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                                                                    torch  1981
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'AREA
                           .  -EOTENTlAL-ELffi4.JgSEEL-EOR. GAUSSIAE-PLUME
                            INTERACTION WITH SB!?LE TERRAIN FEATURES
                                             A.  jBass
                                         D.  G. Strimaitis
                                           B. A. Egan
                            Environmental  Research 5 Technology,  Inc.
                                  Concord,  Massachusetts  01742
                      9-1/8"
                                     Contract No.  68-02-2759

                                                I
                                         Project Officer
                                                i
                                                i
                                          John F.  Clarke
                                                i
                               Meteorology and Assessment Division
                            Environmental Sciences Research Laboratory
                               Research Triangle  Park,  NC  27711
                          ENVIRONMENTAL SCIENCES RESEARCH LABORATORY
                               OFFICE OF RESEARCH AND DEVELOPMENT
                              U.S.  ENVIRONMENTAL PROTECTION AGENCY
                                RESEARCH TRIANGLE PARK,  NC  27711
                         U. K
               3/8'
           EPA-287 ICin i
           (4-70)
                                          PAG- NUMBER
                                                                         RXDDDD13afl5

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[EPA-600/4-8 1-008
3.
I*. TITLE AND SUBTITLE
POTENTIAL FLOW MODEL FOR GAUSSIAN PLUME INTERACTION
HITH SIMPLE TERRAIN FEATURES
7. AUTMOK(S)
A. Bass, D. G. Strimaitis,
B. A. Egan


9. PERFORMING ORGANIZATION NAME AND ADDRESS
Environmental Research and Technology, Inc.
Concord, Massachusetts 01742
12. SPONSORING AGEWCY NAME AND ADDRESS
Environmental Sciences Research Laboratory
Office of Rese?rch and Development
U.S. Environmental Protection Agency
Research Triangle Park, NC 27711

IS. SUF^LEMENTAHY NOTES
\
\ '^
1 RECIPIENT'S ACCESSIOfPMO.
RS^ H °s 1 Q a 7
tin Js. ff K fc3y 

OKT NO. 10. PROGRAM ELEMENT NO. CDTA1D/05-0625 (FY-81) 11. CONf RAC?/G«AWT MO. 68-02-2759 13. TYPE OF flEPOHT AWD PEBIOO COVERED Final 1977 - 1979 1«. Sf'OWSORlWG AGENCY CODE EPA/600/09 *©. ABST.KACT The theory of turbulent plumes embedded within potential flow fields is dis- cussed for flows modified by special complex terrain situations. Both two-dimen- sional and three-dimensional isolated terrain obstacles are considered. Concen- tration estimates are evaluated using a Gaussian solution to the appropriate diffusion equation; dispersion coefficients are modified to account for terrain- induced kinematic constraints, and plume centerlisie trajectory is obtained from s stream line of the potential flow. Specific limitations to the theory and its applicability are reviewed. A computer algorithm is developed and documented to perform these calculations. Dispersion estimates and ground-level concentrations are given for a variety of meteorological situations. Parameters of the problem include obstacle height, effective source height, distance between source and obstacle, crosswind aspect ratio of the oihstacle, and atmospheric stability. The potential flow theory, originally applicable to neutral flows, is extended by an empirical approximation to slightly stable flows. Model computstions are coftipared to laboratory experi- mental results for neutral and stable flows, and to field measurements from the Tennessee Valley Authority UiuJow Creek Power Plant..' 17. a: DESCRIPTORS Meteorology * Plumes * Hills * Three dimensional flow * Two dimensional flow * Mathematical models KEY WOPOS AND OOCUMSNT ANALYSIS 8. DISTPIBUTION STATEROEMT RELEASE TO PUBLIC EPA Form 2228-1 (9-73} b.lBEWTIFIERS/OPEN ENDED T£RMS 19. SECUH5TY CE.AS3 (Thte fteportf UNCLASSIFIED 20. SECURilTV CLASS f Tiiti pagei UNCLASSIFIED c. COSATI fteld/Croup 048 218 08F 20D 12A 21 . WO. OF PAG ES " """ " 202 22. PRICE 1 -1 -1 :J ''' ~~ 4 '( "f 'I ( i


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DISCL
This report h&s been reviewed by
Laboratory, U.Sr Environmental Protect
cation. Approval does not signify tha
views and policies of the U.S. Environ:
mention of trade names or eosnaereial p
recosaendation for UP®.



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\irnn
the Environsental Sciences Research
ion Agency, and approved for publi-
t the contents necessarily reflect the
aentai Protection Agency, nor doss
roduets constitute endorsement or











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BO f TOM OF
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^-ANIJ ILLUS-
TRATIONS
: PAGE NUMBER
EPA-i;87 (Cm.)

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 TVPIWG GUIDE SHEET                                >
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                                                                       TOP OF
              This report describes the _results; of a program to develop and evaluate a
         transport/diffusion siodel for estimating asbient ground-level concentrations ]
         from point sources in areas of complex terrain.                              j
              At the beginning of the investigation, development of two modified      I
         Gsussian-type plums asodels was proposed, as guided by regulatory requirements^
         The first model'was to be a worst-case, single-point-source Eiodel to be used ;
         as a screening tool for esti&ating hourly-averaged ground-level air quality  |
         impact on a variety of individual temin features; the second model was to be
         an extension to'handle multiple terraih features.  At the conclusion ©f a    j
         project technical review held at the Meteorology Laboratory on 20-21 July  1978
         at the request of the goveraraent project officer, it was mutually agreed _thatj
         Implementation of'the worst-case screening model wouliT be" premature."'" Instead"^
         the prograa was, directed toward furt", it model refinements and extensions,  &nd\
         included detailed comparisons of model predictions with field Eeasurenefits and
         laboratory experiments.               ;                                       |
              In the execution of this program, Environmental Research $ Technology,  '
         Inc. (ERT) has:                                                              j
                                                                                      i
              e    adapted the potential flow theory approach for neutral situations b^
                   including the effects of terrain-induced perturbations on pluase    |
                   trajectory, and on vertical and crosswind dispersion;

              e    developed espirieal approximations to the potential flow theory  to
                   address both:               j

                        ^lightly stable flows; and
                        obstacles of arbitrary crosswind aspect ratio;

              e    implemented and documented a' computer algorithm to perform these
                   potential flow theory calculations; »nd investigated the variations;
                   of results with changes in effective stack height, obstacle height,;
                   distance to obstacle, stability, and aspect ratio; and             ;

              e    made a preliminary assessment cf the model through a comparison  ©f !
                   model results with U.S. Environmental Protection Agency tow tenk and
                   wind tunnel experiments and with atmospheric data froo TVA's Widows
                   Creek Power Plant.          j                                       1
 BEG! I;
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            "T—
             «. T
           F.PA-237
                                                                       ] F-OR TABLES
                                                                        AMD ILLUS-
                                                                       ', THATIONS
                                          PAGF. NUMBCi

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         	1	J

            The theory jof turbulent plumes embedded within potential flew  fields  is
       discussed for flows modified by special complex  terrain situations.  Both two-
       dimensional and 'three-diraensional  isolated terrain obstacles are  considered.  I
       Concentration estimates are evaluated sising a Gaussian solution to  the appro-j
       priate diffusion equation; dispersion Coefficients are modified to  account fa?
       terrain-induced'kinematic constraints,land plume centerline trajectory is     i
       obtained frcaj alstreaia line of the potential flow.   Specific limitations  to  j
       the theory and its applicability  are reviewed.                                j
            A computer1algorithm is developed  and documented  to  perform  these cal-   ;
       culations.  Dispersion estimates  and ground-level concentrations  are given fey
       avaTiety_of Eeterolegieal_ situations ,J_ Parameters._pf._ the _problea_include__ .^J
       'obstacle height, effective source height, distance between source and obstacle
       crosswind aspect ratio of the obstacle^ and atmospheric stability.   The       j
       potential flew theory, originally applicable to  neutral flows, is extended by!
       an empirical approximation to slightly;stable flows.  Additionally,  an inter-!
       polation scheme-'is- proposed for objects of arbitrary crosswind aspect ratio   [
       between the limiting cases of a hemisphere and a half-circular cylinder.      j
            For neutral and slightly stable flows over  two-dimensional obstacles,    i
       predicted Eaaxiaum ground level concentrations are similar to those  expected   i
       over flat terrain.  For flews over three-diraensional obstacles, however, the  j
       model predicts an order of magnitude increase in the ground level concen-     j
       tration.  Model 'computations are  compared to laboratory experimental results  i
       for neutral and.stable flows over an isolated obstacle with a crosswind aspect
       ratio equal to that of the hemisphere,'and for neutral flows over obstacles   :
       with aspect ratios that vary between tfeose of the hemisphere and  the circular
       cylinder.  Peak .concentrations at the erests of  these obstacles are feuitd  to
       be overpredicted by no more than  a factor of two- A preliminary  test of the  I
       model against field measurements  indicates that  the model coisputations        i
       generally bracket the observed concentrations, with the major uncertainty
       being the specification of the dispersion parameters.
            The performance of the potential flow raodel differs  markedly froa that   i
       of the level plums and the terrain-following plusis approaches to  predicting   ;
       groraid-iev©! concentrations in complex!terrain.   Th© level pluae  predictions  j
       characteristically overpredict by one $o two orders of magnitude, end the     i
       terrain-following plume predictions characteristically underpredict by several
       orders of magnitude at small aspect ratio.  Consequently, the potential flow
       approach provides a real potential for!simulating physical interactions of a  ,
       plume with terrain features in coaplex!terrain under conditions where the     j
       atssospheric stratification is neutral to slightly stable, and where direct   ;
       plume impingement on the hill -side is aot expected.                           i
            Recomsendaticms are aad© for extending the  applicability of  the modelingi
       approach, and for providing additional:data for  adequate  validation. Several
       j"0f"'the areas cited for enhaaceaent and! extension include  alternate  turbulence'!
                                                                                               rTO',
                                                    iv
                                                                                             VAND 'LHJS
                                                                                             , (RATIONS
 |.
 [
' [

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                     schemes,4&n algorithm for estimating concentrations  in hill wakes,
              generalized potential  flow streass functions for  additional  terrain shapes, ap.3
              additional laboratory  data for stable flow over  a variety of obstacle shapes.!
                                                                           TOP OF
                                                                          ,ifv',AGE
                                                                           AREA
This report is  suteaittcd in fulfillment of Contract
       Environmental Research § Technology,
                      Protection Agency.
                                                                       3-02-2759 by
                                  nc. under the sponsorship of the U.J
                 	[
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                    3/6'
                 EPA-287 (Cm.
                 (4-76)
                                                PAGE

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                           CONTENTS
         Preface. . . . J	iii
         (Abstract . . . J	iv
         Figures. . . . J	X
         Tables ....
         Abbreviations arid Symbols	XV
         Acknowledgement.'	xvifi
         1.   Introductiqa	1
         2.   Summary an4 Conclusions  	  3
         3.   Recommendations	9
                       0 -t ^..
         4.   Complex Terrain  Modeling:   Technical Issues and Current Status.11
              4.1  Terrali-Induced  Kinematic Constraints on Dispersion
                     and Plume Trajectories . . i	11
                         !                       *
              4.2  Enhanced  Dispersion in Complex Terrain	12
              4.3  Buoyant Entrairaaent Effects on Peak Plume Impact in
                     Complex Terrain	;	13
              4.4  Plume ^Dispersion and Transport Under Stable Flow
                     Conditions	j	14
         5.   Application of Potential Flow Theory. . . .	15
              5.1  Modeling  Criteria and Rationale	15
              5.2  Gaussian  Forauiations in Complex Terrain .	15
              5.3  Modeling  Approach,  Applicability, and Limitations	18
                         i                       i
              5.4  Theoretical Basis of Potential Flow Algorithms—
                     Neutral Flows	!	19
                         i                       I
              5.5  PGT Scaling of Dispersion Coefficients	  .26
         6.   Neutral Flew	34
              6.1  Ground-Level and Centerline Concentrations for
                     Neutral Flow	j	34          BOTTOM OF
                        j                                                                 |^A("-£ ARFA*
 BFGIN         6.2  Dependence  on Stack Height and Position	36          OUTSIDE''" '
 LAST LINE)	  6 3  E££ectl 0£ obstacle Size	43      —  DIMENSION
 OF TEXT Sy-	,	„	 i FOR TABLES
         I    A,,8..      '                  :.-.^"<-•••••.•-.•.•                             ^^-ANDILLUS-
         |	 !_'	I	 iiiSli Vil   Jj	( TRATIONS
                                           PAGE Ni IMEt-H
            EPA-287 (Cin.)
            (4-76)

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cEr
OF F
2*. Cozsparisonftifith Laboratory Experis
Over a S4ngle Mound 	
7.1 Background 	
7.2 Dispersion Coefficients, Fla
— - 7.3 Boundary Layer Enhanced Dispi
7.4 Comparison with Flat Terrain
7.5 Comparison in Presence of Tei
8. f4odifi cations for Effects of Strsi
8.1 Qualitative Observations frm
8.2 Incorporating Stratification
8.3 Application to the Atmosphen
9. Comparison with Laboratory Experii
"^ ~9T2 ~Dispersron' Coefficients", Tla;
9.3 Results in Presence of Terra
10. Modifications for Arbitrary Cross*
10.2 Adjustments to Pluse Center!
10.3 Adjustments to Velocity Fie
11. Comparison with Laboratory Experis
Flow Over Hills of Intermediate
11.1 Background 	 	
11.2 Comparison of Hill Shapes .
11.3 Dispersion Coefficients, Fl)
11.4 Comparison for Plurae Height
Obstacle Height 	
11.5 CoiEp4rison for Ploiss Height
the Obstacle Height . . .
i
116 Swsffsify pnd Conclusions . .
12. Model Comparison with Field Obser
1
12.2 The Widows Creek Steaa Elec
12.3 Case 'Selection for Model Cos
12.4 Predicted and Observed Cone
• j2 S Sjnspjsry sn*l Cone l unions . .

k 3/g.- '
PAGE r
EPA-2S7 (Cin.t
(4-761

JTER
'AGE ^
sents — Neutral Flow — -
	 45
	 45



Results 	 46
Tairi Obstacle ........ 50
:ification 	 60
i Laboratory ^?o^®liIls 	 60
Effects 	 60
i 	 65
lents— Stratified Flow .... 67
	 67
rferTalnT~.~7 7~.~7 ~~.~".' T ~67 **"
n Obstacle 	 70
sind Aspect Ratio. ...... 74
	 74
.in@ Trajectory
	 74
d 	 78
ients--Nsutral
Aspect Ratio 	 80
	 80
	 so
it Terrain 	 82
Equal to the
	 84
Equal to Half
	 92
	 101
rations (Widows Creek Data) . . 103
	 103
trie Power Plant 	 103
sparisons 	 	 .105
Sntrations 	 	 120
	 132 —

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yAfv'D ILLUS-
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           ©renees .  ,
        Appendices
        A.    Progs-ass Dssicripticss -  (^PLX
        B.    Prograa Flow Chart.
                         i
             Source __Prpgrsa Listing.
,133


.137
.147
          D.    Sespl© Output  Listing	178
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1 I
1 Horizontal dispersion coefficients for neutral flow
; i 2 Vertical dispersion coefficients for neutral flow over a
> circular ridge 	 I 	 	 29
3 Horizontal dispersion coefficients for neutral flow over a
1 hemispherical hill 	 30
^a--4_ _.„ ..Vertical dispersion coef f icieuts . for neutral _£ low _ovet a_ 	 _SB
: 1
Sa Velocity speed up factors for neutral flow over a
". | 5b Velocity speed up factors for neutral flow over a
hemispherical 'hill 	 	 33
i 6 Centerline and ground- level (
shoissn in Figures 1 through
7 Domain of calculations perfoj
j cylindrical ridge and neutj
' '
J: j 8 Domain of calculations perfoi
vt' hemispherical hill and neu-
';s 9 ttexiaum ground- level concenti
•j ridge and various combinat:
-^ i position
Concentrations for cases
4 (neutral flow) 	 35
•raed for a two-diaensional
ral flow 	 37
iaed for a three-dimensional
tral flow 	 38
rations for a cylindrical
.ons of stack height and
	 39
'**3
't| 10 Position af maximum ground- level concentration for a
:-5 cylindrical ridge and various combinations of stack
'?h 11 Maximum ground- level concentrations for a spherical hill
;-:| and ^various combinations of stack height and
\\ 12 Position of maximum ground- level concentration for a
^ spherical hill and various combinations of stack
V,4 13 Maximina ground- level concentration as a function of
'^ „ , hill height 	 	 44
;j LAST LificL_i4 Position (distance 5rom hill
1 |s/S" ^ :::;i:;j:;-J
crest) o£ maximum ground- 	
mctioiLjcf. hill height ... 44
,,..,..;., ~^
N PAGE DUMBER
'-'4 EPA-??7 (Cm.)
i'l (4-76'
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tL_15& Vertical concentration profile 39.2 cm downwind of a 	
12. § era stack in flat terrain 	 47
15b Vertical concentration profile 84.7 cm downwind of a
12.5 era stack in flat terrain 	 48
15c Vertical concentration profile 130.2 era downwind of a

16a Vertical concentration profile 39.2 era downwind of a
12.5 era stack in presence of a 23 csn hill 	 51
16b Vertical concentration profile 68.2 cm downwind of a
12.5 era stack in presence of a 23 cm hill 	 52 i
16c Vertical concentration profile 84.7 cm downwind of a
12.5 era ''tack in presence of a 23 cm hill 	 53
17 Height of the source streamline (n ) above the hill
crest (height = a) for various slack heights (H )
~v!8a Strearalines over s hemisphere . ...... 62 ,
18b Streamlines over a half circular cylinder 	 62
19 Vertical concentration profile 50 cm downwind of a
^ era stack for stratified flow in flat terrain 	 68 <
i
20 Vertical concentration profile 84.7 cm dcwr.wind of a
'. 9 da stack for stratified flou in flat terrain 	 69 '
21a Ground- level concentration for stratified flow as a
1 function of distance upwind along the ground from
the hill c~est for a 9 cm stack f/id 23 cm hill 	 71
21b Ground- level concentration for stratified flow as a
function of cross-wind distance alcr..1? the ground
from the hill crest for a 9 on stack and
23 cm hill 	 » 	 73
22 Definition sketch for aspect ratio X - b/a for
hills of spherical, intermediate, and i
cylindrical shapes. ...i 	 75
23 Details of hills used in 3PA wind tunnel experiments. . . 81
24 Predicted and observed concentrations for stack
height equal to hill height (23.4 on) 	 86
25 Vertical plume spread at hill crest for stack
height equal to hill height (23,4 cm) 	 89
26 Predicted and observed plume height at hill crest
for stack height equal to hill height (23.4 on) .... 90
27 Vertical concentration profiles over CX, the
i i ~~"
i i 	 1 . . . x>
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;. -| HF.RF :«sK 28 Lateral pluase spread at hill' crest for stsek height 	
i f i equal to hill height (23.4,011). 	 	 	 93
~ - i '' I
DfcOP?:£D 29 Predicted and observed Gaussian rasss flux for stack
: M?AD; height equal to hill height (23.4 on) 	 94
. ' C-EG'N ' ' :
• , ^fcr'OM; ^° Predicted and observed concentrations for stack height
• '-'I Hrce *-^T~~ equal to half the hill heicht (11.7 cm) 	 96

- ;• i 31 Predicted and observed plune! height at hill crest
: .- for stack height equal to half the hill
*' height (11.7 cm) 	 i, 	 97
; 32 Vertical piusae spread at hill crest for stack height
equal to half the hill height (11 7 cm) 	 98
• V 33 Lateral plume spread at hill crest for stack height
• •; equal to half the hill height (11.7 era) 	 99
34 The Widows Creek steam electric power plant and
surrounding features 	 104
, 35_. __ __Cosparison of tne idealized cross- section_o£Saud 	 	 	 	 ^
\ '• feuntain to the southeast of Widows Creek pcwer
plant with the circular cylinder assumed in
the corapIeK terrain issodel 	 	 	 	 108
; 36 Temperature profile used to calculate pluaie rise
. -'"; and Froude number on day 3, hour 1300, 1978 	 113
'? :\-
;" ] 37 T^aperature profile used to calculate plume rise
-=* ! and Froude number on day 40, hour 1300, 1978 	 114
:- 4 | 38 Temperature profile used to calculate plume rise
-. ' -i ' and Froude msaber on day 1^0, hour 0900, 1978 	 115
• -=? i i
•-----' t 39 Temperature profile used to calculate plume rise
• : '• and Froude nusber on day 230, hour 1000, 1978 	 116
'^ i 40 Temperature profile used to calculate plume rise
r'-vi and Froude nuaber on day 4, hour 2100, 1978 	 117
i 41 Temperature profile used to calculate plume rise
—^ and Froude nusber on day 166, hour 240(', 1978 	 118'
'~ yj 42 Temperature profile used to calculate plume rise
;. , ' and Froude number on day 222, hour 2400, 1978 	 119
• '.-'." ' '
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1 TRATIONS ,
3


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                                            CENTER
                                            OF PAGE
 TOP OF
.IMAGE
 AREA
                                       	JABLES.-

        Number
        i                i                       '
        I  1       Range 'of model parameters evaluated in  laboratory
        |            and field tests of the potential flow model	     6
          2       Form Of vertical distribution and vertical spread
        i            implied by solutions of the clv;sical parabolic                   '
        j            equation of diffusion	    17
        j  3       Comparison of predicted and observed normalized
        i            concentrations and plume centerline height for
        |or4_	the 12.5 on high stack in the_ presence, of _th«	._
                    22.9 cm high polynomial bill	    54
          4       Comparison of predicted and observed normalized
        i            concentrations and plume centerline height over
        j            the hill crest for the 9.0 cm height  stack	    55
        j  5       Error ratio R*/R for 10% errors in o  and n	    57
        I  6       Comparison of normalized concentrations and
        j            derived terrain correction factors at the hill crest.  .    58
        )                ,                       ;
        i  7       Plume impact criteria based on Figure 17	    65     j
        |  8       Comparison of predicted and observed concentrations                 !
        I            at hill crest for the 9 cm stack tow  tank experiments  .    72     j
        |  9       Representative,values_of speed-up factor S	    77     i

          10      Observed normalized concentrations at hill crest                    j
                    for stack height equal to hill height 	    84     i
                        |
          11      Comparison of predicted and observed normalized
                    surface concentrations for stack height equal                     j
                    to hill height	j	    85
          12      Comparison of surface concentrations at hill crest
                    between the potential flow model, the wind tunnel
                    observations, the half-height assumption, the
                    terrain-following plume assumption, and the  level
                    plume assumption for a stack height equal to hill
                    height	i	    87
          13      Predicted and observed normalized surface
                    concentrations for a stack height equal to                         QOTTO!,'. OF
                    half hill height	J	    95      IMAGE AREA.
                                                                                       OUTSIDE
LASTUNEj	             |                       j                                     	[DIMENSION
OF TEXT $&•__	,	j	I FOR TABLES
        •   ~T^e       I             ,    .vxix^ — ^r                               ^ANU ILLL'S-


           EPA-287 (Cir,,)

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      OF
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:_i4
15
16
^*"
17
18
19
20
21
22
^23
24
25
26
27
28a
28b
29
30
•&
r
TYPING GUIDE SHEt'T
CENTER
OF PAGE
Comparison of observed to predicted ratios of
plume size parameters and speed-up f actor (s)
as ^ function of aspect ratio 	 	
Hours ' selected for aodel comparisons at Sand ^fountain . .
Hours selected for jaodel comparisons at Sumjnerhouse
Mountain 	 '. 	
Cases of significant inpact that have associated
vertical profiles of temperature 	

Final pluas heights of emissions frosa boilers 7
and 8 both with and withe at full SO- scrubbing 	
Hourly uncontrolled SO- emissions from each boiler
unit Curing hours selected for raodel analysis 	
Sumiaary of results of Froude number calculations 	
Stability classification system 	
Ranges of dispersion stability class designations
appropriate to the case ho'ars based on temperature
profiles winds and tise of day 	
Results of Eodel calculations for hours showing
inpsct on the ne&rby ridge 	
Results of ssodel calculations for hours showing
impact on the isolated sc&Kid 	 	
Ihicontrolled SO- concentration normalization
factors for test cospari^oa hours ...........
Revised S0» emission rates for Units 7 and 8 and
cosbined concentration normalization factors
that include scrubber operations 	
Comparison of predicted and observed S02 concentrations
Cosparison of predicted and observed S0? concentrations
at Widows Creek 	
Comparison of observed concentrations at Widows Creek
and predicted concentrations based on the potential
flow sod el with buoyant plisae enhancement 	
SuEaary of comparisons of the potential flow model
with half-height ard level plume assumptions 	
i j
j
1
L ^V
>
102
106
107
110
111
,12
120
121
121
122
123
124
126
127
128
129
130
131

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V-'-K1"' " • i "; . [
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           [SYMBOL
       i»
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       b
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                                  LIST OF SYMBOLS AMD ABBREVIATIONS
                                                                 TOP OF
                                                                 'AREA
                                                                              ------- r?!S"
 height of obstacl©      ,'
 I
 coefficients of boundary layer enhanced dispersion  coefficientj
 I                        ;
 half of the crosswind breadth of obstacle
 plvaae path coefficient  !
 I                        ;
 coefficients of polynomial fit for  z™
 normal and crosswind dimensionless  diffusivities
-noraal and crosswind "effectiv©"" diffusivities •
 i
 trial solution functions
 i                        i
 Fronde rnsaber           l
 acceleration due to gravity
 trial solution function'
 gross boiler load
 weighting functions for velocity in aspect  ratio
 i  computation           '
 effective source height
 local terrain height    ,
 final plume rise        {
 Monin-Obukhov length
 experimental Bass flux
 distance along normal fsroa pluea centerline to  surface
 i  (assuming no errors)
 distance along normal fro® plume centerlin© to  surface
 I  (with errors)         j
 emission rate of pollutant
 l
 ratio of ground level to centorline concentration
 i  (assuming no errors)
 ratio of ground level to centerline concentration
 ;  (with errors)         i
                         i
 distance frraa axis of syraaetry  to  pisna® centerline
 1  for axisyraetric obstacle
                                                 xv
                                                                                   —--' Pif/: r."'0\
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FIRST
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HFRE E»
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H.LFit &
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CENTER
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SYMBOL 4
RS stack top radius (E)
s along pits® cer&teriine path
s»n,Y curvilinear coordinates for
— 1 pluae centerlin® j
s. ' J
... _ . ,. ._ ... , 	 	 . ^
length
systea that follows the
^CYL SSPH $peed-up factor for cylindrical ridge and hessispherical hill
SC iteospheric dispersion Stability class
             Ta
             Ts
             T(s)
             T
            I"
            lu
             U
              oo
            .V

            !Vs
            j w     w
            !HC¥L* WSPH

            Ix

             Xs
            i ••ru
            I  CF
             ZCYL'  ZSPH
        plus© center line Wveetion time
  tebient average tensperai:ure
  stack exhaust temperature
  Crosswind line integral;
  terrain correction factor
 -along: streamline-velocity	—	~	— •
  !
  horizontal wind speed
  velocity at crest of obstacle
^'velocity field component assuaing potential  flow
  i  over cylindrical ridge,  hemispherical hill respectively
  enifora velocity upwind' of source
  Velocity normal to streaaline
  stack exhaust velocity
                          i
  weighting funetiorss  for  streamline height in aspect
  '  ratio
    LAST LINE
    OF TEXT Bd
  distance along X axis  fro® source
  downwind distance  froa source to obstacle center
  height of streaialine above crest for neutral  flow
  height of streamline above crest for stratified flow
  height of streamline above surface for flow over
  I  cylindrical ridge, hemispherical hill
  roughness length
  i
  ratios of cosjplex  terrain to flat terrain spread
  j  statistics            j
  aspect ratio terra  in speed-up equation
  Streamline depression  at any x due to stratification
  £treaa!ine depression  at crest due to stratification
  stream function gradient factor
                 5 3/8"
               CFA-287 (Cin.)
               (4-76)

                                                    xvl
EOTTOV Q':
I \5i.Gf APf',\
OUTSIDC

FOR TA?i.r-S
•AJW ILLUS-
TRATIONS


                                                                                                  Sl&^i^^iivitnicaS

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i' "BEGIN
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' '•" ' ' " V.
TYPING GUIDE SHEET ••'
. 9 CENTER
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1 HfchE ^SYMBOL |
j? >—~™ f^
1
| DROPPED
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n pltsse height pertiirbatio-jn facto?
A obstacle crosswind sspett ratio
. -h , , ,. ..,,,.,...,..;.. ^ - _. ... .;;, ^i-,.'

TOP Of
	 	 ,., ,. ...,,,. ^^ A n r A
" * ' ' ' J A^ilL>n


I BEGIN \\ limiting two-dimensioraak and three-dimensional aspect
1 SB'.T'ONS
1
I
I



;
i
— - -* j ratios !
o~", ~ ~?ros"swina"«nd •vertical "dispersion ~coeffic
y»z r
— „
'". '"-.



L^Slta , _ ,
o _ „ irosswind and vertical Dispersion coefficients in
' ' i flat terrain
' i
o ' boundary layer enhanced; vertical dispersion
! coefficient j

o * vertical dispersion coefficient with errors
HS) normal to streraline line integral
X Concentration
X*,X diaensionless concentration
- 1 -V . •






i
.
| ^lD,3D stream function for two-dimensional, axi symmetric three- j
t .
I
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• dimensional flows •
i !
ty stream function through source
i
$ u- streassline equation of plume centerline
P i i
6 potential teaperature
; ', 1
ABSREVIATIC»iS
I
cm centimeter
1
EPA U.S. Environmental Protection Agency
ERT Environmental Research $ Technologys Inc.
* •
FMF fluid Itodeling Facility
i i
ka kiloaeter
1
i.
m meter
MAAQS National Ambient Air Quality Standards
PGT Pasquill-Gifford-Turner!
j t
PSD prevention of significant deterioration
TVA Tennessee Valley Authority
LT local time
i j
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     HERE  la
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   HERE   ®
                        ACKNOWL
EDGMENT
                                         TOP OF
                                         IMAGE
                                         AREA
                 The  suthori wish to acknowledge helpful review  and suggestions of Dr. F.
            Pasquill,  a consultant to the project.! We also  acknowledge the helpful
            advice provided'by Drs. J. C. R. Hunt,jft. H. Snyder,  and R.  E.  Britter.
            Special thsnks are extended to John F.jClarke  and  to  George C.  Hoi worth,
            for  their overall judgment and direction on the  project.
                 The  major contributions of R. G.  Isaacs and Dr.  J.  Caiman  to earlier
            versions  of this report are gratefully^ acknowledged.
                 Laboratory,data was kindly furnished by Dr. William H.  Snyder, Environ-
            mental Sciences'Research Laboratory, UPS. Environmental Protection Agency,
            and  Widows Creek Power Plant data was  fcindly furnished  by Mr. John P.  Blackwe|
            Aijr_Re_spurces Program^ ,Tennesse9_Valley Authority._  _   _	^
I    BEGIN
    LAST LINE	
    OF TEXT
                                                                                          _.i
                                                                        BOTTOM OF
                                                                        I Si AGE AREA
                                                                        OLI1SIDE
                                                                        DiMbtvS'Orj
                                                                        f-OR TABLES
                                                                        •AMD ILLbS-
                                                                        TFATIONS
               EPA-237 ICin.
               (4-76)
                                              PAGE NUMEuR

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HERE   B
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TOP OF
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'AREA
                        I                 INTRODllCTION

                        I
             This  study has been motivated by the requirement for & treateent of
         plum®  dispersion  in complex terrain that is practical for regulatory use,
         yet retain-  taieh  of the essential physics of the problem.  For regulatory
        [purposes,  the modeling approach shouldiemphasize cases with potential for
         high ground-level concentrations.  These include:

             •    stable  conditions and low wiitd speeds, under which direct pluse     j
             _ __ _isjp_act  or blodd.ng_ by nearby^terrain obstacles may occur, and_ 	, J

             0    neutral or slightly stable conditions and moderate or high wind     1
                   speeds, under which the pluse centerline trajectory passes over     j
                   and close to the terrain surface.
                        I                       :
             This  report addresses tlie development of modeling methods for neutral
         and  slightly stable conditions.  The general approach employed follows the
         theory of turbulent plua^s embedded within potential flow fields as developed
         by Hunt end Mulhearn (1973) and Hunt and Snyder (1978).  The theory is
         [applied to the calculation of ground-level concentrations using a Gaussian
         jforra of solution to the diffusi-n equation.  Streaiafunctions proper to
         •potential  flow over a cylinder (aspect Jratio = «) astd to potential flow over
         la sphere (aspect ratio = 1) form cornerstones of the model.  These are
         (extended to describe flows over terrairi features of intermediate crosswind
         jaspect ratio by a weighting of the two limiting streamfunctions.  This
         weighting schema was derived in part using results froa wind tunnel experi-
         ments  for flows over obstacles of intermediate aspect ratio (Snyder et al.
         1979).         '                       |
              In addition, although the model is strictly applicable only to neutral
         flows, an empirical approximation scheme is included to define streamline
         lowering caused by increased stratification.  The empirical basis for this
         portion of the oodel is derived from stratified tow-tank experiments (Snyder
         1977  and Snyder 1978).                 j
             Other restrictions in the use of the raodel have not been addressed.
         These  limitations to the eodel arise ftfosi the neglect of boundary layer       '\
         phenomena such aa flow separation, unsteady wake effects, tisae-dependent      \
         effects of stability (e.g., lee wave generation), and surface heating         j
         effects.  In addition, the theory is applicable in a strict sathematical      i
         sense  only for thin plumes.            |                                       j
             This  report discusses the rational© for selecting particular modeling    i
BEGIN    approaches,  provides full technical documentation for the algorithms developed
LAST LINE and presents, for a number of specific test situations, the results of
OF TEXT ^comparisons  between sodel calculations'and laboratory and field observations.1
               3/8'
           EPA-2S7 (C.n.)
           (4-7G»
                                          PAGE NU'MSER

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BEGIN
SECTIONS
HERE   «*=!""•
     Ttia report Consists of twelve sections and  four  appendices.   Section
presents a suBiBsfsy of the study md it^ conclusions,  and  Section  3 states
r«eos!2t©ndations jfor fiiture laboratory and/or field  experiments  to further
        and validate the modeling approaches.  Section 4 briefly overviews
th©  technical  aspects of cossplex terrain modeling.
     Section S describes the theoretical basis for  applying potential flow
Jtiraory to the  sideling of plus© transport and diffusion in coaplex terrain.
                                                                       T^K^m^^^srpr^s^r^^^TO^^gPTTt


                                                                                TOP OF •
                                                                               ^IMAGE
                                                                                AREA
         lunt  sud  coworkers ar© reviewed and approximations ar©  introduced  for  prac-
         tical application of the theory.  A method is presented for  calibrating
         sodsi dispersion coefficients to varies diffusion parameter systesis.   In
         Section 6 th® theory ir applied to the i calculation of ground-level and
         centerliae concentrate /ras for a variety of cases that illustrate the model's
         >©hsvior, under beuf.
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 FIRST
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HERE   Bs-
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 LAST LIN
 OF TEXT
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tiMAGE
 'AREA
                                            AND! CONCLUSIONS
     In complex!terrain, two classes of meteorological  conditions  often are
associated with the likelihood of  large ground-level  concentrations:
(1) low wind speed, stable cases,  and  (2) moderate  or high wind speed,
neutral or slightly stable cases.  The first  class  of conditions generally
leads to high concentrations through direct plume impingement or terrain
blocking.  The present model does  not  treat direct  pluiae impingement  or
terrain blocking under stable conditions.  Specific recosaaendations for
Beating j3lume_dispessiGn under.sjtable. atmospheric, conditions are  presented,-,
in Section 3.   ,    "                  !
     The second'class of situations promotes  high concentrations because,  as
the plume is transported over terrain  features,  it  is forced to pass  close   !
to the terrain  surface.  Physical  mechanisms  relevant to this class of       j
conditions inelude  terrain-induced alteration of the  plume  centerline tra-   i
jectory  and kinematic constraints  on horizontal  and vertical dispersion.     i
The dispersion  process in  these situations  is modeled as a  Gaussian plume    j
embedded in a potential  flow field.  This  approach  falls between the  two     j
extremes found  in present  modeling approaches in neutral situations:          j
                i                       i                                       I
     a)   the terrain-following method, where the plume rises everywhere over;
          the terrain at a local  elevation equal to the height of the pluae
          above the stack  base;  and   i
                i                       i
     b)   the level plume  method,  where  the local terrain height is sub-
          tracted  fri®  the effective height of the  plume.
                i                       i
In Case  a, maximum ground-level  concentrations are  about the same as  over
flat terrain, while in Case b; near-plume axis concentrations are predicted
at ground  level for terrain  elevationsi approximately equal  to effective
stack height.   Neither  extreme deals with terrain-induced changes in plume
trajectory and  pluae dispfrrion  rates.'
     Various model  modifications  have  been adopted (e.g., the CRSTER model
with terrain truncated  at  the height  of the stack top)  to remedy this situa
tion.  However, such  treatments  are ad hoc;  by contrast, the potential flow
theory as described here appears  to offer a practical and more physically
justifiable method for  incorporating  these effects  vjithin a Gaussian plurae
model.                                 |
     A research I computer algorithm based on the potential flow approach
computes ground-level pollutant  concentrations; pluae center1in® concentra
tions; height of plus®  trajectory above the surface; and horizontal and
            EPA-287 (Cir,.)
            (4-76)
                                           PAGE

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FIRST ; TVPING GUIDE SHEET ^n ^r .1
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TOT _ 	 _Of_PAGE 	 __ _ _ X±!E' 1
HERE issF
DROPPED
HEAD;
BEGIN
SECTIONS
vertical dispersion coefficisnts. In ihe method used, for example, the 	 1 |
equation of the ; plums centerline for fjow over a hemisphere provides the ' |
plume trajectory in neutral flow by:
i
M
2 / a3 \

2 S4 7 9 ?/7l *
ME«E -^T . _^__or*o-'7
1 ' 1
1 *
2 / a' \ x« » ' -1
H* f 1 ffl . 	 , i f 2«. 11
s | 2 2 3/21 l '
?.;

In this equation, x and z ar© the horitontal and vertical- cartesian coordinates .{
\of a point on the streasaiina relative to the center of the obstacle, X and i
K are the position and height of the stack, and a is the height of the
jhfll. The velocity along the plume trajectory, u(s), is determined by the


gradient of the stream fimction, ^•3D, describing the trajectory of the pluss©
centerline, such that:
1 f- _,
/

3D 3D 1/2
1 3t« 2 ' »-iVu i */*
1 U(s) » (-r*- )
1

m««^A *• • f
•trt i 9 /
*au(x.t) = 0.5 U^ [l - -
i \ G
* (ft ) (2-2>
	 	 ^
a3 \ r ,>
R2 + Z2} 3/2J U ^;
,
and U^ is equal to the velocity far upstream of the hill. A Gaussian fona
1
1
i
j
j
\
;
i
j
j
'-i
,
;
| of the dispersion equation using coordinates along and normal to the i

















BEGIN
trajectory: :
1
x'(s-n'Y) f ifer exp [-fi (s)

2
n2 - f2 (s) y ] (2-4)
i i 2
provides diir.ensionless concentration estimates, x' " (x^ma /Q)» where by
definition, |
fj(s) = [u(s)R(s)]2/[
f,(s) - l/[4T(s)]
j * i
g(s) = 4it[4i(s)T(s)]
1-
and , i
1 I
f 2
^(s) * 1 D- (s') R (s1) u(s
/ X
o
1
! s
T(s) I j [D2(s')/[u(s')R2(
i O
i
i •
1
LASTLIN!f|____ |
•> TEXT S*1
.

l+(s)] (2-Sa)
(2-5b)
/2 (2-6)


')ds' (2-7)



s')]]ds' (2-8)




— _,

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PAGE NUMBER I
tPA-237 (Cin.) . :
(4-76) ]
•-1
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FiRST TYPING GUIDE SHEET
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HERE »sk siailsr sequels® of Equations (see Section 5, Equations 5-7 through S-13)_ 	 (

DROPPED
HEAD;
BEGIN
SECTIONS!
for flow over two-dimsasiossal obstacles uses the two-dimensional streaa
function for flow over a half -cylinder:
r''
I t
• • 1


ja i ,,_ -,,_

V IX, ZJ » U Z 11 - • - i v- -/
HERE *4~ , 	 	 V ^X * Z ^ /
\





M n C-f-\ i
- 1
-1
-j

.-1
nj
i

i
To account for the effects of stability, an approximation consistent -;
with laboratory observations is adopted to lower the neutral stresalins
[(Section 8, Equations 8-1 through 8-8)
> The height of the neutral streas-
line within two obstacle heights of th© obstacle center is lowered by an
js&ount, 6:

/



\
6(x) = A ll - |4-l , for |x|<2a (2-10)
\ ai/
^^ 	 	 _ 	 -L - -w,yv r ~ 	 w-»~ *v> ._IAI,
! where
i


*

i
A is z_ - z™,, and
'

]
)
j
-i
i
-'

ZC' ZCF ;ar® tjis streamline heights above the crest in neutral flow, ;
a$d in a flow characteriged by Froude number Fr, respectively. \ \

A second approxiaation is derived

(Section 10) to account for an
obscacle with arbitrary erosswind aspect ratio, \. In this case, two and
)


"•= tteee-diaensional streamlines are weighted to provide an intermediate pluse

1
j





ceaterline trajectory:

ZC ' IZSl4C*f X) " ZCYL W'x»x"
(




L1 * ZCYL ^'x) (2"H)





i
>
aiai the velocity components are weighted by the aspect ratio dependent
speed-up factor, S (Equations 10-13 and 10-14):
U(x,ZiX) = 2.0[S(?.; - 1.5] U

I !

+2.012.0 - S(X)]USpH(x,z) (2-12)
1
,
Model computations indicate that
ficantly with obstacle size, effective
aaximum concentrations vary signi-
stack height,, and relative distance
between the stack and the obstacle (Section 6) . Comparisons of model

predictions with available observations test the model perfonaanee for a
limited number of possible combinations of these and other factors. Table 1
BEGIN
suESBarizes the range of sodel parameters involved in the comparisons. Note
LAST LINE 	
•, OF "XT Bj
, .
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TYPING GUiDE SHEET
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Slat X is the c&sswind aspect ratio of the obstacle (Section 10), Fr is the..
Froude number characterizing the iaportance of density stratification in
defining the flow (Section 8), X /a is j the distance between th© stack and
the otctacle normalized by th-j oBstacl® height, and H /& is the effective
stack height normalized by the obstacl^ height. s
~ TA^LE 1. RANGE OF MODEL PARAMETERS EVALUATED IN
1 LABORATORY AND FIELD TESTS OF 'THE POTENTIAL 	 " " ' ' '
I FLOW MODP*.
_MI_>
Comparison Study X Fr X /a H /a
Smooth Tunnel , J. „.„ 939 3.7 0.4,0.6
(Section 7) j
Tow Tank , 1 OJ97 3.7 0.4
(Section 9) !
Rough Tunnel 1,2,3,» 999 3.7 0.5,1.0
^, —(Section. 11) _ ,_,.-, <_•• _ . 	 	 ._^.
Widows Creek 4 1.3-1.7 32 >1
(Section 12) » 0.4-1.0 12 >1

9-1/o '
The "smooth 'tunnel" comparisons (Section 7) and the "tow tank" com-
parisons (Section 9) test the model under conditions that minimize the
influence of processes not contained iii the model. They show that the model
is able to predict the observed maximum surface concentration within a
factor of two (generally, overpredicting) , depending on the interpretation
of the observed plume properties in the absence of the obstacle.
The "rough tunnel" comparisons (Section 11) include t«ie effects of a
strong boundary layer on flow over obstacles with a triangular cross section.
Model predictions of maximum surface concentrations art again within a
factor of two (overprediction) for obstacles of aspect ratio 1. However, as
the crosswind aspect ratio increases, the concentration predictions fall
below th6 observations. The data indicate that the plume size is signi-
ficantly enhanced upstream and over hills with the larger aspect ratios.
The deformations included in the potential flow field approximation are only
partly responsible. A better understanding of plume dispersion in a deforming
boundary layer ijlow is likely to be needed to describe these experiments
more accurately.
The "Widows1 Creek" full-scale comparisons (Section 12) also show the
importance of accurately describing plume dispersion in the atmosphere. In
most cases, predicted surface concentrations aro extremely sensitive to the
dispersion paraS'-ters assumed. The limited comparisons of the modal with
fie\d data show that most of the observations fall between model predictions
when the two most appropriate dispersion parameter classes are used. But,
much more field data will bo required to adequately evaluate the model for
full-scale applications in the atmosphere.
, ,. i
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TYCrtNG GUIDE SHCET
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~ " • ' i • • •• i 	
Tr^ft .^*fMT(T"IS8T>a «rt* tc wl ^ti 1 «ahnT«fl^nw rlafra fava m
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                                        ta are put into perspective by     —j
comparing the observed peak concentrations with  predictions  of a level  plume i
approach and a terrain-following  approach.   FOT  the  level  plume approach,     j
the predicted concentrations  in th©  cases studied equal the  centerline        I
concentrations (in the absence of reflection), which range frosi a factor of  j
     two ordersiof magnitude  greater than the observed surface concentra-  	j
  ons.  In tliejase of the terrain-following approach, predicted concen- ___j
"^rations ar¥~e«bh^IaTIy~zef6"r"Tn~tefiasn6T"a"''lp"artial height  correction^    1
approach, whichjis an intermediate approach  between  the level  pluxae and the  [
terrain-following plume  approaches (Section  7),  the  observations as well as  i
the potential flow aodel indicate that  a plume path  coefficient of 0.35 is
needed to simulate unstratified flow over the symmetric hill (not a ridge)    i
in the smooth tunnel, and a plume path' coefficient of 0.15 to  0.18 may  be an j
approximate choice for a moderately  stratified flow  (Froude  number nearly     !
1.0) or or a symmetric hill in the tow tank.   In  the  rough  tunnel, plume path
coefficients based on the observations] and the potential flow  model pre-
dictions vary between 0.46 and 0.76.  I
     These preliminary assessments suggest that  with verification and
refinement, the]approach may  be applicable to the following  situations:      1

     e    isolated, single terrain obstacles of  arbitrary  height, of cross-
          section approximately circular in  a plane  parallel to the wind
          direction, and of arbitrary aspect ratio in the  crosswind direc-
          tion i1and                    j
                , *~                      !
     9    neutral to slightly stable stratification  (depending on effective
          stack|height).
                i
     A number of  limitations  arise mainly from physical effects that are not
described by the potential flow model.:  The  model should not be applied to
the  following situations:

     •    stable flow cases in which the plume may directly  impact the
          hill; |                       i
     •    dispersion cases dominated by surface  boundary layer effects;

     •    unstable cases (e.g., strongly ccnvective  situations) for which
          potential theory is unsuitable; and

     e    cases dominated by  wake effects.
                1                       i
     The range of suitable applications of the model is also limited by the
theoretical approximations made,  and by the  limited  configurations studied
experimentally.i These limitations incjude:

     «    the "thin plume" approximation (o  /n  « 1.0 where n  is the
          heigh^ of the  plume centerline above the hill crest);
      BEGi.NJ
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           the surface boundary layer effects not considered in the model;

           the Gaussian beha-.io-1 assumed in the model in contrast to non-
           Gaussian behavior seen in some of the experimental results;
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      «    restriction of the available experiments  to  a  small  number of
           stack heights, and to fixed configuration of obstacle relative to
           stack;! and

      o    the hill shapes used in the laboratory  experiments,  as compared to
           the spherical hill shape asswaed  in  the theoretical  calculations.
^	     '	         _        I                                     ~
 KowevHr, frbaTfio preliminary comparisons of tJie""mo^eT'witir~laljbfat6"ry~lafa,
 jit is noted that the "thin pluse" approxiraation iuay effectively be relaxed
 jto o /n  <0.3.  Indeed, tlie errors introduced  by  such  a  relaxation are not
 as serious as those introduced with either  the level plume or  the terrain-
 following pkrae approaches.
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                                        RECOMMENDATIONS
              The following reccsBsendations are proposed for extending  the  applica-
         bility of the Eodel and for its verification.

              e    The complex terrain ssodei uses the PGT diffusion  coefficients
                   derived froa observations made in flat terrain to predict what
                   will happen in cosplex terrain.  The accuracy  of  the model taight
                   be improved by using updated dispersion  curves.   These updated
                   curves would include, for exaspie, changes with roughness length
                   or'intensity of the wind "direction" fluctuations ^                  "^
                   The changes in the properties of the boundary  layer  over a hill
                   are not well understood theoretically.   Further laboratory studies
                   of th© behavior o£ the boundary layer could  lead  to  better engi-
                   neering approximations to so®e of the effects.
                   Developing an approximate treatment for  computation  of ground-
                   level concentrations in the wake of a hill would  extent  the
                   applicability of the present model.

                   The applicability of the model could also be extended by incor-
                   porating known solutions to the potential flows around bodies  of
                   different shapes, e.g., a bluff, or an elliptical ridge.  The
                   problem of very stable flow around an ellipsoidal hill,  or ©f  a
                   stack positioned away from the plane of  syissetry, taight  also be
                   addressed.  Specific laboratory experiments  of these flows fcreuld
                   be important in testing the generalized  model.
                   The present model does not treat a situation in which the wind
                   direction is oriented at sosse arbitrary  (not perpendicular)  angle
                   to an elongated terrain obstacle.  Experiments should be Hade  to
                   gather the data to model the effect of nonnoraal  wind incidence.

                   The effects of varying aspect ratio and  of varying stratification
                   have been independently incorporated into the  model  and  are
                   assumed to be additive.  This superposition  of effects seems
                   reasonable in the absence «f any data to the contrary.   Experi-
                   aents including stratification and varying aspect ratio  would
                   provide useful data from which the approximation  could be refined.
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  Although not discussed in the present work, it is recosmeisded that
  the Epdeling technique used ifor stable esses should  incorporate
  recent suggestions to include (1) effects of enhanced crosswiad
  plume meander,  (2) buoyar.cy effects, (3) modified turbulence
  typing schemes,  and (4) physically realistic treatment of surface
  reflection.   A coaples©ntary* set of sispl© modeling  algorithms
  should be linked to the present @odel to handle those cases not ™!
                                             Sh~	Field -vertflcStteft"!
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                   of such modifications would -enhance the credibility of the
                   approaches substantially.
                         i
                   Routine application of the model in the ateosphere requires  th«j
                   determination of the Froude mosber for the flew at the terrain
                   elevation.  Where only limited data ar© available at  this height,
                   it aay be necessary to infer the Froude rasber frea surface
                   observations.  Observational data should be analysed  to reveal
                   the uncertainties in correspondence estmp Froude nsmbsrs obtained
                   frosa data st terrain elevation and those inferred fros standard
                   airport observations; and model sensitivity to these  uncertainties
                   should be evaluated,.	  '	_.			_^.
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                                           SECTION 4
                 OMPLEX|TERRAIN MODELING: TEOWICAL ISSUES AND CURRENT STATUS
              The current Guideline on Mr gusalat^ j^dgls_ (EPA 1978) lists no ssodsl
         as being generally epplicsble to  complex terrain situations,, leaving the
         matter to the discretion of  the EPA Regional Adainisteator snd to "expert
         advice."  Eecsu^® Esodsiirag is tssed  to ^certain whether a proposed pollutant'
         sourc© will ESS©$ asbieat air quality standards [e.g., national Ambient Air
                 Standards  (MA&QS) and prevention of significant deterioration (PSD)
                      thf decision to permit nsfr or expanded industrial astd energy
                    facilities  i0..e«plex  terrain areas iaay_be_jiighly_sensi._tive_to__
                    ~~        '       "         '
              As baekgresmd  to  the ms&elivtg appffoach adopted,  this section provides a
         brief overview ^£ the  present  state-o£>the-srt for c^splex terrain aodeling,
         including key t^ctsaieal  areas  of interest,  r©eeut advances and current
         research, anid-,rec«jnt field  a?id laboratory expsriiaents .
              Physical processes  of  interest in^ cc^Ies terrain include:
                    terrain-induced perturbatioas on wind speed sad direction and
                    pluaa|trajectories  for different stability conditions;

                                                  ©n the kinematics of plume shape,
                          ted atmospheric turbulfenc© levels and increased plus® dis
                   psrsidn coefficients;
        4.1
              ©     effects  em plyrae rise owing to buoyant entrainsaeBt and vertical
                    shesrjj and, th®rsfore, ©n ®sti®^tes of masiraa ground- level tepsct
                    ia  coapi@x terrain;  and

              e     speci4l  aarodyn^ic  effects,  such as plum® stagnation on the wind-
                    ward  s.id® of terrain features under stable flow conditions, and
                    wake  Effects en the  leeward jside of terrain features.

              Terrain- Xrafuced Kin©®aiie Constraants on Dispersion and Plurae Tra-
              jectories  I

              As a  resul^ of distortion due to air flow around terrain obstacles, a
         plum© will pass ithrough phases ©f acceleration and deceleration along its
         trajectory.  To 'first ordsr, these effects are independent ' of the effects ©f
         turbulent  diffusion.   In  particular, f^r an incoaspressibl© fluid, raass con-
         tinuity requires that an  increase in velocity along a streamtub® will result
         in a decrease ii| streastub© cross-sectional area, and vie© versa.  Thus, for
         ®5a®pl©» a pltm^ passing  up and over ail elevated ridge is expected to      _
                  velocity  over the crest; correspondingly, the plusae vertical spread

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                )$fcntt  and l&ilheam (1973)  applied two-dimensional potential	
jflow theory to quantitatively describe(the resulting ground-level concentra-
tion distribution.  Their method involved superimposing diffusion effects
iato streamline trajectories  defined by the potential flow theory.  The
methods used included both  simple gradient-trimsfer (K-theory) assumption
jctnd the statistical theory  of turbulent diffusion extended to deforming    	
~~®n&.  The results for flow  over a cylindrical hill shewed that for a
jsouree'Ts ~te&~ htll~h@TghtS ""upwind ;~the~ "grmiM-Tever^onceritratldM~ffipproac!ie3~
those expected in the absence of the hill.  Egan (1975) used potential flow
assumptions to describe the closeness of approach of a pluiae to ground
level, and the plus®  spread due to kinematic defamation effects, for too
cases:  flow nonsal to  a half-cylinier, and flow normal to a hemisphere.
;     For  two-dimensional flow noraal to a half-cylinder, an elevated pli&se
that follows a streaaline  is  constrained to pass nearest to the ground just
above the crest of the  cylinder.  However, above the crest the streamline
'spacing  is narrower than elsewhere, which tends to decrease a  over the
jcrest.  These two effects  tend to cospsnsate, such that the ground-level
'^concentrations may not  be  markedly larger than those expected in the absence
bf the hill.  This result  should apply .qualitatively to flow norsal to
jridge-type-terrain features.-  - - - • - ~,~	 "			         1Bsa
!     For  three-disensional neutral flow normal to a hemisphere, the stream-
lines approach  the surface more closely, and converge more than in the flow
over a half  cylinder.  Axial  symmetry results in distortion of a streastube
element  as  it passes  over  the crest.  The flow kinematics cause a marked
local  increase  of a  and a marked local decrease of a  over the crest, and
the effects  eosabine^to increase ground-level concentrations significantly in
jthe vicinity of the hill  top.
i    Hunt and telhearn (1973) could not extend their statistical theory
approach to  predict the concentrations at the surface; rather, they developed
an asymptotic  thin plume solution to the advection-diffusion e«$uation.  This
solution foras  the basis  of the method adopted for this analysis.
j     In  sore recent work,  Britter et al. (1976) generalized the Hunt and
Muihesrn model  to calculate dispersion 'in inhorogeueous turbulent flows
around hills and other obstacles.  They showed th*it wakes downwind of terrain
ban produce  a  30% increase in ground-level concentrations at downwind dis-
jtances as great as 30 hill heights.  They investigated dispersion over low
   lls  and compared theoretical results with experimental laboratory measure-
       to show  that hills with small slopes say have a  large effect on surface
concentrations.   In general,  they conduct 1, terrain-induced convergence and
divergence  in  the flow field will dominate small-scale turbulent diffusion
in controlling  plume  spread.   Hunt and Snyder(1978) provided further evidence
bf the increase of ground-level concentrations for three-dimensional flows
over obstacles.  .                       i

J4.2 Enhanced Dispersion in Complex Terrain
i                !                       |
     Field studies (e.g.,  Miller 1978) suggest that the routine use of the
     dispersion  estimates  in complex terrain situations can lead to erroneous  j BOTTOM OF
estimates of ground-level  concentrations.  Systematic  errors are noteJ both   i IMAGE ^~£f-
an near-field and far-field regimes.  It appears that dispersion coefficients
          a
         Ki
        often be modified toward less stable values.
               -,/o"
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                             in eouplsx terrain settings, a shift of ona  stability __
        classification tcnuard unstable is appropriate  (Hinds 1970 „  Leahey et  ai.
        1973,  Leahey 1974, MscCready et al. 197,4, Cr«aar  1975, Start et al. 1975,
        Start  et al. 197^6, and Shearer et al. 1977).
            During stable conditions th© effect of terrain upwind  of  an  elevated
        source is prissrily to increase th® crdsswind  spread or ae&nder of th©
       ijjiluae, perhaps because of eddies created in th© horizontal  plan®. __Airborne__
        measurements 'bF|>Iuiie" "growth" under "differing wind~direc'tlon-terrain~con-
        figurations (Schierseier and Niesaeyer $970) show  that upwind terrain  is
        important in increasing the crosswind spread,  but has lesser effect in
        jenhancing vertical dispersion rates.  For settings in which the upwind fetch
        does not include high terrain capable of creating eddy flows,  one does not
        pxpect to observe large crosswind iat)cnder at high elevations.  Crosswind
        peander is observed to be largest, othu-- things be equal, for  low horizontal
        Wind speeds.    i                       j
                        '                       !
             Buoyant Entrairaient Effects on Peak Plume Impact in Complex
            Terrain    \                       >.

            "Coliveetive "activity may cause buoyant" plumes to grow" rapidly'liy "entrain-
        bent of Gobient air.  This buoyancy- induced growth becomes  less important  as j
        the pluse travels downwind; and ultimately, the effects of  aebient tur-       j
        bulence dominate  the pluae growth.     '                                       j
        I     Over level terrain, tlie maxiaua ground- level concentration occurs at     j
        jdownwind distances where the vertical spread of the plume is a large  fraction ;
        jof the final plume elevation.  At such distances  the dimensions of the plusse j
        >are largely the result of asbient turbulence and  are largely independent of   i
        {the initial buoyancy- induced entrainment.  For this reason,  Sr-oyancy  effects '•.
        'on the plirae growth rates are often ignored in sir quality  iapact analyses;   i
        Irather, use is srnde of dispersion coefficients based on experiments with      I
        passive, nonbtsoyant pluses  [e.g., the PGT or American Society  of  Mechanical   i
        Engineers  (A^IE 1968) coefficients].   :                                       j
        j      For a plume  traveling toward complex terrain the location of maxiisra     )
        jground- level iispact isay not be far downwind, and  plume dimensions in  the
        {region of EraxiEism ispact ssay be dominated by buoyancy effects  rather  than  by j
        ambient turbulence levels.             j
        j     The growth caused by buoyancy can be estimated on the  basis  of assusp-
        jtions in the Briggs plume rise formulae  (Briggs 1969).  Specifically, Briggs j
        noted from observations of rising plumes that  the radius, T, is about one-   j
        half the plume centerline rise.  This implies  that plume growth is pro-       i
        jportional to pluae rise.  Cramer  (1975)  incorporated this observation into   j
        jestimates of plume expansion by defining a virtual source distance using sn   j
        Initial plume dimension of AH/4.3.  Pasquill  (1978) suggested  that the        |
        jgravth is about AH//lCf and that it can be incorporated by smsming the squares ;
        jof buoyant growth and ambient turbulent  growth.                               j
        j     Egan et al.:  (1976) present exasspiss of the difference  between o  ,  the   I
        passive (nonbuoyant) PGT vertical dispersion coefficient, and  (a  ) ,sthe
        buoyancy- enhanced dispersion coefficient, for  a typical 1,000  megawatt        j
        [fossil-fuel fired power plant under various atmospheric stability conditions. •
BEGIN1    n^jg largest differences occur for stable atmospheric conditions and low wind j
LAST !-!r'lF (speeds; at a downwind distance of about  1,900  ra  (about the  location of  final -';
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	   rise), sigjdficastt differences iij ground level concentration estimates.
would be expected  on high terrain.
     Th® potential flow model results with and without buoyancy enhancement
are ccspsred with  the Widows Creek Pow«*;r Plant data.  But the FMF laboratory
Jexpsriaeaits used! only neutrally buoyant plumes, so for those comparisons
 nly th© no-enhancement calculations a?e appropriate.
                                                   Stable Flow Conditions

             Stably  stratified flow experiments in th© laboratory draonstrate that
         the  flow  properties determining the trajectory ©£ the plums around an
        jobs tad e  ere sensitive to the ratio of'inertia! and buoyancy forces.  Flow
        jnorraal to a  two-dimensional ridge unde£ stable atmospheric conditions may
        pass over the ridge—if stratification .is weak and wind speed is sufficiently
        high.  If the teaperature inversion is 'strong and winds light, the flew may
        f"block" upwind of the terrain; that is,; a plume may not have sufficient
        pdnstic energy to flew over th® ridge.i These situations require special
        'itreatEent of crosswind dispersion and reflection from the ground surface.
        Different modeling approaches have beert taken to characterize enhanced
        jhsrizontal- dispersion by pltaa® aeander during-light" wind-conditions." TtieSfe*3*
        Include:   (a) explicit sector averaging with a variable stability-dependent
        sector width (e.g., EPA VALLEY eodsl); (b) multiple sector averaging (e.g.,
         JERT ERTAQ model); and (c) statistical sector averaging using randomized wind
         fields (e.g., EPA CRSTER modal).       j
              In  flat terrain, the zero surface flux boundary condition leads to the
         inage source argument (Csanady 1973), implying a doubling of ground-level
         concentrations at large downwind distances.  This doubling factor may be
         (incorrect in many coisplex terrain situations.  A rasesber of investigators
         j(Briggs  1973, Cabe 1977, and Williams 1977) have suggested that in abruptly
         (rising terrain Gaussian models should be used without doubling the surface
         Concentrations (the  'reflection effect*).  Britter, Kant and Puttock (1976)
         jand Iftint, Puttock and Snyder  (1979) report, on the basis of physical model
         istudies  of terrain objects, that the peak surface concentration is close to
         the peak pluiae centerline v?lue upwind of the obstacle; doubling of con-
         centrations is not observed.  Egan et al. (1979) have recently developed an
         plgoritha for quantitative estimates of the reflection coefficient as a
         function of terrain slope, pluiae height, and downwind distance.  This
         algorithm gives a reflection coefficient of one for flat terrain, and zero
         for the  limit of direct incidence on a vertical bluff.  The algorithm has
         pot yet  been tested with field or physical raodel experiments.
              The potential flow theory described in Section 5 does not address these
         stable flow incidence situations.      i
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                       T
                             APPLICATION OF POTENTIAL FLOW THEORY
         5.1  Modeling Criteria and Rationale

             As a practical matter, it is neither feasible nor necessary to model
         jail  possible cossbinatioi's of topography and meteorological  flow.   For regu-
         latory purposes,. th«* required modeling'approach  should emphasize those cases
         *ith a demonstrated potential for high ground-level  concentrations.
             The modeling approach described in this report  addresses  the develop-
         aent of methods for neutral and slightly stable  conditions.  For neutral
         afedspheric "stability conditions",""potential flow theory  predicts  that" flow **
         close  to the surface and perpendicular 'to an infinite, semicircular ridge (a
         two-dimensional terrain obstacle) will accelerate and will  lift over the
         ridge.  A typical streamline is only about one-half  as high above the ridge
         crest  as it is above the surface upwind of the obstacle.   (Streamlines for
         potential flow over a cylinder are shown in Figure 18b in Section 8).
              Because the flow accelerates, streamline  spacing d  creases and the
         vertical dimensions cf a non-diffusing plume decrease by approximately a
         factor of two.  Thus, the ratio of plirae centerline  height  to  vertical
         dispersion coefficient a  remains approximately  the  same as the ratio over
         flat terrain.   i                       i
              But when the flow approaches a sphere under neutral flow  conditions,
         the comparable streamline approaches the surface much more  closely,  and (it
         can be shown) this ratio is much smaller.  This  results  in  much larger
         jround-level concentrations.
                                                I
         5.2  Gaussian Formulations in Complex Terrain

             Many of the1 characteristics of flow fields  in flat  terrain are j:ijnifi-
         cantly altered by the presence of terrain obstacles. Flow  field assumptions
         explicit to the application of Gaussian diffusion models include:
                         i                       i
             •    uniform (non-accelerating) velocity  fields,

             •    constant plume centerline height  (equal to stack  height plus plume
                   rise) jabove a flat surface, and

             *    dispersion coefficients (o , ;a ) determined by ambient turbulence
                   levels independent of the mean flow.
 Be GIN
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     Because th^jse assumptions  are not
use of a Gaussim plusae eodal requires,
features in & terrain-influenced situation.   This section discusses the
modifications sjgide in order to  Iceep a Saussian description of pluae disper
                                                thought as to how to include these
>
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TABLE 2. FORM OF VERTICAL DISTRIBUTION AND VERTICAL SPREAD IMPLIED BY SOLUTIONS OF THE CLASSICAL .! .|
PARABOLIC EQUATION OF DIFFUSION*

Wind Speed Form of B in
___ 	 , 	 . !: V'J
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Scale of "-:r;';:i
; . , Case Diffusivity U " x(x,z) - x(x,0) expC-B) Vertical Spread \ 1
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tx -i t x
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o I o


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(3) terrain K(s)f U(s) [U(s)J2z2Cs)/ 4 / K(s')UCs') ds' g^
o *•

_
* U i2L = _i f K -§2U
U 3x 3z 1K 3zJ
s = distance along plume center line trajectory.

Adapted from Pasquill (1978), p. 4.



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BEGIN
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HERE   *
                                                .on; note that the choices
 Ms is an assumed form, not  a derivat
 1 • a « o  » l.p reduce Equation 5-1  tj> the flat terrain Gaussian saodel.
This foraSla conceptually  distinguish©
or shrinkage (decrease in  o )  by flow Reformation and" (b) change of the
 >Iuse centurlin4 trajectory owing to  tie presence of a terrain obstacle.
      Changes in th®  concentration duel to the accompanying changes to the
velocity field are not explicitly accounted for in Equation 5-1 because
                                                          S&al 1
         the transport velocity will result in small, inverse changes to the scaling
         factor or centeriine concentration.   j
              The plume centeriine concentrations will also depend on the product of
         the paraseters o  and o .  The groundx^evel concentration, on the other
         land, will vary with the ratio (n/cs ) |in the exponential term.  Egan (1975)
         has argued thatlfor neutral flow over two-dimensional obstacles—where
           a  s i.o—£io% deformation has little or no effect on ground-level values;
         for flows approaching a three-dimensional obstacle, however, n/a  < 1.0,
         leading to ground-level concentrationsilarger that those in analogous flat
         terrain situations.                   j
              In the discussion in Section 5.4, the quantity nz, the height of the
         ptume «enterline above the-terra±n,~lsTeva:luated"by-a~partiTOl^r two^" or'
         three-dimensional stream function  (seeiSection 5.4.3) and the values of
         a ,a  in Equation 5-1 are defined  (see'Equations 5-56, 5-57; Section 5.5) in
         term! of particular line integrals.  Tfeus, the method adopted is essentially
         a modified Gaussian dispersion model.

         5.3  Modeling Approach, Applicability, and Limitations
                         i
              This technique applies potential flow theory to a Gaussian point source
         model.  It permits explicit evaluationjof the terrain-induced kinematic
         constraints andjtrajectory variations.!  In adopting the present technique,
         an attempt has been made to broaden its applicability.  Approximations have
         been developed to extend tho neutral formulation to slightly stable cases
         and to allow for terrain obstacles with crosswind shapes intermediate between
         those of a. cylinder and a sphere.  These approximations are based both on
         theoretical and Isemi-erapirical grounds!  As presented in the folloifing
                                                                               TOP OF
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         sections, the approach may be suitable
         meteorological situations:
 BEGIN
 LAST LINE
 OF TEXT E
                                        for the following topographic and
              •    isolated, single terrain obstacles of arbitrary height, with
                   approximately circular cross-rsection in the downwind direction and
                   arbitrary aspect ratio in the crosswind direction; and
                         I                       j
              9    neutral to slightly stable stratifications.
                         I                       i
              At the outset, the limitations ofJthe present model should be  clearly
         stressed.  Thes^ limitations arise maialy from physical effects that  are not
         described by thd pot«"tic.l flow model.j The following cases are excluded:
                                                I
                                              luiae
                  flow cases, where plumes are constrained to flow around
           ratheij than over the obstacle;
           cases (dominated by surface boundary layer effects;
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, -, 	
I__ • unstable cases (e.g., convec
9 cases 'dominated by wake effei
i
Specific recommendations based on thesi
Section 3. '
	
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Sipensional difgysivities (length squa:
between these d^ffusivities and the PG'
1970) is explored in Section 5.5.
Substituting the continuity equat
«»• on oS
into Equation 5-43 yields:

U(S) 3s" 1 " 3? 9n" = D1(S)
Solutions to Equation 5-6 are sought tl
XI f f •% 1 1»*^ - _ _._._^ r .
».s,njiyj - , j exp 1 -
•ed/unit time}. The relationship 	
r dispersion coeff -,ients (Turner
ion:
0 (5-5)—

2 , 2 ,
i-| * D2(s) ^- (5-6)
lat are Gaussian in form:
fjCs) n2 - f2 (s) y2] (5-7)
and also satisfy the additional constraint that the mass flux across the ^
pfeffiS is conStarit, i'.e.r
1 +0> +OD
f f u(s) x
9-1 /R" i 1
This constraint, requires that:
g(s) = IT u(s) /
— — 	 	 	 	 — ~ ^^ 	 	 — j&-=*~
dndy =1.0 (5-8)

1/2
ifjCs) f2(s)] (5-9)
Substituting Equation 5-7 into 5-6 yields:
fjCs) = [u(s)]2/
\
f2(s) = l/[4T(s);
where :
s
4>(s) =| D..(s
0
and
s
T(s) = | [D20
o
Kf
| 	
[4 4>(s)] (5-10a)

(5-10b)

;') u(s')ds' (5-11)



;')/u(s')]ds' (5-12)
^
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Jy_ Equation S-9&
g(s) » 4ir[i(>(s) T
,
[n more familiar terms, the dispersion
fee diffusion equation solution, a anc
•» n
fjCO = i/t;
i
f2(s) = i/[:
or
a 2 = I/ [2 f.(s)]
n i
.- . —
s) ]1/2 (5-13)

coefficients in the Gaussian form of
o , are given by: —
a 2] (5-14a)

ay2] (5-14b)

= 2* (s)/[u(s)]2 (5-15)
a 2 = I/ [2 f (3)] = 2T(s) (5-16)
7 *
1
TTie arguments for three dimensions proceed imzch the same as in the
previous section!. 'F-e appropriate non-
:-- t

9-1/8"





t
5-
J.
^
!







BEGIN
LAST LINE
U(S) -jjA- + n -T— -r^— = DI (s]
s n n
dimensional diffusion equation is:

2 , 2 ,
>
«'

'
i
!
1
]
1







i-Ky + D (s) ?-*j (5-17)
3n 3y
tfhere the coordinate system is now with respect to (s,n,y). Here, y is the
angular, azimuthal coordinate from the ;axis of symmetry along the flow with:
y - YR(s) (5-18)
1
*here R(s) is the distance from the axis of symmetry of the obstacle to the
jlume centarline, and y is the cross-wind distance from the plume center-
Liae. The continuity equation in this coordinate system becomes:
i 3v 1 d ,
I "alT UsT dT '
u(s)R(s)] = 0 (5-19)
ITie trial solutipn sought is of the form:
i

X (s,n,y) - g(s) exp[
subject to the constraint:
1
i2n +<»
I j u(s) x'(s,n,Y)
f '

' O —
Cf- TEXT S5!~
jCs) n2 -f2(s)Y2] (5-20)







1

r
f







BOTTOM OF
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, TYPING GUIDE SHEET
,* CENTER
OF PAGE ^
&ihs,itutl(s)  R(s)]
                                       o  2   =  2 [R(s)]2 T(s)
                                                                       (5-26)
                                                                       (5-27)  i
                     5.4.3  Role  of Potential  Flow Theory
      Values of the dispersion coefficients (Equations 5-15, 5-16, 5-26,
'and 5-27)  are determined at a particular distance, s, along the pluae center-!
! line by line integrals (such as Equations 5-23 and 5-24) which are functions  j
jof the velocity along the plume centerline streamline, u(s), and (in the      j
ithree-diaensional case) by the distance, R(s), frosa the axis of syiametry.     |
jIn the potential flow approach adopted, s, u(s), and R(s) are determined for  j
ja particular terrain shape, by a stream function, $.  That is, the variation   ;
'of velocity along the pluse centerline and the distance of the plume center-  i
[line froa  the surface (defining the plume trajectory) are evaluated ai>ily-    i
 tically using the stresaline equation.                                        I
i      It is assumed that the plunie centerline follows tlie stre^line through   j
jthe point  source at the effective source height, H .  Along a streamline,     j
jthe value  of tha streum function is constant, and the particular value of
'the pluzse  centerline streas function is denoted by ij> .  The va'ue of
                                                                                  (2) blight
idetermined by three parameters:  (1) effective source height H ;
lof the obstacle,  a; and (3) distance along the x-axis frosa the base of the
isource to the center of the obstacle, X .  The streaaline associated with a
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                TYPING GUIDE SHEET
 •VW*.-x»«*- - -t"**z?^~?^
 FIRST
 LINE OF
 TEXT

 HERE  s^grticular stre^a  function, *, is determined by the  shape and dmensioa of-
         the terrain obstacle.   The streamline taken to be  the pluae ceaterline is:
                                             CENTER
                                             OF
DROPPED
HEAD;
BEGIN
SECTIONS
HERE   ^Skia
                                 *(x,z)
                                  (5-28)
          is gives  the height of the pluse centerline above the surface at any
                                         TOP OF
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                                         AREA
                         i—3Js«-¥el0©irty—£i«fl4,-j-£®03— is-^eteOTtsed-fey^t&e-atifem-
        function,  i|/,  such that the along-streaeline velocity, u(s), is:
                                                  f3*!
                                                  (If)
                                  (5-29)
              The cases examined in subsequent  sections include flow ever a two-
        dimensional ridge and over a three-dimensional axisysaetric hill.  In the
        two-dimensional case, the stream  function (Mlns-Thosson 1960, p. 156) is:

                                       =U
l; -
        where U^ is the magnitude of  the uniform wind velocity far upstream of the
        source.   The value of the stream function through the source is then:
                                          U-Hs
                                                         H
                                  (5-31)
         and the equatioa of the pluiae  centerline is:
                         >u z 1 -
>S2D
                                                                                (5-32)
        >                 I
        JFor exazsple, the height of  the plume centerline, z , at x = 0 (over
         crest of the ridge) is given by  solving the quadratic equation:
                                                                                (5-33)
                         I                       !
              Analogous equations are valid  in three-dijaensions for flow over a
         hemispherical hill.  The stream  function in this case (f4ilne-Thcason I960,
         p.  464) is:     ,
BEGIN    ;
LAST'JNE'	,
OF TEXT ttr-
                                   0.5 UZ
         Z2,s/;
                                  (5-34)
               3/8"
                                                     .]
                                                    tl
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1
H
i
1


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CENTER ' TOP OF :|
OF PAGE . ^1WAGE 1

th£ stream function throukh
j
i
1

?




3D

C s* s} "






" S




2




and the equatiea ©f the pluae cessterliH®
22
«•

1
1-
**
•
\
(2 2^ 3/2
X
H 2
s "s




,s-7 «r,r^ a
a source at (2 , H ) is: 	
S S


a3

(X 2 + H 2) 3/2
s s J

is:
a3 1
" ** ' ' ** '? /"& v3""<*uj
rw A . u A ^/-£
(X5 * HS } J
5.4.4 Reduction of Solution to Fiat Terrain Case
To clarify
situation of
developed in
'•"Soyr- 	 -*• 	 	
tion reduces
the discussion ia tine previous sections, consider the
uniform flow with velocity I
^Sections -5.4.1, _5.4...?i._ai»4. !
"to
J^ over flat terrain. "Hie equations
j^4,3 are OTPiicsfole, ,asd_.tlie solu.~«M..
a recogisizsbl© for®. '•
The starting poimt is the appropriate stream function, $, which in this
case Oiilue-Hioason 1960) is:





9-1


Note that there
j the x-axis.
3
t
j
1
i
|




'8"


I
4»(z) = Uc
1
j

D z (5-37)


is no dependence OB x, and streamlines are thus parallel to
Th© value of the



!
and, therefore,

!
| 'or
1
t
t
i
\
I



BEGIN
LAST LINE


This is also
so that R(s)







$
stream function through the source, $ 9 is


CHS) = ^
the equation of the pl<





*(z) =


iim?
*,


z * H;
f


HS (5-38)
3 center line is:
,(HS) (5-39a)


(5-39b)

equal to the distance- from the x-axis to the plume centerline,
= t
I .


I
•s
|
j

\
\
-



























>
Substituting Equation S-A7 into Equation 5-29, the velocity along the >
pluEe trajectory is constant and equal to:




	
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N^ _







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u(s)




i
! --
	







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.•.•.-.•-•.•.• L J • •
_ 1^24
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= U^ (5-40)



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DROPPED
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SECTIONS
                                     CENTER
                                    OF PAGE
        TYPING GUIDE SHEET
  solution in tie  fora of Equation 5-20 can now b© evaluated.   In  flat te:
th® aiossg-streasiline  coordinate, s, isj just the downwind distance  from the-
source, x, ami the noy®si to the streamline, n, is just the vertical  distance
fro® th® plume eenterline,  z.  The line integrals $, T, (Equations S-23 sad
5-24) reduce toi
                                                                               TOP OF
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                                      DL(x)  H
                                        U  x
                                                 -98.
                                                                        (S-
                I    T(x)   -  D2(x)
                !
and f., f2,  and,g are by substitution:'


                j     V0  -  U./[4D1(x)xJ

                I     f2(x)  -  UJIs2/[4p2(x)x]


                     cg(x) -* -~4inr
                                                                                 (5-42)




                                                                                 (5-43)

                                                                                 (5-44)
            ----- !•
         Noting that the  crosswind distance froas plume centerline, y, is given by:
                                        y = Hs

         and substituting  Equations 5-43 through 5-46 into Equation 5-20:
                         i
                         !
                                    1
              x'

                               4»
                                        ,1/2
                                                                        (S-46)
                                                                        (5-47)
         This is  the  solution given by Sutton (1953) for a continuous point source.
         The familiar Gaussian dispersion coefficients o ,o  (see Equations 5-26 and
         5-27) becesse:   I                       I         y  z
 BEGIN
 LAST LINE
 OF TEXT »
                                           2D2(x)x/U
                                           2D1(x)x/U
                                                                        (5-48)
                                                                        (5-49)
                   5.4.51  Uraitations
     Although  iaportant features of the terrain-influenced flow field  are
reproduced by  th© potential flow theory approach, inherent limitation
resain:         '
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 HEPE E
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                               CENTER
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DROPPED
HEAD.
BEGIN
SFC TICK'S
HEBE   p
•    tb« p|eser.se of  a realistic surface boundary leyer is ignored;  .
•    relevant physical phenomenon such as velocity shear, radiative
     heatipg, gad flow separation are esitted; and
•    the theoretical  aodel  requires  that the pluae remain "thin"
     coshered to its  height above the terrain.  For short stacks this
     criterion  is often  violated oear the hill crest.
                                                       TOP OF
                                                       IMAGE
                                                       'AREA
         [Strictly speaking, the first two  of these  limitations  also restrict the
         theoretical validity of a conventional Gaussian solution in flat terrain
         situations (Pasquill 197S), unless the set  of dispersion coefficients assumed!
         specifically account for these effects.]  It is prudent to apply the poten-
         tial flow theory approach only to  the windward side of  obstacles and not to
         situations dominated by lee wake or separation effects  not treated in the
         Eodel.  In many; of the results to  be presented, the cosputed plume dimension
         will violate tho restriction to "thin plumes", but it is not unreasonable to
         •push1 the theoretical formulation in these cases (Hunt, Puttock, and Snyder I
         1979).          j                      j
 BEGIN
 LAST LiNE
 OF TEXT &
              PGT-Scslisg ^sf Dispersion  Coefficients
                         I                       1
              Evaluating the terrain-influenced dispersion coefficients (Equations  5-26
         and 5-27) with  this femulation requires  specifying the crosswind and the
         normal diffusivities,  D-  and  D,.   To compare sodel calculations with
         analogous flat  terrain situatiSns, an approximation scheme was implemented,
         using the PGT dispersion  coefficients (Turner 1970) as a calibrating scale.
         Qualitatively,  the diffusivity  at a given distance froa the source along the j
         plume centerlin©  stre^line is  taken as that for the same transit time in     j
         flat terrain.   The consequence  of this assumption is that nodel calculations |
         of dispersion coefficients  reduce to flat terrain values in the limits of
         large downwind  distances  or saall obstacles.
              Newer  and  possibly superior formulations of dispersion coefficients
         have been suggested  (e.g.,  Pasquill 1978 and Irwin 1979), but have not yet
         been adopted in EPA regulatory  sodels.!  Therefore, for ease of ccsparison,
         the familiar PGT  values have  been used in the calculations discussed in this
         report.  Other  dispersion coefficient systems can be easily incorporated
         within the  basic  sethodology  used here.
              Substituting Equations 5-23 and 5-24 into Equations 5-26 and 5-27
         gives explicit  expressions  for  a  and c .  (From here on, the dispersion
         coefficient in  the norsal direction is denoted as a .)  At a distance, s,
         froa the source along  the streamline, the dispersion coefficients are given
         by:
                      a,! Cs)
                        z
2 D. (s)      s i
   1         /  'FTCs') u(s')ds-
                                      R (s)   o
                                                                  (5-50)

         _ 1 ___ I ______
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BEGIN
LAST
OF TEXT
FIRST
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HERE 2«
DROPPED
HEAD;
BEGIN
SECTIONS
HERE *







TYPING GUIDE SHFET
— °As) » 2R2fs) D
where D^, oT are typical mean
These values are assumed
— t
. [ —
i Vs>
1
CENTER
OF PAGE ^
rS 2
2(s) / ds'/[R (s1) u(s')J (5-S£f
o
dif£usiv|lty values at distance s.
to be gissren by the PGT values (a -, a -j :
7
« oz£ (s)/2t • (S-52)
- oy2! (s)/2t (5-53)
where s is the integrated path length ^long the plume trajectory and t is
the advection time:
I
1
i
i s
I
^^ 	 ^ P , /7 .
! t
i
[
s
= / ds« (S-54)
° 1
J_ 	 ^
= 7 ^L. (5-55)
' U (s • )

         the final form of the  dispersion coefficients:
                                           s
                                   yf
[I R2
o
t u
R2(s)
t
(s1)
i
2{s)
rs
r
u(s')ds'~
R2(s)
ds'
7
R (s«) u(s')
                                                                                 (5-56)
                                                                                 (5- 57)
         The bracketed qfiantities  approach 1 asi streaioline deformation becomes
         negligible, and|0  ,a  reduce to their flat terrain values.
              Figures 1 and ^illustrate the plume spread statistics  a  and o ,
         respectively, for  neutral flow over a circular ridge.  The riSge is f.O km
         high; the point^source, 200 ra high, is! 4.5 kia from the ridge center.
         Calculations ar® shown for diffusivities scalx^I to reproduce the- PGT neutral
         stability class[values for a  and o  ip the flat case.  This illustrates
         that only the vertical dimensions of the plume (as characterized by a )
         differ from flat terrain  values in floV over tv/o-diiaensional obstacles.  (In
         each of Figuresjl  through 4, the center of the ridge is indicated by a short
         vertical bar at'the downwind distance 4.5 km; the horizontal bar extending
         frost 3.5 km to 5.5 km denotes the windward-leeward extent of the ridge.)
                         1                       i
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                        I	
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                       flaa&i&fflaaiatfiiaai&aMi
                                                                                       ,xl&e*at*£ U^t^£££Afe^.*a

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SECTIO'-J!
                                                                    Computed Stability Ctass 0 (tidga)
                                                         — — (2) PGT Stabiittv Class D (fl»t)
                                    3    4   5     7     10          20

                                         Downwind Distance from Source (km)
BEfi ,\   I         Figure 1.    Horizontal dispersion coefficients  for neutral flow
LASfI   8                       over a circular ridge.
OF re;
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.  I	
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BEGIN
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                1000
            •§   100
                  10
                                                                      Computed Stability Class 0 (ridge)
                                                           —.__ (2) PGT StatxJity Class D (Rat)
                                           Crest
                                                     I
                         I
                                                  J_
                                       3   4   5     7     10          20

                                           Downv/ind Distance from Sourca (km)
Figure 2.
Vertical  dispersioh  coefficients  for neutral  flow
over a circular ridge.
                   (Cin.)
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BEGIN
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      i
                                                                    TOP OF
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1000
                 100
                  10
                                                                   (1) Computed Stability Class D IhiEl)
                                                                   (21 PGT Stability Class D (flat)
                                           Crest
                                                     I
                                           I
                                      I
                                       3457     10          20

                                           Downwind Distance from Source (km)
BEG!!.'
LAST I.
OF TE)
  Figure 3.
Horizontal  dispersion  coefficients  for neutral flow
over a hemispherical hill.
            EPA-Z-37 iCm.j
            {•5-76}
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HERE   •!
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LAST L!
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                1000
                                      3    4   5     7     10          20

                                           Downwind Distance from Source (km)
                    Figure  4.
                                                                                    f
                                Vertical  dispersion coefficients for neutral flow
                                over a hemispherical hill.
             EPA-237 !Cin.)
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                                                iMi  31    ii;
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HERE
     As streamlines diverge  to the leeward and~windward side of the hill, o
increases.  Oveif the ridg®,  vertical c|jaipression of the streamlines leads to
a drastic decrease in o  .  Over the ridge crest the vertical plume thickness
Ls about equal io the height of the pl^me center!ine above the surface, n .
This marginally I obeys the  thin plume approximation.                      s
     Retaining the saiae  source-obstacle geometry, but changing the terrain
e&stacle type from a circular ridge to a hemispherical hill, Figures 3 and->t~
   iplay-tha-th-Fdo-disefis^iMki-ftetttrai-f^^	
tions 5-26 and -f-27.  In this case, both o  and o  are affected by the
potential flow field, as evidenced by a marked increase in 0  over the hill
top.  Comparing |az values  in Figures 2Jand 4 at x - 4.5 km reveals that the
vertical thickness of the  plume is mor£ severely restricted in three-dimen-
sional flow than two-dimensional flow.)  In fact, as indicated in Figure 4,
downwind of the(hill o   never recovers|from the deformation over ths hill
top.  At the crest, thl  quantity a /n j is approximately 2, clearly violating
the thin plume criterion.  The pote'nti^l flow theory would not, strictly, be
applicable in this situation; however,iat least to the hill crest, useful
estimates should be obtained.  Downwind of the crest, a  is affected by two
factors that tend  to increase its value over that predicted by potential
:E4pw_calculatio4s-alcne2  These-are^  {I>rincrease4-diffysi«a acr0ss-st*eaas*s>
lines because of smaller streamline spacing, and (2) terrain separation
phenomena, which enhance turbulent mixing over that given by ambient tur-
bulence rates.  'Because  of these effects, the model should only be applied
to the upwind side of terrain obstacles.
     Figure S^shows the  evolution of the velocity speed up factor (the ratio
of the source streamline velocity in the presence of the hill to that in the
absence of the hill) for potential flows over the circular ridge and over
the hemispherical  hill.  Both streamline patterns upwind and downwind of the
obstacle crests are symmetric, so the speed-up factor has beer plotted only
from source to 
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SEO
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TYPING GUIDE SHEET
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                             01" PAGE

             m  1.5  -
              a
              3
                                 1.0           2.0           3-0           4.0
                                     Downwind Distance from Sourco (km)
                                                          W^M'WW'Wfl

                                                           TOP OF'
                     Figure Sa.   Velocity  speed up factors  for neutral flow over a
                                  circular  vidge.
                         Sphere
                          (3D)
1.0
                             2.0           3.0
                    Downwind Distance from Sourn (km)
                                                                        4.0
                                  Velocity  speed up factors  for neutral flow over a
                                  hemispherical hi11.
                                            '.1_J  33
                                            PAC.t NJ\
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                            OF PAGE
                                                NEUTRL FLOW
               6.1  Ground-Leve>l and Centerline Concentrations for Neutral Flow
      BEGIN
      LAST LINE
 TOPOF
jJMAGE
 AREA
     The terraiii-influenced dispersion  estimates  developed for neutral  two-
and three-dimensional flow cases were used  to  compute the plume centerline an normalized  by     |
Uraa2/Q (Equatiori 5-4a).  Note that results  are not independent of  obstacle   j
lieight a.  Introduction of the PGT calibration of diffusivities (Section 5.5)]
which are not linear in the length scale, require that all results are
specific for th£ particular obstacle height cited.
     At plume centerline, the concentrations for  the three-dimensional  case,
as well as for the two-dimensional case (not shown) are not appreciably
different from tjhe flat-terrain case.  jBut  they are strikingly different at
ground level; compare curve 3, the ground-level concentration in the flat-
terrain case, with curves 4 and 5, thejground-level concentrations in the
three-dimensional and two-dimensional cases.
     For the two-dimensional ridge the  magnitude  of the maximum ground-level
concentration is about equal to the maximum in flat terrain,  but the maximum
occurs at about ;ridge top (4.5 km downwind  from the source),  whereas in the
flat terrain case the maximum occurs about  9 km downwind.
     For the th^ee-diiaensional case the maximum ground-level, concentration is
roughly 10 times larger than in the flat  terrain  case, and occurs  at the
leading edge of(the hemispherical hilli the concentrations remain  very  high
as the plume parses over the hill.     j
     The ground-level concentrations for  the two-dimensional  flow  are similar
to those for th^ flat case because of flow  acceleration effects:  the reduc-
tion of a  in the vicinity of the two-dimensional ridge crest is largely
      OF TEXT Compensated by £ reduction of about equal magnitude in the  closeness  of
              i"	1——'	\	•	j~-	'	•	
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  . TYPING GUIDE SHEET
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                                                                                 TOP Orc
                                                                                 IMAGE
                                                                                 'AREA
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HERE !
 BrGI
 LAS:  a
 OF'I
100
                 10
                  0.1
                     Hs =0.2
                                       a= 1 km
                                                    cl = centerline; gl = ground level
                                                    a = hill height
                                                   (2)	XsdMll) 3-D

                                                   (3)	 $^0W
                                                   (4)	^(hill) 3-D

                                                   (5)	
                                                   , (hill) 2-D
                                                  10
                                                          20
                                                                              109
                                    ind Distance from Souna (X = -j)


  Figure 6.    Centerline and ground-level concentrations for cases
               shown in Figures 1 through 4  (neutral  flow).
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                                        CENTER
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                                                                                 TOP OF
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       roach of the^plisae to the ridge.  Ik three-dimensional flow over  the    —
   [hemispherical hill, however, the pluse approaches such closer to  the hill  top
                                                                                 ~l
DaOrx>

HEAD
BEG.'N
SECT i
HEP.E
ED
    8111*
                     ground-level concentrations can substantially increase.
         Dependence on Stack Height and Position
gr~     lltc ground-level concentrations, shown in Figure^6^ as ^_func_tipi^of	j
 36wiwiiia~diytMce~f6rn&e~hli^                                  ridge, were  j
 jcoaputed for a particular geometry; that is, hill  (or ridge) height of  1 ka,  i
 jstack height =0.2 [hill (ridgo) height], and stack located 4.5 km upwind of  !
  the hill (ridge).  For each choice of geoaetry, the maxisaim ground-level      |
 iconcentration occurs at a unique location downwind.  Calculations of raaxisua  ,
  ground-level concentration, as well as the position of  the maximua, were Bade
 ifor various gcabinaticas of stack height, H , and  distance betwc ,n stack and
  hill center X., both normalized by hill heifht a.  Figures 7 and 8 illustratej
 ;the regions in paraseter space in which calculations were performed for the   i
 jtwo- and three-disensional cases, respectively.  For exaaple, in the case of  j
 'the hemispherical hill (Figure 8), assuaing a hill height of 0.5 km and a     '•
  diasiisionless effective stack height of H  = 0.6t  calculations were done	 __j
 Varying the cimensionless distance between stact and hill center, X , froa    j
  'values of 10 to 100.  Results of this series of nodel calculations are  shown  i
  in Figures 9 and 10 for the cylindrical ridge and  in Figures 11 and 12  for    j
  :the spherical hill, respectively.                                             j
  j     Figure 9 shows that the maximum ground-level  concentrations are not      I
  affected very ssich by the cylindrical ridge, especially for stack heights     i
  saaller than O.S tises the ridge height.   (In each instance, the dashed line
  is the value of the concentration for flat terrain.)  For a nondisensional    ;
  stack height of 0.8, and for stacks positioned between  about 20 and 100 times;
  !the ridge height upwind of the ridge, the eaxisum  ground-level concentration  ;
  increases sosewhat above the value corresponding to flat terrain.  The
  position of the saxiEua shifts from leewards of the ridge crest to the  crest,
  as shown in Figure 10, as X  goes froa 20 to 100.                             j
       A spherical hill exert! a isuch stronger influence  on ground-level  concen-
  trations than does a cylindrical ridge.  For short stacks not far froa  the
  hill, the laaifitana occurs on the crest of the hill  and can be considerably
  greater than in the flat terrain case (see Figures 11 and 12).  Farther froa
  the hill, the naxisaag ground-level concentration occurs before the pluzae
  'reaches the hill.  This limiting behavior is shown in Figure 11, where, for
  :the smaller stack heights, all the aaximua ground-level concentrations  are
  constant for large X .  The hill exerts negligible effect on the maxisum
  ground-level concentration when the stack is a distance of approximately 10
  .hill heights or sore away from the hill center.
  !     For the higher stacks, the behavior is considerably different.  Figure  ll
  shows that when the taller stacks are fairly close to the hill, the maxims
  ground-level concentration is insensitive to stack position.  When the  stack
  is positioned farther froa the hill, however, the  concentration increases by
  as such as an order of aagnitude before decreasing to its value for flat
  terrain.  This behavior can be understood by looking at the variation in
  position of the ground-level isaxiEais, as shown in  Figure 12.  For tall  stacks
 /relatively close to the hill, the saxiEua occurs far downwind of the hill.
  However, when the stack is farther froa the hill,  the maxims! shifts to the
                                                                                          OF
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                                                                                         r'-ES

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                 Figure 7.    Domain of calculations performed  for a two-dimensional
                              cylindrical ridge and neutral flow.
                                                 37
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                                                                                                                                                           -3

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»„_ 	 .J


Legend
Valuet oft (Hill Hsight)
"•"—'""••""• «0.g *m
— — — - 1.0 km
«ra» «•  • ?.g ftW
«•> . . «.»> "20 km

l, / | i l t i l i
-T
A^^-






«^~^_





i
i

I





0.6 O.S 1.0 1.2 1.4 1.6
A fi4a
1 & 1 • 1 "391 1 Mmifl!Rn>u«tlAnj!il &h»4r ltej^5.»
Figure 8, Domain of calculations performed for & three-dimensional j
hemispherical hill and neutral flow. wj__
,'

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               10.0
                                 o
                                      1.0
                                 1
                                 o
                                      10-
                                 I
                                 i
                                     10-
                                          —•—Flat Terrain
                                          Ridge Height a = 0.5 km
                                        10
                                                    20
                       DsstSRsss Hell to Soui^g
                                                                              Hg°0.2
                                                                              H s - 0.4
                                                                             H$-0!8
                                                     100
Figure 9.
         ground- level  concentrations for a cylindrical
ridge and various combinations  of stack height and
position.                  >
                                                                   TOP OP
                                                                   IMAGE
                                                                   AREA
                                                                   (-"~STT .""•*• * c".r
                                                                   uv •' i t win L-'1"

                                                                   IMAGE AREA; •
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                               10.0
                                1.0
                                   ——Flat Terrain
                                            Ridgo Height a = 0.5 km
                                         Hf - 0.8
                                                                       H
                                             0.4
                                                                       /s
                                                                       H
                                             0.2
                                                                       H s = 0.1
10
                                              20
                                       100
                                                                                         — E*>"
                                                                  TOP Of
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0  Tf
                Figure 10.
         Distsnca Hill to SGWCB fs^ » iSj/a)
Position of maximim ground-level  concentration for a
cylindrical ridge and various combinations  of stack
height and position.      *   -
    	__- -_  ,	^_ 40	rrrr 	-=:.- -=.. -_- -_=
W3TTOM (M-   i
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PORTABLES
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               10.0
            o
            ^
Dest«nce Kin to Sourea (
                                x,,/8)
                  Figure  11.
Maximum ground-level concentrations for a spherical
hill  and various  combinations of stack height and
position.        41
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MFPP tet
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SEGi
SECT
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                                                CENTER
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             100.0
            x
            •
            o
            •5
            §
              to.o  _
                                                                 TOP OF
                                                                 IMAGE
                                                                 "ARffA
                                         Distsnca Hill to Source (x\ •* Kg/a)
BEG In
LAST'
OF It
              Figure  12.
Position of maximum  ground-level  concentration  for a
spherical hill and various combinations of stack height
and position.
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•crest of the hi|l. A notable feature <
maximum concentration occurs at the hi
as 100 hill heights from the hill cent
0.3 Effect of Obstacle Size
i
>f the taller stacks is that the 	
LI crest, even for stacks as far away
sr.
 TOP OF
^IMAGE
 AREA

In one setiof calculations the obstacle size was changed with all other—
         (4.5 km)  upwindlof the spherical hill, and computations were made for hills
         varying between 1500 m and 2,000 m in height.  Variations of fflsxisura ground-
         level concentration are shown in Figure 13.  For these hill heights greater
         than the stack height, the maximum ground-level concentration increases
         rapidly.   The position at which this maximum ground-level concentration
         occurs is shown!in Figure 14.
                       -4
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   ;: .TYPING GUIDE SHEET
     '
                                    CENTER
                          10
                        v
                        a
                                               J L
                                   0.5    1.0    1.5    2.0
                                   b',61 Height  a (km)
      Figure 13.    Maxisum ground-level concentration  as a function
                    of hill height.
1 20<
i "5
I -10
a











) tf






* f






,
«






i

0.5 1.0 1.5 2.0
HSH Height a (km)
      Figure 14.
                              Position  (distance from hill crest) of maximum
                              ground-level  concentration as a function  of hill
                              height.
                                     44
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SECTIONS
HERE   jf
                 TYPING GUIDE SHEET
                                             CENTER
                                             OK PAGE
                                                                                           OF
                                           SECTION 7
                  COMPAR|SON KITH LABORATORY  EXPERIMENTS—NEUTRAL FLOW OVER
                                          A SINGLE MOUND
BEGIN
LAST LINE
OF TEXT S
         7.1  Background!

              Model computations were  compared with experiments conducted at the EPA
         Fluid Modeling  facility  (FMF)  (Hunt etial.  1978)  to study the flow and
         diffusion of pollutants in  idealized cbinplex terrain under neutral conditions
         (and also stably stratified conditionsr-see Section 9).  The primary purpose
         of these neutral and  stably stratified! flow experiments was to understand the
         effects of stability  on,.the flow structure over_a bell-shaped _hill_.	TheJhiJ.1
         fls~placed hear4the entrance "to the~wind"turnei~whefei ~the~flow~~was ess.en-  s  j
         tially uniform  and non-turbulent except for a thin boundary layer small      j
         compared with the hill height.   (The thickness of this boundary layer in the
         wind tunnel matched that  observed over; the baseplate in the towing tank, so
         that the approach flow structures in bpth the tank and the tunnel were
         essentially identical except  for the stability—see Section 9.)   In later
         experiments (Snyder and Britter 1979) the hill was placed in a simulated
         atmospheric boundary  layer, but the earlier experiments are more suitable for
         the model coaparisons because (a) the potential flow model is expected to
         more accurately.predict the behavior of a uniform, non-turbulent air stream
         and  (b) the "thin plume"  assumptions ate more closely met.  Calculations werej
         performed using the complex terrain model for the characteristic dimensions
         used in the EPA experiments (on the centimeter scale).  Therefore, it was
         first necessary}f determine  the appropriate dispersion estimates on the
         laboratory scale i.i the absence of terrain features, so that the line
         integrals 
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•; BEGIN
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                 TYPING GUIDE SHEET
                                             CENTER
                                             OF PAGE
        'Stas  fitted to
DROPPED
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SECTIONS
HERE   Sal1®1"* usetl *n the'model.
sigmas,, a  lineal1  functional  form,  a
                  data.   The measured
(1977) as experiments  HHSWTN.398,  .401
the three downwind distances  39.2,  84.
shown in Figures
Snyder and MarsS
                                                iata are catalogued by Snyder and Mar-sli
                                                 and .403 for the vertical profiles at
                                                7, and 130.2 cm.  These data  points  are
                          15a, 15b and 15c, along with the curves given explicitly by
                          as best Gaussian fits to the data points.  Using  these
                                                i + bx, was fitted to the  three points_
         (y
     According~ko  the Gaussian plume equation, at the plume centerline
     0,  z « H)  ^he normalized mass flux parameter & defined by:

                            U
                                                                                (7-2)

                                                                                  In
is  equal  to uni^y.  
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DRCJ
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200
180
               160
               140
                120
                100
                 80
                60
                 40
                 20
                                  CENTER;.,,
                                  OF PAGEV
                                       JL
                                                 I
                                                       *  Experimant
                                                       ©  Computed Using o
                                                       s  Computed Using o'
                                                       —  Best Fit Curva (Snyder
                                                          and Marsh)
                                                            I
                                                                          I
                                                                                   TOP OF
                                                                                   IMAGE
                                                                                   AREA
                   .001    .005  .01     .05  .1
.5   1

    x
                                                5   10
                                                             50  100    500  1000
                  Source: Snydar and Marsh 1977
BEG;   §
LAS;   2
OF1   S
                 Figure 15a.    Vertical  concentration profile 39.2  cm downwind of a
                                 12.5 cm stack in  flat terrain.
I	J	„
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                                              iii  47  £|v
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180
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                                        I
                                                                I
                                                                     A  Experiment
                                                                     9  Computed Using a
                                                                     s  Computed Using a'
                                                                      •  Best Fit Curve (Snyder
                                                                        and Marsh)
                                                                            I
.001     .005  .01
                                       .05 .1
                                                   .51
                                                5   10
50  100     5OO  1000
BF.G
LAS
                   Source:  Snyder and Marsh 1977
                 Figure 15b.
                                Vertical concentration profile 84.7 cm downwind of a
                                12.5 cm stack in  flat terrain.
                                                   48
            EPA-287 (Cm.)
            (4-76)
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                  TYPSNG GUiDE SHF.T
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                                  CENTER
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                                TOP OF
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                                                                                              Zl.
                                                                                                 AKEA
200
                180
                160
                140
                120
             N
                 80
                 60
                 40
                 20
                            I
                        I
                                                        Experiment
                                                        Computed Using a
                                                        Computed Using o'
                                                        Best Fit Curva (Snydar
                                                        and Marsh)
                                                                            I
                        I
                   .001   .005  .01      .05  .1
                   Source: Snyder and Marsh 1977
                                    .5   1
5  10      50  100    500  1000
 Figure  15c.
                                Vertical concentration profile  130.2 cm  downwind of a
                                12.5  cm stack  in flat  terrain.
                                                                                        OF   *:
                      __. J
                                                                                  OP TABl ZS
                                                                                  .'.'0 ILLUS-
                                                                                 TSAT10NS
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            (4-7S)

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j
FIRST " 	 TYPING GUIDE SHEET
LINT 0;r
TEXT
HEKE asjiiiteaded (since) the observed si
ToEserved concentrations isust be
potential flow saodel must coae
DSOrFL.. terrain obstacle is present.
HEAD |
REG.u 75 Comparison ^ Presence of
?r' . ' i'jN^ 	 j
HRF Ssk
Mhea a *!>olvnaraial hill' w
CENTER
OF MGfc ^
gmas are input to the calculation, the
reproduced). The crucial test of the
froa comparison with experiments in w^ich &
\
i
Terrain Obstacle
1
as imtredMced in the wind tunnel, the con-
TOPOF
-IMAGE
AREA


i
I
1
Icentratien profiles differ substantially from those measured in flat terrain.!
.The resulting profiles at several dc&mdnd distances froa the stack are shown1
jin Figures 16a,'16b, and 16c.  The three profiles were iseasured upstreas of   !
;the hill,  on the j>ide of the hill, and at the crest of the hill, respec-      \
 tively.  The curves drawn are given explicitly in Snyder and Marsh (1977),    I
 drasts smoothly *hrough the experimental data points.  Using the dispersion    ;
 parmeters derived frcs the flat terrain experiments, the centerline and      )
 ground-level concentrations cossputed with ,the model are indicated in          i
i Figures  16a, 16b, and 16c.  The fundamental equations used include 5-20       >,
Ithrough 5-25, 5-56,. and 5-57.                                                 !
i      Centerline values are predicted within a factor of two using either a ,? ]
rat a* at alImpositions;  the centerline concentrations predicted using a  lie
'very close to the observed values at distances 39.2 and 84.7 csa from the      I
 stack.  At the aost upstream position (Figure 16a) the ground-level value is  ;
'not well predicted because of the boundary layer.  The corresponding flat     i
;terrain useasursaeat (Figure ISa) did not extend close enough to the ground to'
|enter the boundary layer  (height of lowest issasurement was 7.5 cm).           i
!     The next measurement is part-aay up the hill.  Using the original values
 of o^, the model predicts an essentially zero ground-level concentration.     i
 .However, using the flat terrain boundary layer-enhanced a * gives a value     |
 joore than double the experimental value.                                      j
      At the crest of the hill (84.7 on) where the ground-level concentration  ,
 is highest, the predictions bracket the observed concentration.  The observed'
 concentration at the crest is the average of four Beasureaents which ranged   j
 •froa 0.2S3 to 0.506, laade through the sampling port at the center of the      i
 hill.                                                                         |
 i     The predicted concentration using the best-fit o  is 1/3 of the observed;
 lvalue, while that computed with the enhanced a * is aBout five tisses the
 ^observed value.  The difference in shape between the polynomial hill used in
;the laboratory experisents and the hemisphere used for the computations ccoild;
Icontribute to sc®e of the differences in concentrations predicted and         I
iobserved sway ."TOD the hill crest, but the difference in shape alone cannot   i
'explain the discrepancy observed in the surface concentrations over the       j
.'crest.                           '                  '                          i
I     Further inspection of the plums profiles in the absence of the hill      !
| (Figures 15a-c) reveals that the centerline of the pluae does not ressain at   ;
;the release height of 12.5 cza.  Instead, the profiles suggest the effective   ;
.pluae centerline height is about 11.5 as.  Because this is evident 45.5 oa
i upwind of the location of the hill center, it is reasonable to assume  that a
Isiiailar depression also affects the plume in the presence of the hill.        I
i      Results of additional computations using a  (best-fit) with an assumed   i
 stack height of 11.5 cm are suuBaarized and compared with the observations and
 the previous calculations in Table 3.  Predictions of the centerline       —j
                             T
                    	 ^  so
                                                                                                TOM Ci
                                                                                                .;:•: A'lEA.;
                                                                                'AMD ILuUS-
                                                                                TPA7IOWS
                      (Cio.l
                • 4-76)

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                                              CCTJTER
                                             OF PAGE
h?E£ &4-

TOPOf
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'AREA
             200
                                                                   Experiment
                                                                   Computed Using o
                                                                e  Computed Using
                 .001
                Source: Snydar and K&reh 1977
               Figure  16a.
                                 Vertical concentration profile 39.2 cm downwind of
                                 12.5 oa stack in presence of a 23 cm hill.   (Hill
                                 crest is 84.7 cm downwind of stack.)
                                                                                                        1
                                               51

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T?P?MG GUIDE SHEET"--7""
                               (T\'7f;R
•'T'C r^ p"rT--r "r -- - - ' '-^-—^-f-'nT^ifV".-

     •'      TOP OF
ijRO?1^:1 t
              200
           N
                                                                      Computed Using o
                                                                  a   Computed Using o
                 Source: Sr ytter and ftSarsh 1S77
                 Figure 16b.   Vertical concentration profile 68.2  raa dwmwirad of a
                                12.5 CT stack  in presence  of a 23 cs hill.  (Hill
                                crest is 84.7  oa de&siwind  of stack.)
                                                                                                             4
            K "5-
                                                  52
                                                                                                           I 1
                                                                                                           ! j

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             200
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                               SHEET
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                                               TOP OF

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                                                                    *  Experiment
                                                                    ®  Computed Using o
                                                                    m  Computed Using a'
.(K)1   .005  .01
                                     .05  .1
.5   1
                                                     /"s
                                                      X
5  10
50  IK)
500  1000
                Source: Snyt&r and Meisfi 1977
                Figure I6c.
          iff. 257 (O-, '
          (4-7PJ
               Vertical  conces&tratiozi profile 84.7 ca downwind of a
               12.5 c® stack in presence 'of a 23  cm hill.   (Hill
               crest is  84.7 ca downwind of stack.)
                                                   .,_..
                                                 .53

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FIRST TYPING GUIDE SHEET
LINE Of CE' - fa
DROPPED j
HEAD. ,
	





SECTIONS __ TABLE 3. COMPARISON OF PREDICTED AND OBSERVED _J
' "~ *&f^ Wrir7?^A T T 7PH (TVT*iTPPf JT*0 A*TT
- nUiVvVuI. £«XrfiJ 4_>V^ld.Cr« 1 X\J\ 1 J
ONS AND PUS4E CENTERLINE -j
', HEIGHT FOR THE 12.5 CM HIGH STACK IN THE
— : PRESENCE OF THE 22.9
CM HIGH POLYNOMIAL HILL

i

i








Observed Value Predicted Value j
Parameter
j X=84.7 on (hill crest):
*C:r Surface Concentration
Hs=12.5 Hs=11.5



0.391 0.118 0.520 H
Centerline Concentration 47.9 53.2 51.4
i Centerline Height (cm)
X=68.2 on:

2.3 2.2 1.9


', 1

Surface Concentration <0.007*
Centerline Concentration 60.4 91.4 91.1
X=39.2 era:
Surface Concentration

0.003*
; Centerline Concentration 181.8 187 187

, !
i




i









-•






1
!
j
3
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*These concentrations were not Beasured right at the surface, !
but 2 to 3 ma above.


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FIPST
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HERE
                TYPING GUIDE SHEET
                                             CENTER
                                            OF PAGE
                                                                                       TOP OF
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        .concentrations  gemain nearly the same,! but the surface concentration at the—
        crest has  increased considerably.  Now; the predicted value has risen froa
DROPPED  °* tne observed(value, to 133%.   Surface concentrations at the two locations
HEAD;   upwind of  the crest remain too small fpr a meaningful coaparison.
BEGIN        Also  included in Table 3 is the centerline height over the hill crest.
SECTIONS JShen the model  ^ssuues the upwind plume height equals 12.5 ca, the predicted!
HERE   ge&eight over thejcrest agrees closely with the observation.	fejJLJjhjLTL-thjL—-—]
        fassumed height is 1J.5 on, the predicted height over the crest is 80% of that]
        observed.       I                       j
        /      In the absence of the obstacle, the dispersion parameters for release
        (points above the  boundary layer were determined using a stack height of
        J12.5  era.   To determine whether these flat terrain dispersion parameters for
        the  12.5  cm stack can be used for other stacks, calculations were made for a
        9 cm stack with the best-fit a  .  The results are compared to experiment in
        jTable 4.   The centerline concentration is overpredicted by 50%, the surface
        jconcentration is  underpv*dicted by 50%, and the centerline height is over-
        I predicted by 30%.  It is expected that the predicted concentrations would be j
        (closer to the observations if specific plume spread data for the 9.0 OP stack-
        Jin the absence of the hill had been obtained andLincorporated in jthe calcula-J
         «•"•(! *»• m           .     <-  -              J"                                      I
                        I                       I
                       TABLE 4.   COMPARISON OF PREDICTED AND OBSERVED
                     ,, JWRMALIZED CONCENTRATIONS AND PLUME CENTERLINE
                   HEIGHT OVER TOE HILL CREST FOR THE 9.0 CM HEIGHT STACK
         Ion.
                 Parameter
                                            Observed Value
                                                        Predicted Value
             X = 84.7 cm:
             Surface Concentration
             Centerline Concentration
             Centerline Height (cm)
                                                 16.6
                                                 30.0
                                                  0.9
                                                               8.0
                                                              45.5
                                                               1.2
             Assessment>of model performance begins by comparing predicted concen-
        trations with observed concentrations.   In comparing results from the model
        and laboratory experiments,  sources of uncertainty are present.  One measure
        of their effect is the change in the ratio R of ground level to centerline
        concentrations.  From the basic Gaussian plume equation, the ratio R is:
                           *Cl
                                      -•"ST
                                                                            (7-3)
 BEGIN
 LASTLINE
 OF TEXT
 where n  is the height of the streamline above the surface and a  is the
 vertical dispersion coefficient.   For a typical wind tunnel experiment, (X ,
 84.7 cm; a, 23.5 oa;  H ,  12.5 cm; and aspect ratio, 1) the model calculations
[predict, at the crest of the hill:    j
                  0   ai  o.58 cm,  n   =  2.16cm.
                   Z _ .  ___ '__ S ______ ,
                    is th~en~ computed" by Equation 7-3.
                                                                                      BOTTOM Oc
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          (4-76)
                                         PAGE NUMBER

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                TYPING GUIDE SHEET
                                             CENTER
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                                                                                       Tnp
                                                                                       TOP OF
^"2__   Now assume4 for example,  that n
DROPPED
HEAD;
BEGIN
SECTIONS
HERE   55
  or
  (1
  V
  as:
                                             .  ,	o  may be  as much as
           too low.   Th* new retio R* is computed from Equation  7-3 with o
           ±  0.1)a,  and,nc* = (1 ± 0.1)n    '           ------
                                                                            too high _
(1  ±-C2)n> '
                          then  the  error ratio
cu iroai cijus!_jLUii  / - j KJ.UJ u   «•
e generally, if o * »  (1 ± £1)0.  and
R*/R from Equation 7-3 can be written
                                                                            (7-4)
                                                                                        AREA
        Note that this ratio  is  sensitive not only to the size of the errors repre-
        sented by C. and  C_,  but also to the value of (n^/a ).
             Several computations were made for the particular values of n  and o
        given above  (n 2/a  2  ~ j
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"1^"" TABLE 5. ERROR RATIO R*/R FOR 10% ERRORS














	

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IN a_ AND n.


: Case I: (n_/oj2 = 14t



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Case II:





i

0.9 ns
ns
1.1 n
S
















0.9 a a
Z Z
1.1 az
1.0 3.7 9.9
0.20 1.0 2.3
0.033 0.23 1.0 ^





i
Cn./aJ2 = 3.5 j

0.9 ng
ns
1.1 ns

-1/2
R* = e

TCase I corresponds to
a =0.58 cm.
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1.0 1.4 1.8
0.66 1.0 1.4
0.42 0.69 1.0

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R = e I'rj

specific choices n = 2




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                                                                               • OP OF
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    terrain correction factor  is  all  that is needed to predict the surface	
concentration in the presence  of  terrain from surface concentrations pre-
dicted in the abjsence of terrain.   The j terrain correction factors can be
derived from thd potential  flow model Results by solving Equation 7-6 for T
in terms of thejknown flat  terrain dispe^ion parameters, and the ground-
level concentration calculated in the presence of the terrain (x
                                                                               (7-7)
             Similarly,'if an observed terrain*influenced surface concentration is
        !known  (as  in  the  wind tunnel experiments),  an observed terrain correction
        factor may be calculated using Equation 7-7.  FIT example, Table 6 lists
        ground-level  concentrations as observed at the hill crest; as predicted with
         the potential flow model (also as predicted by the "half-height assumption"
         be discussed  shortly); and the corresponding terrain correction factors.
        Note that  if  th6  source-obstacle relationship is fixed, a smaller surface
        concentration gives a larger terrain correction.Jfaeior^ _Jh§L correction	n
        factors  based on  the observed ground concentrations vary roughly from .33 to
         .35, while those  based on the potential flow model vary from .36 to  .34.
         is seen that  suall differences in the terrain factors are derived from much
         greater differences in the maximum surface concentration.
                      9-1/8"                     j
                  TABLE 3.  COMPARISON OF NORMALIZED CONCENTRATIONS AND DERIVED
                        t   TERRAIN CORRECTION FACTORS AT THE HILL CREST
BEGIN
                                                                           It
              Observed Data:

              H  = 12.5 cm
              H  = 11.5 cm
              Potential Flow Model:
                                                       Normalized Concentration
      H
                   12.5
                   11.5
              Half-Height Assumption:
              H
           12.5
           11.5
                                     0.325
                                     0.353
                                            0.357
                                            0.344
                                            0.5
                                            O.S
                                                                0.391
                                                                0.391
0.118
0.520
0.0001
0.0011
      Two modeling approaches can he readily compared with the wind tunnel
 data:   (1)  a level trajectory, and (2) a specific partial height trajectory.
 In the level trajectory model the plume centerline does not rise over terrainj
 features.   When ,the terrain exceeds the plume height (as is the case in these;
 wind tunnel experiments) the centerline concentration is assumed to represent
LAST LINEuJxe highest ground concentration (no surface reflection doubling is
OF TEXT eftncluded)_._
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     The partial height  trajectory approach assumes that the plume  rises  ov.gr..
the hill.  The glume's height above th© surface is described as  a fraction of
the initial plusje height.   The fractio^ (which lay vary continuously with
downwind distance—see below) depends 6n the initial plume height H ;  on  the
terrain height ty ;  and on an assumed 'plums path coefficient,1 C.   the
fractional displacement  of the plume atsove the terrain enters into  Equa-   	
      (7-5) as a'multiplier of the ratio H/o --that is, as a terrain correc-
     f actor T-rtFOT^pliaae3~lBt ti ally" 1 wer~ihan~ttt5~te'lfrliln~TH^-^TTpl
                                                                           (7-8)
and  for plusse heights greater than the terrain height  (H

                \                ht      '
                    T   -  1 -  r±  (1-C)
                                                                    >ht):
                                                                         (7-9)

         The plume path coefficient may vary between 0 (level trajectory) and 1
         (terrain following trajectory).  One  common choice for the plume path
         coefficient is the "half-height." assumption:   C  =  0.5.
             _^Predicted ground-level  concentrations^ from_.the_ppten.ti.a_l fJLow_ model
         jcorapared with those based on the half-height assumption in Table 6.   The
         (half-height assumption underpredicts  the surface concentrations at the crest
         of the hill by two to three  orders of magnitude.  (If a pluiae path coeffi-
         cient of 0.35 is used instead, the partial  height approach gives a concen-
         tration of O.lSSrfor H  = 12.5 cm, and>0.432 for H  = 11.5 cm.  These con-
         centrations lie !much closer  to the observed concentration, and to the con-
         centrations calculated with  the potential flow model.)
              These additional comparisons of  surface concentration predictions using
         level plume and half-height  assumptions  emphasize the sensitivity of this
         particular plume configuration to the ratio (H/a ). (It appears the thin
         plume restriction  (oz/n   «1) is not a serious restriction even for ratios
         as  large as a /it  *• O.sf which is the ease in the laboratory experiment with
         the 12.5 cm release height.) In  light of this sensitivity, the performance
         of the potential flow model  in reproducing the laboratory observations is
         acceptable, and ^demonstrates the usefulness of this approach to complex
         terrain problems where the potential  flow approximation is applicable.
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                          MODIFICATIONS FOR EFFECTS OF STRATIFICATION
 8.1  Qualitativls Observations from Laboratory Modeling
                i                       i
      Ambient stratification can significantly affect plume behavior and
 resultant atmospheric pollutant concentrations.  For moderate plume heights
 relative to hill size, and for moderately stable stratification,  laboratory
 experiments suggest that the plume will go over the top of the hill,  but  the
 path of the plume will be closer to the surface, and the  flow over  the  crest
 will be fasterjthan in neutral flow.  |For small plume heights_under_strpng ^^
"ftratificatibnTl t¥e plume will tend to" go around the hill rather  than over "°
 it.  If the hill is a long ridge, the flow may be  "blocked1 and stagnate
 upwind.  To approximate first-order effects of moderate stratification,
 results of FMF experiments on plume behavior in a  stratified water  channel
 flow over a po^ywmial hill (Snyder 19,78) have been incorporated  into the
 complex terrain; model.

 8.2  Incorporating Stratification Effects
                I
      Experimental results of the FMF tow-tank experiments on plume  behavior
 in stratified flow over a polynomial hill are reproduced  in Figure  17 (Hunt
 et al. 1978).  The height of a streamline at the hill crest  (n )  is shown as ,
 a function of stack height (H ) for various stratifications denoted by  Froude
 number, Fr, including the neutral flowi case, Fr =  °°.  For any given stack
 height and Froude number, the height of the streamline at the hill  crest  can
 be compared with the neutral flow case'.  To calculate the streamline displace'*-
 ment at positions upwind of the hill crest, an approximation is made.
      The approximation begins from the! streamlines for neutral flow over  a
 sphere (shown in Figure 18a), and over a circular  cylinder (shown in Figure
 18b).  Note that the effect of the sphere or the cylinder on the  flow is
 negligible for distances greater than jabout two hill radii from the hill
 center; it is a$suiaed that this remains true in the stratified case.  Hence,
 the difference between the plume centerline streamline heights for  neutral
 and for stratified flows is a maximum at the hill  crest and is negligible at
| a distance approximately two hill radii from the center of the hill.
      In the absence of additional experimental data and a sore complete      i
 theory, a linear interpolation scheme is applied to compute the height  of the
 streamline at intermediate distances from the hill.  This linear  approxima-
 tion should be adequate; however, the interpolation scheme can easily be
 changed in future refinements of the model.  The procedure is incorporated
 into the model in the following way.
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                         92    0.3    0.4   0.5
   BEGIN  g
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              Source:   Hunt et al.   1978
Figure  17.    Height of the  source streamline  (ns) above the hill  crest
              (height = a) for various stack heights (Hg) and  Fruude
              numbers (Fr).
                                                   61
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               Figure 18a.   Streamlines over a hemisphere.
                              Circular Cylinder
         Figure ISb.   Streamlines  over a half circular cylinder.
LTA-PS7 (C.i.)

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tti

1_ As describ^l in Section 5.4.3,
center line is gjven by
1
1
where ij> is the $tream
if r££er-_to_-Eaua£ioas. ~5*-.
•
s,x)
                                                                               (8-2)
        (e.g.,  Equation^ 5-32, 5-36).  In particular, the height  of the streamline
        at the center of the terrain obstacle,:zr,  (at x =  0.0)  is  given by
                        1                       i *~
                        I              zr  =   zj (*.,0)
                                       v>       \  S
                                                                               (8-3)
        A^similarjrelationship can be .formed from_the_data in Figure 17_for.the- _a
        iFroude number dependent height of  the  streamline  over the terrain obstacle
        center, zcp:
                                  "CF
                                     = n^.  (Fr, H  ,  a)  +  a
                                                                               (8-4)  j
                                                                        ,H
        land fitting  the data  in  the  figure for the range of data shown (^s_ < 1) by   [
        (second-degree polynomials  of the  form:                           a            |
                                               |H
                                                          H  2
        jwhere  the  coefficients  depend on the Froude number, Fr.
             Define:    !                       1
                                                  - Z
                                                     CF
                                                                               (8-5)
                                                                               (8-6)
        The height  of the streamline,  zp,  for the stable flow is then computed by
                                                 z - 6
                                                                               (8-7)
        where  z  is  completed for neutral flow according to Equation 8-2, and 6 is
        given  by:       '                       j
P.EGIN
LAST [
OF TEXT
        or
                             6(x)   =  0 ;  |x| >J2a

                             6(x)   =
                                                        2a
                                                                        (8-8)
      TTie net effect of modifying the neutral streamline is  to  lower  the
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LAST Lif-jF height of  the plume centerline in the region within two obstacle heights   —I DIM-.NSIC-'-J
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          the obstacleicenter.  The plurae cenierline  is  depressed sost at the crestJ
      Iof the obstacle.                       !                  .                    !
      I      This streaaline depression schesie is,  strictly,  limited to flows similar!
      jto that investigated in Figure 17.  The coefficients  for Equation 8-5 hsve   j
      Ibeen derived for seven Froude nusiber ranges, and  for  stack heights less than j
      •or equal to the height of the polynomial hill.  In practice, the model uses	j
      ^thls scheme for any stack height  and any hill  shap®._ _     __  	
      i     Where 'Equation"S-5" is 'applied"tc"'Ftac&"he"ights~"6utsi3e tSe range"©?
      ,experimental data, two physical constraints are iaposed on the calculated    i
      !value of 2-_.  First, the streamline East  not  pass through the surface of the'
      'sphere. If it does, zrc/a is set  equal to  1.001.   Second,  the depressed      i
       streamline saist not drop belo& its original height at the source.  If it does,
       the stresaline height is set equal to  the  stack height.  Not© that this      ;
       ilatter condition only becomes important for stack heights  isuch greater than  j
       the hill heights.  Also, extrapolation of  thfc  curves  contained in Figure 17  ;
       for stack heights  above the hill  height possibly  introduces errors signi-    ;
       ficant for the wsre stable  applications.   More observations are needed to
       'refine the algorithm for taller stacks.
            An extension  of Equations 8-5 through 8-8 frcsa flow over an isolated
       three-dimensional  mound to  flow over a two-dimensional ridge" raus€~await>3a~
       additional experiments  to redefine the coefficients of Equation 8-5.   Con-
       sequently, the nodel now uses the same depression for all  crosswind aspect
       ratio hills.   In practice,  6(x)  (obtaiaed  frosa Equations 8-5, 8-6, and 8-8)
       for the two-dimensional hill  is set equal  to 6(x) for the three-dimensional
       hill.  This  depression  is  then subtracted  from the source streamline asso-
       ciated with  the  two-diasensional hill.                                         '
             In  addition to the lowering  of  the pluae  csnterline streamline,  changes
        in the along streamline velocity, U(s), nust be computed.   It is observed
        that  stratification speeds  up the flow over the obstacle.   The velocity
        change owing to stratification  is modeled  by assuming that the along stream-
        line velocity is given by  the gradient of  the  neutral flow stream function,
        ty, (Equation 5-29) defined along  the  lower streamline computed by the
        stability modification described  above. Since the gradient of the streamline
        function increases nearer  the surface, the along  streamline velocity, U(s),
        increases as stability lowers the plums centerline.
       ;      A final point concerns the  case  of direct plume  impact on the obstacle.
        The potential flow theory  approach  can only be applied when the pluae center-
        line streamline goes over  the obstacle. The EPA tow  tank experiments have
        shown that as the stratification  is made stronger and the stack is made      ;
       'shorter relative to the obstacle  height, & point is reached at which the
        plume no longer goes over  the obstacle, but impacts and/or goes around the
        obstacle.   Using the c'ata  in Figure 17, a minimum relative stack height,
       ,H /a,  can be determined for a given Frjude number in order that the plume go
        over  the obstacle.  This  is the value of H /a (in Figure 17) for which a
       given Froude nusaber curve  intersects  the ordinate  (i.e., its height above the
        crest of the obstacle is  zero).   Note that as  stratification increases
        (smaller Fr),  the height of the minimum H  /a required for passage over the
       obstacle increases.                                                           ;
             TabJe 7 summarizes the plume impact criteria currently  incorporated into
       the model.   If H /a is  less than  the  given value for a specified Froude      :
       ra^ber,  it is  assumed that the plume  impacts the obstacle and the case is  —-!
      tf*~

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          but not otherwise treated.  The plu&e  ispsct criteria have been  _
tTncorporated in a discrete fora, not a continuous  fora,  because the sodel is
 set up to use discrete Froude umber classes  in determining the streaaline
 depression associated with the particular curves shown in Figure 17.  If
 future refinements to the sodsl alloy a continuous depression algorithm, a
 continuous form of the impact criteria will be  appropriate.
                      TABLE 7.  PLUME IMPACT CRITERIA BASED ON FIGURE 17
         j-SHr	— —
Froude l&raber
(Fr)
Fr < 0.4
0.4 <^Fr <_0.7
0.7 <^Fr < l.S
1.5 < Fr
< Plurae iepacts if
! H /a less than:
; 0.82
0.75
i 0.375
i assumed neutral
                                                       (no plmse impact)
         !8.3  Application to the Atmosphere

         !     To apply this approximate model of stratified flow over a hill to  the
         atmosphere, the atmospheric stratification as described by the Froude nssaber
         ;Fr misr. be known.  The Froude number is defined by:
                             H •£      and  N
                                                         3z
                                                                                (8-9)
         jNote  that  a length  scale, H,  is  incorporated  into  Fr.  Ordinarily  the
         iatmospheric stratification  is specified  for routine  air quality sodeling
         'purposes by the  Pasquill stability  class, rather than by  the  Fronde  number.
         ;The classification  of stratification by  stability  class and the application   !
         jof  the  PGT Oy aad az  curves for  all stack heights  are approximations that
         jignore  the variations with  height of atmospheric stratification asd  turbulent
         diffusion.   These approximations are not as good in  the presence of  a  hill,
         I because of the aew  length scale  that is  introduced into the probiea.  The
         'prograa is  written  in such  a  way th/it  the user must  supply Fr if known, with
         iH in  Equation 8-9 corresponding  to  the hill height,  a.  If no Froude nussber
         )is  specified, the program assusses flow kinematics  corresponding to neutral
         :flow  conditions.  [Application of the  Etodel at Widows Creek  (Section 12)
         'provides an example of  the  use of vertical temperature and velocity  profiles
         Jin  defining Froude  nrabers.j                                                  i
               For routine application  of  the sodel using near-surface  observations,
         accurate Froude numbers are not  available.  Under  these circumstances,
         ;default potential temperature gradients  say be assumed throughout  the  over-   j
         'lying layer of the  ataosphere influenced by the terrain feature.   The  tea-    •
         perature gradient could be  specified for each of the neutral  to stable       j
                   classes in  much the same  way that the gradient  is specified  in
                                              65
                                          P ,'  '-" —

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TEXT   ^	p	
HERE nxycurrent stable $lume rise algorithms.
                                            CENTER
                                            OF PAGF;
-''    ll
   	  	p	__,,.	  Similarly, the stability-dependent
jwind shear algorithms used to infer stack height wind speeds  could  also be
ji»?ed to  infer a ssean elevated wind speed for use in calculating  a Froude
••Eusaber.   To the'extent that plisae rise, transport, and diffusion can be
jroughly  characterized in this way, the Froude number-dependent streamline
'depression aay also be characterized. ' But such an approach should  be fully
^snalyzed for sodel sensitivity to each assumption.
•j	-Additional^3ppToaches"vill have-to be developed" for "cases" wheye~boH
Iplume and terrain are above a confined surface layer.  This is the  problem of
\a true two-layer flow.  Over level terrain, the importance of such  a condi-
jtion is  reduced since ground-level impacts would obviously be small.   In
 cosrplex terrain, however, the model would be required to malce reasonable
.assumptions about plirae rise, transport velocities, plu&e spread, and Froude
 number in order to calculate a. concentration on the elevated  terrain surface.
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                                          SECTION 9
                   COMPARISON WITH LABORATORY EXPERIMENTS—STRATIFIED FLOW
                                                                                TOP OF
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       r
9.1  Introduction

!     The approach used  to test the validity of the potential flow model
modified for stratification effects is the ssse as that used for neutral
flow.  In the modified  potential flow Bodel, calculations are performed using
Equations 5-20  through  5-^5 as in the neutral case, except that the plume
centerline  trajectory is specified using Equations 8-2 through 8-8 to modify
the vertical displacement in neutral flow (Equation 8-1).  In the absence j>f
t
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OnC
HE/
              1000
               500 -
                    A Experiment
                       Computed Using
                       Computed Using a'
                       Best Fit Curve (Snydsr)
                .01
                   Source: Snyder 1977

                  Figure  19.   Vertical concentration profile 50 cm downwind of a
                                9 en stack for stratified flow in flat  terrain.
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           1000
            500
             100

              50
              10

               5
          <*
               .1

              .05
             .01
                       GUIDE SHEET
                 567


                Source: Srtyder 1977
CENTER
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                                           TOP OF

                                         ^"AREA
                    A  Experiment
                    ©  Computed Using a
                    a  Computed Using o'
                   —-  Best Fit Curve (Snyder)
  9
Z(cm)
              10
                       11
12
                                        13
               Figure  20.    Vertical  concentration profile 84.7 cm downwind of a
                             9 cm stack for stratified flow in flat terrain.
                                                69
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     Vertical concentration profiles were not measured in the EPA experiments
on stratified flow.  Instead,  the  ground-level concentrations were measured
along several lines from the crest of  the hill, at various angles to the asean
flow.  Figure 21a shows the measured ground-level concentrations along the ^_
     on the surface going directly from the hill crest to the stack.   In tfiTs
            ;y^^r7~T&e^nT~cT-esl^s~rp~c1it^                   sfacTc~Base at
s « 84.7 on.  The results of the model! computations using the originally
derived sigmas  (circular symbols)  and  the boundary layer-enhanced sigmas
(square symbols) are also shown in Figure 21a.  In the vicinity of the hill
(s <_20 cm), the concentration estimates based on the boundary layer-enhanced
dispersion parameter,  o1, are  within a factor of two of the experimental     |
data.  At the crest of the hill, the ground-level concentrations are 173% and!
208% of the observed concentrations using a  and a ', respectively, while
close  to the upwind edge .of  the hemisphere,Concentrations are underestimated!
by nearly a factor of  four.   In interpreting these results, it should be
noted  that the  ground-level  concentration varies exponentially with the
square of the distance between plume  centerline and surface, and that the
•BSdei -calculations- are based ^m~a hemispherical-hill ^shape,"different frosr *"
the  shape of  the polynomial  hill used  in the laboratory experiments.   The
hemisphere,  for instance, meets the flat surface at s = 23 cm, while the
polynomial  hill used  in the  experiments remains significantly above the flat
surface beyond  s  =  30  cm.  -Therefore,  the model underestimation with
increasing  distance  from the crest is  directly related, in part, to the
differences  in  hill  shape.   Under these circumstances, the comparisons are
 encouraging.    '                       j
      The highest impacts occur at the crest.   The predicted and the observed j
 concentrations  at the crest of the obstacle are shown in Table 8 for the 9 cmi
 stack case.   The terrain correction factor derived from the observations is  j
 0.183, and that,derived from the model; computations using a  is 0.147.  These;
 are extremely low values,  indicating that both the predicted and the observed
 surface concentrations are much larger than those that would have been pre-
dicted by a terrain-following model,  or by a partial height model using
 terrain correction factors  of 0.5 or 0.35.  Concentrations predicted by each
of these three  approaches  are also compared in Table 8.  It is seen that the
potential  flow  model  offers  considerable improvement in predicting the peak
concentration compared to these.other models.   (Finally, if direct centerline
impingement is  assumed, the predicted concentrations are 3 to 4 times larger
than the observed concentration.)     I
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— i

* Experiment
,~ .- • Computed Using o
m Computed Using a'













S*.







1



^
p---»








•
5 10 15 20 25 20 35
| Distance Upwind along th« Ground from Hill Crest Jem)
i
Source: Snydar 1S73
;
;




i
i Figure 21a. Ground- level concentration for stratified flow as a




















! function of distance upwind along the ground !
; from the hill crest for a 9 cm stack and 23cm hill.
( - 	 	
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(4-76)


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FIRST "TYPING GUIDE SHEET
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HERE is
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MEAD'
BEGIN
1_ TAB^ife 8. COMPARISON
CENTER
OF PAGE
TOP OF
> IMAGE
^""/vpf-iv
OF PREDICTED AND OBSERVED 	
CONCENTRATIONS AT HILL CREST F03
STACK TOW TANK EXPERIMENTS


I Normalized Surface
SECTIONS' • Model
MEKE 51







f~-

Potential Flow (o )
Potential Flow (a ')
Level Plume
Terrain Following
Partial Height (0.5)
Partial Height (0.35)
Predicted


63.4
76.9
125.0
1 x 10"25
1 x 10"5
0.11
THE 9 CM

Concentration at Crest
Observed


36
36
36
36
36
36
j " t













            "Measuremer.ts  and computations (using both sets of sigmas)"were arlso
        [compared  at  ground level,  outward from the crest at 90° to the flow.  These   i
        •results are  shown  in Figure 21b.  Again, the model is seen to work best  in    ;
        predicting the maximum concentration close to the hill crest.  Of£-hiil-crest I
        .concentrations, though underpredicted, are less important in regulatory
        japplications since these concentrations are an order of magnitude smaller
        jthan those at the  crest..  Other phenomena are active in the experiment,
        jperhaps producing  (by recirculation?) the secondary peak beyond the
        kargin of the experimental hill.  It is not clear to what extent concen-
        jtrations  closer to the hill are influenced by these phenomena.
        j      Overall, the  approximations used to account for the effects of strati-
        jfication  in  the potential flow model predict ground-level concentrations
        jalong the downwind plume trajectory within a factor of two; but the results   j
        point to  the need  for further consideration of surface boundary layer effects j
        land other hill shapes.  Indeed, more experiments with the same hill configu-  i
        jration, but  a wider range of stack heights, would aid the evaluation of  the   j
        model's performance.
LAST LiNE
OF TEXT
          EPA-2S7 (C-n.l
          (4-76)
                                          __ 72   il;

                                          PAGE NUMSLR
    BOTTOM OF
    WAGE AREA.
   j OUTSIDE
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    FOR TABLES
  VsAND ILI.US-
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                                                                                                ,~^~lm

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1 80
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•••• '• . •"'':••'.'' ' ••••:- •:•- . • • . . •.,
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AGE „.„. ... 	 ^ARFA







"j
/

A Experiment
e Computed Using o
a Computed Using a'
































1

j









5 10 to 20 25 30 35 40 45
Crosawfod Distance along the Ground from Hill Crast (cm)
! Source: Snydar ti73

i
Figure 21b. Ground- level concentration for stratified flow as a





function of cross-wind distance along the ground
trom the hill crest for a 9 cm stack and 23 cm hill. i
,
P^CiN i
LAST 1 |
OF TE, §
— i
1 ......


BUI !UM Ot-
, IMAGE AREA:
j OUTSIDE
i
i . ... -

	 DIMENSION
	 J FOR TARLE3
( ti *>••? vs :-.-:•:•:• '•'•'•'•- \ — — ~-
; 	 JL 	 1~ . 	 . 	 	 iiii 73 ^ 	 	 	 TRATIONS
            EPA 737 (Cin.)
                                          PAGE N'uMBER
1^^
—**^*'H -^**&-^^t'*^^*^^^^''^i[^r&k1rti^^

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   V^j^'V^'ffiTfc'-^^                       ^~v
BEGIN
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LINE OF
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HERE SB
                 TYPING GUIDE SHEET
                                             CENTER
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DROPPED
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BEGIN
SECTIONS
HERE
                     MODIFICATIONS FOR ARBITRARJK  CROSSWIND ASPECT RATIO

                        I
         10.1  Approach |

              The treatment of potential  flow  ifa  previous chapters deals with spheri-
         cal or circular!ridge shaped hills.   The model  has been generalized to allow
         for intermediate shapes by using an approximation technique based on an
         interpolation of two-dimensional and  three-dimensional flow field properties.
         The parameter chosen to characterize  the obstacle shape is the crosswind
         aspect ratio, \, defined .as the  ratio bf_h_alf_ of_ the crosswind^_breadth_pf_the
         "8bstacTefT>, to^the obstacle height,  aj.   Shapes for"several different values*"
         of X, where:   I
BEGIN
LAST LiNE
OF TEXT *
                                         SECTION 10
r^^tf'^^Farvpm**f?^w~7q^^



                TOP OF
               ^JMAGE
                AREA
                                        X  =   b/a
                                                                         (10-1)
                     9-1 '?:"
        are illustrated^ in Figure 22.         j
             Because streamlines are not easiljr defined analytically for non-
        axisyrametric shapes in three dimensions, an approximate procedure was
        developed.   Thi$  procedure uses the analytical description of the streamlines
        for flows over a sphere and over a cylinder, as well as theoretical results
        (J.C.R.  frtait, personal communication to R. G. Isaacs, 20 July 1978) that     |
        describe the changes in velocity at the crest of the hill as the aspect ratio
        is  changed,  and'experimental results that show the changes in the source
        streamline above  the crest as the aspect ratio is changed.
             Changes inihill shape affect the flow field in two ways.  First, the
        shape of the plume centerline is altered and its form is found to be inter-
        mediate  betweenithe limiting two-dimensional and three-dimensional cases.
        Second,  the  velocity along the plume trajectory is changed.  The approach
        used  here to treat hill  shapes intermediate between that of a circular ridge
        and that of  a sphere is  to weight the flow fields of the two extreme cases toi
        produce  an approximation for intermediate cases.

        10.2  Adjustments  to Plume Centerline Trajectory Streamline

            As  described  in Section 5.4.3,  the  height of the streamline,
       specified by  the streamline through  the  source,  i|> ,  such that:
                                                                            z,  is
                                                I                         (10-2)

       where the particular functional dependence  changes  with the stream function,
       u, determined by the shape of the obstacle.   Two complete analytic solutions
      -are available: I flow over a sphere and: flow over a  cylinder.  For a cylinder-
                    — i	m  74
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          (4-76)
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               i FOR TABLES
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               , TR AT IONS

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                      Figure  22.
                                  Definition sketch for aspect ratio Xib/a for hills  of
                                  spherical, intermediate, and cylindrical shapes.
p§j|>
          ~ CD
          - o
g t~ > v.
c/> cr ^ o
                                                                                                          in ^>
                                                                                                          > CD

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BEGIN
F1RST TYPING GUIDE SHEET
i MCHC CENTF'R
L'NE °F or DA -c ^
TFXT . . OF PAuE >
HERE »i
DROPPED
HEAD;
BEGIN
SECTIONS
HERE ^
k 	 I
i r 2 1
Tit .. - i
I *2"T
•and for a sphere (as in Equation 5-35)
,2 a3
j (x2+z2)3/2J
1
where z ij the height of the streamlin
As defined! above, the sphere corr
X = 1, and the cylinder (circular ridg
ratio, X = ». For a general aspect ra
and may be written as :
z =
i ,. < /">••
«2 1
I 1 (10-3)
s 2 2 l
V Hs
I2 1 * (10-4)
's * ,¥2 u2,3/2 U" J
|_ (VHs} J
2 at position x.
esponds to an aspect ratio of unity,
e) corresponds to an infinite aspect
tio the height will be a function of X
!(
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.^^^•M^v^ro^i^?^^
BEGIN •"..•!
FIRST TYPING GUIDE SHEET TOP OF 1
LINE OF C™™ .IMAGE-
n: PAHF xi»' i
TEYJ Ul MU .- -&ARFA !
HERE »»•
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BEGIN
SECTIONS
10.3 Adjustmenls to Velocity Field
	
Changes in, the aspect ratio of the hill also. affect the speed of flow
along the streamline. An approximate scheme, which incorporates theoretical
results of Hunt] has been developed to account for this effect. One way to
- ,}
•j
-j
J

characterize th$ flow is by the so-called "speed-up factor," S, defined as__j
HERE j45Te ratio of the velocity at the crest) of the hill, ,U_, to the velocity, far 	 ,



























BEGIN
LAST LINE
OF TEXT »
upstream, U^:
S =

The speed-up factor (Hunt et al. 1978)
In particular, for X = X. = 1, (the sp
shows that
	 __ ^
U /U^ (10-3)




i
S will depend on the shape of the hi 111
lerical hill), potential flow theory

i c _ ori <\ - i c (10-9)
^OlMI — OIA..J — l.O \.*-U J J
SPH 1 '
and for X = X» -f « (;the.,circular ridge): 	 	 	 -^
C
/'Vf C f\ "\
CYL = S(X_) •
For intermediate -"shapes, the theory (Hi
>• 2 (10-10)
mt et al. 1978) shows that:
i
S(X) = 2/[2 - B(X)] (10-11)
where
1
8(X) 1 + „
1 X -1

^ In IliV \^ 1 flf) I'M
i 9 Til") ln 1A* A L) LiU-lZJ
(X -l)1*'^
Some representative values of B(X) andiS (X) are tabulated in Table 9;
_,


•







note the asymptotic behavior as X-^l. These results apply only to the surface
velocity at the crest of the hill. To; use this result in approximating the
velocity field at other points, let the velocity at any point be considered
as an appropriately weighted average of the velocity corresponding to the
flow over a hill and that over a sphere:
U (x,?) = G^.W U-.- (xiz) + GCDU(X) Ucm, (.-,z) (10-13)
1 L.I L LI L i t>rri orrl
where the weighting functions G,-,. and
.G,,.,., are yet to be determined. These
functions are fc)und by using the theoretical expression for the speed-up
factor to find 1;he weighting functions at the crest of the hill, and by
assuming that the weights determined are applicable everywhere in the clow







field. In addition, the prope^ limiting forms for flow over a sphere and
over a cylinder are again required. "t'Js: P I^k'. ?f.



K
•A:_;C AritA;

v/ ^ i \_ u LJ c
- — DIMENSION
1 . 1 POD T/, D1 LC
I | 3/8" w W ' "rx'-x "YAND li-LUS- !
	 J 	 	 J 	 	 Si 77 ^iiii 	 . 	 	 TRATIONS ;
I • PAGE NUMBER i
I EPA-287 (Gin,) '
I (4-73) 5

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            EPA-237 (Cin.)
            (4-76)
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1YFIWU btHUi: bHttl
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OF PAGE ___^j$
^__ §
i
i— TABLE 9. REPRESENTATIVE
X B
VALUES OF SPEED-UP FACTOR S —
(X) S(X)
1 1.000 0.666...* 1.500* j
i !
1.0001 0.66675 1.50009
^ss. 	 _ _ 1.001 0.6669 1.5003 \ 	 »»-.
i
1.01 0.669 1.502
1.05 0.680 1.515
; 1.1 0.692 1.529
1.2 0.714 1.555
1.5 0.767 1.622
1 \
\ 2.0 0.826 1.703
3.0 0.891 1.803
5.0 0.944 1.894
10.0 0.980 1.961
20.0 0.993 1.986
100.0 0.99957 1.S9914
i

i 	
*Asymptotic value as X-^l
> I
I
; when V+-1, p-»- 2/3 (1+0(X-1))
i JU/0.- r 	 r >
^ " 	 | 	 ilLzi_ &
TOP OF
^ MAGE
AREA










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        TYPING GUIDE SHEET
                                     CENTER
                                     OF PAGE
DROPPED
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BEGIN
SECTIONS
HERE
                                   CYL " SSPH
Substituting S  '  =1.5  and
                I
2.0
         herefore
         where S(X) is determined from  Equation?  10-11 and 10-12.  This correction is
         applied to each component of the  velocity separately.  Thus having modified
         both the velocity field and the plume trajectory (streamline shape),  the
         program-proceeds- as prfevibissly- for -spherical-and-cytindrieal-hrils-. —Note— »
         that because thfij speed-up factor  for X=ilO is within 2% vf its value at  Xsco,
         the interpolation algoritha, for  convenience, equates two dimensional flow
         with all aspect ratios greater than or;equal to 10.

                       9-1/3"
EEGIN
LAST LINE
OF TEXT »
                                       UCYL    *

                                       GSPH  =  2
                                        CYL
                                                         CYL
            CYL " SSPH
                                                                                 (10-14)
results in
    X7Xr*-M~[1



    (S(X) - 1.5)

    (2-S(X))
                                                                        (10-15)
                                             TOP OF
                                             IMAGE
                                             AREA
        I
               3/8'
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SECTIONS
HERE
                                  SECTION  11
JC$I>
                          FLOW OVER HILLS OF HfTEMEDIATE ASPECT BATIO
          11.1  Bsckgrousjd
                         I
              Potential  jflow Kcdel calculations! for hille of aspect  ratios 1,  2, 3,
          end  10  (effectively infinity) are cosspared to observed  laboratory
                         bnd@r nsutral flow $?iadl tuisel conditions*
              Th© wied ttaimel esperiaents wer® Conducted at the  FKF  (by W. H.  Saydsr
              U  E. Britter).  Results of that study ^sre isade  eveilabl© to_^T_iQ_ehe
         •^ersro"ff' sas in£gwsl 'data r*6|»6rt"(Snydesr" el" ®T. ~T97%)T
              Model cc^utatieas retain the dis^isions ©Eployed  in the data report,
          eseept  for the definition of the aspset ratio.  As in the earlier
          c©s$»arisoae for' the polyeoaial hill, linear vsrtieal  sttd horigsatal spread
          statistics near'.the hill location are developed fr^a  the wied tunnel  sata
          obtaiffisd fcr the"'iio-terrain case (Say^ar et al. 1979a). This ^aouEts t©
          opecifyicg dispersion rates present CFE Che laboratory eeale rather
                     to scale ds%m dispersion rates observed in the ateosptere.
                                           TOP OF
                                           IMAGE
                                           'AREA
 BEGIN
 OF TEXT
 11.2  Cospsrison of Hill Shapes
                i
      Four idealised hill sodele are ussd in the wind tunnel esperisasats.
All  h^y«  a trisagulsr longitudinal cro.sa-section.  Hill 'C21 is a circular
corse,  wit> surface  slope of oa® half, j Hille "C4* aad *C6' are fabricated  by
iaeertiag triangular ridge pieces bett^sen the origiaal cone halves, aad hill
 'CX'  is a giisple triangular ridge that; spans the width of the turaalo
DiffiKSsiiKis of  thsse hills are sussasriged in Figure 23.
      Snyder essd:Britter (1979b) define aspect ratios for thees hill shspas
to b@  the crosswiad length of the hill; between the two half-height point®,
divided by the hill height.  In this report, however, the defiaitisa of the
aspect ratio ue@s &BK half the full erosswind hill dimension divided by the
hiil height (se« Pigxire 22).  For the fcwo limiting hill shapes contained  in
the aodel,  the full crosssrfed dimension of the hill is either well defined
and  sharp (sphere), or effectively infinity (cylinder).
     In the esee of the sphere, the surface slope varies froa gero at  the
crest  to  infinity at the base, sad so fehe crosewirad dimsssioa has distinct
end abrupt  end points,   fthea this idealised hill for® is used to represent
hill shapes wita coa@idsrebly smaller slope discontinuities at their basss,
eoas gsiaileg1 erejeswis^  disssssiea gSioald be selected that would insreaoe .the
similarity of  the physical hill to the! spherical hill.  For the wmd tmmel
esperisent® of Sayder  and Britter, the! half hill height ert»8»iR«5 disensioa
 LAST LINE .of_the  cs®e coincides iileocieally with
               3/8"
            EPA-28? (Cin.l
            (4-76)
                                        the base of a spherical hill  of equal-
                                           iiii  80  ^
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TYPING GUIDE SHEET
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                              or PAGE
                                        TOP Of
                                        IMAGr
                                        'AREA
                               HIU.
                               L(cm)
                               Aspect Ratio
                             C2
                              0
                             46
                              1
C4
45
91
 2
C8
 ^)
138
 3
                                                                      CX
             Source:  Sny&r et at.
3E
L/3
'JF
               Figure 23.    Details of hills use'd in EPA wind tunnel

                                                  81
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BEGIN
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TEXT   ^	r	
HERE »ff5f ight.  There^r®, aspect ratioa  foritlss hille studied by Srayto sad
        Britts? are dsfiaed in this report to'be one-half the vstaa dsfiaed by
               sad Britter.  This d@fiEsitic»a iates tte losgittsdiasl bsse  of 6ha
               	* hills to be the diseases !b®te®©a th« half hill haigtst pairaea
                       ratio to be the  hill fe«igh£ divided by 
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HERE Ss
                TYPING GUIDE SHEET
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BEGIN
SECTION'S
HERE
                                                                                TOP OF
                                                                              (JMAGE
                                                                              i ARF.A
                         f v©ff£lc®l pluaa spsreaf (OB) with downrind distsae© feoa
33 ea 6@ 293 ca suggeB&a  etet its linear variation with s tar the regie*
ESS? s » ©4.7 da ess  ba ede^isatftiy retina seated by the  ersrad frea s • 33«0 esa
to a «• §4.7 ess.  Curvature is es(x) ii v®ry saall over the range of
                   bast fit Gauesien ^igtaas derived  fey Snyte et al.
                      .
     A eeecad
     isss
at plissss
                        ossful in
                        eser
                     height t
                                                                 is  the  eeleulatieti of
                                                                    £  the eurfac® ©tsd
                                                                the  eeafcerlisia
                                          set ra^cessarily
                                          two 
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HERt isfTl64  Coseparie^p for Pius® H®igSFEq«sJl to th® Obstacles

             Hirai tsssKssaii ©sperisetat®  for etsca height equal  E® hill height (23.4 ca)
        ere saal?§®d filrst beessss® eha  ra»=hii| obeervseioae  saggaeted that the plus®
                 at 23.J& ea  is  less  affested |«y ehe surface bouradary iaf©r than is
        the plUssa ?®leased at  11.7 eta (see Se^ticjs 11.3).  Surface brnjEfctafy Isyer
                as® ssoe ecasidarsd ia tha aofi^l* 6O feteir pE@Qerae® ®ay rsd«e@ the ~
     s^-__.
               11.4.1
                         I                       i   « • * «        #    ifi**^>
               CeacgtsEraEi^s asss ^sssursd  at  ttte hill  crset vs B 84.7
          tisss for caeh ^obatecle for®.  A  loEig4fc^^Ka^ section i® tokea at  eto  local
                        ^h@ plux^ asi§» preduci^S eae oboervatioa of the surface
                        at ehs eirestj the eesoafi  ©bservatioa is tekoa frcsa a ^ertieal
                        profiia at  Eha er©st|  sssd the third observation is takes in
          cosjuaetiea ^i£ih a lateral profits at iereet height.  All of tfesse  vaisses are
                     by  ^te@ factor  ga^/Q triers ^ is the freestresa velocity  in the
                      ceatissters par second (em/a)]f a ia the hill hei^s6?  sad  Q is
                                 ofosanraEioaa elies? coasid@rsbl@ ee®fcEer  ia  surface
          cmeetstra£ioa@ |at  £b® hill  er®@£s.   Pejr eKcspl®,, multiple cbaainrseiosig at
          the crest o£ hill  C6 daritsg a vertical profile iseasOT-effieat  sequeac
          observctieas r^agisg fires Oo013 to  0.@79.  ffiiea the eoapieee saries ©f
          vertical profile points  ia  fsletted, ss^ average ^aiwe of 0.03 is ©fetaiaed
          fros the ©feg@r¥^  eread.  Sissilaff ®e@et@r is observed in the lateral eed
          l©agitu
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 HFRE B
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HEAD;
BEGIN
TYPING GUIDE SHEET
                         to
                             CENTER
                            OF PAGE
                              T
                  to
                                          emeratraticms befor®  they e«J b@—
                                            Ira both eyotewSp a norBalise^
eeaeestratiea ta wg«ds based  ©a the s^al® Wa^/Q.  The norsalisffid
CGSceBtrstieas 'r®p©?6ed by Sayfisr andJBritfer, aisd listed in Table  10,  us®
400 es/s for Cfe sealing  velocity.  Ttiis is the free stream velocity in the
wisd tunnel.  Tha raedsl eosputatiea® 488K33a £^® scaling velocity  is eqwal to
         sereaehiE® velocity  at somre^ height, eensistemt with  the  OTMS!
                                           ill  TKeeeforei~Oia"~8caTihg
for the wissd £wm@l observations has tieea ehaaged BO that the scaling
         ie that ©bservdd st  seure®  hei^it wit!| no obstacle in the ttnmel,
             issw sarsalilsed eeacetstratioiss are listed in Table 11.
                             11.   COJfPMISOM OP PREDICTED MB QBSEIVED
 BEGIN
 LAST LINE
 OF TEXT
                             STACK HSIG3T EQUAL ifQ HILL BBIGH1g_
    Hill! Crest
                                  C©siceatrati0a j
                                      Rill
             2
             3

             5
            10
       O.J9103
       o.bss
                                JK2S4 4-
                                0.037
                                0.015
                                0.008

                                0.003
0.034

0.019


0.015
                                                                               TOP OF
                                                                               IMAGE
                                                                               AREA
          *The observed vklusa ®rs Rormlised usiag the source hsight velocity
                . coaceatraticaa predietad by  the  csaples terrain ssdel
 iffleorporate verfeieal assd horisontal pl'ssas  spread psr^astar®  derived in
 Seetiea 11.3, attd the aspect ratio weighting fuactioa  derived in
 Section 10.  Cospatatiosaa are raade for; aspect  ratios of 1, 2, 3, 5, sad
 The results srej also listed in Table  1;1.
      Comparing predicted and observed (value® shews  that the  hill crest
 cos^utation ©verprediets by 40% at aapECt  ratio  equal  to 1,  ®sd quickly
 undarpredicts fdr ®@pect ratio equal  to or greater  than 2.   Over 5
 the tasdel prediction is oaly 3.4% of  tihe observed value, llhen the sassisEOTi
 predicted conceatratioa for sny position ©a  the  hill is craspansd with the
 observed concesieratioffl at the crest ia1 the wind  tunnel, better agreesarat is
 found at eost aspect ratios.  OverpredictiKi®  of 100%  and 92 are foussd for
 aspect ratios liand 2j uaderpredictieas of 25% asd  BOX st aspect ratios of 3
 and 10.  Still the tresrf is evident!  predicted  grmiod-ievel ccaceatratiosss
 fall off aich E$re rapidly with aspectj ratio than do the observed
 gr©uBd-l@vsl c«aeeBtratisa3.  This tresssl is  visually appareat in Figure 24.
      The potential flew ussdel comceKtrfltioaB may also  be eospsred with
 observatieas &rs&  other modeling EsthcxSa using  the terrain correctiea factor
 (as in Section 7).  Table 12 evs^stfissB surface  cosjceatrations sss3 Js^lied
 terrain correction factors forj the wihd tuoa@l  ©b®eo?ationa| the  potesatial
 flow eodelf  and'the surface esfjeentratiossg reeultirjg fr©a the half-height
       tion raodelf  the flat terrain aee^ption aodel (i.®.( esEraiffl-i
       5  and  the i level plus® asstreptioa ei>del (no eurfae® reflectioa
           EPA-2S7 (Cin.)
           (4-76!
                                               85
                                           PAGE NUMBER
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                                                                         DIMENSION
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 HERE 36
CnOPFtED
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                 TYPING GIMDE SHEET
              10
                   CENTER
                   OF PAGE
                                            48
                                              Aspect Ratio
              Figure 24.
Predicted and observed  concentrations for stack height
equal to  hill height  (23.4 cm).
 TOP OF
 IMAGE
'AREA
                                                 86
 30 1 I'OM OF
  VAT-i-. AREA,
 XITSIDE
 OIMI-.NSIQN
 FOR TABLES
 AND ll.LUS-
 TRATlON?.
           EPA-2S7 (Cin.l

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TABLE 12. (SWMISOIf 0? STOFJiCE COKCETOATIOWS AT HILL CBEST - .-..,.
BETWEEN THE POTECHM. FLCW MODEL , THg HIHD TOSJ3^L OBSSWATIOK3,
THE H^LF-EEIGST ASSTCfflPTIOH, TSE TESMIE-FOttWIIKS fLIRffi
i- _ ASSSESPTIOWj &E53 TK3 iUT?BS» PLIS4S
ASSDMPTIOS TO! A STACK E3I6HT IC33.i 1
gjiniLJgSISffiLj..,
i
Aspect Surface Concentration ic Kill Great Terrain ^"""J0* F*c*^f ... ...,.,
Eatio Kodel Observed 1/2-Heisfot Ho Hill Laval Model Obs^^ed 1/2-Height Bo HiU. — Level
1 0.199 0.142 0.108 10"6 3.03 0.460
2 0.0103 0.034 0,108 . 10~S 3.03 0.629
3 O.C035 0.019 0.108 10~6 3.03 0.680
0.0005 0.015 0.108 10~6 3.03 0.764
0.483 0.5 1.0
0.567 0.5 1.0
0.598 0.5 1.0
0.610 0.5 1.0
0.0
0.0
0.0
0.0
T- — ' r~ Tl 03
ri; rn ~ = r~i
S 3 & S Q-
r^?~
i
i
SUar-n
(
1
;
«Th« tarr«i» ceyreceion factors asaociatad with the potential flos? faodel and eh« cbaervatieaa era
darivad feea tha ccffissntrstioos that sr« predietsd by tfea s»^el and observed in tha tunnel vsae ,
Equation 7-7). Thosa co??eceiea fsctoso for the etfeer appscadsas are S86use


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                TYPING GUIDE SHEET
                                             CENTER
                                            OF PAGE
BEGIN
FIRST
LIME OF
TEXT •  	____.	________
HERE ^concentrations teo the terrain correcti
       Uesived  frsa tlia observations vary
        crocsvind aspect ratio.
              11.4.2  Otiher Pltssa Characteristics
HEAD;
BEGIN
SF.CTIONS
HERE
                                                                               factors
                                                            Terrain correction
                                                    0.48 and 0.61 depsnding on the
BFolN
'.AST LINE
OF TEXT S
              Th@ algetrdttaa used to predict plt^e  ceaterlira® height at the hill cre««-
                  -  •   - •         "    ••   • '  —°  ve»iaclfi9M-«£-th«-««ataeliiM-	
        height with aspect ratio.  Howsver, the  lied ting cases, in which
        ratio equals either 1 or 10, are cotspletely specified by Che theoretical
        solution to potential flow ©v©r a sphere  and  over a cylinder.  Therefore,
        the overall tasgaitud® of ths predicts^ eenterline hei^it for these esses
        Bust b® coshered to the observatieas Because  only relative variations with
        aspect ratio h£s bees fis®d»  tfote  thit  pluae epresd statistics ar®
            " " "  determned by the spreading equations, by the theoretical
                   solutions for sphere and eflinder, and by the weighting for
                   position end velocities  as|functions of aspect ratio.
             Figures 23| end 26 eots^sre predicted with observed values of vertical
        plume spread, dE,  and plums centerline height, zg, over the crest.  Two

                     o£ thes® represents a  different  interpretation of the vertical
        profiles.      '                       I
             The plsrae ieenterlica height raay  be  defined either as the height at
        which  the easinsss  coaseatratioa occurs,  or ss the height associated with the
        centroid of  ehe'&boerved vertical  ccn^&titratiim distribution.  Tliese two
        height? ar®  ahciwn  in Figure 27  for  th^  triangular ridge.  The results of
        these  two possibilities yield the  twojillustrated curves taarked "ceratroid"
        atyi "msxiisam11 in the cosEpariscsa  figures.
             Similsrly^ o2 is sensitive  to  th4  centerline definition used.  The
        first  choice (labeled as "Snyder et at." oa Figure 25) is derived by fitting
        a  reflected  Gaussian curve  to the  vertical profile.  The other two o~g
        curves  (lab@le^ by "ceatroid" and  "saiifBuia")  are calculated uaing s 2-point
        reflected pl\m% equation sisiilsr to tliat used in Section 11-3.  The surface
        coaeentratiea se taken to be the average of the surface observations, ®a«i
        the elevated concentration is taken eithsr near the centroid height, or at
        the height of fsaxinassa conceotratioii.  iln th®  case of the centroid
        calculation, ttte coacentratioa used i$  the average of the concentration at
        the eeistroid height, end the Eiesieiaa  concentration.
             Th® resuloini curves show that t&e  predicted behavior of the pluise
        centerlins at Che  hill crest is bounded  by the interpretations of the
        experimental data  and, for aspect ratios larger than 2, the predicted
        vertical sprea^ tends to fall below all  of the values derived from the
        observations.  .The ehapa of the predicted zc  curve begins to level off
        quickly at aspect  ratio 3 but, overall,  the predictions of pltmsa centerline
        bright above the crest are within  15% of the  observed heights.  The shape of
        the predicted ojz curve only weakly  echoes that of the observed curves,
        For aspect ratios  less than 3, the  ao4®l overpredicts oz by aa auch ®s 50%
        in  the cass of \az  CsaaKMsun), and oversredicte the corresponding eeraterline
        hei^it by 50% as wall.                j
             However, £f the "eentroid" version  of the observed oz is adopted fe-r
       ^aspect ratios iess thsa or equal to 2^ the predicted vertical plrais spread
       ~SXA the centerlins height agree with  £hose observed to within """•'B
                                                                                        TOP OF
                                                                                        IMAGE
                                                                                        AREA
        I
              3/8"
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          (4-76)
                                          PAGE NUMBER

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= Observed
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                                             4              6
                                              Aspect Ratio
                                                                                      10
               Figure 25.    Vertical plume spread at hill crest for  stack height
                             equal to hill  height (23.4  cm).
                	_-L_~.	--	„	_

                1_  .„ 1_	
                 (Cin.l
   	_.  i . .
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  PACK NUN
                                                                                           TOP OF
                                                                                           IMAGE
                                                                                           AREA
           1

 :T70'/ OF  j
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                                                               A= Observed
                                    flspect  Rate
Predicted and observed plume height at hill crest  for
stack height equal  to hill height (23.4 cm).
                                                                            10
                                                                                           TOM Q
                                                                                           GE ^R

                                                                                           '::;DE:
                                                                                           EN'S 10
                                                                                           TABU
                                                                                           ) It.LU

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                 4Q  _     Stack = 23.4 cm
                       Height of fsSaxsmum (23.4 cm)
                   .001
 BEGIN  r
 LASTi  I
 O;:IE'     Figure 27.    Vertical  concentration profiles  over CX,  the triangular ridge.
           _ X.
            F.PA-237 jCiii.i
            (4-76)
                            ii  91 Jiii'
                            PAGE rjiJMBtR
                                                                              BOTTOM OF
                                                                              I MAG? ARL-A,
                                                                              OUTSIDE
                                                                              DIMENSION
                                                                              =OR TAELk'S
                                                                             'AND ILLUS-
                                                                              1 RATIONS

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 TEXT
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DROPPED
HEAD;
9EGIN
SECTIONS
HERE  fe
        TYPING GUIDE SHEET
                                     CENTER
                                     OF PAGE
	          ..—..4ratios of 3 and larg®^,  the Eodsl predictions of 0g ere   	\
too aaall.  Valets of vertical spread lara  uiadarpredice&d by 271 at aspect
ratio  3S end  by 57S at sspact ratio  1CJ.  Therefore, sssg ©f ete
coBceatratioa uoderpredieticaa with  increasing aspect ratio Esay be directly
related to  qual^tstive esid quantitative  differences in 02.  !?©t@t for
         £hat t|» observed vertical  spread ©v@r the ridge (4.7 eaa) eseeed®
     ^assured ab the SESS doroswiad di^tsnee «wer flat terrains (4.0 ess)
                                                                                        TOPOF
                                                                                       r IMAGE
                                                                                       'AREA
BEGIN
LAST LINE
OF TEXT
                                                iridge acts t© eospress
                                                suit frcsa incr@@s@d  «lisspfi?eioa in

                                                 from the horisoatal spread, o™.
potential  fie?? pwr a
the vertical,  this eshsiieed
the pz^seace efi the terrain
     A simlar coaelusica
                 that the efcspss of
             Thja overlap at aspect  r
ri@@ at aspect pstio 2 is sissirag
ratio  3, £h® trtetsds again agree, bat tfhe predicted curve lies ebcs^t
below  tbe observed. -Over the  two-diEasnsional ridge the observed value
esesede the flat terrain valw® by 40%J  Kota that the observed a,
are t&kea from the lateral profile  in la horigostal plaae through ''the
                                                                                   in
                                                io 1 is virtually  e^actf  toe the
                                                 the taodel reaalts.
              11.4.3  Mass Flrai
              A Ecasure »f hos?
         deecripticn i»'t?ie  vslue of
         plissa has unit ka®3 flus dsfiusd
                                                  jd sass  flus.
                                          by tte  relatieas
                                                         to a
                                                         The ideal
                                       CL
                                                                             (11-3)
         where both  the  velocity 0 and concesstratioa X @re  eeratsrlise valises.
              How wall tfcje wind tunnel esperisa^ra£s preserve a ease £lws of 1.0
         suggests how wall  the tsodel predictions may agree  with the observations.
         Threa curves ofi the observed Bortaaiis^d EJSSS flus  are  plotted in Figure 29.
         The observed."S^yder et el." curve uses the os  and ceneerlina
         conceistratioa vkluea derived by Snyderj and Britter (1979b), ^hile the other
         two curves  are  jbssed oa the og snd concentration KasisOTsa derived for the
         ceatroid heig£it{ and the hei^it of maxitesaa conceiatrationo   Overall, the
         centre-id interpretation of the observe^ profiles yields the esasa flws
         closest to  unity.   All three give tauehi the saae result for aspect ratio
         greater than or| equal to 3.  Figures 25 and 26  indicate that the ceatroid
         interpretation  isf  the observaeioffls taadctes tt»a  predicted  valass of pi USES
         depth aod height better than the other interpretations for sesll aspect
         ratio.          '

         11.5  Coeparisoa for Plueas Height Equsl to Half the Obstacle
                i
      The cosples terrain siodel  is  EOS*
 hill  height stack.  Predicted
-vertical aud hoirisoQt&l pica®  spread
                                                          to
                                                                          with the half
                                                           derived in
               3/8"
           EPA-7SV (Cin.)
           (4-76)
                                          i^ii 92   iii
                                           PAGE NUMBER
                                                                                 BOTTOM OF  I
                                                                                 IMAGE AREA;;
                                                                                 OUTSIDE    i
                                                                      11.3 ea<3 — DIMENSION  j
                                                                                 f'-'RTAELES j
                                                                                 AND ILLUS- j
                                                                                 TRATIONS   I

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                   Figure 28.
Lateral  plume spread at hill  crest for stack height
equal  to hill height (23.4  cm).
                1
              EPA-2S7
              i4-7ui
                   93
                                                                                             Di'TOM CF
                                                                                             /IAGE AREA;
                                                                                             UTSiDE
                                                                                             1MENSION
                                                                                            rof": TABLES
                                                                                            AND ILLUS-
                                                                                            TRATIONS

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A = Observed
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                                             <             e
                                               Aspect  Ratio
                                                                                      to
3EGi\
LAST Li
               Figure 29.
Predicted and observed  Gaussian mass  flux for stack
height  equal to hill  height (23.4  cm).
          EPA-287 IC<».)
          (4-7Si
IOVTOM OF
MAGt AREA;

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 LINE OF
 TEXT
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                TYPING GUIDE SHEET
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        "Table 13, rep
        wall  aa
HERE
                            13.
                 Hill


                 C2
                 C4
                 C6


                 cs
                            1
                            2
                            3
                            5
                           10
                                     2.50

                                     1.30
                                     0.99

                                     0.78
                                     0.57
.»5jlnm^^...^^gT.y^^st^
CENTER
OF PAGE ^j
5 » land SO. The results, listed ira
•©dieted e@ae©a£rsticfiJ8 K©ar the eeest es
:he Mil er©st.
&HD pBiEWOT K0HMLIZS9 OTSF&CS
^I^UJ^ML TO ptMJ? KIM, Rszesf


sd CeaeOTtratira Observed
: 1 Hill KaHisusa Coacenferseios


2.61 2.09
1.43 1.25
1.18 1.18
0.97 —
0.73 0.9§

1 ^'»ffi*^;Aip^*,
TOP OF
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AREA
              Observed ceneetstrstisaa mesetsred at Ehe hill crests,,  aed  corrected for
         soarc® streaali'BS velocity, srs  ares listed in Tsble  13.   These values
         raprsaeat the fi^erage ©f the obaer'at^ons taker.- frss irertiealj lateral^ @ad
         loagitudiEal'profiles through  the hil^ c^est.  These  emrfase ebssr^atioas
         agree very «all (wiehia 5%).   The ob@@s^?ed ecaeeatratiosss  are  easapsred
         directly to ehsj prsdiet©^  cooeentrati^aa in Fisur® 30.  Tina couples terraia
         ratios b©e?i®@a 1 sad  2, aad  smderpretSlets by as such as  422 at aspect
         ratio 10.      j                        j
              Ualike the prS^ious  experiment is ^sieh the stack hsight ^as eqssal to
         th-s hill h@ighe (S^eioa  11.3),  ^ertieal profiles of the pi«ass o^er the hill
                shssssd virtually no elevated eKSsseeratratiOiS ^asiffisjEsa.  App-areratly the
               is eo greatly iafl«eac©d by the^boundary layer that the plasss
         csaterlis® csaaot be  readily ideatifi^ crver the crest.   This ia esp®eially
         the e®s« for the pr®fil@  &&&E the eona.  At larger aspect ratios, a wsak
                         27).
                           predicted sad observed plras® spread  statietieg £EBa©t be
         compared directly (bsesua® the E«sdal as not dssigasd to  eiraslata the physics
         of the espsriEsait)  it  is  iaetrtsctiw eo highlight  the  differences bet®a©ra
         the
         ceaterliee height evaluated at the cr^st.  These ar@
         fchrossgh  33.   Figur© 31 ew^&r&s the predict®*
         hill creets  ag^int the height of the 1 centre id ©f the

         predieted height lisa bst^een an absolute  upper
                   r,  the true ssurce etreamliisal  in  the wissd
                                       Tha greaEffiEt  ^oelitati^e
                                _SH!ELiiiS£_i?-^'0'^^--i.— £h@--^
                                                                     ed ia Figures 31
                                                                    height above the
                                                                 observed wrtiea!
                                                                         that the
                                                                     the hill surface.
BEGIN
LAST LIN!
OF TEXT Ef-predicted_ md

       ,     w 3/8"
           EPA-287 (Cm.|
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IEHSION
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	 i£vi % ^ 	 	 . 	 i TRAT.ONS
PAGE nuMER"

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Figure 31.
                                            4             6
                                            fispect Ratio
                           Predicted sud observed plus© height at hill  crest for
                           stack  height equal to half the hill height  (11.7 cm).
          EPA-2E7 (Cm.)
          (•S-761
                                        ._ >    97
                                           CAGE r,uf
                                                                               iGE AREA;

                                                                               PENSION
                                                                             ruR TABLES
                                                                             AN'D ILLUS-
                                                                             TRATIONS

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Figure 32.
                            Vertical  plume spread at hill crest for stack
                            equal  to  half the  hill height  (11.7 cm).
          EPA-287 (C,r,.|
        1  (4-76)
                                           PAGE r\X!?.-'BL:K
  OT1 Of/, OF i
  OAGE AREA;;
  'UTSIDC   j
 DIMENSION j
 FOft TABLES i
 AND ILL'JS- -|
, TRATIONS  I
         - I

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DROPPED
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HERE  S
                 tive'dieagzeeraene is $otrad~in the vertical  pluasa"

     This  trena is siailaff to the os results in Seetiora  11.5,  al thatch
sore procouaeea.  &pfsar©s£lyj> iacresssd turbulene®  levels in the wind
bsMEdsry layer jstrossgly affect plum® eispersioa E-ear
borna out  by  the turbulemea E®seur6Bea£s contests^  in  the wiad
~   la eenjttneticm &ith their tracer
                   Mean }^@lociti@s syetssatieaily decrease at sll slevatic^s
                   increasing aspect ratio.  V^ry close Co the siarfac® eh©
                   velocity is iffidspeadeat of  t(he hill*® aspect ratio «d is gbout
                   1/4 4^ that in the usdioEurtjed bouadsry layer.  The larger the
                   aspect ratio. Eh® greater is  the hei^it to $?hieh the hill's
           Baeeissa ©f the hills, longitudinal  turbulence is decreased and
           vertical turbulence is (considerably)  iaereased very elo®e to the
           surface.  Surfee® turbulence  increases systets-atically with
              2)
                   longitudinal,  is  oboerved td 3 to 4 hill heights above the
                   surface, the increase bsing larger for the larger-aspect-ratio
                   hilld.
              3)   Negative Reynolds stresses, quite large in Esagnitud®, are ©bssrved
                            Lf  the hill  height.  Although the scatter of the data is
                          large, it  is apparent that the aagaittsde of the K
                   Reynolda stress  increases with aspect ratio.
 BEGIN
 LAST LINE
' OF TEXT
         Msasuressat® over  the  crest® of the hills
              1)
           la very erude teras, hills tfith  aspect  ratio of 2
           si&iiav flew behavior, «feer4as  the esae (C2) shews distinsetly
           different behavior.  For example,  the  speed-up factors are 1.15
           for ehe eoaa aad 0.95 to 1.0  for the other hills.  Yet the changes
           are i|ot taoQotonic with aspect ratio.
                                                                        layer
              2)   Chaages  in turbulence relative to the unobstructed bouadary Is
                   iscressed  with  elevation anc! (in this case, systies&atieatly) wi
                   iracreasirag aspect ratio.
              3)   Very 'large negative EeynoldEi stresses sra observed? negative
                          are observed to one-half hill heists above the crests.
         In es^sary,  tha  ©biservatioas indicate
         surface upwind tof  the  hills increases
                                        that  vertical twrbulsae© sear the
                                        considerably over the unobstrec£®<3
 	, inereasidg systematically with  Aspect ratio.  Lsrgs nagstiw leymold®
 stresses associated with the increase*} turbuleraes are active up to one—half
 the hill haighfi and, craiseqissatly,  hsve a profound effect eras the developasaS
 of vertical pl«sa spread over  the hil^.  Becau@© the turbulence iacresses
 with aspect rafiio, os rises graphically as  8hcw*a in Figare 32.  This
         aspect  ratio  dependeaee of turbulence
              3/8'
                                        intensity is not accouated for ia the
                                                                               TOP OF
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           (4-76)
                                          m± 100   ;£
                                          PAGE NUMBER
                                                                                       BOHOM OF :
                                                                                       IMAGE AREA
                                                                                       OUTSIDE  '
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                                                                                       TRATIONS ':

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                           Cettelusioaa
                                                                            TOP OF
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                                                                            AR'EA
                flew ees?j»l@s terrain wssfsl has batra cffi^arad tdLth
        observations of  flcs? ©ver four hill Efesp®® wi£h a®^@e!
     £r©a 1 to 10  Ce££firig©as with surface coracentratioas issiffig
         the level plwm^ aad terrain-foiloviug jpluaa as®«aptiona  show that the level
         pitesa approeeh ovesrpredicts  observed doneentratiotts by t^o  orders of
         sagaituda, ergi [the terr^ira-follcwiEg jiluiae approach waderprediets by foar
         orders of BSgnitads.
              For aspscti ratios greater  thas lt  os is consistently
                          their  flafc-terraia ^aiusa.  FOP eKffiKpl@s  the  ratio ©S
         over the rid§@ !(X »  10) to o« over fl4£ terraia is  1.45  for  the
         hal£-hill-tei$s!t etaek, eod 1.40 foz-'fihs full-hill-hei^Jt  stack.   The
                                    .06 sad Kl®.  Thee® eahsQeeEseacs  ere  aefc
         observed ts ves'qlt  froa flis? deforsat^eas.  Such  chaagas  certainly eaoaat be
         reproduced by potential flo& deforsaticas aloaso
              Table 14 qo^ares observed to predicted 0y and  0S  ratios for
         fo«r aspect ratios  end fesr bo£h stack jheigjhts.  Als© iscluded in
         are ratios of dbserpsd to prsdiet©^ @pee^-ap factor®.  'i!fe©s@ factors are
 BEGIN
 LAST LINE
 OF TEXT
         to be roughly  inverse to the horis©at4l spread  ratios.   If the tssedel is to
         eo^arg fsr^oral^ly ®i£h these wind ttimtel raeults9  the sa©ehanig®s centrolliag
         th@ observed plu^e  shape wist be bettsr «miersto©d.
        I
I*!!
           EPA-287 (Cin.)
           (4-76)
                                          Siii 101  ii
                                          PAGE NUMBER
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                                              CENTER
                                              Ofl PAGF-
                            14.  COMP&BISGH OF ©BSSCTED  TO PP^BICTSD
                               OF FLTOH  8IZB Pt\R&mTESS  AMD SPEED-UP
                                     AS  A wm&nsm ew ASPECT E&
                  Parameter
                Stack  » 0.5 Hill;
                    (oba.)
                °s  (Sayder et ai.)
                a  Cobs.)
                S  (pred.)
                Stack « Hills
                        .)
                 q'a  (ceatroid)
                8  (oba.)
            S'3/3"
         	y	

          E'A-287 (Gin.
          14-76)
                                          0.65
                                          1.3
0.39
o  (pred.)               0.99


            et al.)
                         0.84
             1.27
             2.43
                                                     0.7S
                                                       1.33
                                                       1.21
                                                       1.21
                                                      0.78
                                                A.
                                                                 1.43
                                                                 2.;
                        1.39
                        1.27
                        1.40
                        0.74
 iii 102  ;:>>
 PAGE NUMBER
                                                            1.40
                                                            3.19
                                                 0.70      0.69
                                                                           i.:
                                                                           1.53
                                                                           1.53
                                                                           0,73
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                                                 TRATION'S

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HERE   V
 SECTION 12
                 MODEL COMPARISON WITH FIELD OBSERVATIONS  (WIDOWS CREEK DATA)


        12.1  Background

             Measured  sulfur dioxide (802) concentrations  near  the  Tennessee ** " '*"
        Vallsy Authority  (TVA) Widows Creek Steam Electric Power Plant in Alabama
        are compared wi£h concentrations predicted by  the  potential flow cr"?aplex
        terrain model.  'The routine laeteorological data  from  two towers, the
        occasional  temperature end velocity profiles,  and  the continuous S02
        measurements at  five monitors on a nearby ridge  and one monitor on a nearby
        ^rnri -make  th e~^rdc&%' Cteetr darts-bsee-'a- proms ittg -te sting- ground -for- ehe   ^
        complex  terrain! modal.  Comparison of the model  predictions with the
        observations at; Widows Creek tests the!  model's ability to  predict
        concentrations  on real terrain feature's under  complex,  uncontrolled
        atmospheric floW conditions.          j
                     o-yfc"                    j
         12.2  The Widows  Creek Steam Electric tower  Plant
              The 2,600 megawatt (Mw) coal-fired  power plant operated by the WA at
         Widows Creek, Alabama, is currently coksposed  of eight individual boilers
         three sain steeds.  Boilers 1  though  61 feed  a single 304.8-meter (ra) stack;
         boilers 7 snd 8, each feed a 152.4-m stack.   The 304.8-ra stack has been in
         use for all six boilers since  early 1978.  Prior to this titse, boilera 1
         through 6 fed separate 82-m stacks that  were subject to frequent dowawash
         events.  To avoid the complicating effects of dowzswash and multiple plusae
         interactions, only data commencing in January 1973 is ueed.
              Figure 34 displays the topography; of  the area.  The terrain feature of
         greatest interest is the bluff located to  the southeast of the plant.  Its
         face rises 840 feet (255 m) in a  distance  of 0.9 kilometers (km), yielding a
         nearly unifona slope of about  1:4 (^16°).  At the top of the rise, roughly
         2.6 km from the) plant, the terrain levels  at the plateau called
         Sand Mountain, 275 m above the power  plant elevation.  Atop this plateau,
         five §02 monitors are positioned  in an arc with a rosais distance of 3.5 km
         from the plant.!  The two monitors closest  to the crest are 3.2 km frora the
         plant, and that at the center  of  the  arc is  4 tea away.  Two meteorological
         towers are identified in Figure 34.   One is  near power plant elevation on
         the valley floor, and the other is nedr the  central monitor of the plateau
         sespling arc.                          |
              Other terrjain features are located to the northwaat of the power
         plant.  Two of these—Suasaerhouse Mountain and Cumberland Plateau—have
 BEGIN    single S©2 tsoni'tore at their  crests.   lOnly SuEasrhouse Mountain (275 sa)  is
 LAST LINE.isolated enough] to be considered  a  second suitable terrain  feature for     —
 OF TEXT g^eoaroaring predicted and observed  cone@nt:ratj.gn_8_.	
TOP OF
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AREA
              3/8"
           EPA-287 (Cin.)
           (4-7P)
      I.
ilS  103 ill
PAGE NUMBEl
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 IMAGE AREA;
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 FOR TABLES
•AND ILLUS-
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r  ..'•'?--V".'•*'f'-r;^v7'";.V- >*• .  '' -
                 •
                       '34. •   The Widows Creek 'steaa electric po-*er plant  and

                               surrounding^features.             _*;.,>.
                                                104

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HERE
^^__   The Saad Mountain  ridge is shmra Jin cross-sectian'in""Figure  35.
"Spplicstisa of tlse eossples terrain aodpl to this feature requires selecting"
 an appropriate circular cylinder and placing it at aa spproprise® dietsraee
          ssureel  The selection as®tJ® in this report ia compared to the
        terrain in Figure 35.  The height, or radius, of the circular-
 cylinder is tak^ra to b© 275 sa, rad its center is placed 3.2 to froa the
-scarce.  This source—to-creat distance! places the eodei crest receptor at —
 BEGIN
 LAST LINE
 OF TEXT
        ere, alttoeragh  traa actual ridge crest lies as  close  eo the sourc® as 2.6 too
        In effect,  the ridg® is modeled as if jit curved  through the easplitsg arc.
        If the  setusl  geometry had been preserved,  the isodel crest would coincide
        with the  true  crast, ead the monitors i^ould li©  on  the downwind side of the
        circular  cyliedibr.                    I
             Applicatioii of the ssedel to SuassteThouse  Mountain follows in sim-leir
        fashion.  For  thia cotspsrison, the hill crest is set a distance of 8.7 ka
        fros the  Widows I Creek facility.  Tne hjeight is  the  ssma as that used at
        San.d ^santsin, 275 ci.  Rovsver, the crbsswind shsp® lies between that of a
        simple  sphere  end cylisder.  The sppro-Kisaate  crosswind distance through the
                 from one 0.5 hill-hei^it pointj to the other is 2.2 tea.  The aspect

        by the  height  of the hill.  Therefore the erossuind aspect ratio for the
        sodal hill  is  set at 4.

         12.3  Case  Selection for Model Comparisons
                      9-1'8"
TOP OF
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'AREA  j
              12.3.1  Analysis of the Tennessee
                      Monitor Bata
                                         Valley Authority Sulfwr Dioxide
      Bigitized S02 coacentratioas and pateorologieal  data  (teEperature and
 wind®  at  10 a afid 61 a) collected at the TVA Widows Creek  Steam Electric
 Poser  Plant Ksre supplied by the TVA far Quality Braach, Mussels Shoals,
       ia.   The ebaptster tape contained,! in part, hourly S02 coacentratioas
      the  five sapnitors oa Sand Mownfcai^j and the single aoaitor on
             Mountain for the period January 1,  1978,  to September 30, 1978.
 This is the period of Eioet interest as! the last of boilers 1-6 was tied into
 the new 304.8-m stack in late December), 1977.
      The  first ptep in selecting the hburs best suited for model cos^arisons
 w&a to search for those hours with at jleaat one monitor reporting an S02
 concentration gireater Ehaa or equal td 0.10 parts psr raillion (ppa) or
 570 Mg/a^. A total of 73 hours %*as identified  for ridge impacts (Sassd
 Mountain), and k& hours for tssouod isapects  (Su^nerhows® tfeuntain).
      West, hours with unstable stability classifications ware rwled oat.
 The stability w?s§ assessed primarily from  the temperature  gradients between
  10 m aad  61 a at the tower atop the ridge.  Because  the layer between 61 sad
  10 m say  not  bei entirely representative of conditions at stack heights of
  150 and 3®) a, the cut-off value for tesperature  differences was sat at
  1.5 tijses the dry adiabatic lapse rate:, or -0.75°C/51 a <-1.35°F/51 a).
 This criterion redsiced the nws&er of eoHparisora cases to 27 houra of ridge
 ispsct, aad 15 hours of saouad ispact. | For ataost  all of these hours, the
 souree-reeeptorj trajectory corresponded readily with  the wind direction
 recorded  by the, 61-a sensor on the ri«£ge.  Table  15  snd 16 list the selected^
        sod corresponding S02 concentrations for  Sand Mountain
                                          m 105 ji^;
                                          PAGE NUMBER
 BOTTOM OF
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           (4-76)

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DROPt'FD
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                               CI7NTEH
                               OF PAGE
         TOTLS 16.   SOTS  SELECTED TOE &SGDBL COSfPABISSES AT
                                 TOP OF
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                                 ARh A
           Yesr
                             802
                 Borar
                                                                    (10
                                                                       .-3
M  15
                             IS
 BEGIN
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 OF TEXT is
78
73
78
78
78
78
78
78
78
78
78
78
78
78
78
4 -
4
24
143
143
166
166
167
220
222
223
258
260
260
262
2000
21GO
1000
660
700
2300
2400
100
660
2400
100
900
2300
2460
200
100
450
130
140
120
120
140
140
190
150
ISO
170
240
260
100
         I
            EPA-287 (Gin.)
            (4-7C)
                                                    I
                                              S^l 107  .^
                                              PAGE l^'J'.'u^.R
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O
00
                                                                                                                -* r^ ^n GO


                                                                                                               i % ™ 3 1
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                                                                                                                 S 3
                    Figure 35.
                             Comparison of  the  idealized cross-section of Sand ^fountain

                             to the southeast of  Widows Creek power plant with the

                             circular cylinder  assumed in the complex terrain model.
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    @eeh of  these feetars the T7A Air Quality Branch £ss«ieft@»I  ell
     t©sgperature, sssd velocity profiles,  md hourly eaiesicas data.

12.3.2  A&alysis of Selected Esaissicaa estd Mraoepheric Data

Dp
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«
. . 1 	 	
Tmi& 17. CASES OF 8IGRI7ICABT KPACT TMT E&VB ASWCIATTO
-. WmC4U FtCFII^S ©F
\
\ Ridge Impact lours
i Profit® Ofee«rTOti©«8 Ti^
j
1 Julisa Bay Month Day tear T©^p>®r®eur® ^eleeity
: 3 13 1300 1227 1332
40 29 1300 1228 1312
^ IfO 79 OS©0 0841 07WJ
226 8 14 1200 1247 1140
230 8 IS 1000 0920 0925
230 8 18 1300 1223 1395
232 8 20 14-1500 1225*163S 1430
Maura! IsspseE Hours
Prefil© Obg©rv®£icn Tiss
Jrali^i Bay Msatb Bsy H©ssc Te^serafturss V®l@ei£y
4 14 2Q-21G0 2030 2355
166 6 15 2400 0005 2340
222 8 10 2400 W04 2322
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BOTTOM OF
WAGE APEA;
OUTSIDE
DIMENSION
1 FOR TAB1 ES
Jj -,,,,., ! ,.,. . ' -.-•.-. "YAN>Q ILLUS-
j_° $ >":1; 110 -i-:X ,1RAT|ONS
EPA-28V (Cin.
(4-76)

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TVPIMG GUIDE SHEET
. . CENTER
OF PAGE ^
ttatendned SOT |aeh g&fcaefe ez&&, with fefag caceptioa of eh© staefe ra^i«ss»
S^p@ssS ®a ft&e individual !boil@r loada per ©seh hour. toiler load® for esete — '
sissit sad tour esday sCwdy we listed ia Tsbl® 10.
J
T&B1S 1®. HOUSE

ifaiiass t
Y GIOSS wm &

Bait ~~
lae© Month 'Day Honr 12345678
3 01 03 1300 100 73
40 02 69 1300 46 60
WO 07 09 0900 123 123
226 08 14 1200 111 Off

230 OS 18 1000 112 59
230 08 IS 1300 112 61
232 OS 20 1400 Off 59
.SI32 	 OS- -4 -20 6-11530— -0£i- -40-
4 01 04 2000 94 90
4 01 04 2100 96 88
166 06 q.,/815 2400 101 57
222 0§ 10 2409 82 Off

114 103 104 106 Off 311
47 55 51 53 Off 344
130 125 129 123 Off 456
129 131 128 123 524 Off

Off 130 122 128 271 281
Off 133 132 130 290 281
129 133 132 127 4SO Off
- 130— 130 — 130 — U7 — 4©&- 4tf- 9*
110 '90 93 101 398, Off
110 90 108 104 413 Off
90 89 59 69 Off 241
88 64 84 51 244 297

i
^relira.eas'V ealeulatieae Cor £h@ tall stack indiesEs tfa&t tfee
ia^oct of emissieaa fstRa this stack Ajferiag £ha hsmr® wader s£«
. ;*
I
•J
J
J

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fa Table 18 £fel«® li®if;tee ia the @ta ©f t
rise Ah.
»
TftHJS IS

Julies Ray K

3
40
190
226


. FinM, 1S1GHTS
10115 WITH £BD TJITflO

stiith Bay lowr

1 3 13G0
2 9 1300
7 9 0900
to ataek height e&& the iiE®l plass


OF EMISSION FROM EOILSSS 7 AHD §
JT FULL S0j> SST5UBSIKG " —
Scrabbsd Pits®
Pltrae Hei^st (is) Height (a)
Jait 7 Unit 8 Halt 7 Prait 8

445 - 422
432 - 4Q9
325 - 307
8 14 1200 k,085 - 855
«^3© 	 1.8— 6-1/218 	 1960 	 	 3SO 	 -345 	 319- 	 	 -§2®-pa=

230
232
4 9-1
1@S

222
Of the aeve
oaly Sowf K®re
day 40 hour 1301
heists daring
other thre© hen
eseeed tsd.es th
The three h
(Sts^erhTOise KB
Te^sratar®
(aft@r eeresaiE
The dasted lies

8 18 1300
8 20 14-1500
,\. 4 20-2100
6 15 2400
1
833 802 73S 733
600 - 533
309 - 289
335 - 317
i
8 10 2400 ! 3S8 374 335 352
i
j tiotsrs identified for impact ess the ridg@ (SasuS Mauntain)
selected for eo^arisoa, with tlse a©d@ls day 3 hoar 1300,
Ss, day 190 hour 0900, esd day 23Q feosar 1000. PIufflQ
£tsae@ bowrs varied from 325 E@E©rs to 445 a. For the
ps 5 pl«s^ hgigtits ^sri^ feet6»sezs SCO IB and 1^085 BS ^iieh
§ height of the ridgs.
«urs idesti£i®fi for iapset oa the isolated jmswisd
«sa£aira) s@w slailar fis^l pl«ffis heights (309 to 375 a).
| profiles for each of the genera ease hoara reEsaiaing
g for pl«ase riae) are presented in Figures 36 thr®«gh 42.
8 ideatify th© s^sa t@s@pfflrs£OT@ gra«!ien£ wssd ia the piusa
rieg cslcalatioa, end tha horizontal lime is the resultant final plwaea
height frea the
place entirely
The S£>2 esi
hourly boiler 1
eseh unit, wti&
' 152.4-ia stacks. la ell e@e@s pltos® rise is s©sm to 6@ke
Within tte layers describes by the indicated mean
*§ * dSTIl ^ £9 !
531U6H.B » 1
iaiesi rates froa each fejsiler unit ss®re cslcule£ed frora
0^8, weskly ewlfwr eraieEt aud hc«t ralue of Ehe coal for
ssartly averagea of the gross energy oatptat of' the
facility p©r he^t input as fuel. The isulfur coaKeat had been adjusted by
WA to reflect


•>
R O /o "
fOJ conversion of the s^lfwr coatent to g02« To eosiput®
1
|

i '

__.

^",:.;,. >
                                                                                         „
                                                                                     TOP OF
    3/8"
EPA-237 (Cin.)
(4-76)
  BOTTOM OF
  IMAGE AREA;
  OUTSIDE
  DIMENSION
._ FOR TABLES
yAND ILLUS-
  TRATKJI^S
                                   PAGE NUMBER

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BEGIN
FIRST
LINE OF
TEXT'
HERE %>
        TYPiNG GUIDE SHfTET
   TOO
  550
I 400
   250

   200

   160

   100

    SO

     0
                                       CENTER'
                                      or PAGE
                5.3 m/s
                                        finsl Plume Height
                                                          \
             Profite Obsssvstion: 1227 LT
  Vetocity ProfiSa Observation: 1332 LT
          I              I              !
                               -3             -2
                                    Temperatura (°C)
                                                           -1
                                                                             TOP OF
                                                                             IMAGE
                                                                             AREA
                                                                      3 m/s
        Figure 36.    Temperature profile  used to  calculate plume rise and
                       Froude nuraber on day 3, hour 1300, 1978.
   'JL
  EPA-287
  (4-76)
„___!.	

 (Cii.)
                                           iiii "3 .-:;
                                           PAGE NUMBtR
                                                                                     OF
                                                                                AGE AREA;
                                                                                JTSIDE
                                                                                WENSION
                                                                                R TABLES
                                                                                ID ILLUS-
                                                                              IKATIOi^JS

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HEAD;
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SECTIONS
HERE  B
  TYPING GUiDE SHEET
                                  CENTER
                                  OF PAGE
750

TOO
               550
               450
            <=»
               150

               100


                50

                0
                                                    2.0 m/s
                                                                Rnal Pfurne Height
                                                                  3.2 m/s
                                                                             1.6 m/s
                                                                     3.3 m/s
        Temperature Profile Observation:  1228 LT
        Vetocrty Profile Obssrvation: 1312 LT
                   I              I
                                 1
 BEGIN'
 LAST I
 Of TE>
 Figure 37.
Tetaperature profile used to calculate  plume rise and
Froude number on day  40, hour  1300,  1978.
           EPA-237 (Cin.J
           I4-7G)
                                                                  TOP OF
                                                                  IMAGE
                                                                 ^
                                                                  AREA
 BOTTOM OF
I IMAGE AREA;
! OUTSIDE
 DIMFNSIOM
 FOR TABLES
 AND ILLUS-
, TRATIOMS

-------
fTjtTE-ss??
  FIRST
  LINE OF
  TEXT
  Ht'RE
DRfl
BEG
SEQ
HEIJ
                                                    ^ Y
-------
       ?£?'Si^                                                            < -?'"'•'''• VT~lL~nS'*?"^, •

         .."':"'•  ' TVPING GUIDE SHEET     '    .
 HERF
DROPPED
HEAD,
BEGIM
SECTIONS
HERE   «
BEGIN  s
LAST  1
        /   i
        t — i
                                                 Temperature Profile Observation:  0320 LT
                                                 Velocity Profile Observation: 0325 LT

                                                                     I
                                                      24

                                                 Temperatuf® (°C)
               Figure  39.    Temperature profile used  to calculate plume rise  and
                             Froude number on  day 230,  hour  1000, 1978.
116
                                                                                                 TOP OF
                                                                                                , IMAGE

                                              nor. OM OF
                                              IMAGf AREA;
                                              OUTSIDE
                                              Dlf/ENClON
                                              FOR TAELFG
                                              Af.;0 !LLUS-
                                              TRA1ION5


-------
                                                                 4.3 m/s
                                             7   = 0.0011 (°C/ml
                                             AZ               /
                                           Temperature Profile Observation: 2030 LT
                                           Velocity Profile Observation:  2355 LT
                                                  I	I	
                                    6             7
                                    Temperature (°C)
                                                                           8
LAST'  1
OF TB  R
    Figure 40.    Temperature profile used  to calculate piume  rise and
                  Froude number on day 4, hour 2100,  1978.
                                       117 _i;
EF6-237 (Cin.)
(4-7-SI
                                                                                    TOP OF
                                                                                    IMAGF.
                                                                                    AREA

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HR.T.T
TYPING GUIDE SHEET
                                               CENTIK
                                               OP PAGE:
                                                                             TOP OF
                                                                             I MAGE   -]

            750


            700

            650


            600


            550


             500


            450
         M. 400
             300


             250


             200


             150


             100


              50
                                       8.4 m/s
                                                   6.9 m/s
                                                                        Rnal Plums Heigfrt
                                                             2.4 m/s
                                      AT
                                      AZ
                                                               1.3 m/s
    Temperature Profile Observation: QQQ5 LT
    Velocity Profite Observation: 2340 LT
                                               I
                                                             I
                  20
                21
22            23

Temperature (°C)
                                                                           24
                                                                         25
                Figure  41.
              Temperature profile used to  calculate plume rise and
              Froude number on day 166, hour 2400, 1978.
                                                 118

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     WING GU'DE SS-ltET
                                     CRMTFfi
                                     OF FAGt
   550

   500

   450

1 400
**
JE
G>
a 350

   300

   250

   200

   150

   100

    SO
                               7.4 m/s
                                       5m/s
                                                       Final Plume Height

                                                      AT - -O.OOS5(°C/m)
                                                              1.9 m/s
         Temperature Profile Observation: 0QQ4 LT
         Velocity Profite Observation:  2322 LT
                                                                 1.0 m/s
       18
                       19
20
                                                  21
                                                                 22
                                          23
     Figure  42.
                  Temperature profile used to  calculate plume rise and
                  Froude number on day 222, hour 2400,  1978.
EPA-«.'37 (Cin.)
(4-76)
                                                                                    TOP OF
                                                 BOTTOM OF
                                                 IMAGE AREA;
                                                 OUTSIDE
                                                 D.PENSION
                                                 FOP. TABLES
                                               -f Au'D ILLUS-
                                                , TRATION3

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HERE Si
j


BEGIN
LAST L'Nt
OF TEXT if


TVPiNG GUIDE SHEET
CENTER
cr- PAGE ,.
n „ r - . j^S
•the hourly ©Eissiea rate, the aulfwr and heat coateat ssffletsrerassit® K&de
oa ea^plea tskea oac@ & week at each boiler srer® 
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BEGIN
1 A^T 1 IMP
a isfrfee height of the hill i
—— * m • *i_tt i
T is itQA fiwerag® tssparatrar?
29/3s is fths petsatiel ten^eratt;
g is Ithe seealeratieai due ta
i j
Kaffl3fl©%® of the tea^sratur© pro file i
-©rust-Vaisaia $r@qo®aey, sad the free-
(a),
(°K) 	
re laps® rat© (°K/a), and
gravity, 9.8 ®/5^«

lone allosro £te calcralatioss o£ H, the
streeia velocity say fea de&srEdaad frsar
MntM





if the available wisd profiles sr® not repraeeffitaeive of the ea@@ hour. Tfee i
particular velcieities chosea srere stib;
rfflrage of 3SO tcj 400 ta. Table 21 pr®e<
those gevca hc-^rs selected for e©dsl 4
actively selected witbia ete height
fflts the Froude nssaSjer remits for
os^arisoa. For all three ftmsrs
shoeing significant impacts on Sussierftouae Ko«Btaisj (mouad), flow cotidjtioaa
era closest Eo jneutral flew; two of tbe four hours shfwiesg sigaificaat
iffipaeta oa SasS Kowataia (ridge) are C
TABT^ 21 j 	 OF RESULTS OB
Julian Day Hour U(Q/S)
.eadiag to stable stratification.
f G&LOJlAfWSS
39/32 (°KAa) Fr
^ 	 ^ - e-i/->- 	 J

40 1300 3^1
190 0900 2.6*
230 1000 2.5
q.l /S"
4r 2100 7.0
166 2400 4.5
222 2400 5.0
*Estrapoiated from towsr dats.
Disp@r@iOiS stability claase® for
0.5932 	 OT91 ^
0.6034 1.02
0.0196 0.37
0.0093 0.52

0.0109 1.30
0.0053 1.24
0.0033 1.73

tteese heurs are root directly
^sasured. Thejtmser dsts give stability elsss estimates f&s the layer b@l®s?
the stacks b@s@d ca the 6es?parst«re gt
appropriat® So 'the el@^®tica of the p1
profiles, eud Stability class csa be «
radiest (Tsfele 22) . Data fssre





















.«ESS cea be takeia frsa fife® fceasperatrar®
iaeenaiaed agaia fir-«aa the ££.s^c«ratore
gradient. Keither of these Esstheds, however , tskes aceoaat of Efee ®iad
speed, or the influetBce of u^mizd tertsin features.
I [
TABIS 22. STABILIT? CL&$SXFICATIOH SYSTEM
|
Stability Bascrigtica Stability C
Estreaaly Casteble 1 or A
Modarately teeEable 2 or B
Sli^itly Uastafele 3 or C
Heutral 4 or D
Sli^tly StabW 5 or E
Moderately Stable 6 or F
Eatresaly Stsbie 7 or G
OF TEXT »f-

I 4
§3/8 | -xv:.:
	 J 	 	 JL_ 	 	 	 ^j 1
Teaperatere asogs
with Height
lass (OC/100 a)
< -1.9
-1.9 to -1.7
-1.7 to -1.5
-1.5 to -0.5
-0.5 to +1.5
+1.5 to +4.0
> +4.0











BOTTOM OF
IMAGE AREA;
OUTSIDE
DIMENSION
FOR TAEtES
•.;.;. ""YAKD ILLUS-
21 J: 	 	 	 TRATIONS
PAGE NUMBER
EPA-287 (Cm.)
(4-76)



i

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                                             CENTER
                                            OF PAGE
                                                                                TOP OF
                                                                               .IMAGE
                                                                                AREA
                                 ffl@si£ 'lesa 8te!b>l®* class.   Th® csee period @ra
       md 40 ©r® bothih@wr  1300 with low wia$! epeeda.  Usadsr these esaditicB®,
       digpsrslou elssS ®sy  fall betwea the {inferred class (0) @a«3 tfoe messt less
       stsble elss® (C).  The  oth©r two perieiSe, h©0r Q9QQ on day 190 end hrnsr 1000
       OB day 2S9, hs^e such sors stable temperature gradients sad slightly
SECTIONS mss^ sp«eds>9 e©j the inferred stabilieyj class  Cl) say fee
HERE	
             All Sfere© feowsd  impact cases
                  that ^orasspeffid to etabilitijss betroea class 0 aad E at night
        (tistsr 21C^ or 2^09).  &sc®«8® of tha ^firnd spesde and terr®£fa rotsghaesSj
        stability els&iss'B eay ha acre approjMfifetej both class 1 eaS class D
        cas® hours.
                           ®ade.  Table 23 suasarizes these chcsices for the
                     23.J  R^SGES OF DISPS1S10H STABILIT? CLASS CSSIGHATIOHS
                                TO
                                                   EASED OH
                                                I
                                                 TIKS 0? DAY
                          Bay
                                           Profile AT
                                                  Raaga. Mofeled
                        13
                        40
                                  1300
                       2SO
                        !

                       166
                       222
                                                       C-D
                                                       C-D
                                                       D-E
                                                       B-E

                                                       D-B
                                                       D-E
                                                       D-E
BEGIN
LAST LINE
OF TEXT S
              The cemplea terraia esdal ^as  risni fcr 28 cases 5 four runs  for  e©dri of
         the  e@v@a ease tetsrs.  Th@  four  TUBS per case hossr arise froa elss  four
         possible eeimisiEatiess of two  pUiae  heights arad two stability classes.   (Hue
         "scsubbsd" sad ftsnscrwbbed" sEaek parsssters give different elusee  rises.)
         Predicted eoacetitr©ticas are  aorssalized by the quantity Q/5JaS  where Q is
         the  eaissioo ra^e, 0 ths steck  top  velbeity, aad a the hill height.
         Table 24 Hat® ph@ resujlta  of the Eodel ctJspwtstions for £fee fonsr  ridge
                caees; sfed Table 25  the  results! for the three ssouad is^sact  eaee®.
              In efee two! cases chsractsrised by, very low Froude nusi&ers  (days  190
         emd  2^), grouad-le^el eoraeeatratieas zncreaBe with plisss height.   This
         effect i@ spariosasi it results  froa tssisg the ®Kpirieally-c!eri¥eii	
                                          PAGE NUMBER
                                                                                         BOTTOM OF
                                                                                         IMAGE AREA;
                                                                                         OUTSIDE
                                                                                         DIMENSION
                                                                                         FOR TABLED
                                                                                         AND ILLUS-
                                                                                        I THAT !OWS

-------
1
*"" 
Q Juiien
• - Day R
•
f 3
r 3
/
I-
40
1 40
2 K 40
c w
g 4Q
^
190
190
190
190
230
230
230
230
Pilrill
v 5 - 2 -
TAILS 24. RESULTS
IMPACT 013 THE

sipht (a)
445
445
422
422
432
432
409
409

325
325
307
307
347
347
322
322

- . . . , -i • . . . -_ .-•


OF JOTS!
BK&tBY S"

, CA
EBCT

LCTLATIOWS S
(SA1ID MOOKI

Stability Ficowda {formalised
Class Ksffijfber Concentration
4(D)
3(C)
4
3
4
3
4
3

4
5(E)
4
5
4
5
4
5

. .
0
0
0
0
1
1
1
1

0
0
0
0
0
0
0
0
	
1 -W
.91
.91
.91
.91
.02
.02
.02
.02

.37
.37
.37
.37
.52
.52
.52
.52
	

0
0
0
0
0
0
0
0

0
0
0
0
0
0
0
.0003
.1497
.0017
.1656
.0009
.1514
.0018
.1671

.4663
.1459
.4371
.1248
.1951
.0182
.1814
0.0133'






poa HOOIS
fAIM)


8HC*™

T '-n CT TT 5
m rp ^ rn ^! ~r — < r— -T
f^j 1^ k; > y fn {J 2 5


CO
m ;
O.i-
Inferred Terrain Infasred Piisiaa
Corrsction Fscfior Path C«3€ffici©®6 ..'
0.597
0.5S3
0.593
0
0
0
0
0

c
0
0
0
0
.599
.611
.613
.617
.618

.344
.344
.372
.372
.412
0.412
0
.452
0.452






0.349
0.349
0.383
0.333
0.390
0.390
0.430
0.430

0.225
0.225
0.299
0.299
0.258
0.25S
0.358
0.35S
-
i> ^; — t
5 5- 0
in > ~a
> Ci 0
mO

j - -
1 ' s



!

-;
\
I
i
1
;
I
: . 5
s
'1
Si

-------
rn ' 3:
x r~
$ ™
-^•j— -

Julian
Day
4
4
4
4
166
166
166
166
222
222
222
222
!
390|§
5< 1 ^ £ 3
J2 ;? rn > '~
CO rv o
^H -?• m is



Plmsa
Height (a)
309
309
289
289
335
335
317
317
370
370
344
344






XraSSdE 25 • iiS!
IMPACT OTI THE I
Stability
4(D)
5(E)
4
5
4
5
4
5
4
5
4
5






JOLTS OP KC
EOLATSD HO
frowda
Knsabar
1.30
1.30
1.30
1.30
1.24
1.24
1.24
1.24
1.73
1.73
1.73
1.73




-C v> cn
SoS
rn — i -^
Q "~
1 1^ S
>BEL CALCTLATIOKS F01 HOUB3 SHOWING
SJ10 (8WSMSR1C08B MOWTAIW)
KorEsaliEcd Inferred Terrain lafar
CoaceatraEicm CorrscEion Psc£©r Faeb C
0.1040 0.638
0.0200 0.653 (
0.1195 0.6S8
0.0296 0.66S i
0.0896 0.64S 1
0.0116 0.649 (
0.0982 0.655 (
0.0170 0.655 (
0.0429 0.703 «
0.0016 0.70S C
0.0558 0.715 (
0.0034 0.715 C
\ 	 " 	



3T. CD ' J
SI O ^x fn ~ ^ m *
- • m r" ""' *T -I 5 '
^LJ, «
-fl ./..,^

? ":
?@d P1SS5S > :
ssf ficicHBt £ • :
o '
C • '"*"
).616 n "v
n • . i
3.616 H 1
: f
0.651 ; J
3.651 j J
5.571 t
3.571 . 1
3.602 : "
).602 ;
1.607 .
>.6©7 1
).643 1
J.643 |
i
	 Uv i
1 ij p- 4
|| B ,1
5 o ^ • ^
m T1 J
:-|


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BEGIN
FIRST
LINE OF
TEXT
HERE »
   TYPING GUIDE SHEET
                                CENTER
                               OF PAGE
                                                                           TOP OF
12.4.2
                      firon
The eessesdtraticus predicted ©S tfill  ers; £
                                                                  ia £h@ eeaeeratratioa
                       fiaetor.
                     e^Lssioa rates end «?iss3  ^p€®ds,  sad the resultant nctnsaliEstioa
        factors for each of the sev&a £®s£  cage  hours are sisaaarised ia Table 26.
        The tt®rssligsti'ca factors ecavere rasdgl  eosieentracioas t© units
        Only £ts©  £®o  1^2-a stacks (boiler wni£3  7 emd 8) are iseladed because the
        iapect froa tha 304-sa stsck is asal!. j Hote that aorsalization
        gives £©r ismsoiitrolled eaiesioas onlyj   The WA Air Qaality Braaeh
        that BO serubbiJBg ocewrred ©a unit  7  oaring these tours, arad either
        quarters  or  ful,l scrubbing (80% resov^l  efficiency) occurred on Unit 8.  1m
                   @ligli£ly different gross  Io4d  values (@@l) wsre reported for both
        ^^saits^&iEiag- ttesa fee^ra-. _JSaia_iaf©r^atioa_iiaa_bei2E_ia£agEate«S Hitb_ the—^
        previous  data, land revised esassioaa  for units 7 sad 8 ©re pressaEed in
        Table 27  along yith the new Eormalissfiicm faetors.
                         plus® risa ce^utatis4s  have besn E^de for £h© seven case
        hours usisg  a gultiple-lsyer plisss  rise  exteasion of the stable Erigga j
        rise equatiotfs'i CHblzworth 1978).  For |hoars tdten wraie 7 dc@3 not  op@rat<
        the scrubbed  pitse rise height  is caismlatedf for all other hours,
                    pluigs height is calculated]   Khea both units 7 and 8 sre
        ©psrstiEg, the 'higher plessa elevatiea jcorresponding £© unit 7 is  used
                 SO2 codeeatrstioas of  this  unscirubbed unit 7 plssie are rassre ehass
         twice  those of .the scrubbed trait  8  plema.  The rasltileyer pl«sas
                  with  the sitjgle  layer pluses feeigtjts in Tables 28® and 2!
         give  aesrly the eeas val«as £0r  days 3,  4, ©r«d 46.  The greatest  difference
         occurs  for dsy ,166, where the  na^ pisses rise esceesds £he previews valua  by
         55 a.   Conceatxlsticas predicted using!the sailtilayer plta^ heists ®re also
             ared with  eh® observed values.    ;
              For the hours of isspaet  ©a  the ridge  (Ssad Koastain) the taadel  caa
BEGIN
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OF TEXT
                                                                           AREA
        in  all eases.
                                                diepsrsiesn  rate  scaewtser® befiweea
         class C e®& el^ss D is  required to match the observed  eoaeentratioa.  The
         class D c©spBt«kion overprediets by 1^8%.  On day 408  however,  the class C
         result overprediets by  less fh&n 201, jaad say therefore  be coasidered e.
         mstch.  
-------
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i: £|
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m~1;? "1=i^O^S5
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"'5 ^ 2 b H
S .'n 	 % '••-> _ 	 jf.
?! .1 . - . .. ,j 51 t f
' A 1
r t ], i
i
TABLE 26. OKCOSTOOLLED SOj COKCHfEATION KOTMALIUTIOH "' '
FACTOSS FOI TEST CCS5PASISOJ8 HOWS t
SO. Emisaioas, . ,' :
Julia.- Terrein Haigbt Unit 7 S 8 Stack Top „ _ L .-
Day o(a) Q (g/s) Velocity 0 (sa/e) Normalisation Factor » Q/OTT (p^/a ) '
3 2~1 1984 2.0 13,117
40 275 1756 2.5 9,288 ;
190 275 3442 1.2 37,928 '
— 230 275 4265 1.5 37 , 598 |~
4 275 2536 3.0 11,178
166 275 1672 4.5 4,913 ,
222 275 4054 1.4 38,574
	 j 	
i
I
f
I
1 f |
"--,1
1~n -,;
j
J C7 .1
o j
m .j
m .'|
m
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"/
o 3- ;;-1
"" 1
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_:i
']
fc -^
^SU -i
SigfS 5f 5S :•:>*
33 S. _( > — ' m J> -D
-i 5 <2 ^ o >oo"''^
>'uo D m < m -n . -."«!
" 5 m S 3 ' -".-f-t
S 2 5 ^ _^


-------
O r~ en
- £ S
— 1 	 j —
X 1™
— 1 =;
$ m
i
O

CO
3
—



hs£ -
1
' I
X lr> OT X 0 • -)5
5 o S S5 o S S 5 3 *
"•ri-^c^ S><^eEc|
^^—l—JL -"^

^ ' i •'''•
TABLE 27. RSVISBD SO, EMISSIOH RATES FOR TOITS 7 AHD 8 1 	
2

AKD COMBITOD COKCEWTMTIOM BOEMM.IS^TIOH FACTORS , ' -r ;

L Taffl 1KCLTO2 SCRUBBER OPE!lft,TIOK3
Juliem 014 Eaiesicas (g/s) Baw load/Old Lo£<3 Unie 8
Osy Unit 7 Unit 8 Bisit 7 Emit 8 Scrubbing Factor*


3 0 1,934 - 0.987 0.4







>

t'TV
^rf
40 0 1,756 - 1.027 0.4
190 0 3,442 - 0.991 0.2
1 230 2,094 2,171 1.036 1.C41 0.4
4 2.53S 0 0.995
i 166 0 1,672 - 1.C4S 0.2
222 1,842 2,242 1.220 0.990 .4


t, ^i Scrubbing factor « 1 - scrubber ueiHsatiea x scrubber efficiency.
C3 I
•m r. •.-.•-•









!





j/










i
— < > "^ O O ^ or
33 -- O — r- ^- C
> ft 3 =i ZJ > -H
-< ^J . m £o (D — i
0 F J> i 5 m §
£ C ^ 0 m S o
(

Rev EajissioTis (g/a) Honsalis-seion "
Unie 7 ttatt 8 Factor ((j^/a3) ;

0 783 5,177
0 721 3,314
0 £82 7,515
2169 904 27,090
2,523 0 11,121 :
0 350 1,028 -.r . •. 1,1- i 	


*
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• " ' •'<;
&'*&v&e^^&jf£HUE&ii&

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r


tS
_ r_ _ --.a
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-n ;> JJJ rri n-- rn rn :;t:) x — * ' — ~n ca -•:'

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fef nn (g (/> _^_, ^ ;
L^*5f">»« .
~ fe' 1 c~*
t ^
1 Q
b
^
^
cc

r|- - - - - - - . - -^ p j'
I
j


^
~» ' ^
: S - 3 'J
| TABLE 28s. COMPARISON OF PREDICTED AHD OBSERVED SO. COMCEWTSATIOHS (pg/m3) AT WIDOWS CEEEK j .^ % 1



[
f
I
f-
1
~c
-1 £*
i (7/
r- rn
V
P  -^ ".I
(7; Cg ' -'{
in -° -^
- 1
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1
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rs
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- 1
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> f=j .-D S iq > -,' m > 13 :--il
rf^^S^^Q >OO -•-'"''
V- f~ CC — J2 J-., 2 Tl , ' -|
oS C ' O ^c O -'1
r /•. in — T ,-rl _ . - liV

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C

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^i r"-
'
TABLE 28b. COMPARISON OF


.
PEEBICTED AKD OBSERVED SO 9 COKCS

.2 5 ^
•••---- • - - [ | i r i
1 1 .• 1
•NTMTIOBJS (pg/ffl3).AT HIlKf^S CIEHK
Julian Crouds Pluao Observed Half-Height Aasumpticn Predictions Level Plum Kodel PretSictloae
Day Musber HaiuJit (ra) Concentration Stability C Stability 0 Stability B Stability C Stability D Stability E

i


E
'i
i.



-^4
r,
3 0.91 422 393
40 1.02 402 550
190 0.37 320 576
230 0.52 370 603
r "
4 1.30 301 1,179
166 1.24 373 367
222 1.73 392 393



i
~^ O O ^ c3
O — <— -- O
33 ^ _| > — (
Eidge ImpeoC
654 1 -
574 3
362 5
, - 136 0
r
H9und Isspact
1,887 864
67 6
1,459 70

t


O ^
Tl ^
" -'&
i m |
i  i 5 J g : ' ™ ° '-I
£ c - o m S o "1

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                                              OF PAGD
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          40
         190
         230
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                   TAHLE  29.   COMPARISON OF OBSERVED
                      AT  WIDOWS CREEK AHD PREDICTED
                   OU THE POTENTIAL  FLOW KOrEL WITH
                 Ifeiltilayer
       Julian    Plusae Height
         Pay	(ta)	
                                  Observed
                                Concestratioa
                                                            Terrain Model Predictions
                                                 Stability C   Stability Q   Stability E
                   422
                   402
                   320
                                    393
                                    550
                                    576
                                    603
Ridge Impact


           932
           729
   270
   157
 4,599
12,038
                                     3,354
                                     7,711
                                           Mound Impact
4
166
222
301
373
392
1,179
367
393
1,529
99
2,123
531
16
246
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                                                                                          •AND ILLUS-
                                                                                          TRATIONS
           FPA-287 !Cn:.l

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FveTTTrotreennfat ions1 ."and eKe~ earee's1
"overpredietsd before are EOW even further off. 	
Additional perspective on the rao
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HER£  B
;	   Given  the j£rreducible rajeer taint ites  in  the  Emissions  and  the
ataoapheric datfi at plv«e hei^it, moral detailed  corapariscns  of the predicted"
and observed concentrations for theee seven  cases are  not  warranted.
                i
12. *   Stsssiary akd Conclusions
     Jlusse interactions with two terrain  features aear the Widows Creek   —
                                                                                TOP OF
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         terrain model. ; Meteorological conditions used in the model correspond to
         soven hours selected  from nine Booths 'of hourly §02 and meteorological
         data collected by the TVA Air Quality iBranch.  The hours selected for
         comparison were, derived by Batching hours of high measured S02
         concentrations 'oa the two terrain features with neutral-to-stable
         atmospheric conditions.   In  addition, ;only those hours with nearly
         coincident vertical temperature and velocity profiles were considered.  Of
         the seven hours^ finally selected, four are associated with impacts oa the
         ridge, and three are  associated with impacts on the isolated raound.  The
         highest saeasured S02  concentration on the ridge during the 9-asosth period
         was 0.85C pps (2,227  pg/ra^)  observed on day 226, and that oa the sound BBS
        •«4fc»450 -p-ps- (1-j 1-7*9 -ng/si-*)''observed- oa-day -4» — — — — —- -—	—
              The hour associated  with the greatest ridge impact ms not selected for |
         saodel analysis because no suitable velocity and temperature profiles exist   j
        ] for that period.  Consequently, the aodel's ability to simulate £h® greatest !
         observed impact on  the ridge is not known.  The case hour of greatest impact j
         on the mound (day 4,  hour 2100) was simulated! cae choice of predicted
         concentration was nearly  equal to that observed.
              A partial heij^t model  using a plwae path coefficient of 0.5 perronaad
         about as well aa the  potential flow sodel for all Froude ntMabers greater
         than 0.6.  For lower  Froisde  nussbers a path coefficient of 0.35 produced
         results sisilar to  potential flow sodsl.  The level plusae jaocSel greatly
         overpredicted sost  of the tiase, and Hatched observed coneentratiois for the
         one hour in which  the other  tsodels markedly ut^erpredicted,
              Uncertainties  is the aeteorological conditions at plssee height, sad ia
         the emssiotis froa the facility, cloud the comparison of ssdei predictions
         with observations.  Given the range of data, reasonable combinations of
         assumptions can produce  good correspondence beteeea the concentrations in
         six of the seven cases.   This dees not, however, constitute an adequate
         evaluation of the Eodel because of thQ uncertainties underlying these
         assumptions.  The  three greatest uncertainties lie in the specification of
         the dispersion parameters, the final plusae height, and the actual emission
         rate.  Data are not available for more accurate estiaates of diffusion rates
         and plume elevation.                   i
              nonetheless,  the prelirainary coasparison for the hour of greatest impact
         on SuaBserhouse Mountain  is encouraging and the bracketing of observed
         concentrations ;(in many  of the other eases) suggests that better
         observations may «ell iaprove raodel perforsaance.
                        i                        t
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LAST LiNEI
Or TEXT
                 (Cin.)
                                          ili 132
                                          PAG? IJ'Jf
                                                                                BOTTOM OF
                                                                                IMAGE ARE)»
                                                                                OUTSIDE
                                                                                DIMENSION
                                                                                FOR TABLES
                                                                                'AND ILLUS-
                                                                                TRATIONS
           (4-76)

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                                    OF PAGF
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SECTIONS
HERE   9
                                             T
        ASMS,   1963.   Recosgseaded Guife for the Prediction of  the Dispersion  of
             Airborae Effluents.  M. §sath, e<3. Hf« York, BY.
        Briggs,  G.  A.   1975. 'Plws® Rise Prediction.  Leetttres  on Air Pollution  amd
             Eavircnggntal Impact Analysts, Aserican Meteorological  Society,
             pp. 80-34.;

        Briggs,  G.  A.   1973.  Diffusion Estimation  for Saall Emissions,
             Ateospheric Turbulence and Diffusion Laboratory Contribution  File
             Ho. 79«   ,

        Briggs,  G.  A.   1969.  Pltcsa Rise, Critical  levies (TIB-25075).  Atoaic
             Energy Ccsgaission, Division of Technical Information, Oak Ridge, TH.
         Britter,  S. E.,1 J. C. R. Hunt, sad J. 'S. Pwttock.
              Pollratioa Concentrations Kear Buildings  and Hills.   ProeaedJBgs  of
              Ccmfareace oa gyetSBa aad Hodel8in Air  and Water Polluti&a.   last.
     Meas. and Control, Louden,

Csbe, D. B. et al.   1977.  Application of the Gaussian Dispersion Model to
     Predicting Masiat^ Pltsse Concentrations ij^Abrtiptl^ Sis ing Terrain.
     Mr Pollution~Coatrol~A8sociation (APCA) Paper Ko. 77-58.2.
                                       )
Cramer, H. B., B. V. G«arys  esd  J.  F. Bowers.  1975.  Mffusion-ffiodel
     CalCTElaSleaa of Long—Tern and  ghort-Tera Growre!-Level gQg
     Coaeeatraticas  in AllssfeCTy
                                                   Peimsylveaia.   SPA 903/9-75-018.
BEGIN
LAST LIKE
OF TEXT S
              Prepared for U.S. Isviron^satal Protection Ageaey,  Eegion III,
              Philadelphia, PA.                j

         Csanady, G. T.  1973.  Turbulent Hffusion  in the BnviroitBsnt_.  Boston:
              D. Seidal.                       >

         Egan, B. A.  1975.  Turbulent Diffusion  in  Cosiplez Terrain.   Proceediaga of
              Workshop on Air Pollatica Meteorology  aad Enwiroametiital AsBeas^ent.
              American Meteorological Society, Boston, MA, Ssp£e^?er  SO-Qctober 3.
                        i                       j
         Eg en, B. A. and A. Bass.  1976.  Air Quality Modeling of Effluent Pltases in
              Sough Terrain.  Proceediafga o£ Tfoird Syisposiisa on^Atgosptsggic_
              Turbaleace, Diffusion and Air  Quality.  Mericaa Meteorological
              Society, Raleigh, KG, October,  19-22.
                                                                               AREA
          EPA-267 (C-n.)
          (4-761
                                          •-^ 133  _-	
                                          PAGf f.'Ui.'iirK

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                                    OF PAGE
              B. A.,  RtjI^'S^i-60* sm^ c« Vaudo.   1979.  AessassiEg Air  Qgaliey
             in Effigies®; of Hsrotaismss Terrai^.
                          Pifftasiea jsad Air PoHafcion.
                                   TOP OF
                                   IMAGE
                                   AREA
     Society, Eaao, m, J«usry 15-18.1
SPA  1978.
                    Protection Ageaey, j
.  1PA-450/2-78-027.  U.S.
  of M
        Hiads,  W.  T.  1970.  Diffusion O^er Coastal Ktoustaies of
                           Atessphagie BaviroEg'sat 4sl@7-124.
         Eoffosgle, G. w.t B. A. Egs0s snd 3, i[. Grains.   1977.   Appileatio®
              Models £H Ceraplex fesraia,,   *mcdino£  JoiatCpngeremea
                       ^^^           ,_
                       Meteorological Seei@ty, Bsseoa,  MA.
                        i                       i
         Holzworth, G. C.  1978.  Estimated Effective Chiaaey H®£^»£s Bssed en
              Essriesoade' Observatieas at Seleceed  Sites ia  Eh® te&ited States.
 BEGIN
 LAST LINE
 OF TEX] Js
             j J. C. R. aad 1. J. Msslheara.   1973.   Ttarfeialeae© Bispersioa from
              Sources Wear Ti?0-DiaEasi©Qal Obstacles.   Joaraal o£ Fluid
              Macbamies 61! 245-274 .
         Hunt, J. C. R.j J. S. Puttock,  end W. te. Saydsr.  1979.  Turbulent
              frca a Point Smsree  in  Stratified  satd Heatral Fls$?s Arowad a
              ?Br@e—DiEsasirassl Hill*  Fart I •*  Diffsasioa Siquatioffl toaly®is.
              Ateospheric Era'gdgi^aeit^ 13; 1227-1239.
                        i            '           !
         Hunt, J. C. R. and W. H.  Sayd^r.   197S.  Plow Strwetwre snd Turbulent
              Diffusion Armmd a Thre®-Bia©a@ieaal Hill.  Fart II - Surface
                                 to Upstreesa
         Hunt, J. C. R.?! Wo H. Stiyderp  and a.  E. LawsoiSj Jr.  1978.  Flo^y
              aad TogbMlent Dif f«@ica ArmiRd a !°rhreg-Bigga@ieaal Hill.  Flusid
                             ®a Effect®  of Stratiflcatica? Part 1, Flow
              EPA-6TO/4-78-041 .  U.S.  Ea^irosigsatal Proteetioa Ageacy, Research
                       Park, HC.
            iay J. S.   1979.  ScheEe  for EstiE^tii8% Dispegsion ParsKst©ra as a
              Fuaetioa  of Sslease. _lfoi^it.  EPA-6CO/4-79-OS2.  U.S.
                                  . _
              Proteetioa Agmey,  Research Triaagl® Park, EIC.
                        1                       i
         Leahey, S. M.  1974.  Ofesanratiojsal SSadies of Atraospheric Diffusion
              Processsa cw©r Irregular Terrsia.   Proceedings e£ the 67th liaetiag
              the Mr Pollutioa Coaerol Association, Dawfei'j CO, J«a@. 9-13.
    §3/8"       Y
	 1	1_	
                                                                                        TRATIONS
           EPA-^87 (Cin.)
           (4-76)

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                TYPING GUIDE SHEET
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        -^e«hey,  D.
                  J.  Bssiitdky.  1973.
                                               Low
                                                                               TOP OF
                                                                              .IMAGE
                                                                              , AREA
             Related Diffusion Estimates  froa a Site Located in the ItsdsOT River
             Valley.  AfeBqfjgherie EB^irorosat 17849-61.
                   P. B>9 L. B. Babeolal, and JP. B.
                        41 of ft over Cffinplsa T@sr®iQ«
                                           Pollutiea.
                                                        1974.  Diffusion
                                                             J!-g_ igQg
                                                                    "
        Miller, C. W.
              for Rough
Milras~The®9©a, t.  M.
                              .  AtiBpsphegie tovigenasot
                                              I
                              1960.  Theoretical
                                                                       Tos&t
                                                        la Pltaae
         Pesqwiil, F.  1978.
              SP4-6DO/4-78-021.  U.S.  Envirssaaatai FroEeseioa ^gsney, Esssarch
                       Park. KC.
                                               ^-- 1970v
         ieEV P-*r As- sa^ L.
     Sttsdy (IAPPBS.) .
                                        1-4.  Kstioosl Air Pollution Control
              Adsiaistrafcicss Pablicaticm Kos.      70-2, 0589.
                        •                        i
         Sb@e?e?t B. L.»'D. a. Miao££,  atsd G. R. Hilat.  1977.
                                   Cos gf ieient8fog
                         ^             _^_ .
     Prepared for the 0.S. EEsrgy Sssearcli
     EY-76-C-02-4
                                                                               ..
                                                                     A&aiaieEratioa.
         Snyder, H. H.  1977.   Safes Report.  Projects  Hnrat Hill Study.  Part?
              Hill.  EPA| Fluid  Modeling Facility (isnpu1blisto@sl aaaascript).
                                                i
                         '                       i
         Snyder, W. H.   1978.   Data Report.  Project!  Huat Bill gtudy.  Part:
              Chaessl -  PolyEBsial Hill.  EPA Fluid Modeling Facility (unpublished
              tsana script).
                         i
         Sayder, U. H. sad R.  B.  Britter.  1979®.  Saadsprsy Bouodary Layer
              Coar^terisation (SSBL4).  Onpiblished EPA data report.
                         !                       I
         Snyder, W. H. ssd 1.  I.  Britter.  197fb.  Aspect Ratio Study (&S2AT).
         Snyder, W. H. aad G.  L. Mar@h.  1977.  ZSat® Report.  Projects  Hunt Hill
              Study.  Parts  Wiad Tttmsel - Polynomial Hill.  U.S
                         Agency Fluid Modeling Facility (umpssfelished
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        I
                                     —r
                                     L 135
                                                                                         Tr;ATiOf-Jrj
           EPA-237 (Cm.)
           (4-761

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                                            OF f'AGE
 BEGIN
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 HERE Bfc'Start»  G.  E., f|. R. licks,  ®®d C. R. ^icksoa.   1976.  Efflweat
                               Terraio.

DROPPED
HEAD,
BEGIN
SECTIONS
HERE   »
             Meteorological g^siefcy, EsleigJ»,i EC, ©eeefe®?  19-22.
                       i                        i
        Start, 6* 1.,  0.  M. Bicfessffa, etsd  L. L
        S«ttosif 0. G.
               , B. B.  11970.   Workshop of Ate&spberic Bispersiea Estimates
                         of Health, Itoc®ti«m  m&  ¥@lf©re.  Fublie Health
                           599-AP-2S, 88 pp.    i
                                                                                U.S.
                 , M. Di   1977.
                                           in Repgrt_to  fch.8EPA of
                                                    __       _             _
                         ' Coafereaea  oa efee BL-'AHo4eliKg^GuIdenBe, pT 210.

        Wilson,  S. B. 4e al.   1976.   DifftBgiea Under
                  Atsassfharie ^saanistratica,
                   Tecfeaical Hsaoraadna 1SL
     Ii'iE _
                                                                                              »?s?wwj™«
                                                                                                  '  fl
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*"AREA
OF TEXT
                                            ^ 136  ;;
          EPA-2S7 (Cm.I
          14-76)"

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            APPENDIX A




PROGRAM DESCRIPTION - CMPLX MODEL
                137

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                                                                                         REA
                               PROGRAM DESCRIPT
                                                   -A	
                                      -  CMPLX MODEL
        Al.  Introduction

             This section susaarizes the essential operating features of the  com-
        puter model  CMFLX developed during the:initial phase of  this work.  Because
        of the research inature of this computer code, it is expected that signi-
        ficant revisions  may evolve based on subsequent experiiaeiital and theoretical
        developments.   Therefore, no attempt has been made to produce coasprehensive
        KP8?8™ documentation at this_time,_particularly_with_respee_t Jt0 .£he_.speci-.s_
        fled input/output format chosen.  Howe¥er, the overview  presented her® will
        enable the potential user to become thoroughly familiar  with the fundamental
        programing  aspects of the code and orient him to its use.
             The CMPLX program is a Gaussian point-source diffusion model applicable
        to isolated  terrain obstacles of arbitrary crosswind aspect ratio in  the
        flow field downwind froa the source.   |The plume is assumed to be easbedded
        in a potential flow field determined by the specific source/obstacle  con-
        figuration involved.  This geometry determines:  (1) the pluiae trajectory
        above the surface, and (2) the kinematic constraints on  pluse dispersion
        imposed by the spatial dependence of the velocity field.  The theoretical
        aspects incorporated within the code have been previously described  (Section
        5) and will  be feferenced by equation  number.  Since the formalism adopted
        has been pursue4 rigorously only for neutral flows and the  limiting aspect
        ratio cases  of a three-dimensional axisyrazaetric hill and a  two-dimensional    j
        circular ridge, certain approximations have been incorporated to extend the   i
        model to a broader class of potential  field situations,  including the effects!
        of stratification and intermediate aspect ratios.  These features are dis-    j
        cussed in Sections 8 and 10, respectively, and will not  be  repeated here.
             The code in its present form consists of a main program, four sub-
        routines s and two function subroutines.  In the course of the discussion to
        follow, reference will be made to the  program flowchart  (Appendix B)  by
        FORTRAN statement numbers in parentheses and flowchart page number and to
        the computer program listing  (Appendix C) by compiler line  number  (at the
        far right of each printed record).  Cement cards have been used extensively
        in the listing, and essential data presented there will  not be repeated.
        Variable and subroutine names are capitalized by convention.  A sample
        output listing is illustrated in Appendix D.

        A2.  Main Program
A flowchart of the main program (Appendix B, p. 148) illustrates the
     features of the calculations performed for each case.
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                 read Input values  for a particular situation (XS, HS, HA, XL,    	
                 ALAM,|DELICT,  RKST,  FROUDE),
                 specify necessary  constants,
                        relevant  nondiffiensionkl parameters,
                       © streamline and velocity field aspect ratio weighting     —
                 factoys for neutral f ICM (A)'
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                 specify two-  and three-dimeniional streamline for neutral flow and
                 weight for given aspect ratio (B),
                 compute empirical streamline!lowering for stable stratification
                 effects  (C),
                 perform along-streamline line integrals (D), and
                 compute dispersion coefficients, centerline and ground-level
                 concentrations;  print out results (E)
                       i                       i
        (Program elements followed by capital letters are explained in the following j
                   	| _  6-1 "2 •
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        A2.1  Aspect Ratio Weighting Factors  (A)
                       !                        i
             As described in Section 10,  the  effects  on a flow field of a hill  with
        intermediate aspect ratio ALAM, falling between the two- and three-
        diEensionai limits, ALAM =  10.0,  ALAM = 1.0,  are defined by streamline  (WZ)
        and velocity field (WV2, WV3) weighting factors.  If the specified value of
        ALAM is less than or equal  to unity  (601)  a  three-dimensional computation is
        made (WV2 = O.OJ  WZ, WV3 =  1.0).   Conversely, all aspect ratios greater than
        or equal to 10.0 are assumed to characterize two-dimensional situations
        (602), and the values  (W2  = 1.0;  WZ,  OT3  =  0.0) are assigned.  If neither
        condition is satisfied, a general weighting  of streamline height based  on
        one set of wind,tunnel experiments is  adopted:
                       !                        I
                       lj?Z  =   l.O/ALAM**!.!

        while velocity fields  are defined based on the speed-up factor SUP (Equation
        10-13), and weights are given by  (Equation 10-17):
                       I
                  WV2  *  2.0  * (SUP - 1.5)
                  WV3  =  2.0  * (2.0 - SUP)    |
                       |                        I
                       1                        <
        A2.2  Neutral Streamline Evaluation  (B)
                       1                        i
             Beginning with statement 603 (Appendix  B, p. 150), two- and three-
        dimensional streamlines are evaluated through the source as (XX,ZZ)  pairs
        assuming the obstacle  to be one of these  limiting cases.  The code sequence
        to statement 60S i:; performed twice:   once for ND = 2 tatd once for KD = 3.
        "The value of the stream function  through  the source PSIP, determined by
        \parameters XS, HS, HA, is first computed  by  calling function subroutines
      V|[.-JP_SIP2D or PSIP3D.  Since this value must  remain constant along the trajectory,,
      '"'streamline Equation 5-28 is solved for each ZZ value to yield a unique
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          value defining the streamline (see aiscussion in Section 5.4.3).   Only _
       positive XX values are  computed, since! the stresaaline is symmetric about the
       origin at the obstacle  center.
            The upper and lower  limits  to possible ZZ values are given by the
       height of tli© streaalirae  HI  above the {rrest 1C (at XX*=0.0) and that at
       XX = 100.0 (tak^ra as infinity),  respectively.  Appropriate ZZ values are   _
      gjSelected within ; this range at two_ £ggo|"tioiB_.  A total of NINC values are
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                                         rang

                          <_ 22 <_ (ZC+KS)/2.0

       and NINCMI  («NI?C-INC2) values such that:

                       (ZC+KS)/2.0 < ZZ <_ ZC

       Dual resolution's adopted since the streamline becomes relatively flat in
       the region  determined by INC2.  Nominal values of NINC « 550 and INC2 « 150
       have been selected to provide adequate j resolution in each region.  Thus a
       total of 550  (XX, ZZ)  pairs are computed.
            Computed  (XX72Z) pairs~are~stored['{lilie~8ri*ppendlx"B,~~151) and" indexeiT'i
       by an integer  v^lue from 1 to NINC in arrays (FITX(ND,II), FITZ(HD, II)),     j
       respectively.   They are placed in common with subroutine ZITRPL  (Appendix B,  j
       p. 163  ), which 'provides a z-value for; any given x-value by linear inter-     j
       polation.   Once. -the two- and three -dissfensional streamlines are evaluated,     j
       the aspect  ratio '"streamline weighting factor (WZ) is used to corapute a
       weighted neutral streamline stored as j(FITX(l, II), FITZ(1, II)).  The
       x-resolutioa chosen is that of the three-dimensional streamline  (i.e.,
       FITX(1, II) =  F|TX(3, II)) necessitating a call to ZITRPL to find the height
       of the  two-disse^sioraal streamline ZEE2,, corresponding to each new x-value
        (two- and three-tdisensional streamlines have different (x,z) resolutions).
       The weighted  z-value is given by:

                 FITZ(},  II) = (1.0-WZ)*ZEE2*tfZ*FITZ(3, II)
                       !                       i
       This sequence  terminates on statement 605.
        A2.3  Streamline Lowering Because  of Stable Stratification Effects (C)
                        1                       I
             As previously discussed  (Section 8),  the predominant effect of stable
        stratification is assumed to be  a  lowering of the streamline below the value
        it would attain at the crest of  the  obstacle in neutral flow.  The magnitude
        of the effect is based on experiment for the three-dimensional case and
        assumed to extead proportionally to  the general case.  This aspect of the
        calculation (statements 605 to 610)  isj illustrated in the flowchart in
        Appendix B, p. 152.                    i
             If PGT stability class (KST)  of 4!or less (A = 1, B = 2,  C = 3, D = 4)
        is specified, no stability effect  is coaputed.  For stably stratified
        cases, a correction is applied to  the neutral streamline with a maximum
        depression at tfe© crest (XX = 0.0),  decreasing linearly with increasing
        |XX|  to no depression for all  |XX| >_ 2.0*HA.  For each KST, a value of the
        -s-treamline height above the crest  ZCF f.s computed as a function of HS and
                                                                   ±MO Jiill. heights...
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      streamline Depression DELTAS  and fractional streamline depression FMC3__
  are evaluated wjlth respect  to  the neutral three-dimensional streaaline.
  Although data is available  only for thje three-dimensional effect, it is
  assumed that a similar depression is applicable to two-diiaensional and
  aspect ratio weighted stresalines.   For the two-dimensional cas®, a frac-
  tional weighting FRAC2 appropriate to {each two-dimensional XX value (=FIYX(2,
sspTT)) is evaluated.  Finally, each streamline value is multiplied by the
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                     FITZ(1, II)
                     FITZ(2, II)
                     FITZQ5, II)
                             FITZ(1,  II)  I* FRAC3
                             FITZ(2,  II)  j* FRAC2
                             FITZ(3,  II)  I* FRACZ
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           (Note:   it is necessary to retain  and weight  the two- snd three-dimensional
           streamlines at this point since they are  used in TKER to compute the filial
           velocity fields!)

           A2.4  Along Streamline Line Integrals  (D)

           **• ~The"line Integrals'3* ~ahd"T"(se~e Sectton~5r~Equatibns 5^117 5-127
           5-23, 5-24) determining the magnitude pf  crosswind and noraal dispersion are
           evaluated by the coding between statements  610 and 101 (See Appendix B,  pp.
           153 to 155 for flowchart.)
                The values1 of these integrals PHID and TEED, respectively,  are stored
           in arrays indexed by integer values JJ  corresponding to a given position
           along the x-axis, S2(JJ), and downwind, distance from the source, DDW(JJ).
           These are related by DDW (JJ) = S2(JJ)  -  XS.   Since these integrals are
           continuous functions of along streamline  distance, s, it was decided to
           sample their values at a discrete  number  of points determined by a user-
           specific dimensional resolution, DELINT (nondimensionally, DEL).  The total
           number of values sampled, JF, is restricted only by the total array size
           (dimension) of the affected variables within  the region of interest along
           the x-axis:

                     JF - AINT((XL-XS)/DEL)
                          I
           where XS is the stack position from obstacle  center and XL is an arbitrary
           point chosen downwind of the obstacle.;  (These arrays are currently
           subscripted for 50 values.)            j
                The integration is performed  by  Simpson's rule along streamline
           segments with upper limit BB and  lower; limit  AA corresponding to one DEL
           interval.  The fine resolution within each segment is selected by specifying
           NN.  The integration mesh size is  then;

                     H = (SB-AA)/FN = DEL/FN
   (FN is  the floating point value of NN.)
        When JJ * 1,  the lower limit is set as XS; the source position  and  the   j >c7iO" >
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                                  DEL    i                                     	S Diy':NS!-:'

                                    ~3~t~~•-.--                                \Ar,
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 HERE »^subsequent iterations,"the upper ii|ait~is  chosen as:

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             =  SS  =  AINT(XS)  + JJ

and lower limitf
AA •»
                   -  DEL
             For each JJ, the values of the   md  T integrals for the specified DEL
        interval are computed as follows:
                  PINT
          TINT
                          AA
                        P dx
                           BB
                          /   Tdx
                         AA
^ejrespective kernels P, T are evaluated at each grid point x by calling_
a sequence  of two subroutines TKER andj D1D2 (see Appendix B, pp. 158, 159,
i61>.J-o.'  .Returned values from those subroutines include the P and T
feesmeiSI  along $treasjline velocity UUU and slope M and the diffusivities
in  each direction Dl,  D2.  (Subroutines will be described in more detail
in  the following,section.)  The segment of the integrals for each JJ value
are summed  iteratively in arrays PHI(JJ), TEE(JJ):
                I
          PHI(JJ)  = PINT «• PHI(JJ-l)
          TEE(JJ)  = TINT + TEE(JJ-l)

These arrays  are the line integral values along the streamline from the
source XS to  the position S2(JJ) along! the x-axis without multiplication
by  the diffusivities Dl, D2.  As described earlier (Section 5.5, Equa-
tions 5-6 and 54-17), effective diffusivities are defined at each downwind
distance  (or  constant values are prescribed, Cl, C2).  The  and T integrals
at  distance S2(JJ) along the x-axis are given by:

          PHID(JJ) = PHI(JJ) * Dl
          TEED(JJ) = TEE(JJ) * D2

This procedure continues for JF iterations and proceeds along the x-axis to
a position  of S2(JF) = AINT(XS) + JF*D£L.  By choosing an appropriate value
of  XL  (say, one hill height along the positive x-axis), calculations are
performed alonglthe windward trajectory and terminate after passing the
obstacle  crest to the leeward side.   I

A3.5 Compute Sigmas,  Centerline and Ground-Level Concentrations  (E)

     Beginning 6n line 101, parallel calculations are begun to compute
dispersion  coefficient estimates and centerline and ground-level concentra-
tions as  a  function of downwind distance from the source for two cases:
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          a flat terrain situation,  with the given stack parameters and   —
          stability class  (left branch in flowchart, Appendix B, p. 156 and
          157 )  and
             2)    the analogous situation with
                  "	  ""	  = -XS (righ
distance DDW(JJ)
                                        the obstacle centered at downwind
                                       t branch).
                                       p;£iH2i enfcs-used -ere-the--
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PGT "flat" terrain values  evaluated asi SIGZM(JJ) and SIGYNH(JJ), respec-
tively, while centerline and ground-lej/el concentrations are computed using
the Gaussian solution  (Equations  5-7 apd 5-20) with height above the surface
taken as a constant value  given by the! effective stack height MS.
     To evaluatfe the functions  in the presence of the obstacle. Equations
5--20 through S-{25 are  used with the dispersion coefficients SIGZH(JJ) and
SIGYH(JJ) given, in terms of  the $ and IT integrals and along streamline
velocity, US(JJ).  Centerline concentrations, CCLH(JJ), are the coefficients
of the exponential term in the Gaussian solution and ground-level values are
cosputed by multiplying the  centerline; values by a factor equal to 2.0 times
the exponential'tena using the appropriate SIGZH(JJ) and height of plume
^fnteriiue above surface,  ANS(JJ>-.-~~This -height—is-det«minsd by -subroutine^
SURF, which computes the distance from! the surface along the normal to the   j
streamline at a given  x-value.  This subroutine will be described further in !
the next section.                      f                                       i
     After printing out the  required tables of the values described above,   j
(see test cas'e,-,Appendix D), the  program computes off-axis, ground-level
concentrations CGL(JJ,K) by  multiplying centerline concentrations by a
crosswind exponential  expressed in fractional increments of SIGYJi(JJ) up to  |
two standard deviations off-axis.  An integer flag, IY, is set to facilitate j
this additional'calculation  if required.
     If new data is encountered by the; read statement 555, the entire
sequence is repeated commencing at start.  Otherwise, the program proceeds
to line 999 where the  job  ends (EGJ means end of job).
A3.  Subroutines
                i
     This section briefly describes
SURF, and ZITRPL.
                !
A3.1  Subroutine  D1D2
                                             subroutines  D1D2,  PSI2D,  PSI3D,  TKER,
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                This subroutine computes the required values of along-streamline
           diffusivities in the vertical (Dl) and! crosswind  (D2) directions.   Basic
           features of D1D2 are schematically presented in the flowchart  on pp. 158
           and 159  of Appendix B.  It consists of a number  of branches that  perform
           the following functions:
                          |
                e    If thfe branching parameter IFLAG = 0, the calculations are per-
                     formed fcv constant diffusivity values  (statement 80)  specified as  j
                     Cl and C2, for the normal and crosswind diffusivities, respec-
                     tively.
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If a &ffusivity is sought  f^r the "flat" case,  such as in
Section E of the main prograi (see Section A.2.5 above), the value
of th$ parameter H is set:
                          H  = 0.0
         s parameter
    and dispersion coefficients  pre read directly from the PGT curves
    as a function of stability class KST for a given downwind distance"!
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                  If IFLAG $ 0 and  H j<  0.0,  thfc calculation continues, and the
                  distance along  the streamline PS and the advection time PT are
                  computed by  D1D2 using a Tay
                               Si

                        il+1

                                  or series of the form:
                  each time  D1D2  is  called during the Simpson's rule integration
                  schema  {Section A72T4).   Forj each ^JJ interval, it "is necessary "to1-"
                  keep Count of the  integration loop counter I.  When both JJ and I
                  are zero  (at  point -XS), diffusivities are set identically equal
                  to ze^o (statement 75).   For each subsequent 1=0, the initial
                  valv.es  of  PS,PT are set equal to the values PSA(JJ-l), PTA(JJ-l)
                  from the previous  DEL interval integration.  Note that calls to
                  D1D2 are arranged  to increase the x-argument linearly from -XS to
                  BB (the upper limit for any integration segment.)  Therefore, when
                  XX = IjIB (statement 97),  i.e., the upper limit for a particular DEL
                  integration limit  is reached, the value of PS and PT are, respec-
                  tively, the along-streamline distance and time.  The PS value is
                  dimensional!zed and used at the downwind distance x (statement 98)
                  to evaluate dimensional vertical and horizontal dispersion
                  coefficients  for the flat case using the PGT prescription for a
                  specified  KST.   Dimensional diffusivities are then computed
                  (beginning at statement 71) using the dimensional advection time
                  PI.  These are  non-dimensional!zed for return to the main program
                  (statement 90).

              In  this manner  the diffusivities from D1D2 are returned as functions of
        downwind distance at a resolution equivalent to DEL, scaled with respect to
        the  "flat"  PGT values.                 j
                        1                       I
        \3.2  StatementiFunctions:  PSI2D, PSI3D
                                               i
              For given diraensionless x- and z-arguments, the statement functions
        PSI2D and PSI3D  (see Appendix B, p. 160 ) return the dimensionless values of '
        the  two- and three-dimensional stream functions for flow over a half cylinder
        and  an axisynsmetric  hemisphere, respectively.
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             Subrouting TKER
                      •                        i
            This subroutine  computes  the aspejct ratio weighted velocity field
       CUU.W), which is used  to  evaluate slope (M), along streamline velocity
       (UUU), and the P and  T  kernels for a given x-value.  It is called repeatedly
       during the Simpson's  rule  integration 'scheme described in the previous
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       section.
       162
The following steps  are  followed (see Appendix B, p. 161  and
                       I
            «    Velocity  components for two-dimensional flow (U2,V2) are computed
                 from  an analytical expression derived from the two-dimensional
                 streams function for given x ^nd z.  (Subroutine ZITRPL is called
                 by setting  argv^aent ND = 2 to obtain the appropriate z-value along
                 the two-dimensional streamline).
            9    An analogous  computation is performed for the components of the
                 corresponding three-dimensional velocity field, first calling
                 ZITRPL  (X,  NINC, 3, Z) to provide the height along the three-
                 dimensional streamline.
           -«	The aspect  ratio "weighted velocity field is" computed" from weighting;
                 factors KV2,  WV3 (see Section 5.2.1):

                       UU = WV2 * U2 «• WV3 * U3
                       VV = WV2 * V2 + WV3 * V3
                    9-1 •„•                     I
                       I                       I
            •    Slope M:

                       y =  w/uu

            o    Finally,  the kernels P and T! are computed for each x within the
                 integration,  in addition to along-streamline velocity.
                                              I
        A3.4 Subroutine  SURF                 )
                                              i
            SURF is  called during evaluation of ground-level concentrations to
        compute the distance  between the plume centerline given by  the streamline
        equation for  a  given  x-value and the surface.  This distance is defined as
        the length  of the  line segment normal to the streamline at  point  (S3, ZEE)
        and intersecting  the  surface.  The point of intersection with  the surface
        may fall into oae of two regions:     j
                       ,                       I
             (1) before  the  windward and after the leeward edge of the obstacle
                  (AXINT  >  1.0); i.e., in the flat part of the topography; or
                                              1
             (2) on  the  obstacle AXINT < 1.0 |
                       ;                       !
             In the first case, the  intersection point XINT obeys the  equation of
        the line normal to the streamline at point  (S3, ZEE)  (i.e., has the negative
        reciprocal  slope  SLO) and has a  zero z-value.  For the second  case, the
        intersection  point XT,ZT obeys the equation of the same  line and  also the
     .,£- equation of the circle defining  the surface in the x,z plane.  For both
OF TEXT "^teases,  the  value  ZNS is calculated from the basic geometric relationship for
       j~the"~dlstance  between~two~points	    i                                      ^
       ,     %'^"      7
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                     ahi'fe-'ifoiii^ifilrrf1* -'^-^'"''^""•sJ"

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    5  Subrouting ZITRPL

      This  is  a sample linear interpolation routine that returns the z-value
  (ZEE) for  any given x-value (SX) within the range defined by arrays FITX(MD,  j
  II), FITZ(ND, II) of NINC discrete, x-iand z-values, respectively, defining   j
  the ND-dimensional streamline C^D equals 1 is the aspect ratio weighted     	j
^Streamline).   Since only positive definite values are stored in these arrays J

  of the  argument is taken.  A DO loop searches down the FITX(ND,II) array in
  order of descending x-magnitude by incrementing the argument until the
  [condition:      i                       i

            FITX(ND, KP1) £XX <_ FITX(ND.K)                                     j

  !is met  at  which point control passes to statement 2 and the DO loop is        j
  [terminated.   At this point, a linear interpolation for the appropriate z-     \
  |value  ZEE  is  performed, and ZEE is returned to the calling program.           j
                                                                                i
TOP OF
IMAGE
AREA
                                                 146
             EPA-287 \Cm.

-------
    APPENDIX B




PROGRAM FLOW CHART
          147

-------
'•'. TYPING iSU IDE SHEET

                Read Input Values
             XS. HS, HA. XL, ALAM,
             DELICT, KKST. FROUDE
                       
-------
     TYPING GUIDE SHtET
                                    CENTER
                                   OF PAGF.

  A.   Compute Streartilirts and Velocity Field Aspect
       Weighting Factors for fSSeutrsl Flow.
t
a
     Enter  vj Tast for 20/30
     fcnter  >&| Umitir,g Cases
                  Streamline Weighting

                  WZ-1.0/ALAM"1.1
                   Velosity Weighting

                     Compute BETA
                     Compute SUP
             = 2.0' (SUP -1.5)
        WV3 = 2.0* (2.0 - SUP)
149
                                             TOP OF
                                             IMAGE
                                                                               -i DIMENSION
                                                 iLu'JS-

-------
       TT**- •^:?g''^V^*W^^?B-'^''ff'V*fl'^j^^

FIRST            TYPING GLHDE SHEET
LINE OF                   -j
TEXT   r	_	     '..	
HcRE J*-    '     ~     T~~
  DROPPED
  HtAD,
I   LASTLir.EL
I   OF TE/,1 ^"*~
                                                 CEWTER
                                                 OF PAGE
               Bl. Spscify Both 20 & 3D Streamline through Source for Neutral
                   Flow; Weight by Aspect Ratio
                                            Compute Value of
                                         Stream Function through
                                          PSIP2D (XS, HS, U, A)
                                          PSJP3D {XS, HS, U, A)
                                           Compute ZC:Z VaSue
                                          of Maximum Streamline
                                           Deflection sbov® Crest
                                               at XX = 0.0
                                           Compute H1:Z Vaiue
                                             of Streamline at
                                               XX =100.0
                                         Solve Streamlirta Eqn:
                                          XX = XX (ZZ. PSiPJ
                                        Using NINC Values of 2Z
                                          « With INC2 Values:
                                          H1 < ZZ < (ZC + HS)/2.0
                                           « NIESSCMI Values:
                                          (ZC + HS)/2.0 < ZZ < ZC
                                                   150
                                                                                          "Z]
TOP OF
IMAGE
'AREA

-------
 BEGIN
 FIRST
 LINE OF
 TEXT
 HERE  as
DROPPED
HEAD
B£G!N
SECTIOM-
HERE   !*?*-
BEGIM
LAST LI I if I  _
OP TEXT &**•
TYPING GUIDE SHEET
;__  x_ .
   EPA 267
                               CEMTER
                               OF-PAG.?
                    82.  (Continued)
                            Values in FiTX.Z
                                                   F!TZ«2,
                            FITXJ3. !
                            FITZ(3,
                                FITX(2or3.
                                       = 0.0
                                               Weight f^sutrsl Streamline
                                                   by Aspect Rstio
                                                                    , II)
                                                Call Subroutine ZITRPL
                                             Find Z Value ol 2D S.F. ZEE2
                                             Corresponding U> FITXd, li)
                                                         ^Return
                                               WEIGHT 2D/3D Z Values
                                          ZZ = (1.0-WZ) * ZEE2 + WZ ' FITZJ3.II)
                                                  Store Weighted S.L.
                                                   FITX(!,H) = XX
                                                 151
                                                                                       TOP OF
                                                                                       IMAGE
                                                                                       AREA
                                                                                              i
                                                                              BOTTOM OP
                                                                              IMAGE AREA;
                                                                              OUTSIDE
                                                                              DIMENSION
                                                                              FOH TABLES
                                                                                  ILLUS-
                                                                              TRATIONS

-------
""BEGIN
  FIRST ,
  LINC ~
, /^ \^^j^^~i^~-''~^vfv^>if'^v^^f^w^yKif',^fM* 'j-|^»Tu*'."'^y"J/yr|y>?gj^JfTiyy'y!~i^p^' I^-M^T"! •> 'n'jm •

 TYPING GUIDE SHEET
           C.  Compute Empirics! StraamBna Depasssfon Due to Stability
                                                                                             ^
                                                                                  TOP OF
                                                                                  IMAGE
                                                                                  'AREA
 DROFPt
 HEAD;.
 BEGIN i
 SECT1G
 HFRE  i
 BEGIN
 LAST L
 Oc TEX
                   Weight S.L. Depression
                   by Froisc'a dumber
                                       Compute Frouds #
                                         Corrected Z at
                                         Crest Based on
                                        Fit to Empirical
                                        Data : ZCF
                                      Compute Depression
                                          at Other XX
                                      Compute Fractional
                                         Depression at
                                         XX : FRAC3
                       Assume Same
                    Fractional! Depression
                         for 2D and
                        Aspect Ratio
                       Weighted S.L.
FITZ'(3, II) l
1 FRAC3
FITZ(2.II)-
  FITZ{2, II) * FRAC2
FiTZ(i.ii)=
  FITZ(1, II) ' FRAC3
                                                                                                     FOR TAPLFS
                                                                                                     Af'JD ILLUS-
            (4-70

-------
 BEGIN
 FIRST
 LINE OF
 TEXT   .
 HERE S
DROPPED
HEAD;
BEGIN
SECTION
HCrlh
BCGIM
LASTLINF|_
OF TEXT 3fi-
TYPING GUIDE SHEET
                 01. Perform along Streamline Line Integrals
           EPA-2&7 (&
           (4-761
                                         Set Up Intention Parameters:
                                       D5EL= Nondtmensional Resolution
                                              of Output
                                       JF  = # of integrations Given by
                                              Region of fnterest from
                                              Source {at XS) to Downwind
                                              Position (XL)
                                       FN = # of Resolution  Points within
                                              Each DEL interval
                                           Begin Integration (JJ = 1, JF)
                                             Upper Limit on X Axis
                                             B = AINT(XS)
                                                                    Lower Limit
                                                                     AA=XS
                                                   Lower Limit
                                                       BB-DEL
                                                        Integration Interval
                                                          Zero Summation
                                                             Variables
                                                     SUM 5 = 0.0 ; SUMS = 0.0
                                                      SU!Vi8 = 0.0 ; SUSV89 = 0.0
                                                           Initialize Loop
                                                             Counter
                                                               1 = 0
                                               „•:; 153  ;,
                                               f: -,!- r,',"•.'',.'-.'•<
                                                                                TOP OF
                                                                                -IMAGE
                                                                                A.
                                                                                ARC A

-------
 BEGIN
 FIRST
 LINE Of'
 TEXT   ^
 HERE

UROPPED
HEAD.
BEGIN
'SECTIONS
H[FiE  i5
    TVPJNG GUIDE SHEET

D2. (Continued)
             Evaluate Integral
             Kerne! Values at
             Lower Limit AA
...,••*-

Give X Its Starting
Value for Loop
X = AA + H
^


Continue
*
XPH = X + H
*
Evaluate integral
Kernel Veiues at
X. XPH :
PX, TX, PXPH, TXPH
£
SUMS = SUMS + PX
SUMS = SU?^S + PXPH
SUM8 = SUft^B H- TX
SUM9 = SUMS -6- TXPH
s
/I - /EM •3\\___- ^^ !»
^N°
1 = 1+2
X=X+2«H


D2
                                                                 'Call
                                                                       Subroutine
                                                                         TKER
                                                                      Kernels : P,T
                                                                      Velocity : U
                                                                        Slops : M
                                                                            j Return

                                                                            I  Call
                                                                       Subroutine
                                                                         D1D2
                                                                      Diffusivities :
                                                                         D1, D2
                                                                       Along S.L
                                                                       Integretion
                                                                             Return
                                                                Evaluate Integral
                                                                Kernel Vslues at
                                                                        08-H,
                                                                 Compute Final
                                                                    Integrals
                                                                   PINT, TINT
                                                  154
                      TOP OF
                     .IMAGE
                    TAREA

                    -\
                                                                                  J.
                                                                                                 UOTTOM OF
                                                                                                 11/. AGE AREA,
                                                                                                 OUTSIDE
                                                                                                 DIMENSION
                                                                                                 FOR TABLES
                                                                                                   ^D ILLUC-
                                                                                                 [RATIONS
-'•I
           (4-7&J

-------
 FIRST
 LINE OF
 TEXT
 HERE  £s
DROPPED
HEAD;
BEGIN
so:nor«;s[__
HERE   Stp-
TVPiNG GUIDE SHEE
 BEGIN
 LAST LIKE
 OF TE:XT 3
               4 3/a-
            _  JL_	

             EPft-287 (Cin.
             (is,yr)

D3. (Continue
	 TE!

(Q2J—& jg

F
T

J


CENTER
OF PAGE
	 . _. >
~
4)
Ad$ Previous Iteration
:{JJ)"TINT + TEE(JJ-

IUJ)-PINT
E(jJ)»TINT
4? 4>
Multiply by Effective
Diffusivity :
•HIDIJJt-PHKJJ) "01
EEDUJ) - TEE(JJ) * D
^
VuJosity at JJ = USJJJ)
Slops stJJ = S LOPE (JJ
A
Xu=jX^
^No
05
V
p. 01
!
I
t
1QC
.„.___ 	 	 „
-1)
', 	 ^
2

)
mi)

TOP OF
(MAGE
"AREA
BOTTOM OF
IMAGE AREA;
OUTolDE
DIMEiJSION
TOR TABLES
f-AND ILLUS-
TRATiONb

-------
FIRST".
LINE OF
TEXT
HERE
DROPPED
HEAD;
BLGIN
SECTIONS
HERE
                 ,^^

                 TYPING GUIDE SHEET
                                                           ^TZrrnT&f r~e-rr-- tr_-~-f
                                                 CENTER
                                                OF PAGE
           El.  Compute Sigmas, Centerline,. and Ground-Level Concentrations
                                     Do Loop for Concentrations
                                     Set Up fJecesssry Parametsrs
                                    for Each Downwind Distance:
                                        DDW(JJ) ;JJ = t,JF
                  No Obstacis
             Evaluate Diffusivities:
                  Ca!IDtD2
               Compute 0 and T
                 Integrals W hen
              No Obsts:!© Present
               Compute Crosswind
                  and Normal
             Dispersion Coefficients
               Compute Centerline
                 Concentration
                                                                         Obstacle
                                                                  Compyte Distance from
                                                                   Surface to S.L. at S2JJ
                                                                  Call Subroutine ZITRPL
                                                                   Call Subroutine SURF
                                                                  Compute Crosswind and
                                                                Normal Dispersion Coefficients
                                                                    Compute Centerline
                                                                       Concentration
                                                                                                TOP OF
             Compute Ground-Level
                 Concentration
           EPA-237 iCin.i
           (4-76)
                                          Print Out Results
ifl
Compute Ground-Level
Concentration


                                             ^ 156    „
                                                                                                   'TOM OF
                                                                                                   ,GE AREA,
                                                                                                   rsiDE
                                                                                                   IENSION
                                                                                                   ! TAELLS
                                                                                                     ILLUS-
                                                                                                 7MAT IONS

-------
?'
'BEGiN
 FIRST
 LINE OF
 HERE »P~
        !
DROPPFD  j
HEAD,   !
BcGIN   |
SECTIONS j__
HERE
      T-
LAST LM\!"L
OF TEXT ?i-
                  "''!:'~^^                            •r*r^m
                   • •:<•.•-'.•••'• •-  .-;  •• .- • •-.'•  \ ' ,   ,-•  ,--
                 TVPiNG GUiDE SHEET
                                                 OF PAGE
                   Compute Sigmas. Centerlin©, and Ground-Level Concentrations (Continued)
                          ¥
                                          Compute Off-Axis
                                            Ground Level
                                           Concentrations
                                              Print Out
                                              Off-Axis
                                           Concentrations
  TOP OF
  IMAGE
T 'AREA
                                                                                                    LOT TOM OF
                                                                                                    IMAGE AREA,
                                                                                                    OUTSIDE
                                                                                                -—I DIMENSION
                                                                                                  ' 1-09 TABLGS
                                                                                                    AND ILI.US-
                                                                                                    TRATIOi-iS

-------
 FIRST
 L)NE OF    Subroutine D1D2 (KST, U, XX, 01. 02, XS. IFLAG, C1. C2. M, H. JJ, I. BB, HA. DO)
 TEXT
 HERS
                                                                       •POP
DROPPED :
HEAD;  '
BEGi.'vl  ;
SECTIONS
HERE   a
Data Statements
 for Dispersion
  Coefficients
                                                   Constant Diffustvitiss
                                                   Dt = C1/(HA * U0»
                                                      = C2/
-------
TYPiMG QUIDS'SHEET""•"
               Subroutine D1D2 (Continued)
                         Dimensionatize X:
                            X = X * HA
                       Go to (10. 20, 30,40, 50, 60), KST
                       Compute PGT Sigmas:
                        For Appropriate Class
                          SZ = S2«KST, X)
                          SY = SY(KST, X)
                         Convert M to KM
                           SZ = SZ/1000.
                           SY = SY/1000.
                         Dimensionaiize PT
                         P1 = PT ' HA/UO
                        Compute Dimensional
                         Diffusivities D1, D2
                         Nondimertsionalize
                            Diffus'^ities
                            •^ Return^)


                           ;L   159

-------
TYPING GU'DE SHEET
                                                                          TO? OF
                                                                         , IMAGE
      Statement Function PSI2D (X. 2. U. A)
                                 -A2/(X2
ReturnJ
      Statement Function PS13D (X, 2, U, A)
      ( Enter
                               160
                                                                                '.i G
                                                                                MO
                                                                                ,ti J
                                                                                LU
                                                                                \5

-------
BEGIN
.F.RST
LINE •>
TEXT
TYPING GUIDE SHEET
                Subroutine TKER (X. Z, A, Y. P. T, RX2, UUU. M. WZ2, WZ3, WV2, WV3)
                                        Evaluate Z{X) along 2D
                                            Streamline:
                                     CallZITRPUX. NINC.2.Z)
                                    Evaluate (U2, V2) Components
                                         of 20 VeEocity FieSd
                                            Given Z(X)
                                        Evaluate 2(X) along 3D
                                            Streamlirss:
                                     Call ZITRPL (X. NINC. 3, Z)
                                    Evaluate JUS, V3) Ccsmponents
                                         of 3D Velocity Field
                                            Given Z(X)
                                        Weight Velocity Fields
                                       According to Aspect Ratio
                                        UU| = IU2 U3\ |WV2|
                                          til   \V2 V3f 1WV3|
                                          Slops M = W/UU
                                       RX2 = W2 ' BX2 + t -
                                          Evaluate Kernels1
                                               M* VV) •
                                         Along S.L Velocity:
                                   UUU = SQRTJUU °* 2 + VV ** 2)
                                                                    Call
                                                           zi;
                                                           fzF
                                                                          TOP OF
                                                161

-------
 BEGIN
 FiKSf
. Lir'JE OF
G GUIDE SHEET
                Subroutine SURF (S3. ZEE. SLD. A. ZMS)
                   Enter
           Evaluate X Value of
          Intercept of Line 1 to
          S.LatXVAL =S3:
                 X!NT
                             Solve for Point (XT, ZT):
                              Interaction of i to S.L
                                and Circular Surface
                           ZNS = SORT ((XVAL - XT»"2
                                 + (ZEE-ZT)«*2)
                                                         Doss not Intercept
                                                         Surface of Obstacle
                                                            = SQRT(ZEE**2
                                                           (S3-XINT)"2
                                                                      TOP OF
                                      Return^
 -ACT Lirj£i_	
 OF TEXT XV-
                                           ^  162
                                            r1 / , - d ; '-1- '•..''


-------
 BEGIN
 FIRST
 LINE CF
TYPING GUIDF SHEE1

                                                                      TOP OF
                                                                     , IMAGE
H   Subroutine ZiTRPL (SX. NIWC. ND, ZEE)
 CF TTX"1"
                          XX = ABS (SX)
NINCMt
= ^ssNc-
1

                        001 K=1,N!fSSCM1
KP1 = K
+ 1
                 FITX«ND, KP1> < XX < FITX(MD.
                                                XD = (FITXtND. K)-XX)/
                                                      (FITX(ND. K» -
                                                      F!TX«ND, KP1»)
                                                               ZEE= FITZ(ND, K) +
                                                                     XD*(FITZ(ND. KP1)
                                                                     FITZ(ND, KU
                                                                          Z2
                                                                          \/
                                                                                    "\
                                              163
           EPA-237 'C-.r.!

-------
      APPBJDIX C
SOURCE PROGRAM LISTING
           164

-------
BEGIN
F'PST
LINE-OP
TLXT  ''
       TYPi^G GUIDE SHEET
                                   CEflTER
                                                                              TOP OF
/ /  KSQLEVEL«-1, CLASSES. TI ME»20
/•ROUTE  PRINT RMT22
//  EXEC FTG1CLG. REGION. GO100K, TIME. G0<=20, PARN-'NOSOURCE, NOMAP'
//FORT. SYSIN DD  *
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
**»»» ERT MODEL   "CPSPLX"   :
*****
VERSION UPDATE 2. 1 JAWARY
 GAUSSIAN DIFFUSION MODEL.
 TERRAIN.
1980
                                                                     COMPLEX****
               THIS PROGRAM COMPUTES THE POTENTIAL FLOW PARAMETERS OF AN OSSTACL
               OF ARBITRARY ASPECT RATIO IMBEDDED IN A MEAN FLOW OF VELOCITY UO
               WITH GIVEN STABILITY CLASSi  KST.
               A TURBULENT PLUME IS IMBEDDED IN THE POTENTIAL FLOW (HUNT AND
               MULNERN.1973)
               R.  C.  ISAACS,  ERT,INC.
                                        1978
               MODIFICATIONS ACCOUNT FOR WIND TUNNEL DATA FOR INTERMEDIATE
               ASPECT RATIOS BETWEEN SPH£RE(CONE> AND CYLINDER (TRIANGULAR
               RIDGF).

               D. C. STRIMAITIS,  ERT INC.   1979

               INPUT PARAMETERS REQUIRED
               XS    - DISTANCE OF SOURCE UPWIWD OF THE CENTER OF THE OBSTACLE
               HS    = PLUME HEIGHT (KM)
               HA    = HEIGHT OF OBSTACLE (KM)
               XL    * UPWIND DISTANCE OF RECEPTOR FROM CENTER OF f>l>jTACLE  (K«>
               ALAM  = OBSTACLE ASPECT RATIO
               DELINT= DOWNWIND RESOLUTION  (KM)
                     NOTE: L(XL-XS)/DELINT3. LE. 50
               PKST  - PGT STABILITY CLASS  (REAL)
               FROUDE= FROUDE NUMBER (U/NH)

               OTHER DEFINITIONS
               UO    = FREE STREAM VELOCITY
               ND    = DIMENSION (2 OR 3)
               YS    = DISTANCE OF SOURCE DISPLACEMENT FROM AXIS Oc SYMMETRY
               PSIP  *• VALUE OF STREAM FUNCTION AT SOURCE
               PSI   = STREAM FUNCTION FOR OBSTACLE (PSI2D OR PSI3D)
               1FLAG = SWITCH CONTROLLING DIFFUS I VI TY CALCULATION
                       IFLAG " 1 .  DIFFUSIVITY VARIES W/ X; =• 0 : CONSTANT
               Dl    - DIFFUSION COEFFICIENT  IN  'N' DIRECTION (COMPUTED)
               D2    » DIFFUSION COEFFICIENT  IN  'GAMMA' DIRECTION  (COMPUTED)
               Cl    = DIFFUSION COEFFICIENT  IN  'N' DIRECTION (CONSTANT)
               C2    = DIFFUSION COEFFICIENT  IN  'GAMMA' DIRECTION  (CONSTANT)
               IY    o SWITCH FOR OFF AXIS CALCULATION; =0( NOT COMPUTED) ; =1 (COMPU
       CALL ERRSET(£08, 400, -1, 1 )
       SPECIFICATION STATEMENTS
       COMMON FITX(3, 600),FITZ(3, 600)
       COMMON NINC
       COMMON ZC, XS
       DIMENSION PHI (50), TEE (50) , US( 50) , R2S( 50)
       DIMENSION PHID(50), TEEIK50)
       DIMENSION S2-'50>, DDW(50), ANS( 50) , SIGZNH( 50 ) . SIGVNH( 50) , CCLNH( 50),
      1CGLNH(50),SIGZH(50),SIGYH(50),CCLH(50), CGLH(50), FNH( 50 > , FH(50)
       DIMtNSION FLUXNH(SO), FLUXH(50>, TFACNH<50>, TFACH(50)
       DIMENSION R(20>
       DIMENSION SLOPE (50)
       DIMENSION YD( 11), CGH50, 11 ). YYD( 11)
       DIMENSION A0(7>- Al <7>, A2(7>, ZCFl7>
                                     165
                                                                                         TTOM OF
                                                                                         5.GE AREA;
                                                                                         TS IDE
                                                                                         iltlvSION
                                                                                         R TABLES
                                                                                         :D H.LUS-
                                                                                         VflONS
                                       C

-------
 BEGIN
 FIRST
 l.iNE OF
 VEXT
 HtRF JB
DIlOPFED
HEAD
flEG'M
JECTiONS
HERL   SB
     TYPING GUIDE SHEET
                                                                             . TOP OF
      REAL  MX.MXPH.MA.M3.MBKH
      DATA  AO/-0. 070.-0. 040,-0. 042,-0. 052. -0 040,-0. 533. -0 476/
      DATA  Al/0. 189. 0. 105, 0. 105, 0. 103, 0. 052, I 047, 0. 924/
      DATA  A2/0. 174, 0. IBS, 0. 142, 0. 141, 0. 173, -0. 418, -0. «09/
C     "•i~ "• ~ ••—™* —— ———————••"••—•»«••••.—-—••———.-»...»_______ ——_——__•_»_____________ _,^_
C     FORMAT STATEMENTS
200   FORMAT(SFIO. 3)
201   FORMATdOX,8dPE12. 3))
202   FQRMATdOX. 13, 4(1PE12 3, 5X»
203   FORMAT(2(1PE12.  3»
204   FORMAT dKO, 3X.  'COEFFS.  =  ', 1P10E11. 4, /. JOX, 1P10E11. 4, /)
205   FDRMATdOX.2dPE12. 5»
206   FQRMAT(Il)
207   FORHATdOX. 1PE12. S>
208   FOSMATOOX. 12)
209   FORMAT('l')
210   FORMAT(49X. 'DIFFUSION EQUATION SOLUTIONS',/, 15X, 'SIGMA Z,  SIGMA Y
      1PLUME CENTERLIf^E AND  GROUND LEVEL CONCENTRATIONS', /. 1SX,
      2'FOR  AN OBSTACLE OF ARBITRARY ASPECT RATIO',////)
211   FORMATdOX, 'FLOW PARAMETERS './/.T15, 'OBSTACLE  HEIGHT  =',F5. 1.T38,
      1'WIND SPEED - ',F3. 1,T60, 'SOURCE HEIGHT =  ',F4.  2,T97, 'CROSSWIWD DI
      2SP=',F3. 1.//.T15, 'DIST.  SOURCE FROM OBSTACLE CENTER='-F6. 1, T60,
      3'DIST.  OF FINAL RECPTR*»  ',F3. 1.T97, 'ASPECT RATIO', ' = '.F4  1.//T15,
      4'VERTICAL DIFFUSIVITY •=  ', 1PE10. 3, T&O, "CROSSWIND DIFFUSIVITY - ',
      51PE10.3,T97.'KST «  ',13,///)
212   FORMAT(T1O, 'DISTANCE', T25, 'DISTANCE', T40, 'DISPLACEMENT', T55,
      1'SIGMA Z',T70, 'SIGMA  Z'-T85, 'SIGMA Y'.TIOO, 'SIGMA Y',T115, 'WIND SP
      2EED'. /.
      3T10. 'FROM OBSTACLE'.T25, 'FRCOT SOURCE'. T40,  'ABOVE SUSP. '.T55, '(K>0 0
      4BSTACLE)', T70, '(OBSTACLE)',T85. '(NO OBSTACLE)'. T100.
      5'(OBSTACLE) ',/>
213   FORMATdX, 1P08S15. 3)
214   FORMAT(//, TiO. 'DISTANCE'.T25, 'DISTANCE'. T40, 'DISPLACEMENT'. T3S,
      l'CENTERLINE'.T70, 'CEMTERLINE'-T85, 'GROUNDLEVEL',T100, 'GROUMDLEVEL

      3T10, 'FROM OBSTACLE',T25, 'FROM SOURCE', T40,  'ABOVE SURF. ', T55.
      4'COWCEPJTRATION'. T70, 'CONCENTRATION', T85, 'CONCENTRATION', T100,
      5'CONCENTRATION', /, T5S, '(NO OBSTACLE)', T7O,  '(OBSTACLE)',
      6T85, '
220   FORMAT(/,T2, 'DOWMWIND', T60, 'OFF AXIS DISTANCE'./.
      1T2, 'DISTANCE'.T12, 1P11E10. 2-/>
221   FORMAT(2X, 1P12E10. 2)
222   FOf»MATX, 'IY=', 12,  //>
223   FOHMAT(//,3X,'PLUME IMPACTS HILL AND DOES  NOT GO OVER TOP'./)
224   FORfAT
231   FORMAT(6X. 'XS'.SX. 'HS'.8X.  HA'.BX, 'XL'.VX,  'ALAM'.&X. 'DlINT',
      16X, 'Rt
-------
BEGIN
FIRST
LINE 01
               TYPING GUIDE SHEET
                                            CENTER
HERt'T'
         C
         C
         555
         C
         c
         c
         c
         c
         c
         c
         c
         c
         c
         c
         c
          601



          602


          603

          C

          C
          C
               SPECIFY CONSTANTS
               PI»3. 14159
               Cl«2. OE-3
               C2-S.OE-3
               YS=0. 0
               ROOT=0. 0
               AA=0. 0
               BB"0. 0
               A-1.0
               IFLAG=1
               IY-1
               ASSLiME DIKENSIQNLESS VALUE  FOR  BOTH FREE STREAM VELOCITY UO
               AND HO8IZOMTA!- WIND SPEED U
               UO-1.0
               U»l. 0
               READ(5, 200, END*>999) XS,HS,HA,XL, ALAM, DELINT, RKST, FROUDE
               W«ITE(6, 230)
               WHITE(6.231)
               WRIT£<6.2OO) XS.HS,HA,XL, ALAM, DELINT, RKST, FROUDE
               KST»RKST
                IF(FROUDE. EG. 0. 0) KST«-4
                IF
-------
 FIRST            TYPING GUIDE SHEET              '
 LINE OF-"~7'---	•—~™	JOPOF

 l':Xl                                                             '"'*                       1'Vjt
 hFRc S»J    C     PSIP3D" VALUE OF STREAMFUNCTION  ALON8  STREAMLINE IN 3D FLOW             ^A
       >    C     STREAMLINE  EQUATION IN EACH CASE EVALUATED BY SOLVING:
           C     PSI2D(X,Z)  »  PSIP2D OR
       I    C     PSI3D(X. Z)  «>  PSIP3D
fspi'JPr1|"'0  t    ^     _-._
U( VJi  '--'  J    \»     — ' — — — --———— — — — — — — — — — — — — — — — — — -• — -• — — — .•.—• — — .•.— —....-.....— ..____.«.______.._____
HP.VJ       C     NEUTRAL STREAMLINE STORED AS:
gFCIN       c     x     " F1TX(ND. II)
SfCT'OHsf    C     2       FITZ4ND, II)
Hn,r'  ^    C     ND    » 3 08  3 (2D OR 3D)

                 DO 604 N0=2.3
           c     	
           C     DEFINE  STREAM FUNCTION. VALUE THROUGH SOURCE,  AND B
                 IF(ND.QT.2)  ©0 TO 1
                 PSIP=PSI2D(XS. HS, U. A)
                 B=PSIPXU
                 GO TO 2
           1     PSIP»PSI3D(XS. HS. U, A)
                 B=2. 0*PSIP/U
           2     WRITE(6, 203) B.PSIP
           c     	
           C     COMPUTE ZC " Z DISPLACEMENT OF  SOURCE STREAMLINE OVER CREST OF  HI
                 IF(ND. QT. 2)  GO TO 3

                 60 TO 4
           C       SOLVE CUBIC EON FOR  3D  ZC
           3     RADCL*--<*«!. 5»/3.
                  2C=EM*COS(THTA)
           C      SECOND AND THIRD SOLNS LESS THAN ZERO
                  ROOT>---1.
                  GO TO 4
           32O    ZC=1.5874*A
                  ROOT-0.
                  GO TO 4
           330    AA= <. 5»A*»3*SQRT(RADCL » *» <1. /3. )
                  BB=(. 5*A*»3-SGf?T(RADCL) )**
       j           ZINC2^(HLFPT-H1>/INC2                                                              ,
       \           ZINC1-/NINCMI                                                  T1OM OF    5
       j           WRITE(6,201> PSIP.B,ROOT,AA- DB, ZC,BETA, HI
 r-c.-j.v   i           NINC=NINC + 1
 L^,:r'l p,(-|           DO 100 1 = 1, NINC
 „/-.'"(•           IF(I. GT. INC2) GO TO 9
 or i L < f s*
       i       .•? -                        ":
       ]__  | "'"_  __  |	  __.  _.^.168   		~_  —i

          EPA-^87 (CiM.)                                   /  ' |
          ("3-7&I                                    ;     ^

-------
DROPPED
HEAD.'
                TYPING GUIDE SHEET

                                                                                         TOP OF
                                                                                        -IMAGE
 ZZ«H1+J«ZINC2
 CO TO 10
 J=I-INC2-1
 ZZ-HLFPT+J«ZINC1
 CONTINUE
 IF(ND. GT. 2) GO TO 5
 1FCZZ. EG. HI) GO TO 61
 ARG»»   ( )
 GO TO 6
 IF(ZZ. EQ. HI) CO TO 61
 ARG=>   < (A«»3/(i. 0-B/ZZ**2) )»*(2. 0/3. O>-ZZ»«2>
 IF(ARG. LT. 0. 0) GO TO 7
 XX«SGRT(ARG)
 GO TO 8
 XX    <• 100.  TAKEN AS EFFECTIVE INFINITY
 XX=100.
 GO TO 8
 XX=0. 0
 ZZ-ZC
 CONTINUE
 11 = 1
 FITZCND, 1I)=ZZ
 FITX(ND, II)=XX
 FITX(ND, NINC>=0. 00
 CONTINUE
 CONTINUE
 »*•«• B-fr-t
 WRITE<6, 218)
 THIS LOOP  (DO 605) WEIGHTS THE NEUTRAL STREAMLINE WITH
 ASPECT RATIO USING WZ
 DO 605 II=1,NINC
 XX=FITX(3, II)
 FITXd, II)=XX
 ZITRPL= SUBROUTINE PROVIDES Z  INTERPOLATION FOR ANY X VALUE
         GIVEN STREAMLINE  IN FITX (ND. 1 1 ) . FITZ  IFR=1
 IF(Ff»nuDE. GE. 1. 10. AND. FROUDE. LT. 1 50) IFR=^2
 IFCFROUDE. GE. 0. 92. AND. FROUDE. LT. 1. 10) IFR=3
 IF (FROUDE. GE. 0. 83. AND. FROUDE. LT 0 9
                                       IFR=4
                                       IFR-5
IF'FRQUDE. GE. 0. 40. AND. FROUDE. LT. 0. 70)  IFR=6
                                                        )
                   IF t FROUDE. GE. 0. 70. AND. FROUDE LT. 0. 83)
                                                        )  WRITE(6,:
                                                        1  WRirfc<6,223>
 IF((-ROl«PE. LT 0. 40
 Ih"( IFR. I.E. 5. AND HS. LT  0. 3VS
 IF< IFR. EQ. 6 AND. HS. i.T  0. 75
 IF ( IFR. EQ. 7. AND HS LT. 0. 82
 URIIE'6.224> IFR
 CALCULATE THE  TOW-TANK ZC  AND CHFCK THAT IT EXCEEDS THf HILL HcIGHl
 ZCF< IFfy ) = 1 -KAO( IFRl+Al ( IFR )»HS+A2< IFR)tftS**2)
 IF(Zi'.F( 1FW). LT. 1.  )  ZCF(IFR) = 1. 001
 DELMAx=FITZ(3.NINC>-ZCF(IFR)
 DO 60cv 11 = 1 , NINC
                                              169


-------
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fiff-'lV
USUiME C
Cf TEXT J
; j ~~^~, - -U— -

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TTTf HTCjnaVJllJC "Oncer-"""'-- •» • T -tr«-— i^"-- ^T-TTT- — »T7 ^:.-":"™--'i"--'-—?-«--~i> -^..r^.,,,,-,^,. ,_^___,-.-. „,,_,„_-„„-
CENTER ' " 	 - " " '•• '
~ 	 . 	 _
XX»FITX(3, ID
IF. LT. (DEL/2. 0» SS»>0. 0
S2(JJ)=SS
INTEGRATE FOR EFFECTIVE SIGMA Y AND Z SQUARED
NUMERICAL INTEGRATION BY SIMPSONS RULE
ADAPTED FROM DQRW AMD KCCRACKEN 1972
SET UP INTEGRATION PARAMETERS
NN=100
FN=NN
AA=SS-DEL
IF(JJ EG. 1) AA=*XS
H=(BB-AA)/FN
TWOH^2. 0*H
SUM5-0. 0
SUM6=-O 0
SUM8=--0. 0
SUM9-0. 0
1=0
CALL TKER(AA, ZA, A, Y, PA- TA, RA, UA, MA. HZ. WV2, WV3 )
CALL D1D2
-------
        ^^^fmWG-GUnre sHttr-
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                                           CENTER
          C
          29
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          28
          92
          93
21
101
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c
c
c
                INITIALIZE  LOOP COUNTER
                1-1
                BEGIN  INTEGRATION
                CONTINUE
                XPH-X+H
                CALL TKER
                 TEE < J J ) =T I NT-t-TEE ( J J- 1 )
                 TEED ( J J ) =TEE ( J J ) «D2
                 PHID( JJ)*>PHI ( JJ)*D1
                 GO TO 93
                 TEE(JJ)=TINT
                 PHK JJ)=PINT
                 PHID( JJ)=PHI ( JJ)*D1
                 TEED ( JJ ) =TEE < JJ ) *D2
                 CONTINUE
                 US( JJ)=UB»U
                 R2S(JJ)=RB
                 SLOPE (JJ>=MB
                 CONTINUE
                 CONTINUE
                 #**« fr*«t»»»«»»***9»«»*fl.«»»**«-»*»**»*6****«-«-*««»»»«**«a «•***«••»»«•*»*
                 COMPUTE SIGMAS, CE.%!TERLINE AND GROUND LEVEL CONCENTRATIONS
                 WITH THE OBSTACLE AND WITHOUT THE OBSTACLE AS A FUNCTION OF
                 DOWNWIND DISTANCE

                 FLAT TERRAIN VALUES
                 DDW   = DOWNWIND DISTANCE FROM SOURCE
                 SIGZNH= NORMAL DISPERSION COEFFICIENT (NO OBSTACLE)
                 SIGYNH= CROSSWIND DISPERSION COEFFICIENT (NO OBSTACLE)
                 CCLNH = CONCENTRATION . CENTERLINE 
-------
                            SHEET"
 LINE OF  —
                                            CENTER
 Hhf!E
HEAD'
      DO 102 JJ-l.JF
      DDWtJJ>=B2-XS
C     EVALUATION  : NO  OBSTACLE (NH)
      P-PHID(JJ)
      T-TEED(JJ)
      U1»US(JJ)
      R2=R2S
      CALL D1D2
      TEENH»D2»DDW < JJ)/< U»HS»«2)
      SIGZNH-= SQRT<2. 0*HS»*2*TEENH>
      CCLNH=<1. 0/(4. 0*PI ) >
      ARC3=HS*«2/(2. 0***2)
      IF(ARG3. GE. 179.5 >  GO TO 70
      CGLNH(JJ)=CCLNH
      SIGYH
      IFCS3  EQ. 0.0)  GO TO 17
C     CORRECTION  FOR  FIT MADE OVER HILL BY INTERPOLATING FROM EXACT S. F
      IF(ABS
      ANS=?. 0»CGLH(JJ>
      GO TO 73
 77    CGLH(JJ)=1  1E-78
73    CONTINUE
      FNH(JJ)=CGLNH(JJ)/CCLKH(JJ>
      FH(JJ>=CGLH(JJ)/CCLNH(JJ)
       IF(FH(JJ). LT. 3 OE-76) FH(JJ)=3. OE-7^
       IF(FMH(JJ)  LT. 3. OE-76) FNHfJJ>=3  OE--~'6
      FLUXNH(JJ>=U*SIGZNH(JJ>«SIGYNH*CCLNH(JJ>
      FLUXH(JJ)=US(JJ)*SI&ZH(JJ)*SIGYH'JJ»«CCLH(J.')
                                             172
                                                                           _TOP OF
                                                                            IMAGE
                                                                            AREA

-------
 •JNtOF
 TEXT  _
                            CENTER
  yi 1.1.'j
-,Cf- TEXT
           102
           C
           904
           903
           906
           999
 TFACNH> )/Hb
 CONTINUE
 ~-—"~ — — — «• -- — — «—•—— — — .— •-.-.-..— ___.-._____.M.___ __ _ ____ __ _» — —«._ ___ __ ___ _ — — ___ ___
 PRINT OUT RESULTANT ARRAYS OF SIGMAS AND CONCENTRATIONS
 WRITE<6. 209)
 WRITE<6, 210)
 WRITE<6, 21 1 ) HA, IK). HS, YS, XS, XL, ALAM, Dl, D2, KST
 WRITE<6, 2S2)
 i4RITE<6, 213)  ,ANS,SIGZNH,SIGZH,
1SIGYNH. JJ=1, JF)
 WRITEC6. 214)
 WRITE<6. 216)  (S2(JJ), DDW( JJ) . ANS( JJ), CCLNH( JJ), CCLH< JJ),
ICGLNH(JJ), CGLH(JJ),  JJ«1,JF )
 WRITE<6, 215)
 WRITE<6, 216)  (S2«=YYD
 CGL(JJ, K)=CGLH< JJ)*EXP<-0. 5*YD(K)**2)
 CONTINUE
 CONTINUE
 WRITE (6, 220) (YYD(K), K=l, 11)
 DO 9O6 JJ=1, JF
 WRITE (6, 223 ) (DDW( JJ), (CGL( JJ, K), K=l, 11 ))
 CONTINUE
 GO TO  555
 STOP
 END
 SUBROUTINE  D1D2(KST, U, XX,  Dl, D2, XS, ITLAG,C1, 02, M, H, JJ, I.BB.HA, UO)
 THIS  SUBROUTINE EVALUATES THE DIMENSJDNLESS  DIFFUPIVITIES Dl AND
 D2 IN  THE Z AND Y  DIRECTIONS .RESPECTIVELY
 REAL  M
 DIMENSION PSA(SO). PTA(50)
 DIMENSION KD(5), AD(6), BD(6)
 DIMENSION XA<7>, XB<2), XE<8). XF(9), AA(8), DA(8), ABO), Bl<3),
1AE(9), BE(9>, AF(10),BF(10)
 DATA  XA/.5, .4, .3.  25, . 2, .  15,  I/
       XB/. 4, . 2/
       XD/30. , 10. , 3. , 1 . , .  3/
       XE/40. , 20. , 10. , 4. ,  2.  , 1. . . 3, .
       XF/60. , 30. , 15. , 7. ,  3.  . 2
                  DATA
                  DATA
                  DATA
                  DATA
                                   I/
                               1. , . 7, . 2/
 DATA AAX 453. 85, 346. 75, 258. 89, 217. 41, 179  52, 170. 22, 158. O8, 122. 8/
 DATA BA/2.  1166, 1. 7283, 1. 4094, 1. 2644,  1. 1262. 1. 0932, 1. 0542, . 9447.'
 DATA AB/109. 30, 98. 483, 90. 673/
 DATA Bl /I.  0971,0. 98332, 0. 93198/
 DATA AD/44. 053, 36. 650, 33. 504, 32. 093, 32. 093, 34. 459/
 DATA BD/0.  51 179, 0. 56589, 0. 60486, 0. 64403, 0 81066, 0. 86974X
 DATA AE/47. 618, 35. 420, 26. 970, 24. 703, 2?. 534, 21 628, 21. 628. 23. 331,
1 2*. 26/
 DATA BE/0.29592,0.37615,0.46713,0.50527.0 S71 54, 0. 63077, 0 7b66C>,
1 0. 81936, 0. S366/
 DATA AK/34  219,27.074,22.651,17.836,16.187,14 823,
1 14 457,  15. 209/
 DATA BF/0.  21716. 0. 27436, 0. 32661. O. 41507, 0 46
-------
 BEGIN
 FIRST
 LINE OF
 TEXT
 HERE S&
DHOPPED
HEAD,
BcGiN
SECTION
TYPING GUIOt SHEET
                                                                         TOP OF
93
96
                          97
         98
         99
         101
         C
         10
         11

         12

         C
         20
               CONTINUE
               IF
               00 TO 93
               IF *H/U
               GO TO 96
               PS-=PSA,KST
                                STABILITY A
                                TH»(24. 167-2. 5334«ALOQ  GO TO 69
                                DO 11 ID"*!. 7
                                IF»8
                                SZ=AA(ID>*X»«BA(ID)
                                GO TO 71
                                STABILITV B
                                TH=( 18. 333-1. 8096»ALQ9(X) )/57. 2958
                                IF(X. QT. 35. ) GO  TO &9
                                DO 21 1D°>1.2
                                IF(X. GE. XB(ID»  GO TO 22
21
i
22

i- 1 c
: so
;

' C
40


• 41
f j
42

C
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51

52

• C
': 60
; BEGIN
! LAST L;ric 	 ,
OF TEXT ^T____^r "l
I
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EPA-?3? (Cin.l
I4-7C.1
^^gfi^iSS^^^^^^^^**^
CONTINUE
ID=3
SZ-AB(ID)«X*»S1(ID)
GO TO 70
STABILITY C
TH=(12. 5-1. OS37&ALOO<8»/57. 2958
SZ=61. 141»X*«K>. 91465
60 TO 70
STABILITY D (NEUTRAL)
TH=<8. 3333-0. 72382«ALOG ( X ) )/57. 2959
DO 41 ID=1.S
IF SO TO 52
CONTINUE

SZ-AE(ID)«X«-*BE
GO TO 70
STABILITY F
TH<=(«. 1667-0. 36191»ALOe
-------
 BEGIN
 HRST
 LINE OF
 TEXT
 HERE
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62

69

70
71
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80

C
102
90
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                                 CBiTER
1D-10
SZ-AF ( ID)«Xt»BF< ID)
SO TO 70
6Z»500O.
SO TO 71
IF(SZ. GT. 3OOO. )  8Z""5000.
SYMOOQ. «X*SSN >
                                                                      TOP OF
                                                                      IMAGE
                                                                      "iREA
      SV«SY/SOOO.
      Dl«SZ»*a/<2. 0*P1
      D2«SY»»a/<2.
D2-D2/
CONTINUE
RETURN
END
FUWTICN PS!2D(K. Z.U, A)
2D STREAM FUNCTION FOR FLOW OVER CIRCULAR RIDGE
PSI2D        «*U*Z«<1. 0-(A««2/ )>
RETURN
END
FUNCTION PSI3D
REAL M
COflHON  NINC
SUBROUTINE WEISHTS VELOCITY FIELD BY ASPECT RATIO

20 VELOCITY FIELD
U2    - VELOCITY IN X DIRECTION
V2    » VELOCITY IW Z DIRECTION
CALL ZITRPL
       R = (X2+Z2>«*. 5O
                                                                      [iOTTOf/ OF
                                                                      IMAGE ARFA.
                                                                      OUTSIDE
                                                                      UiMI-INSION
                                                                      TOR TABLES
                                                                      -A,\D ILUJS-
                                  175

-------
HRST

LINE 'Jr.

TEXT

HF.RE
  TYPING GUIDE SHEET



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         3
                                                                         TOP OF

                                                                         IMAGE
              U3»(l. CH-A3/O. 0««3>-3. 0«A3*X2/<2. 0*R3> )
WEIGHTED V€LDC2TIE8
UU    - VELOCITY  IN K  DIRECTION
W    - VELOCITY  IN Y  DIRECTION
H     • SLOPE
RX2   » D58TAf«E  FROM  AXIS OF SYFOTETRY TO STREAMLINE
UUU   » M.0^9  STREA«.IfS VELOCITY
P     • KERt^EL Of PH!  LIKS INTEGRAL
T     - KERKEL OF T LINS INTESSAL
              M«W/UU
               RETURN
SUiROUTINS BUaF«S3, ZEE. BLQ. A.
THI8  SUEROUTEMS COf^UTES T(« DISTANCE OF THE STREiiWLIMS FROM
TH£ SURFACE CF T(=£ SPHERE  (OR -PLAfiEJ
               XINT»XVAL*SLO«2EE
               IF(AXIMT. LT. A> GO TO i
                               -K IMT ) »«2
               ©O TO 4
               OPOM2-1.
               XFII-.FITZ«3. 60O)
               DO 1 K-1.NINCM1
                                                   .ZEF>
               IFOfX.LE. FITX.AND. XX. CE FI TX »ND. KP1 » GO TO

               CONTINUE
                                              176

-------
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                     RETURN
                     END
              /»
              //GO. FTOSFOOl  DD «
              -3. 2       402      . 279
              /*
              /»EOF
LAST iifir
OF TEXT J&
                                               . KP1 )-FITZ(ND. K> i
                                                        to.
                                                   177
                                                                 . 13
                                                                                       1.05
                                                                                             TOP OF
                                                                                             IMAGE
                                                                                             VJIFA
                                                                                                BO i TOM o:-
                                                                                                IMAGE ARCA;
                                                                                                OLITS10E
                                                                                                DIFFUSION
                                                                                                FOH TABLES
                                                                                                Af-JD ILUI5-
             tFA-23"'
                                                                                                        ^jni^H^i

-------
     APPFNDIX D




SAMPLE OUTPUT LISTING
          178

-------
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                              Hill  Height
                              Pluffle Height
                              Distance Hill to
                              Stability Class
                              Fswde Number
                              Aspect Ratio
                                          .275 ka
                                          .402 ka
                                          3.2 ka
                                          4  (PGT "D")
                                          1.02
                                          10
                                                • 179
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