6-7 AIR POLLUTION METEOROLOGY The Atmospheric Engine

Transcription

1 AIR POLLUTION 491 tration, the direct radiative effect of increasing CO2 alone is not sufficient to explain current trends that show an increase in nighttime temperatures but not an increase in daytime highs.45 The input sources of greenhouse gases and their sinks are not yet well described. The measurement of temperature on a global basis is not sufficiently uniform in technique and separated from local influence to separate the "noise" of local variability from true trends. Natural changes such as increases in cloud cover may not have been accurately depicted in existing models of climate change. In general, projections of global warming have been based on assumptions regarding the growth of greenhouse gases. If it is assumed that they will continue to grow exponentially, by the year 2040 the change in atmospheric concentration of greenhouse gases would be the equivalent of doubling of the CO2 concentration from its preindustrial level. It is this doubling that leads the National Research Council to estimate a temperature rise of 10 to 5 C.46 In another projection of emissions by the Intergovernmental Panel on Climate Change, global temperatures are expected to rise between 0.80 and 3.5 C by Obviously, there is still considerable disagreement about the potential for global warming. On the other hand, the consequences of ignoring these trends are sufficiently dramatic that intensive research will continue in the next decade. Even without the risks of climate change, improvements in energy efficiency to reduce CO2 emissions and to eliminate CFCs are justified. The expectation of damages from climate change provides a rationale for pursuing these programs vigorously. 6-7 AIR POLLUTION METEOROLOGY The Atmospheric Engine The atmosphere is somewhat like an engine. It is continually expanding and compressing gases, exchanging heat, and generally raising chaos. The driving energy for this unwieldy machine comes from the sun. The difference in heat input between the equator and the poles provides the initial overall circulation of the earth's atmosphere. The rotation of the earth coupled with the different heat conductivities of the oceans and land produce weather. Highs and lows. Because air has mass, it also exerts pressure on things under it. Like water, which we intuitively understand to exert greater pressures at greater depths, the atmosphere exerts more pressure at the surface than it does at higher elevations. The highs and lows depicted on weather maps are simply areas of greater and lesser pressure. The elliptical lines shown on more detailed weather maps are lines of constant pressure, or isobars. A two-dimensional plot of pressure and distance through a highor low-pressure system would appear as shown in Figure SG. Kukla and T. R. Karl, "Nighttime Warming and Ihe Greenhouse Effect," Environmental Science and Technology, 27, pp , L. B. Lave and H. Dow1atabadi, "Climate Change: The Effects of Personal Beliefs and Scientific Uncertainty," Environmental Science and Technology, 27, pp , C&E News. p. 20, August 28,1995.

2 492 INTRODUCTION TO ENVIRONMENTAL ENGINEERING Y.-t A A I r p A -""~=~~~"--O kpa (a) A X X I I Y ("E~~ t \,~~~~=~~~ B X P B~:::::~~~~7fO 1. 2 k P a B (b) X FIGURE 6.11 High and low pressure systems. The wind flows from the higher pressure areas to the lower pressure areas. On a nonrotating planet, the wind direction would be perpendicular to the isobars (Figure 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 hemisphere is as shown in Figure 6-12b. The technical names given to these systems are anticyclones for highs and cyclones for lows. Anticyclones are associated with good weather. Cyclones are associated with foul weather. Tornadoes and hurricanes are the foulest of the cyclones. Wind speed is in part a function of the steepness of the pressure surface. When the isobars are close together, the pressure gradient (slope) is said to be steep and the wind speed relatively high. If the isobars are well spread out, the winds are light or nonexistent.

3 AIR POLLUTION 493 I r --<~~~~~~~),,' " If t \,..~ (a) Anticyclone without Coriolis effect '" ---<:::::~~~~~~\.:,I "'/.,1,,/J ---"'.,1.,1 (b) Anticyclone with Coriolis effect FIGURE 6-12 Wind flow due to pressure gradient. Thrbulence Mechanical turbulence. In its simplest terms, we may consider turbulence to be the addition of random fluctuations of wind velocity (that is, speed and direction) to. the overall average wind velocity. These fluctuations are caused, in part, by the fact that the atmosphere is being sheared. The shearing results from the fact that the wind speed is zero at the ground surface and rises with elevation to near the speed imposed by the pressure gradient. The shearing results in a tumbling, tearing motion as the mass just above the surface falls 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 mechanical turbulence, the easier it is to disperse and spread atmospheric pollutants. Thermal turbulence. Like all other things in nature, the rather complex interaction that produces mechanical turbulence is confounded and further complicated by a

4 494 INTRODUCTION TO ENVIRONMENTAL ENGINEERING third party. Heating of the ground surface causes turbulence in the same fashion that heating the bottom of a beaker full of water causes turbulence. At some point below boiling, you can see density currents rising off the bottom. Likewise, if the earth's surface is heated strongly and in turn heats the air above it, thermal turbulence will be generated. Indeed, the "thermals" sought by glider pilots and hot air balloonists are these thermal currents rising on what otherwise would be a calm day. The converse situation 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 above it, causing a sinking density current. I Stability The tendency of the atmosphere to resist or enhance vertical motion is termed stability. It is related to both wind speed and the change of air temperature with 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 atmosphere is classified as unstable, mechanical turbulence is enhanced by the thermal structure. A neutral atmosphere is one in which the thermal structure neither enhances nor resists mechanical turbulence. When the thermal structure inhibits mechanical turbulence, the atmosphere is said to be stable. Cyclones are associated with unstable air. Anticyclones are associated with stable air. Neutral stability. The lapse rate for a neutral atmosphere is defined by the rate of temperature increase (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 temperature decrease (dt/dz) is called the dry adiabatic lapse rate. It is designated by the Greek letter gamma (f). It has a value of approximately 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 shown as a dashed line and the temperature of the atmosphere (ambient lapse rate) is shown as a solid line. Since the ambient lapse rate is the same as f, the atmosphere is said to have a neutral stability. Unstable atmosphere. If the temperature of the atmosphere falls at a rate greater than f (for example, C/100 m), the lapse rate is said to be superadiabatic, and the atmosphere is 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 decrease from to C. At a lapse rate of C/100 m, the temperature of the air outside the balloon will decrease from to C. The air inside the balloon will be warmer than the air outside; this temperature difference gives the balloon buoyancy. It will behave as a hot gas and continue to rise without any further mechanical effort. Thus, mechanical turbulence is enhanced and the atmosphere is unstable. If we adiabatically displace the balloon downward to elevation C, the temperature inside the balloon

5 AIR POLLUTION 495 Volume at Rest T = 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 -AI- = - 00.C/l00 T = 'c"'z~',. Same Temper.ature 100 ~Z' m,"cc" as Surroundmgs ~n Temperature (OC) (0) 500 V I C. 0 ume onhnues Warmer./ to Rise 400 ',#" Dry Adiabat = r Ambient i'}~'~c,,::i,'~ -B', T = "i:-.~'}'_b :g 300 ~:L"""'~ '::, "" c "..,,i.~',,<olume Displaced Upward 100 m -, -A / '" A_~l,tt... ' " Volume Displaced Downward 100 m.-, Q), Ccvc",c" :I: 200 C Ambient ", Ambient clli.~lill C Lapse Rate " ' T = 22.cCCvvv 40 Cj'CCCCCCCCC!c!"C """-""",,~ ~ T.Cooler Volume 100 -xz= C/l00 m Continues ~ rt -t';-sin-k Temperature (OC) \ B'" -', --- Ambient T = Volume Displaced Upward 100 m, " v Volume ~ " v ":c"v Cooler Restored.E 300 -A I ~ A-i~t.itSCcC to Original -DAd' b t -r ~ ' " cccc Cc 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 = Volume Displaced 100 Lapse Rate Downward 100 m ~T Jl ~ - 2 = -0,5 "CIl00 m I~. ) ( (b) Temperature (OC) FIGURE 6-13 Lapse rate and displaced air volume. (Source: Atomic Energy Commission, Meteorology and Atomic Energy, Washington, DC: U.S. Government Printing Office, 1955.) Icl

6 AIR POLLUTION 497 Plume types. The smoke trail or plume from a tall stack located on flat terrain has been found to exhibit a characteristic shape that is dependent on the stability of the atmosphere. The six classical plumes are shown in Figure 6-14, along with the corresponding temperature profiles. In each case, r is given as a broken line to allow ~ Wind,..'. t\ ';:'::t,.i..;.'..'~.;.;~:.~i-.;,:.,.,.."',.! 1:,',;."".'.."(,.".:..:.,.i..':':..'::.':.;.:(."..::::':.:::,.'..,' Z r' ".:"!'(~i;~~';~;.'~';;~i;:l:::'\::;:.',:::~::'~~..,,::.,'i' t;l T --Strong Lapse Condition (Looping) ".,.,.' '.',..,',..,.,;' ".',:":,,,.,',",.',:..:. t \ ""',,',.,",,: ',..'. Z r' "'."":""::'::'::::..::"':'::"',:..:::,;:..':.::',:..:::::.~,..::.::':'..- T -Weak Lapse Condition (Coning) Z t ~ \ / [~~.""'._."'.,...,..'. ". ',..'.."'".."...'...,..,..." 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 types of plume behavior. (Source: P. E. Church, "Dilution of Waste Stack Gases in the Atmosphere,"lndustrial Engineering Chemistry, vol. 41, pp , 1949.)

7 498 INTRODUCTION TO ENVIRONMENTAL ENGINEERING comparison with the actual lapse rate, which is given as a solid line. In the bottom three cases, particular attention should be given to the location of the inflection point with respect to the top of the stack. Terrain Effects Heat islands. A heat island results from a mass of material, either natural or anthropogenic, that absorbs and reradiates heat at a greater rate than the surrounding area. This causes moderate to strong vertical convection currents above the heat island. The effect is superimposed on the prevailing meteorological conditions. It is nullified by strong winds. Large industrial complexes and small to large cities are examples of places that would have a heat island. Because of the heat island effect, atmospheric stability will be less over a city than it is over the surrounding countryside. Depending upon the location of the pollutant sources, this can be either good news or bad news. First, the good news: For ground level sources such as automobiles, the bowl of unstable air that forms will allow a greater air volume for dilution of the pollutants. Now the bad news: Under stable conditions, plumes from tall stacks would be carried out over the countryside without increasing ground level pollutant concentrations. Unfortunately, the instability caused by the heat island mixes these plumes to the ground level. Land/sea breezes. Under a stagnating anticyclone, a strong local circulation pattern may develop across the shoreline of large water bodies. During the night, the land cools more rapidly than the water. The relatively cooler air over the land flows toward the water (a land breeze, Figure 6-15). During the morning the land heats faster than water. The air over the land becomes relatively 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 breeze during the night.

8 AIR POLLUTION 499 ~--,.. '" 1/ / \ -0- WamI Air over Land / I '" Rises " \ ) Air ~ ~ -A Lake Breeze WamI ~- '.":-'~ -,-' /' --,( --~ ~- ~\ "" \."\ ~""' FIGURE 6-16 Lake breeze during the day. The effect of the lake breeze on stability is to impose a surface-based inversion on the temperature profile. 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 stable lapse rate causes a 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 moderate to strong winds, valleys that are oriented at an acute angle to the wind direction channel the wind. The valley z~ zll T T -u Several km Fumigation " :'.-".:';::':...,:..~t:;!.;:::;,;,:~,,",:,:,:;:::,.::..,.:::: :",.;.:,;".';-":'::-:"'.;;:.'Y;"."",,.' Fanmng :.::.....~.'.::::~j,::,:. FIGURE 6-17 Effect of lake breeze on plume dispersion.

9 500 INTRODUCnON TO ENVIRONMENTAL ENGINEERING effectively peels off 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 cause the valley air to be wanned. It will become more buoyant and flow up the valley. At night the cooling process will cause the wind to flow down the valley. Valleys oriented in the north-south direction are more susceptible to 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 enough during the day to dissipate the inversion that formed during the night. 6-8 ATMOSPHERIC DISPERSION Factors Affecting Dispersion of Air Pollutants This discussion follows the training documents of the Texas Air Quality Control Board. The factors that affect the transport, dilution, and dispersion of air pollutants can generally be categorized in terms of the emission point characteristics, the nature of the pollutant material, meteorological conditions, and effects of terrain and anthropogenic structures. We have discussed all of these except the source conditions. Now we wish to integrate the first and third factors to describe the qualitative aspects of 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), area sources, and mobile sources are left for more advanced texts. Source characteristics. Most industrial effluents are discharged vertically into the open air through a stack or duct. As the contaminated gas stream leaves the discharge point, the plume tends to expand and mix with the ambient air. Horizontal air movement will tend to bend the discharge plume 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 beginning to move in a horizontal direction, the gaseous effluents are being diluted by the ambient air surrounding the plume. As the contaminated gases are diluted by larger and larger volumes of ambient air, they are eventually dispersed toward the ground. The plume rise is affected by both the upward inertia of the discharge gas stream and by its buoyancy. The vertical inertia is related to the exit gas velocity and mass. The plume's buoyancy is related to the exit gas mass relative to the surrounding air mass. Increasing the exit velocity or the exit gas temperature will generally increase the plume rise. The plume rise, together with the physical stack height, is called the effective stack height. The additional rise of the plume above the discharge point 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 contaminated gases as they expand and mix downward.

10 AIR POLLUTION 501 For a specific discharge height and a specific set of plume dilution conditions, the ground level concentration is proportional to the amount of contaminant materials discharged from the stack outlet for a specific period of time. Thus, when all other conditions are constant, an increase in the pollutant discharge rate will cause a proportional increase in the downwind ground level concentrations. Downwind distance. The greater the distance between the point of discharge and a ground level receptor downwind, the greater will be the volume of air available for diluting the contaminant discharge before it reaches the receptor. Wind speed and direction. The wind direction determines the direction in which the contaminated gas stream will move across local terrain. Wind speed affects the plume rise and the rate of mixing or dilution of the contaminated gases as they leave the discharge point. An increase in wind speed will decrease the plume rise by bending the plume over more rapidly. The decrease in plume rise tends to increase the pollutant's ground level concentration. On the other hand, an increase in wind speed will increase the rate of dilution of the effluent plume, tending to lower the downwind concentrations. Under different conditions, one or the other of the two wind speed effects becomes the predominant effect. These effects, in turn, affect the distance downwind of the source at which the maximum ground level concentration will occur. Stability. The turbulence of the atmosphere follows no other factor in power of dilution. The more unstable the atmosphere, the greater the diluting power. Inversions that are not ground based, but begin at some height above the stack exit, act as a lid to restrict vertical dilution. Dispersion Modeling General considerations and use of models. A dispersion model is a mathematical description of the meteorological transport and dispersion process that is quantified in terms of source and meteorologic parameters during a particular time. The resultant numerical calculations yield estimates of concentrations of the particular pollutant for specific locations and times. To verify the numerical results of such a model, actual measured concentrations of the particular atmospheric pollutant must be obtained and compared with the calculated values by means of statistical techniques. The meteorological parameters required for use of the models include wind direction, wind speed, and atmospheric stability. In some models, provisions may be made for including lapse rate and vertical mixing height. Most models will require data about the physical stack height, the diameter of the stack at the emission discharge point, the exit gas temperature and velocity, and the mass rate of emission of 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 concentrations where it is impractical to sample, such as over rivers or lakes, or at great distances above the ground; (2) to estimate the required

11 r:e. 502 emergency '""000=0' source ro reductions 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 turbulent 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 assuming 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 (coordinates 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 designated by Sy and Sz, respectively. The standard deviations are functions of the downward 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 of Atmospheric Dispersion Estimates (U.S. Department of Health, Education 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, (Note: Turner provides guidelines on the accuracy of this model. It is an estimating tool and not a definitive model to be used indiscriminately.)

12 - AIR POLLUTION 503 where X(x,y,O,H) = downwind concentration ground level, g/m3 E = emission rate of pollutant, gls Sy' Sz = plume standardeviations, m u = wind speed, m/s x, y, z, and H = distances, m exp = exponential e such that terms in brackets immediately following are powers of e, that is, e[] where e = The value for the effective stack height is the sum of the physical stack height (h) and the plume rise 6.H: H = h + 6.H (6-20) 6.H may be computed from 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 coordinate system. [Source: D. Bruce Turner, Workbook of Atmospheric Dispersion Estimates (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. ~

13 , 504 INTRODUCTION TO ENVIRONMENTAL ENGINEERING where Us = stack velocity, m/s d = stack diameter, m u = wind speed, m/s P = pressure, kpa T s = stack temperature, K T a = air temperature, K The values of Sy and Sz depend upon the turbulent structure or stability of the atmosphere. Figures 6-19 and 6-20 provide graphical relationships between the down- 10,0 5,00 2,00 1,000 5 ~ 20 e -150 t/) " Distance Downwind FIGURE 6.19 Horizontal dispersion coefficient. [Source: Turner, Workbook of Atmospheric Dispersion Estimates (U,S. Department of Health, Education and Welfare; Public Health Service, National Center for Air Pollution Control, Publication No. 999-AP-28), Washington, DC: U.S. Government Printing Office, 1967.J [kin),~

14 AIR POLLUTION 505 5,00 3,00 2,00 1, :g ō C/) / , Distance Downwind FIGURE 6-20 Vertical dispersion coefficient. (Source: Turner, Workbook of Atmospheric Dispersion Estimates.) (km) wind distance x in kilometers and values of s y and s z in meters. The curves on the two figures are labeled "A" through "F." The label "A" refers to very unstable atmospheric conditions, "B" to unstable atmospheric conditions, "c" to slightly unstablec conditions, "D" to stable oonwtions, "E" to stable atmospheric conditions,

15 506 INTRODUCTION TO ENVIRONMENTAL ENGINEERING 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 assumed for overcast conditions 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 considered here. Night refers to the period from one hour before sunset to one hour after sunrise. Note that the neutral class, D, can be assumed for overcast conditions during day or night, regardless of wind speed. "Strong" incoming solar radiation corresponds to a solar altitude greater than 6() with clear skies; "slight" insolation corresponds to 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 solar radiation. Incoming radiation that would be strong with clear skies can be expected to be reduced to moderate with broken (5/8 to 7/8 cloud cover) middle clouds and to slight with broken low clouds. Source: D. Bruce Turner, Workbook of Atmospheric Dispersion Estimates. and "F' to very stable atmospheric conditions. Each of these stability parameters represents an averaging time of approximately 3 to 15 min. Other averaging times may be approximated by multiplying by empirical constants, for example, 0.36 for 24 hours. Turner presented a table and discussion that allows an estimate of stability based on wind speed and the conditions of solar radiation. This is given in Table 6-6. For computer solutions of the dispersion model, it is convenient to have an algorithm to express the stability class lines in Figures 6-19 and D. O. Martin50 TABLE 6-7 Values of a, c, d, and! for calculating Sy and Sz x~lkm x~lkm Stability class a cd/ cd/ A B C D E F Source: D. O. Martin. sod. O. Martin, Comment on the Change of Concentration Standard Deviations with Distance, Journal o/the Air Pollution Control Association, 26, pp , 1976.