EPA-600/4-78-013
                                          February 1978
           USER'S  GUIDE  FOR PAL

       A  GAUSSIAN-PLUME ALGORITHM

    FOR POINT,  AREA, AND LINE SOURCES
             William EL Peters en

      Meteorology and Assessment Division

  Environmental Sciences Research  Laboratory

 Research  Triangle Park, North Carolina  27711
 ENVIRONMENTAL SCIENCES RESEARCH  LABORATORY
     OFFICE OF RESEARCH AND DEVELOPMENT
    U.S.  ENVIRONMENTAL PROTECTION AGENCY
RESEARCH  TRIANGLE PARK, NORTH CAROLINA  27711

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                                 DISCLAIMER

     This report has been reviewed by the Environmental Sciences Research
Laboratory, U.S. Environmental Protection Agency, and approved for publica-
tion. Approval does not signify that the contents necessarily reflect the
views and policies of the U.S. Environmental Protection Agency, nor does
mention of trade names or commercial products constitute endorsement or
recommendation for use.
                            AUTHOR'S AFFILIATION

     The author, William B. Petersen, is on assignment with the U.S.  Environ-
mental Protection Agency from the National Oceanic and Atmospheric Adminis-
tration, U.S. Department of Commerce.
                                     ii

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                                   PREFACE

     The Users'  Guide for PAL was written so that one need not understand the
mathematical formulation to apply the model.  However, I strongly recommend
that the user carefully read Sections 2 and 4, which give valuable insight
into the model's flexibility and limitations, and the assignment of values to
input parameters.

     Although the user's guide is complete in itself, the user may wish to
avoid the step of going from the printed page to a computer source program by
utilizing the PAL program in UNAMAP (Users Network for Applied Modeling of
Air Pollution),  either by executing on the nationwide network or by obtaining
the source code  on magnetic tape (Users Network for Applied Modeling of Air
Pollution (UNAMAP), Accession No. PB 229-771, from NTIS, Springfield, VA,
22151).

     While attempts are made to thoroughly check out computer programs with
a wide variety of data, errors are found occasionally.  In case there is a
need to correct, revise, or update this model, revisions will be distributed
in the same manner as this report.  If your copy was obtained by purchase or
special order, you may obtain revisions as they are issued by completing the
mailing form on  the last page of this report.

     Comments and suggestions regarding this document should be directed to
Chief, Environmental Applications Branch, Meteorology and Assessment Division,
(Mail Drop 80),  EPA, Research Triangle Park, NC  27711.
                                     iii

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                                  ABSTRACT

     PAL is an acronym for this point,  area,  and line  source  algorithm.  PAL
is a method of estimating short-term dispersion using  Gaussian-plume  steady-
state assumptions.   The algorithm can be used for estimating  concentrations
of non-reactive pollutants at 30 receptors for averaging  times of from 1  to
24 hours, and for a limited number of point,  area,  and line sources  (30 of
each type).

     Calculations are performed for each hour.   The hourly meteorological
data required are wind direction, wind speed, stability class, and mixing
height.  Single values of each of these four  parameters are assumed  represen-
tative for the area modeled.

     This algorithm is not intended for application to entire urban  areas but
is intended, rather, to assess the impact on  air quality,  on  scales  of tens
to hundreds of meters, of portions of urban areas such as  shopping centers,
large parking areas, and airports.  Level  terrain is assumed.

     The Gaussian point source equation estimates concentrations  from point
sources after determining the effective height of emission and the upwind and
crosswind distance of the source from the receptor.

     Numerical integration of the Gaussian point source equation  is  used to
determine concentrations from the four types  of line sources. Subroutines
are included that estimate concentrations for multiplelane line and  curved
path sources, special line sources (line sources with  endpoints at different
heights above ground), and special curved path sources.

     Integration over the area source which includes edge effects from the
source region is done by considering finite line sources  perpendicular to the
wind at intervals upwind from the receptor.  The crosswind integration is
done analytically; integration upwind is done numerically by  successive
approximations.
                                     iv

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                                  CONTENTS
Preface	i i i
Abstract	iv
Figures and Tables	vi
Acknowl edgments	vi i
     1.   Introduction	1
     2.   Features and Limitations	3
     3.   Organization of Computer Program	7
               General f 1 ow of the model	7
               Structure of program	9
               Description of subroutines and functions	10
     4.   Preparation of Input Data	14
               Point sources	21
               Area sources	23
               Li ne sources	24
               Meteorology	25
     5.   Example Problem	28
References	37
Appendices
     A.   Technical description of PAL	40
     B.   FORTRAN statements	87

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                                  FIGURES
Number



  1



  2



  3



  4
                                                             Page
General f 1 ow di agram for PAL	8



Structure of subroutines and functions	9



Input data deck for the PAL model	15



Source types included in example problem	31
                                  TABLES
Number



  1



  2



  3



  4



  5
                                                             Page
Description of Input Data	16



Stability Classification	26



Exponents for Wind Profile	27



Input Data for Example Problem	32



Computer Output for Exampl e Probl em	33
                                    vi

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                               ACKNOWLEDGMENTS

     The author wishes to express his appreciation to Bruce Turner, who was
responsible for much of the development of the PAL model; to John Irwin and
Alan Huber for their helpful discussions and review; and to Theresa Burton
and Lea Prince for their aid.
                                     vii

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                             1,   INTRODUCTION
     The first two sections of the User's Guide for PAL should be beneficial
 to those determining the applicability of PAL to their particular need.

     PAL is a multisource Gaussian-Plume atmospheric dispersion algorithm for
estimating concentrations of non-reactive pollutants.   Concentration esti-
mates are based on hourly meteorology, and averages can be computed for
averaging times from 1  to 24 hours.  Six source types  are included in PAL:
point, area, two types  of line sources, and two types  of curved path sources.
As many as 30 sources may be included under each source type.   PAL is not
intended as an urban-wide model but may be applied to  estimate the contribu-
tion of part of an urban area to the concentration.  Portions  of urban areas
assessed by PAL for impact on air quality are:
       Industrial complexes
       Sports stadiums
       Parking lots
       Shopping areas
       Airports

     At the heart of PAL is the Gaussian-Plume point source equation (Gif-
ford, 1960).  The equation is used directly in the computations for point,
line, and curved path sources, and in a modified form  for area sources.  The
point source algorithm  is very similar to the point source models provided
                                      1

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on the UNAMAP tape (Hosier, 1975).  A unique feature of PAL is the computa-
tional technique for estimating the concentration from area sources.   This
technique incorporates edge effects and is theoretically more accurate than
the methods used in the Climatological  Dispersion Model  (COM) (Busse  and
Zimmerman, 1973} and the Air Quality Display Model  (AQDM) (Martin, 1971).
The horizontal line source algorithm is similar to the Highway Air Pollution
Model (HIWAY) (Zimmerman and Thompson,  1975).  Input source types also
include two types of curved paths, one  of which considers variation of
emissions along the path.  PAL will also estimate concentrations from a line
source which has a variation in emission along the source.   This line source
may be slanted or elevated relative to  the ground.   PAL offers considerable
flexibility to the user.  Any or all of the six source subroutines may be
utilized.  The user also has the options of employing an hourly variation  to
emission rates and of allowing the wind speed to change with height.   Concen-
tration estimates can be made at up to  30 user specified receptor locations.

     The User's Guide includes sections on the features and limitations for
use of PAL, the organization of the computer program, a description of input
data, and an example problem with computer output.   A technical discussion of
PAL is presented in Appendix A, and a listing of the source code is available
in Appendix B.

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                    2,   FEATURES  AND  LIMITATIONS
     The analysis power available to the user of PAL cannot be appreciated
unless two features of the model are understood.  One feature of the model
concerns the handling of the wind speed.   While the user is specifying the
kinds of source types which will later be input in the problem, the user also
specifies whether the wind speed varies as a function of height.   The wind
speed can be held constant or can be varied as a function of height and
stability class.  The manner in which the wind speed is handled within PAL is
specified for each source type, allowing considerable flexibility.   A second
feature of the model concerns how the emission rates from the various input
sources are determined.   Unlike some multisource models, such as  the Real-
Time Air-Quality Model (RAM) (Novak  and Turner, 1976), the emissions data for
each source type is input into the model  only once and is not initialized for
each hour of meteorology. However, as each hour of meteorology is input, the
user can specify, independently for  each source type, the fractional amount
of the initial input emission rate to be applied.  For instance,  say we had
specified the maximum sulfur dioxide (SCL) emission rate for a situation in
which we had only point and area sources.  From insight into the  situation,
we might know that the point sources contribute most during the daylight
hours from factory emissions, and that the area sources contribute  most
during the nighttime hours from home heating.  We could model  the above
hypothetical situation by appropriately varying the emission factors, in-
dividually for each source type, for each hour of a 24-hour period  (refer

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to Meteorological Data, Appendix A for further discussion).   The wind speed
feature and the emission rate feature are extremely powerful  when considered
with the various restarting options of the program (A, B, and C of Figure 1).

     PAL, as other Gaussian models, is subject to Gaussian dispersion assump-
tions, such as conservation of mass, steady state atmospheric conditions, and
relatively flat terrain.  Complex aerodynamic effects, like downwash from
buildings, are not considered in PAL.  However, enhanced dispersion can be
simulated by modifying the dispersion parameters to account for initial
mixing caused by buildings. The detail which PAL considers, such as edge
effects from area sources and the finite length of line sources, generally
prohibits the application of PAL to an entire urban area due to excessive
computer cost. Also, since meteorological data are entered hour by hour, a
normal run for PAL would be to simulate a period of 1 to 24 hours. Calcu-
lations for more than several 24-hour periods would also be costly.  The
principal use of PAL is to estimate the increase in pollutant concentration
over that due to other sources not included in the PAL computation.

     In Gaussian models concentration estimates are inversely proportional to
the wind speed.  Besides the unreasonably high concentration estimates calcu-
lated during very low wind speed conditions due to this inverse relationship,
there are other modeling difficulties associated with low wind speeds.  Wind
directions may be extremely variable.  Thus, the hour average wind direction
used in the model may well not be a true representation of the wind direction
during the hour. The dispersion parameters used in PAL do not account for
this kind of variability in the wind.  Because of the extreme variability of

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the wind direction, actual concentrations might well  be much lower than model
estimates.  Gaussian models also assume that there is no build-up of pollu-
tant from hour to hour.  That is, the concentration estimate made for a
particular hour is independent of the concentration estimate made for the
meteorology of the previous hour.  However, during low wind speed conditions
pollutant build-up may occur, particularly for an urban area or a section of
an urban area.  A reasonable lower limit of wind speed to use as input into
PAL is 1.0 m sec" .

     Care must also be exercised when computing high  average concentration
estimates to compare with air quality standards, say  for example 8 hours.  It
would be unrealistic to assume that a combination of  wind direction, wind
speed, and stability class would persist during an 8-hour period.  The per-
sistence of the above variables can be obtained from  meteorological  records
and should be used accordingly in the model.

     PAL is designed to make estimates over relatively level terrain.  Re-
ceptor height should not be used in an attempt to simulate topographic dif-
ferences. The height of the receptor is the height of that receptor above the
local ground level, not the height of the ground above some reference plane.

     The Pasquill-Gifford horizontal dispersion parameter values used in PAL
are strictly applicable only to concentration estimates with a 3-minute
averaging time (Pasquill, 1976). An increase would be expected in horizontal
dispersion for averaging times of 1 hour.  As on-site measurements of tur-
bulence statistics become more routinely available and the state-of-the-art

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in dispersion modeling improves,  PAL could be easily modified to incorporate
such advances.  The dispersion parameters in PAL are applicable for rural
environments.  However, a recommendation is made in Section 4 to account for
the increase dispersion in urban  areas by appropriate change of stability
category.  Finally, PAL does not  require any tape drives  or external  files
for storage.  Storage requirements are approximately 27K words.  The example
problem (Section 5) used 21.8 seconds of computer time on the UNIVAC 1110 at
a cost of $0.78.

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               3,   ORGANIZATION OF COMPUTER  PROGRAM
     The general  framework of PAL is  discussed in this section.  It is in-
tended to give the reader a general knowledge of the computer program, rather
than a detailed description of each subroutine.  Such detailed descriptions
are seldom very profitable without an understanding of the source code and
are of little value in the application of the algorithm.  The general flow of
PAL, the structure of the computer subroutines and the computer functions,
and a brief description of each subroutine and function are included in this
section.

GENERAL  FLOW OF THE MODEL
     Figure 1 depicts the general  flow of the model.  The main routine reads
control information to determine the  integration accuracy for the area and
line sources, the options to be employed if the wind speed change with height
and variation of emission factors  are to be used, and the source types to be
used.  After reading the control  information, the source data are expected
depending upon the indicated controls.  Any number or combination of the six
source types may be used.  All  input  to the program is printed as output
before execution so that a complete listing is available (see Section 5).
Finally, receptor coordinates and meteorological data are read. Meteorologi-
cal data are required for each hour up to 24 hours.

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STRUCTURE  OF PROGRAM
     Figure  2 shows  the structure  of  the  subroutines and functions.  "PAL" is
the main routine;  it reads  input data  and stores the appropriate data in
common with  the six  major subroutines.  All input data for each hour are read
before execution  begins on  any  source  type.  A brief description of the main
program, subroutines,  and functions follows.
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            Figure 2.   Structure  of  subroutines and functions,

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DESCRIPTION OF  SUBROUTINES AND  FUNCTIONS
     Each subroutine and function  of  PAL  is  briefly described in the fol-
lowing pages.
       PAL - PAL is the main  program  that reads in all input data. Source
             input data cards  include point, area, horizontal line, special
             line, horizontal  curved  path, and special curved path sources.
             Subroutines are  called for each source type.  Any combination,
             or all, of the above  subroutines can be called by PAL.  Input
             data cards for receptor  location and hourly meteorology are re-
             quired and not optional  Input as the above.   PAL prints out
             all input data and concentration estimates.

       POINT - This subroutine is  called  by  PAL and makes  concentration
               estimates for  point sources.  POINT calls subroutines XPLUME
               and FPLUME for plume rise  calculation.  Subroutine RCONCP is
               called by POINT to  estimate the relative concentration for a
               receptor at a  given downwind  and crosswind  distance.

       AREA - This subroutine is called by PAL and makes concentration
              estimates from  area  sources.   AREA calls RCONCA, which calcu-
              lates the relative concentration for a receptor downwind of an
              infinite line source.  PGSIG is also called by AREA to determine
              sigma y (a ) and sigma  z (a )  for a given stability class and
              downwind distance.  The concentration from area sources is
              approximated by numerical  integration in the upwind direction
              of the concentration from  infinite crosswind line sources
                                     10

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       corrected for finite crosswind length.







HRZLN - This subroutine is called by PAL and makes concentration



        estimates for multilane horizontal  line sources.   Func-



        tions XVY and XVZ are called by HRZLN to calculate the virtual



        distance necessary to account for the initial  crosswind and



        vertical dispersion, which is specified by the user.  Sub-



        routine RCONCP, called by HRZLN, estimates the relative



        concentration for a receptor at a given downwind  and crosswind



        distance.








CRVLN - This subroutine is called by PAL and makes concentration



        estimates from multilane horizontal  curved path sources.



        CRVLN calls two subroutines, CURLIN and RCONCP.  CURLIN



        calculates the coordinates, if any,  of the intersection points



        of the curved path and the upwind projection from the receptor



        coordinates.  Subroutine RCONCP and functions  XVY and XVZ are



        called by CRVLN and have the same function as  they do in



        HRZLN. The shape of the curved path  is approximated by an arc



        from a circle, determined from the  three points on the curved



        path specified by the user.







SPCLN - This subroutine is called by PAL and makes concentration



        estimates from special line sources.  SPCLN calls subroutine



        RCONCP and functions XVY and XVZ, which are used  in the same



        manner as in HRZLN.  The line sources do not have to be
                              11

-------
        horizontal and emissions per unit length are allowed to vary.

SPCCR - This subroutine is called by PAL and makes concentration
        estimates from special  curved path sources.   Subroutines
        CURLIN and RCONCP and functions XVY, XVZ, DIFANG and ANGARC
        are called by SPCCR and are used in the same manner as in
        CRVLN.  The special curved path sources must be horizontal but
        will allow emissions per unit length to vary along the curved
        path.

XPLUME - This subroutine is called by POINT and calculates the plume
         rise at a given downwind distance x.

FPLUME - This subroutine is called by POINT and calculates the final
         plume rise.

RCONCP - This subroutine is called by POINT, HRZLN, CRVLN, SPCLN, and
         SPCCR.  RCONCP calls PGSIG.  RCONCP determines the relative
         concentration at a receptor from a point source at a given
         upwind and crosswind distance.
PGSIG - This subroutine is called by RCONCP and calculates a  and
        a  for a given stability and downwind distance.
RCONCA - This subroutine is called by AREA and calculates the relative
         concentration normalized for wind speed for a receptor
                              12

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    downwind of a crosswind infinite line source.

CURLIN - This subroutine is called by CRVLN and SPCCR.  CURLIN de-
         termines the coordinates of the intersection points, if any,
         of a curved path source and the line in the direction of the
         wind through the receptor coordinates.

XVY - This function is called by POINT, HRZLN, CRVLN, SPCLN and SPCCR.
      XVY calculates the virtual distance necessary to account for the
      initial crosswind dispersion.

XVZ - This function is called by POINT, HRZLN, CRVLN, SPCLN and SPCCR.
      XVZ calculates the virtual distance necessary to account for the
      initial vertical dispersion.

DIFANG - This function is called by CRVLN and SPCCR.  DIFANG deter-
         mines the angular difference between two angles.

ANGARC - This function is called by CRVLN and SPCCR.  ANGARC deter-
         mines the angle specified by a given slope.  The  resulting
         angle is between 0 and 360 degrees.
                              13

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                     4,   PREPARATION OF INPUT DATA
     The sequence of input data  cards  is shown  in  Figure  3.  The formats for
the input data cards are shown in  Table  1.   All  input data are in  free format,
except card 1  which is  an alphanumeric 20A4 format.  While the free format is
very easy to use, care  should be taken to make  sure every variable is given
a value in the correct  order.  Each  variable should be separated by a comma.
A complete description  of the free format can be found in any Fortran refer-
ence manual.  Integer variable names begin  with the letters  I - N.  Those
input cards which are optional are noted below  the card  type number.  A brief
description of each input parameter  is given in Table 1 with the appropriate
units.  The metric system of units is  used  in PAL.  Horizontal coordinates of
sources are given in units of kilometers.   Temperatures  are  given  in units of
degrees kelvin.  Emission rates  are  given in mgs units (meter-gram-second).
                                     14

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                                                   SPECIAL CURVED
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      TITLE
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Figure 3.  Input data deck for the PAL model.  Card type numbers are in parenthesis.
                                      15

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     Table 1 should be helpful  in organizing data for input into PAL.  However,
there are several variables that may need further explanation.  The  balance  of
this section will be concerned with explaining the use of these input  vari-
ables and should aid the user in assigning values to them.

POINT SOURCES
     In the point source subroutine (POINT) the stack gas velocity  (VSP)  and
stack inside diameter (DP) are ignored if the stack gas volume  flow (VFP) is
greater than zero.   However, VSP and DP must still be specified with dummy
values since the free format requires values for all  variables.  If there are
no point sources in a particular run, then the ambient air  temperature (WTA)
from the meteorology input card type 10 is ignored.   If WTA equals  zero,  then
a value of 293K is assumed in "the program.

     In subroutine  POINT the initial dispersion parameters  SYOP and SZOP
allow for initial dispersion in the horizontal and vertical,  respectively.
For a tall stack these parameters would generally have little influence on
downwind concentrations.  The initial dispersion parameters would be helpful
in accounting for the initial mixing of a plume in the building wake.   Due  to
the complex turbulence in the building wake, plume dispersion is best  modeled
using physical  models.  However, there are some simple cases  where  the ini-
tial dispersion parameters would be applicable.  The values suggested  for
SYOP and SZOP in this report should be considered preliminary in nature.   It
is beyond the scope of this report to undertake a detailed  discussion  of
aerodynamic effects in the wake of a building.  Some pertinent  points  are
discussed below concerning the circumstances in which aerodynamic effects are
a problem and where SYOP and SZOP might be useful.
                                     21

-------
     For a squat building, whose width is >_ its height, a sufficient stack

height and exit velocity for the effluent to escape the influence of the

building is given by the familiar 2% times rule.   The rule simply states that

if the stack height is greater than ?h h (where h is the building height) and

the exit velocity of the plume is greater than 1.5 u (where u is the mean

wind speed), then the plume will escape from the influence of the building.

Stack height always refers to the height of the stack above the ground.   For

a tall building, whose height is greater than its width, the 2^ rule can be

relaxed.  Briggs (1973) suggested that a sufficient stack height would be the

building height plus 1.5  (where a is the smaller of either the building

height, or the maximum width of the building perpendicular to the wind

direction).  If the criteria in either one of the above rules are met, then

the stack can be considered a tall one, and building influences may be

ignored.



     In a recent wind tunnel study, for a squat building, whose width was

twice its height, Huber and Snyder (1976) suggested that the plume was strong-

ly affected by the recirculating flow in the wake "cavity" region behind the

building during the following conditions:  (1) When the stack height was <_

1.2 h and (2) When the exit velocity was <_ 1.5 u". The buoyancy of the plume

is generally not a factor in the initial plume capture within the "cavity"

region.  If the above criteria are met, then SYOP and SZOP can be used to

model the initial mixing. Huber (Communication, May 1977) suggests that

appropriate initial dispersion parameters might be


                          y0 = 0'35 Hb : T-5 Hb
                                          4.3


                                     22

-------
                                = 0.7 h :
                            uzo   "" " - 2.15

where: Hb is the width of the building and h is the building height.
     These findings are applicable for cubical or squat buildings.   For a
building much wider than it is tall, it would be expected that o   would
reach a maximum.  Concentrations very close to the building are extremely
sensitive to the shape and orientation of the building with respect to the
location of the source.  Concentration estimates using the above initial
dispersion parameters are more likely applicable for distances beyond ten
building heights downwind.  The last case that remains is a most difficult
one:  either the stack is not tall enough or the exit velocity of the plume
not great enough for the plume to escape the influence of the building, but
the plume is not totally affected by the building wake.  The plume  may be
totally or partially captured in the displacement zone where it may be
brought near the ground at some distance downwind.  In such cases,  physical
models should be used to examine plume dispersion.  More research is  needed
to determine the extent of the displacement zone and cavity behind  a  variety
of shapes of buildings.  The above initial dispersion parameters are  intended
to provide some guidance until more complete analyses can be obtained.


AREA SOURCES
     It is not mandatory that variables DEST and DNOR on card type  4  have the
same dimensions.  Area sources can be either squares or rectangles.  A special
feature in PAL allows for the area source strength to be negative.   The
advantage of this feature is demonstrated in the example problem in Section
5.
                                     23

-------
LINE  SOURCES
     In all  of the line and curved  path  source  subroutines  the  height of

emissions must be specified.   In  the  past  there has  been  some confusion with

this parameter in the EPA HIWAY model.   The  variables  HLN,  HLNS,  and HCL on

card types 5, 6, and 8, respectively,  represent the  height  of the line or

curved path  above the surrounding terrain.   For a  highway it is not the

height of the highway above the surrounding  terrain,  but  the height of the

emissions above the highway.   It  is assumed  that the  height of  the highway

and surrounding terrain are nearly  the  same.


     A uniform emission rate,  q , must  be  specified  for each line source in

subroutines  HRZLN and CRVLN.   For vehicles  this line-source emission rate can

be found if the emission factor,  EF(g veh"   mi" ), and the  traffic volume,

TV(veh hr~ ), are known.

               q  (g sec"1 m"1) =  EF(g veh  mi"1)  TV(veh  hr"1)
                                 1609.3 (m  mi"1)  3600 (sec hr"1)

                               = 1.726 x  10"7  (EF)  (TV)

A value of the emission factor for automobiles  can be obtained  from supple-

ment No. 5 for Compilation of Air Pollutant  Emission Factors  (EPA 1975).   If

the special  line or special path  sources are used, both  of  which allow  the

emission rate to vary, the user must specify the traffic  volume (veh hr"  )

and the emission factor (g sec" ) since these parameters  are  used internally

to derive the variable emission rate as a  function of location  along the

source.  The reader should note that due to  changes  in the  computer code,  the

emission factors for special sources have  different  units than  the emission

factors, as described in Appendix A.  The  emission factors  for  aircraft,

                                     24

-------
where traffic volumes are low, should be 1-hour average values.   PAL is  not
Intended to predict peak concentrations that are likely to occur from air-
craft emissions but rather is intended to estimate the average concentration
over a 1-hour time period.  The variables VSSL and VSCL on card types 7  and
8, respectively, are a rough estimate of the length of the vehicles  being
considered.  The function of these parameters is discussed in Part 2 of
Appendix A.

METEOROLOGY
    The stability of the atmosphere (MKST) is specified on card type 10.  The
atmospheric stability is used to estimate the horizontal  and vertical dis-
persion parameters, a ,  a .   The dispersion parameters were developed from
data most applicable to  open country (Pasquill, 1961).  When PAL is  used in
urban areas the stability parameters can be modified slightly to account for
the increase in the roughness elements and the generally more unstable air
over urban environments. Busse and Zimmerman (1973) employed a simple tech-
nique in the Climatological  Dispersion Model to account for the  increase  in
dispersion.  This technique  was summarized by Turner (1976).  Table  2 shows
the stability for open country and the recommended stability for point and
area sources in urban areas.
                                    25

-------
                    TABLE 2.   STABILITY CLASSIFICATION
Open                              Equivalent Stability
Country                           for Urban
Stabi1i ty                         Area
                                  Area Sources          Point Sources
A                                      A                     A
B                                      A                     B
C                                      B                     C
D (day)                                C                     D
D (night)                              D                     D
E and F                                D                     D
     Other techniques have been developed for characterizing the dispersion
in urban areas.  Smith (1972) developed a technique for estimating the dis-
persion parameters based on a continuous stability parameter, which incor-
porates effects of roughness.  Weber (1976) has reviewed current systems for
estimating atmospheric dispersion parameters in Gaussian plume models,  PAL
is constructed so that improved techniques to estimate dispersion parameters,
can be incorporated in it as development in this area continues.

     The wind-increase-with-height option allows the user to either specify
the wind speed (constant for all heights) or to use the option and let the
program estimate the wind speed for different heights.  To account for an
increase of wind with height a power law of the form
                                            0
is used in PAL.  Irwin (1977) suggested a theoretical variation of the wind
profile power-law exponent as a function of surface roughness and stability.

                                     26

-------
The exponents given in Table 3 are appropriate for a surface roughness



typical of urban areas.



                   TABLE 3.  EXPONENTS FOR WIND PROFILE



                    Stability class          Exponent (p)



                         A                        0.15



                         B                        0.15



                         C                        0.20



                         D                        0.25



                         E                        0.40



                         F                        0.60








     On card type 2 of the input data, UHGT is the height applicable to the



wind speed, generally anemometer height.   This variable is only used if the



wind increase with height option is used for one or more of the source types.



However, if the option is not used, a value for UHGT is required due to the



free format input.  The usual anemometer height for airport data is in the



range of 7-10 meters.







     If the wind-increase-with-height option is used with sources near the



ground, the wind speed will be estimated at the source height but will not be



allowed to go below 1.0 m  sec~ .   An increase of wind speed with height is



calculated up to 200 meters.  Above this  height the wind speed is assumed to



remain constant.
                                     27

-------
                          5,   EXAMPLE PROBLEM
     An example problem is provided to demonstrate  the  use of  PAL.  The
sources are shown in Figure 4:  one point source,  two  area sources,  three line
sources, one curved path source,  and two special  line sources.   This  example
is intended to be a simplified  model  of an  airport; none of  the  emissions and
physical dimensions should be considered realistic. Also, not  all of  the
sources of emissions, such as taxiways, are included  in this example  problem.
Notice that the two area sources  are overlayed.   In this particular example
the hatched area represents a building with no  emissions and the other area
source is a parking lot with its  associated emissions.  The  area source
strength for the building is the  same as  that for the parking  lot but nega-
tive in sign (see Table 4).  The  effect of  the  negative area source strength
is to make the concentration from the building  equal  to zero.  Also,  using
the negative area source strength reduces  the number  of area source inputs
from three to two in this case. The point  source  is an  incinerator.  Line
sources one and two are fourlane  highways with  a  fourlane curved path source
in between. Line source three is  a twolane  entrance road.  The special line
sources are active runways.

     Table 4 shows the input data cards for this  example.  The numbers in  the
left hand column are the input card type  numbers.  For  a description  of  each
input card type see Table 1.  In  this example there is  no  input  card  type  8,
since there are no special curved path sources.   Input  data  cards for source

                                     28

-------
types, receptor locations, and hourly meteorology have, as a first variable,


an integer called ICARD.  If ICARD equals one, more cards of this type are


expected.  If ICARD equals two, then the last card of this type is expected.


At card type 11 the program will  terminate if KTL = 0 (see Table 1).   Three


other options are also available:




           To start a new problem giving all the input information.


           To leave all sources  the same but input new information on


            receptors and meteorology.


           To input new information on meteorology.




     Table 5 is a computer listing of the output for the example problem.  The


output begins with a listing of all  input parameters  and options used.  PINA


and PINL are the area and line source integration accuracies.   Sources includ-


ed are indicated by "YES's" under  the column titled "Source Included."  In


the second column headed "Wind Increase With Height," the "NO's" mean that


the option of having the wind increase  with height is not used for any of the


sources.  Average concentrations  are calculated based on the number of hours


of meteorology (card type 10).  In this example two 3-hour average concentra-


tions are calculated for each source type.  The hourly variation in emissions


option is not used.  Next, the source input data are listed in the print-out.


Following the source information  are the receptor coordinates  for each recep-


tor. The meteorological data are  printed out to conclude the listing of

                                                                  _3
input.  The "Concentration At Receptors" for each source type, g m  , and a


total concentration for all types  are then printed.  Finally the 3-hour


average concentrations for each source  type are printed out for each  set of



                                     29

-------
meteorology.  Average concentration estimates  are indicated by zeros  in  the



column entitled "Hour."
                                      30

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                                REFERENCES


Breitstein, L., R.E. Gant., 1976:   MIUS SYSTEMS ANALYSIS - Effects of Unfavor-
     able Meteorological Conditions and Building Configurations on Air
     Quality.  ORN/HUD/MIUS-29, U.S. Department of Housing and Urban Develop-
     ment, Oak Ridge, Tennessee.   69 pp.

Briggs, G.A., 1971:  Some Recent Analyses of Plume Rise Observation.  In:
     Proceedings of the Second International  Clean Air Congress, edited by
     H.M. Englund and W.T. Berry.   Academic Press, New York.   pp.  1029-1032.

Briggs, G.A., 1972:  Chimney Plumes in Neutral  and Stable Surroundings.
     Atmospheric Environment, 8:507-510.

Briggs, G.A., 1973:  Diffusion Estimation for Small  Emissions  (Draft).
     Atmospheric Turbulence and Diffusion Laboratory, NOAA, Oak Ridge,
     Tennessee.  59 pp.

Busse, A.D., J.R. Zimmerman., 1973:  User's Guide for the Climatological
     Dispersion Model.   EPA-R4-73-024, U.S. Environmental Protection Agency,
     Research Triangle Park, North Carolina.   131 pp.

Culkowski, W.M., 1967:   Estimating the Effect of Buildings on  Plumes from
     Short Stacks.   Nuclear Safety, 8(3):257-258.

Gifford, F. A., Jr., 1960:  Atmospheric dispersion calculations using the
     generalized Gaussian plume model, Nuclear Safety, 2 (2):56-59.

Halitsky, J., 1962:  Diffusion of Vented  Gas  Around Buildings.   J. Air Pollu-
     tion Control Assoc., 12(1):74-80.

Hosier, C., 1975:   The Meteorology Program of the Environmental Protection
     Agency. Bulletin of the American Meteorological  Society,   56, 12:1261-
     1270.

Huber, A.H., W.H. Snyder., 1976:   Building Wake Effects on Short Stack
     Effluents. In:  Proceedings  of the Third Symposium on Atmospheric
     Turbulence, Diffusion and Air Quality, American  Meteorological  Society.
     Raleigh, North Carolina,  pp. 235-242.

Irwin, J.S., 1977:   A Theoretical  Variation of the Wind Profile Power-Law
     Exponent as a Function of Surface Roughness and  Stability.  Unpublished
     manuscript.  Environmental Sciences  Research Laboratory,  U.S. Environ-
     mental Protection Agency, Research Triangle Park, North  Carolina.  10
     pp.

Kunselman, P., H.T. McAdams, C.J.  Domke,  M. Williams., 1974:   Automobile
     Exhaust Emission Modal Analysis Model.  EPA-460/3-74-005,  U.S.  Environ-
     mental Protection Agency, Research Triangle Park, North  Carolina.
     88 pp.
                                    37

-------
Lucas, D.H., 1962:   Comment 8 from the Symposium on the Dispersion of Chimney
    Gases. International  Journal  of Air and Water Pollution. 6:94.

Martin, D.O., 1971:   An Urban Diffusion Model  for Estimating Long-Term Values
     of Air Quality.  J.  Air Pollution Control  Assoc.. 21(1):16-19.

McAdams, H.T., 1974:  Automobile  Exhaust Emission Modal Analysis Model Exten-
     sion and Refinement.  EPA-460/3-74-024, U.S. Environmental  Protection
     Agency, Research Triangle Park, North Carolina.  72 pp.

Noll, K.E., W.T. Davis.,  1976:  Power Generation Air Pollution Monitoring and
     Control.  Ann Arbor Science  Publishers Inc., Ann Arbor Michigan,  pp.
     65-70.

Novak, J.H., D.B. Turner., 1976:   An Efficient Gaussian-Plume Multiple-Source
     Air Quality Algorithm.  J. Air Pollution Control Assoc., 26 (6)-.570-575.

Pasquill, F., 1961:   The Estimation of the Dispersion of Windborne Material.
     The Meteorological Magazine, 90(1):33-49.

Pasquill, F., 1976:   Atmospheric  Dispersion Parameters in Gaussian Plume
     Modeling Part II.  Possible  Requirements for Change in the Turner Work-
     book Values. EPA-600/4-76-030b, U.S. Environmental Protection Agency,
     Research Triangle Park, North Carolina. 43 pp.

Smith, F.B., 1972:  A Scheme for Estimating the Vertical Dispersion of a
     Plume from a Source Near Ground Level.  In:  Proceedings of the Third
     Meeting of the Expert Panel  on Air Pollution Modeling, NATO/CCMS.
     Paris, France,  pp. XVII 1-14.

Snyder, W.H., R.E. Lawson Jr., 1976:  Determination of Height for Stack Near
     Buildings. EPA-600/4-76-001, U.S. Environmental Protection Agency,
     Research Triangle Park, North Carolina. 31 pp.

Supplement No. 5 for AP-42 Compilation of Air Pollutant Emission Factors.,
     1975: U.S. Environmental Protection Agency, Research Triangle Park,
     North Carolina. 158 pp.

Sutton, O.G., 1953:   Micrometeorology.  McGraw-Hill, New York. 333 pp.

Thompson, R.S., D.J. Lombard!., 1977:  Dispersion of Roof-Top Emissions From
     Isolated BuildingsA Wind Tunnel Study.  EPA-600/4-77-006, U.S.  Environ-
     mental Protection Agency, Research Triangle Park, North Carolina.
     36 pp.

Turner, D.B., 1976:   A Climatological Dispersion Model for 10 Wind  Sectors
     (CDM 36). Submitted to the NATO/CCMS Panel on Modeling.

Turner, D.B., 1970:   Workbook of Atmospheric Dispersion Estimates.   EPA-AP-
     26, U.S. Environmental Protection Agency, Research Triangle  Park, North
     Carolina. 84 pp.
                                     38

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Weber, A.M., 1976:  Atmospheric Dispersion Parameters in Gaussian Plume
     Modeling Part I.  Review of Current Systems and Possible Future Develop-
     ments. EPA-600/4-76-030a, U.S. Environmental Protection Agency, Research
     Triangle Park, North Carolina. 59 pp.

Zimmerman, J.R., R.S. Thompson., 1975:  User's Guide for HIWAY, a Highway Air
     Pollution Model.  EPA-650/4-74-008, U.S. Environmental Protection Agency,
      Research Triangle Park, North Carolina. 59 pp.
                                     39

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                                APPENDIX A
                     TECHNICAL DESCRIPTION OF  PAL
     The technical  description of  PAL is covered in two parts.  Part 1
consists of a reprint from the Proceedings of the Sixth International Techni-
cal Meeting on Air  Pollution  Modeling and its application held 24-26 September,
1975.  The paper appears  in the  NATO Committee on the Challenges of Modern
Society, Series on  Air Pollution,  Volume 42.  The reader will notice that
there have been minor revisions  in the format of the input and output of the
model since the 1975 paper.   However, the following technical description of
the basis and formulation of  the model is accurate.

     Part 2 of Appendix A describes the mathematical formulation for the
special line and special  curved  path sources.  This section was not presented
previously and is given here  for completeness.
                                     40

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6th NATO/CCMS
International Technical Meeting                           ARM 6  /  1
on Air Pollution Modeling
                 A  GAUSSIAN-PLUME ALGORITHM  FOR
                 POINT, AREA, AND LINE SOURCES
                                 by
              D. Bruce Turner and  William  B. Petersen
                Meteorology and Assessment Division
                  Environmental Protection Agency
                  Research Triangle Park,  NC 27711

            At BATTELLE - INSTITUT E.V., Frankfurt/Main
                            Germany, FR
                      24 - 26 September, 1975

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                 A GAUSSIAN-PLUME  ALGORITHM FOR
                 POINT,  AREA,  AND  LINE  SOURCES
                by  D.  Bruce  Turner and William B. Petersen

INTRODUCTION
     The PAL algorithm is  intended for making air pollutant concentration
estimates for a small  portion of  an urban area.  The sources considered
are point, area, and line  sources.  The principal use of the algorithm
is to estimate the  increase  in  pollutant concentrations caused by a
new facility such as a shopping area,  a sports stadium with included
parking lot, or a facility as large as an airport and its associated
emissions.

     PAL is not intended to  estimate concentrations  for an entire urban
area.  Because of the details which the algorithm considers, such as edge
effects from area sources, the  application to an entire urban area would,
in general, be prohibited  by computer  costs.  Also,  since meteorological
data are entered hour by hour,  a  normal run  for  this algorithm would be to
simulate a period of from  1  to  24 hours.  Calculations for more than several
24-hour periods would also be costly.

     The intended users of the  PAL algorithm are the air pollution meteorologist
and the air pollution control engineer who are attempting to estimate air
quality on a scale of tens to hundreds of meters in  the vicinity of the
sources considered.  The PAL algorithm offers a  considerable amount of
flexibility to the user.  Any or  all of the  six  source subroutines may be

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utilized.  The user also has the option of employing a  diurnal  variation
to emission rates, and allowing the wind speed to change  with  height.

     This algorithm is useful  for estimating short-term dispersion  of
stable pollutants using Gaussian plume, steady-state  assumptions.  The
Gaussian point source equation is the heart of the algorithm.   Numerical
integration of the point source equation is used for both line  and  area
sources.  Meteorological data  used by the algorithm  are for  hourly  periods.
Averages of concentrations for up to 24 hours can be obtained  directly by
averaging hourly estimates.

TYPES OF  SOURCES CONSIDERED  AND INPUTS  REQUIRED
     The PAL algorithm can consider six types of sources.   In  any single
execution, any combination of these six source types can  be  used.   However,
the maximum number of input sources for any given type  cannot  exceed thirty.
All input data are read in by the main program.  The input parameters for
the six source types will  be discussed in this section.

POINT SOURCES
     The treatment of point source in PAL is similar to that in many other
air quality simulation models.  In order to calculate plume  rise, the stack
gas temperature in combination with stack gas volume flow, or  stack inside
diameter and stack gas velocity are required.  Point source  information
consists of the following for each source:

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     .   Point source strength,  g sec"
        Physical  stack height,  m
     .   Stack gas temperature,  K
     .   Stack gas velocity,  m sec"
        Stack inside top diameter, m
                                3    -1
     .   Stack gas volume flow,  m  sec
     .   East coordinate of stack, km
     .   North coordinate of  stack, km
        Initial  a ,  m
        Initial  a ,  m

AREA SOURCES
     In PAL the shape of area sources  may be squares or rectangles.  Boundaries
must be oriented north-south and east-west.   There are no special  restrictions
about source size.  A unique feature of PAL is that negative area  source
strengths can be considered  in order to account for smaller areas  with no
emission within larger area  sources.  For example, an area occupied by
buildings within a large parking lot can be given an area source strength
equal to that of the parking lot but negative in sign.  (See "Specific Example"
section.)  Area source information consists of the following for each source:
                                   -1  -2
     .   Area source strength, g sec  m
     .   Area source height,  m   (Assumed to be effective height.)
     .   East coordinate of south-west corner, km
     .   North coordinate of south-west corner, km

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        East-west length of area source, km
     .   North-south length of area source,  km

HORIZONTAL LINE SOURCES
     Line sources of finite horizontal  extent can be considered by PAL.
Single-line sources or multiple-line sources such as parallel  lanes of
traffic, hereinafter referred to as multi-lane sources,  can be input into
the model.  The end points of the line  source are points A and B.   Provision
for some initial  size of the source, such as turbulent mixing  of effluent
in the  wake of vehicles or aircraft engines, is through  initial o  's and
a 's.   Line source information consists of the following for each  source:
        Line source strength, g sec" nf
     .   Line source height, m
     .   Number of lanes if multilane, dimension!ess
        East coordinate of point A, km
     .   North coordinate of point A, km
     .   East coordinate of point B, km
     .   North coordinate of point B, km
        Initial a , m
        Initial o , m

     Line source strength as a 1-hour average for mobile sources can be
calculated in the manner shown on p 3 of Zimmerman and Thompson (1975) by
multiplying appropriate vehicle emission factors  in either g mi   vehicle"
                                 45

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or g km"  vehicle"  by the vehicle flow rate (vehicles hr~  )  and appropriate
conversion factors.   The vehicle emission factor can be found from publications
such as EPA's AP-42  (second edition).   These vehicle emission factors should
be corrected for average vehicle speed along the specific segment, as most
pollutant emissions  vary with vehicle  speed.  For multi-lane  sources,
additional information is needed.   An  emission rate is given  for each lane.
Lanes are ordered from left to right when looking from point  A to point B.
The additional information below is expected by the program if the number
of lanes given above is greater than one.  Only an even number of lanes can
be considered.  For  multi-lane sources, the points A and B are expected
midway between the outermost lanes, that is, in the middle of the median
for a roadway.
     .   Total width  of line source, m
     .   Width of median of line source, m
        Line source  strength for each  lane, g sec" m"

HORIZONTAL CURVED SOURCES
     In addition to  line sources, curved sources can also be  included in
PAL.  The curved sources are assumed to be of constant radius.  Like the
line sources, they can be single or multi-lane sources.  In order to
describe the curved  segment, the coordinates of the end points as well
as the coordinates of one point in between are needed.  This  point need
not be in the middle of the curve.  Emissions are handled the same as for
horizontal line sources.  As with line sources, multi-lane curved sources

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have to have an even number of lanes in order to be handled as one source.
Points A and C are the end points of the curved source.  Point B is a point
on the curve between A and C.  Curved source information consists of the
following for each source:
     .  East coordinate of point A, km
     .  North coordinate of point A, km
        East coordinate of point B, km
     .  North coordinate of point B, km
        East coordinate of point C, km
     .  North coordinate of point C, km
     .  Curved source height, m
     .  Number of lanes, dimensionless
     .  Width of curved source, m
     .  Width of median, m
     .  Initial a , m
     .  Initial a , m
     .  Curved source strength for each lane, g sec" m"

SPECIALIZED LINE SOURCES
     The inclusion of specialized line sources in PAL is to account for
additional  variations in two variables.   The first is to account for  a  changing
effective height of the line source from one end of the source to the other.
The effective height is the height above the surrounding terrain.  The  second is
to account for variations of the emission rate from one end of the source
to the other.

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     For specialized line sources the emission in the usual  line source
units, g sec  m  ,  is calculated within the computer program for each
point evaluated by  dividing the input emission rate by the average velocity
                                                            _2
of vehicles past that point.   The input emission rate, g sec  ,  can be
determined by multiplying the average vehicle emission rate, g min   vehicle  ,
[for example, see pp 59-61 of Kunselman et al. (1974)] by the vehicle flow
rate, vehicles hr  , for this segment and appropriate conversion factors.
Neither the specialized line nor curved source will accept multi-lane input
as a single source.  The input parameters for the specialized line source
follow:
                            _2
        Emission rate, g sec
     .  Height of point A, m
     .  Height of point B, m
     .  East coordinate of point A, km
     .  North coordinate of point A, km
     .  East coordinate of point B, km
        North coordinate of point B, km
        Initial speed of vehicles, m sec   (at point A)
        Final speed of vehicles, m sec   (at point B)
        Initial a  , m
        Initial a  , m

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SPECIALIZED CURVED SOURCES


     The specialized curved source algorithm is very similar to the


specialized line source routine except it incorporates the added feature


of allowing the source to be a curve with a constant radius.  Input for


the curved sources is identical to the specialized line source except for


the addition of the coordinates of a third point along the curved source


to define the curved path.  As with the horizontal curved sources, points A


and C are the ends of the curved segment,and point B is a point on the


curve between A and C.  The initial speed is at point A', the final speed


is at point C.  This speed can be increasing or decreasing from point


A to C.  The input parameters for the specialized curved sources follow:

                                          _2
     .   Curved-source emission rate, g sec


     .   Height of point A, m


     .   Height of point B, m


     .   East coordinate point A, km


     .   North coordinate of point A, km


     .   East coordinate of point B, km


     .   North coordinate of point B, km


     .   East coordinate of point C, km


     .   North coordinate of point C, km


        Initial speed of vehicles, m sec   (at point A)


        Final speed of vehicles, m sec   (at  point C)


        Initial a , m
                 J"

        Initial a , m

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RECEPTORS
     Receptors may be located  at  any position  relative to  the air  pollutant
sources.   However, common sense should  be  used so  that receptors are not
positioned in the center of lanes of traffic,  etc.   The data required for
each receptor consist  of the  east and  north coordinates of the receptor
and the height of the receptor above ground level.   PAL is designed to
make estimates over relatively level terrain.   The receptor height should
not be used in an attempt to simulate topographic  differences.  The height
of a receptor is the distance  of  that receptor above the local ground level,
not the height of the ground above some reference  plane.   The three receptor
parameters are:
        East coordinate of receptor, km
        North coordinate of receptor, km
     .  Height of receptor above  ground, m

METEOROLOGICAL DATA
     The input of meteorological  data for  each simulated hour, up  to 24  hours,
follows all required source and receptor data.  Care should be taken to
ensure that the meteorological data are representative of  the  source-receptor
locality.  Availability airport data may not be representative of  an urban
or suburban site.  Wind speed  and direction are especially sensitive to
the local environment especially  in the vicinity of buildings.  Depending
upon the nature of the problem being considered, special instrumentation
may be established in the field in order to gather representative
                                  50

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meteorological data 	 of wind, in particular.   At the present state of
development of this algorithm, the dispersion parameter values incorporated
in PAL are those given in EPA's Workbook of Atmospheric Dispersion Estimates
(Turner, 1974).  These are most representative for open countryside, that is,
rural areas.   Therefore if the source-receptor locality is in an essentially
rural area, the Pasquill  stability class can be  determined in the usual  way,
as in the Workbook.  However, if the area of concern is in a more built-up
area, the stability may need to be modified toward more unstable conditions
in order to perform the calculations with the increased dispersion caused
by the thermal and roughness characteristics of  the locality.

     Mixing height will frequently be of little  importance if source-receptor
distances are small.  Mixing height is the top of the unstable or neutral
layer near the ground.  Therefore, mixing height is not used if the lowest
atmospheric layer is stable.  Mixing height is usually more nearly the
same over larger areas than wind speed or wind direction.   However, urban
influences may cause the existance of a neutral  layer at the surface and a
mixing height at night compared to stable conditions for this period in  the
rural area.

     The ambient air temperature is used only for the calculation of plume
rise for the point sources.  If there are no point sources, the air temperature
is not required.
                                  51

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     Since a meteorological data card is read for each simulated hour, some
additional  optional  data related to diurnal  emission rates are included with
the meteorological data.  If the option is employed to vary the emission
rates of the sources, a dimensionless factor for each source type is read
in for each hour.  The computations for each source are then multiplied by
this factor using the individual emissions previously read.  For example,
if information indicates that for this hour the emissions from all point
sources are about half the emission rates previously read in, the factor
would be 0.5.  Or, if the emissions are thought to be about 30 per cent
higher for this hour, the factor would be 1.30.

     Thetneteorological and diurnal factor input parameters follow:
     .  Wind direction, deg
        Wind speed, m sec
        Pasquill  stability class, dimensionless
     .  Mixing height, m
     .  Ambient air temperature, K

     .  Diurnal variation for point sources, dimensionless
        Diurnal variation for area sources, dimensionless
        Diurnal variation for horizontal line sources, dimensionless
        Diurnal variation for curved sources, dimensionless
     .  Diurnal variation for specialized line sources, dimcnsionless
        Diurnal variation for specialized curved sources, dimensionless
                                  52

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GENERAL  FRAMEWORK  OF ALGORITHM
     The algorithm consists of a  main  program  which  reads  in  the  information
and also prints the output and subroutines  which  are called to  perform  the
bulk of the calculations.   Control  information is initially read  into the
program to determine what source  types are  going  to  be  used.  Controls  for
the two optional  features are also  included.   The wind  speed  can  be  assumed
constant for all  heights for each simulated hour, or the option employed to
include an increase in wind speed with height  above  10  meters,  assuming the
wind is constant  below 10 meters.  An  exponential increase with height  is
assumed with the  exponent of the  profile  dependent upon the stability class.
Emission raes can be assumed constant with the values  as  read  in, or the
option may be employed to multiply calculations by a factor for each source
type for each simulated hour.

     After reading the control data,  the  emission information - that which
is expected depending upon the indicated  controls -  is  read for each parameter
within each source type.  Any number or combination  of  the six  source types
may be used.  All input to the program is printed as output after being read
so that a complete listing is available.
     Receptor coordinates and heights  are read following all  emission information.
Meteorological data for each hour are  then  included  for up to 24  hours.
                                  53

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     After reading all  required input for sources,  receptors,  and  meteorology,
the subroutines that are needed are  called to  perform  the  calculations  for
each source type.

     The concentration  output is arranged in  a table with  one  line for  each
receptor.  The receptors are numbered sequentially  as  read.  This  receptor
number and the receptor coordinates  are given  on this  printed  line.   In
addition to total  concentration from all  sources, the  partial  concentrations
due to each source type (not each individual  source) are also  included.   For
details, see "Specific  Example" section.

BASIS FOR CALCULATIONS
     The following assumptions are made:   1)   Dispersion from  points, and
area and line elements  result in Gaussian distributions  in both the horizontal
and vertical directions through the  dispersing plume from  that point or
element, and therefore  steady-state  Gaussian  plume  equations can be used
for point sources and the integration of these equations for line  and area
sources.  2)  Concentration estimates may be  made for  each hourly  period
using the mean meteorological conditions appropriate for each  hour.   3)
The total concentration at a receptor is the  sum of the  concentrations
estimated from all point and area sources, that is, concentrations are
additive.

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POINT SOURCES
     The basis for the point source calculations is the point source form
of the Gaussian diffusion equation.  A computation is made for each source-
receptor pair.  The upwind distance of a source from an individual  receptor
is first calculated.  If this distance is negative, indicating that the
source is downwind of the receptor, no calculation  for this source-receptor
pair is needed.  For positive upwind distances, the crosswind distance of
the source from the receptor is also determined.  Plume rise for each source
is calculated once for each hourly simulation period.  The plume rise is
added to the physical stack height to give effective height of emission.
The dispersion equation is then evaluated.  The standard deviations of plume
spreading are determined as functions of the Pasquill stability class and
of the source-receptor distance.  As each concentration from a point source
at a receptor is calculated, it is added to the accumulated concentrations
from point sources for that particular hour.

AREA SOURCES
     The calculation of concentrations from area sources is simulated by a
number of finite crosswind line sources.  If all four corners of the area
source have positive upwind distances from the receptor, an integration
will be performed starting from the corner of minimum distance to the corner
of maximum distance.  If some but not all of the corners have a negative
upwind distance, then the integration will be performed from an upwind
                                  55

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distance of zero to the greatest distance.   If all  four corners have
negative distances from the receptor,  this  indicates the entire area
source is downwind of the receptor position.   A number of crosswind
(that is, perpendicular to the upwind direction) line sources at various
distances from the minimum to the maximum distance are considered.
Concentrations for each of these distances  are calculated using the
infinite line source form of the Gaussian equation.  This concentration
from an infinite line source is corrected for the finite extent of each
individual line by considering the distance in units of a  of each end
                                                         J
of the line from the upwind azimuth line through the receptor.  The
fraction of the area under a Gaussian curve between these limits
determines the correction.  An integration is performed using the
concentration contribution from a number of lines and considering the
distance between lines.  This integration is the first estimate of the
concentration from the area source.  A second estimate is made by using
the first estimate with additional calculations made for lines lying
half-way between all the previously calculated lines.  This second
estimate is compared with the first and if the second falls within a
set criteria the second estimate is taken as the final concentration.
If the second estimate is not within the criteria, additional calculations
are made, each time choosing additional lines lying half-way between
lines of the previous total set.
                                 56

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LINE SOURCES
     The calculation of concentrations from line sources  is  done by an
integration of the point source equation  in the  same manner  as  in Zimmerman
and Thompson (1975).  Distances to the end points of the  lines  are determined
in terms of upwind and crosswind distances.  The line source is limited
to those parts of the line which contribute concentrations to the receptor.
Calculations are made for a number of points on  the line, and,  assuming
linear change in concentration between these points, an estimate of the
concentration from the line is determined.   This first estimate is then
compared to a second estimate, made by taking additional  points between
the existing ones and then assuming linear changes of concentrations
between each of the adjacent points.   The second estimate is compared
to the first, and if it falls within  a set criteria, the  second estimate
is taken as the concentration.  If the second estimate is not within the
criteria, third and subsequent estimates  may be  required  by  taking
additional  points.  Estimates for curved  sources are determined similarly
by evaluating for locations on the curve  and integrating.  For  the
specialized line and curved sources,  provisions  are included to determine
the height and emission rate for each location evaluated.

SPECIFIC EXAMPLE
     In order to help clarify some of the terms  and procedures  mentioned
previously, an example run of the PAL model is shown. The source inputs
                                  57

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into PAL are one point source,  two area sources,  two line sources,  and
one curved source, shown in Figure 1.

     Consider this example as a simple model  of a shopping center,  where
the hatched region is occupied  by buildings and walkways and the rest of
the regions within the rectangular boundary represent the parking lot.
Notice that the area source strength for the shopping area is the same
as that for the parking lot but negative in sign (see Table 1).   The
effect of the negative area source strength is to make the concentration
from the shopping area equal  to zero.   Also within the area source is a
point source whose point source strength and other input variables are
shown in Table 1.

     The highway around the area source consists of two four-lane line
sources and one four-lane curved source.  The length of the two line
sources is one kilometer.  The  line source strengths for each lane of
the two line sources and the curved source are given in Table 1_.  For
this example run no specialized line or specialized curved sources
were used.

     Table 1 is a copy of the computer output from PAL.  The output begins
with a listing of all input parameters and options used.  PINA ana PINL
are the area and line source integration accuracies.  Under the column
titled "Source Included," the "yes's" refer to the different subroutines that
are used in the model.   In the second column headed "Hind Increase With Height,"
                                  58

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the "no's" mean that the option of having the wind increase with height is
not used.   Notice also that no average concentration is calculated,  since
only one hour's data are input, nor is the diurnal variation in emission
option used.   First, the sources are listed in the input section of  the
print-out.  Following the source input information,  the coordinates  of
the receptors are printed out.  Meteorological information follows next
and concludes the listing of the input.  Included in the meteorological
input is the  value of the diurnal  variation fraction for each source type.
In this case  the diurnal variation in emissions is not used, and the
fractions  are set to 1.0 by the program.   The final  output for this
particular run is the "CONCENTRATIONS AT  RECEPTORS."  Concentrations
are given  in  g m   for each source type and a total  for all types.   At the
conclusion of this print-out, three options are available besides termination
of the job.   These depend upon the value  punched on  a control  card.   The
options are:
     1.  To start a new problem giving all the input information.
     2.  To leave all sources the  same but input new information on
         receptors and meteorology.
     3.  To input new information  on meteorology.

SUMMARY
     The PAL  algorithm is intended to evaluate the contribution of sources
within a limited area.  This can be the impact of a  new facility in  a relatively
                                  59

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rural environment or the additional  impact of a  number  of sources  added

to a portion of an urban area.   Gaussian  plume dispersion equations  are

used with straight- and curved-  lines,  sloping-lines, area,  and  point

sources.   Briggs plume rise is  used.   Receptors  may  be  at elevated

heights above ground level.  Level  terrain is assumed.   Concentration

estimates are for short time periods  between one hour and 24 hours.   The

algorithm is not intended for calculations for entire urban  areas  or for

a long period of time.  Although this algorithm  may  be  best  run  in a batch

mode, it is anticipated that a  conversational version will also  be made

available for UNAMAP (Users Network for Applied  Modeling of  Air  Pollution).


 REFERENCES

Compilation of Air Pollutant Emission Factors, 2nd Ed.   U.S. Environmental
  Protection Agency.  Research  Triangle Park, North  Carolina.   Publication
  No. AP-42.  April 1973.

Kunselman, Paul; McAdams, H.T.; Domke, Charles J.; and  Williams, Marcia.
  Automobile Exhaust Emission Modal  Analysis Model.   U. S.  Environmental
  Protection Agency.  Ann Arbor, Michigan.  Publication No.  EPA-460/3-74-005.
  January 1974.  179 pages.

Turner, D.B.  Workbook of Atmospheric Dispersion Estimates.   U.S.  Environmental
  Protection Agency.  Research Triangle Park, North Carolina.   Publication
  No. AP-26.  1970.  84 p.

Zimmerman, John R.; and Thompson, Roger S.  User's Guide For HIWAY,  A
  Highway Air Pollution Model.   U.  S. Environmental  Protection Agency.
  Research Triangle Park, North Carolina.  Publication  No.  EPA-650/4-74-008.
  February 1975.  58 pages.


 ACKNOWLEDGEMENT

     The authors wish to thank Lea Prince for her invaluable assistance.
                                  60

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               APPENDIX - DISPERSION AND  ANALYTIC

                  GEOMETRY EQUATIONS  USED  IN PAL



EXPRESSIONS

     These expressions are used in the discussions that  follow:



                        g1 = exp (-0.5 y2/a2)



             g2 =  exp [-0.5(z-H)2/a2] + exp [-0.5(z+H)2/o2]



   g, =  I   4 exp [-0.5(z-H+2NL)2/a2] + exp  [-0.5(z+H+2NL)2/o2]f
    6   N=_oo L                      Z                        Z J


(This infinite series converges rapidly,and evaluation with the integer,  N,


varying from -4 to +4 is usually sufficient.)

where:H = effective height of emission, meters

      L = mixing height, the top of the unstable  layer,  meters


      y = crosswind distance, meters

      z = receptor height above ground, meters

     o  = standard deviation of plume concentration  distribution in the

            vertical, meters

     a  = standard deviation of plume concentration  distribution in the
      z
            vertical, meters



POINT SOURCE COMPUTATIONS

     The upwind distance, x, and the crosswind  distance, y, of a point source

from a receptor   (see Figure 2) are given by:



                  x = (S -Sr) cos e+ (Rp-Rr)  sin 0                  (Al)



                  y = (S -Sr) sin 0 - (Rp-Rp)  cose                    (A2)


                                  61

-------
where R , S  are the coordinates of the point source; R ,  S  are the
coordinates of the receptor, and 0 is the wind direction (the direction
from which the wind blows).  The units of x and y will be  the same as
those of the coordinate system R, S.   Frequently a conversion is required
in order to express x  and y in meters or kilometers.

     The contribution to the concentration, XD> from a single point source
to a receptor is given by one of the three following equations where  x
         -3                                          -1
is in g m  , Q is point source emission rate in g sec  , u is wind speed
in m sec  , and a  and o  are evaluated for the upwind distance x, and
the stability class,.

     For stable conditions or unlimited mixing:

                         xp = Q g1 g2/(2iroyazu)                        (A3)

     In unstable or neutral conditions and if a  is greater than 1.6 times
the mixing height, L, the distribution below the mixing height is uniform
with height provided that both the effective height, H, and the receptor
height, z, are below the mixing height:

                        xp = Q g1/[oyLu(21r)'s]                          (A4)

(If H or z is above the mixing height, x  = 0.)

     In all other unstable or neutral conditions, that is, if o  is less
than 1.6 times the mixing height:
                                   62

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                         X  = Q g,  g~/(2iro a u)                          (A5)
                          P      10     y z
AREA SOURCE COMPUTATIONS
Equation (Al) is used to determine the upwind distance,  x,  of a  corner of
the area source with coordinates R  , S  from a receptor with coordinates
R , S .
 r   r
     By evaluating x for the four corners of the area  source,  the maximum
and minimum upwind distances of the area source from the receptor are determined
(see Figure 3).(If the x's are negative for all  four corners,  indicating  the
entire area source is downwind, no  calculation is  performed.   If the minimum
x is negative, the minimum considered is zero, as  no computations need to be
performed for that portion of the area source downwind of the  receptor.)
     For a given upwind distance, x, from a receptor at point  R , S , the
north coordinate, S. , of the intersection of a crosswind  line  with a north-
south boundary given by R = R.  is:
                            x - (R.  - R )  sin 0                         (A6)
                       S   =  	5	1	  + s
                       L           cos 0            r
     The coordinates of this intersection are then R. ,  S. .
     Similarly, for a given upwind distance,  x,  from a  receptor at R ,  S ,
the east coordinate, R. , of the intersection  of  a crosswind line with an
east-west boundary given by S = S.  is:
                                   63

-------
                           x - (S,  - S )  cos Q


                      L '	 *                        
     The coordinates of this intersection are then R. ,  S. .
                                                    L   b




     Using the above relationships and special  tests for sin 0=0 and



cos 0=0, along with the equations for the four boundaries of the area



source, the two intersections (A and B) of the crosswind line and the boundaries



of the area source can be found.





     The two crosswind distances, yft and yR, of these points from the receptor



can be found using equation (A2).





     Assuming that the distances y* and yp are in km, the number of standard



deviations in the Gaussian distribution of these points from the upwind azimuth



through the receptor are given by:





                            SA = (1000 yA) / ay                         (A8)





                            SB = (1000 yB) / ay                         (A9)





where a  is in meters and is determined for the distance x and the atmospheric



stability.  sft and SD can be used to determine the fractional portion of the
             A      D


area under a Gaussian curve between these limits.  In PAL this is accomplished



by interpolating between values  in a table.  The values in the table are



from -3.8 s to 3.8 s at intervals of 0.1 s.

-------
     To account for the finite length of the line source, the fraction
 determined above is used to correct the calculation for a crosswind line
 source, infinite in extent.
     The first estimate, C, , for the concentration, XA> from an a>"ea source
 is given by:
CT  = 
 1    U
                                       i = 1
                                               f  (X.  + i A X)
                                                c x mm
Ax.  (A10)
where qA is area emission rate
     u  is mean wind speed
     f  is defined below
 and AX = (x    + x .  ) /10
          v max    mm'
     The second estimate, C^, for the concentration, XA> from an area source
is given by:
                                        fc 
-------
     For stable conditions  or unlimited  mixing:
                                            *                           (A12)
where g~ was defined at the beginning  of  this  appendix.

     In unstable or neutral conditions and  if  a   is  greater than 1.6 times
the mixing height, L, the distribution below the  mixing  height is uniform
with height provided that both the  effective height,  H,  and the receptor
height, z, are below the mixing height:

                               f =  1/L                                  (A13)

(If H or z is above the mixing height, f  =  0.)

     In all other unstable or neutral  conditions,  that is, if a  is less
than 1.6 times the mixing height:

                           f = g3/  [ az(2v}h  ]                          (A14)

LINE SOURCE  COMPUTATIONS
     The line source and receptor relationships  are  shown  in Figure 4.   Points
A and B are the beginning and ending points of the line,   x and y are  the
upwind and crosswind distances from a  receptor to a  point  on the line  source.
x and y are given by equations (AT) and(A2).
                                   66

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     R  and S  are the coordinates  of  any  point on the  line and are functions
      P      p

of length, A, along the line and  total  length of the line, D:





                          RP 4  (RB -  V + RA                          (A15)




                                 SB -V  + SA
Since R  and S  are functions  of a  (see  Figure  2), x and y are also functions


of a.
     The upwind distances, x,  of the  receptor to points A and B are calculated.


If both of these x's are negative, then  the  line source is downwind of the


receptor and the concentration  at  the receptor due to the line source is


zero.  If either or both x's  are positive,  it is determined if there is a


point on the line source directly  upwind  of the receptor.  The equation for


the line source is:




               (R -  RA)  / (S  -  SA) = (RB  -  RA) / (SB - SA)              (A17)





The equation of the  line through the receptor in the upwind direction is:




                          R - R =  (S - S ) tan 0                       (A18)





Solving these two equations simultaneously  for R and S by letting:




                        m= (RB-RA)/ (SB-SA).



                           m  SA -  Sr tan  0  + Rp - RA                    (A19)

                                  m -  tan  0



                                   67

-------
     and                  R = (S - S ) tan 0 + R                        (A20)

     This resulting intersection R, S (see point I, Figure 4) must be tested
to see if it is upwind of the receptor by testing for positive x using
equation (Al), and if it lies on the line source between points A and B.
If both of these conditions are met, the line source is considered to be
made up of two segments:  The first segment from point A to the intersection
point, and the second segment from the intersection point to point B.  The
point directly upwind has a significant contribution to the concentration
at the receptor.  The line is broken into two segments so that this point
will be considered in the integration estimate that follows.  If there are
two segments to the line source, the total concentration is given by the
sum of the two concentrations from the segments.

     The concentration from a line source is then given by the following
equation.

                                q    rD
                            X = TT-  /   f. d*                           (A21)
where:
     q  = line source emission rate, g sec  m
      X/
     u  = wind speed, m sec
     D  = line source length, meters
and  f  = point source dispersion function
                                   68

-------
     The point source dispersion function is given by one of the three


following equations where a  and a  are evaluated for the upwind distance,


x, and the stability class.



     For stable conditions, or unlimited mixing:



                               f  =
                                 9192                              (A22)
                                    2-7T a  a
                                        y  z
                                /


where   g, and g? have been previously defined.



     In unstable or neutral conditions, if a  is greater than 1.6 times the


mixing height, L (meters), the distribution below the mixing height is


uniform with height regardless of source or receptor height, provided both


are less than the mixing height.



                               f  =  - 91                                (A23)

                                P   a ify^\%
In all  other unstable or neutral  conditions:



                                 99

                                      z
                                       193                              (A24)

                                          
     It should be noted that in PAL, initial a 's and oz's, such as to account


for initial dispersion in the turbulent wake behind vehicles, are input values.


The virtual distance for the given stability class is calculated within the


algorithm.  These virtual distances are added to the physical distances prior


to determining a  and a  for each concentration computation.
                                   69

-------
     The integral, A21,  is evaluated using the trapezoidal  rule by making <
first estimate, C,, given by:

     c  =V^Jl   C   fp(o) + fp(lOA)  ]    +     I   f  (TA)l       (A25)
      1    U    \J                                i  =  1       J
where AS, = D/10, and f  is defined above.   For each of the 11  evaluations of
f , the upwind distance, x, of the point on the line from the  receptor is
determined as a function of Ad,and x is used to determine a  and a  in the
                                                           x      y
function f .   Portions of the line where f  equals zero are eliminated and
the line is redefined.  Then equation (A25) is again evaluated.
     A second estimate, C-, is determined from:
                          2u
                                     10
                                      z   M-Ai/2 + JAA)  1            (A26)
                                    .  = ,
                                    J    *
                                           P
     A calculation is made of (C? - C,)/C.  If this value is within a set
criteria, x = C?'  ^ not w""^hin the criteria, a third estimate is made by
evaluating f  for additional points midway between those points previously
calculated and assuming linear concentration change between adjacent points
(trapezoidal rule).  This is continued until the approximation to the integral
converges, that  is, until two successive estimates are within the criteria.
The last estimate is the concentration, x fi"m this line source.
                                   70

-------
     For line sources with an intersection  point  upwind  from  the  receptor,
the contribution from the second  segment  must  also  be  determined.   If  the
point directly upwind was not used  to  break the line into  two segments,
and the entire line source is considered  as one segment, it is  possible
for the entire portion of the line  that contributes significantly to the
concentration to be between two of  the eleven  points, and thus an  erroneous
concentration of zero would result.

     For line sources with multiple lanes,  the integral would be  evaluated
for each lane and the concentration summed  to  represent the total  concentration
at that receptor from the line source.

CURVED SOURCE COMPUTATIONS
     Figure 5 shows the curved source  and receptor  relationships.   Points A
and C are the end points of the curved path.   Point B  is an arbitrary  point
on the curve between A and C.  The  curve  is assumed to be  of  constant  radius.

     The radius of the circle, of which the curve is a part,  is determined
in the following way:  The coordinates of point D midway between  A and B
on a chord are found by averaging the  R and S  coordinates  of  A  and B.  Similarly
the coordinates of point E midway between B and C on a chord  are  found.  The
perpendicular bisector of a chord of a circle  will  pass  through the center
of a circle.  Also the slope of the perpendicular bisector is the negative
reciprocal of the slope of the chord.  The  slope  of chord  AB  is:
                                   71

-------
                          (RB - RA) / (SB - SA)





and the slope of chord BC is:





                          (Rc - RB) / (Sc - SB)





The slope of the bisector through D, call this m,, is:





                       - (SR - S.) / (RR - R.) = m,
                           DM      DM      I




The slope of the bisector through E, call this m?, is:





                       - (Sr - SD) /(Rr - R0) = nu
                           U    D     U    D     L




The resulting equation of the bisector through D is:





                          R  - R= m, (S  - SJ
                           0    D    1   0    D




and the equation of the bisector through E is:





                          R0 - RE = m2 (SQ - SE)                         (A28)





R  and S  can be determined from these two equations, for example:






                So =  (mlSD ' m2 SE " RD + RE) '  (ml " IT12)                (A29)




                      and  RQ = m]  (SQ - SD) + RD                         (A30)
                                    72

-------
The radius of the circle can then be determined from the coordinates of,  the


center (R , S0) and any one of the three points on the curve, for example:
                                    S\ L.  ,  t r\    n  \ 
                        .   ... M    J  +  (RA - RJ
                              f\    \j       r\    \J




     In order to provide a proper estimate-of the concentrations from  the



curved source at a receptor, it is desirable to determine if a line  in the



upwind direction from the receptor intersects the curve.  The equation of



the line through the receptor in the direction of the upwind azimuth is:





                         R - Rr = (S - Sr) tan 0                         (A32)





The equation of the circle of which the curve is a part is:





                        p2 = (S - So)2 +  (R - RQ)2                       (A33)





The two possible intersections of the line and the circle are found  by solving



a quadratic equation for one of the two variables, for example, of the form:





                            a R2 +b R + c = 0                            (A34)



                 2

where a = 1 + cot 0                                                      (A35)





               b = -2 Rr cot20 + 2 Sr cote -2 SQ cote - 2 RQ             (A36)






         and c = Rr  cot 0 - 2 Rr $r cote - 2 R   S  cot -  2 SQ S^




                              o     o     o   9
                          J_C^-LC^-_LI">'-                             tl\?~J\
                          + $r  + SQ  + RQ  -p                           (A37;
                                    73

-------
Two possible values of R are found from:
                                                                          (A38)
    2
If b -4ac is negative, R has imaginary roots and  there is  no  intersection
                                 2
of the circle and the line.   If b -4ac is zero,  the line is tangent to  the
                                           2
circle and there is one intersection.   If b -4ac  is positive  there are  two
intersections and both roots of the equation are  found.   If one or two
values of R are found, then one or two values of  S are found  from:

                           S = (R-Rr)  cote + Sr                            (A39)
     If one or more intersections were found for the line and circle, the
upwind distance of this (these) point(s) from the receptor can be determined
using equation (Al).  If this value is negative, indicating the point is
downwind from the receptor, it need not be considered further.  However,
for a point with a positive x, it must be determined if this intersection
on the circle is also on the curve, that is, between points A and C.

     The direction from the center of the circle (R , S ) to a point (R ,
S ) on the circle is:

                   * - tan"1 [ (Rp-RQ) / (Sp - SQ) ]                      (A40)

-------
The directed azimuth from the circle's center to any intersection and to
points A, B, and C can then be found.  With some logic to consider the
crossover point (from 360 to 0), it can be determined if the  for the
intersection is within the range ot $ swept out by the curve.

     After determining if any intersections are on the curve,  the curve is
considered in three pieces if there are two intersections, two if there is
one intersection, and as a single curve if there are no intersections.  The
computation is done very similarly to that for line sources.   Whereas the
length along the line is used to make calculations at intervals for the
line source, the variation of the azimuth from the center of the circle,
<|>, is used for the curved source.  The coordinates of a point  on the curve
for which the concentration contribution is being evaluated are found
from:
                            R  = RQ + p sin <|>                             (A41)
                            S  = SQ + p sin                              (A42)
     The upwind and crosswind distances, x and y, of a given point on the
curve with coordinates (R ,  S ) from the receptor (R , S ) are calculated
as previously using equations (Al) and (A2).   The same point source dispersion
function, f , as given in the "Line Source Computations" section is used.
                                    75

-------
     Portions of the curve that contribute no concentration to the receptor
are eliminated, and the curve is redefined.   An initial  estimate of the
concentration from the remaining curve is made using eleven equally spaced
points along the curve.  These and the ten pointss in between are then used
for a second estimate.  Comparison is made of the two estimates and, as with
the area and line source estimates, if these two are within the given criteria,
the concentration is that of the second estimate.  If additional estimates
are made, concentration contributions for additional points, midway between
these points already considered, are determined assuming the concentration
varies linearly between adjacent points, that is, trapezodial integration.

     If the curve was broken into pieces because of intersections, the
contribution from the additional pieces must be determined as above.
                                   76

-------
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-------
                                                                                                          CO
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                                         SH3131AI
                                                        79

-------
NORTH
                                      WIND
          SOURCE 1
                                                      SOURCE 2
                                                   RECEPTOR
                                                                      EAST
            Figure 2. Upwind and crosswind distances of point sources
            from a receptor.

                                    80

-------
NORTH
                      WIND
       AREA
      SOURCE
                                                            RECEPTOR
                                                                         -*1 EAST
     Figure 3.  Minimum, XL and maximum, X2, upwind distances of an area source
     from a receptor and crosswind line sources.
                                         81

-------
NORTH
                                                   WIND
               Figure 4.  Line source and receptor relationships.
                                     82

-------
NORTH
      WIND
   (Rp.Sp)
                                                               RECEPTOR
                                                                 (Rr.Sr)
                                                                             EAST
                 Figure 5.  Curved source and receptor relationships.

                                        83

-------
                                   PART  2
     The slant (or special  line) and special  curved path  source  calculations
are made in a similar way as the line source  and  curved source calculations,
respectively. Unlike Equation A21 ,  the concentration from special  sources  is

                                   *  i  ft   ,  


-------
The vehicle acceleration can also be expressed as
                                        2    2
                                       \li - r
where     Xf = total distance of travel.
The distance of travel to any point "P" can be expressed as
where     X  = distance of travel to P.
 Solving for t  in Equation 5 and substituting in Equation 3,
The emission rate q  (  ?  ) is now given by
                   X  S 6C"" m
                                 ,t -      Tr        i                  (7,
                                         3600
where     TV = traffic volume.
The emission rate is inversely proportional to V .   In order to ensure that
q  will not approach infinity as V  goes to zero, a simple technique is used
to set a minimum vehicle speed.  The minimum speed  (V ) is calculated using
the traffic volume and a gross estimate of average  vehicle length (VL).
                                .  	       in\          vtii               \ O /
                                 S          3600
V  is then in (~-)> and physically it is the slowest speed the vehicles
could be going and still maintain the traffic volume.  If V  is less than Vs,
then V  is set equal to Vg.
                                    85

-------
     For most applications this change in vehicle speed will  have negligible
effect on the concentration estimates.
                                     86

-------
    APPENDIX B
FORTRAN STATEMENTS
        87

-------
                         PAL
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
10

C
    PAL   VERSION 78001
     PAL  CALCULATES HOURLY CONCENTRATIONS FROM POINT,AREA, AND
     LINE SOURCES.
     PAL  READS ALL  INPUT DATA CARDS.SOURCE INPUT DATA CARDS
     INCLUDE POINT,AREA,HORIZONAL LINE,SPECIAL LINE.HORIZONAL
     CURVED  PATH,AND SPECIAL CURVED PATH DATA CARDS.
     ALL  SOURCE INPUT DATA CARDS ARE OPTIONAL.
     METEOROLOGY AND RECEPTOR INPUT DATA CARDS ARE
     NOT  OPTIONAL.
     THE  FOLLOWING  SUBROUTINES ARE CALLED BY PAL.
          POINTPOINT SOURCE SUB-MODEL.
          AREA--AREA SOURCE SUB-MODEL.
          HRZLN--HORIZONAL LINE SOURCE  SUB-MODEL.
          CRVLN--CURVED PATH SOURCE SUB-MODEL.
          SPCLN--SPECIAL LINE SOURCE SUB-MODEL.
          SPCCR--SPECIAL CURVED PATH SOURCE SUB-MODEL.
 COMMON  /SOP/ QP(31),HPP(31),TSP(31),VSP(3D,DP(31) ,VFP(3D,RQP(31)
       * \ niri"vTi/^\^>  e~irrr\ri\/'^'*\ *~i /~\ JIT T-\ / o ^ o. 11 \  TNTTTI/^^I \  ~r TI rr r\
                                                             (3D,CO.NA(31
 V^wliiiv/ll /k^^J./  *at  \.J I /}**** \J'/JAfc-'A \ .J  / J * fc-/* V _J ' / ) L/ * V ,J I / )  * A
1 ,SQP(3D ,SYOP(3D ,SZOP(31) ,CONP(31,24) ,DVP(25) ,IUZP
 COMMON /SOA/ QA(3D,HQ(31),RQ(31),SQ(31),DEST(3D ,DNOR
 ,24),DVA(25),IUZA
 COMMON /SOL/ QLN(3D,HLN(31),RAQ(3D ,SAQ(31),RBQ(31),SBQ(3D,SYO(3
1 1),SZO(3D,CONLH(31,24),DVH(25),IUZH
 COMMON /SOCP/ QLNS(3D,HLNS(3D ,RBQS(3D ,SBQS(3D , RMQS( 3 1) , SMQS( 3 1
1) ,REQS(3D ,SEQS(3D ,SIYO(3D ,SIZO(3D , CONCLN( 3 1 , 24) , DDVH( 31 ) , IUZC ,
2RADIUS(3D ,NLANE(3D
 COMMON /SOLS/ QLS( 31) , HAS( 31) ,HBS(3D ,RAS(3D ,SAS(3D , RBS( 3-1 ) ,SBS(
131) ,SYOS(3D ,SZOS(3D ,CONLS(31 ,24) ,DVS(25) , IUZS,SPDI( 3 1 ) ,SPDF(3D ,
2TVSL(3D ,VSSL(3D
 COMMON /SOCS/ QLNA(3D ,HCL(3D ,RBQA(3D ,SBQA( 3 1) , RMQA( 3 1) ,SMQA(3D
1 ,REQA(3D ,SEQA(3D ,SIYA(3D ,SIZA(3D ,CONCLA(31 ,24) ,DVHA(3D ,IUZE,S
2PEK3D ,SPEF(3D ,TVCL(3D,VSCL(3D
 COMMON /EEC/ RR(31),SR(31),ZR(31)
 COMMON /WEA/ WTHET(25),WU(25),MKST(25),WHL(25),WTA(25),UHGT
                        NO','YES'/
                                        ,  ACAC3D,
                                    .   .  QLTS(3D,
                             .IVER/78001/
 DIMENSION ALP(20),  CONT(30,24),  ACP(31)
11),  ACT(3D,  QLT(20),  YAN(3),  ACLC(31)
 DATA YAN /
 IRD = 5
 IWRI=6
 MAXQ=31
 MAXR=31
 READ (IRD,790) ALP
 WRITE (IWRI,800) ALP
    ALP IS 80  COLS OF
                                                        ACLH(3D,
                                                        ACAC(3D
                                                             ACLS(3
                     ,IVER
               .__ _.  ALPHANUMERIC INFORMATION TO HELP IDENTITY OUT
 READ (IRD,810)  PINA,PINL,IQP,IUZP,IQA,IUZA,IQLH,IUZH,IQLC,IUZC,IQL
1S,IUZS,IQAC,IUZE,IAVG,IDRNL,UHGT
C
C
C
C
C
C
C
C
PINA
PINL
IQP
IUZP
IQA
IUZA
IQLH
IUZH
X.
X.
X
X
X
X
X
X
XXXX
XXXX






                   TEST FOR AREA INTEGRATION ACCURACY.
                   TEST FOR LINE INTEGRATION ACCURACY,
                   CONTROL FOR POINT SOURCES.
                   WIND INCREASE WITH HEIGHT,POINT
                   CONTROL FOR AREA SOURCES.
                   WIND INCREASE WITH HEIGHT,AREA.
                   CONTROL FOR HORIZ. LINE SOURCES.
                   WIND INCREASE WITH HOT.,HORIZ.LINE,
                                                   (DIMENSIONLESS)
                                                   (DIMENSIONLESS)
                                                   (DIMENSIONLESS)
                                                   (DIMENSIONLESS)
                                                   (DIMENSIONLESS)
                                                   (DIMENSIONLESS)
                                                   (DIMENSIONLESS)
                                                   (DIMENSIONLESS)
0010
0020
0030
0040
0050
0060
0070
0080
0090
0100
0110
0120
0130
0140
0150
0160
0170
0180
0190
0200
0210
0220
0230
0240
0250
0260
0270
0280
0290
0300
0310
0320
0330
0340
0350
0360
0370
0380
0390
0400
0410
0420
0430
0440
0450
0460
0470
0480
0490
0500
0510
0520
0530
                                        88

-------
                         PAL
c
c
c
c
c
c
c
c
c
c
IQLC
IUZC
IQLS
IUZS
IQAC
IUZE
IAVG
IDRNL
UHGT
CO!
X
X
X
X
X
X
X
X
x:
JT:
c
20

30
C
C
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
40
50

60
C
70

80
C
                   CONTROL FOR CURVED PATH SOURCES.
                   WIND INCREASE WITH HGT.,CURVED PATH.
                   CONTROL FOR SLANT LINE SOURCES.
                   WIND INCREASE WITH HGT.,SLANT LINE.
                   CONTROL FOR SPECIAL PATH SOURCES.
                                                   (DIMENSIONLESS)
                                                   (DIMENSIONLESS)
                                                   (DIMENSIONLESS)
                                                   (DIMENSIONLESS)
                                                   (DIMENSIONLESS)
                   WIND INCREASE WITH HGT. ,SPECIAL PATH. (DIMENSIONLESS '.
                                                         (DIMENSIONLESS)
                                                         (DIMENSIONLESS)
                                                         (M)
              CONTROL FOR AVG.CONCENTRATIONS.
              CONTROL FOR DIURNAL FACTORS.
       XXX.X  HEIGHT APPLICABLE TO WIND SPEED.
            VALUES: IQ ARE 1 FOR NON-INCLUSION, 2 FOR INCLUSION.
 WRITE (IWRI,820) PINA,PINL,YAN(IQP+1),YAN(IUZP+1),YAN(IQA+1),YAN(I
1UZA+1),YAN(IQLH+1),YAN(IUZH+1),YAN(IQLC+1),YAN(IUZC+1),YAN(IQLS+1)
2,YAN(IUZS+1),YAN(IQAC+1),YAN(IUZE+1),YAN(IAVG+1),YAN(IDRNL+1),UHGT
 GO TO (bO,20),  IQP
    WRITE HEADING FOR POINT SOURCE INFORMATION.
 WRITE (IWRI,830)
 1=1
 READ (IRD,810)  ICARD,QP(I),HPP(I),TSP(I),VSP(I),DP(I),VFP(I),RQP(I
1) ,SQP(I) ,SYOP(I),SZOP(I)
 DECIMALS MUST BE INCLUDED IN REAL VARIABLES.
 A COMMA MUST BE PLACED BETWEEN EACH VARIABLE.
 IF A VARIABLE IS NOT USED SET IT = TO 0.
 ICARD=1 ON ALL  SOURCE INPUT CARDS EXCEPT THE LAST THEN ICARD=2.
*
I CARD
QP
HPP
TSP
VSP
DP
VFP
RQP
SQP
SYOP
SZOP
* * P 0 I
X
XXXXX.XX
XXX. X
XXX. X
XX. X
XX. XX
xxxx.x
xxx.xxxx
xxx.xxxx
x.x
x.x
                NT   SOURCE   CARD***
                 EQUALS 1 OR 2 SEE ABOVE.
                 POINT SOURCE STRENGTH.
                 PHYSICAL STACK HEIGHT.
                 STACK GAS TEMPERATURE.
                 STACK GAS VELOCITY.
                 STACK INSIDE DIAMETER.
                 STACK GAS VOLUME FLOW.
                 EAST COORDINATE OF STACK.
                 NORTH COORDINATE OF STACK.
                 INITIAL SIGMA Y.
                 INITIAL SIGMA Z.
(DIMENSIONLESS;
(G/SEC)
(M)
(DEC K)
(M/SEC)
(M)
(M**3/SEC)
(KM)
(KM)
(M)
(M)
 IF (I-MAXQ) 40,40,50
 WRITE (IWRI,840) I,QP(I),HPP(I),TSP(I),VSP(I),DP(I),VFP(I),RQP(I),
1SQP(I),SYOP(I),SZOP(I)
 IF (ICARD.GT.l)  GO TO 60
 1 = 1 + 1
 GO TO 30
 WRITE (IWRI,850) MAXQ
 CALL  EXIT
 GO TO (110,70),  IQA
    tvRITE HEADING FOR AREA SOURCE INFORMATION.
 WRITE (!WRI,b60)
 J=l
 READ  (IRD,810) ICARD,QA(J),HQ(J) ,RQ(J) ,SQ(J) ,DEST(J),DNOR(J)
    *  * * A R E A   SOURCE   CARD***
 ICARD X          EQUALS  1 OR 2 SEE ABOVE.          (DIflKNSIONLESS)
 QA    X.XXXXX   AREA SOURCE STRENGTH.             (G/SEC-M**2)
 HQ    XX.XX     AREA SOURCE HEIGHT.               (M)
0540
0550
0560
0570
0580
0590
0600
0610
0620
0&30
0640
0650
06bO
0670
0680
0690
0700
0710
0720
0730
0740
0750
0760
0770
0780
0790
0800
0810
0820
0830
Ob40
0850
0860
0870
0880
0890
0900
0910
                    0^30
                    0940
                    0^50
                    Oy60
                    Oy70
                    1000
                    1010
                    1020
                    1030
                    1040
                    1050
                    1060
                                        89

-------
                         PAL
C
C
C
C

90
100

110
C
120
C

130

C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C

140
150

C
C
C
C
160
RQ    XXX.XXX
SQ    XXX.XXX
DEST  XX.XX
DNOR  XX.XX
                 EAST COORDINATE OF S.W. CORNER.
                 NORTH COORDINATE OF S.W. CORNER.
                 EAST-WEST SIZE.
                 NORTH-SOUTH SIZE.
 IF (J-MAXQ)  90,yO,100
 WRITE (IWRI,870) J,QA(J),HQ(J),RQ(J) ,SQ(J) ,DEST(J),DNOR(J)
 IF (ICARD.GT.l) GO TO 110
 J=J + 1
 GO TO 80
 WRITE (IWRI,880) MAXQ
 CALL EXIT
 GO TO (210,120) , IQLH
    WRITE HEADING FOR HORIZONTAL LINE SOURCE INFORMATION.
 WRITE (IWRI,890)
    READ A SOURCE CARD.
 K=l
 READ (IRD,810) ICARD,HLN(K),NL,RAQ(K),SAQ(K),RBQ(K),SBQ{K),SYO(K),
1SZO(K),WT,WM,(QLT(J),J=1,NL)
 THE PROGRAM WILL HANDEL 1 LANE OR AN EVEN NUMBER OF LANES.
 AN ODD NUMBER OF LANES MUST BE SEPERATED INTO 2 I
 AN EVEN NUMBER PLUS 1 SOURCE.
* *

ICARD
HLN
NL
RAQ
SAQ
RBQ
SBQ
SYO
SZO
WT
WM
QLT(l)
QLT(2)



QLT(NL;
* H 0 R I Z 0
CARD
X
XX. X
XX.
xxx.xxxx
xxx.xxxx
xxx.xxxx
xxx.xxxx
x.x
x.x
XX. X
XX. X
x.xxxxx
x.xxxxx
x.xxxxx
x.xxxxx
x.xxxxx
1 X.XXXXX
NTAL LINE SOURl
1
EQUALS 1 OR 2 SEE ABOVE.
LINE SOURCE HEIGHT
NO. OF LINES IF MULTI-LINE
EAST COORDINATE, POINT A
NORTH COORDINATE, POINT A
EAST COORDINATE, POINT B
NORTH COORDINATE, POINT B
INITIAL SIGMA Y
INITIAL SIGMA Z
TOTAL WIDTH
WIDTH OF MEDIAN
LINE SOURCE STRENGTH
ONE FOR EACH OF ANL SOURCES
ORDERING IS FIRST SOURCE
STRENGTH IS FOR LEFT-MOST
LINE WHEN LOOKING FROM
POINT A TO POINT B
IF  (K-MAXQ) 140,140,200
IF  (NL-1.) 190,190,150
ANL=NL
IF  (K+NL-1-MAXQ) 160,160,200
    WT IS THE TOTAL WIDTH OF THE LINE  SOURCE  INCLUDING  THE  MEDIAN.
    WM IS THE WIDTH OF THE MEDIAN  (METERS)
    LANES ARE ORDERED FROM LEFT TO  RIGHT WHEN LOOKING FROM  POINT
    TO POINT B.
WRITE (IWRI,900) ANL,WT,WM
WL=(WT-WM)/ANL
RA=RAQ(K)
SA=SAQ(K)
KM)
KM)
KM)
KM)

DNOR(J)






iTION.



,SBQ{K),SYO(K) ,

' LANES.
IRCES

E * * *

(DIMENSIONLESS)
(M)
(DIMENSIONLESS)
(KM)
(KM)
(KM)
(KM)
(M)
(M)
(M)
(M)
(G/SEC-M)
> >
i t
i >
i t
i t





:NG THE MEDIAN.

1G FROM POINT A





1070
1080
1090
1100
1110
1120
1130
1140
1150
1160
1170
1180
1190
1200
1210
1220
1230
1240
1250
1260
1270
1280
1290
1300
1310
1320
1330
1340
1350
1360
1370
1380
1390
1400
1410
1420
1430
1440
1450
1460
1470
1480
1490
1500
1510
1520
1530
1540
1550
1560
1570
1580
1590
                                         90

-------
                         PAL

      RB=RBQ(K)                                                             1600
      SB=5BQ(K)                                                             1610
      SYON=3YO(K)                                                           1620
      SZON=SZO(K)                                                           1630
      HLNN=HLN(K)                                                           1640
      DELR=RB-RA                                                            1650
      DELS=SB-SA                                                            1660
      DIST=SQRT(DELS*DELS+DELR*DELR)                                        1670
      NLIM=NL/2                                                             1660
      ALIM=NLIM                                                             1690
      DO 170 KN=1,NLIM                                                      1700
      A=KN                                                                  1710
      DL=(-0.5)*WM+((-1)*ALIM-0.5+A)*WL                                     1720
      DUM=DL*0.001/DIST                                                     1730
      ID=K+KN-1                                                             1740
      RAQ(ID)=RA+DELS*DUM                                                   1750
      RBQ(ID)=RB+DELS*DUM                                                   1760
      SAQ(ID)=SA-DELR*DUM                                                   1770
      SBQ(ID)=SB-DELR*DUM                                                   1780
      SYO(ID)=SYON                                                          1790
      SZO(ID)=SZON                                                          1800
      QLN(ID)=2LT(KN)                                                        1810
      HLN(ID)=HLNN                                                          1820
170   WRITE (IWRI,910) ID,QLN{ID),HLN(ID),RAQ(ID),SAQ(ID),RBQ(ID),SBQ(ID    1830
     1),SYO(ID),SZO(ID)                                                     1840
      NS=NLIM+1                                                             1850
      AS=NS                                                                 1860
      DO IdO KN=NS,NL                                                       1870
      A=KN                                                                  1880
      DL=0.5*WM+(0.b+A-AS)*WL                                               1890
      DUM=DL*0.001/DIST                                                     1900
      ID=K+KN-1                                                             1910
      RAQ(ID)=RA+DELS*DUM                                                   1920
      RSQ(ID)=RB+DELS*DUM                                                   1930
      SAQ(ID)=SA-DELR*DUM                                                   1940
      SBQ(ID)=SB-DELR*DUM                                                   1950
      SYO(ID)=3YON                                                          1960
      SZO(ID)=SZON                                                          1970
      QLN(ID)=QLT(KN)                                                        1980
      HLN(ID)=HLNN                                                          1990
180   WRITE (IwRI,910) ID,QLN(ID),HLN(ID),RAQ(ID),SAQ(ID),RBQ(ID),SBQ(ID    2000
     1),SYO(ID),SZO(ID)                                                     2010
      K=K+NL                                                                2020
      IP (ICARD.GT.l)  GO TO 210                                             2030
      GO TO 130                                                             2040
C        WRITE LINE  SOURCE INFORMATION.                                    2050
190   QLN(K)=QLT(1)                                                         2060
      WRITE (IWRI,910) K,QLN(K),HLN(K),RAQ(K),SAQ(K),RBQ(K),SBQ(K),SYO(K    2070
     1),SZO(K)                                                              2080
      IF (ICARD.GT.l)  GO TO 210                                             2090
      K=K+1                                                                 2100
      GO TO 130                                                             2110
200   WRITE (IWRI,920) MAXQ                                                 2120
                                          91

-------
                         PAL
210

C
220
C
230

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
240
  CALL EXIT
  CONTINUE
  GO TO (290,220) ,  IQLC
  WRITE HEADING FOR CURVED HORIZONAL LINE SOURCE INFORMATION
  WRITE (IWRI,930)
  READ A SOURCE CARD
  KK=0
  LL=1
  READ (IRD,810) ICARD,HLNS(LL),NL,RBQS(LL),SBQS(LL),RMQS(LL),SMQS(L
 1L),REQS(LL),SEQS(LL),SIYO(LL),SIZO(LL),WT,WM,(QLTS(JJ),JJ=1,NL)
  THE PROGRAM VvILL  HANDEL 1 LANE OR AN EVEN NUMBER OF LANES.
  AN ODD NUMBER OF  LANES MUST BE SEPERATED INTO 2 SOURCES
  AN EVEN NUMBER PLUS 1 SOURCE.
  A COMMA MUST BE PLACED BETWEEN EACH VARIABLE
***  CURVED   PATH  SOURCES  ***
                  EQUALS 1 OR 2 SEE ABOVE.
                  PATH SOURCE HEIGHT.
                  NUMBER OF LANES.
                  EAST COORDINATE,PT.A
                  NORTH COORDINATE,PT.A.
                  EAST COORDINATE,PT.B.
                  NORTH COORDINATE,PT.B.
                  EAST COORDINATE,PT.C.
                  NORTH COORDINATE,PT.C.
                  INITIAL SIGMA Y.
                  INITIAL SIGMA Z.
                  TOTAL WIDTH OF PATH.
                  WIDTH OF MIDIAN.
                  PATH SOURCE STRENGTH.
                  ONE FOR EACH LANE.
                  ORDERING OF EMISSION RATES
                  ARE FROM OUTSIDE LANES TO
                  INSIDE.

  ANL=NL
  NLANE(LL)=NL
  A=l.
  ALIM=ANL/2.
  WL=(WT-WM)/ANL
  DO 270 KL=1,NL
  KK=KK+1
  IF (KK.GT.31) GO TO 280
  QLNS(KK)=QLTS(KL)
    RADIUS IS A CORRECTION FACTOR TO ADJUST THE RADIUS
    FOR DIFFERENT LANES.
  RADIUS(KK)=(A*.5*WM+ALIM*WL-.5*WL*A)*.001
  ALIM=ALIM-1.
  IF (ALIM.LT.O.l.AND.ALIM.GT.-.l) ALIM=-1.
  IF (ALIM.LT.O.) A=-l.
  IF (KL.EQ.l) GO TO 240
  GO TO 250
  WRITE (IWRI,940)  KK,QLNS(KK),HLNS(LL),RBQS(LL),SBQS(LL),RMQS(LL),S
 IMQS(LL),REQS(LL),SEQS(LL),SIYO(LL),SIZO(LL),NL,WT,WM
ICARD X
HLNS  XX.X
      XX
      XXX.XXXX
      XXX.XXXX
      XXX.XXXX
      XXX.XXXX
      XXX.XXXX
      XXX.XXXX
      x.x
      x.x
      XX.X
      XX. X
      x.xxxxx
NL
RBQS
SBQS
RMQS
SMQS
REQS
SEQS
SIYO
SIZO
WT
QLTS
(DIMENSIONLESS)
(M)
(DIMENSIONLESS)
(KM)
(KM)
(KM)
(KM)
(KM)
(KM)
(M)
(M)
(M)
(M)
(G/SEC-M)
2130
2140
2150
2160
2170
2180
2190
2200
2210
2220
2230
2240
2250
2260
2270
2280
2290
2300
2310
2320
2330
2340
2350
2360
2370
2360
2390
2400
2410
2420
2430
2440
2450
2460
2470
2480
2490
2500
2510
2520
2530
2540
2550
2560
2570
2580
2590
2600
2610
2620
2630
2640
2650
                                          92

-------
                         PAL
250

260
270
280
290
C
300
C

310

C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C

320
330

340
C
350
C

360
C
C
 GO TO 270
 IF (KL.GT.2) GO TO 260
 WRITE (IWRI,770)
 WRITE (IWRI,780) KK,QLNS(KK)
 CONTINUE
 IF (ICARD.GT.l) GO TO 290
 LL=LL+1
 GO TO 230
 WRITE (IWRI,950) MAXQ
 GO TO (340,300), IQLS
    WRITE HEADING FOR SLANT OR VERTICAL LINE SOURCE INFORMATION.
 WRITE (IWRI,960)
    READ A SOURCE CARD.
 L=l
 READ (IRD,810) ICARD,QLS(L),HAS(L),HBS(L),RAS(L),SAS(L),RBS(L),SBS
 (L),SPDI(L),SPDF(L),SYOS(L),SZOS(L),TVSL(L),VSSL(L)
 A COMMA MUST BE PLACED BETWEEN EACH VARIABLE
    ***SLANT   OR   VERTICAL   LI
 ICARD X         EQUALS 1 OR 2 SEE ABOVE.
 QLS   X.XXXXX   LINE SOURCE STRENGTH.
 HAS   XX.X      HEIGHT OF POINT A.
 HBS   XX.X      HEIGHT OF POINT B.
 RAS   XXX.XXXX  EAST COORDINATE,POINT A.
 SAS   XXX.XXXX  NORTH COORDINATE,POINT A.
 RBS   XXX.XXXX  EAST COORDINATE,POINT B.
 SBS   XXX.XXXX  NORTH COORDINATE,POINT B.
 SPDI  XXX.X     SPEED AT POINT A.
 SPDF  XXX.X     SPEED AT POINT B.
 SYOS  X.X       INITIAL SIGMA Y.
 SZOS  X.X       INITIAL SIGMA Z.
 TVSL  XXXXX.    VEHICLE VOLUME.
 VSSL  XX.X      GROSS ESTIMATE OF VEH. SIZE.
N E
 (DIMENSIONLESS!
 (G/SEC)
 (M)
 (M)
 (KM)
 (KM)
 (KM)
 (KM)
 (M/SEC)
 (M/SEC)
 (M)
 (M)
 (VEH/HR)
 (M)
 IF (L-MAXQ) 320,320,330
 WRITE (IWRI,970) L,QLS(L),HAS(L),HBS(L),RAS(L),SAS(L),RBS(L),SBS(L
1) ,SPDI(L),SPDF(L),SYOS(L),SZOS(L),TVSL(L),VSSL(L)
 IF (ICARD.GT.l)  GO TO 340
 L=L+1
 GO TO 310
 WRITE (IWRI,980) MAXQ
 CALL EXIT
 GO TO (390,350) , IQAC
 WRITE HEADING FOR SPECIAL PATH SOURCE INFORMATION
 WRITE (IWRI,990)
 READ A SOURCE CARD
 LC=1
 READ (IRD,dlO) ICARD,QLNA(LC),HCL(LC),RBQA(LC),SBQA(LC),RMQA(LC),S
IMQA(LC),REQA(LC),SEQA(LC),SPEI(LC),SPEF(LC),SIYA(LC),SIZA(LC),TVCL
2(LC),VSCL(LC)
 IF (LC.GT.30) GO TO 370
 A COMMA MUST BE  PLACED BETWEEN EACH VARIABLE
**SPECIAL  PATH  SOURCES  ***
2660
2670
2680
2690
2700
2710
2720
2730
2740
2750
2760
2770
2780
2790
2800
2810
2820
2830
2840
2850
2860
2870
2880
2890
2900
2910
2920
2930
2940
2950
2960
2970
2980
2990
3000
3010
3020
3030
3040
3050
3060
3070
3080
3090
3100
3110
3120
3130
3140
3150
3160
3170
3180
                                        93

-------
   PAL
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
ICARD
QLNA
HCL
RBQA
SBQA
RMQA
SMQA
REQA
SEQA
SPEI
SPEF
SIYA
SIZA
TVCL
VSCL

X
X.XXXXX
XX. X
XXX.XXXX
XXX.XXXX
XXX.XXXX
XXX.XXXX
XXX.XXXX
XXX.XXXX
XXX. X
XXX. X
x.x
x.x
xxxxx.
XX. X

370
380
C
390
C

400
C
C
C
C
C
C
C

C
410
420

430
C

C
440
450

460
EQUALS 1 OR 2 SEE ABOVE.
PATH SOURCE STRENGTH.
PATH SOURCE HEIGHT.
EAST COORDINATE,POINT A.
NORTH COORDINATE,POINT A.
EAST COORDINATE,POINT 8.
NORTH COORDINATR,POINT 6.
EAST COORDINATE,POINT C.
NORTH COORDINATE,POINT C.
SPEED AT POINT A.
SPEED AT POINT C.
INITIAL SIGMA Y.
INITIAL SIGMA Z.
VEHICLE VOLUME.
GROSS ESTIMATE OF VEH. SIZE.
                                                   (DlrtENSIONLESS)
                                                   (G/SEC)
                                                   (M)
                                                   (KM)
                                                   (KM)
                                                   (KM)
                                                   (KM)
                                                   (KM)
                                                   (KM)
                                                   (M/SEC)
                                                   (M/SEC)
                                                   (M)
                                                   (M)
                                                   (VEH/HR)
                                                   (M)
)  LC,QLNA(LC) ,HCL(LC) ,RBQA(LC) ,S6QA(LC) ,RMQA(LC) ,S
,SEQA(LC) ,SPEI(LC) ,SPEF(LC) ,SIYA(LC) ,SIZA(LC) ,TVCL
 WRITE
IMQA(LC) ,REQA(LC
2(LC) ,VSCL(LC)
 IF (ICARD.GT.l) GO TO 380
 LC=LC+1
 GO TO 360
 WRITE (IWRI,1010) MAXQ
 CONTINUE
    WRITE HEADING FOR PRINT-OUT OF RECEPTOR INFORMATION.
 WRITE (IWRI,1020)
    READ A RECEPTOR CARD.
 H=l
 READ (IRD,810) ICARD , RR(N ) ,SR(N ), ZR (N )
 A COMMA MUST BE PLACED BETWEEN EACH VARIABLE
    ***RECEPTOR   CARD***
 ICARD X        EQUALS 1 OR 2 SEE ABOVE.
 RR    XXXX.XXX R COORDINATE
 SR    XXXX.XXX S COORDINATE
 ZR    XXX. X    HEIGHT ABOVE GROUND
 A COMMA MUST BE PLACED BETWEEN EACH VARIABLE
 IF UN-MAXR) 4io,4iu,420
    WRITE RECEPTOR INFORMATION.
 WRITE (IWRI,1030) N ,RRU ) ,SR(N ) , ZR(N )
 IF (ICARD.GT.l) GO TO 430
 N=N+1
 GO TO 400
 WRITE (IWRI,1040) MAXR
 CALL EXIT
 M=l
    WRITE MET HEADING.
 WRITE (IWRI,1050)
    READ A METEOROLOGY CARD.
 GO TO (450,460), IDRNL
 READ (IRD,810) ICARD ,WTHET(M) ,WU (M) ,MKST(M) ,
 GO TO 470
 READ (IRD,810) ICARD ,WTHET(M) ,WU (M) ,MKST(M) ,WHL( M) ,WTA(M) ,DVP (M) ,D
1VA(M) ,DVH(M) ,DDVH(M) ,DVS(M) ,DVHA(M)
                                (DIMENSIONLESS )
                                (KM)
                                (KM)
                                (M)
                                   ,WTA(M)
3190
3200
3210
3220
3230
3240
3250
3260
3270
32bO
3290
3300
3310
3320
3330
3340
3350
3360
3370
3380
3390
3400
3410
3420
3430
3440
3450
3460
3470
34bO
34*0
3500
3510
3520
3530
3540
3550
3560
3570
3580
3590
3600
3610
3620
3630
3640
3650
3660
3670
3680
3690
3700
3710
                    94

-------
PAL
                                (DIMENSIONLESS)
                                (DEC AZIMUTH)
                                (M/SEC)
                                (DIMENSIONLESS)
                                (M)
                                (DEC K)
                                (DIMENSIONLESS)
                                (DIMENSIONLESS)
                                (DIMENSIONLESS)
C     A COMMA MUST BE PLACED BETWEEN EACH VARIABLE
C        ***METEOROLOGY   CARD***
C     ICARD     X        EQUALS 1 OR 2 SEE ABOVE.
C     WTHET     XXX.     WIND DIRECTION
C     WU        XX. X     WIND SPEED
C     MKST      X        STABILITY CLASS
C     WHL       XXXX.    MIXING HEIGHT
C     WTA       XXX. X    AMBIENT AIR SURFACE TEMP.
C     DVP       X.XXX    DIURNAL VARIATION, POINT SOURCES (DIMENSIONLESS )
C     DVA       X.XXX    DIURNAL VARIATION, AREA SOURCES (DIMENSIONLESS)
C     DVH       X.XXX    DIUR. VAR. , HORIZ. LINE SOURCES (DIMENSIONLESS)
C     DVS       X.XXX    DIUR. VAR., SLANT LINE SOURCES
C     DDVH      X.XXX    DIUR. VAR., CURVE PATH SOURCES
C     DVHA      X.XXX    DIUR. VAR. , SPECIAL PATH SOURCES
C        THE DIURNAL VARIATION VALUES ARE THE RATIO OF THAT EMITTED
C         DURING THIS HOUR TO THE INPUT Q. IF THE SAME AS THE INPUT,
C         THE VALUE IS 1.000
470   CONTINUE
      IF (M-25) 490,40,480
480   WRITE (IWRI,1060)
      CALL EXIT
490   GO TO (500,510), IDRNL
500   DVP(M)=1.
      DVA(M)=1.
      DVH(M)=1.
      DVS(M)=1.
      DDVH(M)=1.
      DVHA(M)=1.
C        WRITE METEOROLOGY INFORMATION.
510   WRITE (IWRI,1070) M ,WTHET(M) ,WU (M) , MKST (M) ,WHL( M) ,WTA( M) , DVP (M) ,DV
     1A ( M ) , DVH ( M ) , DDVH ( M ) , DVS ( M ) , DVHA ( M )
      IF (ICARD. GT.l) GO TO 520
      M=M+1
      GO TO 440
520   CONTINUE
      DO 530 IM=1,M
      DO 530 IN=1,N
      CONP(IN,IM)=0.
      CONA(IN,IM)=0.
      CONLH(IN,IM)=0.
      CONCLN(IN,IM)=0.
      CONLS(IN,IM)=0.
      CONCLA(IN,IM)=0.
530   CONT(IN,IM)=0.
      GO TO (550,540) , IQP
S40   CALL POINT (M,I,N)
550   GO TO (570,560) , IQA
5bO   CALL AREA U,J,N,PINA)
570   GO TO (590, 5bO), IQLH
580   CALL HRZLN (M,K,N,PINL)
590   GO TO (olO,600), IQLC
bOO   CALL CRVLN (M,LL,N, PINL )
610   GO TO (630,620), IQLS
3720
3730
3740
3750
3760
3770
3780
3790
3800
3810
3820
3830
3d40
3850
3860
3870
3880
3890
3900
3910
3920
3930
3940
3950
3960
3970
3980
3990
4000
4010
4020
4030
4040
4050
4060
4070
4080
4090
4100
4110
4120
4130
4140
4150
4160
4170
4180
4190
4200
4210
4220
4230
4240
                95

-------
                         PAL

620   CALL SPCLN (M,L,N,PINL)                                               4250
630   GO TO (550,640), IQAC                                                 4260
fc.40   CALL SPCCR (M,LC,N,PINL)                                              4270
650   CONTINUE                                                              4280
      DO 660 IM=1,M                                                         4290
      DO 660 IN=1,N                                                         4300
660   CONT(IN,IM)=CONP(IN,IM)+CONA(IN,IM)+CONLH(IN,IM)+CONLS(IN,IM)+CONC    4310
     1LN(IN,IM)+CONCLA(IN,IM)                                               4320
      DO 670 IiH=l,w                                                         4330
      WRITE (IWRI,1080)                                                      4340
      DO b70 IN=1,N                                                         4350
670   WRITE (IWRI,1090)  IM,IN,RR(IN),SR(IN),ZR(IN),CONP(IN,IM),CONA(IN,I    4360
     1M),CONLH(IN,IM),CONCLN(IN,IM),CONLS{IN,IM),CONCLA(IN,IM),CONT(IN,I    4370
     2M)                                                                    4380
      IF (M-l) 740,740,680                                                  4390
680   GO TO (740,690), IAVG                                                 4400
690   DO 700 IN=1,N                                                         4410
      ACP(IN)=0.                                                            4420
      ACA(IN)=0.                                                            4430
      ACLH(IN)=0.                                                           4440
      ACLC(IN)=0.                                                           4450
      ACLS(IN)=0.                                                           4460
      ACAC(IN)=0.                                                           4470
700   ACT(IN)=0.                                                            4480
      DO 710 IM=1,M                                                         4490
      DO 710 IN=1,N                                                         4500
      ACP(IN)=ACP(IN)+CONP(IN,IM)                                           4510
      ACA(IN)=ACA(IN)+CONA(IN,IM)                                           4520
      ACLH(IN)=ACLH(IN)+CONLH{IN,IM)                                         4530
      ACLC(IN)=ACLC(IN)+CONCLN(IN,IM)                                        4540
      ACLS(IN)=ACLS(IN)+CONLS(IN,IM)                                         4 550
      ACAC(IN)=ACAC(IN)+CONCLA(IN,IM)                                        4560
710   ACT(IN)=ACT(IN)+CONT(IN,IM)                                           4570
      DO 720 IM=1,N                                                         4580
      ACP(IN)=ACP(IN)/M                                                     4590
      ACA(IN)=ACA(IN)/M                                                     4600
      ACLH(IN)=ACLH(IN)/M                                                   4610
      ACLC(IN)=ACLC(IN)/M                                                   4620
      ACLS(IN)=ACLS(IN)/M                                                   4630
      ACAC(IN)=ACAC(IN)/M                                                   4640
720   ACT(IN)=ACT(IN)/M                                                     4650
      WRITE (IWRI,1100)  M                                                   4660
      NDUt4=0                                                                4670
      WRITE (IWRI,1080)                                                      4680
      DO 730 IN=1,N                                                         4690
730   WRITE (IrtRI,1090)  NDUM,IN,RR(IN),SR(IN),ZR(IN),,ACP(IN),ACA(IN),AC    4700
     ILH(IN),ACLC(IN),ACLS(IN),ACAC(IN),ACT(IN)                             4710
740   READ (IRD,810,END=760) KTL                                            4720
      IF (KTL) 760,760,750                                                  4730
750   GO TO (10,390,430,760), KTL                                           4740
760   CALL EXIT                                                             4750
C                                                                           4760
770   FORMAT  (/,10X,'SOURCE  STRENGTH FOR THE REMAINING LANES',/,15X,'LAN    4770


                                         96

-------
                          PAL
 780
 790
 800
 810
 820
 830
 840
 850

 860
 870
 880

 890
900
 910
 920

 930
 940

 950
1E',5X,'SOURCE STRENGTH',/)
 FORMAT (17X,I2,T28,F10.8)
 FORMAT (20A4)
 FORMAT (1H1,20A4,5X,'VERSION ',15)
 FORMAT ()
 FORMAT (1HO,'PINA =',F10.5,' PINL =',
1D INCREASE',/,13X,'INCLUDED    WITH
                                      F10.5,//,14X,'SOURCE',5X,'WIN
                                      HEIGHT',//,4X,'POINT',6X,A3,1
      22X,A3,//,4X,'AREA',7X,A3,12X,A3,//,1X,'HORIZONTAL',/,1X,'LINE  SOUR
3CE' , 3X,A3,12X,A3,//,4X, '
                          CURVE' ,/,
                                   1X, 'PATH
                                                  SOURCE' , 3X, A3 , 1 2X , A3 , //
      4,3X,'SPECIAL',/,1X,'LINE  SOURCE',3X,A3,12X,A3,//,3X,'SPECIAL',/,1X
      5,'PATH  SOURCE',3X,A3,12X,A3,1 OX,'AVERAGE',5X,A3,'    DIURNAL',3X,A3
6,5X,'HEIGHT AT WIND SPEED',1X,F6.1,
 FORMAT (1HO,'* **POINT    SO
10INT    PHYSICAL    STACK     STACK
2DINATES       INITIAL SIGMAS'
3   GAS    DIAMETER    FLOW
                                    1X,'METERS',//)
                                    URGES***',/,7X,'NO.     P
                                         STACK    VOLUME       COOR
                              ,/13X,'SOURCE     HEIGHT     TEMP
                                  EAST     NORTH        Y
      4',/12X,'STRENGTH    (METERS)    (DEG-K)   VELOCITY   (METERS)   (CU
                 (KM)
                                  (M)
                                                                  Z
                                                                M/S
                                      (M)V13X,'(G/SEC)',24X,'(M/SE
                                                      THE STORAGE A
                                                                 AR
5EC)   (KM)
6C)',/)
 FORMAT (1H  ,I7,3X,F10.2,2F10.1,3F10.2,2F10.3,2F10.1)
 FORMAT (1HO,'THE NUMBER OF POINT SOURCE CARDS EXCEED
1LLOTTED FOR THEM IN THE DIMENSION STATEMENT:',13)
 FORMAT (///,'* **AREA   SOURCES**  *',/,7X,'NO,
1EA       AREA        COORDINATES        AREA  SIZE',/,13X,'SOURCE
2   SOURCE        SW-CORNER',/,12X,'STRENGTH    HEIGHT      EAST
3 NORTH  EAST-WEST NORTH-SOUTH',/,10X,'(G/SEC-M**2)  (METERS)     (KM
4)      (KM)     (KM)       (KM)',/)
        (1H  ,I7,3X,F10.8,F10.1,4F10.3)
        (1HO,'THE NUMBER OF AREA SOURCE  CARDS  EXCEED  THE STORAGE AL
        FOR  THEM IN THE DIMENSION STATEMENT:',13)
        (///,'* **HORIZONTAL    LINE   SOURCES*
                    LINE       LINE',17X,'COORDINATES',/,13X,'SOURC
 FORMAT
 FORMAT
1LOTTED
 FORMAT
1  * *',/,7X,'NO.
2E     SOURCE
3X,'NO.     TOTAL
4  NORTH      EAST
                     POINT A'
                                    13X,
                                    ,12X,
                           NORTH',8X,'Y'
                     MEDIAN',/,
                                  'POINT B',10X,'INITIAL
                                   'STRENGTH    HEIGHT
                                                         SIGMAS',11
                                                                  W
      5IDTH',/,11X,
              (G/SEC-M)   (METERS)
                                              EXCEED
                                              13)
                                              ALP
                                                     THE STORAGE AL
                                                     A T H
                                                              'S 0
                                                           EAST
                                    9X,'Z',19X,'OF      WIDTH
                                      (KM)       (KM)      (KM)
6 (KM)       (M)       (M)',17X,'LANES   (METERS)  (METERS) ')
 FORMAT (1H ,100X,F10.0,2F10.1)
 FORMAT (1H ,I7,3X,F10.8,F10.1,4F10.3,2F10.2)
 FORMAT (1HO,'THE NUMBER OF  LINE  SOURCE  CARDS
1LOTTED FOR THEM IN THE DIMENSION STATEMENT:',
 FORMAT (///,'* **CURVED  HORIZON
1URCES  *** ',/,2X,'NO.',T10,'PATH',T21
2ES',/,T9,'SOURCE',T20,'SOURCE',T32,'POINT  A'
3INT C',T87,'INITIAL SIGMAS',T108,'NO.',4X,'TOTAL      MEDIAN',/,T8,
4'STRENGTH',T20,'HEIGHT',T29,'EAST',T38,'NORTH',T50,'EAST',T59,'NOR
5TH',T68,'EAST',T77,'NORTH',T89,'Y',T99,'Z',T108,'OF     WIDTH
6WIDTH1,/,T7,'(G/SEC-M)',T19,'(METERS)',T29,'(KM)',T39,'(KM)',T50,'
7(KM)',T60,'(KM)',T68,'(KM)',T78,'(KM)',T88,'(M)',T98,'(M)',T108,'L
8ANES   (METERS)  (METERS)')
 FORMAT (/,2X,I2,T7,F10.8,T17,F9.3,T26,F9.3,T36,F9.3,T47,F9-3,T57,F
19.3,T66,F9.3,T76,F9.3,T86,F7.2,T96,F7.2,T108,I2,T115,F7.2,2X,F7.2)
 FORMAT (///,3X,'THE NUMBER  OF CURVED PATH  SOURCES EXCEEDS',' THE  N
                                                    'PATH',T42,'COORDINAT
                                                              B',T71,'PO
4780
4790
4800
4810
4820
4830
4840
4850
4860
4870
4880
4890
4900
4910
4920
4930
4940
4950
4960
4970
4980
4990
5000
5010
5020
5030
5040
5050
5060
5070
5080
5090
5100
5110
5120
5130
5140
5150
5160
5170
5180
5190
5200
5210
5220
5230
5240
5250
5260
5270
5280
5290
5300
                                          97

-------
                         PAL

     1UMBER ALLOTTED FOR THEM IN THE DIMENSION STATEMENT:',13)               5310
960   FORMAT (///,'* **SLANT   OR   VERTICAL   LINE   S     5320
     10URCES** *',/,7X,'NO.   SOURCE',7X,'SOURCE HEIGHT',10X,'PO     5330
     2INT A1,13X,'POINT B',9X,'INITIAL  FINAL',3X,'INITIAL SIGMAS',2X,'T     5340
     3RAFFIC1,1X,'VEH.',/,12X,'STRENGTH',8X,'(METERS)',4X,2(5X,'EAST         5350
     4  NORTH'),5X,'SPEED1,4X,'SPEED',7X,'Y',6X,'Z',4X,'VOLUME1,2X,'SIZE     5360
     51,/,12X,1 (G/SEC)     POINT A',3X,'POINT B',4X,4('(KM)',6X),2('(M/S     5370
     6EC)',2X),2X,'(M)',4X,'(M)',2X,'(VEH/HR)',1X,'(M)',/)                   5380
970   FORMAT (1H ,17,3X,F10.2,2F10.1,6F10.3,F8.2,F7.2,2X,F5.0,IX,F5.1)       5390
980   FORMAT (1HO,'THE NUMBER OF SLANT  LINE SOURCE CARDS EXCEED THE  STOR     5400
     1AGE ALLOTTED FOR THEM IN THE DIMENSION STATEMENT:',13)                 5410
990   FORMAT (///,'* **SPECIAL  PATH  SOURCES  ***',     5420
     i/, ix, NO. ', ix, SOURCE' ,4x, SOURCE ' ,9x, POINT A' ,nx, 'POINT  B',IIX     5430
     2,fPOINT C1,7X,INITIAL1 ,3X,FINAL1,4X,'INITIAL SIGMAS' ,2X,'TRAFFIC     5440
     3 VEH.',/,4X,'STRENGTH',3X,'HEIGHT',7X,'EAST1,4X,'NORTH1,5X,'EAST1,     5450
     44X,1NORTH',5X,'EAST',4X,'NORTH1,4X,'SPEED1,5X,'SPEED1,7X,'Y',6X,'Z     5460
     51 ,5X,'VOLUME  SIZE',/,5X,' (G/SEC) ' ,2X,( (METERS) ' ,6X,' (KM)' ,5X, ' (KM     5470
     6) ' ,5X,'(KM)',5X,' (KM)',5X,' (KM)',5X,' (KM)',4X,'(M/SEC)',2X,'(M/SEC     5480
     7)',5X,'(M)',4X,'(M)',3X,'(VEH/HR)',1X,'(M)',/)                         5490
1000  FORMAT (IX,12,IX,F8.2,2X,F8.1,2X,6(F8.3,IX),3X,2(F7.3,2X),1X,2F7.3     5500
     1,2X,F5.0,1X,F5.1)                                                       5510
1010  FORMAT (///,' THE NUMBER OF  SPECIAL PATH SOURCES  EXCEEDS THE1,1 ST     5520
     10RAGE ALLOTTED FOR THEM IN THE DIMENSION STATEMENT:',13)               5530
1020  FORMAT (///,'* **RECEPTORS** *',/,7X,'NO.    RREC(KM)      5540
     1 SREC(KM)    Z (M)'/)                                                   5550
1030  FORMAT (1H , 110,2F10.3,FlO.1)                                          5560
1040  FORMAT (1HO,'THE NUMBER OF RECEPTOR CARDS EXCEED  THE STORAGE1,' AL     5570
     1LOTTED FOR THEM IN THE  DIMENSION  STATEMENT: ', 13 )                       5580
1050  FORMAT (///,'* **METEOROLOGY** *1,/,7X,1NO.   THETA1,     5590
     I1 (DEC)    U (M/SEC)     KST   HL  (M)  T (DEG-K)            DIURNAL V     5600
     2ARIATIONS (FRACTIONS OF GIVEN  Q)',/,T90,'HORIZONAL',2X,'CURVED',3X     5610
     3, 'SPECIAL1 ,2X,'SPECIAL' ,/,T74,'POINT',5X,'AREA1 ,5X,1LINE1 ,5X,'PATH     5620
     4',5X,'LINE1,5X,'PATH1)                                                 5630
lObO  FORMAT (1HO,'THE NUMBER OF MET CARDS  EXCEED  24.')                      5640
1070  FORMAT (1H ,19 , ' . ' ,FlO.0,FlO.1,110,2F10.0,10X,6(F8.4,IX))              5650
1080  FORMAT (///,'* **CONCENTRATIONS    AT    RECEP      5660
     IT 0 R S * * *',/,5X,'CONCENTRATIONS IN GRAMS PER CUBIC METER1,T63,     5670
     21FROM',6X,'FROM',6X,'FROM',6X,'FROM',/,lX,'HOUR',1X,'RECEPTOR  ',3X     5680
     3,'RECEPTOR COORDINATES',4X,'FROM1,6X,'FROM',6X,'HORIZONAL',1X,'CUR     5690
     4VED',3X,'SPECIAL',3X,'SPECIAL1,/,8X,'NO.',5X,'EAST',4X,'NORTH',3X,     5700
     5'HEIGHT1,3X,'POINTS',bX,'AREAS',5X,'LINES',5X,'PATHS',5X,'LINES1,5     5710
     6X,'PATHS',5X,'TOTAL',//)                                               5720
1090  FORMAT (1H ,2X,12,T9,12,T14,2(F8.3,IX),F6.2,T43,1P7(E8.3,2X))          5730
1100-  FORMAT (1H1,'AVERAGE CONCENTRATIONS FOR1,14,' HOURS.')                 5740
C                                                                            5750
      END                                                                    5760
                                         98

-------
                         POINT
C
C
C
C
C
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C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
10'

20

30
40
SUBROUTINE POINT (M,I,N)
   POINT CALCULATES HOURLY CONTRATIONS FROM POINT SOURCES,
   THE FOLLOWING SUBROUTINES ARE CALLED BY POINT.
     FPLUME--HEIGHT OF FINAL PLUME HISE(BRIGGS).
                                     A DISTANCE X(BRIGGS)
                                     CONCENTRATION AT
                                     AT A GIVEN UPWIND
     XPLUME--EFFECTIVE PLUME RISE AT
     RCONCPDETERMINES THE RELATIVE
             A RECEPTOR FROM A POINT
             AND CROSSWIND DISTANCE.
    THE FOLLOWING FUNCTIONS ARE CALLED BY POINT.
      XVYCALCULATES THE VIRTUAL DISTANCE NECESSARY
                      FOR THE INITIAL CROSSWIND DISPERTION.
                      THE VIRTUAL DISTANCE NECESSARY
                      FOR THE INITIAL VERTICAL DISPERTION.
COMMON /SOP/ QP(3D ,HPP(3D ,TSP(31) ,VSP(31) ,DP(3D ,VFP(3D ,RQP(3D
,SQP(3O ,SYOP(3D ,SZOP(3D,CONP(31 ,24) ,DVP(25) , IUZP
COMMON /EEC/ RR(31),SR(31),ZR(31)
COMMON /WEA/ WTHET(25),WU(25),MKST(25),WHL(25),WTA(25),UHGT
DIMENSION PUZ(6)
DATA PUZ /O.15,0.15,0.20,0.25,0.40,0.60/
           TO ACCOUNT
      XVZCALCULATES
           TO ACCOUNT
                STACK
                STACK
                STACK
                EAST
QP
HPP
TSP
VSP
DP
VFP
RQP
SQP
SYOP
SZOP
IWRI=6
DO 200 NW=1 ,M
  DO FOR EACH HOUR.
THETA=WTHET(NW)
TR=THETA/57.2958
SINT=SIN(TR)
COST=COS(TR)
U = WU(Nwf)
UZ = U
KST=MKST(NW)
DTHDZ=0.
HL=WHL(NW)
T=WTA(NW)
PWR=PUZ(KST)
   CALCULATE  FOR ALL
DO 190 N3=1,1
KH=1
IF (SYOP(NS))
XVYP=0.
GO TO 30
SYON=SYOP(NS)
XVYP=XVY(SYON,KST)
IF (SZOP(NS)) 40,40,50
XVZP=0.
POTNT SOURCE STRENGTH.
PHYSICAL STACK HEIGHT.
STACK GAS TEMPERATURE.
      GAS VELOCITY.
      INSIDE DIAMETER.
      GAS VOLUME FLOW.
     COORDINATE OF STACK
                NORTH COORDINATE OF STACK
                INITIAL SIGMA Y.
                INITIAL SIGMA Z.
(G/SEC)
(M)
(DEG K)
(M/3EC)
(M)
(M**3/SEC)
(KM)
(KM)
(M)
(M)
                           SOURCES,
                    10,
                 10,20
00010
00020
00030
00040
00050
00060
00070
00080
00090
00100
00110
00120
00130
00140
00150
00160
00170
00180
00190
00200
00210
00220
00230
00240
00250
00260
00270
00230
00290
00300
00310
00320
00330
00340
00350
00360
00370
00380
00390
00400
00410
00420
00430
00440
00450
00460
00470
00480
00490
00500
00510
00520
00530
                                          99

-------
                    POI JT
uu
C
C
7U

C
oO
100
no
120



130

140
loO

C
1/0
      GO  TO oO
      3i,ON=SOP I.MS;
      AV'P=AV2 (S'iDN , v\Sr )
      CONTINUE
          CALCULaT'J  FOR  ALL kF.CCP rOtv3 .
       IF  (X)  lou,loU,"/0
          DETERi'tl.lC CKOSGfl'JD OI3T,AiiCC
       Y=o"SI.MT-K*COST
       GO  TO (30,l4U),  KSil
          E3TI laTf] PLtJ.^F  '0
       CALL XPLliun
                                        ,UZ ,
   ESTInAT1;: UCLATI\/K  CONCBN'f RATION  (CHI*[j/j).
CALL RCONCP (iK(-iC) ,H, flL,XZ,Xy,Y,KST,AN,.'iaUi''.,3Y,Si,RC)
liO
200    CONTINUE
       RETURN
C
210    PORi'lAT (1HO,'WO  COhPGTftTIONS  ARE rtTTKi'.PTBO  AG SOUSCS ' , 13 , ' HAS A  CT
      1ACK GAS TEi-lPERATURE LESS T4AN THK AilSI-JNT AIR TGMPE MATURE . ' )
C
       END
                                                                          COboU
                                                                          J C 00 U
                                                                          UOolJ
                                                                          UUu2U
                                                                          UOb4U
                                                                          OOooO
                                                                          OOo7U
                                                                          OUboO
                                                                          00 '/JU
                                                                          00710
                                                                          00720
                                                                          00730
                                                                          00/40
                                                                          OU/jG
                                                                          007oO
                                                                          U07 70
                                                                          007 !iO
                                                                          00 /yJ
                                                                          OOuOO
                                                                          00o20
                                                                          00o40
                                                                          OUODU
                                                                          OOdoU
                                                                          Ooou
                                                                          uuy20
                                                                          00lj30
                                                                          00^40
                                                                           OO^oO
                                                                           0070
                                                                          01000
                                     100

-------
AREA

c
c
c
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c
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c
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c
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c

SUBROUTINE AREA ( NHR , NQ , NR , PIN )
AREA CALCULATES HOURLY CONCENTRATIONS FROM
AREA SOURCES.
THE FOLLOWING SUBROUTINES ARE CALLED BY AREA.
PGSIG--CALCULATES SIGMA if, AND SIGMA Z.FROM
THE STABILITY AND DOWNWIND DISTANCE.
RCONCA  CALCULATES CHI*U/Q .RELATIVE CONCENTRATION
NORMALIZED FOR WIND SPEED FOR A RECEPTOR
DOWNWIND OF A CROSSWI.'JD INFINITE LINE SOURCE.
COMMON /SOA/ QA(31 ) ,HQ(3D ,RQ(3D ,SQ(3D ,DEST(3D ,DNOR(3D ,COrJA(31
1 ,24) ,DVA(25) ,IUZA
COMMON /REC/ RR( 3 1 ) ,SR( 3 1 ) , ZR(3 1 )
COMMON /WEA/ WTHET(25) ,WU(25) ,MKST(25) , WHL(25) ,VJTA(25) ,UHGT
DIMENSION GA(78), RA(4), SA(4), XL(4), PUZ(6)
GA ARE VALUES OF THE CUMULATIVE NORMAL DISTRIBUTION IN INCREMEN
OF 0.1 S.
DATA GA /.O, .0001 , .000 1 , .0002 , .0002, .0003, .0005, .0007,. 0010,. 0013,
1 .0019, .0026, .0035, .0047, .0062, .0092, .0107, -0139, .0179, .0228, .0287,
2.0359, .0446, .0548, .0668, .0808, .0968, . 1 151 , . 1 357, .1587, . 1841 , .21 19 ,
3.2420, .2743, .3085, .3446, .3821, .4207, .4602, .5000, .5398 , .5793 , .6 179 ,
4.6554, .6915, .7257, .7580, .7881,. 8159,. 8413, .8643, .8849, .9032, .9192,
5.9332, .9452, .9554, .9641, .9713, .9772, .9821, .9861,. 9893, .9918, .9938,
6.9953, .9965, .9974 , .9981 , .9987 , .9990, .9993, -9995 , .9997, .9998, .9998,
7.9999, -9999/
DATA PUZ /O. 15, 0.15, 0.20, 0.25,0. 40, 0.60/
OA AREA SOURCE STRENGTH. (G/SEC-M**2)
HQ AREA SOURCE HEIGHT. (M)
RQ EAST COORDINATE OF S.W. CORNER. (KM)
SQ NORTH COORDINATE OF S.W. CORNER. (KM)
DEST EAST-WEST SIZE. (KM)
DNOR NORTH-SOUTH SIZE. (KM)
SL IS THE Y VALUE (SOURCE UNITS) OF THE INTERSECTION OF LINES
XUSE AND R
RL IS THE X VALUE (SOURCE UNITS) OF THE INTERSECTION OF LINES
XUSE AND S
SL(R)=( (XUSE- ((R-RREC)*SINT)) /COST )+SREC
HL(S)=((XUSE-((S-SREC)COST))/SINT)+RREC
X IS THE UPWIND DISTANCE (SOURCE UNITS) OF SOURCE AT (R,S)
FROM RECEPTOR AT (RPS.SPS)
Y IS THE CROSSWIMD DISTANCE (SOURCE UNITS) OF SOURCE AT (R,S)
FROM RECEPTOR AT (RPS.SPS)
X(R,S)=(R-RREC)*SIMT+(S-SREC)*COST
Y(R,S)=(S-SREC)*SINT-(R-RREC)*COST
IWRI=6
DN IS NUMBER USED TO DETERMINE X (UPWIND FROM RECEPTOR) STEP
SIZE.
IDN=10
DN=IDN
DO 680 NW=1 ,NHR
THETA=WTHET(NW)
T=THETA/57.2958
T IS WIND DIRECTION (RADIANS)
SINT=SIN(T)
00010
00020
00030
00040
00050
00060
00070
00080
00090
00100
00110
00120
00130
00140
00150
00160
00170
00180
00190
00200
00210
00220
00230
00240
00250
00260
00270
00280
00290
00300
00310
00320
00330
00340
00350
00360
00370
00380
00390
00400
00410
00420
00430
00440
00450
00460
00470
00480
00490
00500
00510
00520
00530
                 101

-------
                         AREA
      COST=COS(T)
      U=WU(NW)
      UZ=U
      KST=MKST(NW)
      HL=WHL(NW)
      PWR=PUZ(KST)
      DO 670 NS=1,NQ
C        DETERMINE FOUR BOUNDARIES OF AREA SOURCE. (IN SOURCE UNITS)
      RB1=RQ(NS)
      RB2=RBl+DEST(NS)
      SB3=SQ(NS)
      SB4=S63+DNOR(NS)
      Q=QA(NS)
      H=HQ(NS)
      GO TO (20,10), IUZA
10    UZ=U*(H/UHGT)**PWR
      IF (H.GT.200.) UZ=U*(200./UHGT)**PWR
      IF (UZ.LT.1.0) UZ=1.0
20    DO 660 NC=1,NR
      RREC=RR(NC)
      SREC=SR(NC)
      Z=ZR(NC)
C        INITIALIZE VARIABLES FOR INTEGRATION PROCEDURE.
      KDN=IDN
      KNT=0
      TEST=1.0
      TOT1=0.
      TOT2=0.
      DMLX=0.
C        KROL IS USED FOR PROGRAM FLOW CONTROL (SEE STEP 590).
      KROL=1
C        DETERMINE UPWIND DISTANCE OF EACH SOURCE CORNER FROM RECEPTOR.
      XL(1)=X(RB1,SB3)
      XL(2)=X(RB1,SB4)
      XL(3)=X(RB2,SB3)
      XL(4)=X(RB2,SB4)
C        NEXT 8 STATEMENTS DETERMINE MAX AND MIN X (UPWIND) DISTANCES
C         OF SOURCE CORNERS.
      XMAX=XL(1)
      XMIN=XL(1)
      DO 60 L=2,4
      IF (XMAX-XL(L)) 30,40,40
30    XMAX=XL(L)
40    IF (XMIN-XL(L)) 60,60,50
50    XMIN=XL(L)
60    CONTINUE
      IF (XMAX) 660,660,70
C        NO PART OF AREA SOURCE
C        DETERMINE LIMITS FOR X
70    IF (XMIN) 30,90,90
80    XMIN=0.
C        DELX IS INTEGRATION X WIDTH(SOURCE
90    DELX=(XMAX-XMIN)/DN
IS UPWIND OF RECEPTOR (660)
ITERATION. (IN SOURCE UNITS.)
            UNITS) DMLX IS SAME(METERS)
00540
00550
00560
00570
00580
00590
00600
00610
00620
00630
00640
00650
00660
00670
00680
00690
00700
00710
00720
00730
00740
00750
00760
00770
00780
00790
00800
00810
00820
00830
00840
00850
00860
00870
00880
00890
00900
00910
00920
00930
00940
00950
00960
00970
00980
00990
01000
01010
01020
01030
01040
01050
01060
                                        102

-------
                         AREA

      DMLX=DELX*1000.                                                       01070
C        XUSE IS THE CURRENT VALUE OF UPWIND DISTANCE FROM THE RECEPTOR    01080
C         FOR THIS CALC. OF CONG. (A NUMBER OF ITERATIONS ARE DONE FOR     01090
C         THE TRAPEZOIDAL INTEGRATION.)                                     01100
      XUSE=XMIN                                                            OHIO
C        JDN IS CONTROL FOR PROPER INCLUSION OF FIRST AND LAST TERMS OF    01120
C         TRAPEZOIDAL  INTEGRATION.                                         01130
      JDN=0                                                                01140
100   TOT=0.                                                               01150
C        DETERMINE TWO LOCI.(IN SOURCE UNITS) TO 215 + 1                    01160
      IF (XUSE) 510,560,110                                                01170
110   1=0                                                                  01180
      IF (COST+0.0001) 130,120,120                                         01190
120   IF (COST-0.0001) 160,160,130                                         01200
130   Sl=SL(RBl)                                                           01210
      IF (S1-SB3) 160,140,140                                              01220
140   IF (S1-SB4) 150,150,160                                              01230
150   1=1+1                                                                01240
      RA(I)=RBl                                                            01250
      SA(I)=S1                                                             01260
160   IF (SINT+0.0001) 180,170,170                                         01270
170   IF (SINT-0.0001) 210,210,180                                         01280
IbO   R3=RL(SB3)                                                           01290
      IF (R3-RB1) 210,190,190                                              01300
190   IF (R3-RB2) 200,200,210                                              01310
200   1=1+1                                                                01320
      RA(I)=R3                                                             01330
      SA(I)=SB3                                                            01340
      IF (1-2) 210,330,210                                                 01350
210   IF (COST+0.0001) 230,220,220                                         01360
220   IF (COST-0.0001) 260,260,230                                         01370
230   S2=SL(RB2)                                                           01380
      IF (S2-SB3) 2bO,240,240                                              01390
240   IF (S2-SB4) 250,250,260                                              01400
250   1=1+1                                                                01410
      RA(I)=RB2                                                            01420
      SA(I)=S2                                                             01430
      IF (1-2) 260,330,260                                                 01440
260   IF (SINT+0.0001) 280,270,270                                         01450
270   IF (SINT-0.0001) 310,310,280                                         01460
280   R4=RL(SB4)                                                           01470
      IF (R4-RB1) 310,290,290                                              01480
290   IF (R4-RB2) 300,300,310                                              01490
300   1=1+1                                                                01500
      RA(I)=R4                                                             01510
      SA(I)=SB4                                                            01520
310   CONTINUE                                                             01530
      IF (1-2) 550,330,320                                                 01540
320   IERR=215                                                             01550
      GO TO 52U                                                            01560
C        DETERMINE CROSSWIND DISTANCE OF THE TWO LOCI.                     01570
330   RDUM=RA(1)                                                           01580
      SDUM=SA(1)                                                           015yO
                                       103

-------
                         AREA

      YA=Y(RDUM,SDUM)                                                      01600
      RDUM=RA(2)                                                           01610
      SDUM=SA(2)                                                           01620
      YB=Y(RDUM,SDUM)                                                      01630
C        YA AND YB IN SOURCE UNITS.                                        01640
      XDUM=XUSE                                                            01650
C        XDUM IS UPWIND DISTANCE (IN KM.).                                 01660
C        FIND DISPERSION PARAMETER VALUES FOR THIS DISTANCE.               01670
      CALL PGSIG (XDUM,XDUM,KST,SY,SZ)                                     01680
C        EXPRESS THE CROSSWIND DISTANCE (Y) IN NORMAL DISTRIBUTION         01690
C         DEVIATES.  (SMAX AND SMIN)                                        01700
      IF (YA-YB) 350,550,340                                               01710
340   SMAX=YA*1000./SY                                                     01720
      SMIN=YB*1000./SY                                                     01730
      GO TO 360                                                            01740
350   SMAX=YB*1000./SY                                                     01750
      SMIN=YA*1000./SY                                                     01760
C        DETERMINE THE CUMULATIVE VALUE OF THE NORMAL DIST. FOR EACH S.    01770
3bO   IF (SMAX+3.8)  550,550,370                                            01780
370   IF (SMIN-3.8)  380,550,550                                            01790
380   IF (3MAX-3.8)  400,400,390                                            01800
390   CFMAX=1.0                                                            01810
      GO TO 410                                                            01820
400   SSD=SMAX*10.+40.                                                     01830
      ISD=SSD                                                              01840
      SSO=ISD                                                              01850
      CFMAX=GA(ISD)+(SSD-SSO)*(GA(ISD+1)-GA(ISD))                          01860
410   IF (SMIN+3.8)  420,420,430                                            01870
420   CFMIN=0.0                                                            01880
      GO TO 440                                                            01890
430   SSD=SMIN*10.+40.                                                     01900
      ISD=SSD                                                              01910
      SSO=ISD                                                              01920
      CFMIN=GA(ISD)+(SSD-SSO)*(GA(ISD+1)-GA(ISD))                          01930
440   CONTINUE                                                             01940
C        DETERMINE THE AREA (CFM) OF THE NORMAL DIST. BETWEEN SMIN AND     Oly50
C         SMAX.                                                            01960
      CFM=CFMAX-CFMIN                                                      01970
      IF (CFM) 460,450,470                                                 01980
450   CWI=0.                                                               01990
      GO TO 480                                                            02000
460   IERR=405                                                             02010
      GO TO 520                                                            02020
C        DETERMINE THE CROSS-WIND INTEGRATED CONCENTRATION FOR THIS X.     02030
470   CALL RCONCA  (Z,H,HL,XDUM,KST,AN,M,SZ,CWI)                            02040
C        CWI IS THE  CONCENTRATION FROM AN INFINITE LINE SOURCE             02050
C         IN SECONDS PER SQUARE METER.                                     02060
480   CONTINUE                                                             02070
      GO TO (490,540), KROL                                                02080
C        STATEMENTS  490-530 PROVIDE FOR ADDITION OF THE TERMS IN THE       02090
C         FORMULA FOR TRAPEZOIDAL INTEGRATION THAT CORRESPOND TO THE       02100
C         ENDPOINTS  OF THE INTEGRATION.                                    02110
490   IF (XUSE-XMIN) 510,530,500                                           02120
                                        104

-------
                         AREA
500
510

520

530
C
C
540
C
550
560
570
580

590
C
600
610
C
C
620
630
640
C
C

650

660
670
680

C
690
700
C
                                    TERMS FOR CURRENT INTEGRATION
                                    FINITE LENGTH OF SOURCE.
                                             APPROXIMATION,
IF (JDN-KDN) 540,530,510
IERR=430
GO TO 520
WRITE (IWRI.690) IERR
CALL EXIT
CWI=0.5*CWI
   TOT IS A SUBTOTAL OF INTEGRATION
    (SEC/METER**2) ADJUSTED FOR THE
TOT=TOT+CWI*CFM
       JDN = KDN TERMINATES THIS INTEGRATION
IF (JDN-KDN) 560,570,580
XUSE=XUSE+DELX
JDN=JDN+1
GO TO 110
IF (TOT) 580,660,590
IERR=475
GO TO 520
GO TO (600,610), KROL
   PROGRAM FLOW REACHES 600 ONLY ON FIRST INTEGRATION ATTEMPT,
TOT1=TOT*DMLX
JDN=1
KNT=2
XUSE=XMIN+DELX/2.
KROL=2
GO TO 100
TOTZ=TOT1/2.+(TOT*DMLX)/2.
   TOT1  IS PREVIOUS ESTIMATE OF INTEGRATION (SEC/METER).
   TOT2 IS'CURRENT ESTIMATE OF INTEGRATION (SEC/METEH).
TEST=A8S(TOT2-TOT1)/TOT2
   CHECK PRECISION OF INTEGRATIONS AGAINST DESIRED VALUE.
IF (TEST-PIN) 650,650,620
IF (KNT-10)  640,640,630
WRITE (IWRI.700) IOT1,TOT2
IERR=500
GO TO 520
DELX=DELX/2.
XUSE=XMIN+DELX/2.
DMLX=DMLX/2.
TOT1=TOT2
KNT=KNT+1
JDN=1
KDN=2*KDN
   RETURN TO CALCULATE ADDITIONAL VALUES FOR X DISTANCE
    MIDWAY BETWEEN X DISTANCES USED FOK LAST ITERATION.
GO TO 100
CONTINUE
CONA(NC,NW)=CONA(NC,NW)+TOT2*Q*DVA(NW)/UZ
CONTINUE
CONTINUE
CONTINUE
RETURN
FORMAT
FORMAT

END
       (1HO,'ERROR AT',15)
       (1HO,'INTERVAL HAS BEEN
HALVED 10 TIMES',2E15.8)
                                        105
02130
02140
02150
02160
02170
02180
02190
02200
02210
02220
02230
02240
02250
02260
02270
02230
02290
02300
02310
02320
02330
02340
02350
02360
02370
02380
02390
02UOO
02410
02420
02430
02440
02450
02460
02470
02480
02490
02500
02510
02520
02530
02540
02550
02560
02570
02580
02590
02600
02610
02620
02630
02640
02650
02660
02670
02630

-------
HRZLN

c
c
c
c
c
c
c
c
c
c
c






c
c
c
c
c
c
c
c
r
\s
c
c
c
c
c
c
r1

-------
                         HRZLN

      QL=QLN(NS)                                                           00b40
      H=HLN(NS)                                                            00550
      GO TO (20,10) ,  IUZH                                                  00560
10    UZ=U*(H/UHGT)**PWR                                                   00b70
      IF (H.GT.200.)  UZ=U*(200./UHGT)**PWR                                 00580
      IF (UZ.LT.1.0)  UZ=1.0                                                OOSyO
20    IF (SYO(NS)) 40,30,40                                                OObOO
30    KVYL=0.                                                               00610
      GO TO 50                                                             00620
40    SYON=SYO(NS)                                                         00630
      XVYL=XVY(SYON,KST)                                                   00640
50    IF (SZO(NS)) 70,60,70                                                006^0
60    XVZL=U.                                                               00660
      GO TO 80                                                             00670
70    SZON=SZO(i\IS)                                                         00680
      XVZL=XVZ(SZON,KST)                                                   00690
80    CONTINUE                                                             00700
      DO 920 NC=1,NR                                                       00710
      RREC=RR(NC)                                                          00720
      SREC=SR(NC)                                                          00730
      Z=ZR(NC)                                                             00740
      X1=X(R1,S1)                                                          00750
      X2=X(R2,S2)                                                          00760
      IF (XI)  yO,110,110                                                   00770
90    IF (X2)  100,110,110                                                  00780
100   RC=0.                                                                00790
      GO TO 920                                                            00800
110   DELR=R2-R1                                                           00810
      DELS=S2-S1                                                           00820
      Y1=Y(R1,S1)                                                          00830
      Y2=Y(R2,S2)                                                          00840
      IF (Y1-Y2) 120,420,120                                               00650
C        IF Yl = Y2,  LINE SOURCE IS PARALLEL TO UPWIND AZIMUTH FROM RECE   00860
120   IF (COST+0.0001)  190,130,130                                         00870
130   IF (COST-0.0001)  140,140,190                                         00880
140   IF (DELR+0.0001)  170,150,150                                         00a90
150   IF (DELR-0.0001)  160,160,170                                         00900
160   SLOC=SREC                                                            OOS10
      RLOC=R1                                                               00920
      GO TO 310                                                            00930
170   SLP=DELS/DELR                                                        00940
      IF (SLP) 180,420,180                                                 00950
180   SLOC=SREC                                                            00960
      RLOC=(SLOC-S1)/SLP+R1                                                00970
      GO TO 310                                                            00980
190   IF (SINT+0.0001)  240,200,200                                         00990
200   IF (SINT-0.0001)  210,210,240                                         01000
210   IF (DELR+0.0001)  230,220,220                                         01010
220   IF (DELR-0.0001)  420,420,230                                         01020
230   SLP=DELS/DELR                                                        01030
      RLOC=RREC                                                            01040
      SLOC=SLP*(RLOC-R1)+S1                                                01050
      GO TO 310                                                            01060
                                       107

-------
                         HRZLN

240   IF (DELR+0.0001) 270,250,250                                         01070
250   IF (DELR-0.0001) 260,260,270                                         01080
260   RLOC=R1                                                              01090
      SLOC=(RLOC-RREC)*COST/SINT+SREC                                      01100
      GO TO 310                                                            OHIO
270   IF (DELS+0.0001) 300,280,280                                         01120
280   IF (DELS-0.0001) 290,300,300                                         01130
290   SLOC=S1                                                              01140
      RLOC=(SLOC-SREC)*SINT/COST+RREC                                      01150
      GO TO 310                                                            01160
300   TATH=SINT/COST                                                       01170
C        TATH IS TANGENT (THETA)                                           01180
      SLP=DELS/DELR                                                        01190
C        SLP IS SLOPE OF LINE SOURCE.                                      01200
      RLOC=(RREC/TATH+S1-SLP*R1-SREC)/(1/TATH-SLP)                          01210
      SLOC=(RLOC-RREC)/TATH+SREC                                           01220
C        RLOC, SLOC IS LOCUS OF LINE THROUGH LINE SOURCE AND UPWIND VECT   01230
310   XLOC=X(RLOC,SLOC)                                                    01240
      IF (XLOC) 420,420,320                                                01250
C        XLOC IS POSITIVE IF LOCUS IS UPWIND.                              01260
320   IF (S2-S1) 330,330,340                                               01270
330   SMAX=S1                                                              01280
      SMIN=S2                                                              01290
      GO TO 350                                                            01300
340   SMAX=S2                                                              01310
      SMIN=S1                                                              01320
350   IF (R2-R1) 360,360,370                                               01330
360   RMAX=R1                                                              01340
      RMIN=R2                                                              01350
      GO TO 3bO                                                            01360
370   RMAX=R2                                                              01370
      RMIN=Rl                                                              01380
C        SEE IF UPWIND LOCUS IS ON LINE SOURCE.                            01390
380   IF (RLOC-RMIN) 420,390,390                                           01400
390   IF (RMAX-RLOC) 420,400,400                                           01410
400   IF (SLOC-SMIiO 420,410,410                                           01420
410   IF (SMAX-SLOC) 420,430,430                                           01430
420   INDIC=1                                                              01440
C        INDIC =1 FOR NO LOCUS ON LINE SOURCE.                             01450
      XA=X1                                                                01460
      YA=Y1                                                                01470
      XB=X2                                                                01480
      YB=Y2                                                                01490
      GO TO 440                                                            01500
430   INDIC=2                                                              01510
C        INDIC =2 FOR LOCUS ON LINE SOURCE.                                01520
      XA=X1                                                                01530
      YA=Y1                                                                01540
      XB=XLOC                                                              01550
      YB=0.                                                                01560
440   DISX=XB-XA                                                           01570
      DISY=YB-YA                                                           01580
      DISI=3QRT(DISX*DI3X+DISY*DISY)                                       01590
                                        108

-------
                         HRZLN
C        DISI IS LENGTH(KM) OF LINE CONSIDERED.
      IF (DISI) 460,450,460
450   CURR=0.
      GO TO 660
460   DDI=DI3I*1000./20.
C        ONE-HALF IS INCLUDED IN THE 20.
C        DDI IS ONE-HALF  TIMES 1/10 OF DISI (M).
      DX=DISX/10.
      DY=DISY/10.
      PRE\7=0.
      KNTRL=1
      XI=XA
      YI = YA
      KNT=0
      DO 580 1=1,11
C        STORE EACH XI,YI.
      XST(I)=XI
      YST(I)=YI
      IF (XST(I)) 470,470,480
470   RC=0.
      GO TO 490
480   XZ=XI+XVZL
      XY=XI+XVYL
      CALL RCONCP (Z,H,HL,XZ,XY,YI,KST,AN,M,SY,SZ,RC)
490   GO TO (500,540), KNTRL
C        IF RC IS ZERO, CONTINUE UNTIL RC IS POSITIVE,
500   IF (RC) 570,570,510
510   IF (1-1) 520,520,530
520   KNTRL=2
      GO TO 560
C        RESET POINT A TO LAST ONE PREVIOUS.
530   XA=XST(I-1)
      YA=YST(I-1)
      KNTRL=2
      GO TO 560
540   IF (RC) 550,550,560
C        RESET POINT B IF REACH ZERO CONCENTRATION.
550   XB=XI
      YB=YI
      GO TO 590
560   KNT=KNT+1
570   XI=XI+DX
      YI=YI+DY
580   CONTINUE
590   IF (KNT) 610,610,600
bOO   IF (KNT-6) 440,440,650
C        IF GET TO 610, CONC.  FROM THIS SEGMENT IS 0.
610   GO TO (620,630,640), INDIC
620   RC=0.
      GO TO 920
630   FIRST=0.
      GO TO 890
640   RC=FIRST
01600
01610
01620
01630
01640
01650
01660
01&70
01680
01690
01700
01710
01720
0173U
01740
01750
01760
01770
01780
01790
01800
01810
01820
01830
01840
01850
01860
01870
01880
01890
01900
01910
01920
01930
01940
01950
01960
01970
01980
01990
02000
02010
02020
02030
02040
02050
02060
02070
02080
02090
02100
02110
02120
                                        109

-------
                   HRZLN
t> 50
C
C
C

C
660

670


680




690

700


710



720

730
740
C
750
C
GO TO
CONTINUE
   DO AiMOTHER TRAPEZOIDAL INTEGRATION PROM A TO B IN TEN STEPS,
   IT IS LIKELY THAT A TO B HAVE BEEN REDEFINED.
DISX=XB-XA
DISY=YB-YA
DISI=S2RT(DI3X*DISX+DISY*DISY)
   DISI IS DISTANCE (KH) FROM A TO B
DELD=DISI*10U.
   DELD IS 1/10 DISI IN METERS.
DX=DISX/10.
DY=DI3Y/10.
760
XDIM=XA
YDUM=YA
IF (XDUM) 660,660,670
RC=0.
GO TO 680
XZ=XDUM+XVZL
XY=XDUM+XVYL
CALL RCONCP ( Z , H , HL,XZ ,XY , YDUM ,KST, AN , M,SY ,SZ ,RC )
SUM=SUM+RC/2.
DO 710 1=1,9
XDUM=XDUM+DX
YDUM=YDUM+DY
IF (XDUM) 6yO,690,700
RC=0.
GO TO 710
XZ=XDUM+XVZL
XY=XDUM+XVYL
CALL RCONCP ( Z ,H , HL,XZ ,XY ,YDUM ,KST, AN, M,SY ,SZ ,RC )
SUM=SUM+RC
XDUM=XDUM+DX
YDUM=YDUM+DY
IF (XDUM) 720,720,730
RC=0.
GO TO 740
XZ=XDUM+XVZL
XY=XDUM+XVYL
CALL RCONCP ( Z ,H,HL,XZ ,XY, YDUM ,KST, AN, M,SY ,SZ ,RC )
SUM=SUM+RC/2.
   INTEGRATED VALUE IS CURR.
CURR=SUM*DELD
ILIM=10
PREV=CURR
   EVALUATE FOR POINTS IN BETWEEN THOSE ALREADY EVALUATED.
DELD=DELD/2.
XDUM=XA+DX/2.
YDUM=YA+DY/2.
DO 790 I=1,ILIM
IF (XDUM) 760,760,770
RC = 0.
GO TO 780
02130
02140
02150
02160
02170
02160
02190
02200
02210
02220
02230
02240
02250
02260
02270
02280
02290
02300
02310
02320
02330
02340
02350
02360
02370
02380
02390
02400
02410
02420
02430
02440
02450
02460
02470
02480
02490
02500
02510
02520
02530
02540
02550
02560
02570
02580
02590
02600
02610
02620
02630
02640
02650
                                  110

-------
HRZLN
770
C
780

790
C

800

C
810

820


830

840



850
C
350
870

880
390
900
9 1 0
920
930
940
XZ=XDUM+XVZL
XY=XDUM+XVYL
CALL RCOHCP ( Z ,H, HL ,XZ ,XY , YDUM ,KST, AN , M,SY ,SZ ,RC)
   NOTE ADD THESE TO fiC'S FOUND ABOVE.
SUM=SUM+HC
XDUM=XDUM+DX
YDUM=YDUM+DY
CURR=SUM*DELD
TEST=ABS( (CURR-PREV)/CURR)
   IF WITHIN PIN OF LAST i/ALUE (PREV),  CONSIDER THIS AS FINAL  VALU
IF (TEST-PIN)  860,800,800
ILIM=ILIM*2
PREV=CURR
   EVALUATE POINTS IN BETWEEN.
DELD=DELD/2.
DX=DX/2.
DY=DY/2.
XDUM=XA+DX/2.
YDUM=YA+DY/2.
DO 840 1=1 ,ILIM
IF (XDUH) 810,810,820
RC=0.
GO TO 830
XZ=XDUM+XVZL
XY=XDUM+XVYL
CALL RCONCP ( Z , H , HL , XZ ,XY , YDUM , KST, AN , M,SY ,SZ , RC)
      XDUM=XDUM+DX
      YDUM=YDUM+DY
      CURR=SUM*DSLD
      TEST=ABS((CUrtR-PREV)/CURR)
      IF (TEST-PIN) 860,850,850
      ILIM=ILIM*2
      DX=DX/2.
      DY=DY/2.
      GO TO 750
         AT 860 rlAVt FINAL VALUE
      GO TO (370,380,900), INDIC
      RC=CURH
      GO TO 910
      FIRST=CURH
                           OF INTEGRATION IN CURR
XA=XLOC
YA=0.
Xb=X2
YB=Y2
GO TO 440
RC=FIRST+CURR
CONLH ( NC , NW ) =CONLH( HC , M ) +RC*QL*DVH (KU) /UZ
CONTINUE
CONTINUE
CONTINUE
RETURN
               in
                                                  02660
                                                  02670
                                                  02680
                                                  02690
                                                  02700
                                                  02710
                                                  02720
                                                  02730
                                                  02740
                                                  02750
                                                  02760
                                                  02770
                                                  02780
                                                  02790
                                                  02800
                                                  32810
                                                  02820
                                                  02830
                                                  02840
                                                  02850
                                                  0286G
                                                  02870
                                                  02880
                                                  02690
                                                  02900
                                                  02910
                                                  02920
                                                  02930
                                                  02940
                                                  02950
                                                  02960
                                                  02970
                                                  02980
                                                  02990
                                                  03000
                                                  03010
                                                  03020
                                                  03030
                                                  03040
                                                  03050
                                                  03060
                                                  03070
                                                  03080
                                                  03090
                                                  03100
                                                  03110
                                                  03120
                                                  03130
                                                  03 1 40
                                                  03150
                                                  03160
                                                  03170
                                                  03130
                                                  03190
                                                  03200

-------
                         CRVLN
      SUBROUTINE CRVLN (NHR , NQ , NR , PIN)
C        CRVLN CALCULATES HOURLY CONCENTRATIONS FROM
C        MULTI-LANE CURVED PATH  SOJRCES.
c        THE: FOLLOWING SUBROUTINES  ARE  CALLED BY CRVLN.
C          CURLIi^ CALCULATES THE INTERSECTION OF THE
C                   LINE  FORMED  BY  THE  WIND DIRECTION AND
C                   RECEPTOR  COORDINATES  AND THE CIRCLE
C                   DETEhMINED FROM POINTS A,B,C.
C          RCONCP--DSTERMINES THE RELATIVE CONCENTRATION AT
C                  A RECEPTOR FROM  A POINT AT A GIVEN UPWIND
C                  AND CROSSWIMD DISTANCE.
C         THE FOLLOWING FUNCTIONS ARE CALLED BY CRVLN.
C           XVY--CALCULATliS THE  VIRTUAL DISTANCE NECESSARY
C                TO ACCOUNT FOR  THE INITIAL CROSSWIMD DISPERTION.
C           XVZ---CALCULATES THE  VIRTUAL DISTANCE NECESSARY
C                TO ACCOUNT FOR  THE INITIAL VERTICAL DISPERTION.
C           ANGARA-DETERMINES THE  APPROPRIATE ARCTAM(M/N)
C                   WITH  THE  RESULTING  ANGLE BETWEEN 0  AND
C                   360 DEGREES.
C           DIFAHGDETERMINES THE  DIFFERENCE BETWEEN TWO ANGLES.
C                   THE RESULTING ANGLE IS BETWEEN 0 AND 360 DEGREES,
      COMMON /SOCP/ QLNS(31),HLNS(31),RBQS(31),SBQS(31),RMQS(31),SMQS(31
     1) ,REQS(31 ) ,SEQS(3D ,SIYO(31) ,SIZO(3D ,CONCLN(31 ,24) ,DDVH(3O ,IUZC,
     2RADIU3(31) ,NLANE(3O
      COMMON /REG/ RR(31),SR(31) , ZR(31)
      COMMON /WLA/ WTHET(25),WU(25),MK3T(25),WHL(25),WTA(25),UHGT
      DIMENSION PUZ(6), RRR(11), SSS(11),  DIR(11), ARC(5), XANG(5)

C
c
c
c
c
c
c
c
c
ft
u
c
c
c
c
c
c
c
c
c
c
c
c
DATA P
QLHS
HLNS
RBQS
SBQS
RMQS
SMQS
REQS
SEOS
SIYO
SIZO
CONCLN
DDVH
IUZC
RR EA
SR NO
ZR
WTHET
WU WI
MKST
WHL M
WTA A
WP A
               /O.15,0.15,0.20,0.25,0.40,0.607
            PATH SOURCE  STRENGTH FOR EACH LANE
            HEIGHT OF THE PATH SOURCE
            EAST COORDINATE,POINT A
            NORTH COORDINATE,POINT A
            EAST COORDINATE,POINT B
            NORTH COORDINATE,POINT B
            EAST COORDINATE,POINT C
            NORTH COORDINATE,POINT C
            INITIAL SIGMA Y
            INITIAL SIGMA Z
              CONCENTRATION
                    VARIATION,CURVED
PATH SOURCE
      DIURNAL
      WIND INCREASE WITH HEIGHT
         COORDINATE OF RECEPTOR
         ! COORDINATE OF RECEPTOR
      HEIGHT OF RECEPTOR ABOVE GROUND
       WIND DIRECTION
       D SPEED
      STABILITY CLASS
         NG HEIGHT
         SNT AIR SURFACE TEMP.
     AMBIENT AIR SURFACE PRESSURE
X(R,S)=(R-RREC)*SINT+(S-SREC)*COST
   X IS UPWIND DISTANCE OF R,S FROM RREC.SREC
Y(R,S)=(S-SREC)*SINT-(R-RREC)*COST
(G/SEC-M)
(M)
(KM)
(KM)
(KM)
(KM)
(KM)
(KM)
(M)
(M)
(G/M**3)
(DIMENSIONLESS)
(DIMENSIONLESS)
(KM)
(KM)
(M)
(DEC  AZIMUTH)
(M/SEC)
(DIMENSIONLESS)
(M)
(DEC  K)
(MB)
00010
00020
00030
00040
00050
00060
00070
00080
00090
00100
001 10
00120
00130
00140
00150
00160
00170
00180
00190
00200
00210
00220
00230
00240
00250
00260
00270
00280
00290
00300
00310
00320
00330
00340
00350
00360
00370
00380
00390
00400
00410
00420
00430
00440
00450
00460
00470
00480
00490
00500
00510
00520
00530
                                        112

-------
                         CRVLN
C        Y IS CROSSWTND DISTANCE OF R,S FROM RREC,SREC
C        START DO LOOP FOR EACH HOUR.
      DO 460 NW=1,NHR
      KUMC=0
      THETA=WTHET(NW)
      TR=THETA/57.2958
      SINT=SIN(TR)
      COST=COS(TR)
      U=WU(NW)
      UZ=U
      KST=MKST(Nto)
      HL=WHL(NVv)
      PWR=PUZ(KST)
C        START DO LOOP FOR EACH CURVED PATH.
      DO 460 NS=1,NQ
      RB=RBQS(NS)
      RM=RMQS(NS)
      RE=REQS(NS)
      SB=SBQS(NS)
      SW=SMQS(NS)
      SE=SEQS(iSIS)
      H=HLNS(NS)
      GO TO (20,10), IUZC
10    UZ=U*(H/UHGT)**PWR
      IF (H.GT.200.) UZ=U*(20G./UHGT)**PrtR
      IF (UZ.LT.1.0) UZ=1.0
20    IF (SIYO(NS)) 40,30,40
30    XVYL=0.
      GO TO 50
40    SYON=SIYO(NS)
      XVYL=XVY(SYON,KST)
50    IF (SIZO(NS)) 70,60,70
bO    XVZL=0.
      GO TO 80
70    SZON=SIZO(NS)
      XVZL=XVZ(SZON,KST)
dO    CONTINUE
C        THE COORDINATES OF THE CENTER OF THE CIRCLE,
C         DETERMINED FROM THE INTERSECTION OF THE PERPENDICULAR
C         BISECTORS OF CHORDS AS AND BC,AND THE RADIUS OF THE
C         CIRCLE ARE CALCULATED.
      RMID=(RB+RM)/2.
      SMID=(3B+SM)/2.
      RNID=(Rh+RE)/2.
      SNID=(3M+SE)/2.
      IF (RM-RB.EQ.O) GO TO yO
      IF (RE-RM.Es2.U) GO TO 100
C        SL01 IS THE SLOPE OF THE PERPENDICULAR BISECTOR
C        OF CHORD AB.
C        SL02 IS THE SLOPE OF THE PERPENDICULAR BISECTOR
C        OF CHORD BC.
      SL01( (RM-RB)/(SM-SB) )
      SL02=-((RE-RM)/(SE-SM))
00540
00550
00560
00570
00580
00590
00600
00610
00620
00630
00640
00650
00660
00670
00680
00690
00700
00710
00720
00730
00740
00750
00760
00770
007HO
00790
00800
00810
00820
00830
00840
00850
00860
00b70
00880
00890
00900
00910
00920
00930
00940
00950
00960
00y70
00980
00990
01000
0101J
01020
01030
01040
01050
01060
                                        113

-------
                         CRVLN
C        RC AND SC ARE THE COORDINATES OF THE CENTER OF THE
C        CIRCLE.
      RC=(SL01*RMID+SNID-SMID-SL02*RNID)/(SL01-SL02)
      SC=SL01*(RC-RMID)+SMID
      GO TO 110
90    RC=RMID
      SL02=-((RE-RN)/(SE-SM))
      SC=SL02*(RC-RNID)+SNID
      GO TO 110
100   RC=RNID
      SL01=-((RM-RB)/(SM-SB))
      SC=SL01*(RC-RMID)+SMID
      GO TO 110
C        RAD IS THE RADIUS OF THE CIRCLE.
110   RAD=SQRT((RC-RB)**2+(SC-SB)**2)
      DELM=RB-RC
      DELN=SB-SC
C        ANGB IS THE DIRECTED ANGLE  FROM THE CENTER TO POINT A.
      ANGB=ANGARC(DELM,DELN)
      DELM=RM-RC
      DELN=SM-SC
C        ANGM IS THE DIRECTED ANGLE  FROM THE CENTER TO POINT 8,
      ANGM=ANGARC(OELM,DELN)
      DELrf=RE-RC
      DELN=SE-SC
C        ANGE IS THE DIRECTED ANGLE  FROM THE CENTER TO POINT C,
      ANGE=ANGARC(DELM,DELN)
      ANGBE=ABS(DIFANG(ANGB,ANGE))
      ANGBM=A8S(DIFANG(ANGB,ANGM))
      ANGME=ABS (DIFANG(ANGM, ANGE) )
      IF (ANGBM.LT.ANGBE.AND.ANGME.LT.ANGBE) GO TO 120
      GAMDEG=360.-ANGBE
      GO TO 130
120   GAWDEG=ANGBM+ANGME
130   A=l.
      IF (GAMDEG.GE.180.) GO TO 140
      BEDEG=DIFANG(ANGE,ANGB)
      IF (BEDEG.LT.O.) A=-l.
      GO TO 150
140   RDEG=ANGB+180.
      RMDEG=DIFANG(ANGM,RDEG)
      REDEG=DIFANG(ANGE,RDEG)
      IF (RMDEG.GE.O..AND.REDEG.LE.0.) A=-l.
150   CONTINUE
      NUMLNE=NLANE(NS)
      NUMC=NUMLNE+NUMC
      NLL=NUMC-NUMLNE+1
      RDI=RAD
      DO 460 NL=NLL,NUMC
      RAD=RDI+RADIUS(NL)
      QL=QLNS(NL)
      DO 460 NC=1,NR
      RREC=RR(NC)
01070
01080
01090
01100
OHIO
01120
01130
01140
01150
01160
01170
01180
01190
01200
01210
01220
01230
01240
01250
01260
01270
01280
01290
01300
01310
01320
01330
01340
01350
01360
01370
01380
01390
01400
01410
01420
01430
01440
01450
01460
01470
01480
01490
01500
01510
01520
01530
01540
01550
01560
01570
01580
01590
                                        114

-------
                         CRVLN
      SREC=SR(NC)
      Z=ZR(NC)
C     CURLIN CALCULATES THE COORDINATES OF ANY UPWIND LOCI ON ARC AB
C     FROM HERE TO STATEMENT 310 THE BEGINNING AND ENDING
C     POINTS,WITH THEIR CORRESPONDING DIRECTIONS,FOR EACH SEGMENT
C     OF THE ARC ARE CALCULATED
      CALL CURLIN (RC,SC,RREC,SREC,Z,RAD,THETA,RL,SL,RLl,SLl,NLOCI)
      IF (NLOCI) 160,170,160
C     NLOCI HAS VALUES OF  -1,0,OR 1 FOR:
C     NO UPWIND LOCI ON ARC AB: 1 LOCI ON ARC AB:
C     OR 2 LOCI ON ARC AB
160   XANG(1)=ANGB
      ARC(1)=GAMDEG
      J=l
      GO TO 310
170   K=l
      GO TO 190
IdO   K=2
190   N=l
      DO 270 KK=1,K
      IF (KK.EQ.2) GO TO 200
      DELM=RL-RC
      DELN=SL-SC
      ANGRL=ANGARC(DELM,DELN)
      RANG=ANGRL
      GO TO 210
200   DELM=RL1-RC
      DELN=SL1-SC
      ANGRL=ANGARC(DELM,DELN)
      RLANG=ANGRL
210   IF (GAMDEG.GT.180..AND.A.GT.O. )  GO TO 220
      IF (GAMDEG.GE.180..AND.A.LT.O.)  GO TO 230
      IF (GAMDEG.LT.ldO..AND.A.LT.O. )  GO TO 240
      BIN=DIFANG(ANGRL,ANGB)
      IF (BIN.LE.O..OR.BIN.GE.GAMDEG)  GO TO 260
      ARC(N)=BIN
      GO TO 250
220   BIN=DIFANG(ANGRL,ANGB)
      IF (6IN.GT.O.) ARC(N)=BIN
      IF (BIN.GT.O.) GO TO 250
      IF (BIN.LE.O.) DIF=(GAMDEG-360.)-BIN
      IF (DIF.LT.O.) GO TO 2bO
      ARC(N)=BIN+360.
      GO TO 250
230   BIN=DIFANG(ANGRL,ANGB)
      IF (BIN.LT.O.) ARC(N)=BIN
      IF (BIN.LT.O.) GO TO 250
      IF (BIN.GE.O..AND.BIN.LE.360.-GAMDEG) GO TO 260
      ARC(N)=360.-BIN
      GO TO 250
240   BIN=DIFANG(ANGRL,ANGB)
      IF (BIN.GE.O..OR.BIN.LE.-GAMDEG) GO TO 260
      ARC(N)=BIN
01600
01610
01620
01630
01640
01650
01660
01670
01680
01690
01700
01710
01720
01730
01740
01750
01760
01770
01780
01790
OldOO
01&10
01620
Old30
01840
01850
01660
01870
OlBdO
01390
01900
01910
01920
01930
01940
01950
01960
01970
01980
01990
02000
02010
02020
02030
02040
02050
02060
02070
02080
02090
02100
02110
02120
                                        115

-------
CRVLN
      GO TO 250
250   N=N+1
      INDEX=-1
      IF (KK.EQ.2) INDEX=1
      GO TO 270
260   IF (K.NE.l) GO TO 270
      XANG ( 1 ) =ANGB
      ARC ( 1 ) =GAMDEG
270   CONTINUE
      XANG ( 1 ) =ANGB
      IF (N-l.EQ.O) GO TO 300
      IF (N-1.EQ.2) GO TO 280
      ARC ( 2 ) =GAMDEG-ABS ( ARC ( 1 ) )
      XANG(2)=RANG
      IF (INDEX.EQ.l) XANG(2)=RLANG
      J=2
      GO TO 310
280   ARC(1)=ABS(ARC(1) )
      ARC(2)=ABS(ARC(2) )
      IF (ARC(l) .GT.ARC(2) ) GO TO 290
      ARC(2)=ARC(2)-ARC(1)
      ARC ( 3 ) =GAMDEG-ARC ( 1 ) -ARC ( 2 )
      XANG(2)=RANG
      XANG(3)=RLANG
      J=3
      GO TO 310
290   AA=ARC(1)
      ARC(1)=ARC(2)
      ARC(2)=AA-ARC(2)
      ARC ( 3 ) =GAMDEG-ARC ( 1 ) - ARC ( 2 )
      XANG(2)=RLANG
      XANG(3)=RANG
      J = 3
      GO TO 310
300   J=l
      ARC(1)=GAMDEG
310   TOTAL=0.
      DO 450 M=1,J
      KNT=0
      NM=0
      LCOUNT=0
C     CHI VALUES ARE CALCULATED
C     THE SEGMENT IS REDUCED IN
C     VALUES ARE NON-ZERO.
320   DO 350 L=l,ll
      DIR(L)=XANG(M)+(A*(L-1)/10. )*ABS(ARC(M)
      IF (DIR(L).GT.360.) DIR(L )=DIR(L)-360.
      IF (DIR(L) .LT.O.) DIR(L)=DIR(L)+360.
      DIRRAD=DIR(L)/57. 29578
      RRR(L)=RC+RAD*SIN(DIRRAD)
      SSS(L)=SC+RAD*COS(DIRRAD)
      XZ=X(RRR(L) ,SSS(L) )+XVZL
      IF (XZ-XVZL) 350,350,330
       FOR 11 POINTS
       SIZE UNTIL AT
ON THE ARC
LEAST 7 OF
SEGMENT.
THE 11 CHI
02130
02140
02150
021oO
02170
02160
02190
02200
02210
02220
02230
02240
02250
02260
02270
02280
02290
02300
02310
02320
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02370
02380
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02400
02410
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02480
02490
02500
02510
02520
02530
02540
02550
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02570
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02590
02600
02610
02620
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02650
               116

-------
                   CRVLN
330
340
C
C
350


360
C
C
370
C

380
390
400
XY=X(RRR(L) ,SSS(L) )+XVYL
YI=Y(RRR(L) ,SSS(L) )
CALL RCONCP ( Z ,H-,HL,XZ ,XY, YI ,KST, AN ,MI ,SY,SZ ,CHI )
IF (CHI) 350,350,340
NM=NM+1
THE NEXT TWO STEPS DETERMINE THE DIRECTION FROM
THE CENTER TO THE NEW STARTING POINT
IF (L.EQ.l) DIRINT=DIR(L)
IF (NM.EQ.l.AND.L.GT.l) DIRINT=DIR(L-1 )
IF (L.GT.l.AND.NM.EQ.l) NM=2
LCOUNT=0
IF (L.NE.ll) LCOUNT=1
CONTINUE
NM=NM+LCOUNT
IF (NM) 430,430,360
IF (NM.GT.7) GO TO 370
VAR=NM-1
ARC(M)=ABS(ARC(M) )*(VAR/10. )
XANG(M)=DIRINT
NM=0
GO TO 320
DO A TRAPEZOIDAL INTEGRATION FROM A TO B IN TEN STEPS,
IT IS LIKELY THAT A OR B HAVE BEEN REDEFINED.
11=11
L=l
KK=1
SUM=0 .
VAR=NM-1
ARR=ABS ( ARC ( M ) ) * ( VAR/1 0 . )
DELL=1/10 OF THE ARC LENGTH IN METERS
DELL=( (ARR/10. )/57 . 29578 ) *RAD*1000 .
DO 400 I=L,II,KK
DIRR=DIRINT+ ( A* ( 1-1 ) /DIV ) *ARR
DIRRAD=DIRR/57.29578
RRR1=RC+RAD*SIN(DIRRAD)
SSS1=SC+RAD*COS(DIRRAD)
XZ=X (RRR1 ,SSS1 )+XVZL
IF (XZ-XVZL) 400,400,390
XY=X(RRR1,SSS1)-I-XVYL
YI=Y(RRR1,SSS1)
CALL RCONCP ( Z ,H,HL,XZ ,XY , YI ,KST, AN, MI ,SY,SZ ,CHI )
IF (I.EQ.l) Ql=CHI/2.
IF (I.EQ.II) Q2=CHI/2.
SUM=SUM+CHI
CONTINUE
KNT=KNT+1
IF (KNT.GT.l) GO TO 410
TOTQ=SUM-Q1-Q2
TOTQ2=TOTQ*DELL
SUM=0 .
DELL=DELL/2.
11 = 21
02660
02670
02680
02690
02700
02710
02720
02730
02740
02750
02760
02770
02780
02790
02800
02810
02820
02830
02840
02850
02860
02870
02880
02890
02900
02910
02920
02930
02940
02950
02960
02970
02980
02990
03000
03010
03020
03030
03040
03050
03060
03070
03080
03090
03100
03110
03120
03130
03140
03150
03160
03170
03180
                                  117

-------
410
420
430
440

450

460

C
                   CRVLN

L=2
KK=2
GO TO 380
CONTINUE
TOTQ=TOTQ+SUM
TOTQ1=TOTQ*DELL
TEST=ABS((TOTQ1-TOTQ2)/TOTQl)
IF (TEST-PIN) 440,420,420
TOTQ2=TOTQ1
DELL=DELL/2.
11=2*11-1
SUM=0.
GO TO 380
TOTQ1=0.
CONTINUE
TOTAL=TOTAL+TOTQ1
CONTINUE
CONCLN(NC,NW)=CONCLN(NC,NW)+TOTAL*QL*DDVH(NW)/UZ
CONTINUE
RETURN
      END
03190
03200
03210
03220
03230
03240
03250
03260
03270
03280
03290
03300
03310
03320
03330
03340
03350
03360
03370
03380
03390
03400
                                         118

-------
                         SPCLN

      SUBROUTINE SPCLN (NHR,NQ,NR,PIN)                                     00010
C       SPECIAL  LINE  SOURCE                                00020
C       THIS SUBROUTINE DETERMINES  CONCENTRATIONS FROM                     00030
C       SPECIAL LINE SOURCES.CASES  CONSIDERED INCLUDE                      00040
C       DIFFERENT HEIGHTS*ABOVE GROUND)OF END POINTS;                      00050
C       CONSTANT VELOCITY OF SOURCES ALONG LINE,OR                         00060
C       CONSTANT ACCELERATION(LINEAR VELOCITY CHANGE);                     00070
C       DECELERATION IS NEGATIVE ACCELERATION,AND                          00080
C       VARIATION OF WIND WITH HEIGHT.                                     00090
C         THE FOLLOWING SUBROUTINES ARE CALLED  BY SPCLN.                    00100
C        RCONCP--DETERMINES THE RELATIVE CONCENTRATION AT                  00110
C                  A RECEPTOR  FROM  A POINT AT A GIVEN UPWIND               00120
C                  AND CROSSWIND DISTANCE.                                 00130
C         THE FOLLOWING FUNCTIONS ARE CALLED BY SPCLN.                     00140
C           XVYCALCULATES THE VIRTUAL DISTANCE NECESSARY                 00150
C                TO ACCOUNT FOR THE INITIAL CROSSWIND DISPERTION.           00160
C           XVZ--CALCULATES THE VIRTUAL DISTANCE NECESSARY                 00170
C                TO ACCOUNT FOR THE INITIAL VERTICAL DISPERTION.            00180
      COMMON /SOLS/ QLS(31),HAS(31),HBS(31),RAS(31),SAS(31),RBS(31),SBS(    00190
     13D ,SYOS(3D ,SZOS(3D ,CONLS(31 ,24) ,DVS(25) ,IUZS ,SPDI(31) ,SPDF(3D ,    00200
     2TVSL(3D ,VSSL(3D                                                    00210
      COMMON /REG/ RR(31),SR(31),ZR(31)                                    00220
      COMMON /WEA/ WTHET(25),WU(25),MKST(25),WHL(25),WTA(25),UHGT           00230
      DIMENSION XST(11),  Y3T(11), HST(11), PUZ(6)                          00240
      DATA PUZ /O.15,0.15,0.20,0.25,0.40,0.60/                              00250
C     QLS             LINE SOURCE STRENGTH.             (G/SEC)             00260
C     HAS             HEIGHT OF POINT A.                (M)                 00270
C     HBS             HEIGHT OF POINT 8                 (M)                 00280
C     RAS             EAST COORDINATE,POINT A.           (KM)               00290
C     SAS             NORTH COORDINATE,POINT A.         (KM)               00300
C     RBS             EAST COORDINATE,POINT B.           (KM)               00310
C     SBS             NORTH COORDINATE,POIMT B.         (KM)               00320
C     SPDI            SPEED AT POINT A.                 (M/SEC)             00330
C     SPDF            SPEED AT POINT 3.                 (M/SEC)             00340
C     SYOS            INITIAL  SIGMA Y.                  (M)                 00350
C     SZOS            INITIAL  SIGMA Z.                  (M)                 00360
C     TVSL            VEHICLE  VOLUME.                   (VEH/HR)            00370
C     VSSL            GROSS ESTIMATE OF VEH. SIZE.      (M)                 00330
      X(R,S)=(R-RREC)*SINT-t-(S-SREC)*COST                                   00390
C        X IS UPWIND DISTANCE  OF R,S FROM RREC.SREC                         00400
      Y(R,S)=(S-SRfiC)*SIrlT-(R-RREC)*COST                                   00410
C        Y IS CROSSWIND DISTANCE OF R,S FROM RREC.SREC                     00420
      DISTA(RM,SM,HM)=SQRT((RM-XS)*2.+(SM-YS)*2.+(HM-HGT)*2.)            00430
      DO 1080 NW=1,NHR                                                     00440
C      DO FOR EACH HOUR.                                                    00450
      THETA=WTriET(NW)                                                      00460
      TR=THETA/57.2958                                                     00470
      SINT=SIM(TR)                                                         00480
      COST=COS(TR)                                                         00490
      U=WU(NW)                                                             00500
      UZ=U                                                                 00510
      KST=MKST(NW)                                                         00520
                                                                           00530


                                        119

-------
                         SPCLN

      P^R=PUZ(KST)                                                         00540
      DO 1070 NS=1,NQ                                                      00550
C       DO FOR EACH LINE SOURCE.                                           00560
      R1=RAS(NS)                                                           00570
      S1=SAS(NS)                                                           005dO
      R2=RBS(NS)                                                           00590
      S2=3BS(NS)                                                           00600
      QL=QLS(NS)*(TVSL(NS)/3t>00.)                                           00610
      SCALV=VSSL(NS)*(TVSL(NS)/3600.)                                       00620
      Hl=HA3(NS)                                                           00630
      HGT=H1*0.001                                                         00640
      H2=HBS(NS)                                                           00650
      DELR=R2-R1                                                           00660
      DELS=S2-S1                                                           00670
      DIST=SQRT(DELR**2+DELS**2)                                           00680
      DELH=H2-H1                                                           00690
      VI=SPDI(NS)**2                                                       00700
      VF=SPDF(NS)**2                                                       00710
      DELSPD=VF-VI                                                         00720
      DISTOL=SQRT((R2-R1)**2.+(S2-S1)**2.+(H2*0.001-Hl*.001)**2.)          00730
      IF (SYOS(NS)) 10,10,20                                               00740
10    XVYL=0.                                                              00750
      GO TO 30                                                             00760
20    SYON=SYOS(NS)                                                        00770
      XVYL=XVY(SYON,KST)                                                   00780
30    IF (SZOS(NS)) 40,40,50                                               00790
40    XVZL=0.                                                              00800
      GO TO 60                                                             00610
50    SZON=SZ03(NS)                                                        00820
      XVZL=XVZ(SZON,KST)                                                   00830
60    CONTINUE                                                             00640
      DO 1060 NC=1,NR                                                      00d50
C       DO FOR EACH RECEPTOR.                                              00860
      RREC=RR(NC)                                                          00670
      SREC=SR(NC)                                                          00880
      Z=ZR(NC)                                                             00690
      X1=X(R1,S1)                                                          00900
      XS=X1                                                                00910
      X2=X(R2,S2)                                                          00920
      IF (XI) 70,70,80                                                     00930
70    IF (X2) 1060,1060,80                                                 00940
60    Y1=Y(R1,S1)                                                          00950
      YS=Y1                                                                00960
      Y2=Y(R2,S2)                                                          00970
C       IF Yl AND Y2 ARE BOTH POSITIVE OR BOTH NEGATIVE NO LOCUS           00980
C       ON THE LINE SOURCE ,GO TO 390.                                     00990
      IF (Y1.GE.O.O.AND.Y2.GE.O.O) GO TO 390                               01000
      IF (Y1.LE.O.O.AND.Y2.LE.O.O) GO TO 390                               01010
C        IF Yl = Y2, LINE SOURCE IS PARALLEL TO UPWIND AZIMUTH FROM RECE   01020
      IF (DIST) 90,390,90                                                  01030
90    IF (COST+0.0001) 160,100,100                                         01040
100   IF (COST-0.0001) 110,110,160                                         01050
110   IF (DELR+0.0001) 140,120,120                                         01060
                                        120

-------
                         SPCLN

C       AT (110) COST APPROX. ZERO, WIND 90 DEC. OR 271).                     01070
120   IF (DELR-0.0001) 130,130,140                                         01080
130   SLOC=SREC                                                            01090
C       AT(130) LINE SOURCE IS NORTH-SOUTH.                                01100
      RLOC=R1                                                              OHIO
      GO TO 260                                                            01120
140   SLP=DELS/DELR                                                        01130
C       AT(140) WIND STILL 90 DEC. OR 270.                                 01140
      IF (SLP) 150,390,150                                                 01150
C       IF SLP ZERO LINE PARALLEL TO WIND.                                 OllbO
150   SLOC=SREC                                                            01170
      RLOC=(SLOC-S1)/SLP+R1                                                01180
      GO TO 280                                                            01190
IbO   IF (SINT+0.0001) 210,170,170                                         01200
C       AT(160) WIND NOT yO DEG. OR 270.                                   01210
170   IF (SINT-0.0001) 180,180,210                                         01220
IbO   IF (DELR+0.0001) 200,l90,lyO                                         01230
C       AT(180) wIND 0 DEG. OR 160.                                        01240
190   IF (DELR-O.U001) 390,390,200                                         01250
C      GO TO 390 IF LINE SOURCE PARALLEL TO WIND.                          012bO
200   SLP=DELS/DELR                                                        01270
C       AT(200) WIND 0 DEG. OR 160 DEG. AND DELR IS NOT ZERO.              01280
      RLOC=RREC                                                            01290
      SLOC=SLP*(RLOC-R1)+31                                                01300
      GO TO 280                                                            01310
210   IF (DELR+0.0001) 240,220,220                                         01320
C       AT(210) WIND NOT FROM 4 CARDINAL DIRECTIONS.                       01330
220   IF (DELR-0.0001) 230,230,240                                         01340
230   RLOC=R1                                                              01350
C       AT(230) LINE SOURCE IS NORTH-SOUTH.                                01360
      SLOC=(RLOC-RREC)*COST/SINT+SREC                                      01370
      GO TO 280                                                            0130
240   IF (DELS+0.0001) 270,250,250                                         01390
250   IF (DELS-0.0001) 260,270,270                                         01400
260   SLOC=S1                                                              01410
C       AT(260) LINE SOURCE IS EAST-WEST.                                  01420
      RLOC=(3LOC-SREC)*SINT/COST+RREC                                      01430
      GO TO 280                                                            01440
270   TATH=SINT/COST                                                       01450
C       AT(270) GENERAL CASE,WIND NOT FROM CARDINAL DIRECTION              01460
C       AND LINE SOURCE NOT EAST-WEST NOR NORTH-SOUTH.                     01470
C        TATH IS TANGENT (THETA)                                           01480
      SLP=DELS/DELR                                                        01490
C        SLP IS SLOPE OF LINE SOURCE.                                      01500
      RLOC=(RREC/TATH+S1-SLP*R1-SREC)/(1/TATH-SLP)                         01510
      SLOC=(RLOC-RREC)/TATH+SREC                                           01520
C        RLOC, SLOC IS LOCUS OF LINE THROUGH LINE SOURCE AND UPWIND VECT   01530
280   XLOC=X(RLOC,SLOC)                                                    01540
      IF (XLOC) 390,390,290                                                01550
C        XLOC IS POSITIVE IF LOCUS IS UPWIND.                              01560
290   IF (S2-S1) 300,300,310                                               01570
300   SMAX=S1                                                              01580
      SMIN=S2                                                              01590
                                       121

-------
                         SPCLN
      GO TO 320
310   SMAX=S2
      SMIN=S1
320   IP (R2-R1) 330,330,340
330   RMAX=R1
      RMIN=R2
      GO TO 350
340   RMAX=R2
      RMIN=R1
C        SEE IF UPWIND LOCUS IS ON LINE SOURCE.
350   IF (RLOC-RMIN) 390,360,360
360   IF (RMAX-RLOC) 390,370,370
370   IF (SLOC-SMIN) 390,380,380
380   IF (SMAX-SLOC) 390,400,400
390   INDIC=1
C        INDIC =1 FOR NO LOCUS ON LINE SOURCE.
      XA=X1
      YA=Y1
      HA=H1
      XB=X2
      YB=Y2
      HB=H2
      GO TO 410
400   INDIC=2
C        INDIC =2 FOR LOCUS ON LINE SOURCE.
      XA=X1
      YA=Y1
      HA=H1
      XB=XLOC
      YB=0.
      RDUM=RLOC-Rl
      SDUM=SLOC-S1
      DDUM=SQRT(RDUM*RDUM+SDUM*SDUM)
      HB=(DDUM/DIST)*(H2-H1)+H1
      HLOC=HB
410   DISX=XB-XA
      DISY=YB-YA
      DISH=0.001*(HB-HA)
      DISI=SQRT(DISX**2+DISY**2+DI3H**2)
C        DISI IS LENGTH(KM) OF LINE CONSIDERED.
      IF (DISI) 420,420,430
420   CURR=0.
      GO TO 1000
430   DDI=DISI*1000./20.
C        ONE-HALF IS INCLUDED IN THE 20.
C        DDI IS ONE-HALF TIMES 1/10 OF DISI  (M)
      DX=DISX/10.
      DY=DISY/10.
      DH=(HB-HA)/10.
C       DH IS IN METERS.
      PREV=0.
      KNTRL=1
      XI=XA
01600
01610
01620
01630
01640
01650
01660
01670
01680
01690
01700
01710
01720
01730
01740
01750
01760
01770
01780
01790
01800
01310
01820
01830
01840
01850
01860
01870
01880
01890
01900
01910
01920
01930
01940
01950
01960
01970
01980
01990
02000
0201C
0202C
0203C
0204C
0205C
0206C
02071
02081
0209(
02101
0211
0212
                                       122

-------
                         SPCLN
      YI=YA
      HI=HA
      KNT=0
      DO 570 1=1,11
C        STORE EACH XI,YI.
      XST(I)=XI
      YST(I)=YI
      HST(I)=HI
      IF (XST(I)) 440,440,450
440   RC=0.
      GO TO 480
450   XZ=XI+XVZL
      XY=XI+XVYL
      H=HI
      GO TO (470,460) , IUZS
460   UZ=U*(H/UHGT)**PWR
      IF (H.GT.200.) UZ=U*(200./UHGT)**PWR
      IF (UZ.LT.1.0) UZ=1.0
470   CALL RCONCP (Z,H,HL,XZ,XY,YI,KST,AN,M,SY,SZ,RC)
      RC=RC/UZ
      HH=H*0.001
      DIS=DISTA(XI,YI,HH)/DISTOL
      SPEED=SQRT(VI+DELSPD*DIS)
      IF (SPEED.LT.SCALV) SPEED=SCALV
      RC=RC/SPEED
4dO   GO TO (4yO,530), KNTRL
C        IF RC IS ZERO, CONTINUE UNTIL RC IS POSITIVE.
490   IF (RC)  560,560,500
500   IF (1-1) 510,510,520
510   KNTRL=2
      GO TO 550
C        RESET POINT A TO LAST ONE PREVIOUS.
520   XA=XST(I-1)
      YA=YST(I-1)
      HA=HST(I-1)
      KNTRL=2
      GO TO 550
530   IF (RC)  540,540,550
C        RESET POINT B IF REACH ZERO CONCENTRATION.
540   XB=XI
      YB=YI
      HB=HI
      GO TO 580
550   KNT=KNT+1
560   XI=XI+DX
      YI=YI+DY
      H1=HI+DH
570   CONTINUE
580   IF (KNT) 600,600,5yO
590   IF (KNT-6) 410,410,640
C        IF GET TO 370, CONC. FROM THIS SEGMENT IS 0.
600   GO TO (610,620,b30), INDIC
610   RC=0.
02130
02140
02150
02160
02170
02180
02190
02200
02210
02220
02230
02240
02250
02260
02270
02280
02290
02300
02310
02320
02330
02340
02350
02360
02370
023oO
02390
02400
02410
02420
0243U
02440
02450
02460
02470
024oO
02490
02bOO
02510
02520
02530
02540
02550
02560
02570
025bO
0259U
U2600
U2610
02620
02630
02o40
02o50
                                       123

-------
                         SPCLN
      GO TO 1060
620   FIRST=0.
      GO TO 1030
630   RC=FIRST
      GO TO 1050
640   CONTINUE
C        DO ANOTHER TRAPEZOIDAL INTEGRATION FROM A TO 3 IN TEN STEPS.
C        IT IS LIKELY THAT A TO B HAVE BEEN REDEFINED.
      DISX=X8-XA
      DISY=YB-YA
      DISH=0.001*(HB-HA)
      DISI=SQRT(DI3X**2+DISY**2+DISH**2)
C        DI3I IS DISTANCE(KM) FROM A TO 6
      DELD=DISI*100.
C        DELD IS 1/10 DISI IN METERS.
      DX=DISX/10.
      DY=DISY/10.
      DH=(HB-HA)/1U.
      SUM=0.
      XDUM=XA
      YDUM=YA
      IF (XDUM) 650,650,660
b50   RC=0.
      GO TO 690
660   XZ=XDUM+XVZL
      XY=XDUM+XVYL
      H=HA
      GO TO (680,670), IUZS
b70   UZ=U*(H/UHGT)**PWR
      IF (H.GT.200.) UZ=U*(200./UHGT)**PWR
      IF (UZ.LT.1.0) UZ=1.0
680   CALL RCONCP (Z,H,HL,XZ,XY,YDUM,KST,AN,M,SY,SZ,RC)
      RC=RC/UZ
690   CONTINUE
      HH=H*0.001
      DIS=DISTA(XDUM,YDUM,HH)/DISTOL
      SPEED=SQRT(VI+DELSPD*DIS)
      IF (SPEED.LT.SCALV) SPEED=SCALV
      RC=RC/SPEED
      SUM=SUM+RC/2.
      DO 750 1=1,9
      XDUM=XDUM+DX
      YDUM=YDUM+DY
      H=H+DH
      IF (XDUM) 700,700,710
700   RC=0.
      GO TO 740
710   GO TO (730,720), IUZS
720   UZ=U*(H/UHGT)**PWR
      IF (H.GT.200.) UZ=U*(200./UHGT)**PWR
      IF (UZ.LT.1.0) UZ=1.0
730   XZ=XDUM+XVZL
      XY=XDUM+XVYL
02660
02670
02660
02690
02700
02710
02720
02730
02740
02750
02760
02770
02780
02790
02800
02810
02820
02830
02840
02850
02860
02870
02880
02890
02900
02910
02920
02930
02940
02950
02960
02970
02980
02990
03000
03010
03020
03030
03040
03050
03060
03070
03080
03090
03100
03110
03120
03130
03140
03150
03160
03170
03180
                                      124

-------
                         SPCLN
      CALL RCONCP U,H,HL,XZ,XY,YDUM,KST,AN,il,SY,SZ,RC)
      RC=RC/UZ
740   CONTINUE
      HH=H*0.001
      DIS=DISTA(XDUM,YDUM,HH)/DISTOL
      SPEED=SQRT(VI+DELSPD*DIS)
      IF (SPEED.LT.SCALV) SPEED=SCALV
      RC=RC/SPEED
750   SUM=SUM+RC
      XDUM=XDUM+DX
      YDUM=YDUM+DY
      H=H+DH
      IF (XDUM) 760,760,770
760   RC=0.
      GO TO bOO
770   GO TO (790,7bO), IUZS
780   UZ=U*(H/UHGT)**PWR
      IF (H.GT.200.) UZ=U*(200./UHGT)**PwR
      IF (UZ.LT.1.0) UZ=1.0
7yO   XZ=XDUM+XVZL
      XY=XDUi*l+XVYL
      CALL RCONCP (Z,H,HL,XZ,XY,YDIM ,KST,AN,M,SY,SZ,RC)
      RC=RC/UZ
BOO   CONTINUE
      HH=H*0.001
      DIS=DISTA(XDUM,YDUM,HH)/DI3TOL
      SPEED=SQRT(VI+DELSPD*DIS)
      IF (SPEED.LT.SCALV) SPEED=SCALV
      RC=RC/SPEED
      SUM=SUM+RC/2.
C        INTEGRATED VALUE IS CURR.
      CURR=SUh*DELD
      ILIM=10
810   PREV=CURR
C        EVALUATE FOR POINTS IN BETWEEN THOSE ALREADY EVALUATED.
      DELD=DELD/2.
      XDUM=XA+DX/2.
      YDUM=YA+DY/2.
      H=HA+DH/2.
      GO TO (830,820), IUZS
820   UZ=U*(H/UHGT)**PWR
      IF (H.GT.200.) UZ=U*(200./UHGT)**PVvR
      IF (UZ.LT.1.0) UZ=1.0
830   DO 690 I=1,ILIM
      IF (XDUM) 840,840,850
840   RC=0.
      GO TO 860
850   XZ=XDUM+XVZL
      XY=XDUM+XVYL
      CALL RCONCP (Z,H,HL,XZ,XY,YDUM,KST,AN,rt,SY,SZ,RC)
      RC=RC/UZ
360   CONTINUE
      HH=H*0.001
03200
03210
03220
03230
03240
03250
03260
03270
03280
03290
03300
03310
03320
03330
03340
03350
03360
03370
03380
033^0
03400
03410
03420
03430
03440
03450
03460
03470
03480
03490
03500
03510
03520
03530
03540
03550
03560
03570
03580
03590
03600
03610
03620
03630
03640
03650
03660
03670
03680
03690
03700
03710
                                      125

-------
                         SPCLN

      DIS=DISTA(XDUMfYDUMrHH)/DISTOL                                       03720
      SPEED=SQRT(VI+DELSPD*DIS)                                            03730
      IF (SPEED.LT.SCALV) SPEED=SCALV                                      03740
      RC=RC/SPEED                                                          03750
C        NOTE ADD THESE TO EC'S FOUND ABOVE.                               03760
      SUM=SUM+RC                                                           03770
      H=H+DH                                                               03780
      GO TO (680,870), IUZS                                                03790
870   UZ=U*(H/UHGT)**PfcR                                                   03800
      IF (H.GT.200.) UZ=U*(200./UHGT)**PWR                                 03810
      IF (UZ.LT.1.0) UZ=1.0                                                03820
880   XDUM=XDUM+DX                                                         03830
890   YDUM=YDUM+DY                                                         03840
      CURR=SUM*DELD                                                        03850
      TEST=ABS((CURR-PREV)/CURR)                                           03860
C        IF WITHIN PIN OF LAST VALUE (PREV), CONSIDER THIS AS FINAL VALU   03870
      IF (TEST-PIN) 1000,900,900                                           03880
900   ILIM=ILIM*2                                                          03890
      PREV=CURR                                                            03900
C        EVALUATE POINTS IN BETWEEN.                                       03910
      DELD=DELD/2.                                                         03920
      DX=DX/2.                                                             03930
      DY=DY/2.                                                             03940
      DH=DH/2.                                                             03950
      XDUM=XA+DX/2.                                                        03960
      YDUM=YA+DY/2.                                                        03970
      H=HA+DH/2.                                                           03980
      GO TO (920,910), IUZS                                                03990
910   UZ=U*(H/UHGT)**PWR                                                   04000
      IF (H.GT.200.) UZ=U*(200./UHGT)**PWR                                 04010
      IF (UZ.LT.1.0) UZ=1.0                                                04020
920   DO 980 I=1,ILIM                                                      04030
      IF (XDUM) 930,930,940                                                04040
930   RC=0.                                                                04050
      GO TO 950                                                            04060
940   XZ=XDUM+XVZL                                                         04070
      XY=XDUM+XVYL                                                         04080
      CALL RCONCP (Z,H,HL,XZ,XY,YDUM,KST,AN,M,SY,SZ,RC)                     04090
      RC=RC/UZ                                                             04100
950   CONTINUE                                                             04110
      HH=H*0.001                                                           04120
      DIS=DISTA(XDUM,YDUM,HH)/DISTOL                                       04130
      SPEED=SQRT(VI+DELSPD*DIS)                                            04140
      IF (SPEED.LT.SCALV) SPEED=SCALV                                      04150
      RC=RC/SPEED                                                          04160
      SUM=SUM+RC                                                           04170
      H=H+DH                                                               04180
      GO TO (970,960), IUZS                                                04190
960   UZ=U*(H/UHGT)**PWR                                                   04200
      IF (H.GT.200.) UZ=U*(200./UHGT)**PWR                                 04210
      IF (UZ.LT.1.0) UZ=1.0                                                04220
970   XDUM=XDUM+DX                                                         04230
980   YDUM=YDUM+DY                                                         04240

                                       126

-------
                         SPCLN
      CURR=SUM*DELD
      TEST=ABS((CURR-PREV)/CURR)
      IF (TEST-PIN) 1000,990,990
990   ILIM=ILIM*2
      DX=DX/2.
      DY=DY/2.
      DH=DH/2.
      GO TO 810
C        AT 1000 HAVE FINAL VALUE OF INTEGRATION IN CURR.
1000  GO TO (1010,1020,1040)", INDIC
1010  RC=CURR
      GO TO 1050
1020  FIRST=CURR
1030  INDIC=3
      XA=XLOC
      YA=0.
      HA=HLOC
      XB=X2
      YB=Y2
      HB=H2
      GO TO 410
1040  RC=FIRST+CURR
1050  CONLS(NC,NW)=CONLS(NC , NW)+RC*QL*DVS(NW,
1060  CONTINUE
1070  CONTINUE
1060  CONTINUE
      RETURN
C
      END
04250
04260
04270
04280
04290
04300
04310
04320
04330
04340
04350
04360
04370
04380
04390
04400
04410
04420
04430
04440
04450
04460
04470
044BO
04490
04500
04510
04520
04530
                                        127

-------
                         SPCCR
C
C
C
C
C
C
C
o
u
C
C
C
C
C
C
C
r^
\^
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
 SUBROUTINE SPCCR (MHR,NO,NR,PIM)
    SPCCR CALCULATES HOURLY CONCENTRATIONS FROM A
    SINGLE LANE CURVED PATH SOURCE.  VEHICLES ARE
    ALLOWED TO HAVE A CONSTANT ACCELERATION ALONG
    THE PATH SOURCE.
    THE FOLLOWING SUBROUTINES ARE  CALLED BY SPCCR.
      CURLIN--CALCULATES THE INTERSECTION OF THE
               LINE FORMED  BY THE  WlMD DIRECTION AND
               RECEPTOR  COORDINATES  AwD THE CIRCLE
               DETERMINED FROM POINTS A,B,C.
      RCONCPDETERMINES THE RELATIVE CONCENTRATION AT
              A RECEPTOR FROM A POINT AT A GIVEN UPWIND
              AND CROS3WIND DISTANCE.
     THE FOLLOWING FUNCTIONS ARE CALLED BY SPCCR.
       XVY--CALCULATES THE  VIRTUAL DISTANCE NECESSARY
            TO ACCOUNT FOR  THE INITIAL CROSSWIND DISPERTION.
       XVZCALCULATES THE  VIRTUAL DISTANCE NECESSARY
            TO ACCOUNT FOR  THE INITIAL VERTICAL DISPERTION.
       ANGARA-DETERMINES THE APPROPRIATE ARCTAw(M/N)
               WITH THE  RESULTING  ANGLE BE.TWEEN 0  AND
               360 DEGREES.
       DIFANGDETERMINES THE DIFFERENCE BETWEEN TWO ANGLES.
               THE RESULTING ANGLE IS BETWEEN 0 AND 360 DEGREES.
 COMMON /SOCS/ QLNA(3D ,HCL(3D , RBQA ( 3 1 ) ,SBQA( 3 1) ,RMQA ( 3 1) ,SMQA(3D
1 ,REQA(3D ,SEQA(3D ,SIYA(31) ,SIZA(3D ,CONCLA(31 ,24) ,DVHA(3O ,IUZE,S
2PEK3O ,SPEF(31) ,TVCL(31),VSCL(31)
 COMMON /REC/ RR(31),SR(31),ZR(31)
 COMMON /WEA/ WTHET(25),WU(25),MKST(25),WHL(25),WTA(25),UHGT
 DIMENSION PUZ(6), RRH(11), SSS(11), DIR(11), ARC(5), XANG(5)
 DATA PUZ /0.15,0.15,0.20,0.25,0.40,0.607
 QLNA  PATH SOURCE STRENGTH FOR EACH LANE
 HCL   HEIGHT OF THE PATH SOURCE
 RBQA  EAST COORDINATE,POINT A
 SBQA  NORTH COORDINATE,POINT A
 RMQA  EAST COORDINATE,POINT B
 SMQA  NORTH COORDINATE,POINT B
 REQA  EAST COORDINATE,POINT C
 SEQA  NORTH COORDINATE,POINT C
 SIYA  INITIAL SIGMA Y
 SIZA  INITIAL SIGMA Z
 CONCLA  CONCENTRATION
 DVHA  DIURNAL VARIATION,CURVED PATH SOURCE
 IUZE  WIND INCREASE WITH HEIGHT
 SPEI  INITIAL VEHICLE SPEED
 SPEF  FINAL VEHICLE SPEED
 TVCL  VEHICLE VOLUME
 VSCL  GROSS ESTIMATE OF VEHICLE SIZE
 RR  EAST COORDINATE OF RECEPTOR
 SR  NORTH COORDINATE OF RECEPTOR
 ZR    HEIGHT OF RECEPTOR ABOVE GROUND
 WTHET  WIND DIRECTION
 WU  WIND SPEED
 MKST  STABILITY CLASS
(G/SEC)
(M)
(KM)
(KM)
(KM)
(KM)
(KM)
(KM)
(M)
(M)
(G/M**3)
(DIMENSIONLESS)
(DIMENSIOMLESS)
(M/SEC)
(M/SEC)
(VEH/HR)
(M)
(KM)
(KM)
(M)
(DEG  AZIMUTH)
(M/SEC)
(DIMENSIQNLESS)
00010
00020
00030
00040
00050
00060
00070
00080
00090
00100
00110
00120
00130
00140
00150
00160
00170
00130
00190
00200
00210
00220
00230
00240
00250
00260
00270
00280
00290
00300
00310
00320
00330
00340
00350
00360
00370
00380
00390
00400
00410
00420
00430
00440
00450
00460
00470
00480
00490
00500
00510
00520
00530
                                       128

-------
                         SPCCR
C     WHL  MIXING HEIGHT                               (M)
C     WTA  AMBIENT AIR SURFACE TEMP.                   (DEC
C     Vi/P   AMBIENT AIR SURFACE PRESSURE                (MB)
      X(R,S)=(R-RREC)*SINT+(S-S REC)*COST
C        X IS UPWIND DISTANCE OF R,S FROM RREC,SREC
      Y(R,S)=(3-SREC)*SINT-(R-RREC)*COSr
C        Y IS CROSSWINO OISTA^CS OP R,S FROM RREC,SREC
C     START 00 LOOP FOR SACH HOUR
      DO 500 NW=1,NHR
      THETA=WTHST(iM)
      TR=THETA/57.295ti
      SINT=SIN(IR)
      COST-COS(TR)
      U=VvU(NW)
      UZ=U
      KST=MKST(fW)
      HL=WHL(NW)
      PWR=PUZ{KST)
C     START DO LOOP FOR EACH CURVED PATH
      DO 500 NS=1,NQ
      QL=QLNA(N3)*('IVCL(HS)/3600. )
      SCALV=VSCL(NS)*(TVCL(WS)/3600.)
      RB=RBQA(NS)
      RM=RMQA(NS)
      RE=REQA(NS)
      SB=SBQA(NS)
      SM=SMQA(NS)
      SE=SEQA(NS)
      VI=SPEI(NS)**2
      VF=SPEF(NS)**2
      DELSPD=VF-VI
      H=HCL(NS)
      GO TO (20,10), IUZE
10    UZ=U*(H/UHGT)**P^R
      IF (H.GT.200.) UZ=U*(200./UHGT)**t>^R
      IF (UZ.LT.1.0) UZ=1.0
20    IF (SIYA(NS)) 40,30,40
30    XVYL=0.
      GO TO 50
40    SYON=SIYA(NS)
      XVYL=XVY(SYON,KST)
50    IF (SIZA(NS)) 70,60,70
60    XVZL=0.
      GO TO 80
70    SZON=SIZA(NS)
      XVZL=XVZ(SZOr^,KST)
80    CONTINUE
C     FROM HERE THROUGH STATSMENT 150 THE CENTER AND
C     CIRCLE,THROUGH POINTS A,B AND C,ARE CALCULATED
      RMID=(RB+RM)/2.
      SMID=(SB+SM)/2.
      RNID=(RM+RE)/2.
      SNID=(SM+SE)/2.
RADIUS OF THE
00540
00550
00560
00570
00580
00590
00600
00610
00620
00630
00640
00650
00660
00670
00680
00690
00700
00710
00720
00730
00740
00750
00760
00770
00780
00790
00800
00810
00820
00830
00840
00850
00860
00870
00880
00890
00900
00910
00920
00930
00940
00950
00960
00970
00980
00990
01000
01010
01020
01030
01040
01050
01060
                                       129

-------
                          SPCCR
90
100
110
120
130
C
C
C
140
150
C
C
C
      IF (RM-R13.SQ.O.) GO  TO  90
      IF (RE-RM.EQ.O, ) GO  TO  100
      SL01=-( (RM-RB)/(3'4-SlJ) )
      SL02=-( (RE-Rd)/(3E-SM) )
      RC= ( SL01 *RMI D-K9N I D-SMI D-S L02 *RN I 0 ) / ( SL01-S 002
      SC=SLOl*(RC-RrtIO)-K<3inID
      GO TO 110
      RC=RMID
      SL02=-( (RE-RM)/(3B-SM) )
      SC=SL02*(RC-RNID)-t-SNID
      GO TO 110
      RC=RNIO
      SL01=-( (RM-RI3)/(3>l-Srj) )
      SC=SL01*(RC-RC4IO)+3'<1IO
      GO TO 110
      RAD=SJ.RT( U3-RB)**2+(3C-S!3)**2)
      DELM=RB-RC
      DELN=SB-3C
      ANGB=ANGARC ( OWfjrt , DELN )
      DELM=RM-RC
      DELN=SM-SC
      ANGil=ANGARC ( Ofiij 4 , OfiM )
      DELM=RE-RC
      DEL_N=SE-SC
      ANGE=ANGARC ( O
      ANGBE=A3S ( 0 1 H1
                     L-4 , OELM )
                     ^ 3 ( AMGB , ANGE ) )
      ANGBM=A33 ( 01 PANG ( ANG3 , AMG'1 ) )
      ANGME=ABS ( 0 CFA'.IG ( ANGi , ANGS ) )
      IF (ANGBM.LT.AMGBR.AMD.ANGME.ivr.ANJGBE)
      GAMDEG=360.-AttGBE
      GO TO 130
                                              GO TO 120
      CONTINUE
      GAMDEG 13 THE  ANGLR  SUBTENDED B^
      IF A=l THE  ROTATION  FROM A TO 6
      IF A=-l THE ROTATION FROM A TO ',
      A=l.
      IF (GAMDEG.Gfi. 180. )  GO TO 140
      BEDEG=DIFANG(ANGe,ANGB)
      IF (3EDEG.LT.O.)  A=-l.
      GO TO 150
      RDEG=ANG8+li3U.
 'IMK AUC A.HC
IS CLOCKS [Si:
 C3 COUNTER-CLOCKWISE
                                        A=-l .
      REDEG=DIFASG(ANGE,RO EG)
      IF (RMDEG.GE.O..AND.REDEG.LE. 0.)
      CONTINUE
      DO 500 NC=1,NR
      RREC=RR(NC)
      SREC=SR(NC)
      Z=ZR(NC)
      CURLIN CALCULATES  THE COORDINATES De1 aN\T UPWIND  L.OCI  ON ARC A3
      FROM HERE TO .STA'CE^ENT 31i)  [MS BEGINNING AND ENDING
      POINTS,WITH TUcJtH  CORRESPONDING OIREC PIONS , ^)R EACd  SEGMENT
01070
01080
01090
01100
OHIO
01120
01130
01140
01150
01160
01170
01180
011*0
01200
01210
01220
01230
01240
01250
01260
01270
01280
01290
01300
01310
01320
01330
01340
01350
01360
01370
01380
01390
01400
01410
01420
01430
01440
01450
01460
01470
014bO
01490
01500
01510
01520
01530
01540
01550
01560
01570
01580
01590
                                       130

-------
                         SPCCR
C     OF THE ARC ARE CALCULATED
      CALL CURLIN (RC,SC,RREC,SRBC,2,RAD,THETA,RL,SL,RLl,SL1,NLOCI)
      IF (NLOCI) 160,170,180
C     NLOCI HAS VALUES OF -1,0,OR 1 FOR:
C     NO UPWIND LOCI OM ARC AS: 1 LOCI ON ARC AB:
C     OR 2 LOCI OM ARC AB
160   XANG(l)=AflG8
      ARC(1)=GAMDEG
    .  J=l
      GO TO 310
170   K=l
      GO TO 190
180   K=2
190   N=l
      DO 270 KK=1,K
      IF (KK.EQ.2) GO TO 200
      DELM=RL-RC
      DELN=SL-SC
      ANGRL=ANGARC(OSLM,OELN)
      RANG=ANGRL
      GO TO 220
200   DELM=RL1-RC
210   IF (K.NE.l) GO TO 270
      XANG(1)=ANGB
      ARC(1)=GAMDEG
      DELN=SL1-SC
      ANGRL=ANGARC(DSLM,DELN)
      RLANG=ANGRL
220   IF (GAi4DBG.GT.l80. . ANfD. A.GT. 0. )  GO TO 230
      IF (GAMDEG.GR.180. .AND. A.LT. 0 .)  GO TO 240
      IF (GAMDEG.LT.180..AND.A.LT.0,)  GO TO 250
      BIN=DIFANG(ANGRL,ANGB)
      IF (BIN.LS.O..OR.BIN.GE.GAMDEG)  GO TO 210
      ARC(N)=BIN
      GO TO 260
230   BIN=DIFANG(ANGRL,ANGB)
      IF (BIN.GT.O.) ARC(N)=BIN
      IF (BIN.GT.O.) GO TO 260
      IF (BIN.LE.O.) DIF=(GAMDEG-360.)-BIN
      IF (DIF.LT.O.) GO TO 210
      ARC(N)=BIN+360.
      GO TO 260
240   BIN=DIFAtf3(AN3RL,ANGB)
      IF (BIN.LT.O.) ARC(N)=8IN
      IF (BIN.LT.O.) GO TO 260
      IF (BIN.GE.O..AND.BIN.LE.360.-GAMDEG) GO TO 210
      ARC(N)=360.-BIN
      GO TO 260
250   BIN=DIFANG(ANGRLfANG3)
      IF (BIN.GE.O..OR.BIN.LE.-GAMDEG) GO TO 210
      ARC(N)=BIM
      GO TO 260
260   N=N+1
01600
01610
01620
01630
01640
01650
01660
01670
01680
01690
01700
01710
01720
01730
01740
01750
01760
01770
01780
01790
01800
01810
01820
01830
01840
01850
01860
01870
01880
01890
01900
01910
01920
01930
01940
01950
01960
01970
01980
01990
02000
02010
02020
02030
02040
02050
02060
02070
02080
02090
02100
02110
02120
                                      131

-------
SPCCR
      INDEX=-1
      IF (KK.EQ.2) INDEX=1
      GO TO 270
270   CONTINUE
      XANG(1)=ANGB
      IF (N-l.EQ.O) GO TO 300
      IF (N-1.EQ.2) GO TO 280
      ARC ( 2 ) =GAMDEG-ABS ( ARC ( 1 ) )
      XANG ( 2 ) =RANG
      IF (INDEX. EQ. I) XA4G(2)=RLA43
      J=2
      GO TO 310
280   ARC(1)=AB3(ARC(1) )
      ARC(2)=A3S(ARC(2) )
      IF (ARC(D.GT.ARC(2) )  GO TO  290
      ARC ( 2 ) =ARC ( 2 ) -ARC ( 1 )
      ARC ( 3 ) =GAMOS3-ARC ( 1 ) - ARC ( 2 )
      XANG(2)=RA*I3
      XANG(3)=RLANG
      J = 3
      GO TO 310
2yO   AA=ARC(1)
      ARC(1)=ARC(2)
      ARC ( 2 ) =AA-ARC ( 2 )
      ARC ( 3 ) =G AMD EG -ARC ( 1 ) - ARC ( 2 )
      XANG ( 2 ) =RLAtfo
      XANG(3)=RAMG
      J = 3
      GO TO 310
300   J=l
      ARC(l)=GA:J10f-r,
310   lOTAL-O.
      DISTOT=RAO* ( 3
-------
                         SPCCR
340
3bO
360

C
C
370

C

380
C
C
390
C
400
GO TO 3Si!
CALL RCOMCP U,^,HL,XZ,XY,YI,KS'C,AN,rtl,SY,SZ,CHI)
IF (CHI) 370,370,360
NM=NM+1
NCHI=NCHI+1
THE NEXT TwO STEPS DETERMINE  THc]  DCKECTCON 'R.DM
THE CENTER TO THE MEW START ['IG  P-1CNT
IF (L.EQ.l) DIRI*JT=UIR(L)
IF (NM.EQ.l.ANO.L.GT.l) 01R [N't^-H ( ',-1 )
IF (L.GT.l.ANO.NM.EQ.l) N>1=2
LCOUNT=0
IF (L.NE.ll) LCXINI.^1
CONTINUE
NM=NM+LCOUNT
NM-1 IS T:iE NUMBER OP NON-ZERO  '3ECT CONS  Or' ['HE ARC SEGMENT
IF (NM) 470,470,380
IF (NCHI.GT.6) GO TO 390
VAR=NM-1
ARC(M)=ABS(ARC(M))*(7AR/10.)
XANG(M)=DIRINT
NM=0
NCHI=0
GO TO 320
DO A TRAPEZOIDAL  IN UEGKA'L" ON  t-'ROM  A TO 8 IN TEN STEPS.
IT IS LIKELY THAT A OR B HAVE BEEN REDEFINED.
11=11
L=l
KK=1
SUM=0.
VAR=NM-1
ARR=A3S(ARC(M))*(7AR/10.)
DELL=((ARR/10.)/57.29578)*RAD*1000.
DELL=1/10 OF THE ARC LENGTH IN  METERS
DO 440  I=L,II,KK
410

420
430
DIRR=DIRINT+(A*(I-1)/DIV)*ARR
DIRRAD=DIRR/57.29b78
RRR1=RC+RAD*SIN(DIRRAD)
SSS1=SC+RAD*COS(DIRRAD)
XZ=X(RRR1,SSS1)+XVZL
XY=X(RRR1,SSS1)+XVYL
YI=Y(RRR1,SSS1)
DTHETA=DIFANG(DIRR,ANGB)
IF (A.LT.O..AND.DTHETA.GT.O.)
IF (A.GT.O..AND.DTHETA.LT.O.)
DIS=(RAD*(DTHETA/57.29578))/DISTOT
SPEED=SQRT(\/I+DELSPO*DIS)
IF (SPEED.LT.SCALV) SPEED=SCALV
IF (XZ-XVZL) 410,410,420
CHI=0.
GO TO 430
CALL RCONCP (Z,H,HL,XZ,XY,YI,KST,AN,MI,3Y,SZ,CHI)
CHI=CHI/SPEEO
                                    OTBETA=3 60.-ABS(DTHETA)
                                    DTHETA=360.-ABS(DTHETA)
02660
02670
02680
02690
02700
02710
02720
02730
02740
02750
02760
02770
02780
02790
02800
02810
02820
02830
02840
02850
02860
02870
02880
02890
02900
02910
02920
02930
02940
02950
02960
02970
02980
02990
03000
03010
03020
03030
03040
03050
03060
03070
03080
03090
03100
03110
03120
03130
03140
03150
03160
03170
03180
                                       133

-------
                    SPCCR
440
450
C
C
C

C
C
460
470
460

490

500

C
IF (I.EQ.l) Ql=CHI/2.
IF (I.EO..TT.) Q2=C4I/2.
SUM=SUM+Cfl [
CONTINUE
KNT=KNT+i
IF (KNT.GT.l) 
-------
                         XPLUME

      SUBROUTINE XPLUME (HX,F,DELHF,HP,U,X)
C        BRIGGS EFFECTIVE HEIGHT AT THE DISTANCE X.
C         OUTPUT VARIABLES ARE...
C           HX    EFFECTIVE PLUME HEIGHT FOR DISTANCE X (METERS)
C         INPUT VARIABLES ARE...
C           F     BUOYANCY FLUX (M**4/SEC**3)
C           DELHF FINAL PLUME RISE (METERS)
C           HP    PHYSICAL STACK HEIGHT (METERS)
C           U     WIND SPEED (M/SEC)
C           X     DOWNWIND DISTANCE (KM)
      XM=1000.*X
C        XM IS X IN METERS.
C        STATEMENT 10 IS EQUATION (2), BRIGGS(1971).
10    DELHX=1.6*F**0.333333*XM**0.666667/U
      IF (DELHX.GT.DELHF) DELHX=DELHF
      HX=HP+DELHX
      RETURN
C
      END
00010
00020
00030
00040
00050
00060
00070
00080
00090
00100
00110
00120
00130
00140
00150
00160
00170
00180
00190
                                      135

-------
                         FPLUME

      SUBROUTINE FPLUME (HF,DISTF,F,DELHF,HP,TS,VS,D,VF,KST,U,DTHDZ ,T)     00010
C        BRIGGS FINAL HEIGHT                                               00020
C        D. B. TURNER, ENVIRONMENTAL APPLICATIONS BRANCH                   00030
C         METEOROLOGY LABORATORY, ENVIRONMENTAL PROTECTION AGENCY          00040
C          RESEARCH TRIANGLE PARK, N C 27711                               00050
C             (919) 549 - 8411, EXTENSION 4565                             00060
      IF (T) 10,10,20                                                      00070
C        T = 0. MEANS NO AMBIENT TEMPERATURE GIVEN.  USE T = 293.          00080
10    T=293.                                                               00090
C         OUTPUT VARIABLES ARE...                                          00100
C           HF    FINAL EFFECTIVE PLUME HEIGHT (METERS)                    00110
C           F     BUOYANCY FLUX (M**4/SEC**3)                              00120
C           DELHF FINAL PLUME RISE (METERS)                                00130
C           DISTF DISTANCE OF FINAL PLUME RISE FROM SOURCE (KM)            00140
C         INPUT VARIABLES ARE...                                           00150
C           HP    PHYSICAL STACK HEIGHT (METERS)                           00160
C           TS    STACK GAS TEMPERATURE (DEC K)                            00170
C           VS    STACK GAS EXIT VELOCITY (M/SEC)                          00180
C           D     INSIDE STACK DIAMETER (METERS)                           00190
C           VF    STACK GAS VOLUMETRIC FLOW RATE (iI**3/SEC)                00200
C           KST   STABILITY (CLASS), SEE PAGE 209 OF PASQUILL,             00210
C                  ATMOSPHERIC DISPERSION.  CLASSES DEFINED BY...          00220
C                    1 IS PASQUILL STABILITY CLASS A                       00230
C                    2 IS PASQUILL STABILITY CLASS B                       00240
C                    3 IS PASQUILL STABILITY CLASS C                       00250
C                    4 IS PASQUILL STABILITY CLASS D                       00260
C                    5 IS PASQUILL STABILITY CLASS E                       00270
C                    b IS PASQUILL STABILITY CLASS F                       00260
C           U     WIND SPEED (M/SEC)                                       00290
C           DTHDZ POTENTIAL TEMPERATURE LAPSE RATE (DEG K/METER)           00300
C           T     AMBIENT AIR TEMPERATURE (DEG K)                          00310
C        IF VF IS NOT GIVEN, CALCULATE IT FROM STACK DATA.                 00320
20    IF (VF) 30,30,40                                                     00330
30    VF=0.785398*VS*D*D                                                   00340
C        THE CONSTANT 0.785398 = PI/4                                      00350
40    F=3.12139*VF*(TS-T)/TS                                               00360
C        THE CONSTANT 3.12139 IS THE ACCELERATION DUE TO GRAVITY /  PI.     00370
C        GO TO APPROPRIATE BRANCH FOR STABILITY CONDITION GIVEN.           00380
C        IF UNSTABLE OR NEUTRAL GO TO 50, IF STABLE GO TO 90.              00390
      GO TO (50,50,50,50,90,90,90), KST                                    00400
C        DETERMINE APPROPRIATE FORMULA FOR CALCULATING XST, DISTANCE  AT    00410
C         WHICH TURBULENCE BEGINS TO DOMINATE.  THE FORMULA USED DEPENDS   00420
C         UPON BUOYANCY FLUX. STATEMENTS 60 AND 70 ARE EQUATION  (7),       00430
C         BRIGGS(1971).                                                    00440
50    IF (F-55.) 60,70,70                                                  00450
60    XST=14.*F**.625                                                      00460
      GO TO 80                                                             00470
70    XST=34.*F**.4                                                        00480
80    DISTF=3.5*XST                                                        00490
      DELHF=1.6*F**0.333333*DISTF**0.666667/U                              00500
      GO TO 160                                                            00510
90    IF (DTHDZ) 100,100,130                                               00520
C        IF DTHDZ  IS NEGATIVE OR ZERO ASSIGN TO IT A VALUE OF  0.02  OR     00530
                                       136

-------
                         FPLUME

C         0.035 IF STABILITY IS SLIGHTLY STABLE OR STABLE,  RESPECTIVELY.    00540
100   GO TO (50,50,50,50,110,120,120), KST                                 00550
110   DTHDZ=0.02                                                           00560
      GO TO 130                                                            00570
120   DTHDZ=0.035                                                          00580
130   S=9.8061b*DTHDZ/T                                                    00590
C        THE CONSTANT 9.80616 IS THE ACCELERATION DUE TO GRAVITY.           00600
C        S IS A STABILITY PARAMETER.                                       00610
C        CALCULATE PLUME RISE ACCORDING TO EQUATION (2), BRIGGS(1972).      00620
      DHA=2.4*(F/(U*S))**0.333333                                          00630
C        CALCULATE PLUME RISE BY EQUATION (5), BRIGGS(1971) FOR LIGHT       00640
C         WIND CONDITIONS ACCORDING TO MORTON, TAYLOR, AND TURNER.          00650
      DELHF=5.0*F**0.25/S**0.375                                           00660
      IF (DHA-DELHF)  140,140,150                                           00670
140   DELHF=DHA                                                            00680
C        DISTANCE TO FINAL PLUME RISE IS GIVEN BY THE FOLLOWING            00690
150   DISTF=3.14159*U/S**0.5                                               00700
C        CALCULATE FINAL EFFECTIVE HEIGHT.                                 00710
160   HF=HP+DELHF                                                          00720
      DISTF=DISTF/1000.                                                     00730
      RETURN                                                               00740
C                                                                          00750
      END                                                                  00760
                                       137

-------
                         PGSIG

      SUBROUTINE PGSIG (X,XY,KST,SY,SZ)                                     00010
C        D. B. TURNER, ENVIRONMENTAL APPLICATIONS BRANCH                   00020
C         METEOROLOGY LABORATORY, ENVIRONMENTAL PROTECTION AGENCY          00030
C          RESEARCH TRIANGLE PARK, N C 27711                               00040
C             (919) 549 - 8411, EXTENSION 4565                             00050
C        VERTICAL DISPERSION PARAMETER VALUE, SZ DETERMINED BY             00060
C         SZ = A * X ** B WHERE A AND B  ARE FUNCTIONS OF BOTH STABILITY    00070
C         AND RANGE OF X.                                                  00080
C        HORIZONTAL DISPERSION PARAMETER VALUE, SY DETERMINED BY           00090
C         LOGARITHMIC INTERPOLATION OF PLUME HALF-ANGLE ACCORDING TO       00100
C         DISTANCE AND CALCULATION OF 1/2.15 TIMES HALF-ARC LENGTH.        00110
      DIMENSION XA(7), XB(2), XD(5), XE(8), XF(9), AA(8), BA(8), AB(3),    00120
     1BB(3), AD(6), BD(6),  AE(9), BE(9), AF(10), BF(10)                    00130
      DATA XA /.5,.4,.3,.25,.2,.15,.I/                                     00140
      DATA XB /.4,.2/                                                      00150
      DATA XD /30.,10.,3.,1.,.3/                                           00160
      DATA XE /40. ,20. ,10. ,4. ,2. ,1.,.3,.l/                                 00170
      DATA XF /60.,30. ,15.,7. ,3.,2.,1.,.7,.2/                              00180
      DATA AA /453.85,346.75,258.89,217.41,179.52,170.22,158.08,122.8/     00190
      DATA BA /2.1166,1.7283,1.4094,1.2644,1.1262,1.0932,1.0542,.94477     00200
      DATA AB /109.3j51d7md"51j7gx"/                                       00210
      DATA BB 71.0971,0.98332,0.931987                                     00220
      DATA AD /44.053,36.650,33.504,32.093,32.093,34.459/                  00230
      DATA BD /0.51179,0.56589,0.60486,0.64403,0.81066,0.86974/            00240
      DATA AE 747.618,35.420,26.970,24.703,22.534,21.628,21.628,23.331,2   00250
     14.26/                                                                00260
      DATA BE 70.29592,0.37615,0.46713,0.50527,0.57154,0.63077,0.75660,0   00270
     1.81956,0.83667                                                       00280
      DATA AF /34.219,27.074,22..651,17.836,16.187,14.823,13.953,13.953,1   00290
     14.457,15.2097                                                        00300
      DATA BF 70.21716,0.27436,0.32681,0.41507,0.46490,0.54503,0.63227,0   00310
     1.68465,0.78407,0.815587                                              00320
      GO TO (10,40,70,80,110,140), KST                                     00330
C        STABILITY A (10)                                                  00340
10    TH=(24.167-2.5334*ALOG(XY))/57.2958                                  00350
      IF (X.GT.3.11) GO TO 170                                             00360
      DO 20 ID=1,7                                                         00370
      IF (X.GE.XA(ID)) GO TO 30                                            00380
20    CONTINUE                                                             00390
      ID=8                                                                 00400
30    SZ=AA(ID)*X**BA(ID)                                                  00410
      GO TO 190                                                            00420
C        STABILITY B (40)                                                  00430
40    TH=(18.333-1.8096*ALOG(XY))/57.2958                                  00440
      IF (X.GT.35.) GO TO 170                                              00450
      DO 50 ID=1,2                                                         00460
      IF (X.GE.XB(ID)) GO TO 60                                            00470
50    CONTINUE                                                             00480
      ID=3                                                                 00490
60    SZ=AB(ID)*X**B3(ID)                                                  00500
      GO TO 180                                                            00510
C        STABILITY C (70)                                                  00520
70    TH=(12.5-1.0857*ALOG(XY))/57.2958                                    00530
                                      138

-------
                         PGSIG
      SZ=61.141*X**0.91465
      GO TO 160
C        STABILITY D (faO)
80    TH=(d.3333-0.72382*ALOG(XY))/57.2958
      DO yo 10=1,5
      IF (X.GE.XD(ID))  GO TO 100
yO    CONTINUE
      ID=6
100   SZ=AD(ID)*X**6D(ID)
      GO TO 130
C        STABILITY E (110)
110   TH=(6.25-0.54287*ALOG(XY))/57.2958
      DO 120 ID=1,8
      IF (X.GE.XE(ID))  GO TO 130
120   CONTINUE
      ID=9
130   SZ=AE(ID)*X**BE(ID)
      GO TO 180
C        STABILITY F (140)
140   TH=(4.1667-0.36191*ALOG(XY))/57.2958
      DO 150 ID=l,y
      IF (X.GE.XF(ID))  GO TO 160
150   CONTINUE
      ID=10
loO   SZ=AF(ID)*X**BF(ID)
      GO TO 180
17U   SZ=5000.
      GO TO 190
180   IF (SZ.GT.5000.)  SZ=5000.
190   SY=465.11b*XY*SIN(TH)/COS(TH)
C        465.116 = 1000.  (M/KM) / 2.15
      RETURN
      END
00540
00550
00560
00570
00580
00590
00600
00610
00620
00630
00640
00650
00660
00670
00680
00690
00700
00710
00720
00730
00740
00750
00760
00770
007aO
00790
00800
00810
00820
00830
00840
00850
00860
00870
                                      139

-------
                         RCONCP
c
c
c
c
c
c
c
SUBROUTINE RCONCP (Z,H,HL,X,XY,Y,KST,AN,M,3Y,SZ,RC)
   D.  6. TURNER,  RESEARCH METEOROLOGIST*  MODEL DEVELOPMENT
    DIVISION OF METEOROLOGY,  ENVIRONMENTAL  PROTECTION
  ROOM  314B,  NCriS
 MAILING  ADDRESS-
'  ON
                      BUILDING,  RTF.  PHONE (919)  549-8411
                      DM, EPA,  RESEARCH TRIANGLE  PARK,  NC
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
10
20
30
40

c
c
50
c
60
C
C
C
c
         ASSIGNMENT FROM NATIONAL OCEANIC AND ATMOSPHERIC
          ADMINISTRATION,  DEPARTMENT OF COMMERCE.
   SUBROUTINE RCONCP CALCULATES CHI*U/Q CONCENTRATION VALU
    RCONCP CALLS SUBROUTINE PGSIG TO OBTAIN STANDARD DEV
   THE INPUT VARIABLES ARE....
    Z    RECEPTOR HEIGHT (M)
    H    EFFECTIVE STACK HEIGHT (M)
    HL=L HEIGHT OF LIMITING LID (M)
    X    DISTANCE RECEPTOR IS DOWNWIND OF SOURCE (KM)
    XY   X+VIRTUAL DISTANCE USED FOR AREA SOURCE APPROX.
    Y    DISTANCE RECEPTOR IS CROSSvJIND FROM SOURCE (KM)
    KST  STABILITY CLASS
   THE OUTPUT VARIABLES ARE	
    AU   THE NUMBER OF TIMES THE SUMMATION TERM IS E-VALUAT
          AND ADDED IN.
    RC   RELATIVE CONCENTRATION (SEC/M**3)
   THE FOLLOWING EQUATION IS SOLVED  
     RC = (1/(2*PI*SIGMA Y*SIGMA Z))* (EXP(-0.5*(Y/SIGMA
      (EXP(-0.5*((Z-H)/SIGMA Z)**2)  + EXF(-0.5*((Z+H)/SIGMA
        PLUS THE SUM OF THE FOLLOWING 4 TERMS K TIMES (N=1
         TERM 1- EXP(-0.5*((Z-H-2NL)/SIGMA Z)**2)
         TERM 2- EXP(-0.5*((Z+H-2NL)/SIGMA Z)**2)
         TERM 3- SXP(-0.5*((Z-H+2NL)/SIGMA Z)**2)
         TERM 4- EXP(-0.5*((Z+H+2NL)/SIGMA Z)**2)
   THE ABOVE EQUATION IS SIMILAR TO  EQUATION (5-8) P 36 IN
    WORKBOOK OF ATMOSPHERIC DISPERSION ESTIMATES WITH THE
    OF THE EXPONENTIAL INVOLVING Y,TURNER(1970).
   IWRI IS CONTROL CODE FOR OUTPUT
IWRI=6
   IF THE SOURCE IS ABOVE THE LID, SET RC = 0., AND RETURN
IF(KST.GE.5) GO TO 50
IF (H-HL) 10,10,20
IF (Z-HL) 50,50,40
IF (Z-HL) 40,30,30
WRITE (IWRI,460)
RC = 0.
RETURN
   IF X IS LESS THAN 1 METER, SET RC=0. AND RETURN.  THIS
    PROBLEMS OF INCORRECT VALUES NEAR THE SOURCE.
IF (X-0.001) 40,60,60
   CALL PGSIG TO OBTAIN VALUES FOR SY AND SZ
CALL PGSIG (X,XY,KST,SY,SZ)
    SY = SIGMA Y, THE STANDARD DEVIATION OF CONCENTRATION
    Y-DIRECTION (M)
    SZ = SIGMA Z, THE STANDARD DEVIATION OF CONCENTRATION
    Z-DIRECTION (M)
C1 = 1 .
IF (Y) 70,90,70

1 BRANCH,
CY.
EXT 4564
27711


S3
TION3.





KM)



'ED



)**2))
;A Z)**2)
,K) --





ADDITION



.







AVOIDS




IN THE

IN THE



00010
00020
00030
00040
00050
00060
00070
00080
00090
00100
00110
00120
00130
00140
00150
00160
00170
00130
00190
00200
00210
00220
00230
00240
00250
00250
00270
00280
00290
00300
00310
00320
00330
00340
00350
00360
00370
00380
00390
00400
00410
00420
00430
00440
00450
00460
00470
00480
00490
00500
00510
00520
00530
                                     140

-------
                         RCONCP

70    YD=1000.*Y                                                           00540
C        YD IS CROSSWIND DISTANCE IN METEHS.                                00550
      DUM=YD/3Y                                                            00560
      TEMP=0.5*DUM*DUM                                                     00570
      IF (TEMP-50.)  80,40,40                                               00580
80    C1=EXP(TSMP)                                                         00590
90    IF (KST-4) 100,100,110                                               00600
100   IF (HL-5000.)  190,110,110                                            00610
C        IF STABLE CONDITION OR UNLIMITED MIXING HEIGHT,                    00620
C         USE EQUATION 3.2 IF Z = 0, OR EQ 3.1  FOR NON-ZERO Z,              00630
C          TURNER(1970).                                                   00640
110   C2=2.*SZ*SZ                                                          00650
      IF (Z) 40,120,140                                                    00660
120   C3=H*H/C2                                                            00670
      IF (C3-50.) 130,40,40                                                00680
130   A2=1./EXP(C3)                                                         00690
C        WADE EQUATION 3.2,TURNER(1970).                                    00700
      RC=A2/(3.14159*SY*SZ*C1)                                              00710
      M=1                                                                   00720
      RETURN                                                               00730
140   A2=0.                                                                 00740
      A3=0.                                                                 00750
      CA=Z-H                                                               00760
      CB=Z+H                                                               00770
      C3=CA*CA/C2                                                          00730
      C4=CB*CB/C2                                                          00790
      IF (C3-50.) 150,160,160                                              00800
150   A2=1./EXP(C3)                                                         00810
160   IF (C4-50.) 170,180,180                                              00820
170   A3=1./EXP(C4)                                                         00830
C        WADE EQUATION 3  1 ,TURNEH( 1970) .                                    00840
180   RC=(A24.A3)/(6.2&313*SY*SZ*C1)                                         00850
      M=2                                                                   00860
      RETURN                                                               00870
C        IF SIGMA-Z  IS GREATER  THAN  1.6 TIMES  THE MIXING  HEIGHT,            00880
C         THE DISTRIBUTION BELOW THE MIXING HEIGHT IS UNIFORM WITH         00890
C         HEIGHT REGARDLESS OF  SOURCE HEIGHT.                               00900
190   IF (SZ/HL-1.6)  210,210,200                                           00910
C        WADE EQUATION 3.5,TURMER(1970).                                    00920
200   RC=1./(2.5066*SY*HL*C1)                                              00930
      M=3                                                                   00940
      RETURN                                                               00950
C        INITIAL VALUE OF  AN SET = 0.                                      00960
210   AN=0.                                                                 00970
      IF (Z) 40,370,220                                                    00980
C        STATEMENTS  220 TO 360  CALCULATE  RC, THE RELATIVE CONCENTRATION,    00990
C         USING THE  EQUATION DISCUSSED ABOVE.   SEVERAL INTERMEDIATE         01000
C         VARIABLES  ARE USED TO AVOID REPEATING CALCULATIONS.               01010
C         CHECKS ARE  HADE  TO BE SURE THAT THE  ARGUMENT OF THE              01020
C         EXPONENTIAL FUNCTION  IS NEVER GREATER THAN  50 (OR LESS  THAN       01030
C         -50).  IF  'AN' BECOMES GREATER  THAN  45,  A LINE  OF OUTPUT IS       01040
C         PRINTED INFORMING OF  THIS.                                       01050
C        CALCULATE MULTIPLE EDDY REFLECTIONS FOR RECEPTOR HEIGHT  Z.         01060


                                      141

-------
                         RCONCP

220   A1=1./(6.28318*SY*SZ*C1)                                              01070
      C2=2.*SZ*SZ                                                          01080
      A2=0.                                                                 01090
      A3=0.                                                                 01100
      CA=Z-h                                                               01110
      CB=Z+H                                                               01120
      C3=CA*CA/C2                                                          01130
      C4=CB*CB/C2                                                          01140
      IF (C3-50.) 230,240,240                                              01150
230   A2=1./XP(C3)                                                        01160
240   IF (04-50.) 250,260,260                                              01170
250   A3=1./EXP(C4)                                                        01180
260   SUM=0.                                                               01190
      THL=2.*HL                                                            01200
270   Ari=Atf+1.                                                              01210
      A4 = 0.                                                                 01220
      A5=0.                                                                 01230
      A6=0.                                                                 01240
      A7=0.                                                                 01250
      C5=AW*THL                                                            01260
      CC=CA-C5                                                              01270
      CD=CB-C5                                                              01280
      CE=CA+C5                                                              01290
      CF=CB+C5                                                              01300
      C6=CC*CC/C2                                                          01310
      C7=CD*CD/C2                                                          01320
      C8=CE*CE/C2                                                          01330
      C9=CF*CF/C2                                                          01340
      IF (C6-50.) 280,290,290                                              01350
280   A4=1./EXP(C6)                                                        01360
290   I? (C7-50.) 300,310,310                                              01370
300   A5=1./EXP(C7)                                                        01380
310   IF (C8-50.) 320,330,330                                              01390
320   A6=1./EXP(C8)                                                        01400
330   IF (C9-50.) 340,350,350                                              01410
340   A7=1./EXP(C9)                                                        01420
350   T=A4+A5+A6+A7                                                        01430
      SUM=SUM+T                                                            01440
      IF (T-0.01) 360,270,270                                              01450
360   ftC=A1*(A2+A3+SUM)                                                    01460
      tf=5                                                                  01470
      RETUhN                                                               01480
C        CALCULATE MULTIPLE EDDY REFLECTIONS FOR GROUND LEVEL RECEPTOR H   01490
370   A1=1./(6.28318*SY*SZ*C1)                                              01500
      A2=0.                                                                 01510
      C2=2.*SZ*SZ                                                          01520
      C3=H*H/C2                                                            01530
      IF (C3-50.) 380,390,390                                              01540
380   A2=2./EXP(C3)                                                        01550
390   SUH=0.                                                               01560
      THL=2.*HL                                                            01570
400   AN=AN+1.                                                              01580
      A4=0.                                                                 01590

                                     142

-------
                         RCONCP

      A6=0.                                                                 01600
      C5=AN*THL                                                            01610
      CC=H-C5                                                              01620
      CE=H+C5                                                              01630
      C6=CC*CC/C2                                                          01640
      C8=CE*CE/C2                                                          01650
      IF (C6-50.) 410,420,420                                              01660
410   A4=2./EXP(C6)                                                         01670
420   IF (C8-50.) 430,440,440                                              01680
430   A6=2./EXP(C8)                                                         01690
440   T=A4+A6                                                              01700
      SUM=SUM+T                                                            01710
      IF (T-0.01) 450,400,400                                              01720
450   RC=A1*(A2+SUM)                                                        01730
      M=4                                                                  01740
      RETURN                                                               01750
C                                                                          01760
460   FORMAT (1HO,'BOTH H AND Z ARE ABOVE THE MIXING HEIGHT SO  A  RELIABL    01770
     1E COMPUTATION  CAN NOT BE MADE.')                                      01780
C                                                                          01790
      END                                                                  01800
                                     143

-------
                         RCONCA
C
C
C
C
C
C
C
C
C
C
o
u
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
10
20
30

C
C
40
50
60
SUBROUTINE RCONCA (Z,H,HL,X,KST,AN,M,SZ,RCZ)
   SUBROUTINE RCONCA CALCULATES CHI*U/Q,  RELATIVE CONCENTRATION
    NORMALIZED FOR WIND SPEED FOR A  RECEPTOR  DOWNWIND OF A
    CROSSWIND INFINATE LINE SOURCE.
   D.  B.  TURNER,  RESEARCH METEOROLOGIST*  MODEL APPLICATIONS BRANCH
    METEOROLOGY LABORATORY, ENVIRONMENTAL PROTECTION AGENCY.
      ROOM 316B,  NCHS BUILDING, RTP.  PHONE (919)  549-8411  EXT 4564
   MAILING ADDRESS:  MTL.EPA,  RESEARCH TRIANGLE PARK, NC 27711.
    *  ON  ASSIGNMENT FROM NATIONAL OCEANIC AND ATMOSPHERIC
          ADMINISTRATION, DEPARTMENT OF COMMERCE.
   THE INPUT VARIABLES ARE	
    Z     RECEPTOR HEIGHT (M)
    H     EFFECTIVE STACK HEIGHT (M)
    HL=  HEIGHT OF LIMITING LID (M)
    X     DISTANCE RECEPTOR IS DOWNWIND OF SOURCE  (KM)
    KST  STABILITY CLASS
    SZ =  SIGMA Z, THE STANDARD  DEVIATION  OF CONCENTRATION  IN  THE
    Z-DIRECTION (M)
   THE OUTPUT VARIABLES ARE	
    AN   THE NUMBER OF TIMES THE SUMMATION TERM IS EVALUATED
          AND ADDED IN.
   RCZ   RELATIVE CONCENTRATION (DIMENSIONLESS)
   IWRI 13 CONTROL CODE FOR OUTPUT

   THE FOLLOWING  EQUATION IS SOLVED  --
   RC  = (1/2.5066 *SIGMA Z))* (EXP(-0.5*(Y/SIGMA  Y)**2)) *
      (EXP(-0.5*((Z-H)/SIGMA Z)**2)  + EXP(-0.5*((Z+H)/SIGMA Z)**2)
        PLUS THE  SUM OF THE FOLLOWING 4 TERMS K TIMES (N=1,K) --
                 EXP(-0.5*((Z-H-2NL)/SIGMA Z)**2)
                 EXP(-0.5*((Z+H-2NL)/SIGMA Z)**2)
                 EXP(-0.5*((Z-H+2NL)/SIGMA Z)**2)
                 EXP(-0.5*((Z+ri+2ML)/SIGMA Z)**2)
                 SQUARE HOOT OF 2 *  PI
                  TO 330 CALCULATE RC, THE RELATIVE
         TERM 1-
         TERM 2-
         TEfiM 3-
         TERM 4-
   2.5066 IS THE
   STATEMENTS 190
                                                    CONCENTRATION,
    USING THE EQUATION DISCUSSED ABOVE.   SEVERAL  INTERMEDIATE
    VARIABLES ARE USED TO AVOID REPEATING CALCULATIONS.
    CHECKS ARE MADE TO BE SURE THAT THE  ARGUMENT  OF THE
    EXPONENTIAL FUNCTION IS NEVER GREATER THAN  50 (OR LESS THAN
    -50).  IF 'AN'  BECOMES GREATER THAN  45,  A LINE OF OUTPUT IS
    PRINTED INFORMING OF THIS.
   CALCULATE MULTIPLE EDDY REFLECTIONS FOR RECEPTOR HEIGHT Z.
          SOURCE IS ABOVE
          S) GO TO 40
          10,10,20
          40,40,180
          180,30,30
   IF THE SOURCE IS ABOVE THE LID,  SET HC =  0
IF(KST.GE
IF (ri-HL)
IF (Z-HL)
IF (Z-HL)
WRITE (IivRI,430)
RETURN
   IF X IS LESS THAN 1  METER, SET HC=0.  AND
    PROBLEMS OF INCORRECT VALUES NEAR THE SOURCE
   (X-0.001) 160,50,50
   (KST-4) 60,60,70
   (HL-5000.)  150,70,70
                                                AND RETURN
                                                     THIS AVOIDS
IF
IF
00010
00020
00030
00040
00050
00060
00070
00080
00090
00100
00110
00120
00130
00140
00150
00160
00170
00180
00190
00200
00210
00220
00230
00240
00250
00260
00270
00280
00290
00300
00310
00320
00330
00340
00350
00360
00370
00330
00390
00400
00410
00420
00430
00440
00450
00460
00470
00480
00490
00500
00510
00520
00530
                                     144

-------
                         RCONCA

C        IF STABLE CONDITION OR UNLIMITED MIXING HEIGHT,                    005*10
C         USE EQUATION 3-2 IF Z = 0,  OR EQ 3-1  FOR NON-ZERO Z,              00550
C         TURN-ER(1970) .                                                     00560
70    C2=2.*SZ*SZ                                                          00570
      IF (Z) 180,80,100                                                     00580
80    C3=H*H/C2                                                            00590
      IF (C3-50.) 90,180,180                                               00600
90    A2=2./EXP(C3)                                                        00610
C        WADE EQUATION 3 .2 ,TURNER<1970).                                    00620
      RCZ=A2/(2.5066*SZ)                                                   00630
      M=1                                                                   00640
      RETURN                                                               00650
100   A2=0.                                                                00660
      A3=0.                                                                00670
      CA=Z-H                                                               00680
      CB=Z+H                                                               00690
      C3=CA*CA/C2                                                          00700
      C4=CB*CB/C2                                                          00710
      IF (C3-50.) 110,120,120                                              00720
110   A2=1./EXP(C3)                                                        00730
120   IF (C4-50.) 130,140,140                                              00740
130   A3=1./EXP(C4)                                                        00750
C        WADE EQUATION 3.1,TURNER(1970).                                    00750
140   RCZ=(A2+A3)/(2.5066*SZ)                                              00770
      M=2                                                                   00780
      RETURN                                                               00790
C        IF SIGMA-Z IS GREATER THAN 1.6 TIMES THE MIKING  HEIGHT,            00800
C         THE DISTRIBUTION BELOW THE MIXING HEIGHT IS UNIFORM WITH         00810
C         HEIGHT REGARDLESS OF SOURCE HEIGHT.                              00820
150   IF (SZ/HL-1.6) 170,170,160                                           00830
C        WADE EQUATION 3.5,TURMER(1970).                                    00840
160   RCZ=1,/HL                                                            00850
      M=3                                                                   00860
      RETURN                                                               00870
C        INITIAL VALUE OF  AN SET = 0.                                      00880
170   AN = 0.                                                                00690
      IF (Z) 180,340,190                                                   00900
1BO   RCZ=0.                                                               00910
      RETURN                                                               00920
190   A1=1./(2.506&*SZ)                                                     00930
      C2=2.*SZ*3Z                                                          00940
      A2=0.                                                                00950
      A3=0.                                                                00960
      CA=Z-H                                                               00970
      CB=Z+H                                                               00980
      C3=CA*CA/C2                                                          00990
      C4 = CB*Ct3/C2                                                          01000
      IF (C3-50.) 200,210,210                                              Q1Q10
200   A2=1./EXP(C3)                                                        01020
210   IF (C4-5U.) 220,230,230                                              01030
220   A3=1./EXP(C4)                                                        01Q40
230   3UM=0.                                                               01050
      THL=2.*HL                                                            01060


                                      145

-------
RCONCA
240
250
260
270
260
290
300
310
320
330
C
340
350
360

370
380
390
400
410
420
      A4 = 0.
      A5=0.
      A6 = 0.
      A7=0.
      C5=AM*THL
      CC=CA-C5
      CD=CB-C5
      CE=CA+C5
      CF=CB+C5
      C6=CC*CC/C2
      C7=CD*CD/C2
      C3=CE*CE/C2
      C9=CF*CF/C2
      IF (C6-50.) 250,260,260
      A4=1 ./EXP(C6)
      IF (C7-50.) 270,280,280
      A5=1 ./EXP(C7)
      IF (C8-50.) 290,300,300
      A6=1 ./EXP(C8)
      If (C9-50.) 310,320,320
      A7=1 ./EXP(C9)
      T=A4+A5+A6+A7
      SUM=SUH+T
      IF (T-0.01) 330,240,240
      M=5
      RETUKN
         CALCULATE MULTIPLE EDDY REFLECTIONS FOR GROUND LEVEL RECEPTOR H
      A1=1 ./(2.5066*SZ)
      A2=0.
      C2=2.*SZ*SZ
      C3=H*H/C2
      IF (C3-50.) 350,360,360
      A2=2./EXP(C3)
      SUM=0.
      THL=2.*HL
      A4=0.
      A6=0.
      C5=AN*THL
      CC=H-C5
      CE=H+C5
      C6=CC*CC/C2
      C8=CE*CE/C2
      IF (C6-50.) 380,390,390
      A4=2./EXP(C6)
      IF (C8-50.) 400,410,410
      A6=2./EXP(C8)
      T=A4+A6
      SUM=SUM+T
      IF (T-0.01) 420,370,370
      RCZ=A1*(A2+SUM)
                                                  01070
                                                  01080
                                                  01090
                                                  01100
                                                  01110
                                                  01120
                                                  01130
                                                  01UO
                                                  01150
                                                  01160
                                                  01170
                                                  01180
                                                  01190
                                                  01200
                                                  01210
                                                  01220
                                                  01230
                                                  01240
                                                  01250
                                                  01260
                                                  01270
                                                  01280
                                                  01290
                                                  01300
                                                  01310
                                                  01320
                                                  01330
                                                  01340
                                                  01350
                                                  013&0
                                                  01370
                                                  01330
                                                  01390
                                                  01400
                                                  01410
                                                  01420
                                                  01430
                                                  01440
                                                  01450
                                                  01460
                                                  01470
                                                  01480
                                                  01490
                                                  01500
                                                  01510
                                                  01520
                                                  01530
                                                  01540
                                                  01550
                                                  01560
                                                  01570
                                                  01580
                                                  01590
            146

-------
                         RCONCA

      M=4                                                                  01600
      RETURN                                                               01610
C                                                                          01620
430   FORMAT (1HO,'BOTH H AND Z ARE ABOVE THE MIXING HEIGHT SO A RELIABL   01630
     1E COMPUTATION CAN NOT BE MADE.')                                     01640
C                                                                          01650
      END                                                                  01660
                                     147

-------
                         XVY

      FUNCTION XVY (SYO,KST)
C        XVY CALCULATES THE VIRTUAL DISTANCE NECESSARY TO
C        ACCOUNT FOR THE INITIAL CROSSWIND DISPERTION.
      GO TO (10,20,30,40,50,60), KST
10    XVY=(SYO/213.)**1.1148
      RETURN
20    XVI=(SYO/155.)**1.097
      RETURN
30    XVY=(SYO/103.)**1.092
      RETURN
40    XVY=(SYO/68.)**1.07fa
      RETURN
50    XVY=(SYO/50.)**1.086
      RETURN
60    XVY=(SYO/33.5)**1.083
      RETURN
C
      END
00010
00020
00030
00040
00050
00060
00070
00080
00090
00100
00110
00120
00130
00140
00150
00160
00170
00180
                                     148

-------
                         XV Z

      FUNCTION XVZ (SZO,KST)                                               00010
C        XVZ CALCULATES THE VIRTUAL DISTANCE NECESSARY                     00020
C        TO ACCOUNT FOR THE INITIAL VERTICAL DISPERTION.                   00030
      DIMENSION SA(7), SB(2), SD(5), SE(8), SF(9), AA(d), AB(3), AD(6),     00040
     1AE(9), AF(10),  CA(8), CP(3)r CD(6), CE(9), CF(10)                    00050
      DATA SA 713.95,21.40,29.3,37.67,47.44,71.16,104.657                  00060
      DATA SB /20.23,40./                                                  00070
      DATA SD /12.09,32.09,65.12,134.9,251.2/                              00080
      DATA SE 73.534,8.698,21.626,33.469,49.767,79.07,109.3,141.867        00090
      DATA SF 74.093,10.93,13.953,21.627,26.976,40.,54.89,68.84,83.257      00100
      DATA AA /122.8,158.08,170.22,179.52,217.41,258.89,346.75,453.85/      00110
      DATA AB /90.673,98.483,109.3/                                        00120
      DATA AD /34.459,32.093,32.093,33.504,3b.650,44.053/                  00130
      DATA AE 724.26,23.331,21.628,21.628,22.534,24.703,26.97,35.42,47.6   00140
     118/                                                                  00150
      DATA AF 715.209,14.457,13.953,13.953,14.823,16.187,17.836,22.651,2   00160
     17.074,34.2197                                                        00170
      DATA CA /1.0585,.9486,.9147,.8879,.7909,.7095,.5786,.4725/           00180
      DATA CB /I.073,1.017,.91157                                          00190
      DATA CD 71.1498,1.2336,1.5527,1.6533,1.7671,1.95397                  00200
      DATA CE 71.1953,1.2202,1.3217,1.5854,1.7497,1.9791,2.1407,2.6585,3   00210
     1.3793/                                                               00220
      DATA CF /I.2261,1.2754,1.4606,1.5816,1.8348,2.151,2.4092,3.0599,3.   00230
     16448,4.60497                                                         00240
      GO TO (10,40,70,80,110,140), KST                                     00250
C        STABILITY A(10)                                                   00260
10    DO 20 ID=1,7                                                         00270
      IF (SZO.LE.SA(ID)) GO TO 30                                          00280
20    CONTINUE                                                             00290
      10=8                                                                 00300
30    XVZ=(SZO/AA(ID))**CA(ID)                                             00310
      RETURN                                                               00320
C        STABILITY B  (40)                                                  00330
40    DO 50 ID=1,2                                                         00340
      IF (SZO.LE.SB(ID)) GO TO 60                                          00350
50    CONTINUE                                                             00360
      ID=3                                                                 00370
60    XVZ=(SZO/AB(ID))**CB(ID)                                             00380
      RETURN                                                               00390
C        STABILITY C  (70)                                                  00400
70    XVZ=(SZO/61.141)**!.0933                                             00410
      RETURN                                                               00420
C        STABILITY D  (80)                                                  00430
80    DO 90 ID=1,5                                                         00440
      IF (SZO.LE.SD(ID)) GO TO 100                                         00450
90    CONTINUE                                                             00460
      ID=6                                                                 00470
100   XVZ=(SZO/AD(ID))**CD(ID)                                             00480
      RETURN                                                               00490
C        STABILITY E  (110)                                                 00500
110   DO 120 ID=1,8                                                        00510
      IF (SZO.LE.SE(ID)) GO TO 130                                         00520
120   CONTINUE                                                             00530
                                    149

-------
                         xvz

      ID=9                                                                 00540
130   XVZ=(SZO/AE(ID))**CE(ID)                                             00550
      RETURN                                                               00560
C        STABILITY F(140)                                                  00570
140   DO 150 ID=1,9                                                        00580
      IF (SZO.LE.SF(ID))  GO TO 160                                         00590
150   CONTINUE                                                             00600
      ID=10                                                                00610
160   XVZ=(SZO/AF(ID))**CF(ID)                                             00620
      RETURN                                                               00630
C                                                                          00640
      END                                                                  00650
                                    150

-------
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                    CURLIN

 SUBROUTINE CURLIN (RC,SC,R,S,Z,RAD,THETA,RL,SL,RLl,SL1,NLOCI)

THE INPUT DATA FOR CURLIN ARE THE RECEPTOR AND CENTER
COORDINATES,THE RADIUS OF THE CIRCLE AND THE WIND DIRECTION.

THE FUNCTION OF CURLIN IS TO DETERMINE WHERE THE LINE FORMED BY THE
DIRECTION AND RECEPTOR COORDINATES INTERSECTS THE CIRCLE.

R,S ARE RECEPTOR COORDINATES
RC,SC ARE CENTER COORDINATES
RAD 13 THE RADIUS
THETA IS THE WIND DIRECTION
RL,SL AND RL1,SL1 ARE LOCI ON THE CIRCLE.
 RA=3.141b92bS4/160.
 IF (THETA.EQ.O..OR.THETA.EQ.130.) GO TO 10

IF THE WIND DIRECTION IS 0 OR loO DEGREES THAN THE RECEPTOR
COORDINATE CALCULATIONS FOLLOW.IF THE WIND IS FROM ANY OTHER
DIRECTION THAN THE RECEPTOR COORDINATE CALCULATIONS BEGIN AT
STATEMENT 10.

 GO TO 20
 RL=R
 RL1=R
 A=l.
 B=-2.*SC
 C=SC**2-RAD**2+(R-RC)**2
 DISC=B**2-4.*A*C
 IF (DISC.LT.O.) GO TO 50
 SL=(-B+SQRT(DISC))/(2.*A)
 SLl=(-B-SQRT(DISC))/(2.*A)
 GO TO 30
 IF (THETA.GT.O..AND.THETA.LE.90.) SLOPE=1 ./TAN (THETA*RA)
 IF (THETA.GT.90..AND.THETA.LT.160.) SLOPE=-1./TAN(IdO.*RA-RA*THETA
1)
 IF (THETA.GT.180..AND.THETA.LE.270.)  SLOPE=1./TAN(THETA*RA-RA*lfaO.
1)
 IF (THETA.GT.270..AND.THETA.LT.360.)  SLOPE = -TAN(THETA*RA-RA*270.)
 DEL=-SLOPE*R+S-SC
 A=1.+SLOPE**2
 B=-2.*RC+2.*SLOPE*DEL
 C=-(RAD**2-RC**2-DEL**2)
 DISC=B**2-4.*A*C
 IF (DISC.LT.O.) GO TO 50
 RL=(-B+SQRT(DISC))/(2.*A)
 RL1=(-B-SQRT(DISC))/(2.*A)
 SL=S+SLOPE*(RL-R)
 SL1=S+SLOPE*(RL1-R)
 X=(RL-R)*SIN(THETA*RA)+(SL-S)*COS(THETA*RA)

X AND XI ARE USED TO CHECK IF THE INTERSECTION VALUES ARE UPWIND.
IF BOTH X AND XI ARE POSITIVE THEN THERE ARE TWO UPWIND
INTERSECTIONS. IF BOTH ARE NEGITIVE THEN THERE ARE NO UPWIND
00010
00020
00030
00040
00050
00060
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                                    151

-------
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C
                    CURLIN

INTERSECTIONS. IF EITHER ONE IS POSITIVE AND THE OTHER IS
NEGATIVE THAN THERE IS ONE UPWIND INTERSECTION.

 X1=(RL1-R)*SIN(THETA*RA)+(SL1-S)*COS(THETA*RA)
 NLOCI=1
 IF (X.LT.O..AND.X1.LT.O.) GO TO 50
 IF (X.LT.O.) GO TO 40
 IF (Xl.LT.O.) NLOCI=0
 GO TO 60
 NLOCI=0
 RL=RL1
 SL=SL1
 GO TO 60
 NLOCI=-1
 RETURN

 END
00540
00550
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                                     152

-------
                         DIFANG

      FUNCTION DIFANG (ANGA,ANGB)                                          00010
C        DETERMINES THE DIFFERENCE BETWEEN TWO ANGLES.                     00020
C        THE RESULTING ANGLE IS BETWEEN 0 AND 360 DEGREES.                 00030
      DIFANG=ANGA-ANGB                                                     00040
      IF (DIFANG) 10,40,50                                                 00050
10    IF (DIFANG+laO.) 20,30,40                                            00060
20    DIFANG=DIFANG+360.                                                   00070
      GO TO 10                                                             OOObO
30    DIFANG=ldO.                                                          OOOyO
40    RETURN                                                               00100
50    IF (DIFANG-130.) 40,30,60                                            00110
60    DIFANG=DIFANG-360.                                                   00120
      GO TO 50                                                             00130
C                                                                          00140
      END                                                                  00150
                                     153

-------
                          ANGARC

      FUNCTION AUGARC (DELM,DELN)
C         ANGARC  DETERMINES THE APPROPRIATE ARCTArJ (M/N) WITB
C         THE RESULTING ANGLE BETWEEN  0 AND 360 DEGREES.
      IF  (DELN) 10,40,bO
10    IF  (DELM) 20,30,20
20    ANGARC=57.2y57d*AIAN(DELM/DELN)+ldO.
      RETURN
30    ANGARC=l80.
      RETURN
40    IF  (DELM) 50,60,70
50    ANGARC=27U.
      RETURN
60    ANGARC=0.
      RETURN
70    ANGARC=090.
      RETURN
00    IF  (DELM) 90,100,110
90    ANGARC=57.2957b*ATAN(DELM/DELN)+360.
      RETURN
100   ANGARC=3bO.
      RETURN
110   AHGARC=57.2957b*ATAN(OELM/DELN)
      RETURN
C
      END
00010
00020
00030
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0-0050
00060
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00100
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                                       154
                                                * U.S. GOVERNMENT PRINTING OFFICE: 1978740-261/335 Region No. 4

-------
                                   TECHNICAL REPORT DATA
                            (Please read Instructions on the reverse before completing)
 1. REPORT NO.
 EPA-600/4-78-013
                             2.
                                                           3. RECIPIENT'S ACCESSION-NO.
4. TITLE AND SUBTITLE
  USER'S GUIDE FOR PAL
  A  Gaussian-Plume Algorithm  for Point, Area, and
  Line Sources
             5. REPORT DATE
               February 1978
             6. PERFORMING ORGANIZATION CODE
 . AUTHOR(S)
  William B.  Petersen
                                                           8. PERFORMING ORGANIZATION REPORT NO.
9. PERFORMING ORGANIZATION NAME AND ADDRESS
                                                           10. PROGRAM ELEMENT NO.
                                                              1AA603 AB-25(FY-78)
                                                           11. CONTRACT/GRANT NO.
 12. SPONSORING AGENCY NAME AND ADDRESS
  Environmental Sciences  Research Laboratory - RTP,  NC
  Office of Research and  Development
  U.S.  Environmental Protection Agency
  Research Triangle Park, North Carolina 27711
              13. TYPE OF REPORT AND PERIOD COVERED
                In-house
             14. SPONSORING AGENCY CODE
                EPA/600/09
 15. SUPPLEMENTARY NOTES
16. ABSTRACT
       PAL is an acronym  for  this point, area, and  line  source algorithm.   PAL  is  a
  method of estimating short-term dispersion using  Gaussian-plume steady-state
  assumptions.  The algorithm can be used for estimating concentrations of  non-
  reactive pollutants at  30 receptors for averaging times of from 1 to 24 hours,
  and for a limited number of point, area, and line sources (30 of each type).

       Calculations are performed for each hour.  The  hourly meteorological  data
  required are wind direction, wind speed, stability class, and mixing height.
  Single values of each of these four parameters  are assumed representative for
  the area modeled.
       This algorithm  is  not  intended for application  to entire urban areas  but is
  intended, rather, to assess the impact on air  quality, on scales of tens  to
  hundreds of meters,  of  portions of urban areas  such  as shopping centers,  lar
  parking areas, and airports.   Level terrain  is  assumed.
                                large
 7.
                                KEY WORDS AND DOCUMENT ANALYSIS
                  DESCRIPTORS
b.lDENTIFIERS/OPEN ENDED TERMS  C. COS AT I Field/Group
  * Air pollution
  * Atmospheric models
  * Algorithms
  * Dispersions
                              13B
                              14A
                              12A
 8. DISTRIBUTION STATEMENT

  RELEASE TO  PUBLIC
19. SECURITY CLASS (ThisReport)
   UNCLASSIFIED
21. NO. OF PAGES

    163
                                              20. SECURITY CLASS (This page)

                                                 UNCLASSIFIED
                                                                         22. PRICE
EPA Form 2220-1 (9-73)
                                             155

-------
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