ ~-,-' /' --,( --~ ~- ~\ "" \."\\ ~""' FIGURE 6-16 Lake breezeduring the day. The effect of the lake breezeon stability is to imposea surface-basedinversion on the temperatureprofile. As the air moves from the water over the warm ground, it is heated from below. Thus, for stack plumes originating near the shoreline, the stablelapse rate causesa fanning plume close to the stack (Figure 6-17). The lapse condition grows to the height of the stack as the air moves inland. At some point inland, a fumigation plume results. Valleys. When the general circulation imposes moderateto strong winds, valleys that are oriented at an acuteangle to the wind direction channelthe wind. The valley z~ zLL T T -u Several km Fumigation " : '.-".:';::':...,:..~t:;!.;:::;,;,:~,,";:: ,:,:,:;:::,.::..,.:::: :",.;.:,;".';-":'::-:"'.;;:.'Y;" ."" , ,.' Fanmng :.::... ..~.'.::::~j,::,:. FIGURE 6-17 Effectof lakebreeze on plume dispersion. 500 INTRODUCnON TO ENVIRONMENTALENGINEERING effectively peelsoff part of the wind and forces it to follow the direction of the valley floor. Under a stagnating anticyclone, the valley will set up its own circulation. Warming of the valley walls will causethe valley air to be wanned. It will become more buoyant and flow up the valley. At night the cooling process will causethe wind to flow down the valley. Valleys oriented in the north-southdirection are more susceptibleto inversions than level terrain. The valley walls protect the floor from radiative heating by the sun. Yet the walls and floor are free to radiate heat away to the cold night sky. Thus, under weak winds, the ground cannot heat the air rapidly enoughduring the day to dissipatethe inversion that formed during the night. 6-8 ATMOSPHERIC DISPERSION Factors Affecting Dispersion of Air Pollutants This discussionfollows the training documentsof the Texas Air Quality Control Board. The factors that affect the transport, dilution, and dispersionof air pollutants can generallybe categorizedin terms of the emissionpoint characteristics,the nature of the pollutant material, meteorologicalconditions, and effects of terrain and anthro- pogenicstructures. We havediscussed all of theseexcept the sourceconditions. Now we wish to integrate the first and third factors to describethe qualitative aspectsof calculating pollutant concentrations.We shall follow this with a simple quantitative model for a point source.More complex models for point sources(in rough terrain, in industrial settings, or for long time periods), areasources, and mobile sourcesare left for more advancedtexts. Source characteristics. Most industrial effluents are dischargedvertically into the open air through a stack or duct. As the contaminatedgas stream leaves the dis- chargepoint, the plume tendsto expandand mix with the ambientair. Horizontal air movement will tend to bend the dischargeplume toward the downwind direction. At some point between 300 and 3,000 m downwind, the effluent plume will level off. While the effluent plume is rising, bending, and beginningto move in a horizon- tal direction, the gaseouseffluents are being diluted by the ambientair surrounding the plume. As the contaminatedgases are diluted by larger and larger volumes of ambientair, they are eventually dispersedtoward the ground. The plume rise is affected by both the upward inertia of the discharge gas streamand by its buoyancy.The vertical inertia is related to the exit gas velocity and mass.The plume's buoyancyis related to the exit gas massrelative to the surround- ing air mass. Increasingthe exit velocity or the exit gas temperaturewill generally increasethe plume rise. The plume rise, together with the physical stackheight, is called the effective stack height. The additional rise of the plume abovethe dischargepoint as the plume bends and levels off is a factor in the resultant downwind ground level concentrations. The higher the plume rises initially, the greater distance there is for diluting the contaminatedgases as they expand and mix downward. AIRPOLLUTION 501 For a specific dischargeheight and a specific set of plume dilution conditions, the ground level concentrationis proportional to the amount of contaminantmate- rials discharged from the stack outlet for a specific period of time. Thus, when all otherconditions are constant,an increasein the pollutant dischargerate will causea proportional increase in the downwind ground level concentrations. Downwind distance. The greaterthe distancebetween the point of dischargeand a ground level receptordownwind, the greater will be the volume of air available for diluting the contaminantdischarge before it reachesthe receptor. Wind speed and direction. The wind direction determinesthe direction in which the contaminatedgas stream will move acrosslocal terrain. Wind speedaffects the plume rise and the rate of mixing or dilution of the contaminatedgases as they leave the dischargepoint. An increasein wind speedwill decreasethe plume rise by bend- ing the plume over more rapidly. The decreasein plume rise tends to increasethe pollutant's ground level concentration.On the other hand, an increasein wind speed will increasethe rate of dilution of the effluent plume, tending to lower the down- wind concentrations.Under different conditions, one or the other of the two wind speedeffects becomesthe predominanteffect. Theseeffects, in turn, affect the dis- tance downwind of the source at which the maximum ground level concentration will occur. Stability. The turbulence of the atmospherefollows no other factor in power of di- lution. The more unstablethe atmosphere,the greaterthe diluting power. Inversions that are not ground based,but begin at some height abovethe stackexit, act as a lid to restrict vertical dilution. Dispersion Modeling General considerations and use of models. A dispersionmodel is a mathematical descriptionof the meteorologicaltransport and dispersionprocess that is quantified in terms of sourceand meteorologicparameters during a particular time. The resultant numerical calculations yield estimates of concentrationsof the particular pollutant for specific locations and times. To verify the numerical results of such a model, actual measuredconcentra- tions of the particular atmosphericpollutant mustbe obtainedand comparedwith the calculated values by meansof statistical techniques.The meteorologicalparameters required for use of the models include wind direction, wind speed,and atmospheric stability. In somemodels, provisions may be made for including lapserate and ver- tical mixing height. Most models will require data aboutthe physical stackheight, the diameter of the stack at the emissiondischarge point, the exit gas temperature and velocity, and the massrate of emissionof pollutants. Models are usually classified as either short-term or climatological models. Short-term models are generally used under the following circumstances: (1) to estimate ambient concentrationswhere it is impractical to sample, such as over rivers or lakes, or at great distancesabove the ground; (2) to estimatethe required 502emergency '""000=0' source roreductions BNvmONMBNTAL associated with periods of air stagnations under air pollution episode alert conditions; and (3) to estimate the most probable locations of high, short-term, ground-level concentrations as part of a site selection evaluation for the location of air monitoring equipment. Climatological models are used to estimate mean concentrations over a long period of time or to estimate mean concentrations that exist at particular times of the day for each season over a long period of time. Long-term models are used as an aid for developing emissions standards. We will be concerned only with short-term models in their most simple application. Basic point source Gaussian dispersion model. The basic Gaussian diffusion equation assumes that atmospheric stability is uniform throughout the layer into which the contaminated gas stream is discharged. The model assumes that tur- bulent diffusion is a random activity and hence the dilution of the contaminated gas stream in both the horizontal and vertical direction can be described by the Gaussian or normal equation. The model further assumes that the contaminated gas stream is released into the atmosphere at a distance above ground level that is equal to the physical stack height plus the plume rise. The model assumes that the degree of dilution of the effluent plume is inversely proportional to the wind speed (u). The model also assumes that pollutant material that reaches ground level is totally reflected back into the atmosphere like a beam of light striking a mirror at an angle. Mathematically, this ground reflection is accounted for by as- suming a virtual or imaginary source located at a distance of -H with respect to ground level, and emitting an imaginary plume with the same source strength as the real source being modeled. The same general idea can be used to establish other boundary layer conditions for the equations, such as limiting horizontal or vertical mixing. The model. We have selected the model equation in the form presented by D. B. Turner.48 It gives the ground level concentration (x) of pollutant at a point (coordi- nates x and y) downwind from a stack with an effective height (H) (Figure 6-18). The standard deviation of the 'plume in the horizontal and vertical directions is desig- nated by Sy and Sz, respectively. The standard deviations are functions of the down- ward distance from the source and the stability of the atmosphere. The equation is as follows: X(x,y,O,H) = [~][exp[ -~(* )2]] [exp [ -~ (~)2]] (6-19) 48D. Bruce Turner, Workbook ofAtmospheric Dispersion Estimates(U.S. Department of Health, Ed- ucation and Welfare, Public Health Service, National Center for Air Pollution Control, Publication No. 999-AP-28), Washington,DC: U.S. Government Printing Office, p. 6, 1967. (Note: Turner pro- vides guidelines on the accuracy of this model. It is an estimating tool and not a definitive model to be used indiscriminately.) r:e. - AIRPOLLUTION 503 where X(x,y,O,H)= downwind concentration at groundlevel, g/m3 E = emissionrate of pollutant,glS Sy'Sz = plumestandard deviations, m u = wind speed,m/s x, y, z, andH = distances,m exp = exponentiale suchthat terms in bracketsimmediately fol- lowingare powers of e, thatis, e[] wheree = 2.7182 The valuefor the effectivestack height is the sumof the physicalstack height (h) andthe plumerise 6.H: H = h + 6.H (6-20) 6.H maybe computedfrom Holland's formula as follows:49 6.H = ~ [1.5 + (2.68 X 10-2(P)(¥)d)] (6-21) z x (x. -yo z) (x. -y, 0) FIGURE 6-18 Plume dispersion coordinatesystem. [Source: D. Bruce Turner, Workbook ofAtmospheric Dispersion Es- timates (U.S. Department of Health, Education and Welfare, Public Health Service, National Center for Air Pollution Control, Publication No. 999-AP-26), Washington,DC: U.S. Government Printing Office, 1967.] 49J.Z. Holland, A Meteorological Survey of the Oak Ridge Area (U.S. Atomic Energy Commission Report No. ORO-99), Washington,DC: U.S. Government Printing Office, p. 540,1953. ~ , 504 INTRODUCTIONTO ENVIRONMENTALENGINEERING where Us = stackvelocity, m/s d = stackdiameter, m u = wind speed,m/s P = pressure,kPa T s = stacktemperature, K T a = air temperature,K The values of Syand Szdepend upon the turbulent structure or stability of the atmo- sphere.Figures 6-19 and 6-20 provide graphical relationships betweenthe down- 10,0 5,00 2,00 1,000 5 ~ 20 e -150" t/) 1 50 20 15 10 .- 5 4 - 3 2 3 4 5 20 100 Distance Downwind [kIn) FIGURE 6.19 Horizontal dispersion coefficient. [Source: Turner, Workbook of Atmospheric Dispersion Estimates (U,S. Department of Health, Educationand Welfare; Public Health Service,National Centerfor Air Pol- lution Control, PublicationNo. 999-AP-28), Washington,DC: U.S. GovernmentPrinting Office, 1967.J ,~ AIR POLLUTION 505 5,00 3,00 2,00 1,00 50 40 30 2 10 :g- o C/) 5 40 30 20 ./ 1 4 3 1, ..2.3 .4 .10 20 Distance Downwind (km) FIGURE 6-20 Vertical dispersioncoefficient. (Source: Turner, Workbook ofAtmospheric Dispersion Estimates.) wind distance x in kilometers and values of s y and sz in meters.The curves on the two figures are labeled "A" through "F." The label "A" refers to very unstableatmo- spheric conditions, "B" to unstableatmospheric conditions, "c" to slightly unstableC conditions, "D" to stable oonwtions, "E" to stableatmospheric conditions, 506 INTRODUCTIONTO ENVIRONMENTALENGINEERING TABLE 6-6 Key to stability categories Day" Night" Surface wind Incoming solar radiation speed (at 10 m) Thinly overcast or (m/s) Strong Moderate Slight ~ 4/8 Low cloud ~ 3/8 Cloud <2 A A-B B 2-3 A-B B C E F 3-5 B B-C C D E 5-6 C C-D D D D >6 C D D D D a The neutral class, D, should be assumedfor overcastconditions during day or night. Note that "thinly overcast" is not equivalent to "overcast." Notes: Class A is the most unstable and class F is the most stable class consideredhere. Night refers to the period from one hour before sunsetto one hour after sunrise. Note that the neutral class, D, can be assumedfor overcast conditions during day or night, regardlessof wind speed. "Strong" incoming solar radiation correspondsto a solar altitude greater than 6()° with clear skies; "slight" in- solation correspondsto a solar altitude from 150 to 350 with clear skies. Table 170, Solar Altitude and Azimuth, in the Smithsonian Meteorological Tables, can be used in determining solarradiation. Incoming radiation that would be strong with clear skies can be expected to be reduced to moderatewith broken (5/8 to 7/8 cloud cover) middle clouds and to slight with broken low clouds. Source: D. Bruce Turner, Workbook ofAtmospheric Dispersion Estimates. and "F' to very stable atmosphericconditions. Each of these stability parameters representsan averagingtime of approximately3 to 15 min. Other averagingtimes may be approximatedby multiplying by empirical con- stants, for example, 0.36 for 24 hours. Turner presenteda table and discussionthat allows an estimate of stability basedon wind speedand the conditions of solar radi- ation. This is given in Table 6-6. For computer solutions of the dispersion model, it is convenientto have an algorithm to expressthe stability classlines in Figures 6-19 and6-20. D. O. Martin50 TABLE 6-7 Values of a, c, d, and! for calculating Syand Sz x~lkm x~lkm Stability class a cd/ cd/ A 213 440.8 1.941 9.27 459.7 2.094 -9.6 B 156 100.6 1.149 3.3 108.2 1.098 2 C 104 61 0.911 0 61 0.911 0 D 68 33.2 0.725 -1.7 44.5 0.516 -13 E 50.5 22.8 0.678 -1.3 55.4 0.305 -34 F 34 14.35 0.74 -0.35 62.6 0.18 -48.6 Source:D. O. Martin. soD.O. Martin, Comment on the Change of ConcentrationStandard Deviations with Distance,Journal o/the Air PollutionControl Association, 26, pp. 145-146,1976.