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EPA-454/B-95-003b USER'S GUIDE FOR THE INDUSTRIAL

1. F E 4 2 2 H y H j exp amp 0 5 exp amp o0 5 E is vi Z Z exp amp O 5 3 exp 60 5 a where h h E 2iz i h H H z 2iz h H H a Z 2iz h a Z 2iz h Zz receptor height above ground flagpole m Zz mixing height m The infinite series term in Equation 1 50 accounts for the effects of the restriction on vertical plume growth at the top of the mixing layer As shown by Figure 1 3 the method of image sources is used to account for multiple reflections of the plume from the ground surface and at the top of the mixed layer It should be noted that if the effective stack height h exceeds the mixing height z e i the plume is assumed to fully penetrate the elevated inversion and the ground level concentration is set equal to zero Equation 1 50 assumes that the mixing height in rural and urban areas is known for all stability categories As explained below the meteorological preprocessor program uses mixing heights derived from twice daily mixing heights calculated using the Holzworth 1972 procedures The ISC models currently assume unlimited vertical mixing under stable conditions and therefore delete the infinite series term in Equation 1 50 for the E and F stability categorles The Vertical Term defined by Equation 1 50 changes the form of the vertical concentration distribution from Gaussian to rectangular i e a uniform con
2. Figure 1 8 illustrates representations of a curved line source by multiple volume sources Emissions from a line source or narrow volume source represented by multiple volume sources are divided equally among the individual sources unless there is a known spatial variation in emissions Setting the equal to W 2 15 in Figure 1 8 a O initial lateral dimension F or 2W 2 15 in Figure 1 8 b results in overlapping Gaussian distributions for the individual sources If the wind direction is normal to a straight line source that is represented by multiple volume sources the initial crosswind concentration distribution is uniform except at the edges of the line source The doubling of F by the user in the approximate line source representation in Figure 1 8 b is offset by the fact that the emission rates for the individual volume sources are also doubled by the user TABLE 1 6 SUMMARY OF SUGGESTED PROCEDURES FOR ESTIMATING INITIAL LATERAL DIMENSIONS Eos AND INITIAL VERTICAL DIMENSIONS F FOR VOLUME AND LINE SOURCES Procedure for Obtaining Type of Source Initial Dimension a Initial Lateral Dimensions F Single Volume Source Fo length of side divided by 4 3 Line Source Represented by E length of side divided Adjacent Volume Sources see by 2 15 Figure 1 8 a Line Source Represented by Foo center to center Separated Volume Sources see distance divided by Figure 1 8 b 2 15 b Initial Vertical Dimensi
3. 1 3 1 General This section describes the ISC Short Term dry deposition model which is used to calculate the amount of material deposited i e the deposition flux F at the surface from a particle plume through dry deposition processes The Short Term dry deposition model is based on a dry deposition algorithm Pleim et al 1984 contained in the Acid Deposition and Oxidant Model ADOM This algorithm was selected as a result of an independent model evaluation study EPA 1994 The deposition flux F is calculated as the product of the concentration P and a deposition velocity v computed at a reference height z Fa Py 1 79 The concentration value P used in Equation 1 79 is calculated according to Equation 1 1 with deposition effects accounted for in the vertical term as described in Section 1 1 6 3 The calculation of deposition velocities is described below 1 3 2 Deposition Velocities A resistance method is used to calculate the deposition velocity v The general approach used in the resistance methods for estimating v is to include explicit parameterizations of the effects of Brownian motion inertial impaction and gravitational settling The deposition velocity is written as the inverse of a sum of resistances to pollutant transfer through various layers plus gravitational settling terms Slinn and Slinn 1980 Pleim et al 1984 1 a ee 1 80 r ra JoY YI Ve where Va
4. 2055 2087 INDEX 7 Wesley M L and B B Hicks 1977 Some factors that effect the deposition rates of sulfur dioxide and similar gases on vegetation J Air Poll Control Assoc 27 1110 1116 INDEX 8
5. 4 General 3 Deposition Velocities gt Point and Volume Source Emissions Area and Open Pit Source Emissions 1 4 THE ISC SHORT TERM WET DEPOSITION MODEL 1 5 ISC COMPLEX TERRAIN SCREENING ALGORITHMS 1 i PRPPPPHP UI UI UI UI UT UI UI UT U oo JIDUIRAWNA The Gaussian Sector Average Equation Downwind Crosswind and Radial Distances Wind Speed Profile Plume Rise Formulas The Dispersion Parameters The Vertical Term The Decay Term The Plume Attenuation Correction Factor Wet Deposition in Complex Terrain 1 6 ISC TREATMENT OF INTERMEDIATE TERRAIN 2 0 THE ISC LONG TERM DISPERSION MODEL EQUATIONS 2 1 POINT SOURCE EMISSIONS 2 La NNNNNN hehbhpeap JS NO 0 H4Uuw0DNDn pa The Gaussian Sector Average Equation Downwind and Crosswind Distances Wind Speed Profile Plume Rise Formulas The Dispersion Parameters The Vertical Term The Decay Term iii iv vii viii H x NNNNNNNNDWND I AuKWWWHPHP BE 2 1 8 The Smoothing Function 2 6 2 2 NON POINT SOURCE EMISSIONS E Sock Behe Wks ca 2S 2 2 1 General 2 6 4 ew ee ee ee BET 2 2 2 The Long Term Volume Source Model 2 7 2 2 3 The Long Term Area Source Model 2 7 2 2 4 The Long Term Open Pit Source Model 2 11 2 3 THE ISC LONG TERM DRY DEPOSITION MODEL 2 11 2 3 1 General a a as SSL 2 3 2 Point and Volume Source Emissions 2 11 2 3 3 Area and Open Pit Source Emissions 2 12 3 0 REFERENCES E AA A A Go he A a ae BL
6. 41507 32681 27436 21716 TABLE 1 3 BRIGGS FORMULAS USED TO CALCULATE McELROY POOLER ES Pasquill Stability Category A B C D E F Where x is in meters 0 22 0 16 TABLE 1 4 0 0 0004 ae 0 0 0004 sey 0 0 0004 x 0 0 0004 x 0 0 0004 xy 76 0 0 0004 x F meters BRIGGS FORMULAS USED TO CALCULATE McELROY POOLER F Pasquill Stability Category A B D E F Where x is in meters 0 20 0 14 F meters 0 0 001 x 0 0 001 x 0 0 0003 x 0 0 0015 x 0 0 0015 x 1 1 5 2 Lateral and Vertical Virtual Distances The equations in Tables 1 1 through 1 4 define the dispersion parameters for an ideal point source However volume sources have initial lateral and vertical dimensions Also as discussed below building wake effects Can enhance the initial growth of stack plumes In these cases lateral x and vertical x virtual distances are added by the ISC models to the actual downwind distance x for the F and F calculations The lateral virtual distance in kilometers for the rural mode is given by F 1 q mia ae where the stability dependent coefficients p and q are given in Table 1 5 and F is the standard deviation in meters of the lateral concentration distribution at the source Similarly the vertical virtual distance in kilometers for the rural mode is given by F 1 b x 1 36 where the coefficient
7. For soluble compounds HF SO CL NH set to zero for less soluble compounds NO 1t could be gt 0 Stomatal opening closing is a response to the plant s competing needs for uptake of CO and prevention of water loss from the leaves Stomatal action imposes a strong diurnal cycle on the stomatal resistance and has an important role in determining deposition rates for soluble gaseous pollutants such as SO Stomatal resistance r is given by EPA 1995a E Bad bDy A6 where p a stomatal constant corresponding to the characteristics of leaf physiology u 2 3 x 10 m J z Il the width of the stomatal opening m and the molecular diffusivity of the pollutant m s INDEX 3 The width of the stomatal opening b is a function of the radiation intensity moisture availability and temperature In ISC3 the state of vegetation is specified as one of three states A active and unstressed B active and stressed or C inactive Irrigated vegetation can be assumed to be in an active and unstressed state The variation in stomatal opening width during period A when vegetation is active and unstressed Pleim et al 1984 is b Diaz R Ree Duin A7 where Dj the maximum width m of the stomatal opening 2 5 x 10 m Padro et al 1991 bain the minimum width m of the stomatal opening 0 1 x 10 m R the incoming solar radiation W m received at the ground and is included in
8. H 1 5 Lg where Ly is the lesser of the height of the width H 60 Building Tier 1 East and west wind yy 60 1 5 50 135 Hy 80 1 5 10 95 Therefore the lower building tier 1 width and height H 60 W 50 are used North and South wind Hy 60 1 5 60 150 Hy 80 1 5 70 185 Therefore the upper building tier 2 width and height H 80 W 70 are used tier 2 dominates tter 1 dominates N S wind E W wind FIGURE 1 2 ILLUSTRATION OF TWO TIERED BUILDING WITH DIFFERENT TIERS DOMINATING DIFFERENT WIND DIRECTIONS HAGEN PLUME E Hon FIGURE 1 3 THE METHOD OF MULTIPLE PLUME IMAGES USED TO SIMULATE PLUME REFLECTION IN THE ISC2 MODEL 1 77 Neutral bani ae MIXING HEIGHT MN SR 1400 ss MN SR 1400 ss MN SR 1400 ss MN TIME LST a Urban Mixing Heights DAY DAY DAYi i Neutroi n MIXING HEIGHT MN SR 1400 SS MN SR 1400 ss MN SR 1400 ss MN TIME LST b Rural Mixing Heights FIGURE 1 4 SCHEMATIC ILLUSTRATION OF a URBAN AND b RURAL MIXING HEIGHT INTERPOLATION PROCEDURES UFAV1 ONIXIN JOVIYBNS JO JOL 2 0 oy N 1 5 O E Depletion Factor Profile Correction Ke 1 0 xo C Mm 0 5 D 0 I 0 0 0 0 0 4 0 8 1 2 FIGURE 1 6 ILLUSTRATION OF THE DEPLETION FACTOR E AND THE CORRESPOND CORRECTION FACTOR P x z 2 0 U o O U Original Profile Hei
9. K a scaling coefficient to convert calculated concentrations to desired units default value of 1 x 10 for Q in g s and concentration in yug m V vertical term See Section 1 1 6 D decay term See Section 1 1 7 Fp F standard deviation of lateral and vertical concentration distribution m See Section 1 1 5 u mean wind speed m s at release height See Section 1 1 3 Equation 1 1 includes a Vertical Term V a Decay Term D and dispersion parameters F and F as discussed below It should be noted that the Vertical Term includes the effects of source elevation receptor elevation plume rise limited mixing in the vertical and the gravitational settling and dry deposition of particulates with diameters greater than about 0 1 microns 1 1 2 Downwind and Crosswind Distances The ISC model uses either a polar or a Cartesian receptor network as specified by the user The model allows for the use of both types of receptors and for multiple networks in a single run All receptor points are converted to Cartesian X Y coordinates prior to performing the dispersion calculations In the polar coordinate system the radial coordinate of the point r 2 is measured from the user specified origin and the angular coordinate 2 is measured clockwise from the north In the Cartesian coordinate system the X axis is positive to the east of the user specified origin and the Y axis is positive to the north For either type
10. National Air Pollution Control Administration Cincinnati Ohio Yamartino R J J S Scire S R Hanna G R Carmichael and Y S Chang 1992 The CALGRID mesoscale photochemical grid model Volume I Model formulation Atmos Environ 26A 1493 1512 INDEX Area source deposition algorithm for the Long Term model for the Short Term model Atmospheric resistance Attenuation correction factor in complex terrain Briggs plume rise formulas buoyant plume rise momentum plume rise stack tip downwash Building downwash procedures and buoyancy induced dispersion effects on dispersion parameters for the Long Term model 1 64 2 2 2 4 general Huber and Snyder s Rash OR Ges a wes GR Uae ee Ol Schulman and Scire S tee we oe Ie Sb E Schulman Scire plume rise virtual distances wake plume height Buoyancy flux Buoyancy induced dispersion Buoyant plume rise stable unstable and neutral Cartesian receptor network Complex terrain modeling Short Term model Lo Crossover temperature difference Crosswind distance 1 2 1 3 1 4 1 64 Decay coefficient be Ml A ee Oe Jae ee es Se Decay Termo 224 od Yee th Bee a A a ok o La for the Short Term model Depletion for the dry deposition algorithm for the wet deposition algorithm Deposition layer resistance Deposition velocity Sow eee t Direction specific building dimensions with Huber Snyder downwash Dispersion coefficients see Dispersion para
11. p 96 i 3 F 1 3 h h 2 6 1 20 e u s 1 1 4 9 Stable Momentum Rise Where the stack gas temperature is less than or equal to the ambient air temperature the assumption is made that the plume rise is dominated by momentum If T is less than T as determined by Equation 1 18 the assumption is also made that the plume rise is dominated by momentum The plume height is calculated from Equation 4 28 of Briggs 1969 p 59 1 3 m fun oar Yoda s e 1 21 u s S The equation for unstable neutral momentum rise 1 16 is also evaluated The lower result of these two equations is used as the resulting plume height since stable plume rise should not exceed unstable neutral plume rise 1 1 4 10 All Conditions Distance Less Than Distance to Final Rise Where gradual rise is to be estimated for unstable neutral or stable conditions if the distance downwind from source to receptor x is less than the distance to final rise the equivalent of Equation 2 of Briggs 1972 p 1030 is used to determine plume height He ile nh h7 1 60 1 22 us This height will be used only for buoyancy dominated conditions should it exceed the final rise for the appropriate condition the final rise is substituted instead For momentum dominated conditions the following equations Bowers et al 1979 are used to calculate a distance dependent momentum plume rise a unstabl
12. 1 5 7 The Decay Term See the discussion given in Section 1 1 7 1 5 8 The Plume Attenuation Correction Factor Deflection of the plume by complex terrain features during stable conditions is simulated by applying an attenuation correction factor to the concentration with height in the sector of concern This is represented by the variable CORR in Equation 1 93 The attenuation correction factor has a value of unity for receptors located at and below the elevation of the plume centerline in free air prior to encountering terrain effects and decreases linearly with increasing height of the receptor above plume level to a value of zero for receptors located at least 400 m above the undisturded plume centerline height This relationship is shown in the following equation CORR 1 0 unstable neutral 1 0 H 0m 1 95 gt 000 H 400m 4006 H 400 H lt 400m where CORR attenuation correction factor which is between 0 and 1 H height of receptor above undisturbed plume height including height of receptor above local ground 1 e flagpole height 1 5 9 Wet Deposition in Complex Terrain See the discussion given in Section 1 4 1 6 ISC TREATMENT OF INTERMEDIATE TERRAIN In the ISC Short Term model intermediate terrain is defined as terrain that exceeds the height of the release but is below the plume centerline height The plume centerline height used to define whether a given receptor is on int
13. 24 1 14 2 11 2 11 1 54 2 6 1 34 1 14 1 30 e 1 10 1 8 1 32 1 63 1 63 2 1 1 29 1 10 1 10 1 13 1 11 1 11 1 11 1 43 1 5 1 46 Line source approximation for Schulman Scire sources Line sources modeled as volumes 1 43 1 44 1 45 Linear decay factor Schulman Scire downwash Long term dispersion model McElroy Pooler dispersion parameters see Dispersion parameters Mixing heights Momentum flux Oa ss A n we a Momentum plume rise 1 11 stable unstable and neutral Open pit source deposition algorithm for the Long Term model for the Short Term model Open pit sources Pasquill Gifford dispersion parameters see Dispersion parameters Plume rise for Schulman Scire downwash for the Long Term model for the Short Term model Point source deposition algorithm dispersion parameters for the Long Term model for the Short Term model Polar receptor network Receptors calculation of source receptor distances Rural dispersion parameters virtual distances Schulman Scire downwash algorithm Short term dispersion model Sigma y Sigma z 3 Smoothing function for the Long Term model Stability parameter Stack tip downwash A for wake plume height Uniform vertical mixing Urban decay term for SO2 INDEX 3 1 12 1 46 L 13 1 6 1 23 1 60 1 14 1 13 Del 1 29 21 1 19 T 33 1 13 1 29 1 10 1 8 2 12 2 11 1 50 1 50 1 66 1 14 dispersion
14. Hill North Carolina This effort has been funded by the Environmental Protection Agency under Contract No 68D98006 with Dennis G Atkinson as Work Assignment Manager INDEX vi TECHNICAL DESCRIPTION FOR THE REVISED ISCST3 MODEL DATED 99155 This document provides a technical description of model algorithms for recent enhancements of the ISCST3 model including the most recent version dated 99155 The algorithms described in this Addendum include the gas dry deposition algorithms based on the draft GDISCDFT model dated 96248 and the optimizations of the area source algorithm Both of these enhancements are associated with the non regulatory default TOXICS option introduced with version 99155 of ISCST3 A brief description of the user instructions for these new options is presented in the accompanying Addendum to Volume I of the ISC3 model user s guide ISC3ADD1 WPD Gas Dry Deposition Algorithms The ISCST3 dry deposition algorithm for gaseous pollutants is based on the algorithm contained in the CALPUFF dispersion model EPA 1995a and has undergone limited review and evaluation Moore at al 1995 The deposition flux F is calculated as the product of the concentration 4 and a deposition velocity va computed at a reference height z F POr A1 The concentration value 4 used in Equation A1 is calculated according to Equation 1 1 of the ISC3 model user s guide Volume II EPA 1995b with deposition effects acco
15. INDEX a Boo we A A AA SA a as o ar ENDEX 1 vi FIGURES Fiqure Page 1 1 LINEAR DECAY FACTOR A AS A FUNCTION OF EFFECTIVE STACK HEIGHT H A SQUAT BUILDING IS ASSUMED FOR SIMPLICITY Sen ee E VS a Se 2S Bade S amp S 1 71 1 2 ILLUSTRATION OF TWO TIERED BUILDING WITH DIFFERENT TIERS DOMINATING DIFFERENT WIND DIRECTIONS 1 72 1 3 THE METHOD OF MULTIPLE PLUME IMAGES USED TO SIMULATE PLUME REFLECTION IN THE ISC MODEL A A 1 73 1 4 SCHEMATIC ILLUSTRATION OF MIXING HEIGHT INTERPOLATION PROCEDURES 2040 Bo De Gok ee Oe e 1 74 1 5 ILLUSTRATION OF PLUME BEHAVIOR IN COMPLEX TERRAIN ASSUMED BY THE ISC MODEL 2 1 75 1 6 ILLUSTRATION OF THE DEPLETION FACTOR Fo AND THE CORRESPONDING PROFILE CORRECTION FACTOR P x z 1 76 1 7 VERTICAL PROFILE OF CONCENTRATION BEFORE AND AFTER APPLYING Fo AND P x z SHOWN IN FIGURE 1 6 1 77 1 8 EXACT AND APPROXIMATE REPRESENTATION OF LINE SOURCE BY MULTIPLE VOLUME SOURCES E hee A Sek AN ae a BE a 1 78 1 9 REPRESENTATION OF AN IRREGULARLY SHAPED AREA SOURCE BY 4 RECTANGULAR AREA SOURCES ass E ss o 1 79 1 10 EFFECTIVE AREA AND ALONGWIND LENGTH FOR AN OPEN PIT SOURCE se a ove eee ee e SD eg Eas Ss A ra Go Sh Se a eS 1 80 1 11 WET SCAVENGING RATE COEFFICIENT AS A FUNCTION OF PARTICLE SIZE JINDAL amp HEINOLD 1991 E Sa eh Ge PM at Sal vil TABLES Table 1 1 PARAMETERS USED TO CALCULATE PASQUILL GIFFORD F Y 1 2 PARAMETERS USED TO CALCULATE PASQUILL GIFFORD F 1 3
16. Short Term area source model described in Section 1 2 3 2 3 THE ISC LONG TERM DRY DEPOSITION MODEL 2 3 1 General The concepts upon which the ISC long term dry deposition model are based are discussed in Sections 1 1 6 3 and 1 3 2 3 2 Point and Volume Source Emissions The seasonal deposition at the point located at a particular distance r and direction 2 with respect to the base of a stack or the center of a volume source for articulates in the n particle size category is given by p p KN Q SVD Paion TEET j 2 7 Y2BR 2 ijk R where the vertical term for deposition V was defined in Section 1 3 2 K and D are described in Equations 1 1 and 1 63 respectively Q is the product of the total time during the 1 season of the seasonal emission rate Q for the 2 11 i wind speed category k stability category For example if the emission rate is in grams per second and there are 92 days in the summer season June July and August Q S given by 7 95 x 10 Q It should be noted that the user need not vary the emission rate by season or by wind speed and stability If an annual average emission rate is assumed Q is equal to 3 15 x 10 Q for a 365 day year For a plume comprised of N particle size categories the total seasonal deposition is obtained by summing Equation 2 7 over the N particle size categories The program also sums the seasonal deposition values to obtain the annual deposi
17. St Louis Dispersion Study U S Public Health Service National Air Pollution Control Administration Report AP 53 National Climatic Center 1970 Card Deck 144 WBAN Hourly Surface Observations Reference Manual 1970 Available from the National Climatic Data Center Asheville North Carolina 28801 Pasquill F 1976 Atmospheric Dispersion Parameters in Gaussian Plume Modeling Part II Possible Requirements for Change in the Turner Workbook Values EPA 600 4 76 030b U S Environmental Protection Agency Research Triangle Park North Carolina 27711 Perry S G R S Thompson and W B Petersen 1994 Considerations for Modeling Small Particulate Impacts from Surface Coal Mining Operations Based on Wind Tunnel Simulations Proceedings Eighth Joint Conference on Applications of Air Pollution Meteorology January 23 28 Nashville TN Petersen W B and E D Rumsey 1987 User s Guide for PAL 2 0 A Gaussian Plume Algorithm for Point Area and Line Sources EPA 600 8 87 009 U S Environmental Protection Agency Research Triangle Park North Carolina Pleim J A Venkatram and R Yamartino 1984 ADOM TADAP model development program Volume 4 The dry deposition 373 module Ontario Ministry of the Environment Rexdale Ontario Press W B Flannery S Teukolsky and W Vetterling 1986 Numerical Recipes Cambridge University Press New York 797 pp Schulman L L and S R Hanna 1986 Evaluation of Downwash Modifica
18. frequency of occurrence of each wind direction used for the individual Simulations within a sector based on the frequencies of occurrence in the adjacent sectors This smoothing of the frequency distribution has a similar effect as the smoothing function used for the ISC Long Term point source algorithm described in Section 2 1 8 The frequency of occurrence of the j wind direction between sectors i and i 1 can be calculated as F 94 SF E BL 82 A 2 6c ij i i ij 1 amp l iael where F the frequency of occurrence for the i sector Fi the frequency of occurrence for the i 1 sector Toa the central wind direction for the i sector Eep E the central wind direction for the i 1 sector 2 the specific wind direction between 1 and 1 fei Ss the interpolated smoothed frequency of occurrence for the specific wind direction 2 The ISCLT model uses a set of three criteria to determine whether the process of calculating the sector average concentration has converged The calculation process will be 2 9 considered to have converged and the most recent estimate of the trapezoidal integral used if any of the following conditions is true 1 if the number of halving intervals N in the trapezoidal approximation of the sector average has reached 10 where the number of individual elements in the approximation is given by 1 2 513 for N of 10 if the estimate of the sector average has co
19. is the distance dependent plume rise if the receptor is located between the source and the distance to final rise and final plume rise if the receptor is located beyond the distance to final rise Thus if the user 1 30 elects to use final plume rise at all receptors the distance dependent plume rise is used in the calculation of buoyancy induced dispersion and the final plume rise is used in the concentration equations It should also be noted that buoyancy induced dispersion is not used when the Schulman Scire downwash option is in effect 1 1 6 The Vertical Term The Vertical Term V which is included in Equation 1 1 accounts for the vertical distribution of the Gaussian plume It includes the effects of source elevation receptor elevation plume rise Section 1 1 4 limited mixing in the vertical and the gravitational settling and dry deposition of particulates In addition to the plume height receptor height and mixing height the computation of the Vertical Term requires the vertical dispersion parameter F described in Section 1 1 5 1 1 6 1 The Vertical Term Without Dry Deposition In general the effects on ambient concentrations of gravitational settling and dry deposition can be neglected for gaseous pollutants and small particulates less than about 0 1 microns in diameter The Vertical Term without deposition effects is then given by 2 2 z Sh z Yh v exp 60 5 exp amp O 5
20. model code see Volume I The user must provide the mass mean particle diameter microns the particle density g cm and the mass fraction N for each category being modeled If we denote the value of EF x and P x z for the n particle size category by F x and P x z and substitute these in Equation 1 54 we see that a different value for the vertical term is obtained for each particle size category denoted as V Therefore the total vertical term is given by the sum of the terms for each particle size category weighted by the respective mass fractions Valk 2 Beg N Van Z Beg 1 55 F x is a function of the total deposition velocity v V X Zarea and P X Za X Fo x EXP Sea Vibe zaha P x 24 dx 1 56 o where z is a height near the surface at which the deposition flux is calculated The deposition reference height is calculated as the maximum of 1 0 meters and 20z This equation reflects the fact that the material removed from the plume by deposition is just the integral of the deposition flux over the distance that the plume has traveled In ISC this integral is evaluated numerically For sources modeled in elevated or complex terrain the user can input a terrain grid to the model which is used to determine the terrain elevation at various distances along the plume path during the evaluation of the integral If a terrain grid is not input by the user then the model will linearly
21. of receptor network the user must define the location of each source with respect to the origin of the grid using Cartesian coordinates In the polar coordinate system assuming the 1 3 origin is at X X Y Y the X and Y coordinates of a o o receptor at the point r 2 are given by X R rsin Gx 1 2 Y R rcos2 amp Y 1 3 If the X and Y coordinates of the source are X S and Y S the downwind distance x to the receptor along the direction of plume travel is given by amp X R amp X S sin WD Y R amp Y S cos WD 1 4 where WD is the direction from which the wind is blowing The downwind distance is used in calculating the distance dependent plume rise see Section 1 1 4 and the dispersion parameters see Section 1 1 5 If any receptor is located within 1 meter of a point source or within 1 meter of the effective radius of a volume source a warning message is printed and no concentrations are calculated for the source receptor combination The crosswind distance y to the receptor from the plume centerline is given by y X R amp X S cos WD Y R Y S sin WD 1 5 The crosswind distance is used in Equation 1 1 1 1 3 Wind Speed Profile The wind power law is used to adjust the observed wind speed Uef from a reference measurement height Zep to the stack or release height h The stack height wind speed u is used in the Gaussian plume equation Equatio
22. or a portion of the source area is given by a double integral in the upwind x and crosswind y directions as QK vD 2 po A explso s Jay ax 1 65 2Bu MF F mM F O gare y y where Q area source emission rate mass per unit area per unit time K units scaling coefficient Equation 1 1 V vertical term see Section 1 1 6 D decay term as a function of x see Section 1 1 7 The Vertical Term is given by Equation 1 50 or Equation 1 54 with the effective emission height h being the e physical release height assigned by the user In general h should be set equal to the physical height of the source of emissions above local terrain height For example the emission height h of a slag dump is the physical height of the slag dump Since the ISCST algorithm estimates the integral over the area upwind of the receptor location receptors may be located within the area itself downwind of the area or adjacent to the area However since F goes to 0 as the downwind distance goes to 0 see Section 1 1 5 1 the plume function is infinite 1 50 for a downwind receptor distance of 0 To avoid this singularity in evaluating the plume function the model arbitrarily sets the plume function to 0 when the receptor distance is less than 1 meter As a result the area source algorithm will not provide reliable results for receptors located within or adjacent to very small areas with dimensions on the ord
23. or urban sigmas provided earlier As an example for the rural options Equations 1 34 and 1 37 can be combined to derive the vertical virtual distance x for a squat building First it follows from Equation 1 37 that the enhanced F is equal to 1 2h at a downwind distance of 10h in meters or 0 01h in kilometers Thus x for a squat building is obtained from Equation 1 34 as follows F 0 01h 1 2h a 0 01h x 1 39 Z TORNO ae amp 0 01h 1 40 a where the stability dependent constants a and b are given in Table 1 2 Similarly the vertical virtual distance for tall buildings is given by ic aes ne amp 0 01h 1 41 a For the urban option x 1s calculated from solutions to the equations in Table 1 4 for F 1 2h or F 1 2 h for tall or squat buildings respectively For a squat building with a building width to building height ratio h h less than or equal to 5 the modified F equation is given by F lt 0 35h 0 067 x88h for 3h or 1 42 MR ae 70 for 10h The lateral virtual distance is then calculated for this value of F 5 For a building that is much wider than it is tall h h greater than 5 the presently available data are insufficient to provide general equations for Fo For a stack located toward the center of such a building i e away form either end only the height scale is considered to be significant The modifie
24. the deposition velocity cm s 1 58 the gravitational settling velocity cm s K Il the aerodynamic resistance s cm and Ei the deposition layer resistance s cm Note that for large settling velocities the deposition velocity approaches the settling velocity v 6 v whereas for small settling velocities v tends to be dominated by the r and ra resistance terms In addition to the mass mean diameters microns particle densities gm cm and the mass fractions for each particle size category being modeled the dry deposition model also requires surface roughness length cm friction velocity m s and Monin Obukhov length m The surface roughness length is specified by the user and the meteorological preprocessor PCRAMMET or MPRM calculates the friction velocity and Monin Obukhov length for input to the model The lowest few meters of the atmosphere can be divided into two layers a fully turbulent region where vertical fluxes are nearly constant and the thin quasi laminar sublayer The resistance to transport through the turbulent constant flux layer is the aerodynamic resistance It is usually assumed that the eddy diffusivity for mass transfer within this layer is similar to that for heat The atmospheric resistance formulation is based on Byun and Dennis 1995 stable L gt 0 Z o EL e a 1 81 k er Z L unstable L lt 0 TEA y1 16 z L amp 1 y1 L6 z L Ya n A Te k u
25. z becomes a function of mixing height i e P x Za Zu In the well mixed limit P X Za Z has the same form as P x z in Equation 1 60 but F is replaced by a constant times z Z 4 2 F z 6 ln z Za B B B SESIONES 1 62 2 1 2 a 2 2 2 2 i amp z 6 12 z Ez 3 amp z Z a 2 2 i a B 3 d Therefore a limit is placed on each term involving F in Equation 1 60 so that each term does not exceed the 1 44 corresponding term in z Similarly since the leading order term in P x z for F ax 1 bx corresponds to the 1n 2 F z term in Equation 1 62 F is capped at z V2 for Z this P x z as well Note that these caps to F in Equation 1 60 are broadly consistent with the condition on the use of the well mixed limit on V in Equation 1 51 which uses a ratio F z 1 6 In Equation 1 62 the corresponding ratios are F z 1 4 1 6 and 1 9 In many applications the removal of material from the plume may be extremely small so that F x and P x z are virtually unity When this happens the vertical term is virtually unchanged V V see Equation 1 54 The deposition flux can then be approximated as v P rather than v P The plume depletion calculations are optional so that the added expense of computing F x and P x z can be avoided Not considering the effects of dry depletion results in conservative estimates of both concentration and deposition Since materia
26. 0 2 ds and for F 55 2 3 CPT A 0 00575T 1 11 gue S If the difference between stack gas and ambient temperature T exceeds or equals PENE plume rise is assumed to be buoyancy dominated otherwise plume rise is assumed to be momentum dominated 1 1 4 4 Unstable or Neutral Buoyancy Rise For situations where T exceeds T as determined above buoyancy is assumed to dominate The distance to final rise x s determined from the equivalent of Equation 7 Briggs 1971 p 1031 and the distance to final rise is assumed to be 3 5x where x is the distance at which atmospheric turbulence begins to dominate entrainment The value of x is calculated as follows for Er lt 557 xp 49F 1 12 and for F 55 x 1195 1 13 The final effective plume height h m is determined from the equivalent of the combination of Equations 6 and 7 Briggs 1971 p 1031 for F lt 55 3 4 ho h 79 21 425 gt 1 14 e s and for F 55 3 5 i Se ee 1 15 e s 1 1 4 5 Unstable or Neutral Momentum Rise For Situations where the stack gas temperature is less than or equal to the ambient air temperature the assumption is made that the plume rise is dominated by momentum If T is less than OT from Equation 1 10 or 1 11 the assumption is also made that the plume rise is dominated by momentum The plume height is calculated from Equation 5 2 Briggs 1969 p 59
27. 07 510 Briggs G A 1974 Diffusion Estimation for Small Emissions In ERL ARL USAEC Report ATDL 106 U S Atomic Energy Commission Oak Ridge Tennessee Briggs G A 1975 Plume Rise Predications In Lectures on Air Pollution and Environmental Impact Analysis American Meteorological Society Boston Massachusetts Byun D W and R Dennis 1995 Design Artifacts in Eulerian Air Quality Models Evaluation of the Effects of Layer Thickness and Vertical Profile Correction on Surface Ozone Concentrations Atmos Environ 29 105 126 Chico T and J A Catalano 1986 Addendum to the User s Guide for MPTER Contract No EPA 68 02 4106 U S Environmental Protection Agency Research Triangle Park North Carolina 27711 Cramer H E et al 1972 Development of Dosage Models and Concepts Final Report Under Contract DAAD09 67 C 0020 R with the U S Army Desert Test Center Report DTC TR 609 Fort Douglas Utah Dumbauld R K and J R Bjorklund 1975 NASA MSFC Multilayer Diffusion Models and Computer Programs Version 5 NASA Contractor Report No NASA CR 2631 National Aeronautics and Space Administration George C Marshall Space Center Alabama Dyer A J 1974 A review of flux profile relationships Boundary Layer Meteorol 7 363 372 Environmental Protection Agency 1985 Guideline for Determination of Good Engineering Practice Stack Height Technical Support Document for the Stack Height Regulations Revised E
28. 1 0 Vs h h 3d 1 16 Briggs 1969 p 59 suggests that this equation is most applicable when v u is greater than 4 1 1 4 6 Stability Parameter For stable situations the stability parameter s is calculated from the Equation Briggs 1971 p 1031 NM pa a T a 1 17 As a default approximation for stability class E or 5 M M is taken as 0 020 K m and for class F or 6 M M is taken as 0 035 K m 1 1 4 7 Stable Crossover Between Momentum and Buoyancy For cases with stack gas temperature greater than or equal to ambient temperature it must be determined whether the plume rise is dominated by momentum or buoyancy The crossover temperature difference T is determined by setting Briggs 1975 p 96 Equation 59 equal to Briggs 1969 p 59 Equation 4 28 and solving for T as follows T 0 019582T v ys 1 18 If the difference between stack gas and ambient temperature T exceeds or equals T plume rise is assumed to be buoyancy dominated otherwise plume rise is assumed to be momentum dominated 1 1 4 8 Stable Buoyancy Rise For situations where T exceeds T as determined above buoyancy is assumed to dominate The distance to final rise X is determined by the equivalent of a combination of Equations 48 and 59 in Briggs 1975 p 96 S Ep 2 0715 1 19 The plume height h is determined by the equivalent of Equation 59 Briggs 1975
29. 72 Mixing Heights Wind Speeds and Potential for Urban Air Pollution Throughout the Contiguous United States Publication No AP 101 U S Environmental Protection Agency Research Triangle Park North Carolina 27711 Horst T W 1983 A correction to the Gaussian source depletion model In Precipitation Scavenging Dry Deposition and Resuspension H R Pruppacher R G Semonin W G N Slinn eds Elsevier NY 3 2 Huber A H and W H Snyder 1976 Building Wake Effects on Short Stack Effluents Preprint Volume for the Third Symposium on Atmospheric Diffusion and Air Quality American Meteorological Society Boston Massachusetts Huber A H and W H Snyder 1982 Wind tunnel investigation of the effects of a rectangular shaped building on dispersion of effluents from short adjacent stacks Atmos Environ 176 2837 2848 Huber A H 1977 Incorporating Building Terrain Wake Effects on Stack Effluents Preprint Volume for the Joint Conference on Applications of Air Pollution Meteorology American Meteorological Society Boston Massachusetts Jindal M and D Heinold 1991 Development of particulate scavenging coefficients to model wet deposition from industrial combustion sources Paper 91 59 7 84th Annual Meeting Exhibition of AWMA Vancouver BC June 16 21 1991 McDonald J E 1960 An Aid to Computation of Terminal Fall Velocities of Spheres J Met 17 463 McElroy J L and F Pooler 1968 The
30. BRIGGS FORMULAS USED TO CALCULATE McELROY POOLER E 1 4 BRIGGS FORMULAS USED TO CALCULATE McELROY POOLER F 1 5 COEFFICIENTS USED TO CALCULATE LATERAL VIRTUAL DISTANCES FOR PASQUILL GIFFORD DISPERSION RATES 1 6 SUMMARY OF SUGGESTED PROCEDURES FOR ESTIMATING INITIAL LATERAL DIMENSIONS Fo AND INITIAL VERTICAL DIMENSIONS F FOR VOLUME AND LINE SOURCES viii Symbol Q io D pP p SYMBOLS Definition Linear decay term for vertical dispersion in Schulman Scire downwash dimensionless Effective area for open pit emissions dimensionless Exponential decay term for Gaussian plume equation dimensionless Brownian diffusivity cm s Relative pit depth dimensionless Effective pit depth m Particle diameter for particulate emissions um Stack inside diameter m Buoyancy flux parameter mf s Dry deposition flux g m Momentum flux parameter m s Plume depletion factor for dry deposition dimensionless Terrain adjustment factor dimensionless Wet deposition flux g m Frequency of occurrence of a wind speed and stability category combination dimensionless Acceleration due to gravity 9 80616 m s Building height m Plume or effective stack height m Physical stack height m Height of terrain above stack base m Release height modified for stack tip downwash m ix P x y Crosswind projected width of building adjacent to a stack m von Karman constant 0 4 Monin Obukh
31. Distances See Section 1 1 5 2 for a discussion of the procedures used to calculate vertical virtual distances The lateral virtual distance is given by pea cot pe 2 3 y o 2 where r is the effective source radius in meters For volume sources see Section 2 2 2 the program sets r equal to 2 15F where F is the initial lateral dimension For area sources see Section 2 2 3 the program sets r equal to x yB where x is the length of the side of the area source For plumes affected by building wakes see Section 1 1 5 2 the program sets r equal to 2 15 F where F is given for squat buildings by Equation 1 41 1 42 or 1 43 for downwind distances between 3 and 10 building heights and for tall buildings by Equation 1 44 for downwind distances between 3 and 10 building widths At downwind distances greater than 10 building heights for Equation 1 41 1 42 or 1 43 Fe is held constant at the value of FL calculated at a downwind distance of 10 building heights Similarly at downwind distances greater than 10 building widths for Equation 1 44 2 4 Fae is held constant at the value of ES calculated at a downwind distance of 10 building widths 2 1 5 3 Procedures Used to Account for the Effects of Building Wakes on Effluent Dispersion With the exception of the equations used to calculate the lateral virtual distance the procedures used to account for the effects of building wake e
32. EPA 454 B 95 003b USER S GUIDE FOR THE INDUSTRIAL SOURCE COMPLEX ISC3 DISPERSION MODELS VOLUME II DESCRIPTION OF MODEL ALGORITHMS U S ENVIRONMENTAL PROTECTION AGENCY Office of Air Quality Planning and Standards Emissions Monitoring and Analysis Division Research Triangle Park North Carolina 27711 September 1995 DISCLAIMER The information in this document has been reviewed in its entirety by the U S Environmental Protection Agency EPA and approved for publication as an EPA document Mention of trade names products or services does not convey and should not be interpreted as conveying official EPA endorsement or recommendation ii PREFACE This User s Guide provides documentation for the Industrial Source Complex ISC3 models referred to hereafter as the Short Term ISCST3 and Long Term ISCLT3 models This volume describes the dispersion algorithms utilized in the ISCST3 and ISCLT3 models including the new area source and dry deposition algorithms both of which are a part of Supplement C to the Guideline on Air Quality Models Revised This volume also includes a technical description for the following algorithms that are not included in Supplement C pit retention ISCST3 and ISCLT3 wet deposition ISCST3 only and COMPLEX1 ISCST3 only The pit retention and wet deposition algorithms have not undergone extensive evaluation at this time and their use is optional COMPLEX1 is incorporated to prov
33. L GIFFORD F Zz F meters ax x in km Pasquill Stability Category x km a b A lt 10 122 800 0 94470 0 10 0 15 158 080 1 05420 0 16 0 20 170 220 1 09320 0 21 0 25 179 520 1 12620 0 26 0 30 217 410 1 26440 0 31 0 40 258 890 1 40940 0 41 0 50 346 750 1 72830 0 51 3 11 453 850 2 11660 gt 3 11 B lt 20 90 673 0 93198 0 21 0 40 98 483 0 98332 gt 0 40 109 300 1 09710 c All 61 141 0 91465 D lt 30 34 459 0 86974 0 31 1 00 32 093 0 81066 1 01 3 00 32 093 0 64403 3 01 10 00 33 504 0 60486 10 01 30 00 36 650 0 56589 gt 30 00 44 053 0 51179 If the calculated value of F exceed 5000 m F is set to 5000 m F is equal to 5000 m z TABLE 1 2 CONTINUED PARAMETERS USED TO CALCULATE PASQUILL GIFFORD F Pasquill Stability Category x km E lt 10 0 10 0 30 0 31 1 00 1 01 2 00 2 01 4 00 4 01 10 00 10 01 20 00 20 01 40 00 gt 40 00 F lt 20 0 21 0 70 0 71 1 00 1 01 2 00 2 01 3 00 3 01 7 00 7 01 15 00 15 01 30 00 30 01 60 00 gt 60 00 F meters 24 23 21 21 22 24 26 35 47 15 14 13 13 14 16 17 22 ada 34 260 331 628 628 534 703 970 420 618 209 457 2953 953 823 187 836 651 074 219 b ax x in km O O OSO O G O OG 0O O O O O O OCO GOG O O 83660 81956 75660 63077 57154 50527 46713 37615 29592 81558 78407 68465 63227 54503 46490
34. PA 450 4 80 023R U S Environmental Protection Agency Research Triangle Park NC 27711 NTIS No PB 85 225241 Environmental Protection Agency 1992 Comparison of a Revised Area Source Algorithm for the Industrial Source Complex Short Term Model and Wind Tunnel Data EPA Publication No EPA 454 R 92 014 U S Environmental Protection Agency Research Triangle Park NC NTIS No PB 93 226751 Environmental Protection Agency 1992 Sensitivity Analysis of a Revised Area Source Algorithm for the Industrial Source Complex Short Term Model EPA Publication No EPA 454 R 92 015 U S Environmental Protection Agency Research Triangle Park NC NTIS No PB 93 226769 Environmental Protection Agency 1992 Development and Evaluation of a Revised Area Source Algorithm for the Industrial Source Complex Long Term Model EPA Publication No EPA 454 R 92 016 U S Environ mental Protection Agency Research Triangle Park NC NTIS No PB 93 226777 Environmental Protection Agency 1994 Development and Testing of a Dry Deposition Algorithm Revised EPA Publication No EPA 454 R 94 015 U S Environmental Protection Agency Research Triangle Park NC NTIS No PB 94 183100 Gifford F A Jr 1976 Turbulent Diffusion Typing Schemes A Review Nucl Saf 17 68 86 Hicks B B 1982 Critical assessment document on acid deposition ATDL Contrib File No 81 24 Atmos Turb and Diff Laboratory Oak Ridge TN Holzworth G C 19
35. The procedures used to account for the effects of building downwash are discussed more fully in Section 1 1 5 3 The plume rise calculations used with the Schulman Scire algorithm are discussed in Section 1 1 4 11 1 1 4 11 Plume Rise When Schulman and Scire Building Downwash is Selected The Schulman Scire downwash algorithms are used by the ISC models when the stack height is less than the building height plus one half of the lesser of the building height or width When these criteria are met the ISC models estimate plume rise during building downwash conditions following the suggestion of Scire and Schulman 1980 The plume rise during building downwash conditions is reduced due to the initial dilution of the plume with ambient air The plume rise is estimated as follows The initial dimensions of the downwashed plume are approximated by a line source of length L and depth 2R where Ro V2aF x 3Lp 1 28 ABF EFI ae aip FSF 1 29a 1 1 1 29b Ly 0 x 3b F lt F L equals the minimum of h and h where h is the building height and h the projected crosswind building width Aisa linear decay factor and is discussed in more detail in Section 1 1 5 3 2 If there is no enhancement of Es or if the enhanced F is less than the enhanced F the initial plume will be represented by a circle of radius R The 2 factor converts the Gaussian F to an equivalent uniform circular distribution and y2B converts F t
36. V1 bx z 1 1 bx z amp 1 For this last form the x z and x z must be solved for z and Z respectively by finding the root of the implicit relation B z axyl bx 1 59 2 The corresponding functions for P x z for the special case of Equation 1 57 are given by Case 1 Rural stability A B Urban stability C FL ax Bee z 1 oj Vass E lun 2 F z Sa ua Case 2 Rural stability C D Urban stability D E F F ax 1 bx poz 1 y va Ye E af Sa ua Case 3 1 60 Rural stability E F F ax 1 bx PA 1 y Y Ye Efa F z amp ua b B F F amp Case 4 Urban stability A B F ax 1 bx poz H1 id 2 amp F 24 amp ua In 1 k z 8 amp E k a e For the last form k 2 B and a 2 Fa F 1 6 0006 F F 300m Fa 0 6724 F F gt 300m and 1 61 A es F 1000m F y1000 F F gt 1000m The added complexity of this last form arises because a simple analytical solution to Equation 1 57 could not be obtained for the urban class A and B The integral in P x z for F 1 2 ax 1 bx listed above matches a numerical solution to within about 2 for z 1m When vertical mixing is limited by z the profile correction factor Dix 2 involves an integral from 0 to Ex rather than from 0 to infinity Furthermore V contains terms that simulate reflection from z z as well as z 0 so that the profile correction factor P x
37. ain adjustment procedures used by the ISC models for simple elevated terrain The vertical term used with the complex terrain algorithms in ISC is described in Section 1 5 6 1 1 6 3 The Vertical Term With Dry Deposition Particulates are brought to the surface through the combined processes of turbulent diffusion and gravitational settling Once near the surface they may be removed from the atmosphere and deposited on the surface This removal is modeled in terms of a deposition velocity v which is described in Section 1 3 1 by assuming that the deposition flux of material to the surface is equal to the product v P where P is the airborne concentration just above the surface As the plume of airborne particulates is transported downwind such deposition near the surface reduces the concentration of particulates in the plume and thereby alters the vertical distribution of the remaining particulates Furthermore the larger particles will also move steadily nearer the surface at a rate equal to their gravitational settling velocity v As a result the plume centerline height is reduced and the vertical concentration distribution is no longer Gaussian A corrected source depletion model developed by Horst 1983 is used to obtain a vertical term that incorporates both the gravitational settling of the plume and the removal of plume mass at the surface These effects are incorporated as modifications to the Gaussian plume equat
38. areas deposition directly to the surface may be an important pathway g Ares J A g ref A9 where r ref the reference resistance of SO over ground 1000 s m Padro et al 1991 Over water deposition of soluble pollutants can be quite rapid The liquid phase resistance of the depositing pollutant over water is a function of its solubility and reactivity characteristics and is given by Slinn et al 1978 Dgo H a A10 where H the Henty s law constant which is the ratio of gas to liquid phase concentration of the pollutant H 4x 10 SO 4 x 10 H O 8 x 10 HNO 2 x 10 O 3 5 x 10 NO 1 x 10 PAN and 4 x 10 HCHO OL a solubility enhancement factor due to the aqueous phase dissociation of the pollutant a 10 for SO 1 for CO 10 for O and d aconstant 4 8 x 107 If sufficient data are not available to compute the canopy resistance term r from Equation A4 then an option for user specified gas dry deposition velocity is provided Selection of this option will by pass the algorithm for computing deposition velocities for gaseous pollutants and results from the ISCST3 model based on a user specified deposition velocity should be used with extra caution Optimizations for Area Sources When the non regulatory default TOXICS option is specified the ISCST3 model optimizes the area source algorithm to improve model runtimes These optimizations are briefly des
39. centration within the surface mixing layer at long downwind distances Consequently in order to reduce computational time without a loss of accuracy Equation 1 50 is changed to the form V2BF 2 v 1 51 at downwind distances where the F z ratio is greater than or equal to 1 6 The meteorological preprocessor program RAMMET used by the ISC Short Term model uses an interpolation scheme to assign hourly rural and urban mixing heights on the basis of the early morning and afternoon mixing heights calculated using the Holzworth 1972 procedures The procedures used to interpolate hourly mixing heights in urban and rural areas are illustrated in Figure 1 4 where H max maximum mixing height on a given day H min minimum mixing height on a given day MN midnight SR sunrise SS sunset The interpolation procedures are functions of the stability category for the hour before sunrise If the hour before sunrise is neutral the mixing heights that apply are indicated 1 33 by the dashed lines labeled neutral in Figure 1 4 If the hour before sunrise is stable the mixing heights that apply are indicated by the dashed lines labeled stable It should be pointed out that there is a discontinuity in the rural mixing height at sunrise if the preceding hour is stable As explained above because of uncertainties about the applicability of Holzworth mixing heights during periods of E and F stability the ISC mo
40. concentration in the pit Thompson 1994 The gravitational settling velocity v is computed as described in Section 1 3 2 for each particle size category Thompson 1994 used laboratory measurements of pollutant residence times in a variety of pit shapes typical of actual mines and determined that a single value of 0 029 worked well for all pits studied The adjusted emission rate Q for each particle size category is then computed as 0 90 1 69 where Q is the total emission rate for all particles within the pit N is the original mass fraction for the given size category and gis the escape fraction calculated from Equation 1 68 The adjusted total emission rate for all particles escaping the pit Q is the sum of the Q for all particle categories calculated from Equation 1 69 The mass fractions of particles escaping the pit N for each category is ai Na Q of Q 1 70 Because of particle settling within the pit the distribution of mass escaping the pit is different than that emitted within the pit The adjusted total particulate emission rate Q and the adjusted mass fractions N reflect this change and it ai is these adjusted values that are used for modeling the open pit emissions The following describes the specification of the location dimensions and adjusted emissions for the effective area source 1 54 used for modeling open pit emissions Consider an arbitrary rectangu
41. cribed below In the regulatory default mode the ISCST3 model utilizes a Romberg numerical integration to estimate the area source impacts as described in Section 1 2 3 of the ISC3 model user s guide Volume II EPA 1995b While the Romberg integration performs well INDEX 5 relative to other approaches for receptors located within or adjacent to the area source its advantages diminish as the receptor location is moved further away from the source The shape of the integrand becomes less complex for the latter case approaching that of a point source at distances of about 15 source widths downwind Recognizing this behavior the TOXICS option in ISCST3 makes use of a more computationally efficient 2 point Gaussian Quadrature routine to approximate the numerical integral for cases where the receptor location satisfies the following condition relative to the side of the area source being integrated XU XL lt 5 XL A11 where XL the minimum distance from the side of the area source to the receptor and XU the maximum distance from the side of the area source to the receptor If the receptor location does not satisfy the condition in Equation A11 then the Romberg numerical integration routine is used In addition for receptors that are located several source widths downwind of an area source a point source approximation is used The distance used to determine if a point source approximation is applied is stability dependent and
42. d E equation for a very squat building is then given by F lt 0 35h 0 067 x88h for 3h 2 or 1 43 F x x for x 10h For h h greater than 5 and a stack located laterally within about 2 5 h of the end of the building lateral plume spread is affected by the flow around the end of the building With end effects the enhancement in the initial lateral spread is assumed not to exceed that given by Equation 1 42 with h replaced by 5 h The modified Es equation is given by Fi 1 75h 0 067 x amp h for 3h 3 or 1 44 F x x for cS 20 The upper and lower bounds of the concentrations that can be expected to occur near a building are determined respectively using Equations 1 43 and 1 44 The user must specify whether Equation 1 43 or Equation 1 44 is to be used in the model calculations In the absence of user instructions the ISC models use Equation 1 43 if the building width to building height ratio h h exceeds 5 Although Equation 1 43 provides the highest concentration estimates for squat buildings with building width to building height ratios h h greater than 5 the equation is applicable only to a stack located near the center of the building when the wind direction is perpendicular to the long side of the building i e when the air flow over the portion 1 27 of the building containing the source is two dimensional Thus Equation 1 44 generally is more appropriat
43. dels ignore the interpolated mixing heights for E and F stability and treat such cases as having unlimited vertical mixing 1 1 6 2 The Vertical Term in Elevated Simple Terrain The ISC models make the following assumption about plume behavior in elevated simple terrain i e terrain that exceeds the stack base elevation but is below the release height e The plume axis remains at the plume stabilization height above mean sea level as it passes over elevated or depressed terrain e The mixing height is terrain following e The wind speed is a function of height above the surface see Equation 1 6 Thus a modified plume stabilization height h is substituted for the effective stack height h in the Vertical Term given by Equation 1 50 For example the effective plume stabilization height at the point x y is given by te eZ GZ os 1 52 where Z height above mean sea level of the base of the stack m Z y height above mean sea level of terrain at the receptor location x y m It should also be noted that as recommended by EPA the ISC models truncate terrain at stack height as follows if the terrain height z z exceeds the source release height h s s the elevation of the receptor is automatically chopped off at the physical release height The user is cautioned that concentrations at these complex terrain receptors are subject to considerable uncertainty Figure 1 5 illustrates the terr
44. e the hourly concentration at downwind distance x meters and crosswind distance y meters is given by pa RE ORR 1 93 V2B R 2 u F where Q pollutant emission rate mass per unit time K units scaling coefficient see Equation 1 1 2 the sector width in radians 0 3927 R radial distance from the ie ay source to the receptor x x yl m x downwind distance from source center to receptor measured along the plume axis m 1 68 y lateral distance from the plume axis to the receptor m X lateral virtual distance for volume sources see Equation 1 35 equals zero for point sources m u mean wind speed m sec at stack height F standard deviation of the vertical concentration distribution m V the Vertical Term see Section 1 1 6 D the Decay Term see Section 1 1 7 CORR the attenuation correction factor for receptors above the plume centerline height see Section 1 5 8 Equation 1 93 includes a Vertical Term a Decay Term and a vertical dispersion term F The Vertical Term includes the effects of source elevation receptor elevation plume rise limited vertical mixing gravitational settling and dry deposition 1 5 2 Downwind Crosswind and Radial Distances The calculation of downwind and crosswind distances is described in Section 1 1 2 Since the complex terrain algorithms in ISC are based on a sector average the radial distance is used in calculating t
45. e conditions 1 3 3F x m 2 2 u where x is the downwind distance meters with a maximum value 1 23 he 17 e defined by Xmax as follows x 4d v 3u fae ee for F 0 Vus 1 24 49r for 0 lt F Ht55m s aOR for F gt 55m 8 b stable conditions 1 3 sin xys u he hie delia BIOS 1 25 e 2 u ys where x is the downwind distance meters with a maximum value defined by x as follows x I Bu fea Gas 1 26 Vs The jet entrainment coefficient Se is given by iol u Meee ee 1 27 3 vV As with the buoyant gradual rise if the distance dependent momentum rise exceeds the final rise for the appropriate condition then the final rise is substituted instead 1 1 4 10 1 Calculating the plume height for wake effects determination The building downwash algorithms in the ISC models always require the calculation of a distance dependent momentum plume rise When building downwash is being simulated the equations 1 11 described above are used to calculate a distance dependent momentum plume rise at a distance of two building heights downwind from the leeward edge of the building However stack tip downwash is not used when performing this calculation i e h h This wake plume height is compared to the wake height based on the good engineering practice GEP formula to determine whether the building wake effects apply to the plume for that hour
46. e then Equation 1 43 It is believed that Equations 1 43 and 1 44 provide reasonable limits on the extent of the lateral enhancement of dispersion and that these equations are adequate until additional data are available to evaluate the flow near very wide buildings The modified F equation for a tall building is given by F 7 0 35h 0 067 x88h for 3h gt or 1 45 F x 70x for x5 10 The ISC models print a message and do not calculate concentrations for any source receptor combination where the source receptor separation is less than 1 meter and also for distances less than 3 h for a squat building or 3 h for a tall building under building wake effects It should be noted that for certain combinations of stability and building height and or width the vertical and or lateral plume dimensions indicated for a point source by the dispersion curves at a downwind distance of ten building heights or widths can exceed the values given by Equation 1 37 or 1 38 and by Equation 1 42 or 1 43 Consequently the ISC models do not permit the virtual distances x and x to be less than zero 1 1 5 3 2 Schulman and Scire refined building downwash procedures The procedures for treating building wake effects include the use of the Schulman and Scire downwash method The building wake procedures only use the Schulman and Scire method when the physical stack height is less than h 0 5 L where h is the building h
47. ea source model and Section 1 2 4 provides a description of the open pit model The following subsections give the volume area and open pit source equations used by the long term model 2 2 2 The Long Term Volume Source Model The ISC Long Term Model uses a virtual point source algorithm to model the effects of volume sources Therefore Equation 2 1 is also used to calculate seasonal average ground level concentrations for volume source emissions The user must assign initial lateral F and vertical F yo z5 dimensions and the effective emission height h A discussion of the application of the volume source model is given in Section 1 2 2 2 2 3 The Long Term Area Source Model The ISC Long Term Area Source Model is based on the numerical integration algorithm for modeling area sources used by the ISC Short Term model which is described in detail in Section 1 2 3 For each combination of wind speed class 2 7 stability category and wind direction sector in the STAR meteorological frequency summary the ISC Long Term model calculates a sector average concentration by integrating the results from the ISC Short Term area source algorithm across the sector A trapezoidal integration is used as follows 2 P 2 d2 NS Ej P 2 YE yP 2 y P 1 m 1 1 E P 2 il il iN iN 1 2 S N j 1 2 E 2 6a LD 24 6b where Pe the sector average concentration value for the i sector S the sector widt
48. ecting averages for the entire period of input meteorology 1 1 POINT SOURCE EMISSIONS The ISC Short Term model uses a steady state Gaussian plume equation to model emissions from point sources such as stacks and isolated vents This section describes the Gaussian point source model including the basic Gaussian equation the plume rise formulas and the formulas used for determining dispersion parameters 1 1 1 The Gaussian Equation The ISC short term model for stacks uses the steady state Gaussian plume equation for a continuous elevated source For each source and each hour the origin of the source s coordinate system is placed at the ground surface at the base of the stack The x axis is positive in the downwind direction the y axis is crosswind normal to the x axis and the z axis extends vertically The fixed receptor locations are converted to each source s coordinate system for each hourly concentration calculation The calculation of the downwind and crosswind distances is described in Section 1 1 2 The hourly concentrations calculated for each source at each receptor are summed to obtain the total concentration produced at each receptor by the combined source emissions For a steady state Gaussian plume the hourly concentration at downwind distance x meters and crosswind distance y meters is given by 2 pro ee exp 60 5 Y 1 1 2Bu F F F y where Q pollutant emission rate mass per unit time
49. egulatory applications References Environmental Protection Agency 1995a A User s Guide for the CALPUFF Dispersion Model EPA 454 B 95 006 U S Environmental Protection Agency Research Triangle Park NC Environmental Protection Agency 1995b User s Guide for the Industrial Source Complex ISC3 Dispersion Models Volume II Description of Model Algorithms EPA 454 B 95 003b U S Environmental Protection Agency Research Triangle Park NC Hicks B B 1982 Critical assessment document on acid deposition ATDL Contrib File No 81 24 Atmos Turb and Diff Laboratory Oak Ridge TN Moore G P Ryan D Schwede and D Strimaitis 1995 Model performance evaluation of gaseous dry deposition algorithms Paper 95 TA34 02 88th Annual Meeting amp Exhibition of the Air and Waste Management Association San Antonio Texas June 18 23 1995 Padro J G D Hartog and H H Neumann 1991 An investigation of the ADOM dry deposition module using summertime O measurements above a deciduous forest Atmos Environ 25A 1689 1704 Pleim J A Venkatram and R Yamartino 1984 ADOM TADAP model development program Volume 4 The dry deposition module Ontario Ministry of the Environment Rexdale Ontario Slinn W G N L Hasse B B Hicks A W Hogan D Lai P S Liss K O Munnich G A Sehmel and O Vittori 1978 Some aspects of the transfer of atmospheric trace constituents past the air sea interface Atmos Environ 12
50. eight and L is the lesser of the building 1 28 height or width In regulatory applications the maximum projected width is used The features of the Schulman and Scire method are 1 reduced plume rise due to initial plume dilution 2 enhanced vertical plume spread as a linear function of the effective plume height and 3 specification of building dimensions as a function of wind direction The reduced plume rise equations were previously described in Section 1 1 4 11 When the Schulman and Scire method is used the ISC dispersion models specify a linear decay factor to be included in the F s calculated using Equations 1 37 and 1 38 as follows Foe ARS 1 46 Z where F is from either Equation 1 37 or 1 38 and A is the linear decay factor determined as follows A 1 if h h 1 h Uh 0 o 1 if h lt h h 2L 1 47 eas A 0 if hy shy 2Lg where the plume height h is the height due to gradual momentum rise at 2 h used to check for wake effects The effect of the linear decay factor is illustrated in Figure 1 1 For Schulman Scire downwash cases the linear decay term is also used in calculating the vertical virtual distances with Equations 1 40 to 1 41 When the Schulman and Scire building downwash method is used the ISC models require direction specific building heights and projected widths for the downwash calculations The ISC models also accept direction specific building dim
51. ensions for Huber Snyder downwash cases The user inputs the building height and projected widths of the building tier associated 1 29 with the greatest height of wake effects for each ten degrees of wind direction These building heights and projected widths are the same as are used for GEP stack height calculations The user is referred to EPA 1986 for calculating the appropriate building heights and projected widths for each direction Figure 1 2 shows an example of a two tiered building with different tiers controlling the height that is appropriate for use for different wind directions For an east or west wind the lower tier defines the appropriate height and width while for a north or south wind the upper tier defines the appropriate values for height and width 1 1 5 4 Procedures Used to Account for Buoyancy Induced Dispersion The method of Pasquill 1976 is used to account for the initial dispersion of plumes caused by turbulent motion of the plume and turbulent entrainment of ambient air With this method the effective vertical dispersion F is calculated as follows 1 2 2 Fo JPE 1 48 Ze Z 3 5 where F is the vertical dispersion due to ambient turbulence and h is the plume rise due to momentum and or buoyancy The lateral plume spread is parameterized using a similar expression 1 2 2 h a n F aan where ES is the lateral dispersion due to ambient turbulence It should be noted that h
52. er of a few meters across In these cases the receptor should be placed at least 1 meter outside of the area In Equation 1 65 the integral in the lateral i e crosswind or y direction is solved analytically as follows 2 exp So 5 lady erfc L 1 66 m F F y where erfc is the complementary error function In Equation 1 65 the integral in the longitudinal 1 e upwind or x direction is approximated using numerical methods based on Press et al 1986 Specifically the ISCST model estimates the value of the integral I as a weighted average of previous estimates using a scaled down extrapolation as follows 1 VD y 1 O In T y I extal dx LAA _ mF F El e 3 ene where the integral term refers to the integral of the plume function in the upwind direction and I and I refer to successive estimates of the integral using a trapezoidal approximation with N intervals and 2N intervals The number of intervals is doubled on successive trapezoidal estimates of the integral The ISCST model also performs a Romberg integration by treating the sequence I as a polynomial in k The Romberg integration technique is described in detail in Section 4 3 of Press et al 1986 The ISCST model uses a set of three criteria to determine whether the process of integrating in the upwind direction has converged The calculation process will 1 51 be considered to have converged and the most recent estimate
53. ermediate terrain is the distance dependent plume height calculated for the complex terrain algorithm before the terrain adjustment Section 1 5 6 2 is applied If the plume height is equal to or exceeds the terrain height then that receptor is defined as complex terrain for that hour and that source and the concentration is based on the complex terrain screening algorithm only If the terrain 73 height is below the plume height but exceeds the physical release height then that receptor is defined as intermediate terrain for that hour and source For intermediate terrain receptors concentrations from both the simple terrain algorithm and the complex terrain algorithm are obtained and the higher of the two concentrations is used for that hour and that source If the terrain height is less than or equal to the physical release height then that receptor is defined as simple terrain and the concentration is based on the simple terrain algorithm only For deposition calculations the intermediate terrain analysis is first applied to the concentrations at a given receptor and the algorithm simple or complex that gives the highest concentration at that receptor is used to calculate the deposition value 3 Hg wN HE wN 2 Ha N 1 6 Hg Ha Q lt FIGURE 1 1 LINEAR DECAY FACTOR A AS A EFFECTIVE STACK HEIGHT H ASSUMED FOR SIMPLICITY FUNCTION OF A SQUAT BUILDING IS Height of wake effects is Hy
54. ffects on effluent dispersion are the same as those outlined in Section 1 1 5 3 for the short term model The calculation of lateral virtual distances by the long term model is discussed in Section 2 1 5 2 above 2 1 5 4 Procedures Used to Account for Buoyancy Induced Dispersion See the discussion given in Section 1 1 5 4 2 1 6 The Vertical Term 2 1 6 1 The Vertical Term for Gases and Small Particulates Except for the use of seasons and discrete categories of wind speed and stability the Vertical Term for gases and small particulates corresponds to the short term version discussed in Section 1 1 6 The user may assign a separate mixing height z to each combination of wind speed and stability category for each season As with the Short Term model the Vertical Term is changed to the form BF 2 U 2 4 at downwind distances where the F z ratio is greater than or equal to 1 6 Additionally the ground level concentration is set equal to zero if the effective stack height h exceeds the mixing height z As explained in Section 1 1 6 1 the ISC 2 5 model currently assumes unlimited mixing for the E and F stability categories 2 1 6 2 The Vertical Term in Elevated Terrain See the discussion given in Section 1 1 6 2 2 1 6 3 The Vertical Term for Large Particulates Section 1 1 6 3 discusses the differences in the dispersion of large particulates and the dispersion of gases and small particulate
55. ght z sigmaz Depleted Profile 0 0 0 0 0 5 1 0 1 5 2 0 CONCETTO FIGURE 1 7 VERTICAL PROFILE OF CONCENTRATION BEFORE AND AFTER APPLYIN P x z SHOWN IN FIGURE 1 6 a EXACT REPRESENTATION b APPROXIMATE REPRESENTATION FIGURE 1 8 EXACT AND APPROXIMATE REPRESENTATIONS OF A LINE SOURCE BY MULTIPLE VOLUME SOURCES 1 82 FIGURE 1 9 REPRESENTATION OF AN IRREGULARLY SHAPED AREA SOURCE BY 4 RECTANGULAR AREA SOURCES Wind direction effective area 3 alongwind ee length l q L gt FIGURE 1 10 EFFECTIVE AREA AND ALONGWIND WIDTH FOR AN OPEN PIT SOURCE Wet Scavenging Rate Coefficient 10 s mm h 8 6 v O X e Cc gt 5 O 2 0 0 1 A 10 100 Particle Diameter microns FIGURE 1 11 WET SCAVENGING RATE COEFFICIENT AS A FUNCTION OF PARTICLE SIZE JINDAL amp HEINOLD 1991 2 0 THE ISC LONG TERM DISPERSION MODEL EQUATIONS This section describes the ISC Long Term model equations Where the technical information is the same this section refers to the ISC Short Term model description in Section 1 for details The long term model provides options for modeling the same types of sources as provided by the short term model The information provided below follows the same order as used for the short term model equations The ISC long term model uses input meteorological data that have been summarized into joint frequencies of occu
56. h fi the frequency of occurrence for the j wind direction in the i sector 2 the error term a criterion of 2 lt 2 percent is used to check for convergence of the sector average calculation P 2 the concentration value based on the numerical integration algorithm using Equation 1 58 for the j wind direction in the i sector 2 the j wind direction in the i sector j 1 and N correspond to the two boundaries of the sector The application of Equation 2 6a to calculate the sector average concentration from area sources is an iterative process Calculations using the ISC Short Term algorithm Equation 1 58 are initially made for three wind directions corresponding to the two boundaries of the sector and the centerline direction The algorithm then calculates the concentration for wind directions midway between the three directions for a total of five directions and calculates the 2 8 error term If the error is less than 2 percent then the concentration based on five directions is used to represent the sector average otherwise additional wind directions are selected midway between each of the five directions and the process continued This process continues until the convergence criteria described below are satisfied In order to avoid abrupt changes in the concentrations at the sector boundaries with the numerical integration algorithm a linear interpolation is used to determine the
57. he plume rise see Section 1 5 4 and dispersion parameters see Section 1 5 5 The 1 2 radial distance is calculated as R x y where x is the downwind distance and y is the crosswind distance described in Section 1 1 2 1 5 3 Wind Speed Profile See the discussion given in Section 1 1 3 1 5 4 Plume Rise Formulas The complex terrain algorithm in ISC uses the Briggs plume rise equations described in Section 1 1 4 For distances less 1 69 than the distance to final rise the complex terrain algorithm uses the distance dependent plume height based on the radial distance as described in Section 1 1 4 10 Since the complex terrain algorithm does not incorporate the effects of building downwash the Schulman Scire plume rise described in Section 1 1 4 11 is not used for complex terrain modeling The plume height is used in the calculation of the Vertical Term described in Section 1 5 6 1 5 5 The Dispersion Parameters The dispersion parameters used in the complex terrain algorithms of ISC are the same as the point source dispersion parameters for the simple terrain algorithms described in Section 1 1 5 1 except that the radial distance is used instead of the downwind distance Since the lateral distribution of the plume in complex terrain is determined by the sector average approach the complex terrain algorithm does not use the lateral dispersion parameter F The procedure to account for buoyancy induced disper
58. he volume source option and the area source option may also be used to simulate line sources The algorithms used to model each of these source types are described in detail in the following sections The point source algorithms are described in Section 1 1 The volume area and open pit source model algorithms are described in Section 1 2 Section 1 3 gives the optional algorithms for calculating dry deposition for point volume area and open pit sources and Section 1 4 describes the optional algorithms for calculating wet deposition Sections 1 1 through 1 4 describe calculations for simple terrain defined as terrain elevations below the release height The modifications to these calculations to account for complex terrain are described in Section 1 5 and the treatment of intermediate terrain is discussed in Section 1 6 The ISC Short Term model accepts hourly meteorological data records to define the conditions for plume rise transport diffusion and deposition The model estimates the concentration or deposition value for each source and receptor combination for each hour of input meteorology and calculates user selected short term averages For deposition values either the dry deposition flux the wet deposition flux or the total deposition flux may be estimated The total deposition 1 1 flux is simply the sum of the dry and wet deposition fluxes at a particular receptor location The user also has the option of sel
59. hly turbulent and generally recirculating The ISC models are not appropriate for estimating concentrations within such regions The ISC assumption that this recirculating cavity region extends to a downwind distance of 3h for a squat building or 3h for a tall building is most appropriate for a building whose width is not much greater than its height The ISC user is cautioned that for other types of buildings receptors located at downwind distances of 3h squat buildings or 3h tall buildings may be within the recirculating region The modified F equation for a squat building is given by F 0 7h 0 067 x amp h for 3h x or 1 37 EA x for x 10h where the building height h is in meters For a tall building Huber 1977 suggests that the width scale h replace h in Equation 1 37 The modified F equation for a tall building is then given by F 0 7h 0 067 x amp h for 3h x or 1 38 E x for x 10h where h is in meters It is important to note that F_ is not permitted to be less than the point source value given in Tables 1 2 or 1 4 a condition that may occur The vertical virtual distance x is added to the actual downwind distance x at downwind distances beyond 10h for squat buildings or beyond 10h for tall buildings in order to account for the enhanced initial plume growth caused by the building wake The virtual distance is calculated from solutions to the equations for rural
60. ide a means for conducting screening estimates in complex terrain EPA guidance on complex terrain screening procedures is provided in Section 5 2 1 of the Guideline on Air Quality Models Revised Volume I of the ISC3 User s Guide provides user instructions for the ISC3 models iii ACKNOWLEDGEMENTS The User s Guide for the ISC3 Models has been prepared by Pacific Environmental Services Inc Research Triangle Park North Carolina This effort has been funded by the Environmental Protection Agency EPA under Contract No 68 D30032 with Desmond T Bailey as Work Assignment Manager WAM The technical description for the dry deposition algorithm was developed from material prepared by Sigma Research Corporation and funded by EPA under Contract No 68 D90067 with Jawad S Touma as WAM lv PREFACE ACKNOWLEDGEMENTS FIGURES TABLES SYMBOLS CONTENTS 1 0 THE ISC SHORT TERM DISPERSION MODEL EQUATIONS 1 1 POINT SOURCE EMISSIONS H N Z H UW H EPA O a a o N E ple NNNN ES wos do ute PRPPPPP 1 2 3 4 5 6 S PO 1 2 3 4 The Gaussian Equation Downwind and Crosswind Distances Wind Speed Profile Plume Rise Formulas The Dispersion Parameters The Vertical Term The Decay Term INT SOURCE EMISSIONS General x The Short Term Volume Source Model The Short Term Area Source Model The Short Term Open Pit Source Model ISC SHORT TERM DRY DEPOSITION MODEL 1 2 3
61. ied plume stabilization height h is substituted for the effective stack height h in the Vertical Term given by Equation 1 50 The effective plume Stabilization height at the point x y is given by h h 16F H 1 94 e plume height at point x y without terrain adjustment as described in Section 1 5 4 m Zp Za terrain height of the receptor Ss location above the base of the stack m height above mean sea level of terrain at the receptor location x y m height above mean sea level of the base of the stack m terrain adjustment factor which is 0 5 for stability categories A D and 0 0 for stability categories E and F The effect of the terrain adjustment factor is that the plume height relative to stack base is deflected upwards by an amount equal to half of the terrain height as it passes over complex terrain during unstable and neutral conditions The plume height is not deflected by the terrain under stable conditions 1 5 6 2 The Vertical Term for Particle Deposition The Vertical Term for particle deposition used in the complex terrain algorithm in ISC is the same as described in Section 1 1 6 for the simple terrain algorithm except that the plume height and dispersion parameter input to the vertical term are based on the radial distance as described above and that the adjustment of plume height for terrain above stack base is different as described in Section 1 5 6 2
62. int r 2 is calculated from the seasonal concentrations using the expression P 0 25j P 2 2 1 The terms in Equation 2 1 correspond to the terms discussed in Section 1 1 for the short term model except that the parameters are defined for discrete categories of wind speed wind direction stability and season The various terms are briefly discussed in the following subsections In addition to point source emissions the ISC long term concentration model considers emissions from volume and area sources These model options are discussed in Section 2 2 The optional algorithms for calculating dry deposition are discussed in Section 2 3 2 1 2 Downwind and Crosswind Distances See the discussion given in Section 1 1 2 2 1 3 Wind Speed Profile See the discussion given in Section 1 1 3 2 1 4 Plume Rise Formulas See the discussion given in Section 1 1 4 2 1 5 The Dispersion Parameters 2 1 5 1 Point Source Dispersion Parameters See Section 1 1 5 1 for a discussion of the procedures use to calculate the standard deviation of the vertical concentration distribution F for point sources sources without initial dimensions Since the long term model assumes a uniform lateral distribution across the sector width the model does not use the standard deviation of the lateral dispersion F except for use with the Schulman Scire plume y rise formulas described in Section 1 1 4 11 2 1 5 2 Lateral and Vertical Virtual
63. interpolate between the source elevation and the receptor elevation The profile correction factor P x z is given by 1000 bc za 1 2 1 amp Exp 6w R z 24 Ve 4 1 57a vg amp v v x z o peas 1 8 2222 1 88xpP 8v R z 2 dz vz M 2BFR where R z Zz is an atmospheric resistance to vertical transport that is derived from Briggs formulas for F Gifford 1976 When the product VR Z Za is of order 0 1 or less the exponential function is approximated for small argument to simplify P x z P x z H P fx Z4 4 hv 4 amp v R z Z4q v x z o 1 57b o v2BF P x Z4 M 1 Ava amp v R z z dz This simplification is important since the integral in Equation 1 57a is evaluated numerically whereas that in Equation 1 57b is computed using analytical approximations The resistance R z z is obtained for the following functional forms of F defined by Briggs Case l Rural stability A B Urban stability C I F ax 2 1 R z 24 i in z za B au Case 2 Rural stability C D Urban stability D E F R z Za 2 i B au 1n 2 24 2 E z za a 2 Case 3 Rural stability E F 2 Ln 2 2 2 By amp z Ble amp 22 a 2 2a 2 Case 4 Urban stability A B F ax 1 bx Z 1658 F ax 1 bx Z ees a R z Z4q U c F ax 1 bx sio 2 2 am E ARES Za Aon vi bx z amp 1 yl bx z 1 B au
64. ion First gravitational settling is assumed to result in a tilted plume so that the effective plume height h in Equation e 1 50 is replaced by 1 1 x h ed h amp h h amp v 1 53 us where h x u v is the adjustment of the plume height due to gravitational settling Then a new vertical term V that includes the effects of dry deposition is defined as Va Z Bey V x Zz He Fo x P x z 1 54 V x z h is the vertical term in the absence of any deposition it is just Equation 1 50 with the tilted plume approximation F x is the fraction of material that remains in the plume at the downwind distance x i e the mass that has not yet been deposited on the surface This factor may be thought of as a source depletion factor a ratio of the current mass emission rate to the original mass emission rate P x z is a vertical profile adjustment factor which modifies the reflected Gaussian distribution of Equation 1 50 so that the effects of dry deposition on near surface concentrations can be simulated For large travel times h in Equation 1 53 can become less than zero However the tilted plume approximation is not a valid approach in this region Therefore a minimum value of zero is imposed on h In effect this limits the settling of the plume centerline although the deposition velocity continues to account for gravitational settling near the surface The effect of grav
65. ire pit opening is used to simulate the pit emissions A represents a single area source whose dimensions and location depend on the effective depth of the pit and the wind direction Based on wind tunnel results if D 0 2 then the effective area is about 8 of the total opening of the mine i e A 0 08 If D lt 0 2 then the fractional area increases as follows 1 55 Be or Me ada Ea 1 74 When D 0 which means that the height of emissions above the floor equals the effective depth of the pit the effective area is equal to the total area of the mine opening i e A 1 0 Having determined the effective area from which the model will simulate the pit emissions the specific dimensions of this effective rectangular area are calculated as a function of 2 such that see Figure 1 10 2 1 75 eee A poe e and 1 cos 29 S AL A 1 76 Note that in equations 1 75 and 1 76 W is defined as the short dimension of the pit and L is the long dimension AW is the dimension of the effective area aligned with the short side of the pit and AL is the dimension of the effective area aligned with the long side of the pit see Figure 1 10 The dimensions AW and AL are used by the model to define the shape of the effective area for input to the area source algorithm described in Section 1 2 3 The emission rate Q for the effective area is such that On Q A 1 77 where Q is the emission rate per unit area from
66. is determined as follows X gt FACT WIDTH A12 where X the downwind distance from the center of the source to the receptor FACT a Stability dependent factor see below and WIDTH the crosswind width of the area source AA A gt E AO ss 35 A DB pp lt p los When area sources are modeled with dry depletion the TOXICS option also allows the user to specify the AREADPLT option which applies a single effective dry depletion factor to the undepleted value calculated for the area source The effective dry depletion factor which INDEX 6 replaces the application of dry depletion within the area source integration is intended to provide potential runtime savings to the user Since dry depletion is distance dependent the effective dry depletion factor is calculated for an empirically derived effective distance The effective distance is calculated as the distance from the receptor to a point within the area source that is one third the distance from the downwind edge to the upwind edge For receptors located upwind of the downwind edge including receptors located within the area source the effective distance is one third the distance from the receptor to the upwind edge of the source In addition to the area source optimizations described above when the TOXICS option is specified the dry depletion integration is performed using a 2 point Gaussian Quadrature routine rather than the Romberg integration used for r
67. is performed following Briggs 1974 p 4 The modified physical stack height h is found from il Vs he h a amp 1 5 f r Y lt 15 us 1 7 or a ls for v 1 5 where h is physical stack height m v is stack gas exit velocity m s and d is inside stack top diameter m This h is used throughout the remainder of the plume height computation If stack tip downwash is not considered h h s in the following equations 1 1 4 2 Buoyancy and Momentum Fluxes For most plume rise situations the value of the Briggs buoyancy flux parameter F m s is needed The following equation is equivalent to Equation 12 Briggs 1975 p 63 1 2 T Fa avd 1 8 4T where T T T T is stack gas temperature K and T is ambient air temperature K For determining plume rise due to the momentum of the plume the momentum flux parameter Fa m s is calculated based on the following formula m ss 1 9 1 1 4 3 Unstable or Neutral Crossover Between Momentum and Buoyancy For cases with stack gas temperature greater than or equal to ambient temperature it must be determined whether the plume rise is dominated by momentum or buoyancy The crossover temperature difference T is determined by setting Briggs 1969 p 59 Equation 5 2 equal to the combination of Briggs 1971 p 1031 Equations 6 and 7 and solving for T as follows for F lt 55 C Te 002977 1 1
68. itational settling beyond the plume touchdown point where aa 0 is to modify the vertical structure of the plume which is accounted for by modifying the vertical dispersion parameter F Zz The process of adjusting the vertical profile to reflect loss of plume mass near the surface is illustrated in Figures 1 6 and 1 7 At a distance far enough downwind that the plume size in the vertical has grown larger than the height of the plume significant corrections to the concentration profile may be needed to represent the removal of material from the plume due to deposition Figure 1 6 displays a depletion factor F and the corresponding profile correction factor Plz for a distance at which F is 1 5 times the plume height The depletion factor is constant with height whereas the profile correction shows that most of the material is lost from the lower portion of the plume Figure 1 7 compares the vertical profile of concentration both with and without deposition and the corresponding depletion of material from the plume The depleted plume profile is computed using Equation 1 54 Both F x and P x z depend on the size and density of the particles being modeled because this effects the total deposition velocity See Section 1 3 2 Therefore for a given source of particulates ISC allows multiple particle size categories to be defined with the maximum number of particle size categories controlled by a parameter statement in the
69. l deposited on the surface is not removed from the plume 1 1 7 The Decay Term D The Decay Term in Equation 1 1 is a simple method of accounting for pollutant removal by physical or chemical processes It is of the form D exp RE for R gt 0 ug 1 63 or el for R 0 where R the decay coefficient s7 a value of zero means decay is not considered x downwind distance m For example if T is the pollutant half life in seconds the user can obtain R from the relationship 1 64 The default value for R is zero That is decay is not considered in the model calculations unless R is specified However a decay half life of 4 hours R 0 0000481 s is automatically assigned for SO when modeled in the urban mode 1 2 NON POINT SOURCE EMISSIONS 1 2 1 General The ISC models include algorithms to model volume area and open pit sources in addition to point sources These non point source options of the ISC models are used to simulate the effects of emissions from a wide variety of industrial sources In general the ISC volume source model is used to simulate the effects of emissions from sources such as building roof monitors and line sources for example conveyor belts and rail lines The ISC area source model is used to simulate the effects of fugitive emissions from sources such as storage piles and slag dumps The ISC open pit source model is used to Simulate fugitive emissions from belo
70. lar shaped pit with an arbitrary wind direction as shown in Figure 1 10 The steps that the model uses for determining the effective area source are as follows 1 Determine the upwind sides of the pit based on the wind direction 2 Compute the along wind length of the pit R based on the wind direction and the pit geometry R varies between the lengths of the two sides of the rectangular pit as follows R LOL 2 90 W 2 90 1 71 where L is the long axis and W is the short axis of the pit and 2 is the wind direction relative to the long axis L of the pit therefore 2 varies between OE and 90E Note that with this formulation and a square pit the value of Rwill remain constant with wind direction at R L W The along wind dimension R is the scaling factor used to normalize the depth of the pit 3 The user specifies the average height of emissions from the floor of the pit H and the pit volume V The effective pit depth d and the relative pit e depth D are then calculated as follows r d V LO 1 72 D d 6H R 1 73 4 Based on observations and measurements in a wind tunnel study Perry et al 1994 it is clear that the emissions within the pit are not uniformly released from the pit opening Rather the emissions show a tendency to be emitted primarily from an upwind sub area of the pit opening Therefore an effective area source with A being the fractional size relative to the ent
71. meters Dispersion parameters for the Long Term model McElroy Pooler bag eR A hog an Bee gi di Pasquill Gifford 1 14 1 16 INDEX 1 for the Long Term model a2 1 65 2 12 2 7 1 46 1 56 1 22 1 14 1 42 1 29 1 29 2 4 1 19 1 18 Distance dependent plume rise Downwind distance cosa ep and virtual distance for area sources for building wake dispersion for dispersion coefficients Dry deposition for the Long Term model for the Short Term model Elevated terrain e truncation above stack height Entrainment coefficient Final plume rise distance to stable A unstable or neutral Flagpole receptor Gaussian plume model sector averages for complex terrain sector averages for Long Term GEP stack height Gradual plume rise for buoyant plumes for Schulman Scire downwash stable momentum unstable and neutral momentum used for wake plume height Half life 7 Huber Snyder downwash algorithm Initial lateral dimension for the Long Term model for volume sources Initial plume length Schulman Scire downwash Initial plume radius Schulman Scire downwash Initial vertical dimension for volume sources Intermediate terrain Jet entrainment coefficient Lateral dispersion parameters for the Long Term model Lateral virtual distance for the Long Term model Lateral virtual distances for building downwash INDEX 2 1 13 2 3 1 20 1 47 1
72. n 1 1 and in the plume rise formulas described in Section 1 1 4 The power law equation is of the form ih 1 6 where p is the wind profile exponent Values of p may be provided by the user as a function of stability category and wind speed class Default values are as follows Stability Category Rural Exponent Urban Exponent A 0 07 0 15 B 0 07 0 15 C 0 10 0 20 D 0 15 0 25 E 0 35 0 30 F 0 55 0 30 The stack height wind speed u is not allowed to be less than 1 0 m s 1 1 4 Plume Rise Formulas The plume height is used in the calculation of the Vertical Term described in Section 1 1 6 The Briggs plume rise equations are discussed below The description follows Appendix B of the Addendum to the MPTER User s Guide Chico and Catalano 1986 for plumes unaffected by building wakes The distance dependent momentum plume rise equations as described in Bowers et al 1979 are used to determine if the plume is affected by the wake region for building downwash calculations These plume rise calculations for wake determination are made assuming no stack tip downwash for both the Huber Snyder and the Schulman Scire methods When the model executes the building downwash methods of Schulman and Scire the reduced plume rise suggestions of Schulman and Scire 1980 are used as described in Section 1 1 4 11 1 1 4 1 Stack tip Downwash In order to consider stack tip downwash modification of the physical stack height
73. net force toward the surface which results in a small enhancement of the deposition velocity of the particle A second effect is that the impaction of new water vapor molecules at an evaporating surface displaces a certain volume of air For example 18 g of water vapor evaporating from 1 m will displace 22 4 liters of air at standard temperature and pressure STP conditions Hicks 1982 This effect is called Stefan flow The Stefan flow effect tends to reduce deposition fluxes from an evaporating surface Conversely deposition fluxes to a surface experiencing condensation will be enhanced ELECTROPHORESIS Attractive electrical forces have the potential to assist the transport of small particles through the quasi laminar deposition layer and thus could increase the deposition velocity in situations with high local field strengths However Hicks 1982 suggests this effect is likely to be small in most natural circumstances Phoretic and Stefan flow effects are generally small However for particles in the range of 0 1 1 0 ym diameter which have low deposition velocities these effects may not always be negligible Therefore the ability to specify a phoretic term to the deposition velocity is added i e v N Va Va pnor Where v Nis the modified deposition velocity and Vag S the phoretic term Although the magnitude and sign of Vapor Will vary a small constant value of 0 01 cm s is used in the present implemen
74. nverged to within a tolerance of 0 02 i e 2 percent for two successive iterations and at least 2 halving intervals have been completed a minimum of 5 wind direction simulations or if the estimate of the sector average concentration is less than 1 0E 10 and at least 2 halving intervals have been completed The first condition essentially puts a time limit on the integration process the second condition checks for the accuracy of the estimate of the sector average and the third condition places a lower threshold limit that avoids convergence problems associated with very small concentrations where truncation error may be significant 2 2 4 The Long Term Open Pit Source Model The ISC Long Term Open Pit Source Model is based on the use of the long term area source model described in Section 2 2 3 The escape fractions and adjusted mass distribution for particle emissions from an open pit and the determination of the size shape and location of the effective area source used to model open pit emissions are described in Section 1 2 4 For the Long Term model a sector average value for open pit sources is calculated by determining an effective area for a range of wind directions within the sector and increasing the number of wind directions used until the result converges as described in Section 2 2 3 for the Long Term area source model The contribution from each effective area used within a sector is calculated using the
75. o an equivalent uniform rectangular distribution Both F and F are evaluated at x 3L and are taken as the larger of the building enhanced sigmas and the sigmas obtained from the curves see Section 1 1 5 3 The value of F used in the calculation of L also includes the linear decay term A The rise of a downwashed finite line source was solved in the BLP model Scire and Schulman 1980 The neutral distance dependent rise Z is given by 2 3L 3R 6R L 3R E z z ae 1 30 B B The stable distance dependent rise is calculated by 2 rt 3L 3R 6R L 3R 3F Xx 1 3la me a 6 z2 Lory opto b l Z B 2 7u with a maximum stable buoyant rise given by 2 3L 3R 6R L 3R E z z 1 31b B B where F buoyancy flux term Equation 1 8 mf s F momentum flux term Equation 1 9 m s7 x downwind distance m u wind speed at release height m s v stack exit velocity m s d stack diameter m entrainment coefficient 0 6 jet entrainment coefficient o s M M Ss Stability parameter g T a The larger of momentum and buoyant rise determined separately by alternately setting F or F 0 and solving for Z is selected for plume height calculations for Schulman Scire downwash In the ISC models Z is determined by solving the cubic equation using Newton s method 1 1 5 The Dispersion Parameter
76. odel is used to simulate the effects of emissions from sources such as building roof monitors and for line sources for example conveyor belts and rail lines The north south and east west dimensions of each volume source used in the model must be the same Table 1 6 summarizes the general procedures suggested for estimating initial lateral F and for multiple volume sources used to represent a line and vertical F dimensions for single volume sources yo za source In the case of a long and narrow line source such as a rail line it may not be practical to divide the source into N volume sources where N is given by the length of the line source divided by its width The user can obtain an approximate representation of the line source by placing a smaller number of volume sources at equal intervals along the line source as shown in Figure 1 8 In general the spacing between individual volume sources should not be greater than 1 47 twice the width of the line source However a larger spacing can be used if the ratio of the minimum source receptor separation and the spacing between individual volume sources is greater than about 3 In these cases concentrations calculated using fewer than N volume sources to represent the line source converge to the concentrations calculated using N volume sources to represent the line source as long as sufficient volume sources are used to preserve the horizontal geometry of the line source
77. of the integral used if any of the following conditions is true if the number of halving intervals N in the trapezoidal approximation of the integral has reached 10 where the number of individual elements in the approximation is given by 1 2 513 for N of 10 if the extrapolated estimate of the real integral Romberg approximation has converged to within a tolerance of 0 0001 i e 0 01 percent and at least 4 halving intervals have been completed or if the extrapolated estimate of the real integral is less than 1 0E 10 and at least 4 halving intervals have been completed The first condition essentially puts a time limit on the integration process the second condition checks for the accuracy of the estimate of the integral and the third condition places a lower threshold limit on the value of the integral The result of these numerical methods is an estimate of the full integral that is essentially equivalent to but much more efficient than the method of estimating the integral as a series of line sources such as the method used by the PAL 2 0 model Petersen and Rumsey 1987 1 2 4 The Short Term Open Pit Source Model The ISC open pit source model is used to estimate impacts for particulate emissions originating from a below grade open pit such as a surface coal mine or a stone quarry The ISC models allow the open pit source to be characterized by a rectangular shape with an aspect ra
78. on layer including the ground water surface There are three main pathways for uptake reaction within the vegetation or at the surface EPA 1995a 1 Transfer through the stomatal pore and dissolution or reaction in the mesophyll cells plant tissue that contains chlorophyll 2 Reaction with or transfer through the leaf cuticle 3 Transfer into the ground water surface These pathways are treated as three resistances in parallel r LAI r LAI r 1 r A4 c INDEX 2 where r the internal foliage resistance s m Pathway 1 Transfer through the stomatal pore and dissolution or reaction in mesophyll cells cut LAI Pathway 1 the cuticle resistance s m Pathway 2 Reaction with or transfer through the leaf cuticle a thin film covering the surface of plants the ground or water surface resistance s m Pathway 3 Transfer into the ground water surface and the leaf area index ratio of leaf surface area divided by ground surface area The LAI is specified as a function of wind direction and month season and is included in the meteorological input file provided by the MPRM preprocessor The internal foliage resistance r consists of two components r r A5 where r the resistance s m to transport through the stomatal pore see below and the resistance s m to dissolution or reaction of the pollutant in the mesophyll spongy parenchyma cells user input by species
79. ons F Surface Based Source h 0 Fi vertical dimension of source divided by 2 15 Elevated Source h gt 0 on or F building height Adjacent to a Building divided by 2 15 Elevated Source h gt 0 not FL vertical dimension of on or Adjacent to a Building source divided by 4 3 1 2 3 The Short Term Area Source Model The ISC Short Term area source model is based on a numerical integration over the area in the upwind and crosswind directions of the Gaussian point source plume formula given in Equation 1 1 Individual area sources may be represented as rectangles with aspect ratios length width of up to 10 to 1 In addition the rectangles may be rotated relative to a north south and east west orientation As shown by Figure 1 9 the effects of an irregularly shaped area can be simulated by dividing the area source into multiple areas Note that the Size and shape of the individual area sources in Figure 1 9 varies the only requirement is that each area source must be a 1 49 rectangle As a result an irregular area source can be represented by a smaller number of area sources than if each area had to be a square shape Because of the flexibility in specifying elongated area sources with the Short Term model up to an aspect ratio of about 10 to 1 the ISCST area source algorithm may also be useful for modeling certain types of line sources The ground level concentration at a receptor located downwind of all
80. ort best fit values for 8 as a function of particle size These values of the scavenging rate coefficient are displayed in Figure 1 11 1 66 Although the largest particle size included in the study is 10 um the authors suggest that 8 should reach a plateau beyond 10 pm as shown in Figure 1 11 The scavenging rate coefficients for frozen precipitation are expected to be reduced to about 1 3 of the values in Figure 1 11 based on data for sulfate and nitrate Scire et al 1990 The scavenging rate coefficients are input to the model by the user The wet deposition algorithm requires precipitation type liquid or solid and precipitation rate which is prepared for input to the model through the meteorological preprocessor programs PCRAMMET or MPRM 1 5 ISC COMPLEX TERRAIN SCREENING ALGORITHMS The Short Term model uses a steady state sector averaged Gaussian plume equation for applications in complex terrain 1 e terrain above stack or release height Terrain below release height is referred to as simple terrain receptors located in simple terrain are modeled with the point source model described in Section 1 1 The sector average approach used in complex terrain implies that the lateral crosswind distribution of concentrations is uniform across a 22 5 degree sector The complex terrain screening algorithms apply only to point source and volume source emissions area source and open pit emission sources are excluded The comple
81. ov length m Initial plume length for Schulman Scire downwash sources with enhanced lateral plume spread m Lesser of the building height and crosswind projected building width m Alongwind length of open pit source m Profile adjustment factor dimensionless Wind speed power law profile exponent dimensionless Area Source pollutant emission rate g s Effective emission rate for effective area source for an open pit source g s Adjusted emission rate for particle size category for open pit emissions g s Pollutant emission rate g s Total amount of pollutant emitted during time period J g Precipitation rate mm hr Initial plume radius for Schulman Scire downwash sources m Atmospheric resistance to vertical transport s cm Radial distance range in a polar receptor network m Atmospheric resistance s cm Deposition layer resistance s cm M M T Stability parameter g a Smoothing term for smoothing across adjacent sectors in the Long Term model dimensionless Splip correction factor dimensionless Schmidt number L D dimensionless Stokes number v 9 u L dimensionless Ambient temperature K Stack gas exit temperature K Wind speed measured at reference anemometer height m s Wind speed adjusted to release height m s Surface friction velocity m s Vertical term of the Gaussian plume equation dimensionless Vertical term with dry deposition of the Gau
82. parameters virtual distances Vertical dispersion parameters Vertical term o E Mh ea for gases and small particulates for large particulates for the Long Term model for the Short Term model for uniform vertical mixing in complex terrain in elevated terrain Vertical virtual distances for building downwash Bad A os Virtual distances 1 20 1 21 for the Long Term model for volume sources Virtual point source Volume source gE a ee deposition algorithm for the Long Term model for the Short Term model Wet deposition for the Short Term model Wind speed minimum wind speed for modeling Wind speed profile INDEX 4 1 2 1 2 2 Es 1 E 2 e 19 5 31 6 5 66 32 67 6 25 1 47 2 Te 2 ae 2 2 T 1 20 to A E LS 1 3 1 47 1 65 1 653 2 3 13T 1 33 A a 1 28 1 29 1 44 2 4 1 43 1 64 2 2 1 60 1 4 1 65 5 44 7 46 11 7 43 ADDENDUM USER S GUIDE FOR THE INDUSTRIAL SOURCE COMPLEX ISC3 DISPERSION MODELS VOLUME II DESCRIPTION OF MODEL ALGORITHMS U S ENVIRONMENTAL PROTECTION AGENCY Office of Air Quality Planning and Standards Emissions Monitoring and Analysis Division Research Triangle Park North Carolina 27711 June 1999 ACKNOWLEDGMENTS The Addendum to the User s Guide for the ISC3 Models has been prepared by Roger W Brode of Pacific Environmental Services Inc Research Triangle Park North Carolina under subcontract to EC R Inc Chapel
83. r dimensionless Fraction of mass in a particular settling velocity category for particulates dimensionless Particle density g cm Density of air g cm Horizontal lateral dispersion parameter m Initial horizontal dispersion parameter for virtual point source m Effective lateral dispersion parameter including effects of buoyancy induced dispersion m xii Vertical dispersion parameter m Initial vertical dispersion parameter for virtual point source m Effective vertical dispersion parameter including effects of buoyancy induced dispersion m Viscosity of air H 0 15 cm s Absolute viscosity of air u 1 81 x 10 g cm s Concentration ug m Concentration with dry deposition effects ug m xiii 1 0 THE ISC SHORT TERM DISPERSION MODEL EQUATIONS The Industrial Source Complex ISC Short Term model provides options to model emissions from a wide range of sources that might be present at a typical industrial source complex The basis of the model is the straight line steady state Gaussian plume equation which is used with some modifications to model simple point source emissions from stacks emissions from stacks that experience the effects of aerodynamic downwash due to nearby buildings isolated vents multiple vents storage piles conveyor belts and the like Emission sources are categorized into four basic types of sources i e point sources volume sources area sources and open pit sources T
84. r the program sums the deposition calculated for each hour to obtain the total deposition flux for the period In the case of a volume source the user must specify the effective emission height h and the initial source dimensions Fo and F It should be noted that for computational yo purposes the model calculates the quantity j N Van Van 7 as the vertical term 1 3 4 Area and Open Pit Source Emissions For area and open pit source emissions Equation 1 65 is changed to the form 1 Fan Pan an Qa KN v V4 D 2 1 88 Recs RL qn exp amp 0 5 lay ax 2Bu MFF m F Ye y y where K D V and vg are defined in Equations 1 1 1 54 1 65 and 1 80 The parameter Qy is the total mass per unit area emitted over the time period J for which deposition is calculated The area source integral is estimated as described in Section 1 2 3 1 4 THE ISC SHORT TERM WET DEPOSITION MODEL A scavenging ratio approach is used to model the deposition of gases and particles through wet removal In this approach the flux of material to the surface through wet deposition F is the product of a scavenging ratio times the concentration integrated in the vertical 4 F x y P x y z dz 1 89 where the scavenging ratio 7 has units of s The concentration value is calculated using Equation 1 1 Since the precipitation is assumed to initiate above the plume height a wet deposition flux is calculated e
85. rces For a single stack the mean seasonal concentration is given by p K QfSVD TEN V2B R 27 ae uh where K units scaling coefficient see Equation 1 1 Q pollutant emission rate mass per unit time for the i wind speed category the k stability category and the 1 season f frequency of occurrence of the i wind speed category the j wind direction category and the k stability category for the 1 season 2 the sector width in radians R radial distance from lateral virtual point source for building downwash to the receptor x x y 1 m x downwind distance from source center to receptor measured along the plume axis m y lateral distance from the plume axis to the receptor m x lateral virtual distance see Equation 1 35 equals zero for point sources without building downwash and for downwash sources that do not experience lateral dispersion enhancement m S a smoothing function similar to that of the AQDM see Section 2 1 8 u mean wind speed m sec at stack height for the i wind speed category and k stability category F standard deviation of the vertical concentration distribution m for the k stability category V the Vertical Term for the i wind speed category k stability category and 1 season D the Decay Term for the i wind speed category and k stability category The mean annual concentration at the po
86. rrence for particular wind speed classes wind direction sectors and Stability categories These summaries called STAR summaries for STability ARray may include frequency distributions over a monthly seasonal or annual basis The long term model has the option of calculating concentration or dry deposition values for each separate STAR summary input and or for the combined period covered by all available STAR summaries Since the wind direction input is the frequency of occurrence over a sector with no information on the distribution of winds within the sector the ISC long term model uses a Gaussian sector average plume equation as the basis for modeling pollutant emissions on a long term basis 2 1 POINT SOURCE EMISSIONS 2 1 1 The Gaussian Sector Average Equation The ISC long term model makes the same basic assumption as the short term model In the long term model the area surrounding a continuous source of pollutants is divided into sectors of equal angular width corresponding to the sectors of the seasonal and annual frequency distributions of wind direction wind speed and stability Seasonal or annual emissions from the source are partitioned among the sectors according to the frequencies of wind blowing toward the 2 1 sectors The concentration fields calculated for each source are translated to a common coordinate system either polar or Cartesian as specified by the user and summed to obtain the total due to all sou
87. s 1 1 5 1 Point Source Dispersion Parameters Equations that approximately fit the Pasquill Gifford curves Turner 1970 are used to calculate F and F in meters for the rural mode The equations used to calculate F are of the form F 465 11628 x tan TH 1 32 where TH 0 017453293 c amp d 1n x 1 33 In Equations 1 32 and 1 33 the downwind distance x is in kilometers and the coefficients c and d are listed in Table 1 1 The equation used to calculate F is of the form F ax 1 34 Z where the downwind distance x is in kilometers and F is in meters The coefficients a and b are given in Table 1 2 Tables 1 3 and 1 4 show the equations used to determine ES and F for the urban option These expressions were determined by Briggs as reported by Gifford 1976 and represent a best fit to urban vertical diffusion data reported by McElroy and Pooler 1968 While the Briggs functions are assumed to be valid for downwind distances less than 100m the user is cautioned that concentrations at receptors less than 100m from a source may be suspect TABLE 1 1 PARAMETERS USED TO CALCULATE PASQUILL GIFFORD Es E 465 11628 x tan TH TH 0 017453293 c d ln x Pasquill Stability Category c d 24 1670 2 5334 B 18 3330 1 8096 C 12 5000 1 0857 D 8 3330 0 72382 E 6 2500 0 54287 F 4 1667 0 36191 where F is in meters and x is in kilometers TABLE 1 2 PARAMETERS USED TO CALCULATE PASQUIL
88. s a and b are obtained form Table 1 2 and F is the standard deviation in meters of the vertical concentration distribution at the source It is important to note that the ISC model programs check to ensure that the x used to calculate F at x x in the rural mode is the x calculated using the coefficients a and b that correspond to the distance category specified by the quantity x x To determine virtual distances for the urban mode the functions displayed in Tables 1 3 and 1 4 are solved for x The solutions are quadratic formulas for the lateral virtual distances and for vertical virtual distances the solutions are cubic equations for stability classes A and B a linear equation for stability class C and quadratic equations for 1 20 stability classes D E and F The cubic equations are solved by iteration using Newton s method TABLE 1 5 COEFFICIENTS USED TO CALCULATE LATERAL VIRTUAL DISTANCES FOR PASQUILL GIFFORD DISPERSION RATES 1 0 E y P Pasquill Stability Category p q 209 14 0 890 B 154 46 0 902 C 103 26 0 917 D 68 26 0 919 E 51 06 0 921 F 33 92 0 919 1 1 5 3 Procedures Used to Account for the Effects of Building Wakes on Effluent Dispersion The procedures used by the ISC models to account for the effects of the aerodynamic wakes and eddies produced by plant buildings and structures on plume dispersion originally followed the suggestions of Huber 1977 and Snyder 1976 Their suggestion
89. s and provides the guidance on the use of this option The Vertical Term for large particulates is given by Equation 1 53 2 1 7 The Decay Term See the discussion given in Section 1 1 7 2 1 8 The Smoothing Function As shown by Equation 2 1 the rectangular concentration distribution within a given angular sector is modified by the function S 2 which smooths discontinuities in the concentration at the boundaries of adjacent sectors The centerline concentration in each sector is unaffected by contribution from adjacent sectors At points off the sector centerline the concentration is a weighted function of the concentration at the centerline and the concentration at the centerline of the nearest adjoining sector The smoothing function is given by 2 amp 2 amp 2 2 S for 2 amp 2 2 5 or o for ae where 2 7 the angle measured in radians from north to the centerline of the j wind direction sector 2 the angle measured in radians from north to the receptor point R 2 where R defined above for equation 2 1 is measured from the lateral virtual source 2 2 NON POINT SOURCE EMISSIONS 2 2 1 General As explained in Section 1 2 1 the ISC volume area and open pit sources are used to simulate the effects of emissions from a wide variety of industrial sources Section 1 2 2 provides a description of the volume source model Section 1 2 3 provides a description of the ar
90. s are principally based on the results of wind tunnel experiments using a model building with a crosswind dimension double that of the building height The atmospheric turbulence simulated in the wind tunnel experiments was intermediate between the turbulence intensity associated with the slightly unstable Pasquill C category and the turbulence intensity associated with the neutral D category Thus the data reported by Huber and Snyder reflect a specific stability building shape and building orientation with respect to the mean wind direction It follows that the ISC wake effects evaluation procedures may not be strictly applicable to all situations The ISC models also provide for the revised treatment of building wake effects for certain sources which uses modified plume rise algorithms following the suggestions of Schulman and Hanna 1986 This treatment is largely based on the work of Scire and Schulman 1980 When the stack height is less than the building height plus half the lesser of the building height or width the methods of Schulman and Scire are followed Otherwise the methods of Huber and Snyder are followed In the ISC models direction specific building dimensions may be used with either the Huber Snyder or Schulman Scire downwash algorithms The wake effects evaluation procedures may be applied by the user to any stack on or adjacent to a building For regulatory application a building is considered sufficiently close
91. sion constant 1 x 10 cm um and S the slip correction factor which is computed as 2X la Ya e sie dpl xa Su 1 1 85 84 10 d and X a a a are constants with values of 6 5 x op 1 257 0 4 and 0 55 x 10 respectively The Brownian diffusivity of the pollutant in cm s is computed from the following relationship T S be ON EEE 1 86 a p where T is the air temperature EK The first term of Eqn 1 83 involving the Schmidt number parameterizes the effects of Brownian motion This term controls the deposition rate for small particles The second term involving the Stokes number is a measure of the importance of inertial impaction which tends to dominate for intermediate sized particles in the 2 20 um diameter size range The deposition algorithm also allows a small adjustment to the deposition rates to account for possible phoretic effects Some examples of phoretic effects Hicks 1982 are THERMOPHORESIS Particles close to a hot surface experience a force directed away from the surface because on the average the air molecules impacting on the side of the particle facing the surface are hotter and more energetic DIFFUSIOPHORESIS Close to an evaporating surface a particle is more likely to be impacted by water molecules on the side of the particle facing the surface Since the water molecules have a lower molecular weight than the average air molecule there is a
92. sion in the complex terrain algorithm only affects the vertical dispersion term see Equation 1 48 Since the complex terrain algorithm does not incorporate the effects of building downwash the enhanced dispersion parameters and virtual distances do not apply 1 5 6 The Vertical Term The Vertical Term used in the complex terrain algorithm in ISC is the same as described in Section 1 1 6 for the simple terrain algorithm except that the plume height and dispersion parameter input to the vertical term are based on the radial distance as described above and that the adjustment of plume height for terrain above stack base is different as described in Section 1 5 6 1 1 5 6 1 The Vertical Term in Complex Terrain The ISC complex terrain algorithm makes the following assumption about plume behavior in complex terrain The plume axis remains at the plume stabilization height above mean sea level as it passes over complex terrain for stable conditions categories E and F and uses a half height correction factor for unstable and neutral conditions categories A D The plume centerline height is never less than 10 m above the ground level in complex terrain The mixing height is terrain following i e the mixing height above ground at the receptor location is assumed to be the same as the height above ground at the source location The wind speed is a function of height above the surface see Equation 1 6 Thus a modif
93. ssian plume equation dimensionless Particle deposition velocity cm s Gravitational settling velocity for particles cm s Stack gas exit velocity m s X coordinate in a Cartesian grid receptor network m Length of side of square area source m Y coordinate in a Cartesian grid receptor network m Direction in a polar receptor network degrees Downwind distance from source to receptor m Lateral virtual point source distance m Vertical virtual point source distance m Downwind distance to final plume rise m Downwind distance at which turbulence dominates entrainment m Crosswind distance from source to receptor m Receptor terrain height above mean sea level m xi M M PP DP woo Z Dry deposition reference height m Receptor height above ground level i e flagpole m Reference height for wind speed power law m Stack base elevation above mean sea level m Mixing height m Surface roughness height m Entrainment coefficient used in buoyant rise for Schulman Scire downwash sources 0 6 Jet entrainment coefficient used in gradual momentum Tu plume rise calculations oe v S Plume rise m Potential temperature gradient with height K m Escape fraction of particle size category for open pit emissions dimensionless Precipitation scavenging ratio s Precipitation rate coefficient s mm hr pi 3 14159 Decay coefficient 0 693 T s Stability adjustment facto
94. tation of the model to represent combined phoretic effects 1 3 3 Point and Volume Source Emissions As stated in Equation 1 59 deposition is modeled as the product of the near surface concentration from Equation 1 1 times the deposition velocity from Equation 1 80 Therefore the vertical term given in Equation 1 54 that is used to obtain the concentration at height z subject to particle settling and deposition can be evaluated at height z for one particle size and multiplied by a deposition velocity for that particle size to obtain a corresponding vertical term for deposition Since more than one particle size category is typically used the deposition for the n size category must also include the mass fraction for the category 1 Fan Pir Ya QKN Van Van x Zar h a D 2BF F u exp amp 0 5 de y 1 87 where K N V and D were defined previously Equations 1 1 1 54 and 1 63 The parameter Q is the total amount of material emitted during the time period J for which the deposition calculation is made For example Q is the total amount of material emitted during a 1 hour period if an hourly deposition is calculated To simplify the user input and to keep the maximum compatibility between input files for concentration and deposition runs the model takes emission inputs in grams per second g s and converts to grams per hour for deposition calculations For time periods longer than an hou
95. the Schulman and Scire building downwash method 1 1 5 3 1 Huber and Snyder building downwash procedures The first step in the wake effects evaluation procedures used by the ISC model programs is to calculate the gradual plume rise due to momentum alone at a distance of two building heights using Equation 1 23 or Equation 1 25 If the plume height h given by the sum of the stack height with no stack tip downwash adjustment and the momentum rise is greater than either 2 5 building heights 2 5 h or the sum of the building height and 1 5 times the building width h 1 5 h the plume is assumed to be unaffected by the building wake Otherwise the plume is assumed to be affected by the building wake The ISC model programs account for the effects of building wakes by modifying both F and F for plumes with plume height to building height ratios less than or equal to 1 2 and by modifying only F for plumes from stacks with plume height to building height ratios greater than 1 2 but less than 2 5 The plume height used in the plume height to stack height ratios is the same plume height used to determine if the plume is affected by the building wake The ISC models define buildings as squat h h or tall h lt h The ISC models include a general procedure for modifying F and F at distances greater than or equal to 3h for squat buildings or 3h for tall buildings The air flow in the building cavity region is both hig
96. the meteorological input file for the model by the MPRM preprocessor and Rmax the incoming solar radiation W m at which full opening of the stomata occur assume constant and equal to 600 During periods of moisture stress the need to prevent moisture loss becomes critical and the stomata close Thus for period B active vegetation under moisture stress conditions assume that b bain When vegetation is inactive e g during the seasonal dry period the internal foliage resistance becomes very large essentially cutting off Pathway 1 Assuming the vegetation is in state A active and unstressed ambient temperature provides an additional bound on the value of r During cold periods T lt 10EC metabolic activity slows and b is set by the code to bnin During hot weather conditions T gt 35EC the stomata are fully open b b to allow evaporative cooling of the plant Pathway 2 The resistance due to reaction with or transfer through the leaf cuticle fau is given by EPA 1995a Pout Aer Ay euelref A8 where Aj the reference reactivity parameter of SO 8 0 Ar the reactivity parameter for the depositing gas NO 8 O 15 HNO 18 PAN 4 and the empirically determined reference cuticle resistance s m of SO set equal to 3000 s m Padro et al 1991 Ty ref INDEX 4 Pathway 3 The third resistance pathway for r is transfer into the ground water surface r In sparsely vegetated
97. the pit after adjustment for escape fraction if the emissions were uniformly released from the actual pit opening with an area of L That is if the effective area is one third of the total area then the emission rate per unit area used for the effective area is three times that from the full area Because of the high level of turbulence in the mine the pollutant is initially mixed prior to exiting the pit Therefore some initial vertical dispersion is included to represent this in the effective area source Using the effective pit depth d as the representative dimension over which the pollutant is vertically mixed in the pit the initial vertical dispersion value F is equal to d 4 3 Note that 4 3 represents about 90 of a Gaussian plume in the vertical so that the mixing in the pit is assumed to approximately equal the mixing in a plume Therefore for the effective area source representing the pit emissions the initial dispersion is included with ambient dispersion as FL E F x 12 1 78 Z For receptors close to the pit the initial dispersion value can be particularly important Once the model has determined the characteristics of the effective area used to model pit emissions for a particular hour the area source algorithm described in Section 1 2 3 is used to calculate the concentration or deposition flux values at the receptors being modeled 1 3 THE ISC SHORT TERM DRY DEPOSITION MODEL
98. tio length width of up to 10 to 1 The rectangular pit may also be rotated relative to a north south and east west orientation Since the open pit model does not apply to receptors located within the boundary of the pit the concentration at those receptors will be set to zero by the ISC models The model accounts for partial retention of emissions within the pit by calculating an escape fraction for each particle size category The variations in escape fractions across particle sizes result in a modified distribution of mass escaping from the pit Fluid modeling has shown that within pit emissions have a tendency to escape from the upwind side of the pit The open pit algorithm simulates the escaping pit emissions by using an effective rectangular area source using the ISC area source algorithm described in Section 1 2 3 The shape size and location of the effective area source varies with the wind direction and the relative depth of the pit Because the shape and location of the effective area source varies with wind direction a single open pit source should not be subdivided into multiple pit sources The escape fraction for each particle size catagory Q is calculated as follows 1 1 g EN A A 1 68 1 v AS where v is the gravitational settling velocity m s U is the approach wind speed at 10m m s 1 53 ls the proportionality constant in the relationship between flux from the pit and the product of U and
99. tion 2 3 3 Area and Open Pit Source Emissions The area and open pit source dry deposition calculations for the ISCLT model are based on the numerical integration algorithm for modeling area sources used by the ISCST model Section 1 3 3 Equation 1 61 describes the numerical integration for the Short Term model that is applied to specific wind directions by the Long Term model in a trapezoidal integration to calculate the sector average The process of calculating sector averages for area sources in the Long Term model is described by Equation 2 6 in Section 2 2 3 3 0 REFERENCES Bowers J F J R Bjorklund and C S Cheney 1979 Industrial Source Complex ISC Dispersion Model User s Guide Volume I EPA 450 4 79 030 U S Environmental Protection Agency Research Triangle Park North Carolina 27711 Bowers J R J R Bjorklund and C S Cheney 1979 Industrial Source Complex ISC Dispersion Model User s Guide Volume II EPA 450 4 79 031 U S Environmental Protection Agency Research Triangle Park North Carolina 27711 Briggs G A 1969 Plume Rise USAEC Critical Review Series TID 25075 National Technical Information Service Springfield Virginia 22161 Briggs G A 1979 Some Recent Analyses of Plume Rise Observations In Proceedings of the Second International Clean Air Congress Academic Press New York Briggs G A 1972 Discussion on Chimney Plumes in Neutral and Stable Surroundings Atmos Environ 6 5
100. tions to the Industrial Source Complex Model J Air Poll Control Assoc 36 3 258 264 Schulman L L and J S Scire 1980 Buoyant Line and Point Source BLP Dispersion Model User s Guide Document P 7304B Environmental Research and Technology Inc Concord MA Scire J S and L L Schulman 1980 Modeling Plume Rise from Low Level Buoyant Line and Point Sources Proceedings Second Joint Conference on Applications of Air Pollution Meteorology 24 28 March New Orleans LA 133 139 Scire J S D G Strimaitis and R J Yamartino 1990 Model formulation and user s guide for the CALPUFF dispersion model Sigma Research Corp Concord MA Slinn W G N 1982 Predictions for particle deposition to vegetative canopies Atmos Environ 16 1785 1794 Slinn S A and W G N Slinn 1980 Predictions for particle deposition and natural waters Atmos Environ 14 1013 1016 Thompson R S 1994 Residence Time of Contaminants Released in Surface Coal Mines A Wind Tunnel Study Proceedings Eighth Joint Conference on Applications of Air Pollution Meteorology January 23 28 Nashville TN Touma J S J S Irwin J A Tikvart and C T Coulter 1995 A Review of Procedures for Updating Air Quality Modeling Techniques for Regulatory Modeling Programs J App Meteor 34 731 737 Turner D B 1970 Workbook of Atmospheric Dispersion Estimates PHS Publication No 999 AP 26 U S Department of Health Education and Welfare
101. to a stack to cause wake effects when the distance between the stack and the nearest part of the building is less than or equal to five times the lesser of the height or the projected width of the building For downwash analyses with direction specific building dimensions wake effects are assumed to occur if the stack is within a rectangle composed of two lines perpendicular to the wind direction one at 5L downwind of the building and the other at 2L upwind of the building and by two lines parallel to the wind direction each at 0 5L away from each side of the building as shown below Wind direction gt H 1 2 L IR TR DASS Building x DO ae ae ae O ee O O XK XX X XA XX XX 1 2 Tis lt 2L gt lt 5L gt L is the lesser of the height and projected width of the building for the particular direction sector For additional guidance on determining whether a more complex building configuration is likely to cause wake effects the reader is referred to the Guideline for Determination of Good Engineering Practice Stack Height Technical Support Document for the Stack Height Regulations Revised EPA 1985 In the following sections the Huber and Snyder building downwash method is described followed by a description of
102. unted for in the vertical term as described in Section 1 1 6 3 of Volume II The calculation of deposition velocities is described below for gaseous emissions Deposition Velocities for Gases At a reference height z the deposition velocity v for gases is expressed Wesley and Hicks 1977 Hicks 1982 as the inverse of a sum of three resistances Va fee Wor Yr A2 where r the atmospheric resistance s m through the surface layer La the deposition layer resistance s m and Lo the canopy vegetation layer resistance s m INDEX 1 An alternative pathway that is potentially important in sparsely vegetated areas or over water is deposition directly to the ground water surface Although not involving vegetation it is convenient to include the ground water surface resistance as a component of r The atmospheric resistance term r is given by Equations 1 81 and 1 82 in Section 1 3 2 of the ISC3 model user s guide Volume II EPA 1995b The deposition layer resistance r is parameterized in terms of the Schmidt number EPA 1995a as ry as k u A3 where S the Schmidt number v D v the kinematic viscosity of air 0 15 x 10 m7 s Du the molecular diffusivity of the pollutant m7 s and d d empirical parameters d1 k 5 d2 2 3 Hicks 1982 k the von Karman constant 0 4 Us surface friction velocity m s The canopy resistance r is the resistance for gases in the vegetati
103. ven if the plume height exceeds the mixing height Across the plume the total 1 65 flux to the surface must equal the mass lost from the plume so that YA vaca Q x F x y dy 7 Q x u 1 90 dx m Solving this equation for Q x the source depletion relationship is obtained as follows Oe Oz ert E a 97 where t x u is the plume travel time in seconds As with dry deposition Section 1 3 the ratio Q x Q is computed as a wet depletion factor which is applied to the flux term in Equation 1 89 The wet depletion calculation is also optional Not considering the effects of wet depletion will result in conservative estimates of both concentration and deposition since material deposited on the surface is not removed from the plume The scavenging ratio is computed from a scavenging coefficient and a precipitation rate Scire et al 1990 7 8 1 92 where the coefficient 8 has units s mm hr and the precipitation rate R has units mm hr The scavenging coefficient depends on the characteristics of the pollutant e g solubility and reactivity for gases size distribution for particles as well as the nature of the precipitation e g liquid or frozen Jindal and Heinold 1991 have analyzed particle scavenging data reported by Radke et al 1980 and found that the linear relationship of Equation 1 90 provides a better fit to the data than the non linear assumption 7 8R Furthermore they rep
104. w grade open pits such as surface coal mines or stone quarries 1 2 2 The Short Term Volume Source Model The ISC models use a virtual point source algorithm to model the effects of volume sources which means that an imaginary or virtual point source is located at a certain distance upwind of the volume source called the virtual distance to account for the initial size of the volume source 1 46 plume Therefore Equation 1 1 is also used to calculate concentrations produced by volume source emissions There are two types of volume sources surface based sources which may also be modeled as area sources and elevated sources An example of a surface based source is a surface rail line The effective emission height h for a surface based source is usually set equal to zero An example of an elevated source is an elevated rail line with an effective emission height h set equal to the height of the rail line If the volume source is elevated the user assigns the effective emission height h i e there is no plume rise associated with volume sources The user also assigns initial lateral F and vertical F dimensions for the volume yo zo source Lateral x and vertical x virtual distances are added to the actual downwind distance x for the F and F calculations The virtual distances are calculated from solutions to the sigma equations as is done for point sources with building downwash The volume source m
105. x terrain point source model which is based on the COMPLEX1 model is described below The description parallels the discussion for the simple terrain algorithm in Section 1 1 and includes the basic Gaussian sector average equation the plume rise formulas and the formulas used for determining dispersion parameters 1 5 1 The Gaussian Sector Average Equation The Short Term complex terrain screening algorithm for stacks uses the steady state sector averaged Gaussian plume equation for a continuous elevated source As with the simple terrain algorithm described in Section 1 1 the origin of the source s coordinate system is placed at the ground surface at the base of the stack for each source and each hour The x axis is positive in the downwind direction the y axis is crosswind normal to the x axis and the z axis extends vertically The fixed receptor locations are converted to each source s coordinate system for each hourly concentration calculation Since the concentrations are uniform across a 22 5 degree sector the complex terrain algorithms use the radial distance between source and receptor instead of downwind distance The calculation of the downwind crosswind and radial distances is described in Section 1 5 2 The hourly concentrations calculated for each source at each receptor are summed to obtain the total concentration produced at each receptor by the combined source emissions For a Gaussian sector averaged plum
106. y1 6 z L ML y1 16 z L 1 1 59 1 82 where u the surface friction velocity cm s k the von Karman constant 0 4 Z the height above ground m L the Monin Obukhov length m Zi deposition reference height m and Zo the surface roughness length m The coefficients used in the atmospheric resistance formulation are those suggested by Dyer 1974 A minimum value for L of 1 0m is used for rural locations Recommended minimum values for urban areas are provided in the user s guides for the meteorological preprocessor programs PCRAMMET and MPRM The approach used by Pleim et al 1984 to parameterize the deposition layer resistance terms is modified to include Slinn s 1982 estimate for the inertial impaction term The resulting deposition layer resistance is 1 1 Ey 1 83 s 0243 1 08 St u where Se the Schmidt number Sc L D dimensionless L the viscosity of air u 0 15 cm s Dp the Brownian diffusivity cm s of the pollutant in air St the Stokes number St v 9 ue L dimensionless g the acceleration due to gravity 981 cm s The gravitational settling velocity v cm s is g calculated as D amp Dix 9 a c De A So 1 84 18u where D the particle density g cm Do the air density H 1 2 x 10 g cm dp the particle diameter um u the absolute viscosity of air u 1 81 x 10 g cm s air units conver

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