U Af ••*«;
                                                                   DECEMBER 1986
                                USER'S GUIDE FOR PEM-2:

                         POLLUTION EPISODIC MODEL (VERSION 2)
                       ATMOSPHERIC SCIENCES RESEARCH LABORATORY
                          OFFICE OF RESEARCH AND DEVELOPMENT
                         U.S. ENVIRONMENTAL PROTECTION AGENCY
                     RESEARCH TRIANGLE PARK, NORTH CAROLINA 27711

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            USER'S GUIDE FOR.PEM-2:

     POLLUTION EPISODIC MODEL (VERSION 2)
                      by
                K. Shankar Rao
 Atmospheric Turbulence and Diffusion Division
National Oceanic and Atmospheric Administration
          Oak Ridge, Tennessee 37830
              IAG-DW13930021-01-1
                Project Officer

              James M. Godowitch
      Meteorology and Assessment Division
    Atmospheric Sciences Research Laboratory
 Research Triangle Park, North Carolina 27711
   ATMOSPHERIC SCIENCES RESEARCH LABORATORY
      OFFICE OF RESEARCH AND DEVELOPMENT
     U.S. ENVIRONMENTAL PROTECTION AGENCY
 RESEARCH TRIANGLE PARK, NORTH CAROLINA 27711

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                                  NOTICE

    The information in this document has been funded in part by the United
States Environmental Protection Agency under Interagency Agreement
IAG-DW13930021 to the Atmospheric Turbulence and Diffusion Division of  the
National Oceanic and Atmospheric Administration.  It has been subject to
the Agency's peer and administrative review, and it has been approved for
publication as an EPA document.  Mention of trade names or commercial
products does not constitute endorsement or recommendation for use.

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                                   PREFACE

   This report contains a technical description and complete user instructions
for the Pollution Episodic Model Version 2 (PEM-2) computer program.   The PEM-2
urban air quality dispersion model was developed to simulate the relevant
physical processes in order to predict short-term ground level concentrations
of particulate matter and/or gaseous pollutants from multiple point and area
sources over an urban domain.  Gaussian plume modeling techniques were adapted
to allow for dry deposition processes by a gradient transfer approach and a
chemical reaction between two species by a linear transformation method.   The
deposition and settling velocities for each species, and a transformation rate
constant must be specified by the user.  The model algorithms are subject to
specific assumptions and limitations described in the report.  PEM-2 is currently
a non-guideline model.
   Input requirements include source characteristics and emission rates,  hourly
measurements of meteorological parameters, and upwind boundary concentration.
The latter should be representative of the incoming regional background measured
sufficiently upwind of  the urban emissions region.  A comprehensive quality-
assured emissions inventory and representative, accurate meteorological and
concentration measurements aid in reducing model uncertainty.
   The computer code has been thoroughly tested with example cases; however,
errors are occasionally discovered and revisions may be made.  Future revisions
may be obtained if issued by completing and returning the form on the last page
of this publication.  Comments and questions about this publication should be
directed to; Chief, Atmospheric Modeling Branch, Meteorology and Assessment
Division (MD-80), Environmental Protection Agency, Research Triangle Park, NC
27711.
   This user guide is available from the National Technical Information
Service (NTIS), Springfield, VA 22161.  The computer code is contained on the
UNAMAP Version 6 magnetic tape and it may be obtained from Computer Products,
NTIS, Springfield, VA 22161 (phone: (703) 487-4763).
                                      iii

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                                 ABSTRACT

   The Pollution Episodic Model Version 2 (PEM-2) is an urban-scale model
designed to predict short term average ground-level concentrations and depo-
sition fluxes of one or two gaseous or particulate pollutants  at  multiple
receptors.  The two pollutants may be non-reactive, or chemically-coupled
through a first-order chemical transformation.   Up to 300 isolated point
sources and 50 distributed area sources may be  considered in the  calcula-
tions.  Concentration and deposition flux estimates are made using hourly
mean meteorological data.  Up to a maxiumum of  24 hourly scenarios of
meteorology may be included in an averaging period.

   The concentration algorithms used in PEM-2 are specially developed to
account for the effects of dry deposition, sedimentation, and  first^order
chemical transformation.  The Gaussian plume-type algorithms for  point
sources are derived from analytical solutions of a gradient-transfer model.
In the limit, when deposition and settling velocities of the pollutants and
the chemical transformation rate are zero, these expressions reduce to the
familiar Gaussian plume diffusion algorithms.  The concentrations from area
sources in PEM-2 are calculated by numerical integration of the point: source
algorithms.

   When the chemical transformation option is considered, PEM-2 calculates
the average surface concentrations and deposition fluxes of both  the primary
(reactant) and the secondary (reaction product) pollutants.  The  model
also permits a possible direct emission of the  secondary pollutant.  The
deposition and settling velocities of the two species may be different.
Either of the species may be a gaseous or particulate pollutant.   PEM-2 is
intended for studies of the atmospheric transport, transformation, and
deposition of acidic, toxic, and other pollutants in urban areas  to assess
the impact of existing or new sources or source modifications  on  air
quality for regulatory purposes and urban planning.

   The User's Guide lists the concentration algorithms and computational
techniques used in the PEM-2 program, and describes the input/output parame-
ters, optional features, capabilities, and limitations of the  model.
Modifications to the previos version of the model are outlined.  The
information contained in this report is directed to the model  user and the
programmer.

   This User's Guide to PEM-2 was prepared by NOAA's Atmospheric
Turbulence and Diffusion Division in partial fulfillment of an Interagency
Agreement with the U.S. Environmental Protection Agency.  This work,
covering the period December 1983 to July 1984, was completed  as  of
September 30, 1984.
                                    iv

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                                 CONTENTS




Preface 	  iii




Abstract 	  iv




Figures 	  vii




Tables	  viil




Acknowledgements 	•	  ix







1.  MODEL OVERVIEW




    1.1  Introduction	  1




    1.2  Capabilities and Applications 	  2




    1.3  Assumptions and Limitations 	  3




    1.4  Summary of Input Data 	  5




    1. 5  Summary of Model Output	  7




2.  TECHNICAL DISCUSSION




    2.1  Theoretical Basis 	  9




    2.2  Point Sources 	 10




         2.2.1  Concentration Algorithms	 10




         2.2.2  Plume Rise 	 12




         2.2.3  Dispersion Parameters 	•	 13




         2.2.4  Restrictions on Receptors for Calculations 	 14




    2.3  Area Sources	 15




         2.3.1  Emission Grid 	 15




         2.3.2  Concentration Algorithms 	 21




         2.3.3  Dispersion Parameters 	 24




    2.4  Receptors 	 24




         2.4.1  Receptor Grid 	 24




         2.4.2  Automatic Grid Selection 	 25

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    2.5  Meteorology 	  30

         2.5.1  Atmospheric Stability 	  31

         2.5.2  Wind Speed 	  32

         2.5.3  Wind Direction	  34

         2.5.4  Mixing Depth	  35

3.  COMPUTER PROGRAM OVERVIEW

    3.1  Basis for PEM-2 Program	  37

    3.2  Structure of the Program	  38

    3.3  General Flow of the Program	  40

4.  PROGRAM USER'S GUIDE

    4.1  Summary of Program Input	  42

    4.2  Details of Program Input 	  43

         4.2.1  Control Parameters 	  43

         4.2.2  Scenario Parameters 	.	  50

         4.2.3  Area Source Parameters	  51

         4.2.4  Point Source Parameters	  52

    4.3  Guide to Program Output	  53

    4.4  Discussion of I/O Parameters 	  55

    4.5  Example Problems 	  58

References 	  60

Appendices

    A.   Point Source Algorithms 	  61

    B.   Plume Rise Equations and Plume Penetration Methods 	  70

    C.   Surface Deposition Fluxes, and Deposition and Settling
         Velocities 	  85

    D.   D01AJF - NAG FORTRAN Library Routine Document 	  88

    E.   Input and Output Listings of Example Problems 	  92

    F.   PEM-2 FORTRAN Listing 	 147


                                    vi

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                                  FIGURES

Number                                                                        Page

1.    Schematic diagram showing a single grid square with emissions
      and four downwind calculation grid squares with receptors, and
      the distances used in area-source algorithms.  These distances
      are measured downwind from the source Qo  	   17

2.    Spatial patterns of affected calculation  grid squares downwind
      of an area source 	   18-19

3.    Points used for automatic selection of receptor grid by AUTGRD
      subroutine 	   27

4.    Example of a receptor grid selected by AUTGRD subroutine	   29

5.    Structure of PEM-2 computer program 	   39
                                    vn

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                                  TABLES

Number                                                                      Pag

  1   Values of coefficients in the formulas for Oy(x) and az(x) in
      urban conditions 	    14

  2   Maximum crosswind half-angle values for point source plumes  	    15

  3   Values of i and j for each spatial pattern of affected squares
      downwind of an area source 	    20

  4   Atmospheric stability classes 	    31

  5   Atmospheric conditions defining stability classes	    31

  6   Wind speed classification 	,.    32

  7   Values of exponent p in wind speed power law	    33

  8   Wind direction sectors	    34
                                   vin

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                             ACKNOWLEDGEMENTS






    This report was prepared for  the Office  of Research  and  Development,




Atmospheric Sciences Research Laboratory  (ASRL)  of  the U.  S.  Environmental




Protection Agency  (EPA) to support  the  needs of  EPA's Office  of  Air  Quality




Planning and Standards in urban particulate  modeling.  This  work was




accomplished under interagency agreements  among  the U. S.  Department  of




Energy, the National Oceanic and  Atmospheric Administration,  and the EPA.




The author is grateful to Dr. Jack  Shreffler and James Godowitch of  ASRL




for their interest and advice during the  course  of  this  work.  The author




thanks Atmospheric Turbulence and Diffusion Division Director  Bruce  Hicks




for his support, and Mrs. Mary Rogers for  her excellent  typing and patient




revisions.  Special thanks are due  to Cheryl Stieneke, Martha  Stevens,  and




Mike Ku, who worked as programmers  for  this project at various times and




assisted in the development and testing of the PEM-2 program.




    Several figures and tables shown in this report are  reproduced from the




Users' Guide to Texas Episodic Model with  permission from  the  Texas  Air




Control Board.  The library routine D01AJF used  for numerical  integration




in PEM-2 has been released by the Computer Sciences Division  of  the  Oak




Ridge National Laboratory for inclusion in the program listing.   The




Numerical Algorithms Group (NAG)  holds  the copyright to  this  routine and




its document.  The latter is reproduced in this  report from  the  NAG  FORTRAN




Mini-Manual.
                                    ix

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                                 SECTION  1







                              MODEL OVERVIEW







1.1  INTRODUCTION




     The Pollution Episodic Model Version 2 (PEM-2)  is  an  urban-scale  air




quality model designed to predict short term ground-level  concentrations




and deposition fluxes of one or two, gaseous or  particulate,  reactive  or




non-reactive pollutants in an urban area  with multiple  point  and  area




sources.  PEM-2 uses the concentration algorithms  developed by  Rao  (1982)




which explicitly account for the effects  of dry  deposition, gravitational




settling, and a first-order chemical transformation.  These algorithms,




derived analytically from a gradient-transfer model,  are based  on Gaussian




plume modeling assumptions.  For chemically-coupled  pollutants, the surface




concentrations and deposition fluxes of both the primary (reactant) and the




secondary (reaction product) pollutant are calculated.






     PEM-2 is based on the Pollution Episodic Model  (PEM)  developed by Rao




and Stevens (1982).  The latter, in turn, is based on the  Texas Episodic




Model Version 8 (TEM-8) developed by the  Texas Air Control Board  (1979) for




the atmospheric dispersion of non-reactive pollutants over a  perfectly




reflecting (non-depositing) surface.  In  the limit,  when the  deposition and




settling velocities and the chemical transformation  rate are  zero,  the con-




centration algorithms used in PEM-2 reduce to the  familiar Gaussian plume




dispersion algorithms used in TEM-8.  The two models  share essentially the




same framework for calculations, though there are  differences in  the com-




putational techniques utilized in the models.






                                     1

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     Besides the concentration algorithms, there are other  important  dif-

ferences between PEM-2 and TEM-8 models:


 1.  PEM-2 uses Briggs' (1973) urban dispersion parameters  for  both point
     and area sources  to represent 1-hour average dispersion.   This treat-
     ment is similar to that used in EPA's RAM model (Turner and  Novak,
     1978).  TEM-8 uses the Pasquill-Gifford  (PG) curves  to represent
     10-minute average dispersion from point  sources; for averaging periods
     longer than 10 minutes, the ay values are adjusted to  account for  the
     greater horizontal plume meander due to  fluctuations in wind direction.
     For area sources, TEM-8 uses the oz's from Gifford and Hanna (1970)  to
     represent 1-hour  average dispersion.

 2.  PEM-2 determines  the concentrations for  a period longer than an  hour
     by summing and averaging the concentrations calculated for each  hour
     in the period.  TEM-8 does not do this time-averaging  for  con-
     centrations from  area sources.  Thus, with a constant  meteorology  for
     N hours, the area-source concentration at a receptor predicted by
     TEM-8 would be N  times its hourly concentration.

 3.  TEM-8 estimates the point source concentrations by interpolating bet-
     ween the relative concentrations precalculated for selected  values  of
     model parameters  and stored in large look-up tables.   Because of the
     large number of model parameters, PEM-2  does not use this  inter-
     polation technique.

Other differences between these two models are listed in  Section  3.


1.2  CAPABILITIES AND APPLICATIONS


     The capabilities  of PEM-2 are as follows:

 1.  PEM-2 is an urban-scale air quality model applicable to downwind
     distances of up to 50 km.  Up to a maximum of 300 point sources  and  50
     area sources can  be included in the model inputs to  estimate concentra-
     tions at a maximum of 2500 receptors located on a 50 x 50  square recep-
     tor grid.

 2.  PEM-2 calculates  short-term (1 to 24 hr) average ground-level con-
     centrations and deposition fluxes of one or two gaseous or particulate
     pollutants.

 3.  The two pollutants may be non-reactive,  or chemically-coupled through
     a first-order chemical transformation.   If only one  pollutant is
     calculated, the effects of a first-order chemical decay can  be con-
     sidered.  The chemical transformation (or decay) rate  may  vary from
     0.1 to 100 percent per hour.

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 4.  The deposition  (and settling) velocities  of  the  two  species  may be
     equal or different.  Direct emission  of the  secondary  (reaction
     product) pollutant can be considered  for  both  point  and area sources.

Some areas of potential application of PEM-2 are  the  following:

 1.  Urban particulate modeling.

 2.  Studies of the  transport, diffusion,  transformation, and deposition of
     acidic, toxic,  and other pollutants in urban areas.  An important    _
     example is the  atmospheric transport  and  transformation of S02 to  SO,.

 3.  Impact analyses of existing or new sources or  source modifications for
     regulatory purposes and urban planning.

 4.  Stack design, and fuel conversion/switching  studies.   Evaluation of
     pollution control technology and strategies  for  prevention of signifi-
     cant deterioration.
1.3  ASSUMPTIONS AND LIMITATIONS

     PEM-2 is based on steady state Gaussian plume  modeling  assumptions.

Some of the important assumptions of PEM-2 are  as follows:

 1.  Concentration estimates may be made for each hour  using the  mean
     meteorological conditions for that hour.  Average  concentrations for a
     period longer than an hour are determined  in the program by  averaging
     the hourly concentrations of that period.

 2.  The sources are stationary and the emission rates  are constant  over  the
     concentration-averaging period.  The latter assumption  is  reasonable
     since PEM-2 is designed to predict only short-terra average con-
     centrations; this assumption is intended solely to limit  the amount  of
     input data required by the model.

 3.  If the hourly emission rates are highly variable over the
     concentration-averaging period, then the average concentrations may  be
     obtained by averaging externally, with minimal programming,  the con-
     centrations calculated hourly and stored on tape by the model.   This
     can be done, for example, to calculate the daily mean concentrations
     with diurnally varying emission rates.

 4.  Total concentration at a receptor is the sum of the concentrations
     calculated at the receptor from each source; i.e.,  concentrations are
     additive.

 5.  Pollutants released from a stack are transported downwind  at a  rate
     equal to the mean wind speed at the physical stack height.   The wind
     direction is constant for each hour.  The horizontal wind  field is
     homogeneous and the effects of directional wind shear are  neglected.

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 6.  Diffusion of continuous plumes gives time-averaged Gaussian distribu-
     tions for concentrations in the crosswind and vertical directions.
     The diffusion in the downwind direction is negligible compared to
     advection.  This assumption obviously excludes calm conditions..

 7.  The reactant and the product species are coupled through a first-order
     chemical transformation.  The deposition and settling velocities of
     the species, and the chemical transformation rate are constant over
     the concentration-averaging period.  The diurnal variation of these
     parameters can be considered, if necessary, by averaging the hourly
     concentrations as discussed above.

 8.  Particulate pollutants consist of particles of a known size (or size
     distribution) with a representative settling velocity.

 9.  Pollutant concentration at a receptor due to the distributed area
     sources depends only on sources located in a narrow upwind sector.
     Therefore, horizontal diffusion can be ignored for area sources.

10.  The crosswind variations of urban area source-strength patterns can be
     ignored.  The contributions of more remote upwind area sources to  the
     concentration at a receptor are quite small.  For this reason, it  is
     generally adequate to consider only eight area source grid squares
     immediately upwind of each receptor grid square.

     Every air pollution model is limited by the assumptions used to pre-

dict the pollutant concentrations in the atmosphere.  PEM-2 is subject  to

the same basic limitations as any Gaussian plume-type model.  The limiting

assumptions of the concentration algorithms developed for PEM-2 are

discussed in detail by Rao (1982).  Other general limitations of the model

can be summarized as follows:

 1.  Receptors farther than 50 km downwind of a source are ignored.  Thus
     the maximum downwind distance is limited to 50 km.

 2.  The number of point sources is limited to 300, and the number of area
     sources is limited to 50.  The computer program can be easily modified
     by the user to increase the maximum number of point and/or area sour-
     ces, if necessary.  All sources are stationary.

 3.  The maximum number of scenarios (sets of hourly meteorological data)
     in an averaging period is limited to 24.  PEM-2 is designed to calculate
     only short-term (1 to 24 hr) average surface concentrations and depo-
     sition fluxes of one or two pollutants.

 4.  PEM-2 does not make any adjustment for differences in terrain elevation
     between sources and/or receptors.  The model assumes level terrain.  No
     adjustments are made for building wake-induced downwash, wake entrainment,
     or other building-related effects on the various effluent plumes.

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 5.   Only a first-order chemical transformation/decay is considered.  The
     transformation rate, and the deposition and settling velocities of  the
     species, must be specified by the user, if these options are  selected.

 6.   The model cannot perform calculations for calm conditions; if  such
     conditions occur, the wind speed is arbitrarily set to 1 m/s.

 7.   PEM-2 does not attempt to deal with wet removal processes; hence, the
     model does not apply during periods of precipitation.
1.4  SUMMARY OF INPUT DATA

     Input to PEM-2 is divided into four main sections:

 1)  Control parameters

     Control parameters remain constant throughout the model run.  They

 specify:

 1.  An alphanumeric title

 2.  Time-averaging option

 3.  Options for types of input and output

 4.  Number of scenarios (sets of hourly meteorological data)

 5.  Options for using stack-tip downwash, new plume rise and new plume
     penetration schemes for point sources

 6.  Receptor grid coordinates and spacing

 7.  Automatic receptor grid option

 8.  Potential temperature gradient d9/dz for calculation of plume rise
     with E and F atmospheric stability classes

 9.  Parameters for one or two pollutants:

     a)  Deposition velocity
     b)  Gravitational settling velocity

10.  Option to calculate chemical transformation or decay of first
     pollutant

     a)  Chemical transformation or decay rate
     b)  Ratio of molecular weights of product to reactant

11.  Scaling factors for area source emission rates

12.  Calibration coefficients to be applied to the calculated
     concentrations

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13.   Alphanumeric labels for pollutants

14.   Alphanumeric labels for the calibrated concentrations

15.   Site-specific values of anemometer height and/or wind-profile expo-
     nents (optional)

 2)   Scenario Parameters

     A scenario is a set of mean meteorological data for one hour.  From one

 to  twenty-four scenarios may be included in each run.  Each scenario uses

 the same receptor grid and the same point and area source inventories.

 Meteorological parameters for each scenario are:

 1.   Atmospheric stability class

 2.   Wind speed class or specific wind speed

 3.   Wind direction sector or specific wind direction

 4.   Ambient  temperature

 5.   Mixing height

 6.   Potential temperature gradient in the elevated stable layer above
     mixing height

 3)   Area Source Inventory

     From zero to fifty area sources may be included in each run.   Each

 area source  square is described by:

 1.   Location in receptor grid coordinates

 2.   Length of a side

 3.   Emission rates for pollutants

 4)   Point Source Inventory

     From zero to three hundred point sources may be included in each run.

 Each point source is described by:

 1.   Location in receptor grid coordinates

 2.   Emission rates for pollutants

 3.   Stack height

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 4.  Inside diameter of the stack-tip

 5.  Exit velocity of the plume

 6.  Exit temperature of the plume

 7.  Alphanumeric identification

     Details of the input data to PEM-2 are given  in  Section  4  of  this

report.



1.5  SUMMARY OF MODEL OUTPUT

     For ease of reference, PEM-2 prints out and briefly  explains  all I/O

control parameters and technical options used in a run.   Input  data  for

meteorological conditions, area sources, and  point sources are also listed.


     Calculated values of surface concentrations,  deposition  fluxes, and

other useful information may be displayed in the following optional  forms:

 1.  List Option 	 For each receptor in the grid, the calculated values
     of concentrations and deposition fluxes are listed at the  end of each
     averaging-period consisting of 1 to 24 scenarios.

 2.  Spatial Array Option 	 The calculated values of concentrations and
     deposition fluxes at each receptor are displayed in  map  form  at the
     end of each averaging-period.

 3.  Tape Option 	 The calculated values of concentrations  and deposition
     fluxes at each receptor are written on a magnetic tape  (designated
     for output) at the end of each averaging-period.  This option may be
     used to generate inputs to a contour-plotting routine, or  to  store
     hourly output data for averaging externally in order to  account for
     the variability of hourly emission rates in an averaging-period con-
     sisting of more than one scenario (see Section 1.3).

 4.  Culpability List Option 	 The five point sources which contributed
     most to the total concentration at each receptor are identified by
     point-source sequence number.  A list of these source numbers and
     their percent contributions are printed for one  or two pollutants at
     each receptor in the grid at the end of each  scenario.

 5.  Maximum Concentration Option 	 The maximum  calculated  values  of sur-
     face concentration and deposition flux, and the  receptor where  these
     values occur, are printed for each pollutant  at  the  end  of the  last
     scenario or averaging-period.

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 6.  Point Source List Option 	 The input stack parameters,  the wind
     speed at physical stack height, the maximum effective source height,
     the dominant plume rise influence (buoyancy or momentum), and  the
     plume penetration fraction (see Appendix B) are listed for  each  point
     source at the beginning of each scenario.

     These output options are selected by the user by specifying

appropriate values for the control parameters in the inputs to the  model.

It may not be possible to select some of these options in combination with

others.  The details are discussed in Section 4.

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                                 SECTION 2
                           TECHNICAL DISCUSSION
2.1  THEORETICAL BASIS







     The concentration algorithms used in PEM-2 are derived from analytical




solutions of a steady state gradient-transfer  (K-theory) model, which




describes the atmospheric transport, diffusion, deposition, and first-order




chemical transformation of gaseous or particulate pollutants from an ele-




vated continuous point source.  The eddy diffusivity coefficients in these




analytical solutions are expressed in terms of the empirical Gaussian




plume dispersion parameters, so that the latter can be conveniently spe-




cified as functions of the downwind distance and the atmospheric stability




class within the framework of the standard turbulence-typing schemes.  The




point-source concentration algorithms for the  primary (reactant) and the




secondary (product) pollutants are presented for various stability and




mixing conditions of the atmosphere.  In the limit when deposition and




settling velocities and the chemical transformation rate are zero, these




algorithms reduce to the well-known Gaussian plume dispersion algorithms




presently used in EPA air quality models.  Details of the gradient-transfer




model formulations, analytical solutions, parameterizations, and develop-




ment of the point-source concentration algorithms can be found in the




reports by Rao (1981,  1982).

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     In PEM-2, the ground-level concentrations of the primary  and  secondary




pollutants resulting from urban area source emissions are  computed by




numerical integration of the corresponding point-source  concentration




algorithms.  The urban area-source modeling techniques of  Gifford  and  Hanna




(1970) are utilized in these computations.  For point sources,  PEM-2 provides




options for using the standard or new plume rise formulations  due  to Briggs




(1969, 1984), and new schemes for plume penetration of an  elevated stable




layer.  For both point and area sources, PEM-2 uses the  urban  dispersion




parameters of Briggs (1973) as given by Gifford (1976).









2.2  POINT SOURCES









2.2.1  Concentration Algorithms







     The ground-level concentrations of the primary and  the secondary




pollutants (denoted by subscripts 1 and 2, respectively) from  an elevated




continuous point source are calculated in PEM-2 from one or both of the




following sets of algorithms, depending on the atmospheric stability and




mixing conditions:









Near-source region (0 < x < xm),
                             Ql   gl   g22
                                    10

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Well-Mixed region (x > 2






                             Q
                        ci = IT  • I1  • r1                              <2a)
                             Ql   gl   g42

                             IT  • L1  • r2-                               (2b)
                                   y
where               L  = /2ir a   ,   L  = /2ir  a                           (3)
                     y        y      z        z
In the above, Q, is emission rate  (source strength)  of  the primary  pollu-




tant, U is mean wind speed at physical stack height, L  is mixing  depth




(height of inversion lid), xm is the downwind distance  (from  source)  deter-




mined such that az(xm) = 0.47 L, and L  and LZ are length scales  charac-




teristic of diffusion in the horizontal crosswind and vertical  directions,




respectively.  The nondimensional  functions gi(x,y), g'  (x,0),  g'  (x,0),




g?,(x), and g/2(x), defined in terms of dimensionless parameterized




variables, are given in Appendix A.









    In Eqs. (1) and (2), it should be noted that the concentrations for




both primary and secondary pollutants are expressed  in  terms  of Q,.   This




does not preclude consideration of a non-zero value  for  Q2> the direct




emission rate of the secondary pollutant.  The algorithms for g^ and §/„




provide for this possibility.









    The well-mixed region algorithms, Eq. (2), are generally used under




convective or neutral stability conditions.  The ground-level plume center-




line concentrations of the species in the plume-trapping region (xm < x <  2
                                    11

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can be obtained by calculating the concentrations at x^ and  2xm  from Eqs.




(1) and (2), and interpolating between these values on a  log-log plot of




concentrations versus downwind distance  (Turner,  1970).   PEM-2 uses  this




interpolation approach in the plume-trapping region.









2.2.2  Plume Rise







    Plume rise is calculated from the standard or new equations  given by




Briggs (1969, 1984).  The stack-exit conditions of the plume and the




ambient temperature determine whether the upward motion of the plume is




dominated by momentum or buoyancy.  For  atmospheric stability classes A to




D, the unstable/neutral plume rise equations are used.  For  stability




classes E and F, the stable plume rise equations are used.   Thus,  there are




four different situations for plume rise:




(1)  buoyancy-dominated plume in unstable/neutral atmosphere,




(2)  momentum-dominated plume in unstable/neutral atmosphere,




(3)  buoyancy-dominated plume in stable  atmosphere, and




(4)  momentum-dominated plume in stable  atmosphere.




    In each situation except the last one, the plume rise is calculated as




a function of downwind distance from the stack until the  final plume rise




is attained.  The standard plume rise equations for these four cases, the




optional stack-tip downwash correction following Briggs (1973),  and  the




crossover techniques used in PEM-2 to determine whether the  plume is domi-




nated by momentum or buoyancy are listed in Appendix B.   The optional new




equations of Briggs (1984) for estimating the maximum rise of a  buoyancy-




dominated plume in unstable/neutral atmosphere, and new schemes  for  plume




penetration of an elevated stable layer  are also given in this Appendix.
                                     12

-------
2.2.3  Dispersion Parameters




    The Gaussian dispersion parameters,  a   and  oz, used  in  PEM-2  for  each


scenario are identical to those used in  EPA's RAM model  (Turner and Novak,


1978) to represent a 1-hour average dispersion  over urban areas.  Assuming  a


rectangular cross-section for the plume, Briggs  (1973) gave interpolation


formulas for these urban diffusion coefficients, which are  based  on the


diffusion data from near-surface releases of a  neutrally-buoyant  tracer  in


St. Louis by McElroy and Pooler (1968).  The corresponding  expressions for


0y and az for a Gaussian plume, based on Briggs' formulations, are given by


Gifford (1976, Figure 7, Table 8).  Hosker  (1973) compared  these  urban


dispersion parameter curves to the Pasquill-Gifford (PG) a  curves, and


showed that their values are greater than all but the more  unstable of the


corresponding PG curves because of the enhanced  mechanical  and convective


turbulence over an urban area compared to that  over open country.






    PEM-2 uses the expressions for Briggs'  urban dispersion parameters


given by Gifford (1976).  These formulas are written in  a convenient  form


for programming as follows:
                                                 -1/2
                     az(x) = azx  (l+czx)  (l+bzx)   '                     (4a)
                     ay(x) = ayx  (1+0.0004X)                            (4b)
In Eq. (4), x is given in meters.  The coefficients ay, az, bz, and cz are


functions of atmospheric stability class, and their values are shown in


Table 1.
                                    13

-------
                                  TABLE 1




        Values of Coefficients in the Formulas for  av(x) and  az(x),




                     Equation (4), in Urban Conditions
P-G Stability
Class
A-B
C
D
E-F
ay
.32
.22
.16
.11
az
.24
.20
.14
.08
bz
.001
0
.0003
.0015
cz
.001
0
0
0
2.2.4  Restrictions on Receptors for Calculations






    Pollutants emitted from each point source may not  contribute  to  all of




the receptors in a grid.  The receptors excluded from  the  calculations  are




those located upwind of the source, too far from the plume centerline,  or




more than 50 km downwind of the source.  For each source and  each scenario,




PEM-2 selects a rectangular area of the receptor grid  downwind  of the




source, and calculations for that set of conditions are restricted to  the




receptors located within that area.  The source contribution  is considered




to be zero at receptors located outside the area.  Model inputs used for




determining this area are the source coordinates, grid boundaries, wind




direction, and the crosswind angle (A) between wind direction azimuth  and




the azimuth from the source to the receptor.  If A exceeds the  maximum




crosswind half-angle of the plume (Amax), then the receptor is  excluded




from calculations.  The values of the maximum crosswind half-angle used in




PEM-2 for 1-hour averaging of the plume are shown in Table 2  as a function




of the atmospheric stability class.





                                    14

-------
                                  TABLE  2




                    Maximum Crosswind Half-angle  Values




                          for Point  Source  Plumes
Atmospheric
Stability Class
A-B
C
D
E-F
max
(degrees)
43
33
25
18
    At x = 100 m, these Amax values give  a maximum plume  half-width of  3 ov




for calculations in the lateral direction.  For  x > 100 m,  the  maximum




half-width of the calculated plume is  larger  than 3 0V.









2.3  AREA SOURCES









    2.3.1  Emission Grid







    PEM-2 defines a "calculation grid" by shifting the receptor grid to the




South and to the West by one-half the  side of  a  grid  square  (Ax/2).   Thus




each square in the calculation grid has one receptor  at its  center,  since




the calculation grid squares are of the same  size  (Ax) as  the receptor  grid




squares.







    Each area source used in PEM-2 should be  sized so that  it covers an




integral number of calculation grid squares.   The  size Ax  should be  defined




such that the smallest area source is  at  least as  large as  one  calculation




grid square.






                                    15

-------
    The relationship between area sources and  calculation  grid  squares can




be divided into three cases.  In the first  case,  the  area  source is  of the




same size as a calculation grid square.  Emissions  (Qo)  are  assumed  to be




located at the center of the square; contributions  of  this area source are




determined at the receptor (Ro) located at  the  center  of the emission grid




square, and at the receptors (R, to Rft) located at  the center of each of




the eight calculation grid squares immediately  downwind  of the  source.




This is schematically illustrated in Fig. 1, which  shows only the first




five receptors Ro,	, R^«








    The location of the eight downwind squares  is not  apparent  in cases




when the wind direction is not parallel to  one  of the  calculation grid




coordinate axes as shown in Fig. 2.  The angle, £,  between the  wind  azimuth




and the nearest calculation grid coordinate axis  is defined  such that




0 £ 5 £ 45°.  PEM-2 considers ten ranges of values  for % as  shown in




Table 3.  For each range of 5, the location of  each downwind square  is




denoted by i (the number of calculation grid squares  downwind from the area




source) and j (the number of calculation grid  squares  off  the axis used to




define 5), as illustrated in Fig. 2.  These patterns  of  squares are  stored




in PEM-2 data tables that list values of i  and  j  as shown  in Table 3.  For




a given scenario, each area source will have the  same  spatial pattern of




affected squares downwind.
                                     16

-------
                       cc
 ro
OJ
  CM
(T
o
                                                                                     .  CM
                                                                                      X
                                                                            ro
                                                                          . CM.
                                                                           x
                                                                  CM
                                                                  CM
                                                                 X
                                                     ro
                                                      . CM.
                                                       X
                                           CM

                                          X
                                               O
                                               CM
                                              X
                        O
                       x —
                                                                                   VI
                                                                           (/J T3   D      >-4
                                                                           d  d   o      o
                                                                           o  oj   d     **-*
                                                                           •H      03  en
                                                                           M   - 4J  U /->
                                                                           C/3  W   VI  0) 00
                                                                            £  O T3  -H
                                                                            
g
CU

*
<
ex

cu
u
S-l
3
O
VJ

CU
r"j
4-)

E
O
1^
14-1

•a
c
• H
3
d
5
o
T3

-o
i!
&-t
3

-------
 WIND
 AZIMUTH
CALCULATION GRID  I
COORDINATE AXIS
                             i=4
            j=0
                                                    9.46
       i =4

       i=3

       i=2

       i =^1

       i=0
                 j=0
                 < 20.56°
Figure 2.  Spatial patterns  of affected calculation grid squares downwind
          of an area source.  PEM-2 considers  eight (i.e., i=l,	,8)
          affected grid squares downwind of an area source (i=0), though
          only the first four are shown in this  figure.
                                  18

-------
j=3  j=2  j=1  j=0
"2 O f~\ A O ^~ f ^» "3C Q"7O
o^.ui •
-------
                          TABLE  3
        Values of i and j for Each Spatial  Pattern
               of Affected Squares Downwind
                     of an Area Source
£ range, degrees
0 - 7.12
7.12 - 9.46
9.46 - 14.04
14.04 - 20.56
20.56 - 26.57
26.57 - 32.01
32.01 - 36.87
36.87 - 39.81
39.81 - 41.19
41.19 - 45.00
Values for j**
i=0*
0
0
0
0
0
0
0
0
0
0
i-i
0
0
0
0
0
1
1
1 •
1
1
i-2
0
0
0
1
1
1
1
2
2
2
i-3
0
0
1
1
1
2
2
2
3
3
i=4
0
1
1
1
2
2
3
3
3
4
i=5
0
1
1
2
2
3
3
4
4
5
i=6
0
1
1
2
3
3
4
5
5
6
i-7
0
1
1
2
3
4
5
6
6
7
i-8
0
1
2
2
3
4
5
6
7
8
**
  i  is the number of calculation grid  squares
     downwind from the area source

  j  is the number of calculation grid  squares
     off the axis used to define C
For each value of £, a diagram of  the  first  four  affected
squares downwind of an area source in  square  i=0,  j=0  is
shown in Figure 2.
                            20

-------
    In the second case, the area source is  larger  than  one  calculation grid

square.  Let m be the number of calculation grid squares  covered by  the

source of area A.  Then the emissions, Q, from  the source are  divided into

m component emission rates defined by

                      Qj = Q Aj/A  ,  j = 1,2,  ...,  m

where Aj is the area of the source contained in the  jth square,


                      m                         m
                 A =  I   A.      and     Q =  I    Q,
                     J-l   J                  j-1    J



Then the contributions from each of  the m emission grid squares  are  deter-

mined following a procedure similar  to that  for a  single  emission grid

square.



    In the third case, a small area  source  may  be  imbedded  in  a  large area

source.  The emission rate of the latter source is divided  into  components

for each covered square as described above.   Then  each  square  is considered

as an area source with an emission rate equal to the sum  of  the  component

emission rates from the original area sources.



2.3.2  Concentration Algorithms


    The urban area sources consist of fugitive  dust,  highway,  residential,

commercial and industrial emissions, and their  inventories  are generally

not detailed enough to provide information  on the  source  height  and

plume-release conditions such as plume velocity, temperature,  building

wakes, etc.  Furthermore, there are  no reliable methods to  estimate  the

plume rise from these distributed sources.   Therefore,  their emissions are
                                     21

-------
generally assumed to be located at the ground-level  (i.e., H=0)  for




simplicity.  This assumption, however, may lead to calculation of  large




surface-concentrations, especially under light wind  conditions when




building wake-induced dispersion is less important and hot emissions  from




roof-top sources may have a rise comparable to the building height.   The




area-source concentration algorithms used in PEM-2 permit the user to




specify a value of H j> 0 to represent the average effective height of




emissions from the area sources in the inventory.  This value of H is




assumed to be constant for each concentration-averaging period.






    The ground-level concentrations of the primary and secondary pollutants




resulting from urban area source emissions in PEM-2  are computed by numeri-




cal integration of the corresponding point-source concentration  algorithms.




The urban area-source modeling techniques due to Gifford and Hanna (1970)




are utilized in these computations.  These techniques are based  on the




"narrow plume hypothesis," which postulates that the concentration at a




receptor is influenced only by the distributed area  sources located in a




fairly narrow, plume-shaped upwind sector.  This assumption allows one to




ignore the lateral variation of concentration and the "end effects" due to




the finite size of an area source grid;  the concentration downwind of the




center of the emission grid is then the same as that if the area source




were infinitely wide in the crosswind direction.







    We consider nine calculation grid squares (denoted by i=0, 1,  2,  	,  8),




each with a receptor R^ located at its center.  Figure 1 illustrates  this




schematically for the first five squares.  The source emissions  are assumed




to be located at the center of the first square (i=0) upwind of  the recep-




tors.  The emission rate of the primary pollutant from this single area
                                     22

-------
source is Qj.  Then the ground-level concentrations  of  the primary  and




secondary pollutants, C^ii and CA2i respectively,  at  the  receptor R^  in



the ith calculation grid square downwind are  obtained,  following Rao  (1982),



by integrating the point-source concentration algorithms  as  follows:
                              x2i
                          Q    Z1 g'  (x,z=0)


                                  -^4	dx                          (5a)
                                       7
                              11
                                  g'  (x,z=0)


                   CA2i

                             xli
The nondimensional functions g'  and gl? are defined  in Appendix  A,  and



LZ = /2ir az; x^ and X££ are distances measured  from  the  center of  the
first square (i=0) to the upwind and downwind edges,  respectively,  of  the




calculation grid square with the ith receptor (see Fig.  1); U  is  the




surface wind speed input to the model if  the effective height  of  emissions




H < 10 m, or the adjusted wind speed of H > 10 m  (see Section  2.5.2).
    The relative concentrations, UC^A^ and UCA2l/Qi,  determined  from




Eq. (5) are independent of the emission rates of  the species  (except  for




the ratio 0.2/Ql which appears in goo) atlc* their values at  the  receptors in



the nine downwind calculation grid squares are calculated  only once for




each scenario.  These relative concentrations are then multiplied by  the




emission rate Qi of each area source and U   to obtain the contributions  to
the concentrations CAi and C^2 at each of the nine affected receptors.  Note




that,  for a given scenario, each area source will have the same spatial




pattern of affected receptors downwind.  The contributions of all  area





                                     23

-------
sources affecting each receptor are summed to obtain  the  total  concentra-




tion at that receptor.






    In PEM-2, the integrations indicated in Eq.  (5) are performed  numeri-




cally by the trapezoidal rule together with Romberg's extrapolation  method.




Utilizing a maximum of 14 bisections of the interval  (xi±**2±)>  this method




computes an approximation for the integral to within  1 percent  relative




accuracy between successive approximations.









2.3.3  Dispersion Parameters









    The dispersion parameters, az> used in Eq.  (5) for area-source con-




centrations are the same as those used for point sources  (see Section




2.2.3).  These dispersion coefficients, given by Briggs (1973)  and Gifford




(1976), account for the effects of increased surface  roughness  and heat




flux in the urban environment, and are most representative  for  zo  =•  1 m  and




near-surface releases typical of the area sources.









2.4  RECEPTORS







2.4.1  Receptor Grid






    PEM-2 calculates pollutant concentrations at each receptor  in  a  recti-




linear receptor array.  A maximum of 2500 receptors may be  used, with 50




columns and 50 rows.  The spacing between each  column and row is uniform,




and is specified by the user.  Receptors are located  at the intersections




of grid columns and rows.  The grid spacing, number of columns,  number of




rows, and coordinates of the receptor at the southwest corner of the grid




are used to define the grid.





                                    24

-------
    Point and area sources need not  necessarily  be  located within the grid




boundaries.  If area sources are  included  in  the source inventory,  the




receptor grid spacing  should be selected so that the smallest area source




is of the same size as a grid square.  An  area source is positioned on the




grid by specifying the coordinates of  the  southwest corner of the source.




This corner should be  located in  the center of a receptor grid square, so




that each square covered by the area source is centered on a receptor.  For




computations involving area sources, therefore,  a calculation grid is




defined with its grid  squares the same size as receptor grid squares, but




with a receptor located in the center  of each calculation grid square.  For




details, see Section 2.3.1.









2.4.2  Automatic Grid  Selection









    PEM-2 has an optional subroutine which will  automatically select a




receptor grid for each scenario.  The  size and location of grids  for dif-




ferent scenarios may differ since the  selection  of  the receptor grid is




based upon wind speed, wind direction, and atmospheric stability  class.









    Each source is examined sequentially.  Two orthogonal axes are  used




with the origin located at the origin  of the  coordinate system for  the




point sources.  The y axis is oriented in  the north-south direction with




positive values in the northerly direction.   The x  axis is oriented in the




east-west direction with positive values in the  easterly direction.   Angle




E is defined by







                                E =  90° -  W
                                    25

-------
where W is the angle  (measured relative to north)  of  the  direction of  the



flow (see Fig. 3).  The axes are then rotated through angle E  such that  the



wind blows down the x axis.  Negative values of E  correspond to  a  clockwise



rotation of coordinate axes; positive values correspond to a counter-



clockwise rotation.







    For each scenario, the grid is automatically selected so as  to provide



good coverage by receptors near the point of maximum  concentration.  This



point is estimated from the Gaussian plume concentration  algorithm without



the pollutant removal or transformation mechanisms.   For  a point source,



the downwind distance to the point of maximum concentration, x^*  is calcu-



lated from the equation
                      a  dx    a  dx    a 2
                       y        z      L z
                                                                         (6)
by the Newton-Raphson iterative method.  In Eq.  (6), H  is  the  effective



source height and ay and 0Z are the dispersion parameters  given  by  Eq.  (4).



Equation (6) is derived by differentiating the expression  for  ground-level



centerline concentration due to an elevated point  source with  respect  to x,



and equating it to zero.







    Equation (6) is also used to determine x^,  the point  of maximum con-



centration using the physical stack height hs instead of H.  Then let



                             XTM(l) = XT + xml



                             XTM(2) = XT + xm2



where XT is the x coordinate of the point source in the rotated  coordinate



system.
                                    26

-------
                                                   EMISSION  SOURCE
Figure  3.  Points used for  automatic selection  of receptor grid by AUTGRD
          subroutine.

-------
    The largest value of XTM(2) for all point  sources  Is  GX2 and the




smallest value of XTM(l) for all point sources  is  GX1.  Let  YT be the y




coordinate of the point source in the rotated  coordinate  system.  Then GY2




is the largest value YT for all point sources  and  GY1  is  the smallest value




of YT for all point sources.  These points are  illustrated in Fig. 3.









    Next, the points (GX1, GY1), (GX2, GY1),  (GX2,  GY2) and  (GX1,  GY2) are




rotated back to the original coordinate system.  The  largest of the. four x




values and the largest of the four y values  are  chosen for the coordinates




of the northeast corner of the grid.  The smallest  of  the four x values and




the smallest of the four y values are chosen for the  coordinates of the




southwest corner of the grid.









    Then XT is defined as the distance between  the  x  coordinates of the grid




corners and YT is the distance between the y coordinates  of  the grid cor-




ners.  Let DJJ^X be the larger of XT and YT.  Then  Dmax is used to determine




the number of columns and rows in the receptor  grid and the  grid spacing.




If Dmax is larger than 10 km, then the number  of rows  (or columns) is 50




and the grid spacing is XT/50 (or YT/50) km.   If 5  <  Dmax <  10 km, then a




grid spacing of 0.2 km is used and the number  of rows  (or columns) is




XT/0.2 (or YT/0.2).  If 0.25 < Dmax < 5 km,  then the  number  of rows (or




columns) is 25, and the grid spacing is Dmax/25.   If  Dmax <  0.25 km, the




grid spacing is 0.01 km, the smallest possible,  and the number of rows (or




columns) is XT/0.01 (or YT/0.01).  A typical example  of the  receptor grid




selected by the automatic grid option is illustrated  in Fig.  4.
                                    28

-------
                                            (GX2,GYi)
     WIND
            (GX1, GY2)
                                                         NORTH
                                       EMISSION SOURCE
Figure 4.  Example of a receptor grid  selected by AUTGRD subroutine.




                               29

-------
    If the culpability list option is elected in PEM-2, the receptor  grid




is limited to 25 rows and 25 columns.  In this case,  the grid  spacing is




increased so that the number of rows  (or columns) does not exceed  25.









    The automatic grid selection procedure, outlined  above, considers only




point sources.  Therefore, the chosen receptor grid may not be suitable if




area sources are included in the inventory.  Furthermore, the  point of




maximum concentration determined from Eq. (6) may be  in error  for  problems




which include significant deposition, sedimentation,  and chemical  decay




or transformation.  The optimum receptor grid in this case should  be




determined by trial and error, using the receptor grid defined by  this




automatic grid option as the first approximation.








2.5  METEOROLOGY






    The meteorological data used as input to PEM-2 consist of  the




atmospheric stability class index, wind speed, wind direction,  ambient




temperature, mixing depth, and the potential temperature gradient  in  the




elevated stable layer.  This data set, which represents the mean




atmospheric conditions over an hour, is called a scenario.  The maximum




number of scenarios in an averaging period is limited to 24, i.e., PEM-2  is




designed to predict only short-term (1 to 24 hr) average concentrations.




When available, quality-assured on-site meteorological data are preferable




to the National Weather Service (NWS) data.
                                    30

-------
2.5.1  Atmospheric Stability



    The Pasquill-Gifford atmospheric stability classes used in PEM-2 are

defined in Table 4.


                                  TABLE 4

                       Atmospheric Stability Classes
Stability
Class Index
1
2
3
4
5
6
Atmospheric
Stability Class
A
B
C
D
E
F
Description
of Conditions
Extremely unstable
Moderately unstable
Slightly unstable
Neutral
Slightly stable
Moderately stable
    The relationship between the atmospheric stability classes and wind

speed, incoming solar radiation, and cloud cover is given by Turner (1970)

and shown below in Table 5.


                                  TABLE 5

                      Atmospheric Conditions Defining
                             Stability Classes


Surface Wind Speed
(at





10 meters ),m/s
<2
2-3
3-5
5-6
>6

Incoming
Day
Solar
Strong Moderate
A
A-B
B
C
C
A-B
B
B-C
C-D
D

Radiation Thin
Slight >4/8
B
C
C
D
D
Night
overcast or
low clouds <3/

E
D
D
D


'8 cloud

F
E
D
D
                                    31

-------
    Class A is the most unstable, while class F is the most stable  class




considered in PEM-2.  Night refers to the period from one hour  before  sun-




set to one hour after sunrise.  Note that the neutral class, D,  should be




assumed for overcast conditions during day or night, regardless  of  wind




speed.









2.5.2  Wind Speed









    PEM-2 gives the user an option for specifying either an hourly  mean




wind speed or the wind speed class number.  The latter is based  on  National




Weather Service (NWS) classification.  Any wind speed which lies  in a  given




range is assigned that class number; PEM-2 uses a representative  wind  speed




for each class as shown in Table 6.
                                  TABLE 6




                         Wind Speed Classification
NWS Wind Speed Wind Speed Range
Class (knots)
1 0
2 4
3 7
4 11
5 17
6
- 3
- 6
- 10
- 16
- 21
> 21
Representative
Wind Speed (m/s)
1.50
2.46
4.47
6.93
9.61
12.52
     Wind speed near the surface generally increases with  height.   Most  NWS




wind speed measurements are taken at a height  (ho)  of  10 m above  the  sur-




face and are listed as "ground-level" wind speeds  (UQ)  in  knots.   Then the
                                     32

-------
wind speed (U) at the physical stack height  (hg)  is  determined  as  follows:


                              U = UQ (hs/h0)P                            (7)


The adjusted wind speed U is used (in  meters/sec)  in the  plume  rise calcu-

lations and the point-source concentration algorithms.  Equation (7) is

applied only when the stack height  is  greater  than 10 m.   The exponent  p is

a function of atmospheric stability class.  The standard  (default) values

of p used in PEM-2 are shown in Table  7.  For  "ground-level" area  source

releases, the input wind speed (Uo) is used directly without any adjust-

ment.  If the effective height of area source  emissions exceeds  10 m,  then

Eq. (7) is used to adjust the wind  speed.  For calm  conditions  (UQ = 0),

the wind speed Uo is arbitrarily set to  1 m/s.  However,  since  it  is dif-

ficult to specify the wind direction under these  conditions, it  is better

to remove "calm" hours from the input  data.



                                  TABLE  7

               Values of Exponent p in Wind Speed  Power Law
        Atmospheric Stability                       p
       	Class	

                A = 1                             0.15
                B = 2                             0.15
                C = 3                             0.20
                D = 4                             0.25
                E = 5                             0.30
                F = 6                             0.30
    PEM-2 includes an option that allows  the user  to  input  site-specific

values for ho and/or p derived from local  observations.  The user  should

refer to Section 4.2.1 for details.
                                    33

-------
2.5.3  Wind Direction









    By convention, wind direction is defined as the direction  from which




the wind is blowing.  PEM-2 gives the user an option for specifying  either




an hourly mean wind direction, or the wind direction sector number based  on




the standard 16-point compass.  Wind blowing from any angle in a  22.5°  sec-




tor is assigned the number of that wind direction sector, and  the  wind




direction is represented in the calculations by the median of  that sector,




as shown in Table 8.








                                  TABLE 8




                          Wind Direction Sectors
Sector Number
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Compass Point
N
NNE
NE
ENE
E
ESE
SE
SSE
S
SSW
SW
WSW
w
WNW
NW
NNW
Representative
Wind Direction (deg)
0.0
22.5
45.0
67.5
90.0
112.5
135.0
157.5
180.0
202.5
225.0
247.5
270.0
292.5
315.0
337.5
     PEM-2 also includes an option in which the user specifies  the wind




direction in degrees for the first of four sub-scenarios; for each suc-




ceeding sub-scenario, the wind direction is automatically shifted clockwise






                                    34

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by 90, 45, 30, 15, 10, or 5 degrees  depending  on  the  option number speci-




fied in the input, while keeping  the other  meteorological parameters




constant.  Details of these I/O control  parameters  are given in Section




4.2.1.









2.5.4  Mixing Depth









    The turbulent mixing layer near  the  ground is frequently bounded  by a




layer of stable air aloft.  The latter effectively  limits vertical disper-




sion to the mixing layer.  The height of  the base of  the  inversion above the




ground is called the mixing depth, L.  The  hourly mixing  depths are spe-




cified in the input to PEM-2.









    If vertical mixing is limited, pollutants  emitted from a point source




into the mixing layer will be trapped and,  beyond some point downwind,  will




become uniformly mixed in the vertical.   PEM-2 uses different sets of con-




centration algorithms for the (near-source) mixing  region and the  well-mixed




region.  The concentrations in the intermediate plume-trapping region are




then obtained by interpolation as described in Section 2.2.1.   The deter-




mination of the mixing regime and the algorithms  to be used in the model




depend on the atmospheric stability  class,  mixing depth,  effective height of




the source, and the downwind distance.









    If the physical stack height exceeds  the mixing depth,  pollutants are




emitted in the stable layer aloft; these  pollutants will  not be brought to




the ground level and the source is neglected.
                                    35

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    If the physical stack height is less  than  the  mixing  depth,  but:  the




effective source height H exceeds L, then the  plume  may or  may  not  escape




the mixing layer.  A buoyant plume rising into a convectively or mechani-




cally mixed layer may partially or completely  penetrate the capping  stable




layer, depending on the stratification strength and  elevation of the latter




with respect to the plume.









    The default penetration scheme in PEM-2 does not  allow  partial  penetra-




tion of the elevated stable layer.  For H ^ L, no  penetration occurs;  for




H > L, complete penetration occurs and the source  is  ignored.   However,




PEM-2 includes optional new penetration schemes that  consider the potential




temperature gradient 39a£/3z in the elevated stable  layer to estimate the




extent of its penetration by a buoyancy-dominated  plume in  unstable/neutral




atmosphere.  The value of 39aj;/9z is specified by  the  user  in the meteoro-




logical data input to PEM-2; otherwise, a default  value of  O.Ol°C/m




(corresponding to an isothermal atmosphere) will be  assumed in  the  calcula-




tions.  The plume penetration schemes used in  PEM-2  are discussed in detail




in Appendix B.
                                    36

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                                 SECTION 3







                         COMPUTER PROGRAM OVERVIEW







3.1  BASIS FOR PEM-2 PROGRAM







     The PEM-2 computer program, listed in Appendix F, was  developed  by




modifying the FORTRAN program of the Pollution Episodic Model  (Rao  and




Stevens, 1982).  The latter, in turn, was based on the computer program  of




the Texas Episodic Model Version 8  (TEM-8) and its Users' Guide (1979).




TEM-8 uses the Gaussian plume concentration algorithms developed  for  non-




reactive pollutants and a perfectly reflecting lower boundary.  Chemical




and physical depletion processes are therefore ignored, except for  an




option which allows a simple exponential decay of pollutant concentration




with travel time.  This method requires an accurate estimate of Che




pollutant's half-life.









     In contrast, both PEM-2 and PEM explicitly account for dry deposition,




gravitational settling, and a first-order transformation of two chemically-




coupled gaseous or particulate pollutants in the concentration algorithms.




The surface concentrations and deposition fluxes of both the primary  pollu-




tant (species-1 or reactant) as well as the secondary pollutant (species-2




or reaction product) are calculated.  Thus, since PEM-2 accounts  for  these




processes,  the concentration algorithms used in PEM-2 and TEM-8 are dif-




ferent, though both models share essentially the same framework for calcu-




lations.
                                    37

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    The PEM-2 model is developed from the PEM (Rao and Stevens,  1982)  and

the TEM-8 (Texas Air Control Board, 1979) with the following key

modifications:
1.  PEM-2 uses Briggs' (1973) urban dispersion parameters  (based  on  the
    St. Louis diffusion data of McElroy and Pooler, 1968)  for  both point
    and area sources, whereas PEM and TEM-8 use power laws based  on
    Pasquill-Gifford  (PG) o's for point sources and Gifford-Hanna (1970)
    oz's for area sources.


2.  The number of atmospheric stability classes in PEM-2 are reduced to
    six, from seven in PEM and TEM-8, by combining the DD  (neutral/day) and
    the DN (neutral/night) classes into a single D (neutral) class to con-
    form with the current regulatory practice of the EPA.


3.  For buoyancy-dominated plumes in unstable/neutral atmosphere, Briggs'
    (1984) new plume  rise equations and plume penetration  (of  an  elevated
    stable layer) schemes are included as optional features in PEM-2. On
    the other hand, PEM and TEM-8 use only the standard "all or none" cri-
    terion for determining plume penetration, and simulate inversions of
    various strengths by arbitrarily specifying an inversion penetration
    factor.


4.  An option is provided in PEM-2 to use site-specific input  values for
    the exponents of  the wind-profile power law and anemometer height.


5.  Concentrations from area source emissions (located at  any  effective
    height H>0) are computed by numerical integration in PEM-2, while con-
    centrations from  area source emissions (assumed to be  at ground-level)
    in PEM and TEM-8  are calculated from analytical concentration algorithms,
    The number of calculation grid squares used for each area  source has
    been increased from 5 (in PEM and TEM-8) to 9 in PEM-2 to  increase the
    calculated plume  length and improve the model accuracy.
3.3  STRUCTURE OF THE PROGRAM


     Figure 5 shows the structure of the PEM-2  computer  program,  its

subroutines and functions.  All input data to the model  are  read  through

subroutine INMOD.  In order to calculate the relative  concentrations  of

the species from area sources, the main program calls  subroutine  XINTEG  to
                                     38

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MAIN
                 Input
    	 INMOD

 	Start loop on scenarios

    	 INMOD
                   1
      AUTGRD	1  RISE
                   ROOT	FUNR
                 Area Sources
         XINTEG	1  FUN 3
                      FUNS
         XINTEG	FUN4	
                               ARGCHK
                               EXPO
                             D01AJF	FUN1A	EXPO
                             ARGCHK
                             EXPO
 	Start loop on area sources


    -End loop on area "sources

                 Point Sources

    -Start loop on point sources

    	RISE
         QZCAL 	
                  RISE
                  EXPO
                  ARGCHK
                  PSG4P	D01AJF	FUN2
                  D01AJF	FUN1	1  ARGCHK
                                       I  EXPO
-End loop on point sources

              Output

	 WORST

	 WOROUT
         OUTMOD
                    WOROUT
                    ARRAY
                    SCENMX
   •-End loop on scenarios
    	 MAXOUT

     Figure 5.  Structure of computer program.

                         39

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perform the numerical integrations.  For each scenario,  these  numerical




integrations are done only once, and each area source will  have  the. same




spatial pattern of affected squares downwind.  These relative  con-




centrations are then multiplied with the effective  emission rates  of the




area sources to obtain the contributions to  the  concentrations at  each




receptor.  After the area source calculations are completed, the program




starts point source calculations by calling  subroutines  RISE and QZCAL»




The latter calculates the probability densities  of  vertical distributions




of concentrations of the two pollutants using the appropriate  algorithms.




All output is printed in subroutine OUTMOD,  which calls  and uses other




optional output routines.  This procedure is repeated for all  scenarios.









3.3  GENERAL FLOW OF THE PROGRAM







     At the beginning of the run, PEM-2 reads in all input  data, screens




them, prints warning messages, and sets default  values as necessary.  All




control parameters are listed and explained.  Input data for meteorological




conditions, area sources, and point sources  are  also listed.   Some errors




in input data may be serious enough to cause cancellation of the run;




however, in general, PEM-2 attempts to recover from input errors and




complete the run using default values.  The  program prints  an  appropriate




message whenever it resets an important input parameter  to  a default




value.







    Inventories of area and point sources must include the  locations of the




sources on a receptor grid, their emission rates, the size  for area sources,




and stack parameters for point sources.
                                    40

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    These inventories are used with  sets  of  hourly  meteorological data




called scenarios.  For each scenario,  the concentration and surface deposi-




tion flux are calculated at each impacted receptor  in  the  grid.









    Output options are many and varied.   Concentration and surface deposi-




tion flux may be presented in the form of lists,  array maps,  or  records  on




tape.  Other options include a culpability list  of  point sources,  and




information on plume rise and effective stack heights  for  each scenario.




At the end of the averaging period,  a  list of receptors with  the highest




concentration for each pollutant may be printed.  The  details  of these I/O




options are given in Section 4.  The calculation  of  the surface  deposition




fluxes of the pollutant species is discussed in Appendix C.
                                    41

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                          SECTION  4


                    PROGRAM  USER'S  GUIDE
4.1  SUMMARY OF PROGRAM INPUT

Control Parameters  (7 cards)

         Control parameters remain constant throughout the run.  They
specify  1) a title;  2) run options for time-averaging, and types of
input and output, and technical options for use of stack-tip downwash
algorithm, new plume rise equations and plume penetration schemes;
3) receptor grid coordinates and spacing;  4) deposition and settling
velocities of pollutants and an option to calculate chemical transforma-
tion or decay at a given rate;   5) scaling factors for area source emis-
sions and calibration coefficients to be applied to the calculated concen-
trations; 6) labels for the pollutants and calibrations; and  7) an
option for using site-specific values for wind-profile exponents and
anemometer height.

Scenario Parameters  (1-24 cards)

         Each card contains information for one scenario; i.e.  , the
meteorological data for one hour.  It includes atmospheric stability
class, wind speed, wind direction, temperature, mixing height,  and poten-
tial temperature gradient in the elevated stable layer above the mixing
height.

Area Source Parameters  (0-50 cards)

         Each card contains information for one area source. It includes
the location of the area source on the receptor grid, the size  of the
area source, and its emission rates.

         A blank card must follow the last area source card to  signal the
end of the area source data.

Point Source Parameters  (0-300 cards)

         Each card contains information for one point source. It includes
the location of the point source on the receptor grid; its emission
rates; the stack parameters of height, diameter, plume velocity and
temperature; and a label which identifies the point source.

         A blank card must follow the last point source card to
signal the end of the point source data.
                              42

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4.2  DETAILS OF PROGRAM INPUT


  4.2.1  Control Parameters  (7 cards)

  Card  1 :  Title          FORMAT (20A4)

    Information identifying the run,  which is  printed at  the top of  each
    page of output.  Up to 80 alphanumeric characters are  allowed.


  Card  2 :  Input and output options      FORMAT (1814)

    NTOPT   Averaging time option

       =1      One hour:  Concentrations are calculated for each scenario.
               No averaging done.
       =2      Twenty-four hours:  Concentrations are calculated for
               exactly 24 scenarios .and averaged.
       =3      Variable (2 to 23 hours):  Concentrations are calculated
               for a given number of  scenarios and averaged.
           The default value is NTOPT = 1  .

   NWDOPT   Wind direction input option

       =0      The user will specify  wind direction in degrees  for each
               scenario.
       =1      The user will specify  a wind direction sector number  (from
               1 to 16) for each scenario.
       =2-7    The user will specify  wind direction in degrees  for the
               first of four sub-scenarios. For each succeeding sub-
               scenario,  the wind direction is automatically shifted
               clockwise by 90, 45, 30, 15, 10,  or 5 degrees for option
               numbers 2, 3, 4, 5, 6, and 7, respectively.
               NWDOPT = 2-7 is not allowed with time-averaging,  i.e.,
               when NTOPT = 2 or 3   .
           The default value is NWDOPT =  0  .

   NWSOPT   Wind speed input option

       =0      The user will specify  surface wind speed in meters/sec for
               each scenario.
       =1      The user will specify  a wind speed class number  (from 1  to
               6) for each scenario.
           The default value is NWSOPT =  0  .

   NWPOPT   Wind-profile exponents input  option

       =0      The model uses the standard (default) values for the  urban
               wind—profile exponents.   The anemometer height for surface
               wind observations is assumed to be 10 m.
                                 43

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    =1      The user will input site-specific values for wind-profile
            exponents and anemometer height on Card 7.
        The default value is NWPOPT = 0  .

 NSCEN   Number of scenarios

    =1-24   The number of sets of hourly meteorological data to be
            read and processed by the program. If NTOPT=2 is specified,
            then NSCEN must equal 24 . If NSCEN is not  specified
            correctly, then either the input data file  will be misread
            or the run will be terminated.
        The default value is NSCEN = 1

 NLIST   Output option for printing lists of uncalibrated concentration
         and surface deposition flux, and calibrated concentration at
         each receptor in the grid.

    =0      The lists are not printed.
    =1      Lists of concentration and surface deposition flux are
            printed, for one or two pollutants, at grid receptors with
            uncalibrated concentrations of at least 1 microgram per
            cubic meter.
            NLIST = 1 may not be used with the automatic windshift
            option (NWDOPT > 1) .
        The default value is NLIST - 0  .

NARRAY   Output option for array maps of calculated concentration and
         surface deposition flux at each receptor in the grid.

    =0      No array maps are printed.
    =1      Separate maps of uncalibrated concentration and surface
            deposition flux, and calibrated concentration are printed
            	 a total of three maps for each pollutant.
    =2      Maps of uncalibrated concentration and surface deposition
            flux are printed 	 two maps for each pollutant.
    =3      Maps of calibrated concentration and surface deposition
            flux are printed 	 two maps for each pollutant.
        The default value is NARRAY = 0  .

 NTAPE   Tape output option for a list of both uncalibrated and cali-
         brated concentrations and surface deposition fluxes at each
         receptor in the grid.

    =0      The list is not written on tape.
    =1      A list of concentrations and deposition fluxes is written
            on a separate output tape, one receptor per record. Control
            parameter INTER may be set to limit the number of receptors
            written on tape. The program checks the total number of
            records to be written; if the number is greater than
            62500, a message is printed and NTAPE is set to zero.
                              44

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            NTAPE=1 may not be used with the automatic windshift
            option (NWDOPT > 1). NTAPE=1 may he used with NTOPT=1 to
            store the hourly concentrations, in order to calculate
            average concentrations externally for problems with highly
            variable emission, transformation, and deposition rates
            (see Section 1.3).
        The default value is NTAPE = 0  ,

NCSOPT   Output option for a culpability list of the five point sources
         which contribute most to the total concentration calculated
         at each receptor.

    =0      The culpability list is not printed.
    =1      For each receptor in the grid, the program lists up to
            five point sources and the percentages of total concentra-
            tion contributed by these sources. The total concentration
            and surface deposition flux at each receptor are also
            listed. This information is printed, for one or two pollu-
            tants, only at receptors with the highest contributions
            exceeding 1 microgram per cubic meter.  NCSOPT=1 can be
            used only with NTOPT=1 . This option may not be used for
            more than one scenario with the automatic windshift option
            (NWDQPTM).  It also may not be used when the number of
            columns (LX) or the number of rows (LY) in the grid is
            greater than 25 .
        The default value is NCSOPT = 0  .

  NMAX   Output option for listing the maximum concentration and
         surface deposition flux calculated for each pollutant.

    =0      The lists are not printed.
    =1      At the end of the run, for each scenario or averaging
            period, lists are printed to show the receptor which
            received the highest concentration and deposition flux for
            each pollutant.
        The default value is NMAX = 0  .

NSTDWN   Technical option for stack-tip downwash algorithm for point
         sources.

    =0      The stack-tip downwash algorithm is used in the program to
            include the downwash effects.
    =1      The downwash algorithm is not used.
        The default value is NSTDWN = 0  .

NPRISE   Technical option to use Briggs' new equations for maximum
         rise of buoyancy-dominated plumes from point sources.

    =0      Standard Briggs' plume-rise equations are used for all
            stability classes.
                             45

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    =1      New equations are used for maximum plume rise of buoyancy-
            dominated plumes for stability classes A-D (unstable/neu-
            tral atmosphere).
          The default value is NPRISE = 0  .

 NINPEN   Technical option to use new schemes  for penetration
          of buoyancy-dominated plume above mixing height.

    =0      Standard "all or none" criterion for plume penetration
            above mixing height is used.

    =1      New schemes are used for buoyancy-dominated plume penetra-
            tion of elevated stable layer for stability classes A-D
            (unstable/neutral atmosphere).
         The default value is NINPEN = 0  .
 INTER   Output option for interval of receptors written on tape.

    =N      When the output option NTAPE=1 is  selected,  the value  of
            INTER determines which receptors are written on the tape.
            When INTER is specified as integer N, every  Nth receptor
            in each column and row is listed.   Thus,  if  INTER=2,  one
            fourth of the receptors will be listed; if INTER=5, one
            twenty-fifth will be listed.  Effectively, an output grid
            is set up with "new" spacing equal to the value of
            INTER*GRID, and only those receptors on the  "new" grid
            will be listed on the tape.
        The default value is INTER = 1  .
NPRINT   Output option for point source information.

    =0      Input point source data is printed only at the beginning
            of each run.
    =1      A list of input point source parameters and calculated
            plume rise information is printed for each scenario.
        The default value is NPRINT = 0  .
INPTSC   Input option for point source data.

    =1      Point source data is read from the normal input stream (on
            cards, for example).
    =2      Point source data is read from a disk file specified by
            the user.
        The default value is INPTSC = 1  .
                            46

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  NGPR    Gradual plume rise option for point sources.

   =0       Gradual plume rise used close to point source(s).
   =1       Final effective plume rise height used for  all distances.

  NBID    Option to consider bouyancy induced dispersion (BID).

   =0        BID is not used.
   =1        BID is considered for elevated point sources.
Card  3 :  Grid information
FORMAT  (2F10.0,2I10,3F10.0)
  XRSWC      The x, or east-west coordinate of receptor at the southwest
             corner of the grid, in kilometers.
         The default value is XRSWC =0.0  .

  YRSWC      The y, or north-south coordinate of receptor at the south-
             west corner of the grid, in kilometers.
         The default value is YRSWC =0.0  .

     LX      The number of columns of receptors  in the grid.  Allowable
             values are 1 to 50 .
         The default value is LX = 1

     LY      The number of rows of receptors  in  the grid.  Allowable
             values are 1 to 50 .
         The default value is LY = 1

   GRID      Automatic grid option or grid spacing.

     =0.0    The program designs the receptor grid for each scenario
             such that there is good receptorcoverage near the point of
             maximum concentration.  For point sources, this location is
             determined from the Gaussian plume  algorithm without
             deposition or transformation. For problems that include
             these removal mechanisms and area source emissions, there-
             fore, this automatic grid may not be the optimum grid.
             This option cannot be used when NTOPT > 1 .

     >0.0    The size of the spacing between columns and rows of recep-
             tors in the grid, in kilometers.
         The default value is GRID =0.0  .

DTDZ(l),     The atmospheric potential temperature gradient for
DTDZ(2)      E and F stability classes, respectively, in
             deg. C/meter.  These values are used in the plume
                                 47

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             rise equations under stable conditions.
         The default values are DTDZ(l) = 0.02 and
                                DTDZ(2) = 0.035  .

Card  4 :  Pollutant deposition and chemical transformation
          parameters             FORMAT (215, 6F10.0)

   NPOL      The number of pollutants  (1 or 2)
         The default value is NPOL = 1  .

    ICT      Chemical transformation or decay option.
     =0      Transformation/decay of pollutant-1 is ignored.
     =1      If NPOL = 1, a first-order chemical decay of
             the pollutant-1 is considered.
             If NPOL = 2, a first-order chemical transforma-
             tion of pollutant-1 to pollutant-2 is considered.
         The default value is ICT = 0  .

   VD1       Deposition velocity of pollutant-1, in cm/sec.

    Wl       Settling velocity of pollutant-1, in cm/sec.

   VD2       Deposition velocity of pollutant-2, in cm/sec.

    W2       Settling velocity of pollutant-2, in cm/sec.

         The default values of W and VD for both species are
         zeros.  If either W or VD is less than 0.01 cm/sec,
         then the value of that parameter is set to zero.
         This reduces computer run times and job costs
         without significantly altering the calculated
         concentrations.
         In general, for deposition to occur, the settling
         velocity (W) should be less than or equal to the
         deposition velocity (VD).  For gases and very small
         particles, W should be zero.  For small particles,
         W should be less than VD.  For particles of size
         d > 50 microns,  W should equal VD.

    XKT      Chemical transformation or decay rate of pollu-
             tant-1 , in percent/hour.  Allowable values are
             0.1 to 100.0 ; input values outside this range
             are set to the nearer limit.  For example,
             if XKT=0.0 is specified (when ICT-1), then the
             program prints a message and sets XKT=0.1 .

  GAMMA      The ratio of molecular weights of pollutant-2
             (product) to pollutant-1 (reactant) in the
             chemical transformation (when ICT=1).
         The default value is GAMMA =0.0  .
                                  48

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 Card  5 :   Scaling and calibration            FORMAT  (7F10.0)

      HAS      The effective height of area source emissions in
               meters.  Note that a single value is used  to
               approximate the height of emissions from all urban
               area sources.
           The default value is HAS = 0.0 .

ASCALE(l),      Area source scaling factors for pollutants  1 and  2.
ASCALE(2)      All area source emission rates are multiplied
               by ASCALE(l) for pollutant-1 and by ASCALE(2)
               for pollutant-2. These factors may be utilized to
               scale the entire area source inventory  to  account
               for higher emission rates expected in future years
               (from an increased traffic volume, for  example),
               or to convert the units of emission rates  in the
               inventory to grams/sec.
           The default values are ASCALE(l) =1.0  and
                                  ASCALE(2) = 1.0 .

     A(l),      Coefficients used to calibrate the calculated
     B(l)      concentration of pollutant-1.
               The calibrated concentration, C* , is computed
               from the formula  C*  =  A  +  B . C  ,
               where C is the uncalibrated concentration.
               The normal output units of the latter are
               micrograms per cubic meter.  The calibration
               coefficients can be used to convert the units
               to percent allowable, parts per million, or
               any other convenient units.
           The default values are  A(l) = 0.0 and B(l) =  0.0 .

     A(2),      Coefficients used to calibrate the calculated
     B(2)      concentration of pollutant-2.
           The default values are  A(2) = 0.0 and B(2) =  0.0 .

Card  6 :  Labels                FORMAT (3A4,7A4,3A4,7A4)

POLNAM(l)      Name for pollutant-1
               Up to 12 alphanumeric characters are allowed.

CALNAM(l)      Label for calibrated values of concentration
               of pollutant-1, computed from calibration
               coefficients  A(l) and B(l).
               Up to 28 alphanumeric characters are allowed.

POLNAM(2)      Name for pollutant-2
               Up to 12 alphanumeric characters are allowed.

CALNAM(2)      Label for calibrated values of concentration
               of pollutant-2, computed from calibration
               coefficients  A(2) and B(2).
               Up to 28 alphanumeric characters are allowed.

           Defaults for all labels are blanks.


                                    49

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Card  7 (optional):  Site-specific values of anemometer height and/or
                    wind-profile exponents  FORMAT (10F7.0)

    HA      Anemometer height of wind speed measurement in  meters.
            This is  the height at which the surface wind speed is measured.
            The default value is HA = 10.0   ..
    HMIN    Wind speed held constant  below this  height  in meters.
            Default value is HMIN = 10.

    HMAX    Wind speed held constant  above this  height  in meters.
            Default value is HMAX - 200.

    TJMIN    Wind speed not allowed less  than this value (raeters/s).
            Default value is UMIN = 1.0

    P1(I),     Wind profile exponents derived from local observations
    1=1,6      for stability classes  1 to 6 .
           The default values are given  in Section 2.5.2.

        Note that site-specific values for anemometer height and/or
        wind-profile exponents can be specified  only if the wind-profile
        option NWPOPT on Card 2 is specified as  NWPOPT=1.
4.2.2  Scenario Parameters
FORMAT(3I5,5F10.0)
       One to 24 cards, each containing a set of meteorological data for
       one hour.

      NSC      Atmospheric stability class number
               Allowable values  are 1 to 6 ;  an input  value  outside that
               range will be set to the nearer limit.

      NWS      Wind speed class
               Allowable values  are 1 to 6 ;  an input  value  outside that
               range will be set to the nearer limit.   Note  that NWS is
               used only when the windspeed input option NWSOPT on Card 2
               is specified as NWSOPT=1 .

      NWD      Wind direction sector
               Allowable values  are 1 to 16 ; an input value outside that
               range will be set to the nearer limit.   Note  that NWD is
               used only when the wind direction input option NWDOPT on
               Card 2 is specified as NWDOPT=1 .

       WS      Surface wind speed in meters/sec
               This is assumed to be measured at a height of 10 meters
               unless a different value for anemometer height is specified
               on Card 7 above.   Note that WS is used  only when the wind
               speed input option NWSOPT on Card 2 is  specified as NWSOPT
               = 0 .  If WS=0.0  (calm) is specified
                                    50

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               under this option, a message is printed  and WS
               is set to 1.0 meter/sec.

       WD      Wind direction
               The azimuthal angle in degrees of  the  direction
               from which the wind is blowing.  Allowable values
               are 0.0 through 360.0 degrees.  Note that WD  is
               used only when the wind direction  input  option on
               Card 2 is specified as NWDOPT=0 or  2 through  7.
           The default value is WD = 0.0, wind from the north.

       TA      Ambient temperature at 10 m height  in  deg. C.
           The default value is TA = 0.0  .

     HMIX      Mixing height in meters
               The height of the base of the inversion  above
               the ground.  This is also effectively  the depth
               of the turbulent mixing layer.
           The default value is HMIX = 9999.99   .

    DTDZI      Potential temperature gradient in  the  elevated
               stable layer above mixing height in deg. C/meter.
           The default value is DTDZI =0.01  .
4.2.3  Area Source Parameters            FORMAT(5F10.0)

       Zero to 50 cards, each containing parameters  for  one
       area source.  A blank card must follow the last area
       source data card.

       XA      The x, or east-uest, coordinate of southwest
               corner of the area source, in kilometers.
           The default value is XA = 0.0 .

       YA      The y, or north-south, coordinate of  southwest
               corner of the area source, in kilometers.
           The default value is YA = 0.0 .

     SIZE      The length of a. side of area source in meters.
           The default value is SIZE = GRID*1000.0,  the  side
           of a receptor grid square in meters. If GRID=0.0
           (i.e., automatic grid option is elected), then
           SIZE is arbitrarily set to 1.0 .

    EA(1),     Emission rates for pollutants 1 and 2 in  gms/sec.
    EA(2)
               Note that EA is not an emission rate  per  unit
               area; this is the emission rate of an equiva-
               lent point source located at the center of the
               area source.
           The default values are EA(1) =0.0
                              and EA(2) = 0.0 .
                                    51

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   Note that area source inventory must be followed by a
   blank card to signal the end of area source data.

4.2.4  Point Source Parameters        FORMAT(8F9.0, 2A4)

       Zero to 300 cards, each containing parameters for one
       point source.  A blank card must follow the last point
       source data card.

       XP      The x, or east-west, coordinate of point
               source, in kilometers.
           The default value is XP = 0.0 .

       YP      The y, or north-south, coordinate of point
               source, in kilometers.
           The default value is YP = 0.0 .

    EP(1),     Emission rates for pollutants 1 and 2 in gms/sec.
    EP(2)
           The default values are EP(1) =0.0
                              and EP(2) = 0.0 .

       HP      The physical height of the stack in meters.
           The default value is HP = 0.0 .

       DP      The inside diameter of the stack-tip in meters.
               If DP=0.0 is specified, a message is printed and
               DP is set to l.OE-4 meters.

       VP      The stack-exit velocity of plume in meters/sec.
           The default value is VP = 0.0, which results in
           zero plume rise.

       TP      The stack-exit temperature of plume in deg. C.
           The default value is TP = 0.0 , which usually
           results in a momentum-dominated plume rise.

     NAME      Label which identifies the point source. Up to
               eight alphanumeric characters may be used.
           The default is blanks.

   Note that the point source inventory is followed by a blank
   card to signal the end of the point source data.
                                    52

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4.3  GUIDE TO PROGRAM OUTPUT

     PEM-2 has several output options which are outlined below.
   In order to avoid a large output, the user may select only
   the necessary options on Card 2.

   NPRINT 	 Point source information

       At the beginning of each scenario or sub-scenario*, for
   each point source, the output lists its coordinates on the
   receptor grid, emission rates, stack parameters, dominant
   influence (momentum or buoyancy) of plume rise, wind speed
   at physical stack height, maximum effective source height,
   and plume penetration fraction (see Appendix B).

   NCSOPT 	 Point source culpability list

       At the end of each scenario or sub-scenario , for each
   receptor in the grid, the five point sources which contri-
   buted most to the total concentration at that receptor are
   identified.  For each receptor, the output includes the
   five point-source sequence numbers, the percentage of total
   concentration each of the five produced, and the total
   concentration and surface deposition flux at the receptor.
   This information is printed for one or two pollutants.
   To reduce the amount of output produced, only receptors
   with highest contributions exceeding 1 microgram per cubic
   meter are printed.

   NLIST 	 Concentration and surface deposition flux list

       At the end of an averaging-period consisting of 1 to
   24 scenarios, the uncalibrated concentration and deposition
   flux, as well as the calibrated concentration, of one or two
   pollutants are listed at each receptor in the grid. To reduce
   the amount of output produced, only receptors with uncalib-
   rated concentrations of at least 1 microgram per cubic meter
   are listed.

   NTAPE 	 Concentration and surface deposition flux tape

       At the end of the averaging-period, for each receptor in
   the grid, the calculated concentration and surface deposition
   flux are written on to a separate output tape.  All records on
   the tape contain eighty alphanumeric characters.  A separate
   record is written for every receptor in the grid, unless the
   interval parameter INTER has been specified as greater than
  *When the automatic windshift option is selected (NWDOPT > 1),
   a scenario is divided into four sub-scenarios, each with the
   same meteorological data except for the wind direction.  The
   latter is shifted automatically by a given number of degrees
   for each sub-scenario.
                                    53

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one.  The first record on the tape  contains  the  title  infor-
mation given on Card 1 of the Control Parameter  cards,
written by FORMAT(20A4).  Succeeding records  contain the
x,y coordinates of the receptor, values  for  concentration,
deposition flux, calibrated concentration, and calibrated
surface deposition flux for pollutant-1,  followed  by the
values of these parameters for pollutant-2.   These values
are written by FORMAT(10F8.2).

NARRAY 	 Array maps of concentration and surface deposi-
           tion flux

    At the end of each averaging-period,  separate  maps  are
printed for concentration and deposition flux for  each
pollutant.  The values are printed  at each receptor at
its relative location on the grid to aid in  visualization
of the distribution of the pollutant.

    The value specified for NARRAY  determines which maps
are printed.  If NARRAY=1, separate maps of  uncalibrated
and calibrated concentrations, and  uncalibrated  deposition
flux are printed (3 maps); if NARRAY=2,  maps  of  uncali-
brated concentration and deposition flux only are  printed
(2 maps); and if NARRAY=3, two maps of only  the  calibrated
values are printed. Each map may require one, two,  or  four
pages of output to display the entire grid,  since  each  page
can display values for up to 25 columns  and  25 rows of  the
grid.

NMAX 	 Maximum concentration and  surface deposition  flux

    At the end of the last scenario or sub-scenario (if
NTOPT=1) or at the end of the averaging  period (if NTOPT>1),
the receptors which receive the highest  concentrations  of
pollutants-1 and 2, and the values  of these  concentrations,
are listed.  A second list gives the surface  deposition
fluxes at these receptors.
Note : The NCSOPT option can be used only with  NTOPT=1;
therefore, the output data printed with this  option  refer
to hourly concentrations. When the NMAX option  is  used
with NTOPT=1 and NSCEN > 1, the list of hourly  maximum
concentration and deposition flux values, and the  receptors
where they occur, is printed only after the last scenario
has been processed.

    When the time-averaging is selected (NTOPT=2 or  3),  the
output for option NPRINT is printed after each  scenario,
but the output for options NLIST, NTAPE, NARRAY, and NMAX
is printed only after all scenarios of the averaging period
have been processed. Thus, the concentrations and  surface
deposition fluxes printed in the output of the  latter set
of options represent the time-averaged values.
                                  54

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4.4  DISCUSSION OF I/O PARAMETERS







     The PEM-2, designed to predict short-term  (1  to  24 hr)  average  ground-




level concentrations, assumes that emission  rates  are constant  over  the




averaging period for NTOPT > 1.  This may not be a good assumption for




cases where the emissions are strongly  time-dependent.  For  these  cases,




concentration estimates may be made for each hour  with NTOPT =  1, using  the




appropriate emissions data and the mean meteorological conditions for that




hour.  Then concentrations for a period longer  than an hour  can be




determined by averaging the hourly concentrations  of  that  period.  This  can




be done externally with minimal programming.  The  tape output option




NTAPE=1 may be used to store the hourly concentration data.







     The deposition and sedimentation velocities of the species and  the




chemical transformation rate are also assumed to be constant over the




concentration-averaging period.  If it is important to consider the  diurnal




variations of these parameters, a procedure  similar to that  described above




for emissions can be used in concentration calculations.







     The meteorological data input to PEM-2  consist of atmospheric stability




class, wind speed, wind direction, temperature, mixing height,  and the




potential temperature gradient in the elevated  stable layer.  Each of these




hourly data sets is called a scenario.  For  a given set-up of the receptor




grid, the pattern of the impacted receptors  downwind  of a  source depends




primarily on the wind direction.  For urban-planning  or regulatory




purposes, it may be necessary to investigate the effects of  different wind




directions on the calculated concentration patterns in the receptor  grid.




The PEM-2 has an option which divides each scenario into four sub-




scenarios, each consisting of the same hourly meteorological data except






                                    55

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for the wind direction.  When the user selects  this  automatic  windshift

option (i.e., NWDOPT > 1), the wind direction for  only  the  first  of  the

four sub-scenarios is specified by the user.  For  each  succeeding sub-

scenario, the wind direction is automatically shifted clockwise  by a fixed

number of degrees and the concentration calculations are  repeated.   The

magnitude of this shift may be as large as  90°  (for  NWDOPT  = 2),  or  as

small as 5°  (for NWDOPT = 7).

     The calculated concentrations, C^, of  the  species  in the  PEM-2  are
             3
given in yg/m ; these are referred to as uncalibrated values,  and represent

only the contributions of the sources to the concentrations at the recep-

tors.  The user may add the background concentrations,  or express the

calculated concentrations in parts per million  or  percent allowable,  by the

formula

         C*  = A! + Bi' C± ,   i = 1 or 2,


where A^ and B^ are the user-specified calibration coefficients  (with
                              *
default values of zero), and C-^ are the calibrated concentrations of  the

species.  Depending on the value specified  for  NARRAY,  the  PEM-2  output may

consist of array maps of either uncalibrated values  or  calibrated values,

or both, of  concentrations and surface deposition  fluxes.

    The culpability list output option, NCSOPT,  is used for evaluation of

control strategies.  When this option is in effect,  the five point sources

which contributed most to the total concentration  at each receptor are

identified and their percent contributions  are  printed  for  each  scenario.

This option  may be used for one or two pollutants, but  only when  the  model

calculates hourly concentrations with the time-averaging  option NTOPT = 1.

                                    56

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    Based on the number of pollutants  (NPOL =  1 or  2)  and  the  chemical

transformation/decay option parameter  (ICT = 0 or  1) specified in  the input

to the model, the PEM-2 program does one of the following:
 1.  If NPOL = 1 and ICT = 0 or 1, surface concentrations and  deposition
     fluxes of one gaseous or particulate pollutant, with the  given
     deposition and settling velocities, VD1 and Wl respectively,  are
     calculated.  If ICT = 1, then chemical decay  of the pollutant is  also
     considered if the decay rate XKT > 0. is given.

 2.  If NPOL = 2 and ICT = 0, surface concentrations and deposition  fluxes
     of two different and uncoupled gaseous or particulate pollutant
     species with the given deposition and settling velocities, VD1  and Wl
     (for species-1) and VD2 and W2 (for species-2) respectively,  are
     calculated.  Emission rates for both species  may be different.
     Chemical decay is not considered for either species even  if XKT > 0.

 3.  If NPOL = 2 and ICT = 1, the two gaseous or particulate pollutant
     species are coupled through a first-order chemical transformation.
     The surface concentrations and deposition fluxes of both  the  primary
     pollutant (species-1 or reactant) as well as  the secondary pollutant
     (species-2 or reaction product) are calculated.  The chemical
     transformation rate (XKT > 0.) should be given.  Non-zero direct
     emissions of the secondary pollutant from the point and/or area
     sources may also be specified as input for this case.
     The specification of the deposition and gravitational settling veloci-

ties in the model is discussed in Appendix C.
                                    57

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4.5  EXAMPLE PROBLEMS

        Three example problems are described below and the
    input data and output results of PEM-2 runs for these
    problems are shown in Appendix E to illustrate the use
    of the PEM-2 model.
    Example  1

        This problem deals only with area sources of all types.
    The first area source is of the same size as one receptor
    (or calculation) grid square. The second and third area
    sources are large and each covers several receptor grid
    squares. The fourth area source, covering one grid square,
    is imbedded in the third.  All area source emissions are
    assumed to be at 10 m height.  The receptor grid has 25
    columns and 25 rows with a fine spacing of 1 km. Two
    chemically-coupled pollutants with a transformation rate
    of 1 percent per hour, and deposition velocities of
    VD1=1.0 and VD2=0.1 cm/sec, are calculated.  Direct
    emission rates for pollutant-2 are specified to be one-
    tenth of the emission rates for pollutant-1. The input
    meteorology consists of three scenarios, each with the
    same wind direction but different wind speed and stabi-
    lity class.  The output consists of array maps of 3-hour
    average surface concentrations and deposition fluxes, and
    a listing of the receptor with the highest average con-
    centration of each pollutant.
    Example 2(a)

        This example considers two isolated point sources
    with tall stacks and very hot emissions to illustrate the
    new schemes in PEM-2 for buoyancy—dominated plume rise and
    plume penetration above mixing height. The direct emission
    rate of pollutant-2 is assumed to be 5 percent of the
    emission rate of pollutant-1.  The chemical transformation
    rate is 10 percent/hour, and the deposition parameters are
    VD1=2.0, Wl=0.0, VD2=0.5, and W2=0.2 cm/sec.  The receptor
    grid has 25 columns and 25 rows, each spaced 2 km apart.
    Only one scenario is specified with stability class D, wind
    speed class 2, wind direction sector number 9, and a
    potential temperature gradient of 0.001 deg C/m above a
    mixing height of 550 m. The low values of the last two
    parameters are selected so that the plumes from the two
    stacks show significant penetration above the mixing height;
    the calculated plume penetration fractions (see Appendix B),
    printed by output option NPRINT (which gives the plume rise
    information), are 0.450 and 0.163 for stacks 1 and 2,
    respectively. Other output options selected print array maps
    of surface concentration and deposition flux for each
    pollutant, and the receptor with the highest concentrations
    for the hour.
                               58

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Example 2(b)

    The problem described above  is  repeated  here,  but  with
the standard  (default) plume  rise and  penetration  schemes  in
PEM-2; all of the other input-option parameters  and  data
remain the same as given above,  in  order  to  facilitate
comparison of the surface concentrations  calculated  by the
"old" and "new" methods of accounting  for the  plume  rise and
penetration. The maximum effective  source heights  calculated
by the two methods are about  the same  for stack  1, but the
new penetration scheme (Example  2a) estimates  that only 55
percent of the plume remains  in  the mixed layer  and  contri-
butes to the concentrations,  whereas the  entire  plume
remains in the mixed layer in Example  2b.  Therefore, for
stack 1, the concentrations calculated in Example  2b are
nearly twice as large as the  corresponding values  in
Example 2a.  For stack 2, the new schemes give a larger
effective source height and estimate that only 84  percent
of the plume remains within the  mixed  layer; therefore,
the concentrations calculated in Example  2a  are  again
smaller than in Example 2b.

    This comparison clearly illustrates the  need for the
new plume rise equations which account for the differences
between unstable and neutral  conditions,  and the new pene-
tration schemes which consider partial plume penetration
while accounting for the stratification in the elevated
stable layer.  In general, the standard "all or  none"  cri-
terion predicts more occurences  of  plume  penetration (which
results in zero ground-level  concentrations) than  the  new
penetration schemes; the Examples given above  are  clearly
designed to show the opposite in order to facilitate
comparison.
Example 3

    This problem deals with one large ground-level  area
source and three isolated point sources. The  average
direct emission rate of pollutant-2 is about  10  percent
(or less) of the emission rate of pollutant-1. The  chemi-
cal transformation rate is 5 percent/hour, and the  depo-
sition parameters are VD1=2.0, Wl=0.0, VD2=0.2,  and
W2=0.0 cm/sec.  The receptor grid has 25 columns and  25
rows with 1.5 km spacing.  Six scenarios, representing
moderately stable conditions, low temperatures,  and
variable wind speeds and directions, are specified.   The
input option NWPOPT=1 is elected; this requires  the use
of site-specific values for wind profile exponents  and
anemometer height given on Card 7. The atmospheric
potential temperature gradients for E and F stability
classes are specified as 0.015 and 0.030 deg  C/m, respecti-
vely. The output includes array maps of 6-hour average
concentrations and deposition fluxes for each pollutant,
and the receptor with the highest concentrations for  the
averaging period.

                         59

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                                REFERENCES
Briggs, G. A., 1969:  Plume Rise.  AEG  Critical  Review Series.   Available
     as TID-25075 from NTIS, Springfield, VA,  81 pp.

           , 1973:  Diffusion estimation for  small emissions.  ATDL
     Annual Report, NOAA, Oak Ridge, TN,  83-146.

	, 1984:  Plume rise and buoyancy effects. Atmospheric  Science and
     Power Production, D. Randerson, ed., DOE/TIC-27601,  Tech.  Info'.
     Center, Oak Ridge, TN, Chapter  8,  327-366.

Gifford, F. A., and S. R. Hanna, 1970:   Urban  air  pollution  modeling.   jLn_
     Proc. of 2nd Int. Clean Air Congress, Washington,  D.C.

	, 1976:  Turbulent diffusion-typing  schemes:  A review.   Nuclear
     Safety 17, 68-86.

Hosker, R. P., 1973:  Estimates of dry deposition  over  forests  and  grass-
     land.  Proc. IAEA Symposium. IAEA-SM-181/19.  Vienna,  291-309.

McElroy, J. L., and F. Pooler,  1968:  St. Louis  dispersion study.   U.S.
     Public Health Service.  National Air Pollution  Control Administration,
     Publication AP-53, Vol II, 51 pp.

Rao, K. S., 1981:  Analytical solutions of a  gradient-transfer  model for
     plume deposition and sedimentation.  EPA-600/3-82-079,  U.S.
     Environmental Protection Agency, Research Triangle Park, NC,  75 pp.
     [NTIS PB  82-215 153].

	, 1982:  Plume concentration algorithms  with  deposition,
     sedimentation, and chemical transformation.  EPA-600/3-84-042,  U.S.
     Environmental Protection Agency, Research  Triangle  Park,  NC,  87 pp.
     [NTIS PB 84-138 742].

	, and M. M. Stevens,  1982:  Pollution Episodic Model User's
     Guide.  EPA-6QQ/8-84-008,  U.S. Environmental Protection Agency,
     Research Triangle Park, NC, 186, pp.   [NTIS PB  84-164  128].

Texas Air Control Board,  1979:  User's Guide:   Texas  Episodic  Model.
     Permits Section, Austin, TX, 215 pp.

Turner, D. B., 1970:  Workbook  of Atmospheric Dispersion Estimates.   Public
     Health Service.  Publication No. 999-AP-26, U.S.  Environmental
     Protection Agency, Research Triangle Park, NC,  84 pp.

	     , and J. H. Novak,  1978:  User's  Guide for  RAM.
     EPA-600/8-78-016a, U.S. Environmental Protection Agency,  Research
     Triangle Park, NC, Vol. 1, 60 pp.
                                     60

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                                APPENDIX A
                          POINT SOURCE ALGORITHMS









    The algorithms used in PEM-2 to calculate  ground-level  concentrations




of gaseous or particulate pollutants  released  from an elevated  continuous




point source are derived by Rao (1982).  These algorithms are based on a




gradient-transfer model which describes  the  atmospheric  transport,  dif-




fusion, dry deposition, sedimentation, and a first-order chemical  transfor-




mation of pollutants.  The analytical solutions  of  the model are expressed




in terms of the empirical Gaussian plume dispersion parameters  and extended




to various atmospheric stability and  mixing  conditions.  Details of the




model and the solutions can be found  in  that reference.  Here we only list




the parameterized point source algorithms for  the  primary (reactant) and




the secondary (reaction product) pollutants, denoted by  subscripts  1 and 2,




respectively.









    For convenience, we adopt the following  nondimensionalization  scheme:




All velocities are nondimensionalized by U,  the  constant mean wind speed.




The horizontal downwind distance x and all vertical height  quantities are




nondimensionalized by  /2~ az; the chemical transformation time scale T  is




nondimensionalized by  /2~ az/U.  The horizontal crosswind distance  y is




nondimensionalized by  /2 oy.  Thus, we define
                                     61

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where
                     Vdl • V     '     Vd2 ' V
                     V   =V   -W/2     V   =V   — W/2
                      11    dl   V   '   12    d2   V
                                     -W2)/2                             (A-l)
                     V   =V   -W        V   =V   -W
                      21   Vdl    1    '   22    d2   W2
                     x = x//2 oz       ,  S = z//2
                     H = H//2 a_       ,  L = L//2
                             U//2 az   ,  y = y//2
a
                                                    z
H               = effective height of source

L               = height of the inversion lid or mixing depth
                      deposition velocities of primary and secondary
                  pollutants

W, , W_         = gravitational settling velocities of primary and
                  secondary pollutant particles

x, y, z         = horizontal downwind, horizontal crosswind, and vertical
                  coordinates

ay , az         = Gaussian dispersion parameters in y and z directions

TC              = characteristic time scale of first-order chemical
                  transformation.
    The nondimensional functions g«i and g~2 used in Eq.  (1) of Section

2.2.1 are now defined as follows:
                                    62

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                                 >y)  = exp(- y
                                                (A-2)
 = 2
                                       -  X/TC)
(A-3)
where
 a  = 2/rF V   x  e   erfc £.
                                    x - H
                                H  + 2
                                                (A-4)
               g^2(X>0)  =  2  e
                               $
                        - Y  exp(-  X/TC)  •  (1
                             2/TT  (V21  - V22)  x •  e
                                                (A-5)
where
     2/iT V    x 'e   erfc
a
                               2/TT  V     x e   erfc Co
                                      - H
                      H +  2 V12 x  ,   C3  = H + 2 V13 x
                                                (A-6)
                                     63

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and
                     [" 1 - /?  U4 - H//t)   e  4  erfc  £4  "1
                      fl - /IT 55  e  5   erfc  £5 J  dt                      (A-7)
where                  C4 - H//t +  2 V13  x  /t
                       ?5 = 2 V12 x /I - t                               (A-8)




In Eq. (A-5), y is the ratio of molecular weight  of  the  secondary pollutant


to molecular weight of the primary pollutant,  and Qo/Q,  is  the


corresponding ratio of emission rates of species. In  Eq.  (A-7),  t is a


parameterized dimensionless variable of integration  with limits  of 0 and 1.



     The nondimensional functions g/, and g/«  used in  Eq.  (2)  of  Section

2.2.1 are defined as follows:




For Vdl * Wl or V21 * 0,
                   */TC)  I  (Vt1/V01) e   erfc  ?,                        (A-9)
                                              P,         -i
                                   (W1/2V21)  e   erfc  &l J
                                     64

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where     £, = 2 V,.  x  and  3, = W, x.
For Vdl = Wj or V^ = 0,
               •? - X/T )   f (1 + 2 ??) e * erfc
               l      c    I          l
                                                 / i/IT   I
                                                                         (A-10)
where    5, = 2 V
                               W, x.
For V21 * 0 and V22 # 0,
    (x) = e
           -e.
        (Q2/Qi
                                  e   erfc
                                                         ~ (W2/2V22} e   erfc
~Ye
                       (V13/V21)  e J erfc
                                      (W2/2
                                                            e   erfc
- Y
                               H . F2(x)
                                                                        (A-11)
where
                   = 2
                                     W
                   = 2
                           x ,
                                                - W2)/2
                                                             (A-12)
                                    65

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F2(
        i    r1 i
   x) - ^  I   -^
           •'o  /t
                ~  "    r       —      4
           exp(-xt/T )  J   1 - /TT £,  e   erfc
                   e   erfc
                                           e   erfc
                                                                (A-13)
where
                                              /1-t
                                                                (A-14)
For V21 * 0 and V22 = 0,
           .2
           '2
                       + Y)    (1 + 2 $> e   erfc C  ~ 2
           -Ye       J  (V13/V21) e J erfc C3 - (W2/2V21> e * erfc
                 F V21 x • F2(x)
                                                                        (A-15)
where
                      x
                      x  = W2 x
                                          S   ,   C  = 2 V
                                                         13
F2(x)
1   f  1      / - /" N   f
5-     —  exp(-xt/T )
2ir Jo  yT           c   L
                                   1 -
S4 e   erfc ?4
[
        (1 + 2 C.) e   erfc
                                        -  2
                                                    1 dt,
                              (A-16)
                                    66

-------
with
     /t  ,
                             /1-t
For V21 = 0 and V   * 0,
         -5-
                          e   erfc
                                                          e   erfc
              -X/T
-ye
                       (1 + 2 g   e   erfc ?   - 2
             Y  4/Tr V22 x • F2(x)
                                                                 (A-17)
where
       = 2
                                  "  1O     O   """ P O  J
and F2(x) is given by Eq.  (A-13).
For V2i = 0 and V22 = 0,
 • [v^i
                       Y  (1 -
                                 /s
                                '%,]
                2

                2
            (1 + 2 ?)  e 2 erfc
                                          ~  2
                                                                 (A-18)
where
                                 67

-------
     In Eqs. (A-7), (A-13), and  (A-16), t is a parameterized  integration



variable.  The integrand functions in these equations  have  singularities



at the end-points t=0 and t=l of the integration domain  it  t.  Because  of



their complexity, these integrations cannot be carried out  analytically;



therefore, they should be evaluated by numerical integration  to  a  suf-



ficiently high degree of accuracy.





     A computer-library subroutine named D01AJF, developed  by the  Numerical



Algorithms Group (NAG), is utilized in PEM-2 for the numerical integration.



This general purpose integrator  routine, which is  capable of  handling the



singularities, has been selected because of its accuracy and  applicability.



It estimates the value of a definite integral of an externally defined



function over a finite range to  a specified absolute or  relative accuracy,



using Gauss-Kronrod rules in an  adaptive strategy  with extrapolation.



Further details of this subroutine can be found in Appendix D.





     In the limit, when V,. = W. = 0 and T  and «, the algorithms  for g'  ,
                         di    ic                             2.1


g'  , gJ. , and gj™ (defined above) reduce to the  familiar  Gaussian-plume



diffusion algorithms currently used in EPA air quality models.   Thus  the



new algorithms given in this section may be though of  as extensions  of  the



latter to include deposition, sedimentation, and chemical transformation.





     It should be noted that the algorithms for gl. and  gl_ are  also  used



in Eq. (5) of Section 2.3.2 to calculate ground-level  concentrations  from



area sources.
                                    68

-------
                                 REFERENCE
Rao, K. S., 1982:  Plume Concentration Algorithms with Deposition
     Sedimentation, and Chemical Transformation.  EPA-60Q/3-84-Q42,  U.S.
     Environmental Protection Agency, Research Triangle Park, NC,  87 pp.
     [NTIS PB 84-138 742].
                                    69

-------
                                APPENDIX B








            PLUME RISE EQUATIONS AND PLUME PENETRATION METHODS








    The various optional schemes used in PEM-2 for treatment  of  the  stack-




plume downwash, plume rise (including criteria for the crossover between




momentum and buoyancy), and plume penetration of elevated stable layers are




briefly described and the equations listed here.  For further information,




the user should consult the references cited.








Stack Downwash






    PEM-2 provides a default option (NSTDWN=0) to account for the stack-tip




downwash of the plume, following Briggs (1973), as follows:
                   h' = h  + 2 (R - 1.5) d  , for R < 1.5
                    s    s
                   h' = h                  , for R >  1.5
                    s    s                         =
where R = Vg/U and h' > 0 is the "reduced" physical stack height.  The
                    S ~~



various symbols are defined below.  If the user specifies NSTDWN=1,  the




downwash correction is not used.
                                                                         (B-l)
                                    70

-------
Plume Rise






    The plume rise is estimated using Briggs '  (1969,  1971)  standard



equations if the default option NPRISE=0 is used in PEM-2.  There  are



four different situations for plume rise, and  the  corresponding equations



can be written as follows:




1)  For a buoyancy-dominated plume in unstable/neutral atmosphere,
              Ah(x) = 1.6 F    X2/3 iT1 , for x  < x                      (B-2)
                           b                       max
and
              Ah = 1.6 F     x2/3 U l , for x > x                        (B-3)
                        b     max             =  max
where         x     =49 F    , for F, < 55
               max         b          b
                           2/5

and           Xmax  = 119 Fb   > for Fb >=
                                                                         (B-4)
Note that by substituting (B-4) in (B-3), the maximum plume rise can also



be expressed as
                                                                         (B-5)
                            3/4  -1
               Ah = 21.425 F;;'  U   ,  for F, < 55
                            b               b
                           3/5  -1
and            Ah = 38.71 F£   U    ,  for Ffe ^ 55
2)  For a momentum-dominated plume in unstable/neutral atmosphere,
                Ah(x) = 1.89 [R2d/(R+3)]2/3 X1/3 , for x < x            (B-6)
                                                            max
                                    71

-------
and             Ah = 3 R d , for x > x                                   (B-7)
                                   =  max




where           x    = 4d(R+3)2/R   and   R = V /U                       (B-8)
                 max                           s




3)  For a buoyancy-dominated plume in stable atmosphere,
                 Ah(x) =1.6 F     x2/3 if1 , for x < x                  (B-9)
                              b                        max
and              Ah = 2.6 (F,/U s)1/3 , for x > x                        (B-10)
                            D                 —
where            x     = 2.0715 U s                                      (B-ll)
                  max
and              s = (g/T ) 39 /3z                                       (B-12)
                         3.    a




In (B-12), 89 /8z > 0 is the vertical gradient of potential temperature  in
             a


stable atmosphere.  Its value may be specified by the user; otherwise,



PEM-2 uses the default values of 0.02 and 0.035°K/m for E and F  stability



classes, respectively.





4)  For a momentum-dominated plume in stable atmosphere,





                  Ah = 1.5 (Fm/U)1/3 s"1/6                               (B-13)





and               x    =0
                   max




For this case, there is no expression given for Ah(x) since (B-13) is



assumed to apply for all values of x.  The  smaller of the two Ah values



calculated from (B-7) and (B-13) is taken as the final plume rise in this



case.
                                    72

-------
    After calculating the maximum plume rise from  one  of  the  equations  given



above, the effective source height can be obtained from



                             H = h' + Ah                                 (B-14)
                                  s




The variables used in the equations listed above are defined  here:



        F, = 0.25 (g/T ) V  d2 AT                                        (B-15)
         b            s   s

                                                 4 3
           = plume buoyancy flux at stack exit, m  /s



        Fm = 0.25 (T /T ) V2 d2                                          (B-16)
                    3.  S   S

                                                 4 2
           = plume momentum flux at stack exit, m  /s



        d  = inside diameter of stack-tip, m


                                                 2
        g  = acceleration due to gravity, 9.8 m/s



        h  = physical stack height, m
         S


        h1 = "reduced" physical stack height for downwash cases,  m
         S


        H  = effective source height, m


                                   -2
        s  = stability parameter, s



        T  = atmospheric temperature, °K
         3,


        T  = plume temperature at stack exit, °K



        U  = mean wind speed at physical stack height, m/s



        V  = plume velocity at stack exit, m/s
         S


        x  = downwind distance from stack, m



     x     = downwind distance at maximum plume rise,  m
      max


    Ah(x)  = distance-dependent plume rise, m



        Ah = maximum or final plume rise, m



        AT = T - T , plume temperature excess, °K
              s   a
                                    73

-------
Crossover Between Momentum and Buoyancy






    In order to properly use the plume rise equations given above, one



should know whether the plume is dominated by momentum or buoyancy.  This



determination is generally based on the crossover temperature difference,


(AT) .  Analytic expressions for (AT)  can be derived, for given
    c                                c


atmospheric conditions, by setting the maximum plume rise equation for the



buoyancy-dominated plume equal to the corresponding equation for the



momentum-dominated plume.




    For unstable/neutral atmosphere, equating (B-5) to (B-7), we obtain the



expressions




                (AT)  = .02964 T  V1/3 d~2/3, for Fv < 55               (B-17)
                    c           s  s               b



and             (AT)  = .00575 T  V2/3 d"1/3, for Fu > 55               (B-18)
                    c           s  s               b =



    For stable atmosphere, equating (B-10) to (B-13), we obtain the



expression


                (AT)  = .01957 T  V  s1/2                               (B-19)




    For any given atmospheric stability, the plume is assumed to be.


buoyancy-dominated if T  > T  and AT = T  - T  exceeds the crossover tem-
                       s    a           s    a


perature difference (AT)  calculated from the appropriate expression given



above.  If T  < T  or if AT < (AT) , the plume is assumed to be momentum-
            s =  a          =     c


dominated.




    From (B-15), (B-17) and (B-18), the crossover criteria for



unstable/neutral atmosphere may also be expressed in terms of the crossover



plume-buoyancy flux, (F ) , as follows:





                                    74

-------
                   (F  )  =  .0727  (V d)4/3  , for Fv  <  55                  (B-20)
                     be           s              b
                   (Fj  =  .0141  (V d)5/3  , for Fv  >  55                  (B-21)
                     DC           S              D  =



If F  > 0 and F  > (F  ) , then the plume is buoyancy-dominated;  otherwise,
    D          b     b c


it is momentum-dominated.




    Similarly, from (B-12)  and (B-19), the crossover  criteria  for  stable



conditions can be expressed in terms  of the crossover plume  velocity,


(V ) , as follows:
  s c
                                         1/2
                     (V  )  = 115.28 AT/T      for E-stability
                       s c               a
                     (V )  = 87.14 AT/T1/2   for F-stability
                       s c             a
                                                                         (B-22)
The default values of 0.02 and 0.035°K/m for E and F  stability  classes,



respectively, are assumed for 39 /3z in the above expressions.   If  the
                                a


values specified by the user are significantly different,  then  the



following general expression may be utilized:



                                                  1/2
                      (V )  = 16.30 AT/(T  36 /3z) '                     (B-23)
                        s c              a   a



If (V )  > 0 and V  < (V ) , then the plume is buoyancy-dominated;  other-
     o C          S     S C


wise, it is momentum-dominated.
New Plume Rise Equations





    For a buoyancy-dominated plume, the maximum plume rise given  by  (B-5)


compromises substantial differences between unstable  (convective  turbulence)


and neutral (mechanical turbulence) atmospheric conditions.  The  inverse




                                    75

-------
dependence of final plume rise on wind speed in  (B-5) is  rather  simplistic,




and the equations may seriously overpredict Ah for  low-level  sources  at




high wind speeds.






    PEM-2 provides an option (NPRISE=1) to use Briggs '  (1975,  1984) new




equations to estimate the maximum rise of a buoyancy-dominated plume  in




unstable/neutral atmosphere.  The new plume-rise equations  show  a weaker




dependence of Ah on U in unstable conditions and a  considerably  stronger




dependence on U in neutral conditions.  These equations,  which contain the




minimum essential physics with the maximum allowable  simplifications, can




be written as follows:




For unstable atmosphere,




                     Ah = 30 (F, /U)3/5 , for x > x                       (B-24)
                               D               =  max





where                x    = 81.2 F2/5 U3/5                               (B-25)
                      max         b





For neutral atmosphere,






           Ah = 24 (Fb/u3)3/5 (h^ + 200 Fb/U3)2/5 , for x ^ x^        (B-26)









where      xmaY  = 58.1 (F, /U3)2/5 (h' + 200 F,/U3)3/5                   (B-27)
                          D          S        D
    In PEM-2, for unstable /neutral conditions, Ah is evaluated  from both



(B-24) and (B-26), and the lower of these two values is selected  as the




maximum buoyancy rise of the plume.  Generally,  (B-24) gives  the  lower  Ah




value for low wind speeds, and (B-26) gives the  lower value for high wind




speeds.  The maximum buoyancy rise thus determined is then compared with



the maximum momentum rise of the plume evaluated from (B-7),  and  the




higher of these two values is selected as the maximum plume rise.   The
                                     76

-------
distance to the maximum plume rise, x    ,  is  then  obtained  from one  of  the
                                     max


equations (B-8), (B-25), and (B-27) that is appropriate  for the selected



final plume rise.  For x < x    , the distance-dependent  plume  rise is
      r                     max


determined from (B-2), as before.  This  procedure  was  suggested by Turner



(1985).
Plume Penetration of Elevated Stable Layer







    The daytime turbulent mixed layer with  a  near-adiabatic  lapse  rate



above the ground is frequently bounded  by a thick  layer  of stably-stratified



air aloft.  This situation also occurs  in the marine  inversion  layer  in



some coastal areas.  The elevated stable layer  then effectively limits  ver-



tical dispersion to the mixed layer of  depth  L.  A buoyant plume rising



into a convectively or mechanically mixed layer may partially or completely



penetrate the capping stable layer, depending on the  stratification



strength and elevation of the latter with respect  to  the  plume.





    The default penetration-option (NINPEN=0) in PEM-2 does  not  consider



partial penetration of the elevated stable  layer.  If the maximum  effective



source height, H = h' + Ah, exceeds the mixing  depth  L,  then the pollutants
                    s


are assumed to be emitted into the stable layer aloft; these pollutants



will not be brought to the ground and,  therefore,  the source is  ignored.   If



H <£ L, then the plume is assumed to be  trapped within the mixed  layer with



no ability to penetrate the stable layer aloft.  This treatment, which



assumes either complete penetration of  the  elevated stable layer or no



penetration at all, is similar to that  used in EPA air quality models such



as CRSTER.
                                    77

-------
    PEM-2 provides an option  (NINPEN=1) to use new penetration schemes  that



allow consideration of the strength of stratification  of  the  elevated



stable layer in estimating the extent of its penetration  by a buoyancy-



dominated plume in unstable/neutral atmosphere.  These schemes,  based on



the work of Briggs (1975, 1984), Weil and Brower (1982),  Turner (1985),  and



others, are briefly described below.





    For a buoyant bent-over plume, the penetration criteria are based on



the heights of the upper and  lower edges of the plume  at  final rise,  rela-



tive to the stable layer height, z.', above the stack:







                           z.' = L - h                                    (B-28)
                            1        S




Based on field observations, Briggs approximated the heights  (above  the



stack) of the upper and lower edges of the bent-over plume by 1.5  Ah  and



0.5 Ah, respectively, where Ah is the final rise of the plume.   Penetration



commences only when the upper edge of the plume is at  the top of the  mixed



layer, i.e., 1.5 Ah = zj or Ah = (2/3) z!.  Therefore,  the minimum effec-



tive plume centerline height necessary to consider penetration is  given by





                           H    = h  + (2/3) z!                          (B-29)
                            pen    s          i




where H    is referred to, hence, as the penetration height.   If the  effec-



tive source height, H, estimated from the standard or  new plume-rise  formulas



given above, is less than H   , then no penetration occurs.   If H  > H   ,
                           pen          r                          =   pen


then the fraction of the plume that penetrates the elevated stable layer is



computed as given below.
                                    78

-------
    Following Briggs, we define the plume  penetration  fraction,  P,  as  the



ratio of the depth of the plume above  the  elevated  stable  layer  to  the



total plume depth:
          P =  (1.5 Ah - zj)/(1.5  Ah  -  0.5  Ah)  =  1.5  - z^/Ah             (B-30)
As a simple and conservative approach  to  estimate  the  final  plume  rise,



Briggs assumed that the mixed layer  is  stably-stratified with  the  same



atmospheric potential temperature gradient,  36  ./3z, as that in the  ele-



vated stable layer.  Thus Ah in  (B-30)  is  estimated  from an  expression



similar to (B-10) for a buoyancy-dominated plume in  stable atmosphere:





                         Ah = 2.6(FU/U  s.)1/3                            (B-31)
                                   b   i




where                    s. = (g/T ) 39   /3z                             (B-32)
                          i       a     ai




The value of the atmospheric potential  temperature gradient  in the elevated



stable layer is specified by the user  in  PEM-2;  if it  is not specified,  a



default value of O.Ol°C/m (corresponding  to  an  isothermal atmosphere)  will



be assumed by the model.  This approach is conservative since  the  plume



rise thus estimated will be much lower  than  that computed using a  near-



adiabatic lapse rate which is appropriate  for the mixed layer.





    The plume penetration fraction P is calculated from (B-30)  and (B-31)



such that 0 £ P ^ 1.  No penetration (P=0) is assumed  to occur  when  the



plume upper edge is at or below the  top of the  mixed layer,  i.e.,  Ah < (2/3)z.'.



Complete penetration (P=l) occurs when  the lower edge  of the plume is  at or



above the top of the mixed layer, i.e., Ah > 2z.'.  Partial penetration



(0 < P < 1) occurs for 0.5 Ah < z\ < 1.5  Ah.
                                    79

-------
    In PEM-2, we assume that only the  fraction  (1-P)  of  the plume material



remaining within the mixed layer contributes  to  the ground-level con-



centrations  (GLC); essentially, the  fraction  P of  the plume material is



lost.  The effective source strength,  Q ,  ,  is then given by





                           Qek = (1~P) \ '   k  =  1)2                   (B"33)



where Q  is  the emission rate of species-k  from  the stack.   In the con-
       K.


centration algorithms, the effective source height H  represents only the



height of the centerline of the plume, and  not the heights  of  its upper and



lower edges, when the plume is within  the mixed  layer.   For partial



penetration  cases, therefore, a new  effective source  height (H ) should be



determined for the fraction of the plume  remaining within the  mixed layer.



First, we consider the two limiting  cases,  P-K) and P>1.   For P-K), H  is



obviously given by H   , the penetration  height  defined  in  (B-29).  As P > 1,
                    pen


the new effective source height should approach  L, or H   •»•  h  + zl from (B-28),
                                                       c    S     1


since the small fractional plume of  thickness (l-P)Ah that  is  left at the



top of the mixed layer vanishes in the limit  P-*-!.




    Now, from simple geometric considerations, a general expression for



H  valid for any value of P (0 < P < 1) can be written as




                     H  = h  + [zj - 0.5  (l-P)Ah]
                      e    s     i



Substituting Ah = z'/(1.5-P) from (B-30)  in the  above, we obtain




                     H  = h  + [(1-0.5 P)/(1.5-P)]zJ                     (B-34)
                      63                       1



This equation for H  is consistent with the definition of P, and also



satisfies the limiting behavior, for P=0  and  P=l,  discussed above.  The



elevations (above the stack) of the .upper and lower edges of the plume




                                     80

-------
material whose centerline  is given  by  (B-34)  are  z'  and z|/(3-2P),  respec-


tively.  The solid lines in Figure  (B-l)  show the variations of normalized



elevations of the centerline and  edges  of  this  plume as functions of P.




    Equation (B-34) for H  differs  from that  given by Weil and Brower (1982),
                         e


who interpolated linearly  between the  limiting  values of H  at P=0 and P=l,



as follows:




                     H  = h  +  [(2+P)/3]z.'                               (B-35)
                      e    s              i



The elevations of the upper and lower  edges of  the plume whose centerline



is given by (B-35) are z! and (l+2P)z.'/3,  respectively.   Figure (B-l)


shows the centerline and lower edge  of  this plume in broken lines.   It is


clear that, though both (B-34) and  (B-35)  give  the same values for H  at



P=0 and P=l, the linear model consistently overpredicts the effective


source height of the fractional plume  left in the mixed layer for 0 < P  < 1.


At P=0.5, for example, (B-35) overpredicts H  by  about 11 percent,  and the



elevation of the lower edge is overestimated  by about 33 percent.




    For 0 < P < 1, the distance downwind  from the stack to the location



where the new effective source height H  occurs can  be obtained by equating


the plume rise from (B-34) to the distance-dependent plume rise given by


(B-2) and solving for x:




                x     =  [(l-0.5P)z! U  /  1.6(1.5-P)]3/2 F""1/2           (B-36)
                 max               i                      b



For x < x^    the plume rise is predicted from  (B-2);  for x > x   ,  H is


given by (B-34).




    The various formulas for computing  the effective source height  and


effective source strength can be  summarized as  follows:



                                     81

-------
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                                                         82

-------
(a)  For H < H   , the plume does not penetrate  the  elevated  stable  layer,
              pen
and penetration need not be considered.
                H  = H
                 e                                                       (B-37)
                Qek=Qk,   k-1,2
(b)  For H > H   , the plume penetration  fraction  P  should  be  computed from

(B-30) and (B-31).  Then, depending on  the value of  P,  one  of  the  following

applies:


   (i)  For P=l, the entire plume penetrates  the elevated stable layer,  and

the source is ignored since it does not contribute to the GLC.

             H  > L
              6 ~                                                        (B-38)
             Q   = 0
              ek

  (ii)  For P=0, the entire plume remains within the mixed  layer and

contributes to the GLC.

             H  = H
              e    Pen                                                   (B-39)

             Qek = Qk

  (iii)  For 0 < P < 1, the plume partially penetrates  the  elevated stable

layer; only the fraction (1-P) of the plume material left in the mixed layer

contributes to the GLC.


             H  = h  + [(l-0.5P)/(1.5-P)]z'
              8    S                      i                              (B-40)

             Q .  = (1-P) Q,
              ek         xk

For cases (ii) and (iii), the downwind distance x    to the effective
                                                 max
source height is estimated from (B-36).
                                    83

-------
                                REFERENCES
Briggs, G. A., 1969:  Plume Rise.  AEG Critical Review  Series.  Available
   as TID-25075 from NTIS, Springfield, VA, 81 pp.

          , 1971:  Some recent analyses of plume rise observations.   Proc.
   of 2nd Int. Clean Air Congress, H. M. Englund and W. T. Beery,  eds.
   Academic Press, New York, 1029-1032.

  	, 1973:  Diffusion estimation for small emissions.  ATDL  Annual
    Report, NOAA, Oak Ridge, TN, 83-146.

  	, 1975:  Plume rise predictions.  Lectures on Air Pollution  and
   Environmental Impact Analysis, D. A. Haugen, ed.  Amer. Meteorol.  Soc.,
   Boston, MA, 59-111.

	, 1984:  Plume rise and buoyancy effects.  Atmospheric  Science  and
   Power Production, D. Randerson, ed.  DOE/TIC-27601, Tech.  Info.  Center,
   Oak Ridge, TN, Chapter 8, 327-366.

Turner, D. B., 1985:  Proposed pragmatic methods for estimating  plume rise
   and plume penetration through atmospheric layers.  Atmos.  Environ.  19,
   1215-1218.

Weil, J. C., and R. B. Brower, 1982:  The Maryland PPSP Dispersion  Model
   for Tall Stacks.  Report PPSP-MP-36, Environ. Center, Martin  Marietta
   Corp., Baltimore, MD.
                                    84

-------
                                APPENDIX C





                      SURFACE DEPOSITION FLUXES, AND


                    DEPOSITION AND SETTLING VELOCITIES





C.I  SURFACE DEPOSITION FLUXES




     The surface deposition fluxes of the primary  and the  secondary


pollutants at ground level receptors are calculated directly as
                                         C^x.y.O)                       (C-l)
                         D2(x,y) = Vd2  • C2(x,y,0)                       (C-2)



D£ gives the amount of pollutant i deposited per unit time per unit

                                                                  2
surface area, and is usually calculated in the short term as  yg/m -hr  or

     2                                                    2
kg/km -hr, while seasonal estimates are expressed as kg/km -month.  The


estimation of the monthly or yearly surface deposition fluxes at  a given


downwind distance x from the source in a given wind-directional sector


requires the knowledge of the fraction of the time that a mean wind of a


given magnitude blows in that direction in a month or a year, respectively.

                     2                                            3
To obtain Dj[ in kg/km -hr when V^i is given in cm/s and C^ in yg/m , the
right-hand side of the equations should be multiplied by 0.036.  To obtain

          2                                            3
D^ in yg/m -hr when Vji is given in cm/s and C^ in yg/m , the
corresponding multiplication factor is 36.  For D^ calculations, the


ground-level receptor is generally defined as any receptor which is not


higher than 1 meter above the local ground-level elevation.
                                     85

-------
    PEM-2 calculates the surface deposition fluxes of  one  or  two


pollutants.  These values are printed in a map or list form,  as specified


by the user, in the same way the program prints  the  concentrations.   The

                             2
flux units are generally yg/m -hr; however, if these values are too  large


to be clearly printed in a map format, the program automatically  converts

               2
them into kg/km -hr before printing.
C.2  DEPOSITION AND SETTLING VELOCITIES



     The values of the settling and deposition velocities  primarily  depend


on the particle diameter d.  (i) In the trivial  case  of W  =  V^  = 0,


settling and deposition effects are negligible.   (ii)  For very small


particles (d < 0.1 ym), gravitational settling can  be neglected,  and dry


deposition occurs primarily due to nongravitational effects.  In this case,


W = 0 but V 0.  (iii)  For small to medium-sized particles  (d = 0.1 ~ 50ym),


0 < W < Vjj; deposition is enhanced here beyond that due to gravitational


settling, primarily because of increased turbulent  transfer  resulting from


surface roughness.  (iv)  For larger particles (d > 50 ym),  it  is generally


assumed that V^ = W > 0, since gravitational settling is the dominant depo-


sition mechanism.  (v)  When W > V, > 0, turbulent  re-entrainment of the


deposited particles from the surface back into the  atmosphere is implied,


as in a dust storm, for example.  Model parameters  such as those given


above for cases (i) to (iv) are widely used in the  atmospheric  dispersion


and deposition of particulate material.  The deposition of gases is  a spe-


cial case of the particulate problem with W = 0;  this is similar to  case


(ii).  Thus, one has to carefully select the values of W and V(j for  use Ln


the models.  A more complete discussion of these  model parameters is given


by Rao (1982).



                                    86

-------
                                 REFERENCE
Rao, K. S., 1982:  Plume Concentration Algorithms with Deposition,
    Sedimentation, and Chemical Transformation.  EPA-600/3-84-042,  U.S.
    Environmental Protection Agency, Research Triangle Park, NC, 87 pp.
    [NTIS PB 84-138 742].
                                    87

-------
                                        APPENDIX  D
                    D01AJF - NAG FORTRAN Library Routine Document
 NOTE: before tiling thii routine, please read the appropriate implementation document to check the interpretation of bold iial
 terms and other implementation-dependent details. The routine name may be precision-dependent
 I. Purpose
   DOlAJFisa general-purpose integrator which calculates an approximation to the integral of a function
   F(jr) over a finite interval (A,B):

                                         / - | F(*) dx.

 2, Specification
        SUBROUTINE DOIAJF (F. A. B. EPSABS. EPSREL, RESULT. ABSERR,
       1   W.LW, IW, LIW. IFAIL)
  C    INTEGER LW, IW(LIW), LIW, IFAIL
  C    real F. A. B. EPSABS, EPSREL, RESULT. ABSERR, W(LW)
  C    EXTERNAL F
 3.  Description
  DOIAJF  is based  upon the QUADPACK [3]
  routine OQAGS. It is an adaptive routine, using
  the Gauss 10-point and Kronrod 21-point rules.
  The algorithm, described in [1], incorporates a
  global  acceptance  criterion  (as  defined  by
  Malcolm  and Simpson [2]) together with the
  c—algorithm [4] to perform extrapolation. The
  local error estimation is described in [3].
  The routine  is suitable as  a  general  purpose
  integrator, and can be used when the integrand
  has singularities, especially  when these arc of
  algebraic or logarithmic type.


4. References
{!] DEDONCKER, E.
    An  Adaptive  Extrapolation  Algorithm  for
    Automatic Integration.
    Signum -Newsletter 13.  No.  2, pp.  12-18,
    1978.
[2] MALCOLM, M.A. and SIMPSON. R.B.
    Local versus Global Strategics for Adaptive
    Quadrature.
    A.C.M.  Trans.   Math.   Software   I,   pp.
    129-146, 1976.
(3)  PIESSENS.  R..   DE   DONCKER,   E.,
    U BERHUBER,  C. and KAHANER. D.
    'QUADPACK',   A  Quadrature Subroutine
    Package.
    To be published,  1980.
HI  \YYNN, P.
    On a  Device for  Computing  the  em ($„)
    Transformation.
    M.T.A.C, 10. pp. 91-96. 1956.

 5. Parameters

 F - real FUNCTION, supplied by the user.
  F must return  the value of the integrand at a
  given point.
  Its specification is:
   real FUNCTION F(X)
   realX

   X - real.
     On entry, X specifics the point at which the
     integrand value is required by  DOIAJF. X
     must not be  reset by F.
  F must  be declared  as  EXTERNAL  in  the
  (sub)program from which DOIAJF is called.

A - real.
  On entry,  A  must specify the lower  limit  of
  integration.
  Unchanged on exit.

B - real.
  On entry,  B  must specify  the  upper  limit  of
  integration.
  Unchanged on exit.

EPSABS -real.
 On  entry, EPSABS must  specify  the  absolute
 accuracy  required. If EPSABS is negative, the
 absolute value is used. Sec Section 10.
 Unchanged on exit.
                                            88

-------
 EPSREL - real.
   On entry, EPSREL must specify the relative
  .accuracy required. If EPSREL is negative, the
   absolute value is used. See Section 10.
   Unchanged on exit

 RESULT -real.
   On exit, RESULT contains the approximation to
   the integral /.

 ABSERR - real.
   On exit, ABSERR contains an  estimate of the
   modulus of the absolute error, which should be
   an upper bound for (/—RESULT).

 W - real array of DIMENSION (LW).
   Used as workspace.

 LW-INTEGER.
  On entry. LW must specify the dimension of W
  as declared in the calling (sub)program. LW/4 is
  an upper bound for the number of subintervals
  into which the interval of integration is divided.
  A value in the range 800 to 2000 is adequate for
  most problems. The more difficult the integrand,
  the larger LW should be. Trivially LW > 4. See
  IW below.
  LW is unchanged on exit.

 IW - INTEGER array of DIMENSION (LIW).
  Used as workspace.
  On  exit, IW(1)  contains  the amount of real
  workspace actually used (the smallest possible
  value of LW).

 LIW - INTEGER.
  On  entry, LIW must specify the dimension of
  IW, as declared  in  the calling  (sub)program.
  LIW > LW/8 +  2.
  Unchanged on exit.

 IFAIL- INTEGER.
  Before entry, IFAIL must  be assigned a  value.
  For users  not familiar  with this parameter
  (described in Chapter  P01)  the recommended
  value is 0.
  Unless the  routine  detects an error (see next
  section).  IFAIL contains 0 on exit.

6. Error Indicators and \Yarnings

Errors detected by the routinc.-
   IFAIL - 1
    The maximum number of subdivisions allowed
    with the given workspace has  been reached
    without  the   accuracy  requirements  being
    achieved. Look at the  integrand  in order  to
    determine the integration  difficulties. If the
    position of a local difficulty within the interval
    can be determined (e.g. a singularity of the
    integrand  or   its  derivative,  a  peak,   a
    discontinuity...) one will probably gain  from
    splitting up the interval at this point and calling
    the integrator on the subranges. If necessary.
    another integrator  which  is   designed  for
    handling the type of difficulty involved, must be
    used.  Alternatively  consider   relaxing   the
    accuracy  requirements specified by  EPSABS
    and EPSREL, or increasing the  amount  of
    workspace.

  IFAIL - 2
    Roundoff  error   prevents  the   requested
    tolerance from  being achieved. The error  may
    be under-estimated.  Consider  requesting less
    accuracy.

  IFAIL - 3
    Extremely  bad  local  integrand  behaviour
    causes a very strong subdivision around one (or
    more) points of the interval. The same advice
    applies as in the case of IFAIL = 1.

  IFAIL  - 4
    The requested  tolerance cannot  be achieved,
    because the extrapolation docs not increase the
    accuracy satisfactorily; the  returned  result  is
    the best which can be obtained.  The same
    advice applies as in the case of IFAIL = 1.

  IFAIL  - 5
   The integral is  probably divergent, or slowly
   convergent. It must be noted  that  divergence
   can also occur with  any  non-zero value of
   IFAIL.

  IFAIL  - 6
   On entry, LW < 4, or LIW < LW/8  -r-  2.

7. Auxiliary Routines
  This  routine  calls   NAG   Library  routines
  D01AJV,   D01AJX,   D01AJY.   D01AJZ,
  P01AAF. X02AAF, X02ABF and X02ACF.

8. Timing
  This depends on the integrand and the accuracy
  required.
                                          89

-------
  9. Storage                                        returns the quantity ABSERR which, in normal
   The  storage  required  by  internally  declared      CAirDC"£^nc"'  , Satisfics   I'-RESULT|   ^
   arrays b 107 real elements.                         ABSERR < lol.

  10. Accuracy                                     11. Further  Comments
   The routine cannot  guarantee, but in practice      Labelled COMMON block AD01AJ is used by
   usually achieves, the following accuracy:             this routine and must therefore be avoided by the
   |/-RESULT|
-------
     • F10.4/IH , 2X. 1MB, 6X. 3IH- UPPER LIMIT OF INTEGRATION - .
     • F10.4/1H , 2X. 39HEPSABS - ABSOLUTE ACCURACY REQUESTED - .
     • E9.2/IH . 2X. 39HEPSREL - RELATIVE ACCURACY REQUESTED - .
     • E9.2/)
 99997 FORMAT (JH . 2X. 41HRESULT - APPROXIMATION TO THE INTEGRAL - .
     • EU.J/IH , 2X 42HABSERR - ESTIMATE OF THE ABSOLUTE ERROR  - .
     • E10.3/IH , 2X. 42HKOUNT - NUMBER OF FUNCTION EVALUATIONS - ,
     • 14/1H . 2X. 43HIW(1)  - ELEMENTS OF REAL WORKSPACE USED -  .
     • I4/1H . 2X. 22HIFAIL  - ERROR FLAG -  . I4/)
 99996 FORMAT (1H . 7X, 27H - EXACT ABSOLUTE ERROR - , E10.3)
     END
     REAL FUNCTION FST(X)
 C  • _ SCALAR ARGUMENTS _
     REAL X
 C
 C   - SCALARS IN COMMON _
     REAL PI
     INTEGER KOUNT
 C
 C   _ FUNCTION REFERENCES _
     REAL SIN, SQRT
 C
     COMMON /TELNUM/ PI, KOUNT
     KOUNT -  KOUNT + I
     FST - X*S1N(30.EO'X)/SQRT(1.EO-X"2/(4.EO'P1"2))
     RETURN
     END
C    DOIAJF EXAMPLE PROGRAM TEXT
C    MARK > RELEASE. NAG COPYRIGHT 1979.

 13.2. Program Data
None.


133. Program Results
 DOIAJF EXAMPLE PROGRAM RESULTS

  A     - LOWER LIMIT OF INTEGRATION -    0.0000
  B     - UPPER LIMIT OF INTEGRATION -     6.2S?:
  EPSABS - ABSOLUTE ACCURACY REQUESTED  - O.OOE 00
  EPSREL - RELATIVE ACCURACY REQUESTED -  O.lOE-03

  RESULT - APPROXIMATION TO THE INTEGRAL -   -0.25-J33E 0!
  ABSERR - ESTIMATE OF THE ABSOLUTE ERROR -  0.12SE-04
  KOUNT - NUMBER OF FUNCTION EVALUATIONS -  777
  IW{1)  - ELEMENTS OF REAL WORKSPACE USED -   76
  IFAIL  - ERROR FLAG -   0

       - EXACT ABSOLUTE ERROR -  0.893E-OS
   (This document is reproduced  from NAG FORTRAN Library Mini-Manual,
    Mark 8,  1980; Copyright of Numerical Algorithms Group,  1131 Warren
    Ave., Downer's Grove,  IL 60515).
                                  91

-------
                                APPENDIX E



               INPUT AND OUTPUT LISTINGS OF EXAMPLE PROBLEMS



    The input data and output listings for the PEM-2 example problems

described in Section 4.5 are shown in the tables of this Appendix as

follows:


Table
Number                                                            Page


 E-l  Input data for Example Problem 1	   93

 E-2  Output listing for Example Problem 1	  .   94

 E-3  Input data for Example Problem 2(a)	106

 E-4  Output listing for Example Problem 2(a) 	  107

 E-5  Input data for Example Problem 2(b)	120

 E-6  Output listing for Example Problem 2(b) 	  121

 E-7  Input data for Example Problem 3	134

 E-8  Output listing for Example Problem 3  	  135
                                    92

-------
                                  TABLE E-l

                       INPUT DATA FOR EXAMPLE  PROBLEM 1
                                    CARD  IMAGES
CONTROL CARDS
1  TITLE   PEM-2 EXAMPLE 1: MULTIPLE AREA SOURCES,  2  SPECIES,  3-HR AVG CONG & DEP FLUX
2  OPTIONS    300030200111110110
3  GRID            0.         0.        25        25        1.         0.         0.
4  POLLUTANTS  21         1.0.        0.1        0.        1.0       1.5
5  SCALING        10.         1.        1.         0.        0.         0.         0.
6  LABELS  S02                                      SULFATE
SCENARIO CARDS

               4   4    11        4.       225.          5.      550.       0.
               5   4    11        3.       225.          5.      500.       0.
               6   4    11        2.       225.          5.      500.       0.
AREA SOURCE CARDS
                 1.5       10.5     1000.        10.        1.
                 3.5        3.5     4000.        90.        9.
                 9.5         .5     2000.        20.        2.
                 9.5         .5     1000.         5.        .5
            (A BLANK CARD-  TO SIGNAL END OF AREA SOURCE INVENTORY)
                                          93

-------
                      TABLE E-2




         OUTPUT LISTING FOR EXAMPLE PROBLEM 1
               PEM-2   (VERSION  84130)
               POLLUTION EPISODIC MODEL
                      INCLUDING




DEPOSITION, SEDIMENTATION,  AND CHEMICAL TRANSFORMATION




                    OF POLLUTANTS
                          94

-------
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-------
                                      TABLE E-3

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                                         106

-------
                      TABLE E-4
        OUTPUT LISTING FOR EXAMPLE PROBLEM 2A
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DEPOSITION, SEDIMENTATION, AND CHEMICAL TRANSFORMATION




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                         107

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POLLUTION EPISODIC MODEL (PEM-2)
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-------
POLLUTION EPISODIC MODEL (PEM-2)
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                                      TABLE E-5

                          INPUT DATA FOR EXAMPLE PROBLEM 2B
CONTROL CARDS
1
2
3
4
5
6
TITLE
OPTIONS
GRID
POLLUTANTS
SCALING
LABLES  S02
PEM-2 EXAMPLE
1   1
           1
                         2B;
                          0
SCENARIO CARDS
        0.
        1.
        0.
                   2.
        CARD IMAGES

2 POINT SOURCES, STANDARD PLUME RISE & PENETRATION  SCHEMES
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2.
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0
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  10.
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1
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1.5
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0
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                               0.
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                                                     25.
                                   550.
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POINT SOURCE CARDS
           30.      2.    1000.      50.       200.          5.
           10.      2.     500.      25.       200.          4.
      (A BLANK CARD TO SIGNAL END OF POINT SOURCE INVENTORY)
                                                                    10.
                                                                     8.
              0.001
                                                                        450.
                                                                        400.
                                                                     STACK 1
                                                                     STACK 2
                                         120

-------
                      TABLE E-6




        OUTPUT LISTING FOR EXAMPLE PROBLEM 2B
               PEM-2   (VERSION  84130)
               POLLUTION EPISODIC MODEL
                      INCLUDING




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                                      TABLE  E-7

                           INPUT DATA FOR EXAMPLE  PROBLEM 3
                                     CARD  IMAGES
CONTROL CARDS
1
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6
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TITLE   PEM-2 EXAMPLE 3: 1 AREA SOURCE & 3 POINT  SOURCES,  6-HR AVG CONCENTRATIONS
OPTIONS    :
GRID
POLLUTANTS
SCALING
LABELS  S02
WIND PROFILE 15.
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  280.
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                2.     150.  STACK 3
              (A BLANK CARD TO SIGNAL END OF POINT  SOURCE  INVENTORY)
                                          134

-------
                       TABLE E-8




         OUTPUT LISTING FOR EXAMPLE PROBLEM 3
               PEM-2   (VERSION  84130)
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DEPOSITION, SEDIMENTATION, AND CHEMICAL TRANSFORMATION




                    OF POLLUTANTS
                         135

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-------
                                    APPENDIX F
                              PEM-2 FORTRAN LISTING
    The PEM-2 (Version 84130)  computer program was  developed  and  tested on an
IBM computer at the Oak Ridge  National Laboratory.   The  program was  later
modified slightly to run on a  UNIVAC 1100  computer at Research Triangle Park.
A listing of the UNIVAC-compatible FORTRAN program  follows.   The  PEM-2 code is
also contained on UNAMAP Version 6 magnetic tape available  through the National
Technical Information Service.  The code listing printed herein should be used
as the reference.
                                       147

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                     PEM-2.0  (DATED 86016)
                     AN AIR QUALITY DISPERSION MODEL
                     SECTION 2.  NON-GUIDELINE MODELS
                     IN UNAMAP (VERSION 6) JULY 86.
                     SOURCE:     	 	
C
C
C
C
C
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C
C
C
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C
C *** PEM-2 PROGRAM DEVELOPMENT
C
      K. SHANKAR RAO
      ATMOSPHERIC TURBULENCE AND DIFFUSION DIVISION
      NATIONAL OCEANIC AND ATMOSPHERIC ADMINISTRATION
      U.S. DEPARTMENT OF COMMERCE
      P.O. BOX - E
      OAK RIDGE, TENN 37831
                                  IN
                 *** PEM-2   (VERSION  84130) ***
                    POLLUTION EPISODIC MODEL
                           INCLUDING
     DEPOSITION, SEDIMENTATION, AND CHEMICAL TRANSFORMATION
                         OF POLLUTANTS
                                  	MAY 1984
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
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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
C
C
C
C
C
                                   (ATDD)
                                   (NOAA)
      PHONE:
576-1238
626-1238
                        UNAMAP FILE ON EPA'S UNIVAC AT RTP,  NC.
                                                                  PMT00010
                                                                  PMT00020
                                                                  PMT00030
                                                                  PMT00040
                                                                  PMT00050
                                                                  PMT00060
                                                                  PMT00070
                                                                  PMT00080
                                                                  PMT00090
                                                                  PMT00100
                                                                  PMT00110
                                                                  PMT00120
                                                                  PMT00130
                                                                  PMT00140
                                                                  PMT00150
                                                                  PMT00160
                                                                  PMT00170
                                                                  PMT00180
                                                                  PMT00190
                                                                  PMT00200
                                                                  PMT00210
                                                                  PMT00220
                                                                  PMT00230
                                                                  PMT00240
                                                                  PMT00250
                                                                  PMT00260
                                                                  PMT00270
                                                                  PMT00280
                                                                  PMT00290
                                                                  PMT00300
                                                                  PMT00310
   THE POLLUTION EPISODIC MODEL (PEM) DESCRIBED BY RAO AND STEVENSPMT00320
(1982) IS AN URBAN SCALE (UP TO 50 KM DISTANCES) AIR POLLUTION    PMT00330
MODEL CAPABLE OF PREDICTING SHORT-TERM (1 TO 24-HOUR) AVERAGE     PMT00340
SURFACE CONCENTRATIONS AND DEPOSITION FLUXES OF TWO CHEMICALLY    .PMT00350
COUPLED GASEOUS OR PARTICULATE POLLUTANTS AT UP TO A MAXIMUM OF   PMT00360
2500 GROUND-LEVEL RECEPTORS LOCATED ON A 50X50 SQUARE RECEPTOR    PMT00370
GRID. PREDICTIONS ARE BASED ON STEADY-STATE GAUSSIAN PLUME ASSUMP-PMT00380
TIONS, BRIGGS' PLUME RISE FORMULATIONS, AND PASQUILL-GIFFORD (PG) PMT00390
DISPERSION PARAMETERS.  THE SURFACE CONCENTRATION AND DEPOSITION  PMT00400
FLUX ESTIMATES OF TWO INDEPENDENT NONREACTIVE (GASEOUS OR PARTICU-PMT00410
LATE) POLLUTANTS OR ONE POLLUTANT WITH FIRST-ORDER CHEMICAL DECAY PMT00420
CAN BE OBTAINED AS SPECIAL CASES OF THE MODEL.  UP TO 300 POINT   PMT00430
SOURCES AND UP TO 50 AREA SOURCES MAY BE INCLUDED IN THE MODEL    PMT00440
INPUTS.  CALCULATIONS ARE PERFORMED FOR EACH HOUR USING THE SPECI-PMT00450
FIED METEOROLOGICAL DATA. UP TO 24 DIFFERENT SETS OF HOURLY METEO-PMT00460
ROLOGICAL DATA MAY BE SPECIFIED AS INPUTS FOR THE DETERMINATION OFPMT00470
AIR QUALITY FOR 24 DISTINCT WEATHER SCENARIOS.  POLLUTANT CONCENT-PMT00480
RATIONS AND DEPOSITION FLUXES FOR A 2 TO 24 HOUR AVERAGING PERIOD PMT00490
      ( THIS WORK WAS DONE UNDER AN INTERAGENCY AGREEMENT
      BETWEEN THE ENVIRONMENTAL PROTECTION AGENCY AND THE
      NATIONAL OCEANIC AND ATMOSPHERIC ADMINISTRATION )


  *** EXTENDED ABSTRACT : PEM-2 (VERSION 84130).
      ARE CALCULATED BY AVERAGING THE CORRESPONDING VALUES CALCULATED
      FOR EACH  HOUR IN THE  PERIOD.
                                                     PMT00500
                                                     PMT00510
                                                     PMT00520
                                                     PMT00530
                                                     PMT00540
         PEM  IS BASED ON  THE TEXAS EPISODIC MODEL  (TEM, VERSION  8)
      DEVELOPED BY THE TEXAS AIR CONTROL BOARD  (1979).  TEM-8 USES  THE
      GAUSSIAN PLUME CONCENTRATION ALGORITHMS DEVELOPED FOR  NONREACTIVE  PMT00550
      POLLUTANTS AND A PERFECTLY REFLECTING SURFACE. CHEMICAL AND PHYSI-PMT00560
      CAL  DEPLETION PROCESSES  ARE THEREFORE IGNORED  EXCEPT FOR AN OPTIONPMT00570
      WHICH ALLOWS A SIMPLE EXPONENTIAL DECAY OF POLLUTANT WITH  TRAVEL   PMT00580
      TIME. THIS METHOD REQUIRES AN  ACCURATE ESTIMATE OF  THE POLLUTANT'SPMT00590
      HALF-LIFE.                                                         PMT00600
                                                                         PMT00610
         IN CONTRAST, PEM EXPLICITLY ACCOUNTS FOR  THE DRY DEPOSITION,    PMT00620
      GRAVITATIONAL SETTLING,  AND A  FIRST-ORDER CHEMICAL  TRANSFORMATION  PMT00630
                                     148

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C     OR DECAY OF GASEOUS OR PARTICULATE POLLUTANTS (OF ANY SIZE) IN    PMT00640
C     THE CONCENTRATION ALGORITHMS.  THESE ALGORITHMS, BASED ON EXACT   PMT00650
C     SOLUTIONS OF A GRADIENT-TRANSFER (K-THEORY) MODEL, WERE GIVEN BY  PMT00660
C     RAO (1981, 1982) AS ANALYTICAL EXTENSIONS OF THE WIDELY USED      PMT00670
C     GAUSSIAN PLUME DISPERSION ALGORITHMS UNDER VARIOUS ATMOSPHERIC    PMT00680
C     STABILITY AND MIXING CONDITIONS.  THUS, PEM TREATS DEPOSITION,    PMT00690
C     SEDIMENTATION. AND CHEMICAL TRANSFORMATION IN A PHYSICALLY REAL-  PMT00700
C     ISTIC AND STRAIGHTFORWARD MANNER, AND IT IS SUBJECT TO THE SAME   PMT00710
C     BASIC ASSUMPTIONS AND LIMITATIONS ASSOCIATED WITH ALL GAUSSIAN    PMT00720
C     PLUME-TYPE MODELS.  FOR FURTHER DETAILS REGARDING THE GRADIENT-   PMT00730
C     TRANSFER MODEL FORMULATIONS, ANALYTICAL SOLUTIONS, PARAMETERI-    PMT00740
C     ZATIONS, AND THE DEVELOPMENT OF THE ALGORITHMS FOR PEM, THE USER  PMT00750
C     SHOULD CONSULT THE REPORTS BY RAO (1981, 1982).  AN EVALUATION OF PMT00760
C     OF THE PEM USING THE ST.LOUIS/RAPS DATA FOR FIVE POLLUTANT SPECIESPMT00770
C     CAN BE FOUND IN THE REPORT BY PENDERGRASS AND RAO (1983).         PMT00780
C                                                                       PMT00790
C        THE PEM-2 MODEL (RAO, 1984)  IS DEVELOPED FROM THE PEM  (RAO AND PMT00800
C     STEVENS, 1982) WITH THE FOLLOWING KEY MODIFICATIONS:              PMT00810
C                                                                       PMT00820
C     (1) PEM-2 USES BRIGGS' URBAN DISPERSION PARAMETERS  (BASED ON THE  PMT00830
C         ST. LOUIS DIFFUSION DATA OF MCELROY AND POOLER) FOR BOTH POINTPMT00840
C         AND AREA SOURCES, WHEREAS PEM USES THE SAME DISPERSION PARAME-PMT00850
C         AS THE TEM-8.                                                 PMT00860
C     (2) THE NUMBER OF STABILITY CLASSES IN PEM-2 ARE REDUCED  TO SIX   PMT00870
C         (FROM SEVEN IN THE PEM).                                      PMT00880
C     (3) FOR BUOYANCY-DOMINATED PLUMES IN UNSTABLE/NEUTRAL ATMOSPHERE, PMT00890
C         BRIGGS' NEW PLUME RISE EQUATIONS AND PLUME PENETRATION  (OF AN PMT00900
C         ELEVATED STABLE LAYER) SCHEMES ARE INCLUDED AS OPTIONAL FEATU-PMT00910
C         RES IN PEM-2.                                                 PMT00920
C     (4) AN OPTION IS PROVIDED TO USE SITE-SPECIFIC VALUES FOR THE     PMT00930
C         EXPONENTS OF THE WIND-PROFILE POWER LAW AND ANEMOMETER HEIGHT PMT00940
C         AS INPUTS TO PEM-2.                                           PMT00950
C     (5) CONCENTRATIONS FROM AREA SOURCES ARE COMPUTED BY NUMERICAL IN-PMT00960
C         TEGRATION IN PEM-2, WHILE THEY ARE CALCULATED FROM CONCENTRA- PMT00970
C         TION ALGORITHMS BASED ON MASS BUDGETS OF THE SPECIES  IN PEM.  PMT00980
C         THE USER MAY SPECIFY AN EFFECTIVE HEIGHT OF EMISSIONS FOR     PMT00990
C         URBAN AREA SOURCES IN PEM-2, WHEREAS THESE EMISSIONS  ARE      PMT01000
C         ASSUMED TO OCCUR ONLY AT GROUND-LEVEL IN PEM.                 PMT01010
C         THE NUMBER OF CALCULATION GRID SQUARES USED FOR EACH  AREA     PMT01020
C         SOURCE HAVE BEEN INCREASED  TO 9 (IN PEM-2) FROM 5 IN  PEM TO   PMT01030
C         INCREASE THE PLUME LENGTH AND IMPROVE THE MODEL PERFORMANCE.  PMT01040
C                                                                       .PMT01050
C        BASED ON THE NUMBER OF POLLUTANTS  (NPOL=1 OR 2)  AND THE CHEMI- PMT01060
C     CAL TRANSFORMATION/DECAY OPTION PARAMETER  (ICT=0 OR 1) SPECIFIED  PMT01070
C     IN THE MODEL  INPUT, PEM-2 PROGRAM DOES ONE OF THE FOLLOWING:      PMT01080
C                                                                       PMT01090
C     (1) IF NPOL=1 AND ICT=0 OR  1, SURFACE  CONCENTRATIONS AND  DEPOSI-  PMT01100
C        TION FLUXES OF ONE GASEOUS OR PARTICULATE POLLUTANT. WITH THE  PMT01110
C        GIVEN DEPOSITION AND SETTLING VELOCITIES, VD1 AND Wl RESPECTI- PMT01120
C        VELY, ARE CALCULATED.  IF ICT=1, THEN CHEMICAL DECAY OF POLLU- PMT01130
C        TANT IS ALSO CONSIDERED  IF THE DECAY RATE XKT >  0.  IS  GIVEN    PMT01140
C        IN PERCENT PER HOUR.                                           PMT01150
C                                                                       PMT01160
C     (2) IF NPOL=2 AND ICT=0, SURFACE CONCENTRATIONS AND DEPOSITION    PMT01170
C        FLUXES OF  TWO DIFFERENT  AND  UNCOUPLED GASEOUS OR PARTICULATE   PMT01180
C        POLLUTANT  SPECIES WITH THE GIVEN DEPOSITION AND  SETTLING VELOC-PMT01190
C        ITIES  VD1  AND Wl  (FOR SPECIES-1) AND VD2 AND W2  (FOR SPECIES~2)PMT01200
C        RESPECTIVELY, ARE CALCULATED.  EMISSION RATES FOR BOTH SPECIES PMT01210
C        MAY BE DIFFERENT.  CHEMICAL  DECAY  IS NOT CONSIDERED FOR  EITHER PMT01220
C        SPECIES EVEN IF A VALUE  OF XKT > 0.  IS SPECIFIED.              PMT01230
C                                                                       PMT01240
C     (3) IF NPOL=2 AND ICT=1, THE TWO GASEOUS OR PARTICULATE POLLUTANT PMT01250
C        SPECIES ARE COUPLED  THROUGH  A FIRST-ORDER CHEMICAL  TRANSFORMA- PMT01260
C        TION.  THE SURFACE CONCENTRATIONS  AND DEPOSITION FLUXES  OF BOTHPMT01270
C        THE  PRIMARY POLLUTANT ?SPECIES-1 OR REACTANT)  AS WELL  AS THE   PMT01280
C        SECONDARY  POLLUTANT  (SPECIES-2 OR  REACTION PRODUCT) ARE  CALCU- PMT01290
C  .      LATED.  THE CHEMICAL TRANSFORMATION RATE  (XKT  >  0._) SHOULD BE  PMT01300
C        GIVEN.  BOTH SPECIES MAY BE  GIVEN  NON-EQUAL  DEPOSITION AND SET-PMT01310
C        TLING  VELOCITIES.   A NON-ZERO DIRECT EMISSION  RATE  FOR THE     PMT01320
C        SECONDARY  POLLUTANT  FROM THE POINT AND/OR AREA  SOURCES  MAY    PMT01330


                                      149

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c
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c
      ALSO  BE  SPECIFIED  AS  INPUT  FOR THIS  CASE.
       FOR FURTHER DETAILS  REGARDING THE MODIFICATION OF THE PEM TO
    DEVELOP PEM-2,  THE USE  OF THE  PEM-2 AND ITS I/O OPTIONS. INPUT
    PARAMETERS  AND UNITS, AND EXAMPLE PROBLEMS,  THE USER SHOULD
    CONSULT THE PEM-2  USER'S GUIDE BY RAO (1984).
    (1)
    (2)
    (3)
    (4)
                                                                  PMT01340

                                                                  PMT01350
                                                                  PMT01360
                                                                  PMT01370
                                                                  PMT01380
                                                                  PMT01390
                                                                  PMT01400
                                                                  PMT01410
                                                                  PMT01420
                                                                  PMT01430
                                                                  PMT01440
                                                                  PMT01450
                                                                  PMT01460
                                                                  PMT01470
                                                                  PMT01480
                                                                  PMT01490
                                                                  PMT01500
                                                                  PMT01510
                                                                  PMT01520
    RAO,  K.  S.,  1981:   ANALYTICAL SOLUTIONS OF A GRADIENT-TRANSFERPMT01530
    MODEL FOR PLUME DEPOSITION AND SEDIMENTATION.                  PMT01540
    EPA-600/3-82-079,  U.S.E.P.A., RESEARCH TRIANGLE PARK, NC;
    NOAA TECH. MEMO. ERL ARL-109, NOAA-ATDL,  OAK RIDGE,  TN 37831
    75 PP.   ATDL CONTRIBUTION FILE NO.  81/14.
                   *** REFERENCES ***


STAFF OF THE TEXAS AIR CONTROL BOARD, 1979:  USER'S GUIDE  :
TEXAS EPISODIC MODEL.  TEXAS AIR CONTROL BOARD, PERMITS
SECTION, AUSTIN, TEXAS 78723, 215 PP.


PENDERGRASS, W. R.,  AND K. S. RAO, 1983:  EVALUATION OF THE
POLLUTION EPISODIC MODEL USING THE RAPS DATA.
EPA-600/3-84-087, U.S.E.P.A., RESEARCH TRIANGLE PARK, NC:
NOAA TECH. MEMO. ERL ARL-128, NOAA-ATDL, OAK RIDGE, TN 37831,
47 PP.  ATDL CONTRIBUTION FILE 83/18.
    RAO,  K.  S.,  1982:   PLUME CONCENTRATION ALGORITHMS WITH
    DEPOSITION,  SEDIMENTATION,  AND CHEMICAL TRANSFORMATION.
    EPA-600/3-84-042,  U.S.E.P.A.,  RESEARCH TRIANGLE PARK, NC;
    NOAA TECH. MEMO.  ERL ARL-124,  NOAA-ATDL,  OAK RIDGE,  TN 37831,
    87 PP.   ATDL CONTRIBUTION FILE NO.  82/27.


(5) RAO,  K.  S..  AND M.  M. STEVENS, 1982:   POLLUTION EPISODIC
    MODEL USER'S GUIDE.
    EPA-600/8-84-008,  U.S.E.P.A.,  RESEARCH TRIANGLE PARK, NC;
    NOAA TECH. MEMO.  ERL ARL-125,  NOAA-ATDL,  OAK RIDGE,  TN 37831,
    186 PP.   ATDL CONTRIBUTION FILE NO.  82/28.
    (6)  RAO,  K.  S..  1984:   PEM-2 :
        (VERSION 2)  USER'S GUIDE.
        EPA-            ,  U.S.E.P.
        NOAA TECH.  MEMO.  ERL ARL-
        ATDL CONTRIBUTION FILE NO.
                               POLLUTION EPISODIC MODEL


                              A.,  RESEARCH TRIANGLE PARK, NC:
                                ,  NOAA-ATDL,  OAK RIDGE, TN 37831,
    QUESTIONS OR COMMENTS MAY BE REFERRED TO:


        JAMES M. GODOWITCH

        ATMOSOSPHERIC MODELING BRANCH - M.D.
        U.S.  ENVIRONMENTAL PROTECTION AGENCY
        RESEARCH TRIANGLE PARK, NC 27711
                                         80
        PHONE:
                 541-4802
                 629-4802
*** PEM-2 (VERSION 84130) :  FORTRAN LISTING.
*** COMMON BLOCKS, DIMENSIONS, AND DATA STATEMENTS.



    CONWON/PEMCOM/CONC(50.50,2),SDF(50,50,2),TT(20),

   1 XP(300).YP(300T,EP(300,2),HP(300),DP(300),VP(360),TP(300).
   2 XA(50),YA(50),EA(50.2),SIZE(50),
   3 WD(24),WS(24),TA(24),HMIX(24),DTDZI(24),
   4 AZ(6),BZ(6),CZ(6),P(6),SCLAB(6),DTDZ(2),SECTAN(16),
   5 XSWC,YSWC,GRID,LX,LY,A(2),B(2),POLNAM(3,2),CALNAM(7,2),
                                                              PMT01550
                                                              PMT01560
                                                              PMT01570
                                                              PMT01580
                                                              PMT01590
                                                              PMT01600
                                                              PMT01610
                                                              PMT01620
                                                              PMT01630
                                                              PMT01640
                                                              PMT01650
                                                              PMT01660
                                                              PMT01670
                                                              PMT01680
                                                              PMT01690
                                                              PMT01700
                                                              PMT01710
                                                              PMT01720

                                                              PMT01730
                                                              PMT01740
                                                              PMT01750
                                                              PMT01760
                                                              PMT01770
                                                                  PMT01780
                                                                  PMT01790
                                                                  PMT01800
                                                                  PMT01810
                                                                  PMT01820
                                                                  PMT01830
                                                                  PMT01840
                                                                  PMT01850
                                                                  PMT01860
                                                                  PMT01870
                                                                  PMT01880
                                                                  PMT01890

                                                                  PMT01900
                                                                  PMT01910
                                                                  PMT01920
                                      150

-------
C
C

C
C
C
     6 ITA,IRD,IWR,IDSK,D80,D47,D8047,D1ST,DELTA,HPRIME,
     7 ESH(2),PEAK,IBUOY,IRISE,IDWN,EFF,XS,UINV,WVEC,
     8 NAS.NPS,INDEX,IGRID,lAV.ISCEN.IWDOPT,IWD,ISC,IPS,
     9 NTOPT,NWDOPT,NWSOPT,NWPOPT,NSCEN,NLIST,NARRAY,NTAPE,NCSOPT,
     * NMAX,NSTDWN,NPRISE,NINPEN,INTER,NPRINT,NGPR,NBID

      COMMON/PARM1/NPOL,VD1,Wl,VD2,W2
      COMMON/PARM1A/ICT,TAUC,GAMMA
      COMMON/PARM2/ISPEC,UTAUC,Q2Q1,XCT,EXCT
      COMMON/PARM2A/HAS,KSC,AA,BA,CA
      COMMON/PARM3/HC.VDC1,WC1,VDC2,WC2
      COMMON/PARM4/V11,V21,V12,V22,V13
      COMMON/PARM5/D11,D21,D12,D22,D31,D32,D33,D6
      COMMON/PARM6/R11,R21,R12,R22,R13,R23,R31,R41,R32,R42
      COMMON/PARM7/QZC1,QZC2,HGT
      COMMON/PARM7A/HA,PI(6)
      COMMON/BLOCK1/PI,SQPI,SQRT2,A1B,A1C
      COMMON/BLOCK2/AI,BI,EPSABS,EPSREL,LW,NIW
      COMMON/EXPCHK/EXPMAX,EXPMIN.ETAMAX
      COMMON/WND/HMIN,HMAX,UMIN,IUFLG

      EXTERNAL FUNS,FUN4,FUN5
      HEAL*8 FUNS,FUN4,FUN5,X1A,X2A
      REAL*8 AI.BI,EPSABS,EPSREL,RESULT
      DIMENSION IW(102)
      DIMENSION PRL(2,2),DWL(4),ANGLIM(6)
      DIMENSION ITABLE(9,10).EPSLIM(10l,AY(6)
      DIMENSION XA1(9),XA2(9),RCA1(9).RCA2(9),AUX(25)
      DIMENSION RCA2CH(9),RCA2CT(9,50),QA2QA1(50)

      DATA PRL/4HMOME,4HNTUM,4HBUOY,4HANCY/
      DATA DWL/4H    ,4H    .4HDOWN.4HWASH/
      DATA EPSLIM/.12427,.16511,.24504,.35884,.46373,
     1            .55868' 64350,.69482,.71890,.78540/
      DATA ITABLE/0,0,0,0,0,0,0,0,0,  0,0,0,0,1,1,1,1,1,
     1            0,0,0,1,1,1,1,1,2,  0,0,1,1,1,2,2,2,2,
     9            0 nil 9 9 *3 *? 1  0 I  1 9 9 ? ? 4 4.
     £•            U,U,X,J.,^,^,O,O,*3,  UjX.jLj^j^jOjOjH,^,
     3            0,1 1 2 3,3 4 5 5,  0,12,2,3 4 5,6,6
     4            0,1,2,3,3.4,5.6.7,  0,1.2.3,4,5.6.7.8/
      DATA ANGLIM/0.750492,0.750492,0.575959,0.436332,
     1 0.314159.0.314159/
      DATA AY/.32,.32,.22,.16,.11,.ll/
      CALL WSTCLK

  *** DEFINE PROGRAM CONSTANTS.

      PI=3.1415927
      PI2=PI/2.
      SQPI=SQRT(PI)
      SQRT2=SQRT(2.)
      A1B=1000./(SQRT2*SQPI)
      A1C=2.*SQPI
      A1D=SQRT2/SQPI
      AI=0.
      BI=1.
      EPSABS=1.0E-3
      EPSREL=1.0E-3
      LW=800
      NIW=102
C     FOR IBM-3033
C     EXPMAX=174.
C     FOR UNIVAC-1100
      EXPMAX=87.
      EXPMIN=50.
      ETAMAX=SQRT(EXPMAX)
C
      WRITE(IWR,5430)
 5430 FORMAT ('1',21X,'PEM-2.0
PMT01930
PMT01940
PMT01950
PMT01960
PMT01970
PMT01980
PMT01990
PMT02000
PMT02010
PMT02020
PMT02030
PMT02040
PMT02050
PMT02060
PMT02070
PMT02080
PMT02090
PMT02100
PMT02110
PMT02111
PMT02120
PMT02130
PMT02140
PMT02150
PMT02160
PMT02170
PMT02180
PMT02190
PMT02200
PMT02210
PMT02220
PMT02230
PMT02240
PMT02250
PMT02260
PMT02270
PMT02280
PMT02290
PMT02300
PMT02310
PMT02320
PMT02330
PMT02340
PMT02350

PMT02360
PMT02370
PMT02380
PMT02390
PMT02400
PMT02410
PMT02420
PMT02430
PMT02440
PMT02450
PMT02460
PMT02470
PMT02480
PMT02490
PMT02500
PMT02510
PMT02520
PMT02530
PMT02540
PMT02550
PMT02560
PMT02570
PMT02580
                                  (DATED 86016)',/,22X,
                                     151

-------
     1 'AN AIR QUALITY DISPERSION MODEL IN',/,22X,'SECTION 2.
     2 'NON-GUIDELINE MODELS',/J22X,		~ 	  '
     3 'JULY 86.',/,22X,'SOURCE:
     4 'UNIVAC AT RTF, NC.')
                               MODEL  IN',/,22X,'SECTION 2
                               2X,'IN  UNAMAP (VERSION 6)  '
                               UNAMAP FILE  ON EPA"S ',
      WRITE (IWR,5432)
 5432 FORMAT (///////45X,'PEM-2   (VERSION
     1 45X,'POLLUTION EPISODIC MODEL'/////
     2 52X,'INCLUDING'//
                                          84130)'/////
C
C
C
C
C
C

C
C
   3  SOX,'DEPOSITION,  SEDIMENTATION,  AND CHEMICAL  TRANSFORMATION'//
   4  SOX,'OF POLLUTANTS'/)

   INDEX=0

 CALL MODEL  INPUT ROUTINE  TO READ  ALL CONTROL PARAMETERS,  GRID
   INFORMATION,  METEOROLOGICAL  AND EMISSION DATA,  AND  POLLUTANT
   DEPOSITION AND TRANSFORMATION  PARAMETERS.

   ************
   CALL INMOD
   ************

   VD136=VD1*36.
   VD236=VD2*36.
C
C
C *** DETERMINE VALUE OF PARAMETER ISPEC.
C
C
C
C
C
C

C
C
C
C

C
C
C
C
C
C
C
C
C
C
C
    ISPEC IS AN INTERNAL ROUTING PARAMETER USED IN PEM-2
    TO DETERMINE THE APPROPRIATE CONCENTRATION ALGORITHMS
    TO BE USED FOR A GIVEN PROBLEM.
    VALUE OF ISPEC  IS BASED ON NUMBER OF POLLUTANTS,
    AND CHEMICAL TRANSFORMATION OPTION PARAMETER.

    IF(NPOL.EQ.2) GO TO 41
    ONLY ONE POLLUTANT SPECIES.   FIRST-ORDER CHEMICAL  DECAY CAN BE
    CONSIDERED BY SPECIFYING ICT = 1 AND XKT > 0.
    ISPEC=1
    GO TO 43

    TWO POLLUTANT SPECIES.
 41 IF(ICT.EQ.l) GO TO 42
    NO CHEMICAL COUPLING. THE TWO SPECIES ARE INDEPENDENT
    OF EACH OTHER.  CHEMICAL DECAY IS NOT CONSIDERED FOR
    EITHER SPECIES.
    ISPEC=2
    GO TO 43

    CHEMICAL COUPLING EXISTS BETWEEN SPECIES-1 (REACTANT)
    AND SPECIES-2 (PRODUCT). FIRST-ORDER TRANSFORMATION.
 42 ISPEC=3
 43 CONTINUE
*** DEFINE TIME-AVERAGING MULTIPLIER CONSTANTS.
       IF(NTOPT.EQ.l)
       IFfNTOPT.EQ.2
       IF(NTOPT.EQ.3J

       INDEX=1
                   STCONV = 1.
                   STCONV= 0.04166667
                   STCONV= 1.0/FLOAT(NSCEN)
C
C  CALL INPUT ROUTINE TO BRING IN METEOROLOGICAL DATA FOR ONE SCENARIO
C     (NUMBER OF SCENARIO = ISCEN).
C
C     ************
100   CALL  INMOD
C     ************
C
C  CALCULATE WIND VECTOR (WVEC) FOR SCENARIO. IFLAG IS USED BELOW
PMT02590
PMT02600
PMT02610
PMT02620
PMT02630
PMT02640
PMT02650
PMT02660
PMT02670
PMT02680
PMT02690
PMT02700
PMT02710
PMT02720
PMT02730
PMT02740
PMT02750
PMT02760
PMT02770
PMT02780
PMT02790
PMT02800
PMT02810
PMT02820
PMT02830
PMT02840
PMT02850
PMT02860
PMT02870
PMT02880
PMT02890
PMT02900
PMT02910
PMT02920
PMT02930
PMT02940
.PMT02950
PMT02960
PMT02970
PMT02980
PMT02990
PMT03000
PMT03010
PMT03020
PMT03030
PMT03040
PMT03050
PMT03060
PMT03070
PMT03080
PMT03090
PMT03100
PMT03110
PMT03120
PMT03130
PMT03140
PMT03150
PMT03160
PMT03170
PMT03180
PMT03190
PMT03200
PMT03210
PMT03220
PMT03230
                                      152

-------
C    (STMT. 275) TO DETERMINE METHOD OF RESTRICTING THE AREA OF THE
C    RECEPTOR GRID AFFECTED BY EACH SOURCE.
C
175   IF(NWDOPT.EQ.l) GO TO 200
      DO 180 IWD=1,16
      DETA=ABS(WD(ISCEN)-SECTAN(IWD))
      IF(DETA.LE.0.19634954) GO TO 205
180   CONTINUE
      GO TO 205
200   WD(ISCEN)=SECTAN(IWD)
205   IF(IWD.LT.8.0R.IWD.GT.10) GO TO 210
      IFLAG=1
      GO TO 241
210   IF(IWD.NE.ll) GO TO 215
      IFLAG=2
      GO TO 241
215   IF(IWD.LT.12.0R.IWD.GT.14) GO TO 220
      IFLAG=3
      GO TO 241
220   IF(IWD.NE.IS) GO TO 225
      IFLAG=4
      GO TO 241
225   IF(IWD.LT.16.AND.IWD.GT.2) GO TO 230
      IFLAG=5
      GO TO 241
230   IF(IWD.NE.3) GO TO 235
      IFLAG=6
      GO TO 241
235   IF(IWD.LT.4.0R.IWD.GT.6) GO TO 240
      IFLAG=7
      GO TO 241
240   IFLAG=8
241   WVEC= WD(ISCEN) + 3.14159265
      IF(WVEC.GT.6.2831853) WVEC=WVEC - 6.2831853
      WDV=4.712388981-WD(ISCEN)
      IF(WDV.LT.O.)WDV=WDV+6.283185307
      WDPANG=WDV+ANGLIM(ISC)
      WDMANG=WDV-ANGLIM(ISC)
C
      AA=AZ(ISC)
      BA=BZ(ISC)
      CA=CZ(ISC)
      KSC=ISC
C
C
C
C

C
C
C
C
C
PARAMETERS AUTOMATICALLY.
C
C
C
 CALL AUTGRD TO CALCULATE RECEPTOR GRID
    ************
    IF(IGRID.EQ.l) CALL AUTGRD
    ************

*** INITIALIZATION.

 INITIALIZE CONCENTRATION AND SURFACE DEPOSITION FLUX ARRAYS
    IF(NTOPT.GT.LAND.ISCEN.GT.l) GO TO 4
    DO 2 1=1,LX
    DO 2 J=1,LY
    CONC(I,J,1)=0.
    SDF(I,J,1)=0.
    IF(ISPEC.EQ.l.AND.NCSOPT.EQ.O) GO TO 2
    CONC(I,J,2)=0.
    SDF(I.J,2)=0.
  2 CONTINUE
    4 VGRID=  l./GRID
      GRIDSQ= GRID*GRID
      ELX= LX
      ELY= LY
      XB1= XSWC + 0.5*GRID
PMT03240
PMT03250
PMT03260
PMT03270
PMT03280
PMT03290
PMT03300
PMT03310
PMT03320
PMT03330
PMT03340
PMT03350
PMT03360
PMT03370
PMT03380
PMT03390
PMT03400
PMT03410
PMT03420
PMT03430
PMT03440
PMT03450
PMT03460
PMT03470
PMT03480
PMT03490
PMT03500
PMT03510
PMT03520
PMT03530
PMT03540
PMT03550
PMT03560
PMT03570
PMT03580
PMT03590
PMT03600
PMT03610
PMT03620
PMT03630
PMT03640
PMT03650
PMT03660
PMT03670
PMT03680
PMT03690
PMT03700
PMT03710
PMT03720
PMT03730
PMT03740
PMT03750
PMT03760
PMT03770
PMT03780
PMT03790
PMT03800
PMT03810
PMT03820
PMT03830
PMT03840
PMT03850
PMT03860
PMT03870
PMT03880
PMT03890
PMT03900
PMT03910
PMT03920
PMT03930
                                      153

-------
c
c
c***
c
c
c
c
c
c
c
c
      XB2= XSWC
      YB1= YSWC
      YB2= YSWC
                  (ELX-0.5)*GRID
                  0.5*GRID
                  (ELY-0.5)*GRID
      AREA   SOURCE   CALCULATIONS  ***

     IF NO AREA SOURCES,  SKIP AREA SOURCE CALCULATIONS.
      IF(NAS.LT.l)  GO TO 245

     IWV HELPS DETERMINE THE PATTERN OF GRID SQUARES AFFECTED BY EACH
     AREA SOURCE.   PATTERN DEPENDS ONLY ON WIND DIRECTION.
     EPS IS THE ANGLE BETWEEN THE WIND VECTOR AND THE NEAREST
     COORDINATE AXIS.

      IWV= 1 + WVEC/0.78540
      GO TO (2411,2412,2413,2414,2415,2416,2417,2418),IWV
2411  ITABX=1
      ISIGNX=1
      ISIGNY=1
      EPS= WVEC
      GO TO 2419
2412  ITABX=0
      ISIGNX=1
      ISIGNY=1
      EPS= 1.5708 - WVEC
      GO TO 2419
2413  ITABX=0
      ISIGNX=1
      ISIGNY=-1
      EPS= WVEC - 1.57080
      GO TO 2419
2414  ITABX=1
      ISIGNX=1
      ISIGNY=-1
      EPS= 3.1416 - WVEC
      GO TO 2419
2415  ITABX=1
      ISIGNX=-1
      ISIGNY=-1
      EPS= WVEC - 3.1416
      GO TO 2419
2416  ITABX=0
      ISIGNX=-1
      ISIGNY=-1
      EPS= 4.7124 - WVEC
      GO TO 2419
2417  ITABX=0
      ISIGNX=-1
      ISIGNY=1
      EPS= WVEC - 4.7124
      GO TO 2419
2418  ITABX=1
      ISIGNX=-1
      ISIGNY=1
      EPS= 6.2832 - WVEC
2419  IF(ITABX.EQ.O) GO TO 2420
      ITABY=0
      INCRX=0
      INCRY=1
      GO TO 2421
2420  ITABY=1
      INCRX=1
      INCRY=0
2421  DO 2422 L=l,10
      IF(EPS.GT.EPSLIM(L)) GO TO 2422
      IEPS=L
      GO TO 2423
2422  CONTINUE
      IEPS=10
PMT03940
PMT03950
PMT03960
PMT03970
PMT03980
PMT03990
PMT04000
PMT04010
PMT04020
PMT04030
PMT04040
PMT04050
PMT04060
PMT04070
PMT04080
PMT04090
PMT04100
PMT04110
PMT04120
PMT04130
PMT04140
PMT04150
PMT04160
PMT04170
PMT04180
PMT04190
PMT04200
PMT04210
PMT04220
PMT04230
PMT04240
PMT04250
PMT04260
PMT04270
PMT04280
PMT04290
PMT04300
PMT04310
PMT04320
PMT04330
PMT04340
PMT04350
PMT04360
PMT04370
PMT04380
PMT04390
PMT04400
PMT04410
PMT04420
PMT04430
PMT04440
PMT04450
PMT04460
PMT04470
PMT04480
PMT04490
PMT04500
PMT04510
PMT04520
PMT04530
PMT04540
PMT04550
PMT04560
PMT04570
PMT04580
PMT04590
PMT04600
PMT04610
PMT04620
PMT04630
                                      154

-------
 2423 DXA=1000.*GRID/COS(EPS)
      IF(NWPOPT.EQ.l)  THEN
:   OPTIONAL WIND PROFILE EXPONENTS USED
      CALL WIND(WS(ISCEN),P1(ISC),HAS,UPL)
      ELSE
:    DEFAULT URBAN WIND PROFILE EXPONENTS USED
      CALL WIND(WS(ISCEN),P(ISC),HAS,UPL)
      END IF
      UINV=1./UPL
      UPL=1./UINV
      UINV1=UINV/100.

      DEFINE NONDIMENSIONAL DEPOSITION AND SEDIMENTATION PARAMETERS.

      ISPEC = 1 OR 2 OR 3
      VDC1=VD1*UINV1
      WC1=W1*UINV1
      V11=VDC1-0.5*WC1
      V21=VDC1-WC1
      IF(ISPEC.EQ.l) GO TO 46

      ISPEC = 2 OR 3
      VDC2=VD2*UINV1
      WC2=W2*UINV1
      V12=VDC2-0.5*WC2
      V22=VDC2-WC2
      IF(ISPEC.EQ.2) GO TO 47

      ISPEC = 3
      V13=Vll-0.5*(WC1-WC2)

      ISPEC = 1 OR 3
   46 UTAUC=TAUC*UPL
   47 CONTINUE


      CALCULATE RELATIVE CONCENTRATIONS AT A RECEPTOR LOCATED AT THE
      CENTER OF THE CALCULATION GRID SQUARE CONTAINING THE AREA SOURCE
      EMISSIONS,  AND AT THE CENTER OF EACH OF THE EIGHT GRID SQUARES
      IMMEDIATELY DOWNWIND OF THE SOURCE.

      NDIM=15
      EPSAXI=.01
      XA1(1)=1.0
      XA2(1;=0.5*DXA
C
C
C
C
C
C
C
C

C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
      START LOOP ON NINE CALCULATION GRID SQUARES WITH RECEPTORS
      DO 111 1=1,9
      X1A=XA1(I)
      X2A=XA2(I)

      SPECIES-1 CONCENTRATION  (ISPEC = 1 OR 2 OR 3)
      COMPUTE INTEGRAL F3(X1A,X2A); FUNS IS THE EXTERNALLY
      DEFINED INTEGRAND FUNCTION.
      ************
      CALL XINTEG(X1A,X2A,EPSAXI,NDIM,FUNS,RESULT,IER1.AUX)
      ************
      RCA1(I)=A1D*RESULT
      IF(ISPEC.EQ.l) GO TO 108

      SPECIES-2 CONCENTRATION
      ISPEC=2 OR ISPEC=3 (DIRECT EMISSION CONTRIBUTION)
      COMPUTE INTEGRAL F5(X1A,X2A); FUN5 IS THE EXTERNALLY
      DEFINED INTEGRAND FUNCTION.
      ************
      CALL XINTEG(X1A,X2A,EPSAXI,NDIM,FUN5,RESULT,IER2.AUX)
      ************
      RCA2(I)=A1D*RESULT
      IF(ISPEC.EQ.2) GO TO 108
 PMT04640
 PMT04650
 PMT04660
 PMT04670
 PMT04680
 PMT04690
 PMT04700
 PMT04710
 PMT04720
 PMT04730
 PMT04740
 PMT04750
 PMT04760
 PMT04770
 PMT04780
 PMT04790
 PMT04800
 PMT04810
 PMT04820
 PMT04830
 PMT04840
 PMT04850
 PMT04860
 PMT04870
 PMT04880
 PMT04890
 PMT04900
 PMT04910
 PMT04920
 PMT04930
 PMT04940
 PMT04950
 PMT04960
 PMT04970
 PMT04980
 PMT04990
 PMT05000
 PMT05010
 PMT05020
 PMT05030
 PMT05040
.PMT05050
 PMT05060
 PMT05070
 PMT05080
 PMT05090
 PMT05100
 PMT05110
 PMT05120
 PMT05130
 PMT05140
 PMT05150
 PMT05160
 PMT05170
 PMT05180
 PMT05190
 PMT05200
 PMT05210
 PMT05220
 PMT05230
 PMT05240
 PMT05250
 PMT05260
 PMT05270
 PMT05280
 PMT05290
 PMT05300
 PMT05310
 PMT05320
 PMT05330
                                     155

-------
c
C     SPECIES-2 CONCENTRATION
C     ISPEC=3 (CHEMICAL TRANSFORMATION CONTRIBUTION)
C     COMPUTE INTEGRAL F4(X1A,X2A); FUN4 IS THE EXTERNALLY
C     DEFINED INTEGRAND FUNCTION.
C     ************
      CALL XINTEG(X1A,X2A,EPSAXI,NDIM,FUN4,RESULT,IER3,AUX)
C     ************
      RCA2CH(I)=A1D*GAMMA*RESULT
C
  108 IF(I.EQ.9) GO TO 111
      XA1(I+1)=XA2(I)
      XA2(I+1)=XA1(I+1)+DXA
  111 CONTINUE
C     END LOOP ON 1=1,9 CALCULATION GRID SQUARES.
C
      IF(ISPEC.NE.3) GO TO 114
C     START LOOP ON ALL AREA SOURCES IF ISPEC=3
      DO 114 K=1,NAS
      IF(EA(K,l).LT.l.E-6) EA(K,l)=l.E-6
      QA2QAl(k)=EA(K,2)/EA(K,l)
      DO 113 1=1.9
      RCA2CT(I,K)=QA2QA1(K)*RCA2(I) + RCA2CH(I)
  113 CONTINUE
  114 CONTINUE
      END LOOP ON K=1,NAS AREA SOURCES IF ISPEC = 3


   LOOP THROUGH ALL AREA SOURCES.  EMISSIONS FROM EACH AREA SOURCE
     ARE APPORTIONED AMONG THE RECEPTOR GRID SQUARES WHOLLY OR
     PARTIALLY COVERED BY THE SOURCE.  EACH AFFECTED RECEPTOR GRID
     SQUARE IS TREATED AS A SOURCE.

      START LOOP ON K=1,NAS AREA SOURCES.
      DO 2429 K=1,NAS
      AREA= SIZE(K)*SIZE(K)
      AX1= XA(K)
      AX2= AX1 + SIZE(K)
      NX1= (AX1-XSWC)*VGRID + 9.
      NX2= (AX2-XSWC)*VGRID + 9.
      IF(NXl.GT.LX+16.0R.NX2.LT.l) GO TO 2429
      IF(NXl.GE.l) GO TO 32
      NX1= 1
      AX1= XSWC - 8.*GRID
32    IF?NX2.LE.LX+16) GO TO 34
      NX2= LX+16
      AX2= XSWC + (ELX + 8.)*GRID
34    Xl= XSWC + (FLOAT(NX1)-9.)*GRID
      X2= XSWC + (FLOAT(NX2)-8.)*GRID
      AY1= YA(K)
      AY2= AY1 + SIZE(K)
      NY1= (AY1-YSWC)*VGRID + 9.
      NY2= (AY2-YSWC)*VGRID + 9.
      IF(NYl.GT.LY+16.0R.NY2.LT.l) GO TO 2429
      IF(NYl.GE.l) GO TO 36
      NY1= 1
      AY1= YSWC - 8.*GRID
      IF(NY2.LE.LY+16) GO TO 38
      NY2= LY+16
      AY2= YSWC + (ELY + 8.)*GRID
      Yl= YSWC + (FLOAT(NY1)-9.)*GRID
      Y2= YSWC + (FLOAT(NY2)-8.)*GRID

      START LOOP ON IX=NX1,NX2 COLUMNS OF THE RECEPTOR GRID.
      DO 2428 IX=NX1,NX2
      IF(NX1.NE.NX2) GO TO 10
      DXQ= AX2-AX1
      GO TO 13
      IF(IX.NE.NXl) GO TO 11
      DXQ= GRID+X1-AX1
36
38

C
C
10
PMT05340
PMT05350
PMT05360
PMT05370
PMT05380
PMT05390
PMT05400
PMT05410
PMT05420
PMT05430
PMT05440
PMT05450
PMT05460
PMT05470
PMT05480
PMT05490
PMT05500
PMT05510
PMT05520
PMT05530
PMT05540
PMT05550
PMT05560
PMT05570
PMT05580
PMT05590
PMT05600
PMT05610
PMT05620
PMT05630
PMT05640
PMT05650
PMT05660
PMT05670
PMT05680
PMT05690
PMT05700
PMT05710
PMT05720
PMT05730
PMT05740
PMT05750
PMT05760
PMT05770
PMT05780
PMT05790
PMT05800
PMT05810
PMT05820
PMT05830
PMT05840
PMT05850
PMT05860
PMT05870
PMT05880
PMT05890
PMT05900
PMT05910
PMT05920
PMT05930
PMT05940
PMT05950
PMT05960
PMT05970
PMT05980
PMT05990
PMT06000
PMT06010
PMT06020
PMT06030
                                     156

-------
11
12
C
C
13
20
21
22
23
C
C
C
C
C
C
C
C
C
C
C
C
C
C
     GO  TO  13
     IF(IX.NE.NX2)  GO  TO 12
     DXQ= GRID+AX2-X2
     GO  TO  13
     DXQ=GRID

     START  LOOP  ON  JY=NY1,NY2  ROWS  OF THE RECEPTOR GRID.
     DO  2427 JY=NY1,NY2
     IF(NY1.NE.NY2) GO TO 20
     DY= AY2-AY1
     GO  TO  23
     IF(JY.NE.NYl)  GO  TO 21
     DY= GRID+Y1-AY1
     GO  TO  23
     IF(JY.NE.NY2)  GO  TO 22
     DY= GRID+AY2-Y2
     GO  TO  23
     DY=GRID
     SPLIT= DXQ*DY/(AREA*GRIDSQ)

  LOOP FOR  THE NINE RECEPTORS  AFFECTED BY EACH RECEPTOR GRID SQUARE
    CONTAINING EMISSIONS.  THE RECEPTORS IN THE EIGHT DOWNWIND SQUARES
    AND  IN  THE SOURCE  SQUARE ITSELF ARE AFFECTED.
      DO 2426 L=l,9
      NX= IX + ISIGNX*(ITABLE(L,IEPS)*ITABX
      IF(NX.LT.l.OR.NX.GT.LX) GO TO 2426
      NY= JY + ISIGNY*(ITABLE(L,IEPS)*ITABY
      IF(NY.LT.l.OR.NY.GT.LY) GO TO 2426
                                             (L-1)*INCRX) - 8

                                             (L-1)*INCRY) - 8
     CALCULATE GROUND-LEVEL CONCENTRATIONS CONG (MICROGRAMS PER CUBIC
     METER)  AND SURFACE DEPOSITION FLUXES SDF (MICROGRAMS PER SQUARE
     METER PER HOUR)  OF POLLUTANTS AT RECEPTOR IN COLUMN NX, ROW NY
     OF THE RECEPTOR GRID DUE TO AREA SOURCE K.

     ISPEC = 1 OR 2 OR 3
     CINC1=RCA1(L)*EA(K,1)*SPLIT*STCONV*UINV
     CONG(NX,NY,1)=CONC(NX,NY.1)+CINC1
     SDF(NX,NY,l)=SDF(NX.NY,li+VD136*CINCl
     IF(ISPEC.EQ.l) GO T6 2426
     IF(ISPEC.EQ.3) GO TO 2425

     ISPEC = 2
     CINC2=RCA2(L)*EA(K,2)*SPLIT*STCONV*UINV
     CONG(NX,NY.2)=CONC(NX,NY.2)+CINC2
     SDF(NX,NY,2)=SDF(NX,NY,2)+VD236*CINC2
     GO TO 2426

     ISPEC = 3
2425 CINC2=RCA2CT(L,K)*EA(K,1)*SPLIT*STCONV*UINV
     CONC(NX.NY,2)=CONC(NX,NY.2)+CINC2
     SDF(NX,NY,2)=SDF(NX,NY,2)+VD236*CINC2
C
2426
C
C
2427
C
C
2428
C
C
2429
C
C
C
C
C ***
C
C

CONTINUE
END LOOP

CONTINUE
END LOOP

CONTINUE
END LOOP

CONTINUE
END LOOP





ON


ON


ON


ON





L=l,9 CALCULATION GRID SQUARES WITH RECEPTORS.


JY=NY1,NY2 ROWS OF THE RECEPTOR GRID.


IX=NX1,NX2 COLUMNS OF THE RECEPTOR GRID.


K=1,NAS AREA SOURCES.



POINT SOURCES.






PMT06040
PMT06050
PMT06060
PMT06070
PMT06080
PMT06090
PMT06100
PMT06110
PMT06120
PMT06130
PMT06140
PMT06150
PMT06160
PMT06170
PMT06180
PMT06190
PMT06200
PMT06210
PMT06220
PMT06230
PMT06240
PMT06250
PMT06260
PMT06270
PMT06280
PMT06290
PMT06300
PMT06310
PMT06320
PMT06330
PMT06340
PMT06350
PMT06360
PMT06370
PMT06380
PMT06390
PMT06400
PMT06410
PMT06420
PMT06430
PMT06440
PMT06450
PMT06460
PMT06470
PMT06480
PMT06490
PMT06500
PMT06510
PMT06520
PMT06530
PMT06540
PMT06550
PMT06560
PMT06570
PMT06580
PMT06590
PMT06600
PMT06610
PMT06620
PMT06630
PMT06640
PMT06650
PMT06660
PMT06670
PMT06680
PMT06690
PMT06700
PMT06710
PMT06720
PMT06730
                                      157

-------
C  IF NO POINT SOURCES, SKIP POINT SOURCE CALCULATIONS.
  245 IF(NPS.LT.l) GO TO 603
C
C
C
C***  POINT   SOURCE   CALCULATIONS  ***
C
C  LOOP THROUGH ALL POINT SOURCES.
      DO 600 1=1,NPS
      IF
      IF
      IF
      IF
      IF
      WR
       (NWDOPT.GT.1.AND.IWDOPT.GT.1).OR.NTOPT.EQ.2) GO TO 247
       NPRINT.EQ.O) GO TO 247
        I-1)/50*50.NE.I-1) GO TO 247
        INPEN.EQ.0) GO TO 246
       ISC.GE.5) GO TO 246
       TE?IWR,1001) TT,ISCEN,HMIX(ISCEN),DTDZI(ISCEN)
C
C
C
C
C
C
C
C

C
C
C
C
    WRITE(IWR,1003)
    GO TO 247
246 WRITE(IWR,1005}  TT,ISCEN,HMIX(ISCEN)
    WRITE(IWR,1007)
247 IPS=I
    IF PHYSICAL STACK HEIGHT EXCEEDS MIXING HEIGHT, THE SOURCE
    IS IGNORED.
    IF(HP(I).GE.HMIX(ISCEN)) GO TO 600
    EFF= 2.45*VP(I)*DP(I)*DP(I)*(TP(I)-TA(ISCEN))/TP(I)
    IFCEFF.LT.O.) EFF=1.0E-7

 CALCULATE INVERSE WIND SPEED (UINV) AT THE PHYSICAL HEIGHT (HP(I))
   OF POINT SOURCE I.  DO NOT CHANGE IF STACK HEIGHT IS LESS
   THAN 10 METERS.

     IF(NWPOPT.EQ.l) THEN
   USE OPTIONAL POWER LAW EXPONENTS
    CALL WIND(WS(ISCEN),P1(ISC),HP(I),UPL)
    ELSE
   USE DEFAULT URBAN WIND PROFILE EXPONENTS
    CALL WIND(WS(ISCEN),P(ISC),HP(I),DPL)
    END IF
    UINV=1./UPL

 DEFINE EMISSION RATES (SOURCE STRENGTHS) OF POLLUTANT SPECIES,
   AND NONDIMENSIONAL DEPOSITION AND SEDIMENTATION PARAMETERS.
    UINV1=UINV/100.

    ISPEC = 1 OR 2 OR 3
    Q1=EP(I,1)
    VDC1=VD1*UINV1
    WC1=W1*UINV1
    V11=VDC1-0.5*WC1
    V21=VDC1-WC1
    IF(V21.EQ.O.) GO TO 251
    R11=V11/V21
    R21=0.5*WC1/V21
251 IF(ISPEC.EQ.l) GO TO 255

    ISPEC = 2 OR 3
    Q2=EP(I.2)
    VDC2=VD2*UINV1
    WC2=W2*UINV1
    V12=VDC2-0.5*WC2
    V22=VDC2-WC2
    IF(V22.EQ.O.) GO TO 253
    R12=V12/V22
    R22=0.5*WC2/V22
253 IFUSPEC.EQ.2) GO TO 257

    ISPEC = 3
    IF(Q1.EQ.O.) Ql=l.E-6
    Q2Q1=Q2/Q1
    V13=V11-0.5*(WC1-WC2)
    IF(V21.EQ.O.) GO TO 255
PMT06740
PMT06750
PMT06760
PMT06770
PMT06780
PMT06790
PMT06800
PMT06810
PMT06820
PMT06830
PMT06840
PMT06850
PMT06860
PMT06870
PMT06880
PMT06890
PMT06900
PMT06910
PMT06920
PMT06930
PMT06940
PMT06950
PMT06960
PMT06970
PMT06980
PMT06990
PMT07000
PMT07010
PMT07020
PMT07030
PMT07040
PMT07050
PMT07060
PMT07070
PMT07080
PMT07090
PMT07091
PMT07095
PMT07100
PMT07110
PMT07120
PMT07130
PMT07140
PMT07150
PMT07160
PMT07170
PMT07180
PMT07190
PMT07200
PMT07210
PMT07220
PMT07230
PMT07240
PMT07250
PMT07260
PMT07270
PMT07280
PMT07290
PMT07300
PMT07310
PMT07320
PMT07330
PMT07340
PMT07350
PMT07360
PMT07370
PMT07380
PMT07390
PMT07400
PMT07410
                                     158

-------
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
    R13=V13/V21
    R23=0.5*WC2/V21

    ISPEC = 1 OR 3
255 UTAUC=TAUC*UPL
257 KLID=0


*** PEAK EFFECTIVE SOURCE HEIGHT CALCULATIONS.

 CALL SUBROUTINE RISE WITH IRISE=2 TO GET PEAK EFFECTIVE SOURCE
   HEIGHT, ESH(2).

    IRISE=2
    ************
    CALL RISE
    ************
    IRISE=1

 CALCULATE DISTANCE AT WHICH PLUME REACHES MAXIMUM HEIGHT  (PEAK).

    IF(IBUOY.EQ.O) GO TO 263
    IF(ISC.LT.51 GO TO 261
    PEAK=0.00207148/(UINV*SQRT(DTDZ(ISC-4)*9.8/TA(ISCEN)))
    GO TO 265
261 PEAK=0.001*XS
    GO TO 265
263 PEAK= 0.
    IF(ISC.GE.5) GO TO 265
    IF(ABS(VP(I)).LT.. 000001) GO TO 265
    PEAK=(0.004*UINV*DP(I)*(VP(I) + 3./UINV)**2)/VP(I)

265 IF(NINPEN.EQ.O) GO TO 264
    IF(ISC.GE.5.0R.IBUOY.EQ.O) GO TO 264
    GO TO 267

 STANDARD TREATMENT OF PLUME PENETRATION ABOVE MIXING HEIGHT:
    IF MAXIMUM EFFECTIVE SOURCE HEIGHT EXCEEDS THE MIXING  HEIGHT,
    PLUME ESCAPES THE MIXED LAYER, AND SOURCE IS IGNORED.
264 IF(NPRINT.EQ.O) GO TO 266
    IF(NWDOPT.LE.l.OR.IWDOPT.LE.l) WRITE(IWR.1010)
   1 I,XP7l),YP(I).Ql,Q2,HP(I),DP(I),Vp7l),TP(I),PRL(l,IBUOY+l),
   2 PRL(2,IBUOY+ij,DWL(IDWN)JDWL(lDWN+l),UPL,ESH(2)
266 IF(ESH(2).GT.HMIX(ISCEN)) GO TO 600
    GO TO 275

 NEW SCHEMES TO ACCOUNT FOR PLUME PENETRATION OF ELEVATED  STABLE
    LAYER FOR UNSTABLE/NEUTRAL ATMOSPHERE &  BUOYANCY-DOMINATED PLUME.
267 PPF=0.
    IPPF=0
    ZIP=HMIX(ISCEN)-HP(I)
    HPEN  IS THE MINIMUM EFFECTIVE PLUME CENTERLINE HEIGHT  NECESSAY TO
    CONSIDER PENETRATION.
    HPEN=HP(I)+2.*ZIP/3.
    IF(ESH(2).LT.HPEN) GO TO 270

    ESTIMATE MAXIMUM PLUME RISE ASSUMING THAT THE MIXED  LAYER IS
    STABLY-STRATIFIED WITH THE SAME POT.TEMP.GRADIENT AS THAT IN THE
    ELEVATED STABLE LAYER.  THIS IS A SIMPLE, CONSERVATIVE APPROACH
    SINCE THE ACTUAL PLUME RISE WILL BE GREATER.
    S1=9.8*DTDZI(ISCEN)/TA(ISCEN)
    DELHP=2.6*(EFF*UINV/SI)**0.333333

    CALCULATE PLUME PENETRATION FRACTION (PPF) DEFINED AS  THE RATIO
    OF DEPTH OF PLUME ABOVE THE MIXING HEIGHT, (1.5*DELHP  - ZIP),
    TO THE  TOTAL  PLUME DEPTH,  (DELHP).
    PPF=1.5-ZIP/DELHP

    COMPLETE PENETRATION (PPF=1.): THE ENTIRE PLUME ESCAPES THE  MIXED
    LAYER.  IGNORE THIS SOURCE SINCE IT DOES  NOT CONTRIBUTE TO THE GLC
PMT07420
PMT07430
PMT07440
PMT07450
PMT07460
PMT07470
PMT07480
PMT07490
PMT07500
PMT07510
PMT07520
PMT07530
PMT07540
PMT07550
PMT07560
PMT07570
PMT07580
PMT07590
PMT07600
PMT07610
PMT07620
PMT07630
PMT07640
PMT07650
PMT07660
PMT07670
PMT07680
PMT07690
PMT07700
PMT07710
PMT07720
PMT07730
PMT07740
PMT07750
PMT07760
PMT07770
PMT07780
PMT07790
PMT07800
PMT07810
PMT07820
PMT07830
PMT07840
PMT07850
PMT07860
PMT07870
PMT07880
PMT07890
PMT07900
PMT07910
PMT07920
PMT07930
PMT07940
PMT07950
PMT07960
PMT07970
PMT07980
PMT07990
PMT08000
PMT08010
PMT08020
PMT08030
PMT08040
PMT08050
PMT08060
PMT08070
PMT08080
PMT08090
PMT08100
.PMT08110
                                      159

-------
c
c
c
c
c
c
c
    IF (PPF.GT.0.999) GO TO 268
    GO TO 269
268 IPPF=1
    PPF=1.
    Ql=0.
    IF(ISPEC.GT.l) 02=0.
    GO TO 270

    NO PENETRATION (PPF=0.): THE
                                     PMT08120
                                     PMT08130
                                     PMT08140
                                     PMT08150
                                     PMT08160
                                     PMT08170
                                     PMT08180
                                     PMT08190
ENTIRE PLUME REMAINS WITHIN THE MIXEDPMT08200
C
C
C

C
C
C
C
    LAYER. SET MAXIMUM EFFECTIVE STACK HEIGHT AS EQUAL TO HPEN.
269 IF(PPF.LT.0.001) PPF=0.

    PARTIAL PENETRATION (0. < PPF < 1.): CALCULATE THE NEW MAXIMUM
    EFFECTIVE STACK HEIGHT.  THIS IS THE HEIGHT OF CENTERLINE OF THE
    PLUME FRACTION REMAINING WITHIN THE MIXED LAYER.
    RATP=(1.-0.5*PPF)/(1.5-PPF)
    ESH(2)=HP(I)+ZIP*RATP
    DETERMINE DOWNWIND DISTANCE (PEAK) IN KILOMETERS WHERE THIS
    MAXIMUM HEIGHT OCCURS.
    PEAK=.001*((RATP*ZIP/(1.6*UINV))**1.5)/SQRT(EFF)
    REDEFINE THE SOURCE STRENGTH SO THAT ONLY (l.-PPF) FRACTION OF THEPMT08330
    PLUME MATERIAL REMAINING WITHIN MIXED LAYER CONTRIBUTES TO THE GLCPMT08340
                                     PMT08210
                                     PMT08220
                                     PMT08230
                                     PMT08240
                                     PMT08250
                                     PMT08260
                                     PMT08270
                                     PMT08280
                                     PMT08290
                                     PMT08300
                                     PMT08310
                                     PMT08320
C
C
C
C
C
C
275
    Q1=(1.-PPF)*Q1
    IF(ISPEC.EQ.l) GO TO 270
    Q2=(1.-PPF)*Q2

    PRINT CALCULATED PLUME RISE PARAMETERS.
270 IF(NPRINT.EQ.O) GO TO 271
    IF(NWDOPT.LE.1.OR.IWDOPT.LE.1) WRITE(IWR,1012)
   1 I,XPa),YP(I).Ql,Q2,HP(I),DPm,Vp7l),TP(I),PRL(l,IBUOY+l)
   2 PRL(2,IBUOY+i),DWL(IDWN),DWL(IDWN+I),UPL,ESH(2),PPF
271 IF(IPPKEQ.I) 66 TO 600
 SET LIMITS (XMIN,XMAX,YMIN,YMAX) ON PORTION OF RECEPTOR GRID
   EXAMINED FOR EACH SOURCE. THE EXTENT OF THIS PORTION DEPENDS
   ON SOURCE LOCATION, GRID DIMENSIONS, AND WIND DIRECTION.

    XMAX= XB2
    XMIN= XB1
    YMAX= YB2
    YMIN= YB1
    IFfXPfl +50.0.LT.XB2  XMAX= XP I  + 50.
    IFfXPfl -50.0.GT.XB1  XMIN= XP I  - 50.
    IF(YP(I +50.0.LT.YB2  YMAX= YP I  +50.
    IF(YP(I -50.0.GT.YB1  YMIN= YP I  - 50.
242
C

280
282
    DO 242 11=1,2
    FANGC=FLOAT(2*(I1-1)+1)*PI2
    DIF1=ABS(ABS(WDPANG)-FANGC)
    DIF2=ABS(ABS[WDMANG)-FANGC)
    IF(DIF1.LT..001) WDPANG=WDPANG+.001
    IFCDIF2.LT..001) WDMANG=WDMANG-.001
    CONTINUE

    GO TO (280,285,290,295,300,305,310,315),IFLAG
    IF(WDPANG.GT.3.14)GOT0282
    IF(WDMANG.LT.0)GOT0284
    YMIN=YP(I)
    XL1=XP(I)+(YB2-YP(I))/TAN(WDPANG)
    IF(XL1.GT.XMIN)XMIN=XLl
    IF(XL1.GT.XP(I))XMIN=XP(I)
    XL2=XP(I)+(YB2-YP(I))/TAN(WDMANG)
    IF(XL2.LT.XMAX)XMAX=XL2
    IF(XL2.LT.XP(I))XMAX=XP(I)
    GOT0320
    YMIN=YP(I)+(XB1-XP(I))*TAN(WDPANG)
    XMAX=XP(I)-K YB2-YP(I))/TAN(WDMANG)
    GOT0320
                                     PMT08350
                                     PMT08360
                                     PMT08370
                                     PMT08380
                                     PMT08390
                                     PMT08400
                                     PMT08410
                                     PMT08420
                                     PMT08430
                                     PMT08440
                                     PMT08450
                                     PMT08460
                                     PMT08470
                                     PMT08480
                                     PMT08490
                                     PMT08500
                                     PMT08510
                                     PMT08520
                                     .PMT08530
                                     PMT08540
                                     PMT08550
                                     PMT08560
                                     PMT08570
                                     PMT08580
                                     PMT08590
                                     PMT08600
                                     PMT08610
                                     PMT08620
                                     PMT08630
                                     PMT08640
                                     PMT08650
                                     PMT08660
                                     PMT08670
                                     PMT08680
                                     PMT08690
                                     PMT08700
                                     PMT08710
                                     PMT08720
                                     PMT08730
                                     PMT08740
                                     PMT08750
                                     PMT08760
                                     PMT08770
                                     PMT08780
                                     PMT08790
                                     PMT08800
                                     PMT08810
                                      160

-------
284


285
290
292


294


295
300
302


304


305
310
YMIN=YP(I}+(XB2-XP(I))*TAN(WDMANG)
XMIN=XP(I)+(YB2-YP(I))/TAN(WDPANG)
GOT0320
XL1=XP(I)+(YB2-YP(I))/TAN(WDPANG)
IF(XL1.GT.XMIN)XMIN=XL1
IF(XL1.GT.XP(I))XMIN=XP(I)
YL1=YP(I1+(XB2-XP(I))*TAN(WDMANG)
IF?YL1.GT.YMIN)YMIN=YL1
IF(YL1.GT.YP(I))YMIN=YP(I)
GOT0320
IF(WDPANG.GT.1.57.AND.WDMANG.LT.0.)GOT0292
IF(WDPANG.GT.6.28.AND.WDMANG.LT.4.712)GOT0294
XMIN=XP(I)
YL1=YP(I)+(XB2-XP(I))*TAN(WDMANG)
IF(YL1.GT.YMIN)YMIN=YL1
IF(YL1.GT.YP(I))YMIN=YP(I)
YL2=YP(I)+(XB2-XP(I))*TAN(WDPANG)
IF(YL2.LT.YMAX)YMAX=YL2
IF(YL2.LT.YP(I))YMAX=YP(I)
GOT0320
YMIN=YP(I)+(XB2-XP(I))*TAN(WDMANG)
XMIN=XP(I)-KYB2-YP(I;;/TAN(WDPANG)
GOT0320
XMIN=XP(I)+(YB1-YP(I))/TAN(WDMANG)
YMAX=YP(I)+(XB2-XP(I})*TAN(WDPANG)
GOT0320
XL1=XP(I) + (_YB1-YP(I))/TAN(WDMANG)
IF?XL1.GT.XMIN)XMIN=XL1
IF(XL1.GT.XP?I))XMIN=XP(I)
YL2=YP(I)+(XB2-XP(I))*TAN(WDPANG)
IF(YL2.LT.YMAX)YMAX=YL2
IF(YL2.LT.YP(I))YMAX=YP(I)
GOT0320
IF(WDPANG.GT.6.28)GOT0302
IF(WDMANG.LT.3.14)GOT0304
YMAX=YP(I)
XL1=XP(I)+(YB1-YP(I))/TAN(WDMANG)
IF(XL1.GT.XMIN)XMIN-XL1
IF(XL1.GT.XP(I))XMIN=XP(I)
XL2=XP(I)-(-(YBl-YP(I) )/TAN(WDPANG)
IF(XL2.LT.XMAX)XMAX=XL2
IF(XL2.LT.XP(I))XMAX=XP(I)
GOT0320
YMAX=YP(I)+(XB2-XP(I))*TAN(WDPANG)
XMIN=XP(I) + ( -~-
GOT0320
           -(YBI-YP(I))/TAN(WDMANG)
312
YMAX=YP(I)+(XB1-XP(I))*TAN(WDMANG)
XMAN=XP(I;+(YB1-YP(I;)/TAN(WDPANG)
GOT0320
YL2=YP(I)+(XB1-XP(I))*TAN(WDMANG)
IF(YL2.LT.YMAX)YMAX=YL2
IF(YL2.LT.YP(I))YMAX=YP(I)
XL2=XP(I)+(YB1-YP(I))/TAN(WDPANG)
IF(XL2.LT.XMAX)XMAX=XL2
IF(XL2.LT.XP(I))XMAX=XP(I)
GOT0320
IF(WDMANG.LT.1.57)GOT0312
IF(WDPANG.GT.4.712)GOT0314
XMAX=XP(I)
YL1=YP(I)+(XB1-XP(I))*TAN(WDPANG)
IF(YL1.GT.YMIN)YMIN=YL1
IF(YL1.GT.YP(I))YMIN=YP(I)
YL2=YP(I)+(XB1-XP(I))*TAN(WDMANG)
IF7YL2.LT.YMAX)YMAX=YL2
IFifY12.LT.YP(I))YMAX=YP(I)
GOT0320
XL2=XP(I) + CYB2-YP(I))/TAN(WDMANG)
IF?XL2.LT.XMAX)XMAX=XL2
IF(XL2.LT.XP(I))XMAX=XP(I)
YL1=YP(I)+(XB1-XP(I))*TAN(WDPANG)
 PMT08820
 PMT08830
 PMT08840
 PMT08850
 PMT08860
 PMT08870
 PMT08880
 PMT08890
 PMT08900
 PMT08910
 PMT08920
 PMT08930
 PMT08940
 PMT08950
 PMT08960
 PMT08970
 PMT08980
 PMT08990
 PMT09000
 PMT09010
 PMT09020
 PMT09030
 PMT09040
 PMT09050
 PMT09060
 PMT09070
 PMT09080
 PMT09090
 PMT09100
 PMT09110
 PMT09120
 PMT09130
 PMT09140
 PMT09150
 PMT09160
 PMT09170
 PMT09180
 PMT09190
 PMT09200
 PMT09210
 PMT09220
.PMT09230
 PMT09240
 PMT09250
 PMT09260
 PMT09270
 PMT09280
 PMT09290
 PMT09300
 PMT09310
 PMT09320
 PMT09330
 PMT09340
 PMT09350
 PMT09360
 PMT09370
 PMT09380
 PMT09390
 PMT09400
 PMT09410
 PMT09420
 PMT09430
 PMT09440
 PMT09450
 PMT09460
 PMT09470
 PMT09480
 PMT09490
 PMT09500
 PMT09510
                                      161

-------
314
315
320
   IF(YL1.GT.YMIN)YMIN=YL1
   IF(YL1.GT.YP(I))YMIN=YP(I)
   GOT0320
   XL2=XP(I)+(YB1-YP(I))/TAN(WDPANG)
   IF(XL2.LT.XMAX)XMAX=XL2
   IF(XL2.LT.XP(I))XMAX=XP(I)
   YL2=YP(I)+(XB1-XP(I))*TAN(WDMANG)
   IF(YL2.LT.YMAX)YMAX=YL2
   IF(YL2.LT.YP(I))YMAX=YP(I)
   GOT0320
   XL2=XP(I)+(YB2-YP(I))/TAN(WDMANG)
   IF(XL2.LT.XMAX)XMAX=XL2
   IF(XL2.LT.XP(I))XMAX=XP(I)
   YL1=YP(I1+(XB1-XP(I))*TAN(WDPANG)
   IF(YL1.GT.YMIN)YMIN=YL1
   IF(YL1.GT.YP(I))YMIN=YP(I)
   GOT0320
   IFCXMIN.GT.XB2.0R.XMAX.LT.XB1.0R.YMIN.GT.YB2.0R.YMAX.LT.YB1)
C
C
C
C
C
C
C
C
C
C
C
C
C

C
C
C
     1 GO TO 600
      IFfXMIN.LT.XBl
      IF(XMAX.GT.XB2
      IFCYMIN.LT.YBl
      IF(YMAX.GT.YB2
                   XMIN=XB1
                   XMAX=XB2
                   YMIN=YB1
                   YMAX=YB2
DETERMINE THE RANGE OF RECEPTOR GRID ROW AND COLUMN NUMBERS (LXMAX,
  LXMIN,LYMAX,LYMIN) CORRESPONDING TO XMAX, ETC. ABOVE -
      LXMAX=
      LXMIN=
      LYMAX=
      LYMIN=
          'XMAX-XSWC
           XMIN-XSWC
          (YMAX-YSWC
          ;YMIN-YSWC
/GRID
/GRID
/GRID
/GRID
+ 1.
+ 1.
+ 1.
+ 1.
   START LOOP ON ALL AFFECTED RECEPTORS.
   DO 500 IX=LXMIN,IXMAX
   XI=IX
   XG= XSWC + (XI-0.5)*GRID
   XD= XG - XP(I) + 0.00001
   XDSQ=XD*XD
   DO 500 JY=LYMIN,LYMAX
   YJ=JY
   YG= YSWC + (YJ-0.5)*GRID
   YD= YG - YP(I) + 0.00001
DSQ= SQUARE OF SOURCE-RECEPTOR DISTANCE. IF SOURCE-RECEPTOR DISTANCE
  IS GREATER THAN 50 KM., RECEPTOR IS SKIPPED.
   DSQ= XDSQ + YD*YD
   IF(DSQ.GT.2500.) GO TO 500
   DELTA= ATAN(XD/YD)
   IF(DELTA.LT.O.) DELTA = DELTA + 3.1415927
   IF(XD.LT.O.) DELTA = DELTA + 3.1415927
   DELTA= ABSHDELTA - WVEC)
   IF(DELTA.GT.3.1415927) DELTA= ABS(6.2831853 - DELTA)
   DIF1=ABS(DELTA-PI2)
   IF(DIF1.LT..001) DELTA=DELTA+.001
IF THE CROSSWIND ANGLE (DELTA) EXCEEDS A LIMITING VALUE WHICH
  DEPENDS ON STABILITY CLASS (ANGLIM), THE RECEPTOR IS SKIPPED.
    ANGLIM = 43.,43.,33.,25.,18., AND 18. DEGREES FOR 1-HOUR AVERAGE
    FOR STABILITY CLASSES A, B, C, D, E, ANDF RESPECTIVELY.

   IF(DELTA.GT.ANGLIM(ISC)) GO TO 500
DELTA IS THE ANGLE BETWEEN THE WIND VECTOR AND THE SOURCE-RECEPTOR
  DIRECTION.  THE DOWNWIND DISTANCE USED IN THE GAUSSIAN PLUME
  EQUATION IS=   DIST= SQRT(DSQ)*COS(DELTA).
   DIST=SQRT(DSQ)*COS(DELTA)
   IF(DIST.LT.0.002) GO TO 500
C
C
C  *** DETERMINE PROBABILITY DENSITIES OF VERTICAL DISTRIBUTIONS
C
C
   OF  SPECIES-1 AND SPECIES-2 POLLUTANT CONCENTRATIONS.

   IF(DIST.GT.D47) GO TO 330
PMT09520
PMT09530
PMT09540
PMT09550
PMT09560
PMT09570
PMT09580
PMT09590
PMT09600
PMT09610
PMT09620
PMT09630
PMT09640
PMT09650
PMT09660
PMT09670
PMT09680
PMT09690
PMT09700
PMT09710
PMT09720
PMT09730
PMT09740
PMT09750
PMT09760
PMT09770
PMT09780
PMT09790
PMT09800
PMT09810
PMT09820
PMT09830
PMT09840
PMT09850
PMT09860
PMT09870
PMT09880
PMT09890
PMT09900
PMT09910
PMT09920
.PMT09930
PMT09940
PMT09950
PMT09960
PMT09970
PMT09980
PMT09990
PMT10000
PMT10010
PMT10020
PMT10030
PMT10040
PMT10050
PMT10060
PMT10070
PMT10080
PMT10090
PMT10100
PMT10110
PMT10120
PMT10130
PMT10140
PMT10150
PMT10160
PMT10170
PMT10310
PMT10320
PMT10330
PMT10340
                                      162

-------
c
c
c
c
c
c
c
c
c
c
**** NEAR-SOURCE REGION (DIST .LE. D47).
    CALCULATE QZC1 AND QZC2 FROM QZCAL (MODULE M=l).
    ************
    CALL QZCAL
    ************
    GO TO 350

330 IF(DIST.LT.D80) GO TO 331
**** WELL-MIXED REGION (DIST .GE. D80).
    CALCULATE QZC1 AND QZC2 FROM QZCAL (MODULE M=2).
    ************
    CALL QZCAL
    ************
    GO TO 350

331 IF(KLID.EQ.l) GO TO 337
    CALCULATE QZC1 AND QZC2 FOR POLLUTANT SPECIES
    AT DIST=D47 AND DIST=D80 FOR USE IN INTERPOLATION
    IN PLUME-TRAPPING REGION.
    DUMX=DIST
    DIST=D47
    ************
    CALL QZCAL
    ************
    QZC11=QZC1
    IF(ISPEC.EQ.l) GO TO 332
    QZC21=QZC2

332 DIST=D80
    ************
    CALL QZCAL
    ************
    QZC12=QZC1
    IRC1=1
    IF(QZC11.EQ.O.OR.QZC12.EQ.O.) IRC1=0
    IF(ISPEC.EQ.l) GO TO 333
    QZC22=QZC2
    IRC2=1
    IF(QZC21.EQ.O.OR.QZC22.EQ.O.) IRC2=0

333 KLID=1
    DIST=DUMX
    IF(IRCl.EQ.O) GO TO 334
    DIFX1=ALOG(D80/D47)
    DIFC1=ALOG(QZC12/QZC11)
    GO TO 335
334 DIFC1=QZC12-QZC11
335 IF(ISPEC.EQ.l) GO TO 337
    IF(IRC2.EQ.Oj GO TO 336
    DIFX2=ALOG(D80/D47)
    DIFC2=ALOG(QZC22/QZC21)
    GO TO 337
336 DIFC2=QZC22-QZC21

**** PLUME-TRAPPING REGION (D47 < DIST < D80).
    CALCULATE QZC1 AND QZC2 BY LINEAR  INTERPOLATION
    (BETWEEN VALUES AT DIST=D47 AND DIST=D80) ON
    A LOG-LOG PLOT OF QZC VERSUS DOWNWIND DISTANCE.
    IF EITHER OF THE QZC VALUES AT D47 AND D80 ARE
    ZERO, USE A LINEAR PLOT FOR INTERPOLATION.
337 IF(IRCl.EQ.O) GO TO 338
    RATX1=ALOG(DIST/D47)/DIFX1
    QZC1L=ALOG(QZC11)+RATX1*DIFC1
    QZC1=EXP(QZC1L)
    GO TO 339
338 RATX1=(DIST-D47)/D8047
    QZC1=QZC11+RATX1*DIFC1
339 IF(ISPEC.EQ.l) GO TO 350

    IF(IRC2.EQ.O) GO TO 340
 PMT10350
 PMT10360
 PMT10370
 PMT10380
 PMT10390
 PMT10400
 PMT10410
 PMT10420
 PMT10430
 PMT10440
 PMT10450
 PMT10460
 PMT10470
 PMT10480
 PMT10490
 PMT10500
 PMT10510
 PMT10520
 PMT10530
 PMT10540
 PMT10550
 PMT10560
 PMT10570
 PMT10580
 PMT10590
 PMT10600
 PMT10610
 PMT10620
 PMT10630
 PMT10640
 PMT10650
 PMT10660
 PMT10670
 PMT10680
 PMT10690
 PMT10700
 PMT10710
 PMT10720
 PMT10730
 PMT10740
 PMT10750
.PMT10760
 PMT10770
 PMT10780
 PMT10790
 PMT10800
 PMT10810
 PMT10820
 PMT10830
 PMT10840
 PMT10850
 PMT10860
 PMT10870
 PMT10880
 PMT10890
 PMT10900
 PMT10910
 PMT10920
 PMT10930
 PMT10940
 PMT10950
 PMT10960
 PMT10970
 PMT10980
 PMT10990
 PMT11000
 PMT11010
 PMT11020
 PMT11030
 PMT11040
                                     163

-------
      RATX2=ALOG(DIST/D47)/DIFX2
      QZC2L=ALOG(QZC21)+RATX2*DIFC2
      QZC2=EXP(QZC2L)
      GO TO 350
  340 RATX2=(DIST-D47)/D8047
      QZC2=QZC21+RATX2*DIFC2
C
C *** DETERMINE PROBABILITY DENSITY OF CROSSWIND DISTRIBUTION
C     OF CONCENTRATIONS.
C
350   XM=DIST*1000.
      SIGY=AY(ISC)*XM/(SQRT(1.+.0004*XM))
C. CHECK FOR BID OPTION.  OMIT BID IF NBID=0.
      IF(NBID.EQ.O) GO TO 351
C. CONSIDER BOUYANCY INDUCED DISPERSION. DH IS SAME AS DELTAH.
      DH=HGT-HPRIME
      SIGB=DH/3.5
      SIGB=SIGB*SIGB
      SIGY=SQRT(SIGY*SIGY + SIGB)
351   YM=XM*TAN(DELTA)
      DUMY=YM/SIGY
      ARG=0.5*DUMY*DUMY
      IF(ARG.GE.EXPMIN) GO TO 500
      EXPA=EXP(-ARG)
      PYC=(A1B/SIGY)*EXPA
C
C
C
C
C     CALCULATE GROUND-LEVEL CONCENTRATIONS CONC (MICROGRAMS PER CUBIC
C     METER) AND SURFACE DEPOSITION FLUX SDF (MICROGRAMS PER SQUARE
C     METER PER HOUR) OF POLLUTANTS AT RECEPTOR IN COLUMN IX, ROW JY
C     OF THE RECEPTOR GRID DUE TO POINT SOURCE I.
C
C     ISPEC = 1 OR 2 OR 3
      C1=Q1*UINV*PYC*QZC1
      IF(NCSOPT.EQ.O) GO TO 355
      CALL WORST(IX,JY,C1,1)
C
  355 CINC1=C1*STCONV
      CONC(IX,JY.1)=CONC(IX,JY.1)+CINC1
      SDF(IX,JY,1)=SDF(IX,JY,1)+VD136*CINC1
      IF(ISPEC.EQ.l) GO TO 370
      IF(ISPEC.EQ.3) GO TO 360
C
C     ISPEC = 2
      C2=Q2*UINV*PYC*QZC2
      GO TO 363

      ISPEC = 3
  360 C2=Q1*UINV*PYC*QZC2
C
  363 IF(NCSOPT.EQ.O) GO TO 365
      CALL WORST(IX,JY,C2,2)
C
  365 CINC2=C2*STCONV
      CONC(IX,JY,2)=CONC(IX,JY,2)+CINC2
      SDF(IX,JY,2)=SDF(IX,JY,2)+VD236*CINC2
  370 CONTINUE
C
500   CONTINUE
      END LOOP ON ALL AFFECTED RECEPTORS.
C
C
C
C
600
C
C
C
C
C *** PRINT OUTPUT.
      CONTINUE
      END LOOP ON ALL POINT SOURCES.
 PMT11050
 PMT11060
 PMT11070
 PMT11080
 PMT11090
 PMT11100
 PMT11110
 PMT10180
 PMT10190
 PMT10200
 PMT10210
 PMT10220
 PMT10221
 PMT10222
 PMT10223
 PMT10224
 PMT10225
 PMT10225
 PMT10226
 PMT10230
 PMT10240
 PMT10250
 PMT10260
 PMT10270
 PMT10280
 PMT10290
 PMT10300
 PMT11120
 PMT11130
 PMT11140
 PMT11150
 PMT11160
 PMT11170
 PMT11180
 PMT11190
 PMT11200
 PMT11210
 PMT11220
 PMT11230
 PMT11240
 PMT11250
.PMT11260
 PMT11270
 PMT11280
 PMT11290
 PMT11300
 PMT11310
 PMT11320
 PMT11330
 PMT11340
 PMT11350
 PMT11360
 PMT11370
 PMT11380
 PMT11390
 PMT11400
 PMT11410
 PMT11420
 PMT11430
 PMT11440
 PMT11450
 PMT11460
 PMT11470
 PMT11480
 PMT11490
 PMT11500
 PMT11510
 PMT11520
 PMT11530
 PMT11540
                                     164

-------
c
c
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C
C
     OUTPUT AT END OF EACH AVERAGING-PERIOD.

     TIME AVERAGING:  NTOPT=2 OR 3
       IF NOT LAST SCENARIO, GO TO  100  FOR  THE  NEXT  SCENARIO.
       IF LAST SCENARIO, CALL OUTMOD TO PRINT OUTPUT FOR NLIST,  NTAPE,
         AND NARRAY OPTIONS, AND THEN CALL  MAXOUT  TO PRINT OUTPUT
         FOR NMAX.

     OUTPUT AT END OF EACH SCENARIO (OR SUB-SCENARIO)
     NO TIME AVERAGING: NTOPT=1
       AT END OF EACH SCENARIO  (OR  SUB-SCENARIO WHEN NWDOPT.GT.1),
         CALL OUTMOD TO PRINT OUTPUT FOR  NCSOPT, NLIST,  NTAPE,
         AND NARRAY OPTIONS.
       IF LAST SCENARIO (AND LAST SUB-SCENARIO  WHEN  NWDOPT.GT.1),
         CALL MAXOUT TO PRINT OUTPUT FOR  NMAX OPTION.
       IF NOT LAST SCENARIO, GO TO  100  FOR  THE  THE NEXT SCENARIO
         OR SUB-SCENARIO.

 603 IF(NTOPT.EQ.l) GO TO 620

     TIME AVERAGING: NTOPT=2 OR 3
     IF(ISCEN.NE.NSCEN) GO TO 100

     CALL OUTMOD
     ************
     GO TO 999

     NO TIME AVERAGING: NTOPT=1
     ************
 620 CALL OUTMOD
     ************
     IF(ISCEN.NE.NSCEN) GO TO 100
     IF(NWDOPT.LE.l) GO TO 999
     IF(IWDOPT.LT.4) GO TO 100

     ************
 999 IF(NMAX.GT.O) CALL MAXOUT
     ************

     CALL WAUDIT
     STOP


'1001 FORMAT(1H1.37X,'POLLUTION  EPISODIC MODEL  (PEM-2)'///4X,'OUTPUT:
 PMT11550
 PMT11560
 PMT11570
 PMT11580
 PMT11590
 PMT11600
 PMT11610
 PMT11620
 PMT11630
 PMT11640
 PMT11650
 PMT11660
 PMT11670
 PMT11680
 PMT11690
 PMT11700
 PMT11710
 PMT11720
 PMT11730
 PMT11740
 PMT11750
 PMT11760
 PMT11770
 PMT11780
 PMT11790
 PMT11800
 PMT11810
 PMT11820
 PMT11830
 PMT11840
 PMT11850
 PMT11860
 PMT11870
 PMT11880
 PMT11890
 PMT11900
 PMT11910
 PMT11920
 PMT11930

 PMT11940
.PMT11950
 PMT11960
'PMT11970
     1.20A4//4X.'SCENARIO'  12.4X,'POINT  SOURCE  PLUME  RISE CALCULATIONS'/PMT11980
                                                                         PMT11990
                                                                         PMT12000
                                                                         PMT12010
                                                                         PMT12020
                                                                        /PMT12030
                                                                         PMT12040
     JL. • i*\//iT/ / -TA ,  t-jv/oiuxiij-v • JL£* « -in. *  i \Jx.
     221X,'MIXING HEIGHT:  HMIX=',F7.2,'  M'/
     321X,'POTENTIAL TEMPERATURE GRADIENT ABOVE MIXING HEIGHT^',
     4F6.4,' DEG/M'/)
 1003 FORMAT(1IX,'SOURCE',6X,'EMISSION RATES',2X,'STACK'  4X,'EXIT'.
     15X,'EXIT'  4X 'EXIT',17X,'WIND SPEED AT',2X,'MAX.EFF.',6X,'PLUME
     2'  POINT',3x,'COORDINATES',3x,'poL-i'3x'POL-2'3x.'HEIGHT',
     3'  DIAMETER VELOCITY  TEMP.',5X,'DOMINANT',3X,'STACK HEIGHT  SOURCEPMT12050
     4 HT.   PENETRATION'/'  SOURCE X(KM)    Y(KM)  (G/S)   (G/S)',4X,      PMT12060
     5'(M)',6X,'(M)',4X,'(M/S)   (DEG K)',4X,'INFLUENCE',7X,'(M/S)',8X,  PMT12070
     6'(M)',7X,'FRACTION'/)                                              PMT12080
 1005 FORMAT(1H1.37X,'POLLUTION EPISODIC MODEL (PEM-2)'//4X,'OUTPUT:   '.PMT12090
     120A4//4X  'SCENARIO',12,4X'POINT SOURCE  PLUME  RISE  CALCULATIONS'/ PMT12100
     221X,'MIXING HEIGHT:  HMIX=',F7.2,'  M'/)                             PMT12110
 1007 FORMAT(14X,'SOURCE',8X.'EMISSION RATES',61X  'WIND SPEED AT',4X,   PMT12120
     1  'MAXIMUM',/'  POINT',6X,'COORDINATES',4X,'POL-1',6X,'POL-2',4X,   PMT12130
     2  'HEIGHT   DIAMETER  EXIT VEL  EXIT TEMP',6X,'DOMINANT',5X,         PMT12140
     ^  'STACK HEIGHT',4X.'EFFECTIVE'/'  SOURCE',3X,'X(KM)',4X,'Y(KM)'.3X.PMT12150
       '(G/S)'  6X,'(G/S)J,5X,'(M)',6X,'(M)',7X,'(M/S)',4X,'(DEG K)*,6X, PMT12160
       'INFLUENCE',8X,'(M/S)',6X,'SOURCE HEIGHT(M)'/)                   PMT12170
 1010 FORMAT(1X,I4.2X.F8.2,IX,F8.2.2X,F8.2,2X,F8.2,2X,F7.2,3X,F6.3,3X,  PMT12180
     1  F8.3,3X,F7.2,2X,2A4,1X,2A4,3X,F7.3.8X,F8.2)                       PMT12190
 1012 FORMAT(2X,I3,5(1X,F7.1),3(2X,F6.2),2(1X,2A4),2X,F6.2,              PMT12200
     1 5X,F8.2,8X,F5.3)                                                  PMT12210
      END                                                                PMT12220
1                                                                       PMT12230
     2
     3
     4
     5
                                      165

-------
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    SUBROUTINE QZCAL
                    SUBROUTINE QZCAL ,  PART OF PEM-2 (VERSION 84130).


 SUBROUTINE QZCAL CALCULATES QZC1 AND QZC2,  REPRESENTING THE
    PROBABLITY DENSITIES OF VERTICAL DISTRIBUTIONS OF CONCENTRATIONS
    OF POLLUTANT SPECIES 1 AND 2, RESPECTIVELY, AT A GIVEN
    DISTANCE DOWNWIND OF A POINT SOURCE.


*** PEM  ALGORITHMS AND PROGRAM DEVELOPMENT:  	DECEMBER 1982
*** PEM-2 MODIFICATIONS: DECEMBER 1983

    K. SHANKAR RAO, PHYSICAL SCIENTIST
    ATMOSPHERIC TURBULENCE AND DIFFUSION LABORATORY (ATDL)
    NATIONAL OCEANIC AND ATMOSPHERIC ADMINISTRATION (NOAA)
    U.S. DEPARTMENT OF COMMERCE, P.O. BOX - E
    OAK RIDGE, TENNESSEE 37831

    ( THIS WORK WAS DONE UNDER AN INTERAGENCY AGREEMENT
    BETWEEN THE ENVIRONMENTAL PROTECTION AGENCY AND THE
    NATIONAL OCEANIC AND ATMOSPHERIC ADMINISTRATION )
c
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c.
cr.
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COMMON/PEMCOM/CONC(50,50.2),SDF(50,50
 XP(300) , YP(300) ,EP(36o,2) ,HP(300) ,DP
                                 '
            ,        ,,  ,
   2 XA(50) YA(50),EA(50.2) SIZEfSO) '
   3 WD(24) ,WS(24) ,TA(24) ,HMIX(24) ,DTD
                        SCLABf
           ,       ,       ,
   4 AZC6) ,BZ(6) ,CZ(6) ,P(6) .
   5 XSWC,YSWC,GRID,LX,LY,A(2),B(2T,
                         , D47
                                        ZI(24)
                                               TT(20).
                                               ) , VP(300) ,TP(300) ,
                                               SECTAN(16) ,
                                              J2),CALNAM(7,2),
           ,,,,,
     6 ITA, IRD , IWR, IDSK, D80 , D47 ,08047 , D 1ST, DELTA, HPRIME ,
     7 ESH(2),PEAK,IBUOY,IRISE,IDWN,EFF,XS,UINV,WVEC,
     8 NAS , NPS , INDEX , IGRID , IAV , ISCEN, IWDOPT , IWD . ISC , IPS ,
     9 NTOPT , NWDOPT , NWSOPT , NWPOPT , NSCEN , NLIST , NARRAY , NTAPE , NCSOPT ,
     * NMAX,NSTDWN,NPRISE,NINPEN, INTER, NPRINT.NGPR.NB ID

      CONMON/PARM1/NPOL, VD1, Wl . VD2, W2
      COMMON/PARM1A/ICT , TAUC , GAMMA
      COMMON/PARM2/ISPEC,UTAUC,Q2Q1,XCT,EXCT
      COMMON/PARM3/HC , VDC1 , WC1 , VDC2 , WC2
      CONWON/PARM4/V11 , V21 , V12 , V22 , V13
      COMMON/PARM5/D11,D21,D12,D22,D31,D32,D33,D6
      CCfWON/PARM6/Rll, R21 , R12 , R22 , R13 , R23 , R31 , R41 , R32, R42
      COMMON/PARM7/QZC1 , QZC2 , HGT
      C01WON/BLOCK1/PI , SQPI , SQRT2.A1B , A1C
      COMMON/BLOCK2/ AI , B I , EPS ABS , EPSREL , LW , NIW
      COMMON/EXPCHK/EXPMAX , EXPMIN, ETAMAX
      EXTERNAL FUN1
      REAL*8 FUN1
      REAL*8 WORK(800).AI,BI,EPSABS, EPSREL, RESULT, ABSERR
      DIMENSION IW(102)
    IF(D1ST.GE.PEAK) GO TO 5
 TEST FOR GRADUAL PLUME RISE AND BID OPTIONS.
 IF DIST IS LESS THAN FINAL RISE, THEN USE GRAD. RISE IF BID SELECTED
 AND USE THE GRADUAL RISE HEIGHT FOR EFFECTIVE PLUME HEIGHT,
  OTHERWISE USE FINAL PLUME HEIGHT  (ESH(2)).

 OMIT CALL RISE. IF NGPR=1 (I.E. FINAL RISE) AND NBID=0 (I.E. NO BID)
    IF(NGPR.EQ.l.AND.NBID.EQ.O) GO  TO 5

 CALL SUBROUTINE RISE FOR EFFECTIVE SOURCE HEIGHT AT DOWNWIND
   DISTANCE = DIST, LESS THAN DISTANCE TO MAXIMUM HEIGHT (PEAK).
    ************
    CALL RISE
PMT12240

PMT12250
PMT12260
PMT12270
PMT12280
PMT12290
PMT12300
PMT12310
PMT12320
PMT12330
PMT12340
PMT12350
PMT12360
PMT12370
PMT12380
PMT12390
PMT12400
PMT12410
PMT12420
PMT12430
PMT12440
PMT12450
PMT12460
PMT12470
PMT12480
PMT12490
PMT12500
PMT12510
PMT12520
PMT12530
PMT12540
PMT12550
PMT12560
PMT12570
PMT12580
PMT12590
PMT12600
PMT12610
PMT12620
PMT12630
.PMT12640
PMT12650
PMT12660
PMT12670
PMT12680
PMT12690
PMT12700
PMT12710
PMT12720
PMT12730
PMT12740
PMT12750
PMT12760
PMT12770
PMT12780
PMT12790
PMT12800
PMT12801
PMT12802
PMT12803
PMT12804
PMT12805
PMT12806
PMT12807
PMT12810
PMT12820
PMT12830
PMT12840
PMT12850
                                      166

-------
c
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c.
c.
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    HGT= ESH(l)
    GO TO 6

 USE MAXIMUM EFFECTIVE SOURCE HEIGHT,  SINCE DOWNWIND DISTANCE
   EXCEEDS THE DISTANCE TO MAXIMUM HEIGHT.
5   HGT= ESH(2)


3   HL=HMIX(ISCEN)
    X=DIST
    XM=X*1000.
    SIGZ= AZ(ISC)*XM*(1.+CZ(ISC)*XM)/(SORT(1.+BZ(ISC)*XM))
 CHECK FOR BID OPTION. NBID=1 ,  BID ON
    IF(NBID.EQ.O)  GO TO 3
  CONSIDER BOUYANCY INDUCED DISPERSION (BID)
    DH=HGT-HPRIME
    SIGB=DH/3.5
    SIGB=SIGB*SIGB
    SIGZ=SQRT(SIGZ*SIGZ + SIGB)
    IF(SIGZ.GT.5000.) SIGZ=5000.
    SZ=SIGZ
    C2=SQRT2*SZ
    HC=HGT/C2
    IF(NGPR.EQ.l)  HC=ESH(2)/C2
    XC=XM/C2

    ISPEC = 1 OR 2 OR 3
    D31=2.*V11*XC
    D11=WC1*XC
    D21=D11*D11
    R31=1.+2.*D21
    R41=2.*D11/SQPI
    IF(ISPEC.EQ.l)  GO TO 9

    ISPEC = 2 OR 3
    D32=2.*V12*XC
    D12=WC2*XC
    D22=D12*D12
    R32=1.+2.*D22
    R42=2.*D12/SQPI
    IF(ISPEC.EQ.2)  GO TO 10

    ISPEC = 3
    D33=2.*V13*XC
    D6=4.*SQPI*(V21-V22)*XC

  9 TCC=UTAUC/C2
 10 IF(ICT.EQ.O) XCT=0.
    IF(ICT.EQ.l) XCT=XC/TCC
    EXCT=EXP(-XCT)

    TERM1=0.
    TERM2=0.
    TERM3=0.

    DUM1=D47+0.001
    DUM2=D80-0.001
    IF(X.LT.DUMl)  GO TO 100
    IF(X.GT.DUM2)  GO TO 200

 11 QZC1=0.0
    QZC2=0.0
    RETURN
**** NEAR-SOURCE REGION (X .LE. D47).

100 M=l
    A1=A1B/SZ
PMT12860
PMT12870
PMT12880
PMT12890
PMT12900
PMT12910
PMT12920
PMT12930
PMT12940
PMT12950
PMT12960
PMT12970
PMT12980
PMT12981
PMT12982
PMT12983
PMT12984
PMT12985
PMT12986
PMT12987
PMT12990
PMT13000
PMT13010
PMT13020
PMT13021
PMT13030
PMT13040
PMT13050
PMT13060
PMT13070
PMT13080
PMT13090
PMT13100
PMT13110
PMT13120
PMT13130
PMT13140
PMT13150
PMT13160
PMT13170
PMT13180
PMT13190
PMT13200
PMT13210
PMT13220
PMT13230
PMT13240
PMT13250
PMT13260
PMT13270
PMT13280
PMT13290
PMT13300
PMT13310
PMT13320
PMT13330
PMT13340
PMT13350
PMT13360
PMT13370
PMT13380
PMT13390
PMT13400
PMT13410
PMT13420
PMT13430
PMT13440
PMT13450
PMT13460
PMT13470
                                      167

-------
c
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    C3=HC*HC
    IF(C3.GE.EXPMIN)  GO TO 11
    A2=1./EXP(C3)

    ISPEC = 1 OR 2 OR 3
    SPECIES-1 (PRIMARY) POLLUTANT:  GAS OR PARTICLES.
    ETA1=HC+D3I
    ETA1SQ=ETA1*ETA1
    IF(ETAISQ.GT.EXPMAX) CALL ARGCHK(ETAI.ETAISQ)
    B11=EXP(ETA1SQ)*ERFC(ETA1)
    ALPHA1=A1C*D31*B11
    SUM=2.-ALPHA1
    IFfSUM) 115,115,116
115 G21P=0.0
    GO TO 120
116 IFfWCl.EQ.O.)  GO  TO 117
    BETAl=-2.*D11*HC+D21
    CALL EXPO(-BETAl.EBTl)
    GO TO 118
117 EBT1=1.0
118 G21P=EXCT*EBT1*A2*SUM
120 QZC1=A1*G21P
    IF(ISPEC.EQ.l) RETURN


    ISPEC = 2 OR 3
    SPECIES-2 (SECONDARY) POLLUTANT:  GAS OR PARTICLES.
    ETA2=HC+D32
    ETA2SQ=ETA2*ETA2
    IF(ETA2SQ.GT.EXPMAX) CALL ARGCHK(ETA2,ETA2SQ)
    B12=EXP(ETA2SQ)*ERFC(ETA2)
    ALPHA2=A1C*D32*B12
    SUM1=2.-ALPHA2
    IF(ISPEC.EQ.3) GO TO 145

    ISPEC = 2
    IF(SUMl) 135,135,140
135 G22P=0.0
    QZC2=0.0
    RETURN
140 IF(WC2.EQ.O.)  GO  TO 141
    BETA2=-2.*D12*HC+D22
    CALL EXPO(-BETA2,EBT2)
    GO TO 142
141 EBT2=1.0
142 G22P=EBT2*A2*SUM1
    QZC2=A1*G22P
    RETURN

    ISPEC = 3
145 TERM1=(Q2Q1+GAMMA)*A2*SUM1

    ETA3=HC+D33
    ETA3SQ=ETA3*ETA3
    IF(ETA3SQ.GT.EXPMAX) CALL ARGCHK(ETA3,ETA3SQ)
    B13=EXP(ETA3SQ)*ERFC(ETA3)
    ALPHA3=A1C*D33*B13
    TERM2=-GAMMA*EXCT*A2*(2.-ALPHAS)

    IF(V21.EQ.V22) GO TO 150
    COMPUTE  INTEGRAL  FUNC=F1(XC,0.;HC);  FUN1 IS THE INTEGRAND
    CALL DO1AJF(FUN1,AI,BI,EPSABS,EPSREL,RESULT,
   1   ABSERR.WORK.LW.IW.NIW.IFAIL)
    RES=RESULT
    FUNC=RES/PI
    TERM3=-GANWA*D6*FUNC

150 SUMT=TERM1+TERM2+TERM3
    IF(SUMT) 155,155,160
155 G22P=0.0
        PMT13480
        PMT13490
        PMT13500
        PMT13510
        PMT13520
        PMT13530
        PMT13540
        PMT13550
        PMT13560
        PMT13570
        PMT13580
        PMT13590
        PMT13600
        PMT13610
        PMT13620
        PMT13630
        PMT13640
        PMT13650
        PMT13660
        PMT13670
        PMT13680
        PMT13690
        PMT13700
        PMT13710
        PMT13720
        PMT13730
        PMT13740
        PMT13750
        PMT13760
        PMT13770
        PMT13780
        PMT13790
        PMT13800
        PMT13810
        PMT13820
        PMT13830
        PMT13840
        PMT13850
        PMT13860
        PMT13870
        PMT13880
        PMT13890
        PMT13900
        PMT13910
        PMT13920
        PMT13930
        PMT13940
        PMT13950
        PMT13960
        PMT13970
        PMT13980
        PMT13990
        PMT14000
        PMT14010
        PMT14020
        PMT14030
        PMT14040
        PMT14050
        PMT14060
        PMT14070
FUNCTIONPMT14080
        PMT14090
        PMT14100
        PMT14110
        PMT14120
        PMT14130
        PMT14140
        PMT14150
        PMT14160
        PMT14170
                                     168

-------
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      QZC2=0.0
      RETURN
  160 IFOVC2.EQ.0.1 GO TO 161
      BETA2=-2.*D12*HC+D22
      CALL EXPO(-BETA2,EBT2)
      GO TO 162
  161 EBT2=1.0
  162 G22P=EBT2*SUMT
      QZC2=A1*G22P
      RETURN
C
C
C

C
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**** WELL-MIXED REGION (X .GE. D80).

    IN THIS REGION, THE CONCENTRATION BELOW THE MIXING HEIGHT IS
    UNIFORM REGARDLESS OF THE SOURCE OR RECEPTOR HEIGHTS BECAUSE
    OF THOROUGH MIXING OF POLLUTANT BETWEEN THE GROUND AND THE
    MIXING HEIGHT.

200 M=2
    A1A=1000./HL
    CALL PSG4P(G41P,G42P)
    QZC1=A1A*G41P
    IF(ISPEC.EQ.l) RETURN
    QZC2=A1A*G42P
    RETURN
    END
    SUBROUTINE PSG4P(G41P,G42P)
                    SUBROUTINE PSG4P
PART OF PEM-2 (VERSION 84130),
    THIS SUBROUTINE CALCULATES AND RETURNS VALUES OF G41P AND G42P.
    THESE ARE NONDIMENSIONAL VERTICALLY-INTEGRATED PROBABILITY
    DENSITY FUNCTIONS USED IN THE WELL-MIXED REGION CONCENTRATION
    ALGORITHMS FOR SPECIES-1 AND SPECIES-2, RESPECTIVELY, DOWNWIND
    OF A POINT SOURCE.  THESE FUNCTIONS ARE INDEPENDENT OF BOTH
    SOURCE HEIGHT AND RECEPTOR HEIGHT.
*** PEM ALGORITHMS AND PROGRAM DEVELOPMENT: 	 DECEMBER 1982

    K. SHANKAR RAO, PHYSICAL SCIENTIST
    ATMOSPHERIC TURBULENCE AND DIFFUSION LABORATORY  (ATDL)
    NATIONAL OCEANIC AND ATMOSPHERIC ADMINISTRATION  (NOAA)
    U.S. DEPARTMENT OF COMMERCE, P.O. BOX - E
    OAK RIDGE, TENNESSEE 37831

    ( THIS WORK WAS DONE UNDER AN INTERAGENCY AGREEMENT
    BETWEEN THE ENVIRONMENTAL PROTECTION AGENCY AND  THE
    NATIONAL OCEANIC AND ATMOSPHERIC ADMINISTRATION  )
      EXTERNAL FUN2
      REAL*8 FUN2
      REAL*8 WORK(800).AI,BI,EPSABS,EPSREL,RESULT,ABSERR
      DIMENSION  IW(102l
      COMMON/PARM1A/ICT,TAUC,GAMMA
      COMMON/PARM2/ISPEC,UTAUC,Q2Q1.XCT,EXCT
      COMMON/PARM4/V11, V21, V12, V22, V13
      COMMON/PARM5/D11,D21,D12,D22,D31,D32,D33,D6
      COMMON/PARM6/R11,R21,R12,R22,R13,R23,R31,R41,R32,R42
      COMMON/BLOCK1/PI,SQPI,SQRT2,AlB,A1C
      COMMON/BLOCK2/AI,BI,EPSABS,EPSREL,LW,NIW
      COMMON/EXPCHK/EXPMAX,EXPMIN,ETAMAX
 PMT14180
 PMT14190
 PMT14200
 PMT14210
 PMT14220
 PMT14230
 PMT14240
 PMT14250
 PMT14260
 PMT14270
 PMT14280
 PMT14290
 PMT14300
 PMT14310
 PMT14320
 PMT14330
 PMT14340
 PMT14350
 PMT14360
 PMT14370
 PMT14380
 PMT14390
 PMT14400
 PMT14410
 PMT14420
 PMT14430
 PMT14440
 PMT14450
 PMT14460

 PMT14470
 PMT14480
 PMT14490
 PMT14500
 PMT14510
 PMT14520
 PMT14530
 PMT14540
 PMT14550
 PMT14560
 PMT14570
.PMT14580
 PMT14590
 PMT14600
 PMT14610
 PMT14620
 PMT14630
 PMT14640
 PMT14650
 PMT14660
 PMT14670
 PMT14680
 PMT14690
 PMT14700
 PMT14710
 PMT14720
 PMT14730
 PMT14740
 PMT14750
 PMT14760
 PMT14770
 PMT14780
 PMT14790
 PMT14800
 PMT14810
 PMT14820
 PMT14830
 PMT14840
 PMT14850
 PMT14860
                                      169

-------
                                      GAS OR PARTICLES.
C
C     ISPEC = 1 OR 2 OR 3
C***** SPECIES-1 (PRIMARY) POLLUTANT:
C
      IF(D21.GT.EXPMAX) CALL ARGCHK(D11,D21)
      B11=EXP(D21)*ERFC(D11)
      IF(V21.EQ.O.) GO TO 201
      D31SQ=D31*D31
      IF(D31SQ.GT.EXPMAX) CALL ARGCHK(D31,D31SQ)
      SUM=R11*£EXP(D31SQ)*ERFC(D31))-R21*B11
      GO TO 202
  201 SUM=R31*B11-R41
  202 IF(SUM.LT.O.) SUM=0.0
      G41P=EXCT*EXP(-D21)*SUM
      IF(ISPEC.EQ.l) RETURN
C
C     ISPEC = 2 OR 3
C***** SPECIES-2 (SECONDARY) POLLUTANT:  GAS OR PARTICLES.
C
      IF(D22,GT.EXPMAX) CALL ARGCHK(D12,D22)
      B12=EXP(D22)*ERFC(D12)
      IF(V22.EQ.O.) GO TO 203
      D32SQ=D32*D32
      IF(D32SQ.GT.EXPMAX) CALL ARGCHK(D32,D32SQ)
      SUM1=R12*(EXP(D32SQ)*ERFC(D32))-R22*B12
      GO TO 204
  203 SUM1=R32*B12-R42
  204 IF(ISPEC.EQ.3) GO TO 205
C
C
      ISPEC = 2
      IF(SUM1.LT.O.) SUM1=0.0
      G42P=EXP(-D22)*SUM1
      RETURN

      ISPEC = 3
  205 TERM1=(Q2Q1+GAMMA)*SUM1

      IF(V21.EQ.O.) GO TO 206
      D33SQ=D33*D33
      IF(D33SQ.GT.EXPMAX) CALL ARGCHK(D33,D33SQ)
      SUM2=R13*(EXP(D33SQ)*ERFC(D33))-R23*B12
      GO TO 207
  206 SUM2=R32*B12-R42
  207 TERM2=-GAMMA*EXCT*SUM2

      IF(V21,EQ.V22) GO TO 208
      COMPUTE INTEGRAL FUNC=F2(XC); FUN2 IS THE INTEGRAND FUNCTION.
      CALL D01AJF(FUN2,AI,BI,EPSABS.EPSREL,RESULT,
     1  ABSERR,WORK,LW,IW,NIW,IFAIL)
      RES=RESULT
      FUNC=RES/(2.*PI)
      TERM3=-GAMMA*D6*FUNC
      GO TO 209
  208 TERM3=0.0
C
C
C

C
C
C
C
C
C
  209 SUMT=TERM1+TERM2+TERM3
      IF(SUMT.LT.O.) SUMT=0.0
      G42P=EXP(-D22)*SUMT
      RETURN
      END
      DOUBLE PRECISION FUNCTION FUN1(T)
                  REAL*8 FUNCTION FUN1
      INTEGRAND FUNCTION USED IN THE NUMERICAL INTEGRATION
      QZCAL  (FOR POINT SOURCES) IS DEFINED HERE.
                               PMT14870
                               PMT14880
                               PMT14890
                               PMT14900
                               PMT14910
                               PMT14920
                               PMT14930
                               PMT14940
                               PMT14950
                               PMT14960
                               PMT14970
                               PMT14980
                               PMT14990
                               PMT15000
                               PMT15010
                               PMT15020
                               PMT15030
                               PMT15040
                               PMT15050
                               PMT15060
                               PMT15070
                               PMT15080
                               PMT15090
                               PMT15100
                               PMT15110
                               PMT15120
                               PMT15130
                               PMT15140
                               PMT15150
                               PMT15160
                               PMT15170
                               PMT15180
                               PMT15190
                               PMT15200
                               PMT15210
                               PMT15220
                               PMT15230
                               PMT15240
                               PMT15250
                               PMT15260
                               PMT15270
                              .PMT15280
                               PMT15290
                               PMT15300
                               PMT15310
                               PMT15320
                               PMT15330
                               PMT15340
                               PMT15350
                               PMT15360
                               PMT15370
                               PMT15380
                               PMT15390
                               PMT15400
                               PMT15410
                               PMT15420
                               PMT15430
                               PMT15440
                               PMT15450
                               PMT15460
                               PMT15470
                               PMT15480
                               PMT15490
PART OF PEM-2 (VERSION 84130). PMT15500
                               PMT15510
                               PMT15520
                  IN SUBROUTINEPMT15530
                               PMT15540
                               PMT15550
                                     170

-------
c
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   PEM-2 ALGORITHMS AND PROGRAM DEVELOPMENT:  DECEMBER 1982
   K.  SHANKAR RAO
   NOAA-ATDL,  P.O.  BOX-E
   OAK RIDGE,  TENN  37830


     FOR UNIVAC-1100
     REAL*8 T

   COMMON/PARM2/ISPEC,UTAUC,Q2Q1, XCT, EXCT
   COMMON/PARM3/HC,VDCl.WCl,VDC2.WC2
   COMMON/PARM5/D11,D21,D12,D22,D31,D32,D33,D6
   COMMON/BLOCKl/PI,SQPI,SQRT2,A1B,A1C
   COMMON/EXPCHK/EXPMAX,EXPMIN,ETAMAX


   SQT=SQRT(T)
   SQ1T=SQRT(1.-T)
   HC1=HC/SQT

   ARG1=(HC1*HC1)-KT*XCT)
   CALL EXPO(-ARGl.EXPl)
   IF(EXP1.EQ.O.) GO TO 10
   TERM1= EXP1/(SQT*SQ1T)

   ETA4=HC1+D33*SQT
   ETA4SQ=ETA4*ETA4
   IF(ETA4SQ.GT.EXPMAX) CALL ARGCHK(ETA4,ETA4SQ)
   TERM2A= EXP(ETA4SQ)*ERFC(ETA4)
   HC1SQ=HC1*HC1
   IF(HCISQ.GT.EXPMAX) CALL ARGCHK(HCl.HClSQ)
   TERM2=1.-SQPI*(ETA4-HC1)*TERM2A
   IF(TERM2.LE.O.)  GO TO 10

   ETA5=D32*SQ1T
   ETA5SQ=ETA5*ETA5
   IF(ETA5SQ.GT.EXPMAX) CALL ARGCHK(ETA5,ETA5SQ)
   TERM3=1.-SQPI*ETA5*(EXP(ETA5SQ)*ERFC(ETAS))
   IF(TERM3.LE.O.)  GO TO 10

   FUN1=TERM1*TERM2*TERM3
   GO TO 11
10 FUN1=0.0
11 RETURN
   END
   DOUBLE PRECISION FUNCTION FUNIA(T)
              REAL*8 FUNCTION FUN1A , PART OF PEM-2 (VERSION 84130)


   INTEGRAND FUNCTION USED IN THE NUMERICAL INTEGRATION FOR AREA
   SOURCES (POLLUTANT SPECIES-2) IN FUNCTION FUN4 IS DEFINED HERE.


   PEM-2 ALGORITHMS AND PROGRAM DEVELOPMENT: DECEMBER 1983
   K. SHANKAR RAO, NOAA-ATDL, OAK RIDGE, TENN.

   FOR UNIVAC-1100
   REAL*8 T

   COMMON/BLOCKl/PI.SQPI,SQRT2,AlB,AlC
   COMMON/CLOCK1/ET2,ET3,HCA,XCAT
   COMMON/EXPCHK/EXPMAX,EXPMIN,ETAMAX


   SQT=SQRT(T)
   SQ1T=SQRT(I.-T)
PMT15560
PMT15570
PMT15580
PMT15590
PMT15600
PMT15610
PMT15620
PMT15630
PMT15640
PMT15650
PMT15660
PMT15670
PMT15680
PMT15690
PMT15700
PMT15710
PMT15720
PMT15730
PMT15740
PMT15750
PMT15760
PMT15770
PMT15780
PMT15790
PMT15800
PMT15810
PMT15820
PMT15830
PMT15840
PMT15850
PMT15860
PMT15870
PMT15880
PMT15890
PMT15900
PMT15910
PMT15920
PMT15930
PMT15940
PMT15950
PMT15960
PMT15970
PMT15980
PMT15990
PMT16000
PMT16010

PMT16020
PMT16030
PMT16040
PMT16050
PMT16060
PMT16070
PMT16080
PMT16090
PMT16100
PMT16110
PMT16120
PMT16130
PMT16140
PMT16150
PMT16160
PMT16170
PMT16180
PMT16190
PMT16200
PMT16210
PMT16220
PMT16230
PMT16240
                                      171

-------
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      HC1=HCA/SQT
      D33SQT=ET3*SQT

      ARG1=HC1*HC1+XCAT*T
      CALL EXPO(-ARG1,EXP1)
      TERM1=EXP1/(SQT*SQ1T)
      IF(TEEM1.LE.O.) GO TO 10

      ETA4=HC1+D33SQT
      ETA4SQ=ETA4*ETA4
      IF(ETA4SQ.GT.EXPMAX)  CALL ARGCHK(ETA4,ETA4SQ)
      TERM2=1.-SQPI*D33SQT*EXP(ETA4SQ)*ERFC(ETA4)
      IF(TEHM2.LE.O.) GO TO 10

      ETA5=ET2*SQ1T
      ETA5SQ=ETA5*ETA5
      IF(ETA5SQ.GT.EXPMAX)  CALL ARGCHK(ETA5,ETA5SQ)
      TERM3=1.-SQPI*ETA5*EXP(ETA5SQ)*ERFC(ETA5)
      IF(TERM3.LE.O.) GO TO 10

      FUN1A=TERM1*TERM2*TERM3
      GO TO 20
   10 FUN1A=0.
   20 RETURN
      END
DOUBLE PRECISION FUNCTION FUN2(T)
            REAL*8 FUNCTION FUN2
PART OF PEM-2 (VERSION 84130),
INTEGRAND FUNCTION USED IN THE NUMERICAL INTEGRATION FOR POINT
SOURCES (POLLUTANT SPECIES-2) IN SUBROUTINE PSG4P IS DEFINED HERE


PEM ALGORITHMS AND PROGRAM DEVELOPMENT: DECEMBER 1982
K. SHANKAR RAO
NOAA-ATDL, P.O. BOX-E
OAK RIDGE, TENN 37830


FOR UNIVAC-1100
REAL*8 T

C01WON/PARM2/ISPEC,UTAUC, Q2Q1, XCT, EXCT
COMMON/PARM4/V11.V21,V12,V22.V13
COMVION/PARM5/D11, D21, D12, D22, D31, D32, D33, D6
COMMON/PARM6/R11,R21,R12,R22,R13,R23,R31,R41,R32,R42
COMMON/BLOCKl/PI.SQPI, SQRT2, A1B, AlC
COWMON/EXPCHK/EXPMAX,EXPMIN,ETAMAX


SQT=SQRT(T)
SQ1T=SQRT(1.-T)
ETA4=D33*SQT
ETA5=D32*SQ1T
ETA6=D12*SQ1T
ETA6SQ=ETA6*ETA6
IF(ETA6SQ.GT.EXPMAX) CALL ARGCHK(ETA6,ETA6SQ)

ARG1=T*XCT
EXP1=EXP(-ARG1)
TERM1=EXP1/SQT

ETA4SQ=ETA4*ETA4
IF(ETA4SQ.GT.EXPMAX) CALL ARGCHK(ETA4,ETA4SQ)
TERM2=1.-SQPI*ETA4*(EXP(ETA4SQ)*ERFC(ETA4))
IF(TERM2.LE.O.) GO TO 15
PMT16250
PMT16260
PMT16270
PMT16280
PMT16290
PMT16300
PMT16310
PMT16320
PMT16330
PMT16340
PMT16350
PMT16360
PMT16370
PMT16380
PMT16390
PMT16400
PMT16410
PMT16420
PMT16430
PMT16440
PMT16450
PMT16460
PMT16470
PMT16480
PMT16490

PMT16500
PMT16510
PMT16520
PMT16530
PMT16540
PMT16550
PMT16560
.PMT16570
PMT16580
PMT16590
PMT16600
PMT16610
PMT16620
PMT16630
PMT16640
PMT16650
PMT16660
PMT16670
PMT16680
PMT16690
PMT16700
PMT16710
PMT16720
PMT16730
PMT16740
PMT16750
PMT16760
PMT16770
PMT16780
PMT16790
PMT16800
PMT16810
PMT16820
PMT16830
PMT16840
PMT16850
PMT16860
PMT16870
PMT16880
PMT16890
PMT16900
PMT16910
PMT16920
PMT16930
                                     172

-------
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   11 IF(V22.EQ.O.) GO TO 12
      ETA5SQ=ETA5*ETA5
      IF(ETA5SQ.GT.EXPMAX) CALL ARGCHK(ETA5,ETA5SQ)
      T3A=EXP(ETA5SQ)*ERFC(ETAS)
      T3B=EXP(ETA6SQ) *ERFC (E-TA6)
      TERM3=RI2*T3A-R22*T3B
      IF(TERM3.LE.O.) GO TO 15
      GO TO 13

   12 T3A=(1.+2.*ETA6SQ)*(EXP(ETA6SQ)*ERFC(ETA6))
      T3B=2.*ETA6/SQPI
      TERM3=T3A-T3B
      IF(TERM3.LE.O.) GO TO 15

   13 FUN2=TERM1*TERM2*TERM3
      GO TO 16
   15 FUN2=0.
   16 RETURN
      END
DOUBLE PRECISION FUNCTION FUN3(XA)
            REAL*8 FUNCTION FUNS  , PART OF PEM-2 (VERSION 84130)


INTEGRAND FUNCTION USED IN THE NUMERICAL INTEGRATION FOR AREA
SOURCES (POLLUTANT SPECIES-1) IN MAIN PROGRAM IS DEFINED HERE.


PEM-2 ALGORITHMS AND PROGRAM DEVELOPMENT: DECEMBER 1983
K. SHANKAR RAO
NOAA-ATDL, P.O. BOX - E
OAK RIDGE, TENN 37830


FOR UNIVAC-1100
REAL*8 XA
      COMMON/PARM1A/ICT,TAUC,GAMMA
      COMMON/PARM2/ISPEC.UTAUC,Q2Q1,XCT,EXCT
      COMMON/PARM2A/HAS,KSC,AA,BA,CA
      COMMON/PARM3/HC.VDC1,WC1,VDC2.WC2
      COMMON/PARM4/V11,V21,V12,V22,V13
      COMMON/BLOCKl/PI.SQPI,SQRT2,AlB,AlC
      COMMON/EXPCHK/EXPMAX,EXPMIN,ETAMAX
      SIGZ=AA*XA*(1.+CA*XA)/SQRT(1.+BA*XA)
      C2=SQRT2*SIGZ
      XCA=XA/C2
      HCA=HAS/C2
      D31=2.*V11*XCA

      ETA1=HCA+D31
      ETA1SQ=ETA1*ETA1
      IF(ETA1SQ.GT.EXPMAX) CALL ARGCHK(ETA1,ETA1SQ)
      TERM1=1.-SQPI*D31*EXP(ETA1SQ)*ERFC(ETA1)
      IF(TERM1.LE.O.) GO TO 25

      BETA1=HCA-WC1*XCA
      ARG1=BETA1*BETA1
      IF(ISPEC.EQ.2) GO TO 20
      IF(ISPEC.EQ.l.AND.ICT.EQ.O) GO TO 20
      IF(UTAUC.GT.0.) ARG1=ARGH-XA/UTAUC
   20 CALL EXPO(-ARG1,EXP1)

      FUN3=EXP1*TERM1/SIGZ
      GO TO 30
   25 FUN3=0.
PMT16940
PMT16950
PMT16960
PMT16970
PMT16980
PMT16990
PMT17000
PMT17010
PMT17020
PMT17030
PMT17040
PMT17050
PMT17060
PMT17070
PMT17080
PMT17090
PMT17100
PMT17110
PMT17120

PMT17130
PMT17140
PMT17150
PMT17160
PMT17170
PMT17180
PMT17190
PMT17200
PMT17210
PMT17220
PMT17230
PMT17240
PMT17250
PMT17260
PMT17270
PMT17280
PMT17290
PMT17300
PMT17310
PMT17320
PMT17330
PMT17340
PMT17350
PMT17360
PMT17370
PMT17380
PMT17390
PMT17400
PMT17410
PMT17420
PMT17430
PMT17440
PMT17450
PMT17460
PMT17470
PMT17480
PMT17490
PMT17500
PMT17510
PMT17520
PMT17530
PMT17540
PMT17550
PMT17560
PMT17570
PMT17580
PMT17590
PMT17600
PMT17610
PMT17620
                                     173

-------
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   30 RETURN
      END
   DOUBLE  PRECISION FUNCTION FUN4(XA)
               REAL*8 FUNCTION FUN4  ,  PART  OF  PEM-2  (VERSION 84130).


   INTEGRAND  FUNCTION USED  IN THE  NUMERICAL INTEGRATION FOR AREA
   SOURCES (POLLUTANT SPECIES-2) IN  THE MAIN PROGRAM IS DEFINED HERE
   THIS FUNCTION CONSISTS ONLY OF  THE  CHEMICAL TRANSFORMATION
   CONTRIBUTION TO THE SPECIES-2 CONCENTRATION BUDGET.


   PEM-2 ALGORITHMS AND PROGRAM DEVELOPMENT: DECEMBER 1983
   K.  SHANKAR RAO
   NOAA-ATDL,  P.O.BOX-E
   OAK RIDGE,  TENN 37830


   REAL*8  WORK(800),AI,BI,EPSABS,EPSREL,RESULT,ABSERR
   EXTERNAL FUN1A
   REAL*8  FUN1A
   FOR UNIVAC-1100
   REAL*8  XA

   DIMENSION  IW(102)
   COMMON/PARM2/ISPEC,UTAUC,Q2Q1,XCT,EXCT
   COMMON/PARM2A/HAS,KSC,AA,BA.CA
   COMMON/PARM3/HC,VDC1,WC1,VDC2,WC2
   COMMON/PARM4/V11,V21,V12,V22,V13
   COMMON/BLOCK1/PI,SQPI,SQRT2,A1B,A1C
   COMMON/BLOCK2/AI.BI,EPSABS.EPSREL,LW,NIW
   COMMON/CLOCK1/ET2,ET3,HCA,XCAT
   COMMON/EXPCHK/EXPMAX,EXPMIN,ETAMAX

   SIGZ=AA*XA*(1.+CA*XA)/SORT(1.+BA*XA)
   C2=SQRT2*SIGZ
   XCA=XA/C2
   HCA=HAS/C2
   D32=2.*V12*XCA
   D33=2.*V13*XCA

   ETA2=HCA+D32
   ETA2SQ=ETA2*ETA2
   IF(ETA2SQ.GT.EXPMAX) CALL ARGCHK(ETA2,ETA2SQ)
   TERM1=1.-SQPI*D32*EXP(ETA2SQ)*ERFC(ETA2)
   IF(TERM1.LE.O.) GO TO 30
      ETA3=HCA+D33
      ETA3SQ=ETA3*ETA3
      IF(ETA3SQ.GT.EXPMAX)
      TERM2A=1.-SQPI*D33*EXP(]
      IF(TERM2A.LE.O.) TERM2A=0.
      XCAT=XA/UTAUC
      TERM2=EXP(-XCAT)*TERM2A
                        CALL ARGCHK(ETA3,ETA3SQ)
                          ETA3SQ)*ERFC(ETA3)
   IF(V21.EQ.V22)  GO TO 20
   TERM3A=SQPI*2.*(V21-V22)*XCA
   ET2=D32
   ET3=D33
   COMPUTE INTEGRAL FIA(AI.BI);  FUN1A IS THE EXTERNALLY DEFINED
   INTEGRAND FUNCTION.
   CALL D01AJF(FUN1A,AI,BI,EPSABS.EPSREL,RESULT,
  1   ABSERR,WORK,LW,IW,NIW,IFAIL)
   TERM3=TERM3A*RESULT/PI
   GO TO 25
20 TERM3=0.
 PMT17630
 PMT17640

 PMT17650
 PMT17660
 PMT17670
 PMT17680
 PMT17690
 PMT17700
 PMT17710
.PMT17720
 PMT17730
 PMT17740
 PMT17750
 PMT17760
 PMT17770
 PMT17780
 PMT17790
 PMT17800
 PMT17810
 PMT17820
 PMT17830
 PMT17840
 PMT17850
 PMT17860
 PMT17870
 PMT17880
 PMT17890
 PMT17900
 PMT17910
 PMT17920
 PMT17930
 PMT17940
 PMT17950
 PMT17960
 PMT17970
 PMT17980
 PMT17990
 PMT18000
 PMT18010
 PMT18020
.PMT18030
 PMT18040
 PMT18050
 PMT18060
 PMT18070
 PMT18080
 PMT18090
 PMT18100
 PMT18110
 PMT18120
 PMT18130
 PMT18140
 PMT18150
 PMT18160
 PMT18170
 PMT18180
 PMT18190
 PMT18200
 PMT18210
 PMT18220
 PMT18230
 PMT18240
 PMT18250
 PMT18260
 PMT18270
 PMT18280
 PMT18290
 PMT18300
 PMT18310
                                     174

-------
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   25 BETA2=HCA-WC2*XCA
      B2SQ=BETA2*BETA2
      CALL EXPO(-B2SQ,EB2SQ)
      B3SQ=B2SQ-HCA*HCA
      CALL EXPO(-B3SQ,EB3SQ)
      FUN4=(EB2SQ*(TERM1-TERM2)-EB3SQ*TERM3)/SIGZ
      GO TO 35
   30 FUN4=0.
   35 RETURN
      END
   DOUBLE PRECISION FUNCTION FUN5(XA)
               REAL*8 FUNCTION FUN5 ,  PART OF PEM-2 (VERSION 84130).
   INTEGRAND FUNCTION USED IN THE NUMERICAL INTEGRATION FOR AREA
   SOURCES (POLLUTANT SPECIES-2)  IN THE MAIN PROGRAM IS DEFINED HERE
   THIS FUNCTION CONSISTS ONLY OF THE CONTRIBUTION OF THE DIRECT
   EMISSION OF SPECIES-2 TO THE CONCENTRATION BUDGET.
   PEM-2 ALGORITHMS AND PROGRAM DEVELOPMENT:
   K.  SHANKAR RAO
   NOAA-ATDL, P.O.  BOX-E
   OAK RIDGE, TENN 37830
FEBRUARY 1984
   FOR UNIVAC-1100
     REAL*8 XA

   COMMON/PARM2A/HAS,KSC,AA,BA,CA
   COMMON/PARM3/HC.VDC1,WC1,VDC2,WC2
   COMMON/PARM4/V11,V21,V12,V22,V13
   COMMON/BLOCK1/PI,SQPI,SQRT2,A1B,A1C
   COMMON/EXPCHK/EXPMAX,EXPMIN,ETAMAX

   SIGZ=AA*XA*(1.+CA*XA)/SORT(1.+BA*XA)
   C2=SQRT2*SIGZ
   XCA=XA/C2
   HCA=HAS/C2
   D32=2.*V12*XCA

   ETA2=HCA+D32
   ETA2SQ=ETA2*ETA2
   IF(ETA2SQ.GT.EXPMAX) CALL ARGCHK(ETA2,ETA2SQ)
   TERM1=1.-SQPI*D32*EXP(ETA2SQ)*ERFC(ETA2)
.   IF(TEHM1.LE.O.) GO TO 10

   BETA2=HCA-WC2*XCA
   B2SQ=BETA2*BETA2
   CALL EXPO(-B2SQ,EB2SQ)
   FUN5=EB2SQ*TERM1/SIGZ
   GO TO 20
10 FUN5=0.
20 RETURN
   END

   SUBROUTINE EXPO(BX.EX)


                    SUBROUTINE EXPO , PART OF PEM-2 (VERSION 84130)


   GIVEN THE ARGUMENT BX,  SUBROUTINE EXPO CALCULATES AND
   RETURNS EX=EXP(BX).  EXPO LIMITS THE ARGUMENT TO AVOID
   OVERFLOW/UNDERFLOW ERRORS.
 PMT18320
 PMT18330
 PMT18340
 PMT18350
 PMT18360
 PMT18370
 PMT18380
 PMT18390
 PMT18400
 PMT18410

 PMT18420
 PMT18430
 PMT18440
 PMT18450
 PMT18460
 PMT18470
 PMT18480
 PMT18490
.PMT18500
 PMT18510
 PMT18520
 PMT18530
 PMT18540
 PMT18550
 PMT18560
 PMT18570
 PMT18580
 PMT18590
 PMT18600
 PMT18610
 PMT18620
 PMT18630
 PMT18640
 PMT18650
 PMT18660
 PMT18670
 PMT18680
 PMT18690
 PMT18700
 PMT18710
.PMT18720
 PMT18730
 PMT18740
 PMT18750
 PMT18760
 PMT18770
 PMT18780
 PMT18790
 PMT18800
 PMT18810
 PMT18820
 PMT18830
 PMT18840
 PMT18850
 PMT18860
 PMT18870
 PMT18880
 PMT18890

 PMT18920
 PMT18900
 PMT18910
 PMT18930
 PMT18940
 PMT18950
 PMT18960
 PMT18970
 PMT18980
 PMT18990
                                      175

-------
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    PEM ALGORITHMS  AND  PROGRAM DEVELOPMENT:  DECEMBER 1982
    K.  SHANKAR RAO
    NOAA-ATDL,  P.O.  BOX-E
    OAK RIDGE,  TENN 37831
    COMMON/EXPCHK/EXPMAX,EXPMIN,ETAMAX


    BXABS=ABS(BX)
    IF(BX)  5,10,15
  5 IF(BXABS-EXPMIN)  6,7,7
  6 EX=EXP(BX)
    GO TO 20
  7 EX=0.
    GO TO 20
 10 EX=1.
    GO TO 20
 15 IF(BXABS.GT.EXPMAX)  BXABS=EXPMAX
    EX=EXP(BXABS)
 20 RETURN
    END
    SUBROUTINE ARGCHK(E,ESQ)
                   SUBROUTINE ARGCHK ,  PART OF PEM-2 (VERSION 84130),


    SUBROUTINE ARGCHK LIMITS  THE ARGUMENTS OF EXP(ESQ)*ERFC(E)
    TO AVOID OVERFLOW/UNDERFLOW ERRORS.
    PEM ALGORITHMS AND PROGRAM DEVELOPMENT:
    K.  SHANKAR RAO
    NOAA-ATDL,  P.O.  BOX-E
    OAK RIDGE,  TENN 37831
    COMMON/EXPCHK/EXPMAX,EXPMIN,ETAMAX
      ESQ=EXPMAX
      IFfE.LT.O.) NSIGN=-1
      IFfE.GE.O.) NSIGN=1
      E=NSIGN*ETAMAX
      RETURN
      END
      DECEMBER 1982
    SUBROUTINE INMOD
                   SUBROUTINE INMOD
PART OF PEM-2 (VERSION 84130)
 SUBROUTINE INMOD READS IN ALL INPUTS TO THE MODEL,  SCREENS THEM,
   PRINTS WARNING MESSAGES, AND INSERTS DEFAULT VALUES AS NEEDED.
   THE SUBROUTINE PRINTS OUT LISTS OF THE CONTROL PARAMETERS,
   SCENARIO PARAMETERS, AND SOURCE DATA FOR REFERENCE.
   INMOD ALSO PROCESSES THE INPUT FOR EACH SCENARIO BEFORE
   TRANSMITTING IT TO THE MAIN PROGRAM.


*** PEM MODIFICATIONS AND FORMATS BY M.M. STEVENS,
    NOAA-ATDL, P.O.  BOX-E, OAK RIDGE, TENN 37831
    DECEMBER 1982
*** PEM-2 MODIFICATIONS AND FORMATS BY K. SHANKAR RAO,
    APRIL 1984
PMT19000
PMT19010
PMT19020
PMT19030
PMT19040
PMT19050
PMT19060
PMT19070
PMT19080
PMT19090
PMT19100
PMT19110
PMT19120
PMT19130
PMT19140
PMT19150
PMT19160
PMT19170
PMT19180
PMT19190
PMT19200
PMT19210
PMT19220

PMT19230
PMT19240
PMT19250
PMT19260
PMT19270
PMT19280
PMT19290
PMT19300
PMT19310
PMT19320
PMT19330
PMT19340
PMT19350
PMT19360
PMT19370
PMT19380
PMT19390
.PMT19400
PMT19410
PMT19420
PMT19430
PMT19440
PMT19450
PMT19460
PMT19470

PMT19480
PMT19490
PMT19500
PMT19510
PMT19520
PMT19530
PMT19540
PMT19550
PMT19560
PMT19570
PMT19580
PMT19590
PMT19600
PMT19610
PMT19620
PMT19630
PMT19640
PMT19650
PMT19660
PMT19670
                                     176

-------
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COWMON/PEMCOM/CONC(50,50,2) ,SDFf50,50, 2) . TT(20) .
1 XPf300),YP(300).EP?300,2),HP(300),DP(300),VPC300)>TP(300),
2 XA(50),YA(50),EA(50.2),SIZE(50),
3 WDC24) ,WS(24) ,TA(24) .HMIX(24) ,DTDZI(24) ,
4 AZ(6),BZ(6),CZ(6),P(6),SCLAB(6),DTDZ(2),SECTAN(16),
5 XSWC,YSWC.GRID,LX,LY,Af2),B(2),POLNAM(3,2).CALNAM(7,2),
6 ITA,IRD,IWR,IDSK,D80,D47,D8047,DIST, DELTA, HPRIME,
7 ESH(2J,PEAK, IBUOY, IRISE, IDWN.EFF.XS.UINV, WVEC,
8 NAS.NPS, INDEX, IGRID, IAV, ISCEN, IWDOPT, IWD, ISC, IPS,
9 NTOPT, NWDOPT, NWSOPT, NWPOPT, NSCEN, NLIST, NARRAY, NTAPE, NCSOPT,
* NMAX,NSTDWN,NPRISE,NINPEN, INTER, NPRINT, NGPR, NBID

COMMON/CSWOR/NWORS T ( 25 , 25 , 5 , 2 ) , CWORST ( 25 , 25 , 5 , 2 )
COMMON/PARM1/NPOL, VD1.W1. VD2.W2
COMMON/PARM1A/ICT, TAUC, GAMMA
COMMON/PARM2A/HAS ,KSC. AA, BA, CA
COMMON/PARM7A/HA , PI ( 6 )
COMMON/WND/HMIN, HMAX, UMIN, IUFLG

DIMENSION NAME(2),WDINC(6),SUMAQ(2),SUMPQ(2),SUMAR(2),EAR(2),
1 CWS(6)
DIMENSION DCRC24. 2) , NSC(24) , NWD(24) , NWS (24) , ASCALE(2)
DIMENSION XX (100)
DATA NAME/4H ,4H /
DATA WD INC/1. 5707963, 0.7853982, 0.5235988, 0.2617994,
1 0. 1745329. 0.08726646/
DATA CWS/1.5,2.46,4.47.6.93,9.61,12.52/
DATA HMIN/10./,HMAX/200./,UMIN/1. /.HA/IO./

IF(INDEX.NE.O) GO TO 300

ISTOP=0

READ ALL INPUT DATA.

**** READ FIRST CONTROL PARAMETER CARD (TITLE).

READ(IRD,800)TT
WRITE(IWR,900) TT

**** READ SECOND CONTROL PARAMETER CARD (OPTIONS).

NTOPT = AVERAGING TIME OPTION (1 OR 2 OR 3).
NWDOPT = WIND DIRECTION INPUT OPTION (0 TO 7).
NWSOPT = WIND SPEED INPUT OPTION (0 OR 1).
NWPOPT = WIND PROFILE EXPONENTS INPUT OPTION (0 OR 1).
NSCEN = NUMBER OF SCENARIOS (1 TO 24).
NLIST = OUTPUT OPTION: LISTS OF CONG AND SURF DEP FLUX (0 OR 1)
NARRAY = OUTPUT OPTION: MAPS OF CONG AND SURF DEP FLUX (0 TO 3)
NTAPE = OUTPUT OPTION: TAPE OF CONC AND SURF DEP FLUX (0 OR 1)
NCSOPT = OUTPUT OPTION: POINT SOURCE CULPABILITY LIST (0 OR 1).
NMAX = OUTPUT OPTION: MAXIMUM CONC. FOR EACH SCENARIO (0 OR 1).
NSTDWN = STACK-TIP DOWNWASH CORRECTION OPTION (0 OR 1).
NPRISE = NEW PLUME RISE EQUATIONS OPTION (0 OR 1).
NINPEN = NEW PLUME PENETRATION METHODS OPTION (0 OR 1).
T»TTtT?n _ TIT^y-ITJT'MnXM-* T^TmnT"m A T *N»T fn A T^fi s\rimv^rim /"TO \
lIVlaK — tilH/tirluH INlCiKVAL ON lAFc OL/rrUr (1,^:, ).
NPRINT = OUTPUT OPTION: POINT SOURCE PLUME RISE INFO (0 OR 1)
INPTSC = INPUT OPTN: POINT SOURCE DATA ON UNIT IRD OR IDSK (1 OR
NGPR = GRADUAL PLUME RISE OPTION NEAR PT. SOURCE (= 0 ),
NGPR = 1, THEN FINAL EFFECTIVE PLUME RISE AT ALL DISTANCES
NBID = BOUYANCY INDUCED DISPERSION (BID), (=0 NO BID, =1 YES)

READ ( IRD , 805 ) NTOPT , NWDOPT , NWSOPT , NWPOPT , NSCEN , NL 1ST , NARRAY ,
PMT19680
PMT19690
PMT19700
PMT19710
PMT19720
PMT19730
PMT19740
PMT19750
PMT19760
PMT19770
PMT19780
PMT19790
PMT19800
PMT19810
PMT19820
PMT19830
PMT19840
PMT19850
PMT 19851
PMT19860
PMT19870
PMT19880
PMT 19890
PMT19900
PMT19910
PMT19920
PMT19930
PMT19940
PMT19941
PMT19950
PMT19960
PMT19970
PMT19980
PMT19990
PMT20000
PMT20010
PMT20020
PMT20030
PMT20040
PMT20050
PMT20060
PMT20070
PMT20080
PMT20090
PMT20100
PMT20110
PMT20120
PMT20130
PMT20140
PMT20150
PMT20160
PMT20170
PMT20180
PMT20190
PMT20200
PMT20210
PMT20220
PMT20230
2)PMT20240
PMT20241
PMT2024 ?
PMT2024 3
PMT20250
PMT20260
1 NBID                                                             PMT20271
                                                                   PMT20280
 IF(NTOPT.GE.l .AND  NTOPT.LE.3) GO TO 2                           PMT20290
 WRITE(IWR,660) NTOPT                                              PMT20300
 NTOPT=1                                                           PMT20310
                                177

-------
c
c
c
c
c
c
c
c
c
c
c
c
c
    2 IF(NWDOPT.LE.l) GO TO 6
      IFfNWDOPT.GT.7) GO TO 5
      IF(NTOPT.EQ.l .OR. NWDOPT.IE.l) GO TO 6
      WRITE(IWR,615)
    " NWDOPT=0
   10
   20
   IF
   IF
   IF
   IF
   IF
   IF
   IF
   IF
   IF
   WE
         NWSOPT.GT.r
         NWPOPT.GT.l
             NWSOPT=0
             NWPOPT=0
NSCEN.EQ.O) NSCEN=1
NTOPT.EQ.3.AND.NSCEN.EQ.24) NTOPT=2
NTOPT.EQ.2 .AND. NSCEN.NE.24) GO TO 500
NSCEN.GT.24)  GO TO 510
NLIST.EQ.O;
NLIST.GT.l)
NWDOPT.LE.l
TE(IWR,605)
 GO TO 25
 GO TO 22
) GO TO 25
   22 NLIST=0
   25 IF(NARRAY.GT.S) NARRAY=0
      IF(NTAPE.EQ.O) GO TO 40
      IF(NTAPE,GT.l) GO TO 30
      IF(NWDOPT.LE.l) GO TO 40
      WRITE(IWR,620)
   30 NTAPE=0
   40 IF(NCSOPT.EQ.O) GO TO 51
      IF(NCSOPT.GT.l) NCSOPT=0
      IF(NTOPT.EQ.l) GO TO 45
      NCSOPT=0
      WRITE(IWR,625)
   45 IF(NWDOPT.GT.l.AND.NSCEN.GT.l) GO TO 50
      GO TO 51
   50 NCSOPT=0
   51 IF
      IF
      IF
      IF
      IF
      IF
      IF
      WRITE(IWR,635)
      NMAX.GT.l) NMAX=0
      NSTDWN.GT.l
      NPRISE.GT.i;
      NINPEN.GT.l
             NSTDWN=0
             NPRISE=0
             NINPEN=0
      INTER.EQ.O) INTER=1
      NPRINT.GT.l) NPRINT=0
      INPTSC.LT.l .OR. INPTSC.GT.2) INPTSC=1
    SET LABEL FOR TIME AVERAGING
   IAV=1
   IF(NTOPT.EQ.2) IAV=24
   IF (NTOPT.EQ.3) IAV=NSCEN

**** READ THIRD CONTROL PARAMETER CARD (GRID, DTDZ)

  XRSWC.YRSWC = COORDINATES OF SOUTHWEST CORNER OF RECEPTOR GRID
  LX
  LY
  GRID
        NUMBER OF COLUMNS IN RECEPTOR GRID.
        NUMBER OF ROWS IN RECEPTOR GRID.
        SPACING BETWEEN ROWS AND COLUMNS OF RECEPTOR GRID
115
C
C
C
  DTDZ(1&2) = VERTICAL POTENTIAL TEMPERATURE GRADIENT
                FOR STABILITY CLASSES E & F.

   READ(IRD,810)XRSWC,YRSWC.LX.LY,GRID,DTDZ(l),DTDZ(2)

   IF(LX.EQ.O) LX=1
   IF(LY.EQ.O) LY=1
   IF(NTAPE.EQ.O) GO TO 115

   NRECS=((LX+1)/INTER)*((LY+1)/INTER)*NSCEN
   IF(NTOPT.EQ.2) NRECS= NRECS/24
   IF(NTOPT.EQ.3) NRECS= NRECS/NSCEN
   IFfNRECS.LT.62500) GO TO 115
   WRITE(IWR,600)
   NTAPE=0
   CONTINUE

**** READ FOURTH CONTROL PARAMETER CARD (POLLUTANTS)
     PMT20320
     PMT20330
     PMT20340
     PMT20350
     PMT20360
     PMT20370
     PMT20380
     PMT20390
     PMT20400
     PMT20410
     PMT20420
     PMT20430
     PMT20440
     PMT20450
     PMT20460
     PMT20470
     PMT20480
     PMT20490
     PMT20500
     PMT20510
     PMT20520
     PMT20530
     PMT20540
     PMT20550
     PMT20560
     PMT20570
     PMT20580
     PMT20590
     PMT20600
     PMT20610
     PMT20620
     PMT20630
     PMT20640
     PMT20650
     PMT20660
     PMT20670
     PMT20680
     PMT20690
     PMT20700
     PMT20710
     PMT20720
    .PMT20730
     PMT20740
     PMT20750
     PMT20760
     PMT20770
 (KM)PMT20780
     PMT20790
     PMT20800
(KM)  PMT20810
     PMT20820
     PMT20830
     PMT20840
     PMT20850
     PMT20860
     PMT20870
     PMT20880
     PMT20890
     PMT20900
     PMT20910
     PMT20920
     PMT20930
     PMT20940
     PMT20950
     PMT20960
     PMT20970
     PMT20980
     PMT20990
     PMT21000
     PMT21010
                                     178

-------
C NPOL = NUMBER OF POLLUTANTS (1 OR 2)
C ICT = CHEMICAL TRANSFORMATION OR DECAY OPTION (0 OR 1)
C VD1 = DEPOSITION VELOCITY FOR POLLUTANT SPECIES-1 (CM/S)
C Wl = SETTLING VELOCITY FOR POLLUTANT SPOECIES-1 (CM/S)
C VD2 = DEPOSITION VELOCITY FOR POLLUTANT SPECIES-2 (CM/S)
C W2 = SETTLING VELOCITY FOR POLLUTANT SPECIES-2 (CM/S)
C XKT = CHEMICAL TRANSFORMATION OR DECAY RATE OF POLLUTANT
C SPECIES-1 (PERCENT PER HOUR)
C GAMMA = RATIO OF MOLECULAR WEIGHTS OF SPECIES-2 (PRODUCT)
C TO SPECIES-1 (REACTANT) IN CHEMICAL TRANSFORMATION
C
C NOTE: FOR DEPOSITION TO OCCUR, W SHOULD BE LESS THAN OR EQUAL TO VD.
C FOR DEPOSITION OF GASES AND VERY SMALL PARTICLES, W=0.
C FOR DEPOSITION OF SMALL PARTICLES, W IS LESS THAN VD.
C FOR DEPOSITION OF PARTICLES OF SIZE > 50 MICRONS, W=VD.
C
READ (IRD.812) NPOL, ICT, VD1.W1, VD2.W2, XKT, GAMMA
C
IF NPOL.LT.l .OR. NPOL.GT.2) NPOL=1
IF W1.GT.VD1) W1=VD1
IF Wl.LT.0.01) Wl=0.0
IF VDl.LT.0.01) VD1=0.0
IF NPOL.EQ.2) GO TO 117
VD =0.0
W2=0.0
GO TO 118
117 IF W2.GT.VD2) W2=VD2
IF W2.LT.0.01) W2=0.0
IF VD2.LT.0.01) VD2=0.0
118 IF ICT.EQ.l) GO TO 119
XKT=0.0
GAMMA=0.0
GO TO 122
119 IF(XKT.GE.0.1 .AND. XKT. LE. 100.) GO TO 120
TXKT=0.1
IF(XKT.GT.100.) TXKT=100.
WRITE (IWR, 640) XKT.TXKT
XKT=TXKT
C
C CONVERT CHEMICAL TRANSFORMATION RATE XKT (PERCENT PER HOUR) TO
C THE EQUIVALENT TIME SCALE TAUC (SECONDS).
120 TAUC=0.36E06/XKT
C
122 IF(NCSOPT.EQ.O .OR. (LX.LE.25 .AND. LY.LE.25)) GO TO 125
WRITE (IWR, 645)
NCSOPT=0
C
C SHIFT THE RECEPTOR GRID TO THE COMPUTATION GRID.
125 XSWC= XRSWC - 0.5*GRID
YSWC= YRSWC - 0.5*GRID
C
130 IF(DTDZ(1).LT. 0.00001) DTDZ(1)=0.020
IF(DTDZ(2).LT. 0.00001) DTDZ(2)=0. 035
C
C IF GRID IS ZERO, SWITCH ON AUTOMATIC GRID OPTION.
IGRID=0
IF(GRID.LT.1.0E-5) IGRID=1
IF(IGRID.EQ.l.AND.NTOPT.GT.l) GO TO 520
C
C **** READ 5TH CONTROL PARAMETER CARD (AREA SOURCE EMISSIONS HEIGHT
C AND SCALING , AND CONCENTRATION CALIBRATION)
C
C HAS = EFFECTIVE HEIGHT OF AREA SOURCE EMISSIONS (METERS).
C ASCALE(1&2) = AREA SOURCE EMISSION SCALING FACTORS
C FOR POLLUTANT SPECIES-1 AND 2.
C A(l&2) = CONCENTRATION CALIBRATION FACTOR (INTERCEPT)
C FOR POLLUTANT SPECIES-1 AND 2.
C B(l&2) = CONCENTRATION CALIBRATION FACTOR (SLOPE)
C FOR POLLUTANT SPECIES-1 AND 2.
C
PMT21020
PMT21030
PMT21040
PMT21050
PMT21060
PMT21070
PMT21080
PMT21090
PMT21100
PMT21110
PMT21120
PMT21130
PMT21140
PMT21150
PMT21160
PMT21170
PMT21180
PMT21190
PMT21200
PMT21210
PMT21220
PMT21230
PMT21240
PMT21250
PMT21260
PMT21270
PMT21280
PMT21290
PMT21300
PMT21310
PMT21320
PMT21330
PMT21340
PMT21350
PMT21360
PMT21370
PMT21380
PMT21390
PMT21400
PMT21410
PMT21420
. PMT21430
PMT21440
PMT21450
PMT21460
PMT21470
PMT21480
PMT21490
PMT21500
PMT21510
PMT21520
PMT21530
PMT21540
PMT21550
PMT21560
PMT21570
PMT21580
PMT21590
PMT21600
PMT21610
PMT21620
PMT21630
PMT21640
PMT21650
PMT21660
PMT21670
PMT21680
PMT21690
PMT21700
PMT21710
179

-------
  135 READ(IRD,815) HAS,ASCALE(l),ASCALE(2),A(l),B(1),A(2),B(2)
C
C
C
C
C
C
C
C
C
C
C
      IF(ASCALE(1).LE.O.)
      IF(ASCALE(2).LE.O.)
                        ASCALE(1)=1.0
                        ASCALE(2)=1.0
 **** READ CARD 6 (POLLUTANT AND CALIBRATION LABELS)
      READ(IRD,817)(POLNAM(I,1).1=1,3
                                    ,fCALNAM(I,l),I=l,7),
                                    ,(CALNAM(I,2),I=1,7)

    IF(NWPOPT.EQ.O)  GO TO 136
 **** READ CARD 7 (WIND PROFILE EXPONENTS AND ANEMOMETER HEIGHT)
 NOTE:  THIS IS AN OPTIONAL CARD
   HA
   Pl(I)
   HMIN
   HMAX
   UMIN
                 =  ANEMOMETER HEIGHT (METERS)
          ,1=1,6 =  WIND  PROFILE  EXPONENTS  FOR  STABILITY CLASSES ]
                 =  WIND  CONSTANT BELOW THIS HEIGHT (DEFAULT 10 M)
                 =  WIND  CONSTANT ABOVE THIS HEIGHT (DEFAULT 200MJ
           =  WIND SPEED  NOT ALLOWED LESS THEN  THIS VALUE (DEFAUL3
TO 6
C
C
C
C
C
C
C
C
C
C
C
C
    READ(IRD,818)  HA,  HMIN,  HMAX,  UMIN,(PI(I),1=1,6)
    CHECK FOR DEFAULTS AND SET THEM EQUAL TO STANDARD
    IF(HA.LT.O.Ol) HA=10.
    IF(HMIN.LT.O.Ol)  HMIN=10.
    IF(HMAX.LT.O.Ol)  HMAX=200.
    IF(UMIN.LT.O.Ol)  UMIN=1.
    DO 136 1=1,6
    IF(P1(I).LT.0.01)
136 CONTINUE

 **** READ ONE TO 24 SCENARIO PARAMETER CARDS.
                                                        VALUES.
   140
   NSC       = STABILITY CLASS NUMBER (1 TO 6)
   NWS       = WIND SPEED CLASS NUMBER (1 TO 6)
   NWD       = WIND SECTOR NUMBER (1 TO 16)
   WS        = WIND SPEED (M/S)
   WD        = WIND DIRECTION (DEGREES)
   TA        = AMBIENT TEMPERATURE (DEGREES CELSIUS)
   HMIX      = MIXING HEIGHT (METERS)
   DTDZI     = POT.TEMP.GRADIENT IN ELEVATED STABLE LAYER (DEG.C/M)

    DO 150 IS=1.NSCEN
    READ(IRD.820)NSC(IS),NWS(IS),NWD(IS),WS(IS),WD(IS),TA(IS),
   1 HMIX(ISj,DTDZI(IS)

    IF(NSC(IS).GE.l .AND. NSC(IS).LE.6) GO TO 140
    NUM=1
    IF(NSC(IS).GT.6) NUM=6
    WRITE(IWR,535) IS,NSC(IS),NUM
    NSC(IS)=NUM
    IF(NWSOPT.EQ.O) GO TO 142
    IF(NWS(IS).GE.l
    NUM=1
    IF(NWS(IS).GT.6) NUM=6
    WRITE(IWR,545) IS.NWS(IS),NUM
                       .AND. NWS(IS).LE.6) GO TO 144
      IHl J. JLli I J. IT tl. • \J~
      NWS(IS)=NUM
      GO TO  144
  142 IF(WS(IS).GT.O
                   ) GO TO 144
      WRITE(IWR.565)  IS,WS(IS)
      WS(IS)=1.6
   144  IF(NWDOPT.NE.l)
                   5.1
                    GO TO 146
                    .AND. NWD(IS).LE.16) GO TO 146
      IF(NWD(IS).GE
      NUM=1
      IF(NWD(IS).GT.16) NUM=16
      WHITE(IWR,555) IS,NWD(IS),NUM
      NWD(IS)=NUM
  146 IF(HMIX(IS).LT.1.0E-5) HMIX(IS)= 9999.9
      IF(NINPEN.EQ.O) GO TO 150
      IF(DTDZI(IS).LT.0.00001) DTDZI(IS)=0.010
150   CONTINUE
C
    PMT21720
    PMT21730
    PMT21740
    PMT21750
    PMT21760
    PMT21770
    PMT21780
    PMT21790
    PMT21800
    PMT21810
    PMT21820
    PMT21830
    PMT21840
    PMT21850
    PMT21860
    PMT21870
    PMT21871
    PMT21872
M/S)PMT21873
    PMT21880
    PMT21890
    PMT21900
    PMT21901
    PMT21902
    PMT21903
    PMT21910
    PMT21920
    PMT21930
    PMT21940
    PMT21950
    PMT21960
    PMT21970
    PMT21980
    PMT21990
    PMT22000
    PMT22010
    PMT22020
    PMT22030
    PMT22040
    PMT22050
    PMT22060
    PMT22070
    PMT22080
    PMT22090
    PMT22100
    PMT22110
    PMT22120
    PMT22130
    PMT22140
    PMT22150
    PMT22160
    PMT22170
    PMT22180
    PMT22190
    PMT22200
    PMT22210
    PMT22220
    PMT22230
    PMT22240
    PMT22250
    PMT22260
    PMT22270
    PMT22280
    PMT22290
    PMT22300
    PMT22310
    PMT22320
    PMT22330
    PMT22340
    PMT22350
                                      180

-------
c
c
PRINT INPUT CONTROL PARAMETERS
      IF(ISTOP.EQ.l
      WRITE(IWR,902
      WRITE(IWR,904
      WRITE(IWR,906
      WRITE?IWR,908
      IF(IGRID.EQ.O
      WRITE(IWR,900
      WRITE(IWR,922
                  WRITE(IWR,900) TT
                  NTOPT
                  NWDOPT
                  NWSOPT
                  NSCEN
                  WRITE(IWR,916) IX,LY,GRID,XRSWC,YRSWC
                  TT
                  NPOL,(POLNAM(I,1),I=1,3)
      IF(NPOL.EQ.2) WRITE(IWR.923)  (POLNAM(I,2),1=1,3)
      WRITE(IWR,924) ASCALE(l}
      IF(NPOL.EQ.2) WRITE(IWR.935)  ASCALE(2)
      WRITE(IWR,925) A(1),B(1)
      IF(NPOL.EQ.2) WRITE(IWR,926)  A(2).B(2)
      WRITE(IWR,927) (CAINAM(l.l),1=1,7J
      IF?NPOL.EQ.2J WRITE(IWR,921)  (CALNAM(I,2),1=1,7)
      WRITE(IWR,928) VDl
      IF(NPOL.EQ.2T WRITE(IWR,931)  VD2
      WRITE(IWR,929) Wl
      IF(NPOL.EQ.2) WRITE(IWR,933)  W2
      WRITE(IWR,930) ICT
      IF(NPOL.EQ.l) WRITE(IWR,932)
      IF(NPOL.EQ.2) WRITE(IWR,934)
      IF(ICT.EQ.O) GO TO 152
      WRITE(IWR,936) XKT
      IF(NPOL.EQ.lj GO TO  152
      WRITE(IWR,938) GAMMA
  152 WRITE(IWR,940
C
C
C
      IF
      IF
      IF
      IF
      IF
      IF
      IF
      NLIST.GT.O) WRITE(IWR,942) NLIST
      NARRAY.GT.O
      NARRAY.EQ.l
      NARRAY.EQ.2
      NARRAY.EQ.3
      NTAPE.GT.O)
  WRITE
  WRITE
  WRITE
  WRITE
IWR,944
IWR,946
IWR,948
IWR,950
NARRAY
 WRITE?IWR.952) NTAPE,INTER
      ii J.fu ia * va i » v / iiLi.LJUuvJ.rriL* J*Jt* J  LI in.
      NMAX.GT.O) WRITE(IWR,958) NMAX
  PRINT INPUT PARAMETERS FOR SCENARIOS
      WRITE
      WRITE
      WRITE
      WRITE
         IWR,960
         IWR,962
         IWR,963
         IWR,964
TT
C
C
C
C
      DO  162  IS=1,NSCEN
      KS=NSC(IS)
      WRITE(IWR,966)  IS.SCLAB(KS)
      IF(NWSOPT.EQ.O) GO  TO  153
      KW=NWS(IS)
      WS(IS)=CWS(KW)
      WRITE(IWR,970)  KW
      GO  TO 154
   153 WRITE(IWR,972)  WS(IS)
   154 IF(NWDOPT.EQ.l) GO  TO  155
      WDOUT=WD(ISy
      WRITE(IWR,973)  WDOUT
      GO  TO 156
   155 KD=NWD(IS)
      WDOUT=SECTAN(KD) *  180./3.14159265
      WRITE(IWR,974)  KD
   156 IF	   	
      IF
      WD
      TA
      NINPEN.EQ.1)WRITE(IWR,978)TA(IS).DTDZI(IS),HMIX(IS)
      NINPEN.EQ.O)WRITE(IWR,979)  TA(IS),HMIX(IS)
      IS)= WD(IS}*3.14159265/180.
       IS)=  TA(IS) +  273.15

FOR EACH SCENARIO, CALCULATE  THE  CRITICAL DOWNWIND DISTANCES
  AT WHICH  VERTICAL  MIXING  IMPENDS (DCRIT(IS,1)) AND IS COMPLETE
  (DCHIT(IS,2)).
   JSC=NSC(ISJ
   PC1=0.47*HMIX(IS)/AZ(JSC)
PMT22360
PMT22370
PMT22380
PMT22390
PMT22400
PMT22410
PMT22420
PMT22430
PMT22440
PMT22450
PMT22460
PMT22470
PMT22480
PMT22490
PMT22500
PMT22510
PMT22520
PMT22530
PMT22540
PMT22550
PMT22560
PMT22570
PMT22580
PMT22590
PMT22600
PMT22610
PMT22620
PMT22630
PMT22640
PMT22650
PMT22660
PMT22670
PMT22680
PMT22690
PMT22700
PMT22710
PMT22720
PMT22730
PMT22740
PMT22750
PMT22760
PMT22770
PMT22780
PMT22790
PMT22800
PMT22810
PMT22820
PMT22830
PMT22840
PMT22850
PMT22860
PMT22870
PMT22880
PMT22890
PMT22900
PMT22910
PMT22920
PMT22930
PMT22940
PMT22950
PMT22960
PMT22970
PMT22980
PMT22990
PMT23000
PMT23010
PMT23020
PMT23030
PMT23040
PMT23050
                                      181

-------
c
c
c
c
c
c
c
162
C
C
C
C
C
C
C
C
C
    IF(JSC.NE.S) GO TO 157

 STABILITY CLASS C
    DCR(IS.1}=.001*PC1
    GO TO 161
157 IF(JSC.LT.S) GO TO 158

 STABILITY CLASSES D,E,  AND F
    PC2=PC1*PC1*BZ(JSC)
    PC3=2./(PC1*BZ(JSC))
    DUMMY= 0.5*PC2*(1-+SQRT(1.+PC3*PC3))
    DCR(IS.1)=.001*DUMMY
    GO TO 161

 STABILITY CLASSES A AND B
 FIRST APPROXIMATION
158 XX(1)=PC1
    DO 159 1=1,100
    11=1+1
    XX(I1)=PC1/SQRT(1.+BZ(JSC)*XX(I))
    DIFF=ABS(XX(I1)-XX(I))
    IF(DIFF.LE.0.5) GO TO 160
159 CONTINUE
160 DCR(IS,1)=.001*XX(I1}
161 DCR(IS,2)=2.*DCR(IS,1)
    CONTINUE

 **** READ UP TO 50 AREA SOURCE CARDS.
   XA.YA
   SIZE
= COORDINATES OF SOUTHWEST CORNER OF AREA SOURCE (KM).
= LENGTH OF A SIDE OF AREA SOURCE (M).
   EA(1&2)= EMISSION RATES OF 2 POLLUTANTS (G/S).
    NOTE THAT EA(1&2) ARE EMISSION RATES OF AN EQUIVALENT POINT
    SOURCE LOCATED AT THE CENTER OF THE AREA SOURCE.

    WRITE(IWR,990) TT
    NAS=1
    SUMAQ(1)=0.
C
170
C
SUMAQ(2)=0.
SUMAR(1)=0.
SUMAR(2)=0.
RE AD ( IRD , 825 ) XA ( NAS )
,YA(NAS),SIZE(NAS),EA(NAS,1),EA(NAS,2)
175
C
    IF(NPOL.EQ.l) EA(NAS,2)=0.0
    IF((SIZE(NAS)+EA(NAS,1)+EA(NAS,2)).LT.1.0E-04) GO TO 180
    IF(SIZE(NAS).GE.1.0) GO TO 172
    SIZE?NAS)=1.0
    IF(GRID.NE.O.) SIZE(NAS)=GRID*1000.
    WRITE(IWR,585) NAS.SIZE(NAS)
172 DO 175 K=l,2
    EAR(K)=EA(NAS,K)
    SUMAR(K)=SUMAR(K)+EAR(K)
    EA(NAS,K)= EA(NAS,K)*ASCALE(K)
    SUMAQ(K)=SUMAQ(K)+EA(NAS,K)
180
C
C
C
  PRINT INPUT PARAMETERS FOR THIS AREA SOURCE
    WRITE(IWR,992)NAS,XA(NAS),YA(NAS),SIZE(NAS),EAR(1),EA(NAS,1),
   IEAR(2),EA(NAS,2)

    SIZE(NAS)=SIZE(NAS)*0.001
    IF(NAS/50*50.EQ.NAS) WRITE(IWR,990)TT
    NAS=NAS-fl
    GO TO 170
    NAS=NAS-1
    WRITE(IWR,994)  SUMAR(l),SUMAQ(1),SUMAR(2),SUMAQ(2)
    WRITE(IWR,996)  HAS


 **** READ UP TO 300 POINT SOURCES
 PMT23060
 PMT23070
 PMT23080
 PMT23090
 PMT23100
 PMT23110
 PMT23120
 PMT23130
 PMT23140
 PMT23150
 PMT23160
 PMT23170
 PMT23180
 PMT23190
 PMT23200
 PMT23210
 PMT23220
 PMT23230
 PMT23240
 PMT23250
 PMT23260
 PMT23270
 PMT23280
 PMT23290
 PMT23300
 PMT23310
 PMT23320
 PMT23330
 PMT23340
 PMT23350
 PMT23360
 PMT23370
 PMT23380
 PMT23390
 PMT23400
 PMT23410
 PMT23420
 PMT23430
 PMT23440
 PMT23450
 PMT23460
.PMT23470
 PMT23480
 PMT23490
 PMT23500
 PMT23510
 PMT23520
 PMT23530
 PMT23540
 PMT23550
 PMT23560
 PMT23570
 PMT23580
 PMT23590
 PMT23600
 PMT23610
 PMT23620
 PMT23630
 PMT23640
 PMT23650
 PMT23660
 PMT23670
 PMT23680
 PMT23690
 PMT23700
 PMT23710
 PMT23720
 PMT23730
 PMT23740
 PMT23750
                                     182

-------
c
c
c
c
c
c
c
c
c
   XP,YP   =  COORDINATES OF POINT SOURCE (KM).
   EP(1&2)  =  EMISSION RATES OF 2 POLLUTANTS (G/S).
   HP      =  SOURCE HEIGHT (M).
   DP      =  INSIDE DIAMETER (M).
   VP      =  VELOCITY (M/S).
   TP      =  TEMPERATURE (DEGREES CELSIUS).
   K  jffl    =  IDENTIFICATION.
  184 WRITE(IWR,980)
      NPS=1
      SUMPQ(1)=0.
                   TT
      SUMPQ(2
           )=0.
           )=0.
C
C
  185 IF(INPTSC.EQ.2)READ(IDSK,830)XP(NPS),YP(NPS),EP(NPStl),EP(NPS,2)
     1 HP(NPS),DP(NPS),VP(NPS),TP(NPS),NAME(1),NAME(2)
      IFCINPTSC.EQ.1) READ(iRD,830)XP(NPS'),YP(NPS),EP(NPS,l),EP(NPS,2)
     1 HP(NPS),DP(NPS),VP(NPS);TP(NPS),NAME(1),NAME(2)

      IF(NPOL.EQ.l) EP(NPS,2)=0.0
      IF(HP(NPSy+DP(NPS)+VP(NPS)+TP(NPS).LT.1.0E-4) GO  TO  190
      IF(DP(NPS).GT.O.O) GO TO 187
      WRITE(IWR,575) NPS
      DP(NPS)=1.0E-4
 PRINT INPUT PARAMETERS FOR THIS POINT SOURCE
187 WRITE?IWR.984) NPS,NAME_(1) ,NAME(2) ,XP(NPS), YP(NPS) ,EP(NPS, 1)
   1 EP(NPS,2;,HP(NPS),DP(NPS),VP(NPS),TP(NPS)
190
    TP(NPS)=TP(NPS)+273.15
    IF(NPS/50*50.EQ.NPSJ WRITE(IWR,980)TT
    SUMPQ(1)=SUMPQ(1)+EP(NPS,1)
    SUMPCK2)=SUMPQ(2)+EP(NPS,2)
    NPS=NPS+1
    GO TO 185
    NPS= NPS-1
    WRITE(IWR,986) SUMPQ(l),SUMPQ(2)
      IF(NPS.LT.l) GO TO
                 301)
    ..A .   	fc .... 192
    WRlTE(IWR,90l)
    WRITE_(IWR,907) NWPOPT
      IF(NWPOPT.EQ.i) WRITE(IWR,959)  (P1(I),1=1,6),HA ,HMIN,HMAX,UMIN
 915
 919
WR]
WR]
WR]
WR]
IF
IF
IF
IF
IF
IF
[TE(IWR,910
:TE(IWR,911
[TE(IWR,920
.rTE(IWR,912
IGRID.EQ.l
NCSOPT.GT.
NCSOPT.GT. (
NPRINT.GT.C
NGPR.EQ.O)
NGPR.EQ.l)
NSTDWN
NPRISE
DTDZ?1),DTDZ(2)
NINPEN
WRITE(IWR,914)
.OR.NPRINT.GT.O) WRITE (IWR, 940)
)) WRITE? IWR, 954) NCSOPT
)) WRITE (IWR. 956) NPRINT
WRITE (IWR, 9 15) NGPR
WRITE(IWR,919) NGPR
    FORMATC ',10X,'GRAD. PLUME RISE OPTION WHEN NGPR=0  : NGPR =
    FORMAT(' ',10X,'  FINAL EFFECTIVE PLUME RISE USED: NGPR =',!!)
    WRITE?IWR.918) NBID
    FORMAT(' J,9X,'BOUYANCY INDUCED DISPERSION FOR NBID=1
 918
 C
 C     IF  THERE WERE  SERIOUS
   192 IF(ISTOP.EQ.O) GO  TO
       WRITE (IWR, 630)
       CALL WAUDIT
       STOP
                         ERRORS
                         195
               IN INPUT PARAMETERS, STOP
           PMT23760
           PMT23770
           PMT23780
           PMT23790
           PMT23800
           PMT23810
           PMT23820
           PMT23830
           PMT23840
           PMT23850
           PMT23860
           PMT23870
           PMT23880
           PMT23890
           PMT23900
           PMT23910
           PMT23920
           PMT23930
           PMT23940
           PMT23950
           PMT23960
           PMT23970
           PMT23980
           PMT23990
           PMT24000
           PMT24010
           PMT24020
           PMT24030
           PMT24040
           PMT24050
           PMT24060
           PMT24070
           PMT24080
           PMT24090
           PMT24100
           PMT24110
           PMT24120
           PMT24130
           PMT24140
           PMT24150
           PMT24160
           PMT24170
           PMT24180
           PMT24190
           PMT24200
           PMT24210
           PMT24220
           PMT24230
           PMT24240
           PMT24250
           PMT24251
           PMT24252
        IDPMT24253
           PMT24254
           PMT24255
NBID=',I2) PMT24256
           PMT24260
           PMT24270
           PMT24280
           PMT24290
 C
 C
 C
 C
 C
  INITIALIZE FOR
195 IWDOPT= 0
    ISCEN=0
    RETURN
FIRST CALL TO INMOD FOR SCENARIO PREPARATION
 PREPARE   SCENARIO   INFORMATION
           PMT24300
           PMT24310
           PMT24320
           PMT24330
           PMT24340
           PMT24350
           PMT24360
           PMT24370
           PMT24380
                                      183

-------
C                                                                       PMT24390
300   IF(NWDOPT.LE.l) GO TO 350                                         PMT24400
      IFCISCEN.EQ.O.OR.IWDOPT.GE.4) GO TO 320                           PMT24410
      IWDOPT= IWDOPT + 1                                                PMT24420
      WD(ISCEN)= WD(ISCEN) + WDINC(NWDOPT-l)                            PMT24430
      IF(WD(ISCEN).GE.6.2831853) WD(ISCEN)=WD(ISCEN) - 6.2831853        PMT24440
      GO TO 353                                                         PMT24450
320   ISCEN= ISCEN + 1                                                  PMT24460
      IWDOPT= 1                                                         PMT24470
      GO TO 353                                                         PMT24480
350   ISCEN= ISCEN + 1                                                  PMT24490
353   ISC=NSC?ISCEN)                                                    PMT24500
      IWD=NWD(ISCEN)                                                    PMT24510
      D47= DCR(ISCEN,1)                                                 PMT24520
      D80= DCR(ISCEN,2)                                                 PMT24530
      08047= D80 - D47                                                  PMT24540
      IF(NCSOPT.EQ.O) GO TO 400                                         PMT24550
      DO 380 1=1,25                                                     PMT24560
      DO 380 J=l,25                                                     PMT24570
      DO 380 K=l,5                                                      PMT24580
      DO 380 N=l,2                                                      PMT24590
      NWORST(I,J,K,N)=0                                                 PMT24600
380   CWORST(I,J,K,N)=0-                                                PMT24610
400   RETURN                                                            PMT24620
C                                                                       PMT24630
C   ERROR MESSAGES                                                      PMT24640
C                                                                       PMT24650
  500 WRITE(IWR.505)                                                    PMT24660
  505 FORMAT(1HO,'WHEN TIME AVG OPTION NTOPT=2, NUMBER OF SCENARIOS MUSTPMT24670
     1 =24')                                                            PMT24680
      ISTOP=1                                                           PMT24690
      GO TO 10                                                          PMT24700
  510 WRITE(IWR,515) NSCEN                                              PMT24710
  515 FORMAT?1HO,'MAXIMUM NUMBER OF SCENARIOS ALLOWED IS 24. NSCEN=',I4)PMT24720
      ISTOP=1                                                           PMT24730
      GO TO 20                                                          PMT24740
  520 WRITE(IWR,525)                                                    PMT24750
  525 FORMAT(1HO,'AUTOGRID MAY NOT BE USED WITH TIME AVG OPTION NTOPT>1'PMT24760
     1)                                                                 PMT24770
      ISTOP=1                                                           PMT24780
      GO TO 135                                                         PMT24790
  535 FORMAT(1HO  'IN SCENARIO',13,' STABILITY CLASS NUMBER NSC=',I2,    PMT24800
     1' IS OUT OF RANGE.  NSC SET TO',12)                               PMT24810
  545 FORMAT(1HO,'IN SCENARIO',13,' WIND SPEED CLASS NUMBER NWS=',I2,   PMT24820
     1' IS OUT OF RANGE.  NWS SET TO',12)                               PMT24830
  555 FORMAT(1HO,'IN SCENARIO',13,' WIND DIRECTION SECTOR NUMBER NWD=', PMT24840
     1 13,' IS OUT OF RANGE.  NWD SET TO',13)                           PMT24850
  565 FORMAT(1HO,'IN SCENARIO',13,' SPECIFIED WIND SPEED WS =',F7.3,' ISPMT24860
     1 LESS THAN ZERO.  WS SET TO 1.0 M/S')                             PMT24870
  575 FORMAT?1HO,'POINT SOURCE',14.':  INSIDE DIAMETER MUST BE GREATER  TPMT24880
     1HAN ZERO.  DP SET TO .0001 M3)                                    PMT24890
  585 FORMAT(1HO  'AREA SOURCE'.13.':  LENGTH OF SIDE MUST BE GREATER THAPMT24900
     IN ZERO.  SIZE SET TO ' F9.2)                                      PMT24910
  600 FORMAT?1HO,'RUN REQUESTED WOULD PRODUCE OVER 62500 RECORDS ON TAPEPMT24920
     I'/' OUTPUT OPTION NTAPE HAS BEEN SET TO ZERO')                    PMT24930
  605 FORMAT?1HO  'OUTPUT OPTION NLIST MAY NOT BE USED WITH AUTOMATIC WINPMT24940
     ID SHIFT OPTION  (NWDOPT>1)'/' NLIST HAS BEEN SET TO ZERO')         PMT24950
  615 FORMAT?1HO,'AUTOMATIC WIND SHIFT OPTION  (NWDOPT>1) MAY NOT BE USEDPMT24960
     1 WITH TIME AVG OPTION NTOPT>1'/' NWDOPT HAS BEEN SET TO ZERO')    PMT24970
  620 FORMAT(1HO,'OUTPUT OPTION NTAPE MAY NOT BE USED WITH AUTOMATIC WINPMT24980
     ID SHIFT OPTION  (NWDOPT>1)'/' NTAPE HAS BEEN SET TO ZERO')         PMT24990
  625 FORMAT?1HO,'CONTROL STRATEGY OUTPUT OPTION NCSOPT MAY NOT BE USED PMT25000
     1WITH NTOPT>1'/' NCSOPT HAS BEEN SET TO ZERO')                     PMT25010
  630 FORMAT(1H1//" SERIOUS ERROR(S) IN INPUT PARAMETERS',5X,           PMT25020
     1  'RUN CANNOT BE CONTINUED5)                                       PMT25030
  635 FORMAT?1HO,'CONTROL STRATEGY OUTPUT OPTION NCSOPT MAY NOT BE USED PMT25040
     IFOR MORE  THAN'/' ONE SCENARIO WITH AUTOMATIC WINDSHIFT OPTION'/,  PMT25050
     2' NCSOPT  HAS BEEN SET TO ZERO')                                   PMT25060
  640 FORMAT(1HO,'CHEMICAL TRANSFORMATION RATE XKT=',F7.3,' IS OUT OF RAPMT25070
     INGE'/' XKT  HAS BEEN SET TO',F8.3)                                 PMT25080


                                     184

-------
  645 FORMAT(1HO 'CONTROL STRATEGY OUTPUT OPTION NCSOPT MAY NOT BE USED PMT25090
     1WHEN NUMBER OF COLUMNS OR ROWS IN RECEPTOR GRID IS GREATER THAN 25PMT25100
     2'/' NCSOPT HAS BEEN SET TO ZERO')
  660 FORMAT(1HO,'TIME AVERAGING OPTION NTOPT=',I2,' IS OUT OF RANGE
     1TOPT SET TO 1')
C
C
C
800
INPUT FORMATS
805
810
812
815
817
818
820
825
830
C
C
C
FORMAT
FORMAT
FORMAT
FORMAT
FORMAT
FORMAT
FORMAT
FORMAT
FORMAT
FORMAT
20A4)
1814)
2F10. 0.2110, 3F10.0)
2I5.6F10.0)
7F10.0)
3A4,7A4,3A4,7A4)
10F7.0)
3I5.5F10.0)
5F1&.0)
8F9.0.2A4)
OUTPUT FORMATS
                                                                      PMT25110
                                                                     NPMT25120
                                                                      PMT25130
                                                                      PMT25140
                                                                      PMT25150
                                                                      PMT25160
                                                                      PMT25170
                                                                      PMT25180
                                                                      PMT25190
                                                                      PMT25200
                                                                      PMT25210
                                                                      PMT25220
                                                                      PMT25230
                                                                      PMT25240
                                                                      PMT25250
                                                                      PMT25260
                                                                      PMT25270
                                                                      PMT25280
                                                                      PMT25290
900 FORMAT(1H1.37X,'POLLUTION EPISODIC MODEL (PEM-2)'///4X,'INPUT CONTPMT25300
   1ROL PARAMETERS:  ',20A4//)                                        PMT25310
901 FORMAT(//4X 'INPUT CONTROL PARAMETERS:'//)                        PMT25320
902 FORMAT(10X,}AVERAGING TIME OPTION: NTOPT=* II//                   PMT25330
   1 18X,'A SCENARIO IS A SET OF METEOROLOGICAL DATA FOR ONE HOUR'//  PMT25340
   2 13X,'l  1 HOUR: CONCENTRATIONS ARE CALCULATED FOR EACH SCENARIO'/PMT25350
   3 13X,'2  24 HOURS:  CONCENTRATIONS CALCULATED FOR 24 SCENARIOS ARE PMT25360
   4AVERAGED'/13X  '3  VARIABLE: CONCENTRATIONS CALCULATED FOR A GIVEN PMT25370
   5NUMBER (2 TO 23) OF SCENARIOS ARE AVERAGED'//)                    PMT25380
904 FORMAT(10X,'WIND DIRECTION OPTION: NWDOPT=' II//                  PMT25390
   113X,'0  DIRECTION IN DEGREES TO BE SPECIFIED FOR EACH SCENARIO'/  PMT25400
   213X,'l  SECTOR NUMBER TO BE SPECIFIED FOR EACH SCENARIO'/         PMT25410
   312X,'2-7 DIRECTION IN DEGREES TO BE SPECIFIED FOR THE FIRST OF FOUPMT25420
   4R SUB-SCENARIOS.'/17X,'FOR EACH SUCCEEDING SUB-SCENARIO. WIND DIREPMT25430
   5CTION IS AUTOMATICALLY INCREASED'/17X,'BY 90,45,30,15,10,OR 5 DEGRPMT25440
   6EES, DEPENDING ON THE OPTION NUMBER SELECTED.'//)                 PMT25450
906 FORMAT(1OX,'WIND SPEED OPTION: NWSOPT=',II//                      PMT25460
   113X,'0  SPEED  IN M/S TO BE SPECIFIED FOR EACH SCENARIO'/          PMT25470
   213X,'l  WIND SPEED CLASS NUMBER TO BE SPECIFIED FOR EACH SCENARIO'PMT25480
   3//)                                                               PMT25490
907 FORMAT(10X,'WIND PROFILE EXPONENTS OPTION: NWPOPT=',II//          PMT25500
   113X,'0  EXPONENTS AND ANEMOMETER HEIGHT ARE STANDARD DEFAULT VALUEPMT25510
   2S'/                                                               PMT25520
   313X,'l  EXPONENTS AND ANEMOMETER HEIGHT TO BE SPECIFIED BY THE USEPMT25530
   	                                                               PMT25540
                                                                      PMT25550
                                                                      PMT25560
                                                                      PMT25570
                                                                      PMT25580
911 FORMATS10X,'NEW PLUME-RISE EQUATIONS OPTION: NPRISE='  II//        PMT25590
   1 13X,'0  STANDARD PLUME-RISE EQS. ARE USED FOR ALL STABILITY CLASSPMT25600
   2ES'/                                                              PMT25610
   3 13X,'l  NEW EQS. ARE USED FOR PEAK BUOYANCY RISE FOR STABILITY CLPMT25620
   4ASSES A-D'//)                                                     PMT25630
912 FORMAT(10X,'PLUME PENETRATION ABOVE MIXING HEIGHT OPTION: NINPEN='PMT25640
   1,1I//,                                                            PMT25650
   2 13X,'0  STANDARD TREATMENT OF PLUME PENETRATION ABOVE THE MIXING'PMT25660
   3,' HEIGHT'?,                                                      PMT25670
   4 ISX.'l  NEW SCHEMES FOR PLUME PENETRATION OF ELEVATED STABLE LAYEPMT25680
   5R  USED'/16X,'  FOR STABILITY CLASSES A-D AND BUOYANCY-DOMINATED PLUPMT25690
   6ME'//)                                                            PMT25700
914 FORMAT(10X,'AUTOMATIC RECEPTOR GRID OPTION IS IN EFFECT'//)       PMT25710
916 FORMAT(10X,'RECEPTOR GRID:',                                      PMT25720
   16X,'COLUMNS: LX=' 13,4X,'ROWS: LY=',I3/                           PMT25730
   230X,'SPACING:  GHID=',F7.3,' KM'/                                  PMT25740
   330X,'SOUTHWEST CORNER    XRSWC=  '.F8.3,' KM W'/                   PMT25750
   450X,'YRSWC=  '.F8.3,' KM S'//)                                     PMT25760
920 FORMATQOX, 'POTENTIAL TEMPERATURE GRADIENT: DTDZ(1)=  ',F7.3,      PMT25770
   1'  DEG/M     STABILITY CLASS E'/                                    PMT25780
     4R')'
  908 FORMATS10X,'NUMBER OF SCENARIOS: NSCEN=',I2//)
  910 FORMAT(//10X,'STACK-TIP DOWNWASH ALGORITHM OPTION: NSTDWN=',II//
     1  13X,'0  ALGORITHM IS IN EFFECT'/
     2  13X,'1  ALGORITHM IS NOT USED'//)
                                      185

-------
   242X,'DTDZ(2)= '  F7.3,' DEG/M    STABILITY CLASS F'//)             PMT25790
921 FORMAT(1H+.85X.7A4)                                               PMT25800
922 FORMAT(10X,'NUMBER OF POLLUTANTS: NPOL=',I1/                      PMT25810
   1 51X,'POLLUTANT-1:  *,3A4)                                         PMT25820
923 FORMAT(lH+,85X,'POLLUTANT-2: ',3A4)                               PMT25830
924 FORMAT?/10X 'AREA SOURCE SCALING FACTOR:',17X,'ASCALE=',F9.3)     PMT25840
925 FORMAT(iox,'CALIBRATION COEFFICIENTS:',                           PMT25850
   1 16X 'A=',F10.3'  B='.F10.3)                                     PMT25860
926 FORMAT 1H+.85X,!A=',Fl6.3,'   B=',F10.3)                           PMT25870
           10X,'CALIBRATION IDENTIFICATION:',14X,7A4.6X.7A4)          PMT25880
           		  	   ' 	 'VDl=',F8.3)         PMT25890
927 FORMAT
928 FORMAT
929 FORMAT
930 FORMAT
931 FORMAT
932 FORMAT
10X, 'DEPOSITION VELOCITY (CM/S) : ' ,20X, ' VD1=' ,F8.3)         PMT25890
10X.' SETTLING VELOCITY (CM/S) : ' ,23X ,'W1=' , F8.3)            PMT25900
           10X.' SETTLING VELOCITY (CM/S) :  ,23X ,'W1=' , F8.3)
           //10X 'CHEMICAL TRANSFORMATION OPTION: ICT=',I1/)
           1H+.91X 'VD2=',F8.3)
           13X,'NPOL=1'/
                                                           PMT25910
                                                           PMT25920
                                                           PMT25930
   215X,'ICT=0  CHEMICAL TRANSFORMATION LOSS OF POLLUTANT IS IGNORED'/PMT25940
   315X,'ICT=1  FIRST-ORDER CHEMICAL TRANSFORMATION LOSS OF POLLUTANT PMT25950
   4IS CONSIDERED'//)                                                 PMT25960
933 FORMAT71H+,92X,'W2=',F8.3)                                        PMT25970
934 FORMAT(13X,'NPOL=2'/                                              PMT25980
   215X.'ICT=0  CHEMICAL TRANSFORMATION LOSS OF POLLUTANTS IS IGNORED'PMT25990
   3/15X,'ICT=1  FIRST-ORDER CHEMICAL TRANSFORMATION OF POLLUTANT-1 TOPMT26000
   4 POLLUTANT-2 IS CONSIDERED'//)                                    PMT26010
935 FORMAT(1H+.88X,'ASCALE=' F9.3)                                    PMT26020
   1 POLLUTANT-1 (REACTANT): GAMMA=',F6.3/)                           PMT26060
940 FORMATQOX,'OUTPUT OPTIONS SELECTED:'//)                          PMT26070
942 FORMAT(13X,'NLIST=',II,3X,'LISTS OF CONCENTRATION AND SURFACE DEPOPMT26080
   1SITION FLUX AT EACH RECEPTOR IN THE GRID,'/24X,'ONE COLUMN PER PAGPMT26090
   2E')                                                               PMT26100
944 FORMAT(13X,'NARRAY=',I1,2X,'MAPS OF CONCENTRATION AND SURFACE DEPOPMT26110
   1SITION FLUX AT EACH RECEPTOR IN THE GRID ')                       PMT26120
948 FORMAT(24X,'CALIBRATED AND UNCALIBRATED';                         PMT26130
948 FORMAT(24X,'UNCALIBRATED ONLY')                                   PMT26140
950 FORMAT(24X,'CALIBRATED ONLY')                                     PMT26150
952 FORMAT(13X,'NTAPE=',I1.3X,'TAPE CONTAINING COORDINATES, CONCENTRATPMT26160
   HON. AND SURFACE DEPOSITION FLUX'/24X,'AT EACH RECEPTOR IN THE GRIPMT26170
   2D'/13X'INTER=',I2,2X,'INTERVAL OF RECEPTORS WHICH WILL BE WRITTENPMT26180
   3 ON TAPE')                                                        PMT26190
954 FORMAT(13X.'NCSOPT=' I1.2X 'LIST OF POINT SOURCE CULPABILITY FOR CPMT26200
   lONCENTRATION AND SURFACE DEPOSITION FLUX'/24X,'AT EACH RECEPTOR INPMT26210
   2 THE GRID'//)                                                     PMT26220
956 FORMAT(13X,'NPRINT=',I1,2X,'LIST OF POINT SOURCE PARAMETERS AND EFPMT26230
   1FECTIVE STACK HEIGHTSV24X,'PRINTED AT BEGINNING OF EACH SCENARIO'PMT26240
   2//)                                                               PMT26250
958 FORMAT(13X,'NMAX=',I1.4X  'LIST OF RECEPTORS WITH HIGHEST CONCENTRAPMT26260
   1TION AND SURFACE DEPOSITION FLUX'/24X,'FOR EACH SCENARIO - PRINTEDPMT26270
   2 AT END OF  RUN')                                                  PMT26280
959 FORMAT(/16X 'USER  SPECIFIED WIND PROFILE EXPONENT VALUES:'/20X,   PMT26290
   16(F4.2,3X)/20X,'ANEMOMETER HEIGHT = 'F4.1, IX,'METERS',           PMT26300
   23X,'HMIN =',1X,F4.1,' ,HMAX =  ',F4.0,   ,UM1N =  r,F3.1)            PMT26301
960 FORMAT(1H1.37X,'POLLUTION EPISODIC MODEL (PEM^2)V//4X,'INPUT SCENPMT26310
   1ARIO PARAMETERS:   '.20A4//26X  'WIND DIRECTIONS',27X,'WIND SPEED CLPMT26320
   2ASSES',12X,'STABILITY CLASSES'/)                                  PMT26330
962 FORMATUOX  'SECTOR    DIRECTION4,6X ' SECTOR    DIRECTION', 9X,     PMT26340
   1'CLASS   SPEED    CLASSM5X,'CLASS1/                             PMT26350
   «>1f\Y »WTIMTJPn» RY >l'T\'Pn\' fiY 'MTIMnPO' QV  *fT\Vfl\' QV » TXJTIT7V   /M/c\  nua'OC">on
963.FOHMAT(13Xt14_. ENfi  _.67.5| LSxt 112._  WSW.  >7.5» .lix, !3' ,6X,   PMT26410
                                                                      WPMT26420
                                                                       PMT26430
   SiiT-8
964 FORMAT(5X,'SCENARIO',3X,'STABILITY',3X, 'WIND SPEED',5X,'WIND',8X,  PMT26480

                                    186

-------
  966
  970
  972
  973
  974
  978
  979
  980
l'WIND',6X, 'WIND', 8X ' AMBIENT' 4X, 'TEMP GRADIENT ABOVE', 8X,
2 'MIXING' /6x, * NUMBER' , ex , ' CLASS ' , 7x , ' CLASS ' , sx, ' SPEED ' , 6x ,
3' SECTOR' ,3X, ' DIRECTION' . 3X, ' TEMPERATURE ' . 5X 'MIXING HEIGHT
411X, 'HEIGHT J/43X, ' (M/S) ' , 17X, ' (DEC) ' ,7X, ' (DEG C) ' , 10X,
5'(DEG/M)M5X. '(
 FORMAT 8X.I2.10X
    FORMAT
    FORMAT
    FORMAT
    FORMAT
    FORMAT
    FORMAT
    FORMAT
     IT SOUR
                    .A2
        1H+.42X.F6.3
        1H+,63X,F6.2
        1H+.55X.I2)
        1H+,76X,F7.2,11X,F6.3.11X,F7.1)
        1H+,76X,F7.2,28X,F7.1J
        1H1.37X 'POLLUTION EPISODIC MODEL  (PEM-2)
           j.nj.,o/A, rwjjijuij-uiii crioiu*
           E PARAMETERS:  ',20A4///
                 PMT26490
                 PMT26500
                 PMT26510
                 PMT26520
                 PMT26530
                 PMT26540
                 PMT26550
                 PMT26560
                 PMT26570
                 PMT26580
                 PMT26590
                 PMT26600
///4X,'INPUT POINPMT26610
                 PMT26620
                 PMT26630
                 PMT26640
                 PMT26650
   6'(M/S)',8X,'(DEG C)V)                                            PMT26670
984 FORMAT(6X,13,3X,2A4.3X,F8.2,2X,F8.2,10X,F9.3,10X,F9.3,6X,F6.2,5X, PMT26680
   1F6.3.6X,F7.3,6X,F8.3)                                             	
986 FORMAT(1HO,5X,'SUMS OF THE POINT SOURCE EMISSION RATES',6X,F9.3,
   1' G/S',6X.F9.3,' G/SM
990 FORMAT(1H1,37X,'POLLUT
                                                                        PMT26690
                                                                        PMT26700
                                                                        PMT26710
                            ION EPISODIC MODEL (PEM-2)'///4X,'INPUT AREAPMT26720
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
     1 SOURCE PARAMETERS:   ',20A4///
     270X,'POLLUTANT-1'17X,'POLLUTANT-2'/5X.'AREA SOURCE'.8X.
     3'COORDINATES',9X, LENGTH OF SIDE',11X, EMISSION RATE'.ISX,
     4'EMISSION RATE'/
     57X,'NUMBER',9X,'X(KM)',5X,'Y(KM)' 13X,'(M)',12X,'INPUT  (G/S)
     64X,'SCALED'!7X|'INPUT 5G/S)',4X,'SCALEDV)
  992 FORMAT(9X,I2,8X,F8.2,2X,F8.2,10X,F8.2,9X,F9.3,4X,F9.3,6X,
     1 F9.3,4X,F9.3)
  994 FORMATUHO, ISX.'SUMS OF THE AREA SOURCE EMISSION RATES',
     1 7X,F9.3.4X,F9.3,6X,F9.3,4X,F9.3)
  996 FORMAT(/17X,'EFFECTIVE HEIGHT OF THE AREA SOURCE EMISSIONS',
     1 ' = '.F6.2,'  M')
      END
    SUBROUTINE
            OUTMOD
                SUBROUTINE
                              OUTMOD  , PART OF PEM-2  (VERSION  84130)
***
***
 SUBROUTINE OUTMOD COORDINATES  OUTPUT OF THE  CONCENTRATION(S)
 AND SURFACE DEPOSITION FLUX(ES)  CALCULATED FOR EACH RECEPTOR
 IN THE GRID FOR EACH  SCENARIO  OR AVERAGING-PERIOD.
 ON OPTION, THE OUTPUT MAY  BE IN  THE  FORM OF  LISTS,  ARRAY
 MAPS, OR  TAPE.
 ON OPTION, OUTMOD CALLS SUBROUTINE WOROUT TO PRINT  A CULPABILITY
 LIST OF POINT SOURCES.
 OUTMOD ALSO CALLS SUBROUTINE SCENMX  TO DETERMINE AND STORE THE
 RECEPTORS WITH MAXIMUM CONCENTRATION^) AND  SURFACE DEPOSITION
 FLUX(ES)  FOR THE AVERAGING-PERIOD.


 PEM MODIFICATIONS AND FORMATS  BY MARTHA M. STEVENS,
 NOAA-ATDL, P.O. BOX-E,  OAK RIDGE, TENN 37831
 DECEMBER  1982
 PEM-2 MODIFICATIONS BY K.  SHANKAR RAO
 DECEMBER  1984


 COMMON/PEMCOM/CONC(50,50,2),SDF(50,50,2).TT(20).
 1  XP(300).YP(300),EP(360,2),HP(300),DP(300),VP(360),TP(300),
 2  XA(50),YA(50))EA(50.2))SI^E(50),
 3  WD(24),WS(24),TA(24),HMIX(24),DTDZI(24),
 4  AZ(6),BZ(6),c£(6),P(6),SCLAB(6),DTDZ(2),SECTAN(16),
                        ......           2).CALNAM(7,2),
       XSWC,YSWC,GRID,LX,LY,A(2),B('2),POLNAM(3,2),CALNAM
       ITA,IRD,IWR,IDSK,D80,D47)D8047,DIST,DELTA,HPRIME,
                 PMT26730
                 PMT26740
                 PMT26750
                 PMT26760
                 PMT26770
                 PMT26780
                 PMT26790
                 PMT26800
                 PMT26810
                 PMT26820
                 PMT26830
                 PMT26840
                 PMT26850

                 PMT26860
                 PMT26870
                 PMT26880
                 .PMT26890
                 PMT26900
                 PMT26910
                 PMT26920
                 PMT26930
                 PMT26940
                 PMT26950
                 PMT26960
                 PMT26970
                 PMT26980
                 PMT26990
                 PMT27000
                 PMT27010
                 PMT27020
                 PMT27030
                 PMT27040
                 PMT27050
                 PMT27060
                 PMT27070
                 PMT27080
                 PMT27090
                 PMT27100
                 PMT27110
                 PMT27120
                 PMT27130
                 PMT27140
                 PMT27150
                 PMT27160
                 PMT27170
                                      187

-------
c
c
c
c
c
c
c
c
c
c
c
c
c
c
   7 ESH(2),PEAK,IBUOY,IRISE,IDWN,EFF,XS,UINV,WVEC,
   8 NAS.NPS,INDEX.IGRID,IAV,ISCEN,IWDOPT.IWD,ISC,IPS,
   9 NTOPT,NWDOPT,NWSOPT,NWPOPT,NSCEN,NLIST,NARRAY,NTAPE,NCSOPT,
   * NMAX,NSTDWN,NPRISE,NINPEN,INTER,NPRINT,NGPR,NBID

    COMMON/PARM1/NPOL,VD1.Wl.VD2,W2
    DIMENSION CON(2),CALCON(2),SD(2),CALSD(2),AVD(2)


    CONTROL STRATEGY RESULTS OUTPUT BY SUBROUTINE WOROUT
    IF(NCSOPT.GT.O)  CALL WOROUT

    PRINT AND/OR WRITE-ON-TAPE LISTS OF CONCENTRATIONS) AND
    SURFACE DEPOSITION FLUX(ES)
    IFfNLIST.EQ.O .AND.  NTAPE.EQ.O)  GO TO 350
    IF(NTAPE.GT.O)  WRITE(ITA,900)TT

    NDEP=0
    IF(VD1.GE.0.01.OR.VD2.GE.0.01) GO TO 100
    GO TO 150
100 NDEP=1
    DEFINE CALIBRATION COEFFICIENTS FOR DEPOSITION FLUX
    AVD(1)=A(1)*VD1*36.
    AVD(2)=A(2)*VD2*36.

150 IF(NLIST.EQ.O)  GO TO 200
    WOUT=WD(ISCEN)*180./3.1415927
    PRINT TITLE, SCENARIO,  AND AVERAGING-PERIOD INFORMATION
    IF(NTOPT.EQ.l)  WRITE(IWR,905)TT,ISCEN,SCLAB(ISC),WS(ISCEN),WOUT,
   1 HMIX(ISCEN).IAV
    IF(NTOPT.GT.l)  WRITE(IWR,906)  TT,ISCEN,IAV
    PRINT TITLES FOR UNCALIBRATED  CONCENTRATION AND DEPOSITION FLUX,
    AND CALIBRATED CONCENTRATION
    WRITE(IWR,910)(CALNAM(L,1),L=1,7),(CALNAM(L,2),L=1,7)

    BEGIN DO-LOOP ON RECEPTOR GRID COLUMNS
200 DO 325 1=1,LX
    XI=I
    X=XSWC+(XI-0.5)*GRID

    BEGIN DO-LOOP ON RECPTOR GRID  ROWS
    DO 300 J=1,LY
    YJ=J
    Y=YSWC+(YJ-0.5)*GRID
C
C
C
    INITIALIZE CONCENTRATION AND SDF VARIABLES
    DO 260 K=l,2
    CON(K)=0.
    CALCON(K)=0.
    SD(K)=0.
    CALSD(K)=0.
260 CONTINUE

    DEFINE AND PRINT UNCALIBRATED CONCENTRATIONS AND DEPOSITION
    AND CALIBRATED CONCENTRATIONS
    DO 280 K=1,NPOL
    CON(K)=CONC(I,J,K)
    CALCON(K)= A(K) + B(K) * CON(K)
    IF(NDEP.EQ.O) GO TO 280
    SD(K)=SDF(I,J,K)
    IF(NTAPE.GT.O) CALSD(K)= AVD(K) + B(K) * SD(K)
280 CONTINUE
      IF(NLIST.EQ.O) GO TO 290
                O)
                .1.
C
C
                                          GO TO 290
    WRITE ON TAPE ALL CALIBRATED AND UNCALIBRATED OUTPUT DATA
290 IF (NTAPE. EQ.O) GO TO 300
      PMT27180
      PMT27190
      PMT27200
      PMT27210
      PMT27220
      PMT27230
      PMT27240
      PMT27250
      PMT27260
      PMT27270
      PMT27280
      PMT27290
      PMT27300
      PMT27310
      PMT27320
      PMT27330
      PMT27340
      PMT27350
      PMT27360
      PMT27370
      PMT27380
      PMT27390
      PMT27400
      PMT27410
      PMT27420
      PMT27430
      PMT27440
      PMT27450
      PMT27460
      PMT27470
      PMT27480
      PMT27490
      PMT27500
      PMT27510
      PMT27520
      PMT27530
      PMT27540
      PMT27550
      PMT27560
      PMT27570
      PMT27580
     .PMT27590
      PMT27600
      PMT27610
      PMT27620
      PMT27630
      PMT27640
      PMT27650
      PMT27660
      PMT27670
      PMT27680
      PMT27690
      PMT27700
FLUXESPMT27710
      PMT27720
      PMT27730
      PMT27740
      PMT27750
      PMT27760
      PMT27770
      PMT27780
      PMT27790
      PMT27800
      PMT27810
      PMT27820
      PMT27830
      PMT27840
      PMT27850
      PMT27860
      PMT27870
                                     188

-------
      IF(((I-1)/INTER)*INTER.NE.(I-l).OH.((J-1)/INTER)*INTER.NE.
     1 (J-l)) GO TO 300
      WRITE(ITA,975)X,Y,(CON(K),SD(K),CALCON(K),CALSD(K),K=1,2)
  300 CONTINUE
C
C     END LOOP ON GRID ROWS
  325 CONTINUE
C     END LOOP ON GRID COLUMNS
C
C
C     PRINT ARRAY MAPS OF CONCENTRATIONS
  350 IF(NARRAY.GT.O) CALL ARRAY
C
C
C

C
                                                                        PMT27880
                                                                        PMT27890
                                                                        PMT27900
                                                                        PMT27910
                                                                        PMT27920
                                                                        PMT27930
                                                                        PMT27940
                                                                        PMT27950
                                                                        PMT27960
                                                                        PMT27970
                                                                        PMT27980
                                                                        PMT27990
                                                                        PMT28000
   DETERMINE MAXIMUM PREDICTED CONCENTRATION(S)  FOR SCENARIO VIA SCENMX PMT28010
      IF(NMAX.GT.O.AND.(NTOPT.EQ.1.0R.ISCEN.EQ.NSCEN))  CALL SCENMX      PMT28020
                                                                        PMT28030
      RETURN                         •                                   PMT28040
                                                                        PMT28050
                                                                        PMT28060
                                                             ,           PMT28070
                                                             F5.2 '  M/S.PMT28080
                                                              AVERAGING PMT28090
                                                                        PMT28100
                                                     	    .           PMT28110
     120A4/1X.I2,'  SCENARIOS,',2X,'AVERAGING TIME=',13,'  HRS.'//)       PMT28120
  910 FORMAT(15X,'RECEPTOR',4X,'UNCALIBRATED CONCENTRATION',2X,'UNCALIB.PMT28130
     1DEPOSITION FLUX',2X 'CALIBRATED CONCEN.POL-1:'.7A4/14X,'COORDINATEPMT28140
     2S',3X,'(MICROGRAMS/CUBIC METER)',3X,'(MICROGRAMS/SQ.M/HOUR)',3X.  PMT28150
     3'CALIBRATED CONCEN.POL-2:'.7A4/1X,'COL ROW',5X.'X(KM)',3X.^YfKM)'.PMT28160
     44X,'POL-l',llX,'POL-2',9X,}POL-l')8X,)POL-2',4X,'POL-l5,8X,'POL-2'PMT2817g

  970 FORMAT(2(2X.I2),2X,2(2X,F6.2),2X,F8.2,8X,F8.2,2(3X,F10.1),
  900 FORMAT(20A4)
  905 FORMAT(1H1, PEM-2 OUTPUT:  PREDICTED CONCENTRATIONS:
     120A4>' SCENARIO ',12,', STABILITY=',A2,', WIND SPEED='
     2 WIND DIRECTION=',F6,2,' DEC, MIXING HEIGHT^',F7.1,' M
     3TIME=',I2  ' HR.'//)
  906 FORMAT(1H1,'PEM-2 OUTPUT:  PREDICTED CONCENTRATIONS:
                  .
     1 2(2X,Ell.4)1
  975 FORMAT(10F8.2)
      END
      SUBROUTINE ARRAY
                     SUBROUTINE ARRAY
                                         PART OF PEM-2 (VERSION 84130),
C
C
C

C
C
C
C
C
C
C
C
C
C
C
C *** PEM MODIFICATIONS AND FORMATS BY M.M. STEVENS,
C     NOAA-ATDL. P.O. BOX E, OAK RIDGE, TN 37831
C     DECEMBER 1982
C *** PEM-2 MODIFICATIONS AND FORMATS BY K. SHANKAR RAO
   SUBROUTINE ARRAY CREATES ARRAY MAPS OF THE CONCENTRATIONS AND
     SURFACE DEPOSITION FLUXES  IN THE RECEPTOR GRID AND
     PRINTS THEM AT THE END OF  EACH SCENARIO OR AVERAGING PERIOD.
     UNCALIBRATED AND CALIBRATED CONCENTRATIONS OF EACH  POLLUTANT
     APPEAR ON SEPARATE MAPS OF UP TO FOUR SECTIONS (PAGEST EACH.
     EACH SECTION (PAGE) ACCOMODATES VALUES AT 25X25  RECEPTORS.
C
C
C
      JULY  1984


      COMMON/PEMCOM/CONC(50.50.2),SDF(50,50,2),TT(20).
      1 XP(300) .YP(300) ,EP(300,2) ,HP(300) ,DP(300) , VP(300) , TP(300) ,
      2 XA(50),YA(50),EA(50.2);Sl£E(50),
      3 WD(24),WS(24),TA(24).HMIX(24),DTDZI(24),
      4 AZ(6),BZ(6),CZ(6),P(6),SCLAB(6),DTDZ(2),SECTAN(16),
      5 XSWC,YSWC,GRID,LX,LY,A[2),B(2),POLNAM(3,2),CALNAM(7,2),
      6 ITA, IRD , IWR, IDSK, D80 , D47 , D8047 , DIST, DELTA, HPRIME ,
      7 ESH(2) .PEAK, IBUOY, IRISE, IDWN.EFF.XS.UINV.WVEC,
      8 NAS, NFS , INDEX, IGRID, IAV, ISCEN, IWDOPT, IWD, ISC, IPS,
      9 NTOPT , NWDOPT, NWSOPT , NWPOPT, NSCEN, NLIST, NARRAY, NTAPE , NCSOPT ,
      * NMAX, NSTDWN, NPRISE , NINPEN, INTER, NPRINT, NGPR, NBID

      COMMON/PARM1/NPOL , VD 1 , Wl , VD2 , W2
 PMT28180
 PMT28190
 PMT28200
 PMT28210
 PMT28220

 PMT28250
 PMT28230
 PMT28240
 PMT28260
 PMT28270
.PMT28280
 PMT28290
 PMT28300
 PMT28310
 PMT28320
 PMT28330
 PMT28340
 PMT28350
 PMT28360
 PMT28370
 PMT28380
 PMT28390
 PMT28400
 PMT28410
 PMT28420
 PMT28430
 PMT28440
 PMT28450
 PMT28460
 PMT28470
 PMT28480
 PMT28490
 PMT28500
 PMT28510
 PMT28520
 PMT28530
 PMT28540
 PMT28550
 PMT28560
                                      189

-------
      DIMENSION X(50),CC(50),SSDF(50),DV(2),AVD(2)
      INTEGER CC.SSDF

      DV(1)=VD1
      DV(2)=VD2
      WOUT= WD(ISCEN)*180./3.1415927
      NLX=1
      NLY=1
      IF(LX.GT.25) NLX=2
      IF(LY.GT.25J NLY=2
      NSECT=NLX*NLY
C
  100 ISECT=0
      DO 700 JLX=1,NLX
      MX2= JLX*25
      IF(MX2.GT.LX) MX2=LX
      MX1=1
      IF(JLX.EQ.2) MX1=26
      DO 125 I=MX1,MX2
      XI=I
125   X(I) = XSWC + (XI-0.5)*GRID
      DO 600 JLY=1,NLY
      ISECT=ISECT+1
      IF(JLY.EQ.l) GO TO 150
      MY1=26
      MY2=LY
      GO TO 175
150   MY1=1
      MY2=25
      IF(LY.LT.25) MY2=LY
C
C
175   DO 500 N=1,NPOL
      NREP=0
  180 IF(NARRAY.EQ.S) GO TO 181
C     PRINT UNCALIBRATED ARRAYS OF CONCENTRATION AND DEPOSITION FLUX
C     (FOR NARRAY = 1 OR 2)
      IF(NTOPT.EQ.l) WRITE(IWR,900)ISECT,NSECT,ISCEN,TT
      IF(NTOPT.GT.l) WRITE(IWR.901)ISECT,NSECT,TT
      IF(NTOPT.EQ.1)WRITE(IWR,902)SCLAB(ISC),WS(ISCEN),WOUT,HMIX(ISCEN)
     1             IAV.N,(POLNAM(L.N),L=l,3)
      IF(NTOPT.GT.l) WRITE(IWR,903)ISCEN,IAV,N,(POLNAM(L.N),L=1,3)

      IF(NREP.EQ.O) GO TO 185
C    LOOP THROUGH SDF ARRAY TO FIND ANY VALUE GE 1000. IN THAT CASE.
C     SET FLAG TO SCALE SDF VALUES AS THEY ARE SET IN SSDF ARRAY
  181 IFLAG=0
      DO 183 NX=1,LX
      DO 183 NY=1,LY
      IF(NARRAY.EQ.3]
      IF(SDF(NX,NY,N
      GO TO 183
  182 DUMMY=AVD(N)+B(N)*SDF(NX,NY,N)
      IF(DUMMY.GT.999.49) GO TO 184
  183 CONTINUE
      IF(NARRAY.EQ.3) GO TO 320
      WRITE(IWR,905)
      GO TO 190
  184 IFLAG=1
      IF(NARRAY.EQ.3) GO TO 320
      WRITE(IWR,910)
      GO TO 190
  185 WRITE(IWR,904)
  190 WRITE(IWR,915) (X(I),I=MX1,MX2,2)
      DO 300 J=MY1,MY2
      IY= MY2 + MY1 - J
      Y=IY
      Y= YSWC + (Y-0.5)*GRID
C
      IF(NHEP.EQ.l) GO TO 240
GO TO 182
GT.999.49) GO TO 184
                                   PMT28570
                                   PMT28580
                                   PMT28590
                                   PMT28600
                                   PMT28610
                                   PMT28620
                                   PMT28630
                                   PMT28G40
                                   PMT28650
                                   PMT28660
                                   PMT28670
                                   PMT28680
                                   PMT28690
                                   PMT28700
                                   PMT28710
                                   PMT28720
                                   PMT28730
                                   PMT28740
                                   PMT28750
                                   PMT28760
                                   PMT28770
                                   PMT28780
                                   PMT28790
                                   PMT28800
                                   PMT28810
                                   PMT28820
                                   PMT28830
                                   PMT28840
                                   PMT28850
                                   PMT28860
                                   PMT28870
                                   PMT28880
                                   PMT28890
                                   PMT28900
                                   PMT28910
                                   PMT28920
                                   PMT28930
                                   PMT28940
                                   PMT28950
                                  .PMT28960
                                   PMT28970
                                   PMT28980
                                   PMT28990
                                   PMT29000
                                   PMT29010
                                   PMT29020
                                   PMT29030
                                   PMT29040
                                   PMT29050
                                   PMT29060
                                   PMT29070
                                   PMT29080
                                   PMT29090
                                   PMT29100
                                   PMT29110
                                   PMT29120
                                   PMT29130
                                   PMT29140
                                   PMT29150
                                   PMT29160
                                   PMT29170
                                   PMT29180
                                   PMT29190
                                   PMT29200
                                   PMT29210
                                   PMT29220
                                   PMT29230
                                   PMT29240
                                   PMT29250
                                   PMT29260
190

-------
230
300
      DO 230 I=MX1,MX2
      CC(I)= CONC(I,IY,N)  +0.5
      WRITE(IWR,920)Y,(CC(I),I=MX1,MX2)
      GO TO 300
  240 DO 250 I=MX1.MX2
      IF(IFLAG.EQ.O)  GO TO 245
      SSDF(I)=SDF(I,IY,N)*1.0E-03 + 0.5
      GO TO 250
  245 SSDF(I)= SDF(I,IY,N) +0.5
  250 CONTINUE
      WRITE(IWR, 920)  Y,(SSDF(I),I=MX1,MX2)
      WRITE(IWR,925)Y
C
C
C
C
      WRITE(IWR,915)(X(I),I=MX1,MX2,2)
      IF(NARRAY.EQ.2) GO TO 450
      PRINT CALIBRATED ARRAYS OF CONCENTRATION (FOR NARRAY = 1 OR 3)
      AND DEPOSITION FLUX (FOR NARRAY = 3 ONLY)
  320 IF(NTOPT.EQ.l) WRITE(IWR,900)ISECT,NSECT,ISCEN.TT
      IF(NTOPT.GT.l) WRITE(IWR,901)ISECT,NSECT,TT
      IFCNTOPT.EQ.1)WRITE(IWR.902)SCLAB(ISC),WS(ISCEN),WOUT,HMIX(ISCEN)
                    AVtN,(POLNAM(L.N),L=l,3)
      IF
      IF
      IF
      IF
      IF
      IF
                   xnT 9 u, ^ i \sjjii niTx\ jj.iiyjjj—j.joy
         NTOPT.GT.l) WRITE(IWR.903)ISCEN,IAV,N,(POLNAM(L,N).L=1,3)
         NREP.EQ.O) WRITE(IWR,906)(CALNAM(L,N),L=1,7),A(N),B(N)
         NARRAY.EQ.l) GO TO 322
         NREP.EQ.O) GO TO 322
                 .0) WRITE(IWR,907)
IFLAG.EQ
IFLAG.EQ
.0)
.1)  WRITE(IWR;909)
  322 WRITE(IWR,915)(X(I),I=MX1,MX2,2)
      DO 400 J=MY1.MY2
      IY= MY2 + MY1 - J
      Y=IY
      Y= YSWC + (Y-0.5)*GRID
330
      IF(NREP.EQ.l) GO TO 340
      DO 330 I=MX1,MX2
      CC(I)= A(N) + B(N)*CONC(I,IY,N) + 0.5
      WRITE(IWR,920}" 	     "	
      GO TO 400
      V v \ •»• /  t» \ LI y  • .feryny-'-wi.wy.j.i.kj.i&i/  •

      WRITE(IWR,920)Y,(CC(I),I=MX1,MX2)
  340 IF(NARRAY.EQ.l) GO TO 500
      DO 350  I=MX1,MX2
      SSDF(I)= AVD(N) + B(N) * SDF(I.IY.N)
      IF(IFLAG.EQ.l) SSDF(I)=SSDF(I)*1.0E-03
      SSDF?I)^SSDF(I)+0.5
  350 CONTINUE
      WRITE(IWR,920) Y,(SSDF(I),I=MX1,MX2)
400   WRITE(IWR,925)Y
      WRITE(IWR,915)(X(I),I=MX1,MX2,2)
C
  450 IF(NREP.EQ.l) GO TO 500
C   IF NO SURF DEP FLUX WAS CALCULATED,  SKIP  PRINT
      IF(DV(N).LE.0.01) GO TO 500
      NREP=I
      AVD(N)=A(N)*DV(N)*36.
      GO TO 180
      CONTINUE
      CONTINUE
      CONTINUE
500
600
700
C

C
900
      RETURN
                                    'SECTION

                                    'SECTION
                                     ,11,

                                     ,11,
                                  OF

                                  OF
',11,',  SCENARIO

M1.3X,
      FORMAT(lHl,'PEM-2 OUTPUT:
     1,I2,2X,20A4)
  901 FORMAT(1H1,*PEM-2 OUTPUT:
     1 20A4)
902   FORMATC STABILITY=' A2 '.  WIND SPD='.F5.2,' M/S. WIND DIR=',F6.2
     1 '  DEG, MIXING HT=>,F7.1,'  M, AVERAGING TIME=',I2,' HE.',6X,
     2 'POLLUTANT-'.II,': ',3A4J
  903 FORMAT(IX,12,' SCENARIOS,*,2X,'AVERAGING TIME=',I3,' HRS.',64X,
 PMT29270
 PMT29280
 PMT29290
 PMT29300
 PMT29310
 PMT29320
 PMT29330
 PMT29340
 PMT29350
 PMT29360
 PMT29370
 PMT29380
 PMT29390
 PMT29400
 PMT29410
 PMT29420
 PMT29430
 PMT29440
 PMT29450
 PMT29460
.PMT29470
 PMT29480
 PMT29490
 PMT29500
 PMT29510
 PMT29520
 PMT29530
 PMT29540
 PMT29550
 PMT29560
 PMT29570
 PMT29580
 PMT29590
 PMT29600
 PMT29610
 PMT29620
 PMT29630
 PMT29640
 PMT29650
 PMT29660
 PMT29670
.PMT29680
 PMT29690
 PMT29700
 PMT29710
 PMT29720
 PMT29730
 PMT29740
 PMT29750
 PMT29760
 PMT29770
 PMT29780
 PMT29790
 PMT29800
 PMT29810
 PMT29820
 PMT29830
 PMT29840
 PMT29850
 PMT29860
 PMT29870
 PMT29880
'PMT29890
 PMT29900
 PMT29910
 PMT29920
.PMT29930
 PMT29940
 PMT29950
 PMT29960
                                      191

-------
     1 'POLLUTANT-',11,':  ',3A4)                                        PMT29970
904   FORMATC UNCALIBRATED  CONCENTRATION - MICROGRAMS PER CUBIC METER')PMT29980
  905 FORMATC UNCALIBRATED  SURFACE DEPOSITION FLUX - MICROGRAMS PER SQUPMT29990
     1ARE METER PER HOUR')                                              PMT30000
906   FORMATC CALIBRATED CONCENTRATION - ',7A4,18X,'CALIBRATION COEFFICPMT30010
     1IENTS:  A = ' F11.4'   B=',F11.4)                                PMT30020
  907 FORMATC CALIBRATED SURFACE DEPOSITION FLUX - MICROGRAMS PER SQUARPMT30030
     IE METER PER HOUR')                                                PMT30040
  909 FORMATC CALIBRATED SURFACE DEPOSITION FLUX - KILOGRAMS PER SQUAREPMT30050
     1 KILOMETER PER HOUR')                                              PMT30060
  910 FORMATC UNCALIBRATED  SURFACE DEPOSITION FLUX - KILOGRAMS PER SQUAPMT30070
     IRE KILOMETER PER HOUR')
      FORMAT(1HO,14X,13F8.2)
      FORMAT(1HO,4X,F8.2,4X,25I4)
      FORMAT(1H+,122X,F8.2)
      END
915
920
925

C
C
C

C
C
C
C
C
C
C
C
C
C *** PEM MODIFICATIONS BY M.M. STEVENS,
      SUBROUTINE WORST(I,J,CHI,N)
                     SUBROUTINE WORST
                                         PART OF PEM-2 (VERSION 84130)
                                                                   THE
   SUBROUTINE WORST DETERMINES THE FIVE POINT SOURCES CONTRIBUTING
     MOST TO THE TOTAL CONCENTRATION AT EACH RECEPTOR. SOURCE
     IDENTIFICATIONS AND CONTRIBUTIONS ARE STORED IN NWORST AND CWORST
     RESPECTIVELY, FOR OUTPUT BY SUBROUTINE WOROUT.
      NOAA-ATDL, P.O.
      DECEMBER 1982
                      BOX-E, OAK RIDGE, TENN 37831
C
C
C
C *** PEM-2 MODIFICATIONS BY K.  S.  RAO
C
C
C
                                                           ,2),
C
C
205
210
215
220
225

250
      DECEMBER 1984
      COMMON/PEMCOM/CONC(50.50,2),SDF{50,50,2).TT(20).
     1 XP(300),YP(300),EP(360,2),HP(300),DP(306),VP(36o),TP(300)
     2 XA(50) YA(50),EA(50.2)JSIZE(50),
     3 WD(24),WS(24),TA(24),HMIX(24),DTDZI(24),
     4 AZ(6).BZ(6),CZ(6),P(6),SCLAB(6) JDTDZ(2},SECTAN(16),
     5 XSWC,YSWCIGRID,LX,LY,A(2),B(2),POLNAM(3,2),CALNAM(7,:
     6 ITA,IRD.IWR,IDSK.D80,D47,D8047,DIST)DELTA,HPRIME,
     7 ESH(2))PEAK,IBUOY,IRISE,IDWN,EFF)XS,UINV,WVEC,
     8 NAS.NPS,INDEX,IGRID,IAV,ISCEN,IWDOPT,IWD.ISC.IPS,
     9 NTOPT,NWDOPT,NWSOPT,NWPOPT,NSCEN,NL1ST,NARRAY,NTAPE,NCSOPT,
     * NMAX,NSTDWN,NPRISE,NINPEN,INTER,NPRINT,NGPR,NBID

      COMMON/CSWOR/NWORST(25,25,5,2),CWORST(25,25,5,2)
      IF(CHI.LE.CWORST(I,J,5,N)} RETURN
      IF(CHI.GT.CWORST(I,J,4,N)) GO TO 205
      CWORST(I,J,5,N)= CHI
      NWORST(I,J,5,N)= IPS
      RETURN
      IF(CHI.GT.CWORST(I,J,3,N)) GO TO 210
      NW=1
      GO TO 225
      IF(CHI.GT.CWORST(I,J,2,N)) GO TO 215
      NW=2
      GO TO 225
      IF(CHI.GT.CWOHST(I,J,1,N)) GO TO 220
      NW=3
      GO TO 225
      NW=4
      DO 250 IW=1,NW
      CWORST(I,J,6-IW,N)= CWORST(I,J.5-IW.N
      NWORST(I,J,6-IW,N)= NWORST(I,J.5-IW.N
PMT30080
PMT30090
PMT30100
PMT30110
PMT30120

PMT30130
PMT30140
PMT30150
PMT30160
PMT30170
PMT30180
PMT30190
PMT30200
PMT30210
PMT30220
PMT30230
PMT30240
PMT30250
PMT30260
PMT30270
PMT30280
PMT30290
PMT30300
PMT30310
PMT30320
PMT30330
PMT30340
PMT30350
PMT30360
PMT30370
PMT30380
PMT30390
PMT30400
PMT30410
PMT30420
PMT30430
PMT30440
PMT30450
PMT30460
PMT30470
PMT30480
PMT30490
PMT30500
PMT30510
PMT30520
PMT30530
PMT30540
PMT30550
PMT30560
PMT30570
PMT30580
PMT30590
PMT30600
PMT30610
PMT30620
PMT30630
PMT30640
PMT30650
                                      192

-------
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
      CWORST(I,
      NWORST(I,
      RETURN
      END
             J,5-NW,N)= CHI
             J,5-NW,N)= IPS
                                                                  PMT30660
                                                                  PMT30670
                                                                  PMT30680
                                                                  PMT30690
                                                                      PMT30700
                                                                      PMT30710
                                                                      PMT30720
                                                                      PMT30730
                                                                      PMT30740
                                                                      PMT30750
 SUBROUTINE WOROUT PRINTS A CULPABILITY LIST OF THE FIVE POINT SOURCESPMT30760
   WHICH CONTRIBUTE MOST TO THE TOTAL CONCENTRATION OF EACH POLLUTANT.PMT30770
SUBROUTINE WOROUT
               SUBROUTINE
WOROUT ,  PART OF PEM-2 (VERSION 84130)
   THIS ROUTINE LISTS THE FIVE POINT SOURCES AND THEIR PERCENTAGE
   CONTRIBUTIONS TO THE TOTAL CONCENTRATION AND SURFACE DEPOSITION
   FLUX AT EACH RECEPTOR.
   TO REDUCE OUTPUT. ONLY RECEPTORS WITH THE HIGHEST CONTRIBUTIONS
   EXCEEDING 1 MICROGRAM PER CUBIC METER ARE PRINTED.
   USING DATA COMPILED BY SUBROUTINE WORST, THIS INFORMATION IS
   PRINTED AT THE END OF EACH SCENARIO OR SUB-SCENARIO FOR NTOPT=1.


*** PEM MODIFICATIONS AND FORMATS BY M.M. STEVENS,
    NOAA-ATDL. P.O. BOX E, OAK RIDGE, TN 37831
    DECEMBER 1982
*** PEM-2 MODIFICATIONS BY K. S. RAO
    DECEMBER 1984
C
C
C
                                                         TP(300)
    COMMON/PEMCOM/CONC(50.50,2),SDF[50,50,2).TT(20).
     XP 300),YP(300y.EP(36o,2),HP(300),DP(3o6),VP(36o),
     XA 50),YA(50),EA(50,2),SIZE(50),
     WD 24),WS£24),TA(24),HMIX(24).DTDZI(24),
     AZ 6),BZ(6),CZ(6)JP(6),SCLABr6),DTDZ(2)>SECTAN(16),
     XSWC,YSWC,GRIDiLX,LY,A(2),B(2),POLNAM(3,2).CALNAM(7,2),
     ITA,IRD,IWR,IDSK,D80,D47,D8047,DIST,DELTA,HPRIME,
   7 ESH(2_) .PEAK, IBUOY, IRISE, IDWN.EFF, XS.UINV.WVEC,
   8 NAS.NPS,INDEX,IGRID,IAV,ISCEN,IWDOPT.IWD,ISC,IPS,
   9 NTOPT,NWDOPT,NWSOPT,NWPOPT,NSCEN,NLIST,NARRAY,NTAPE,NCSOPT,
   * NMAX,NSTDWN,NPRISE,NINPEN,INTER,NPRINT,NGPR,NBID

    COMMON/CSWOR/NWORST(25,25,5.2),CWORST(25,25,5,2)
    COMMON/PARM1/NPOL,VD1,Wl,VD2,W2
    START DO-LOOP ON POLLUTANT SPECIES
    DO 400 K=1,NPOL
    WRITE(IWR,905) TT,ISCEN
    IF(NWDOPT.LE.l) GO TO 200
    WOUT=WD(ISCEN)*180./3.1415927
    WRITE(IWR,910) WOUT
C
C
C
C

C
C

C
C
C
  200 WRITE(IWR,920)
      WRITE(IWR,915)
                   K,(POLNAM(M,K),M=1,3)
    START DO-LOOP ON RECEPTOR GRID COLUMNS
    DO 350 1=1,LX
    XI=I
    X= XSWC +  (XI-0.5)*GHID

    START DO-LOOP ON RECEPTOR GRID ROWS
    DO 300 J=1,LY

    SUPPRESS PRINT IF THE HIGHEST CONCENTRATION IS INSIGNIFICANT
    IF(CWORST(I,J,1,K).LT.1.0) GO TO 300

    START DO-LOOP TO CONVERT FIVE HIGHEST CONTRIBUTIONS TO
    PERCENTAGES OF TOTAL CONCENTRATION AT THE RECEPTOR
    DO 250 L=l,5
    CWORST(I,J,L,K)=CWORST(I,J,L,K)*100./CONC(I,J,K)
                                                                  PMT30780
                                                                  PMT30790
                                                                  PMT30800
                                                                  PMT30810
                                                                  PMT30820
                                                                  PMT30830
                                                                  PMT30840
                                                                  PMT30850
                                                                  PMT30860
                                                                  PMT30870
                                                                  PMT30880
                                                                  PMT30890
                                                                  PMT30900
                                                                  PMT30910
                                                                  PMT30920
                                                                  PMT30930
                                                                  PMT30940
                                                                  PMT30950
                                                                  PMT30960
                                                                  PMT30970
                                                                  PMT30980
                                                                  PMT30990
                                                                  PMT31000
                                                                  PMT31010
                                                                  PMT31020
                                                                  PMT31030
                                                                  PMT31040
                                                                  PMT31050
                                                                  .PMT31060
                                                                  PMT31070
                                                                  PMT31080
                                                                  PMT31090
                                                                  PMT31100
                                                                  PMT31110
                                                                  PMT31120
                                                                  PMT31130
                                                                  PMT31140
                                                                  PMT31150
                                                                  PMT31160
                                                                  PMT31170
                                                                  PMT31180
                                                                  PMT31190
                                                                  PMT31200
                                                                  PMT31210
                                                                  PMT31220
                                                                  PMT31230
                                                                  PMT31240
                                                                  PMT31250
                                                                  PMT31260
                                                                  PMT31270
                                                                  PMT31280
                                                                  PMT31290
                                                                  PMT31300
                                                                  PMT31310
                                                                  PMT31320
                                                                  PMT31330
                                                                  PMT31340
                                      193

-------
c
c
250 CONTINUE
    END LOOP ON FIVE HIGHEST CONTRIBUTIONS
      YJ=J
      Y= YSWC
                               PMT31350
                               PMT31360
                               PMT31370
                               PMT31380
                               PMT31390
              (;YJ-0.5)*GRID                                           	
    WRITE(IWR,925)I.J,X,Y,NWORST(I,J,1.K),CWORST(I,J,1.K),NWORST(I,J,2PMT31400
   1,K),CWORST(I,J,2.K),NWORST(I,J,3.K5,CWORST(I,J)3.K ,IWORST(I,J 4 KPMT31410
   2),CWORST(I,J,4,K),NWORST(I,J,5,K))CWORST(I,J,5IK),CONC(I,J,K),SDF(PMT31420
   3I,J,K)                                                            PMT31430
  300 CONTINUE
C     END LOOP ON GRID ROWS
  350 CONTINUE
C     END LOOP ON GRID COLUMNS
  400 CONTINUE
C     END LOOP ON SPECIES
C

C
    RETURN
                               PMT31440
                               PMT31450
                               PMT31460
                               PMT31470
                               PMT31480
                               PMT31490
                               PMT31500
                               PMT31510
                               PMT31520
  905 FORMAT(1H1.37X,'POLLUTION EPISODIC MODEL (PEM-2)V//4X,'OUTPUT:
     .	v... ..—i	RODUCE THE HIGHESPMT31550
    :\yiu'ui. j. i xiix * *J t f\ * i vjjuu J. j-v/n ui J.LJI/I/ j-vy riwu u v *• t^L"1 ** J / / / *"*A « l/u IfU 1 •   PMT31540
   1.20A4//4X,'LIST OF THE FIVE POINT SOURCES WHICH PRODUCE THE HIGHESPMT31550
   2T VALUES OF CONCENTRATION AND SURFACE DEPOSITION FLUX AT EACH  RECEPMT31560
   3PTOR'//5X,'SCENARIO',14X,'   -  CONCENTRATION IN MICROGRAMS PER ', PMT31570
   4'CUBIC METER'/6X,'NUMBER: '12,16X,'SURFACE DEPOSITION FLUX IN MICPMT31580
   5ROGRAMS PER SQUARE METER PER HOUR'/}                              PMT31590
910 FORMAT(6X.'WIND DIRECTION = ',F5.1,* DEC'/)                       PMT31600
915 FORMAT(45X,'POINT SOURCE SEQUENCE NUMBER AND PERCENT'/            PMT31610
   115X,'COORDINATES'.15X,'OF TOTAL CONCENTRATION AND SURFACE DEPOSITIPMT31620
   20N FLUX',14X,'TOTAL'.8X,'TOTAL SURFACE'/                          PMT31630
   3' COL ROW',4X,'X  (KMr,4X,'Y (KM) ' 9X, 'HIGHEST' ,6X.' SECOND' 8X,   PMT31640
    'THIRD',7X,'FOURTH',8X,'FIFTH*,6X,JCONCENTRATION',3X,'DEPOSITION FPMT31650
     4
     SLUX'/l
  920 FORMAT(45X,'POLLUTANT-',II,' :',3A4
                                                                      PMT31660
                                                                      PMT31670
C
C
C

C
C
C
C
C
C
C
C
C
C
C
C
  925 FORMAT(2(2X,I2),3XJF8.2,2X>F8.2,3X,5(3X,I3,F7.2)J6X,F8.2,9X,F8.2)  PMT31680
                                                                         PMT31690
      END                                                                PMT31700
    SUBROUTINE SCENMX
                   SUBROUTINE SCENMX
PART OF PEM-2 (VERSION 84130)
                                                                     PMT31710
                                                                     PMT31720
                                                                     PMT31730
                                                                     PMT31740
                                                                     .PMT31750
                                                                     PMT31760
                                                                     PMT31770
                                                                     PMT31780
                                                                     PMT31790
                                                                     PMT31800
                                                                     PMT31810
                                                                     PMT31820
THE STORED VALUES ARE PRINTED BY SUBROUTINE MAXOUT AT THE END OF RUN.PMT31830
                                                                     PMT31840
                                                                     PMT31850
                                                                     PMT31860
 SUBROUTINE SCENMX LOCATES AND STORES THE COORDINATES, CONCENTRATION,
 AND SURFACE DEPOSITION FLUX AT THE RECEPTOR GRID POINTS RECORDING
 THE HIGHEST CONCENTRATION AND SURFACE DEPOSITION FLUX OF EACH
 POLLUTANT IN EACH SCENARIO (IF NTOPT=1) OR AVERAGING-PERIOD  (IF
 NTOPTM).
C *** PEM MODIFICATIONS BY M.M. STEVENS,

C
C
C
                                                          TP(300)
    NOAA-ATDL. P.O.BOX - E, OAK RIDGE, TN 37831
    DECEMBER  1982


    COMMON/PEMCOM/CONC(50.50.2).SDF(50,50,2).TT(20).
    1 XP 300),YP(300),EP(360,2),HP(300),DP(30&),VP(3&0),
    2 XA 50T,YA(50),EA(50,2),SIZE(50),
    3 WD 24),WS(24),TA(24),HMIX(24),DTDZI(24),
    4 AZ 6).BZ(6),CZ(6),P(6),SCLAB(6),DTDZ(2i,SECTAN(16),
    5 XSWC,YSWC,GRID,LX,LY,A(2),B(2),POLNAM(3,2),CALNAM(7,2),
    6 ITA,IRD,IWR,IDSK,D80,D47,08047,DIST,DELTA,HPRIME,
    7 ESH(2),PEAK,IBUOY,IRISE,IDWN,EFF,XS,UINV,WVEC>
    8 NAS.NPS,INDEX,IGRID,IAV,ISCEN,IWDOPT,IWD,ISC,IPS,
    9 NTOPT,NWDOPT,NWSOPT,NWPOPT,NSCEN,NLIST,NARRAY,NTAPE,NCSOPT,
    * NMAX,NSTDWN,NPRISE,NINPEN,INTER,NPRINT,NGPR,NBID

    COMMON/MAX/XMX(24,4,2),YMX(24,4,2),ZMX(24,4,2),SMX(24,4,2)
                               PMT31870
                               PMT31880
                               PMT31890
                               PMT31900
                               PMT31910
                               PMT31920
                               PMT31930
                               PMT31940
                               PMT31950
                               PMT31960
                               PMT31970
                               PMT31980
                               PMT31990
                               PMT32000
                               PMT32010
                               PMT32020
                               PMT32030
                                      194

-------
c
c
120
130
140
150
350
400
C
C
C

C
C
C
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
      COMMON/PARM1/NPOL,VD1,Wl,VD2, W2
   IF(NTOPT.EQ.l) GO TO 120

   GO TO 130
   1= ISCEN
   IF(NWDOPT.LE.l) GO TO 140
   J= IWDOPT
   GO TO 150
   J= 1
   DO 400 K=1,NPOL
   Z= 0.
   DO 350 NX=1,LX
   DO 350 NY=1.LY
   IF(CONC(NX,NY,K)
   Z= CONG(NX.NY.K)
   ZS=SDF(NX,NY,K)
   ZX=NX
   ZY=NY
   CONTINUE
   ZMX(I,J,K
   SMX(I,J,K
   XMX(I,J,K
   YMXCI.J.K
                       LT.Z) GO TO 350
   X L 1*\ I J- • fc/ • X
   CONTINUE
   RETURN
   END
                = Z
                =ZS
                = xswc
                = YSWC
(ZX -
(ZY -
                             0.5)*GRID
                             0.5)*GRID
   SUBROUTINE MAXOUT
                  SUBROUTINE MAXOUT
                                       PART OF PEM-2 (VERSION 84130)
SUBROUTINE MAXOUT PRINTS THE COORDINATES, CONCENTRATION, AND
SURFACE DEPOSITION FLUX AT THE RECEPTOR GRID POINTS RECORDING
THE HIGHEST CONCENTRATION OF EACH POLLUTANT IN EACH SCENARIO OR
AVERAGING PERIOD. THESE VALUES WERE SELECTED AND STORED BY SUB-
ROUTINE SCENMX.
*** PEM MODIFICATIONS AND
    NOAA-ATDL. P.O.BOX E,
    DECEMBER 1982
*** PEM-2 MODIFICATIONS BY K. S. RAO
    DECEMBER 1984
                         FORMATS BY M.M. STEVENS,
                         OAK RIDGE, TN 37831
      COMMON/PEMCOM/CONC(50.50,2),SDF(50,50,2).TT(20).
       XP(300),YP(300),EP(300,2),HP[300),DP(300),VP(300),TP(300),
       v A fm\  v i / cn\ #il/ —•*  ~» — '-*—xi->  ' '   *    ''   v    ''   v    •" '
       XA(50),YA(50),EA(
         ir,YA(50),EA(50.2r,SIZE(50}, '
    WD(24),WS(24),TA(24},HMIX(24),DTDZI(24;
                                                        2),
C
C
              ,,,,,
        AZ(6),BZ(6),CZ(6),P(6).SCLAB(6),DTDZ(2),SECTAN(16),
     ^  XSWC,YSWC,GRID,LX,LY,A(2),B72T,POLNAM(3,2),CALNAM(7,
     6  ITA.IRD,IWR,IDSK,D80,D47,D8047,D1ST,DELTA,HPRIME,
  .  ESH(2),PEAK,IBUOY,IRISE,IDWN,EFF,XS,UINV,WVEC,
  8 NAS,NPS,INDEX,IGRID,IAV,ISCEN,IWDOPT,IWD.ISC,IPS.
  9 NTOPT,NWDOPT,NWSOPT,NWPOPT,NSCEN,NLIST,NARRAY,NTAPE,NCSOPT,
  * NMAX,NSTDWN,NPRISE,NINPEN,INTER,NPRINT,NGPR,NBID

   COMMON/MAX/XMX(24,4,2),YMX(24,4,2))ZMX(24)4,2),SMX(24,4,2)
   COMMON/PARM1/NPOL,VD1,Wl,VD2,W2
   DIMENSION ZC(2),ZS(2),AVD(2)

 CHECK WHETHER SURF DEP FLUX WAS CALCULATED AND SET FLAG
   NREP=0
   IF(VD1.GE.0.01 .OR. VD2.GE.0.01) GO TO 100
   GO TO 110
PMT32040
PMT32050
PMT32060
PMT32070
PMT32080
PMT32090
PMT32100
PMT32110
PMT32120
PMT32130
PMT32140
PMT32150
PMT32160
PMT32170
PMT32180
PMT32190
PMT32200
PMT32210
PMT32220
PMT32230
PMT32240
PMT32250
PMT32260
PMT32270
PMT32280
PMT32290
PMT32300
PMT32310

PMT32320
PMT32330
PMT32340
PMT32350
PMT32360
PMT32370
PMT32380
PMT32390
PMT32400
PMT32410
PMT32420
PMT32430
.PMT32440
PMT32450
PMT32460
PMT32470
PMT32480
PMT32490
PMT32500
PMT32510
PMT32520
PMT32530
PMT32540
PMT32550
PMT32560
PMT32570
PMT32580
PMT32590
PMT32600
PMT32610
PMT32620
PMT32630
PMT32640
PMT32650
PMT32660
PMT32670
PMT32680
PMT32690
PMT32700
PMT32710
PMT32720
                                      195

-------
c
c
c
c
c
c
c
c
c
c
100 NREP=1
    AVD(1)=A(1)*VD1*36.
    AVD(2)=A(2)*VD2*36.

110 IF(NWDOPT.GT.l) GO TO 300

    J=l
    N=l
    IF(NTOPT.EQ.l) N=NSCEN
  PRINT HIGHEST CONCENTRATIONS
    WRITE(IWR,900) TT
    WRITE(IWR.902) 7cALNAM(L.l).L=1.7)
    IF(NPOL.EQ.2) WRITE(IWR,903) (CALNAM(L,2),L=1,7)
    WRITE(IWR.910) ?POLNAM(L.1).L=1,3)
    IF(NPOL.EQ.2) WRITE(IWR,911) (POLNAM(L,2),L=1,3)
    WRITE(IWR,912)
    WRITE(IWR.915)
    DO 200 1=1,N
    DO 120 K=l NPOL
120 ZC(K) = A(K} + B(K)*ZMX(I,1,K)
    WRITE(IWR,920)
    WRITE(IWR.923) I,(XMX(I,1,K),YMX(I,1,K),ZMX(I,1,K),ZC(K),
   1 K=1,NPOL)
200 CONTINUE

  PRINT SURFACE DEPOSITION FLUX VALUES
  IF NO SURF DEP FLUX WAS CALCULATED, SKIP PRINT
    IF(NREP.EQ.O) RETURN
    WRITE(IWR,900) TT
    WRITE(IWR,932) (CALNAM(L.l).1=1,7)
    IF(NPOL.EQ.2) WRITE(IWR,933) (CALNAM(L,2),L=1,7)
    WRITE (IWR. 910) _(POLNAMJ'L,1).L=1.3)
    IF(NPOL.EQ.2) WRITE(IWR,911) (POLNAM(L,2),L=1,3)
    WRITE(IWR,942)
    WRITE[IWR.915)
    DO 250 1=1,N
    DO 220 K=1,NPOL
220 ZS(K)= AVD(K) + B(K)*SMX(I,1,K)
    WRITE(IWR,920)
    WRITE(IWR,923) I,(XMX(I,1,K),YMX(I,1,K),SMX(I,1,K),ZS(K),
   1 K=1,NPOL)
25JO CONTINUE

    RETURN

  PRINT FOR CASE OF NWDOPTH  -  SUB-SCENARIOS
300 N=NSCEN
  PRINT HIGHEST CONCENTRATIONS
    DO 500 1=1,N
    IF((?I-1)/8)*8.NE.I-1) GO TO 310
    WRITE(IWR,900) TT
    WRITE(IWR,902) (CALNAM(L.1),L=1,7)
    IF(NPOL.EQ.2) WRITE(IWR,903) (CALNAM(L,2),L=1,7)
    WRITE(IWR, 910) _(POLNAM(L. 1) . L=1.3)
    IF(NPOL.EQ.2) WRITE(IWR,911) (POLNAM(L,2),L=1,3)
    WRITE(IWR,912)
    WRITE(IWR,915)
310 WRITE(IWR,920)
    DO 400 J=l,4
    DO 320 K=1.NPOL
320 ZC(K)= A(K) + B(K)*ZMX(I,J,K)
    WRITE(IWR.925) I,J,(XMX(I,J,K),YMX(I,J,K),ZMX(I,J,K),ZC(K),
   1 K=1,NPOL)
400 CONTINUE
500 CONTINUE

  PRINT SURFACE DEPOSITION FLUX VALUES
  IF NO SURF DEP FLUX WAS CALCULATED, SKIP PRINT
    IF(NREP.EQ.O) RETURN
    DO 600 1=1,N
PMT32730
PMT32740
PMT32750
PMT32760
PMT32770
PMT32780
PMT32790
PMT32800
PMT32810
PMT32820
PMT32830
PMT32840
PMT32850
PMT32860
PMT32870
PMT32880
PMT32890
PMT32900
PMT32910
PMT32920
PMT32930
PMT32940
PMT32950
PMT32960
PMT32970
PMT32980
PMT32990
PMT33000
PMT33010
PMT33Q20
PMT33030
PMT33040
PMT33050
PMT33060
PMT33070
PMT33080
PMT33090
PMT33100
PMT33110
PMT33120
PMT33130
PMT33140
PMT33150
PMT33160
PMT33170
PMT33180
PMT33190
PMT33200
PMT33210
PMT33220
PMT33230
PMT33240
PMT33250
PMT33260
PMT33270
PMT33280
PMT33290
PMT33300
PMT33310
PMT33320
PMT33330
PMT33340
PMT33350
PMT33360
PMT33370
PMT33380
PMT33390
PMT33400
PMT33410
PMT33420
                                     196

-------
      IF(((I-1)/8)*8.NE.I-1)  GO TO 510
      WRITE(IWR,960)  TT
      WRITE(IWR,932)  ?CALNAM(L.1).L=l.7)
      IFONPOL.EQ.2) WRITE(IWR,933)  (CALNAM(L,2),L=1,7)
      WRITE(IWR,910)  ?POLNAM(L.1).L=1,3)
      IF(NPOL.EQ.2) WRITE(IWR,911)  (POLNAM(L,2),1=1,3)
      WRITE(IWR,942
      WRITE(IWR,915)
  510 WRITE(IWR,920)
      DO 550 J=I,4
      DO 520 K=ltNPOL
  520 ZS(K)= AVD
      WRITE(IWR,
     1 K=1,NPOL)
  550 CONTINUE
  600 CONTINUE

  700 RETURN
                    B(K)*SMX(I,J,K)
                   I,J,(XMX(I,J,K),YMX(I,J,K),SMX(I,J,K),ZS(K)
                                                                     PMT33430
                                                                     PMT33440
                                                                     PMT33450
                                                                     PMT33460
                                                                     PMT33470
                                                                     PMT33480
                                                                     PMT33490
                                                                     PMT33500
                                                                     PMT33510
                                                                     PMT33520
                                                                     PMT33530
                                                                     PMT33540
                                                                     PMT33550
                                                                     PMT33560
                                                                     PMT33570
                                                                     PMT33580
                                                                     PMT33590
                                                                     PMT33600
                                                                     PMT33610
                                                                     PMT33620
  900 FORMAT(1H1.37X,'POLLUTION EPISODIC MODEL (PEM-2)V//4X,'OUTPUT:
     1.20A4//)                                                          PMf33630
  902 FORMAT(4X,'HIGHEST PREDICTED CONCENTRATION OF EACH POLLUTANT FOR EPMT33640
     1ACH SCENARIO OR AVERAGING PERIOD'//4X,'UNCALIBRATED CONCENTRATION PMT33650
     2IN MICROGRAMS PER CUBIC METER  -  CALIBRATION, POLLUTANT-1: ',7A4)PMT33660
  903
                                         *,7A4)
    FORMAT 65X.'CALIBRATION, POLLUTANT-2:
910 FORMAT //40X.'POLLUTANT-1: ',3A4)
911 FORMAT 1H+.93X.'POLLUTANT-2:  ',3A4)
912 FORMAT /' SCENARIO  WIND DIRECTION*,7X 'COORDINATES' 14X,
   1'CONCENTRATION' 16X,'COORDINATES',14X.'CONCENTRATION1)
915 FORMAT(2X,'NUMBER',4X,'SUB-SCENARIO',6X.'X(KM)',5X.'Y(KM)',
   1'UNCALIBRATED',4X,'CALIBRATED',7X,'X(KM)',5X,'Y(KM)' ,6X,
   2'UNCALIBRATED',4X,'CALIBRATED'/)
920 FORMAT(IX)
923 FORMAT(4X.I2,21X,F9.2,1X,F9.2,5X,F11.4,4X,F11.4,4X,F9.2,1X,
   1F9.2.5X.F11.4.4X F11.4)
                                                                 6X,
PMT33670
PMT33680
PMT33690
PMT33700
PMT33710
PMT33720
PMT33730
PMT33740
PMT33750
PMT33760
PMT33770
  925 FORMAT(4x,I2,ilX,I2.8X.F9.2,lX,F9.2,5X,Fll.4,4X,F11.4,4X,F9.2,lX, PMT33780
     lF9.2.5X.Fil.4,4X,Fli.4J                                           PMT33790
  932 FORMAT(4X,'HIGHEST PREDICTED SURFACE DEPOSITION FLUX OF EACH POLLUPMT33800
     1TANT FOR EACH SCENARIO OR AVERAGING PERIOD'//4X 'UNCALIBRATED VALUPMT33810
     2ES IN MICROGRAMS PER SQUARE METER PER HOUR  -  CALIBRATION, POLLUTPMT33820
     3ANT-1: ',7A4)                                                     PMT33830
  933 FORMAT(68X,'CALIBRATION, POLLUTANT-2: '.7A4)                      .PMT33840
  942 FORMAT(/' SCENARIO  WIND DIRECTION' 7X  'COORDINATES' 9X,          PMT33850
     1'SURFACE DEPOSITION FLUX',11X,'COORDINATES',9X,'SURFACE DEPOSITIONPMT33860
C
C
C

C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
     2 FLUX')
      END
   SUBROUTINE RISE
                  SUBROUTINE RISE
                                       PART OF PEM-2  (VERSION  84130)
SUBROUTINE RISE CALCULATES PLUME RISE VIA THE STANDARD EQUATIONS
  OF BRIGGS (1971,1969) IF NPRISE=0. IF NPRISE=1 OPTION IS SELECTED
PMT33870
PMT33880

PMT33890
PMT33900
PMT33910
PMT33920
PMT33930
PMT33940
PMT33950
PMT33960
  wr onxuvio i i j i i , i^i^jj i i.c nr nioc. — \j , LC vtcHJLLJO — JL wr i J.WH j.o ^cuUCiU iCiii, ri'iiuo^ou
  THE NEW PLUME RISE EQUATIONS OF BRIGGS (1984,1975) ARE USED FOR THEPMT33970
  BUOYANCY-DOMINATED PEAK PLUME RISE IN UNSTABLE/NEUTRAL CONDITIONS. PMT33980
  IF IRISE=1,  THE DISTANCE-DEPENDENT EFFECTIVE SOURCE HEIGHT (ESH(l))PMT33990
  IS RETURNED. IF IRISE=2, MAXIMUM EFFECTIVE SOURCE HEIGHT (ESH(2)  ISPMT34000
  RETURNED. RISE IS CALLED ONLY ONCE PER SOURCE PER SCENARIO WITH    PMT34010
  IRISE=2. IT IS CALLED WITH IRISE=1 WHENEVER THE DOWNWIND DISTANCE
  (DIST) IS LESS THAN THE DISTANCE TO MAXIMUM PLUME RISE (PEAK).
  SUBROUTINE RISE IS CALLED IN THE MAIN PROGRAM, AND IN SUBROUTINES
  QZCAL AND AUTGRD.
   PEM-2 MODIFICATIONS: APRIL 1984
   K.SHANKAR RAO
   NOAA-ATDL, P.O. BOX-E
   OAK RIDGE, TENN 37831
                                                                       PMT34020
                                                                       PMT34030
                                                                       PMT34040
                                                                       PMT34050
                                                                       PMT34060
                                                                       PMT34070
                                                                       PMT34080
                                                                       PMT34090
                                                                       PMT34100
                                                                       PMT34110
                                      197

-------
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
   COMMON/PEMCOM/CONC(50,50,2) ,SDF(50,50,2) ,TT(20) .
    XP(300),YP(300y.EP(300,2),HP(300),DP(306),VP(36o),TP(300),
    XA(50),YA(50),EA(50.2)  SIZE(50),
1
2
3 WD
4
5
6
          50),YA(50),E(50.2) SIZE(50),
          24),WS(24),TA(24).HMIX(24).DTDZI(24),
          6)z6ci(6)P6)SCLAB6DT22
    AZ(6),BZ(6),CZ(6),P(6),SCLAB(6),DTDZ(2),SECTAN(16),
    XSWC,YSWC,GRID,LX,LY,A(2),B(2),POLNAM73,2).CALNAM(7,2),
  u ITA,IRD,IWR,IDSK,D80,D47,D8047,DIST,DELTA,HPRIME,
  7 ESH(2_) .PEAK, IBUOY, IRISE, IDWN.EFF,XS.UINV.WVEC.
  8 NAS.NPS,INDEX,IGRID,IAV,ISCEN,IWDOPT,IWD,ISC,IPS,
  9 NTOPT,NWDOPT,NWSOPT,NWPOPT,NSCEN,NL1ST,NARRAY,NTAPE,NCSOPT,
  * NMAX,NSTDWN,NPRISE,NINPEN,INTER,NPRINT,NGPR,NBID
   IDWN=1
   IF(IRISE.EQ.l)  GO TO 200

   IRISE=2:  DETERMINE WHETHER THE PLUME IS DOMINATED BY MOMENTUM OR
   BUOYANCY,  AND CALCULATE OPTIONAL STACK-TIP DOWNWASH CORRECTION,
   MAXIMUM EFFECTIVE SOURCE HEIGHT, AND VALUES OF CONSTANT FACTORS
   RELATED DISTANCE-DEPENDENT PLUME RISE EQUATIONS.
   HPRIME=HP(IPS)
   IF(NSTDWN.EQ.i) GO TO 10

   NSTDWN=0;  DOWNWASH CORRECTION.
   RATV=VP(IPS)*UINV
   IF(RATV.GE.1.51 GO TO 10
   DWNWSH=2.0*(1.5-RATV)*DP(IPS)
   IDWN=3
   IF(DWNWSH.GE.HP(IPS)) DWNWSH=HP(IPS)
   HPRIME=HP(IPS)-DWNWSH

   DETERMINE IF PLUME IS MOMENTUM-DOMINATED (IBUOY=0)
                      OR BUOYANCY-DOMINATED aBUOY=l),
   USING THE BUOYANCY - MOMENTUM CROSSOVER TECHNIQUES.
10 IBUOY=1
   CVD3=3.0*VP(IPS)*DP(IPS)
   DELHUM=CVD3*UINV
   IF(ISC.LT.S) GO TO 20
   STABILITY CLASSES E AND F.
   IF(ISC.EQ.6) GO TO 15
   BRIGC=115.28
   DIF=ABS(DTDZ(1)-0.02)
   GO TO 16
15 BRIGC= 87.14
   DIF=ABS(DTDZ(2)-0.035)
16 IFfDIF.GT.0.001) BRIGC=16.30/SQRT(DTDZ(ISC-4))
   IF(VP(IPS).GT.BRIGC*(TP(IPS)-TA(ISCEN))/SQRT(TA(ISCEN))) IBUOY=0
   IF(IBUOY.EQ.O)  GO TO 90
   GO TO 60
20 IF(NPRISE.EQ.l) GO TO 50

   NPRISE=0:  STANDARD (DEFAULT) PLUME RISE EQS. STABILITY CLASSES A
   IF(EFF.GE,55.)  GO TO 30
   AF=21.425
   BF=0.75
   GO TO 40
30 AF=38.710
   BF=0.6
40 IF(CVD3.GT.AF*EFF**BF) IBUOY=0
   IFCIBUOY.EQ.O)  GO TO 80
   IF(EFF.LT.55.)  XS=49.*(EFF**0.625)
   IF(EFF.GE.55.)  XS=119.*(EFF**0.4)
   GO TO 60

   NPRISE=1:  NEW  (OPTIONAL) PLUME RISE EQS. STABILITY CLASSES A-D.
50 DELH1=30.*(EFF*UINV)**0.6
   FOU3=EFF*(UINV**3)
   TERMH2=HPRIME+200.*FOU3
   DELH2=24.*(FOU3**0.6)*(TERMH2**0.4)
  PMT34120
  PMT34130
  PMT34140
  PMT34150
  PMT34160
  PMT34170
  PMT34180
  PMT34190
  PMT34200
  PMT34210
  PMT34220
  PMT34230
  PMT34240
  PMT34250
  PMT34260
  PMT34270
  PMT34280
  PMT34290
  PMT34300
INPMT34310
  PMT34320
  PMT34330
  PMT34340
  PMT34350
  PMT34360
  PMT34370
  PMT34380
  PMT34390
  PMT34400
  PMT34410
  PMT34420
  PMT34430
  PMT34440
  PMT34450
  PMT34460
  PMT34470
  PMT34480
  PMT34490
  PMT34500
  PMT34510
  PMT34520
 .PMT34530
  PMT34540
  PMT34550
  PMT34560
  PMT34570
  PMT34580
  PMT34590
  PMT34600
  PMT34610
  PMT34620
  PMT34630
-DPMT34640
  PMT34650
  PMT34660
  PMT34670
  PMT34680
  PMT34690
  PMT34700
  PMT34710
  PMT34720
  PMT34730
  PMT34740
  PMT34750
  PMT34760
  PMT34770
  PMT34780
  PMT34790
  PMT34800
  PMT34810
                                     198

-------
C SELECT THE LOWER VALUE GIVEN BY THE TWO BUOYANCY RISE EQUATIONS.
DELTAH=DELH1
IF(DELH2.LT. DELHI) DELTAH=DELH2
C SELECT THE HIGHER VALUE GIVEN BY THE MOMENTUM RISE AND DELTAH.
IF DELHUM.GT. DELTAH) IBUOY=0
IF IBUOY.EQ.O) GO TO 80
IF DELH2.GE. DELHI) XS=81. 19*(EFF**0.4)/(UINV**0. 6)
IF DELH2.LT. DELHI) XS=58.09*(FOU3**0.4)*(TERMH2**0. 6)
C
60 CTB= 1.6*UINV*EFF**0. 333333
IF(ISC.GE.5) GO TO 70
IF(NPRISE.EQ.l) GO TO 100
C
C PEAK PLUME RISE: BUOYANCY-DOMINATED PLUME, UNSTABLE AIR (A-D).
DELTAH= CTB*XS**0. 666667
GO TO 100
C
C PEAK PLUME RISE: BUOYANCY-DOMINATED PLUME, STABLE AIR (E,F).
70 DELTAH= 2. 6*(EFF*UINV*TA(ISCEN)/(9. 8*DTDZ(ISC-4) ) )**0. 333333
GO TO 100
C
C PEAK PLUME RISE: MOMENTUM-DOMINATED PLUME, UNSTABLE AIR (A-D).
PMT34820
PMT34830
PMT34840
PMT34850
PMT34860
PMT34870
PMT34880
PMT34890
PMT34900
PMT34910
PMT34920
PMT34930
PMT34940
PMT34950
PMT34960
PMT34970
PMT34980
PMT34990
PMT35000
PMT35010
PMT35020
PMT35030
80 CTMU= 1.89*(VP(IPS)*VP(IPS)*DP(IPS)*UINV/(VP(IPS)+3./UINV))**0.666PMT35040
1667
DELTAH= DELHUM
GO TO 100
C
C PEAK PLUME RISE: MOMENTUM-DOMINATED PLUME, STABLE AIR (E,F).
C
90 FACT=UINV*TA(ISCEN)/TP(IPS)
DELTAH= 1 . 5* (0 . 5*VP ( IPS ) *DP ( IPS ) ) **0 . 666667*FACT**0 . 333333
1 *(TA( ISCEN) / (DTDZ ( ISC-4) *9 . 8) ) **0 . 166667
IF(DELHUM.LT. DELTAH) DELTAH=DELHUM
C
100 ESH(2)= HPRIME + DELTAH
RETURN
C
200 IF(IBUOY.EQ.O) GO TO 210
C
C DISTANCE-DEPENDENT PLUME RISE: BUOYANCY-DOMINATED PLUME,
C ANY STABILITY (A-F) .
DELTAH= CTB*(DIST*1000. )**0. 666667
ESH?1)=DELTAH + HPRIME
IF(ESH(1).GT.ESH(2)) ESH(1)=ESH(2)
RETURN
C
C DISTANCE-DEPENDENT PLUME RISE: MOMENTUM-DOMINATED PLUME,
C UNSTABLE AIR (A-D).
210 IF? ISC. GE. 5) GO TO 220
DELTAH= CTMU*(DIST*1000.)**0. 333333
ESH?1)=DELTAH + HPRIME
IF(ESH(1).GT.ESH(2)) ESH(1)=ESH(2)
RETURN
C
C THERE IS NO DISTANCE-DEPENDENT PLUME RISE GIVEN FOR A
C MOMENTUM-DOMINATED PLUME IN STABLE AIR. DISTANCE TO MAXIMUM PLUME
C RISE FOR THIS SITUATION IS SET EQUAL TO ZERO IN THE MAIN PROGRAM,
C SO THE MAXIMUM HEIGHT, ESH(2), IS USED AT ALL DISTANCES.
220 ESH(1>ESH(2)
RETURN
C
END
C
C
C
C
SUBROUTINE AUTGRD
C SUBROUTINE AUTGRD , PART OF PEM-2 (VERSION 84130).
C
C
PMT35050
PMT35060
PMT35070
PMT35080
PMT35090
PMT35100
PMT35110
PMT35120
PMT35130
PMT35140
PMT35150
PMT35160
PMT35170
PMT35180
PMT35190
PMT35200
PMT35210
PMT35220
. PMT35230
PMT35231
PMT35240
PMT35250
PMT35260
PMT35270
PMT35280
PMT35290
PMT35300
PMT35301
PMT35310
PMT35320
PMT35330
PMT35340
PMT35350
PMT35360
PMT35370
PMT35380
PMT35390
PMT35400
PMT35410

PMT35420
PMT35430
PMT35440
PMT35450
PMT35460
PMT35470
PMT35480
199

-------
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
  SUBROUTINE AUTGRID CALCULATES THE FIVE PARAMETERS DEFINING THE
    RECEPTOR GRID (XSWC.YSWC,LX.LY.GRID) WHEN THE AUTOMATIC GRID
    OPTION IS USED.  THIS IS DONE BY SETTING GRID=0.0 IN THE INPUT
    DATA.  GRID PARAMETERS WILL BE CHOSEN FOR EACH SCENARIO SO AS
    TO INSURE GOOD COVERAGE BY RECEPTORS NEAR THE POINT OF
    MAXIMUM CONCENTRATION.  THIS POINT IS DETERMINED USING GAUSSIAN
    PLUME  ALGORITHMS WITHOUT POLLUTANT REMOVAL MECHANISMS.  THIS
    POINT IS THEREFORE ONLY APPROXIMATE FOR PROBLEMS WHICH INCLUDE
    DEPOSITION,  SEDIMENTATION,  AND CHEMICAL DECAY/TRANSFORMATION.
    THE OPTIMUM RECEPTOR GRID IN THIS CASE SHOULD BE DETERMINED BY
    TRIAL  AND ERROR, USING THE RECEPTOR GRID DEFINED BY AUTGRD AS
    THE FIRST APPROXIMATION.
    NOTE THAT THE AUTOMATIC GRID OPTION CANNOT BE USED WHEN NTOPT>1


*** PEM-2  MODIFICATIONS BY K.  SHANKAR RAO,
    NOAA-ATDL, OAK RIDGE, TENN.
    APRIL 1984


    COMMON/PEMCOM/CONC(50,50,2),SDF(50,50,2),TT(20),
   1 XP 300),YP(300).EP(300,2),HP7300),DP(300),VP(300),TP(300),
   2 XA 50),YA(50},EA(50.2),SIZE(50),
   3 WD 24),WS(24),TA(24KHMIX724),DTDZI(24),
   4 AZ 6),BZ(6),CZ(6),P(6),SCLAB(6),DTDZ(2),SECTAN(16),
   5 XSWC,YSWC,GRID,LX,LY,A(2),B(2LPOLNAM(3,2),CALNAM(7,2))
   6 ITA,IRD,IWR,IDSK,D80,D47,D8047,DIST,DELTA,HPRIME,
   7 ESH(2J),PEAK, IBUOY,IRISE,IDWN,EFF,XS,UINV,WVEC,
   8 NAS.NPS,INDEX,IGRID,IAV,ISCEN,IWDOPT,IWD,ISC,IPS,
   9 NTOPT,NWDOPT,NWSOPT,NWPOPT,NSCEN,NLIST,NARRAY,NTAPE,NCSOPT,
   * NMAX,NSTDWN,NPRISE,NINPEN,INTER,NPRINT,NGPR,NBID
C
C
      COMMON/PARM2A/HAS,KSC.AA,BA,CA
      COMMON/PARM7A/HA.PI(6|
      DIMENSION XCRNR(4),YCRNR
                            (4),HL(2),DL(2),XTM(2)
    EPS=.005
    NSTOP=100
    AART2=SQRT(2.)*AA

    E= 1.570796 -WVEC
    SINEE= SIN(E)
    COSNE= COS(E)
    GX1= XP(1)*COSNE
    GX2= GX1
    GY1= YP(1)*COSNE
    GY2= GY1
    GXl=GXl+5.
    GYl=GYl+5.
    DO 200 1=1,NPS
    XT= XP(I)*COSNE
    YT= YP(I)*COSNE
                        + YP(1)*SINEE

                        - XP(1)*SINEE
                         YP(I)*SINEE
                         XP(I)*SINEE
      UINV = l./WS(ISCEN)
      IF(NWPOPT.EQ.l) GO TO  165
      IF(HP(I).GT.10.) UINV  = UINV*((10./HP(I))**P(ISC))
      GO TO  166
   165 IF(HP(I).GT.HA) UINV = UINV*((HA/HP(I)))**P1(ISC)
   166 EFF= 2.45*VP(I)*DP(I)*DP(I)*(TP(I)-TA(ISCEN))/TP(I)

      HL(1)= HP(I)
      XSTAR1=HL(1)/AART2
      CALL ROOTf XCMAX1.XSTAR1,EPS,NSTOP,IER)
      DL(1)=.001*XCMAX1

   .   IPS=I
      IRISE=2
      CALL RISE
      HL(2)=ESH(2)
PMT35490
PMT35500
PMT35510
PMT35520
PMT35530
PMT35540
PMT35550
PMT35560
PMT35570
PMT35580
PMT35590
PMT35600
PMT35610
PMT35620
PMT35630
PMT35640
PMT35650
PMT35660
PMT35670
PMT35680
PMT35690
PMT35700
PMT35710
PMT35720
PMT35730
PMT35740
PMT35750
PMT35760
PMT35770
PMT35780
PMT35790
PMT35800
PMT35810
PMT35820
PMT35830
PMT35840
PMT35850
PMT35860
PMT35870
PMT35880
PMT35890
PMT35900
PMT35910
PMT35920
PMT35930
PMT35940
PMT35950
PMT35960
PMT35970
PMT35980
PMT35990
PMT36000
PMT36010
PMT36020
PMT36030
PMT36040
PMT36050
PMT36060
PMT36070
PMT36080
PMT36090
PMT36100
PMT36110
PMT36120
PMT36130
PMT36140
PMT36150
PMT36160
PMT36170
PMT36180
                                      200

-------
300
400
420
500
540
560
580
      XSTAR2=HL(2)/AART2
      CALL ROOT(XCMAX2,XSTAR2,EPS,NSTOP,IER)
      DL(2)=.001*XCMAX2
                   DL(
XTM(1)= XT +
XTM(2)= XT + DL
      IF
      IF
      IF
      IF
   XTM(2
   XTM(1
        ).GT.GX2)  GX2= XTM(2)
        J.LT.GXl)  GX1= XTM(l)
200   CONTINUE
   YT.GT.GY2)
   YT.LT.GY1)
                  GY2=
                  GY1=
YT
YT
XCRNR 1 = GX1
XCRNR 2 = GX2
XCRNR 3 = GX2
XCRNR 4 = GX1
YCRNR 1 = GY1
YCRNR 2 = GY1
YCRNR 3 = GY2
YCRNR 4 = GY2
DO 30   =1,4
XCRNRT= XCRNR(J)
XCRNR(J)= XCRNR(J)*COSNE  - YCRNR(J)*SINEE
YCRNR(J)= YCRNR(J)*COSNE + XCRNRT*SINEE
XSWC= XCRNR(l)
XNEC= XSWC
YSWC= YCRNR(l)
YNEC= YSWC
DO 400 1=2 4
IF XCRNR
IF XCRNR
IF YCRNR
IF YCRNR
XT= XNEC
YT= YNEC
DMAX= XT
IF(YT.GT.XT) DMAX=
IFfDMAX.LT.lO.)
IF(XT.GT.YT) GO
LY=  50
GRID= YT/50.
LX= XT/GRID
IF(LX.LT.50) LX= LX+1
GO TO 600
LX= 50
GRID= XT/50.
LY= YT/GRID
IF(LY.LT.SO) LY=LY+1
GO TO 600
IF(DMAX.LT.5.) GO TO 540
GRID= 0.2
LX= XT/GRID
LY= YT/GRID
1 I MUMl-l
.GT.
.LT.
.GT.
.LT.
XSWC
YSWC
XNEC
XSWC
YNEC
YSWC
XNEC=
XSWC=
YNEC=
YSWC=
XCRNR
XCRNR
YCRNR
YCRNR
I-IMI-HM
                         YT
                      GO TO 500
                      TO 420
      IF(LX.LT.50)
             LX=LX+1
             LY=LY+1
IF(LY.LT.50]
GO TO 600
IF(DMAX.LT.0.25) GO TO 580
IF(XT.GT.YT) GO TO 560
LY= 25
GRID= YT/25.
LX= XT/GRID
IF(LX.LT.25) LX=LX+1
GO TO 600
LX= 25
GRID= XT/25.
LY= YT/GRID
IF(LY.LT.25) LY=LY+1
GO TO 600
GRID= 0.01
LX= XT/GRID
LY= YT/GRID
 PMT36190
 PMT36200
 PMT36210
 PMT36220
 PMT36230
 PMT36240
 PMT36250
 PMT36260
 PMT36270
 PMT36280
 PMT36290
 PMT36300
 PMT36310
 PMT36320
 PMT36330
 PMT36340
 PMT36350
 PMT36360
 PMT36370
 PMT36380
 PMT36390
 PMT36400
 PMT36410
 PMT36420
 PMT36430
 PMT36440
 PMT36450
 PMT36460
 PMT36470
 PMT36480
 PMT36490
 PMT36500
 PMT36510
 PMT36520
 PMT36530
 PMT36540
 PMT36550
 PMT36560
 PMT36570
 PMT36580
 PMT36590
.PMT36600
 PMT36610
 PMT36620
 PMT36630
 PMT36640
 PMT36650
 PMT36660
 PMT36670
 PMT36680
 PMT36690
 PMT36700
 PMT36710
 PMT36720
 PMT36730
 PMT36740
 PMT36750
 PMT36760
 PMT36770
 PMT36780
 PMT36790
 PMT36800
 PMT36810
 PMT36820
 PMT36830
 PMT36840
 PMT36850
 PMT36860
 PMT36870
 PMT36880
                                     201

-------
      IF(LX.LT.25) LX=LX+1
      IF(LY.LT.25) LY=LY+1
600   XSWC= XSWC - 0.5*GRID
      YSWC= YSWC - 0.5*GRID
      IF(NCSOPT.LT.l.OR.(LX.LE.25.AND.LY.LE.25)) GO TO 700
      XL=LX
      YL=LY
      IF(LX.GT.LY) GO TO 640
      DELG= YL/25.
      LY=25
      GRID= GRID*DELG
      LX= XL/DELG
      IF(LX.LT.25) LX=LX+1
      GO TO 700
640   DELG= XL/25.
      LX=25
      GRID= GRID*DELG
      LY= YL?DELG + 1.
700   CONTINUE
      WRITE(IWR,900)TT, ISCEN, IWDOPT
      XRSWC=XSWC+0.5*GHID
      YRSWC=YSWC+0.5*GRID
      WRITE(IWR.905)LX,LY,GRID,XRSWC,YRSWC
  900 FORMAT(1H1.37X  'POLLUTION EPISODIC MODEL  (PEM-2)V//4X  'OUTPUT:   rmio/i^u
     li2pA4//4XLlAyTOMATICALLY_GENERATED RECEPTOR GRID PARAMETERS FOR SCPMT37130

                                                                  ,' ROWPMT37150
                                                                  F8.3, PMT37160
                                                                        PMT37170
                                                                        PMT37180
                                                                        PMT37190
                                                                        PMT36890
                                                                        PMT36900
                                                                        PMT36910
                                                                        PMT36920
                                                                        PMT36930
                                                                        PMT36940
                                                                        PMT36950
                                                                        PMT36960
                                                                        PMT36970
                                                                        PMT36980
                                                                        PMT36990
                                                                        PMT37000
                                                                        PMT37010
                                                                        PMT37020
                                                                        PMT37030
                                                                        PMT37040
                                                                        PMT37050
                                                                        PMT37060
                                                                        PMT37070
                                                                        PMT37080
                                                                        PMT37090
                                                                        PMT37100
                                                                        PMT37110
C
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C

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C
C
     4.U \SL LJi fi\s xiiw — » JL' r • ~t •   iu*i / / ~rn.
     2' KM WEST,',F8.3,'  KM SOUTH'/)
      RETURN
      END
      SUBROUTINE FUNR(X,R,FX,FPRIMX)
                       SUBROUTINE FUNR
PART OF PEM-2 (VERSION 84130),
      FUNR IS THE EXTERNAL SUBROUTINE CALLED IN SUBROUTINE ROOT.
PMT37200
PMT37210
PMT37220
PMT37230
PMT37240
PMT37250
PMT37260
      FOR ANY GIVEN X, THIS SUBROUTINE DEFINES THE FUNCTION, F(X), AND  PMT37270
      ITS FIRST DERIVATIVE WITH RESPECT TO X, FPRIM(X).
C
C
C
C
      THESE FUNCTIONS ARE OF THE FORM: F(X)=P(X)*Q(X)-R. AND
      FPRIM(X)=P(X)*DQDX(X)+Q(X)*DPDX(X)
      PEM-2 PROGRAM DEVELOPMENT: JANUARY 1984
      K. SHANKAR RAO
      NOAA-ATDL, P.O. BOX-E
      OAK RIDGE, TENN 37831
      COMMON/PARM2A/HAS,KSC,AA,BA,CA

      STABILITY CLASS C
      IF(KSC.NE.S) GO TO 10
      PX=X;)tX
      DX=1.+.0004*X
      QX=7l.+.0003*X)/DX
      DPDX=2.*X
      DQDX=-'.0001/(DX*DX)
      GO TO 25
   10 DX=1.+BA*X
      IF(KSC.GT.S) GO TO 15

      STABILITY CLASSES A AND B
      PX=0.5*X*X*DX
      DPDX=X*(1.5*BA*X+1.)
      GO TO 20
                               PMT37280
                               PMT37290
                               PMT37300
                               PMT37310
                               PMT37320
                               PMT37330
                               PMT37340
                               PMT37350
                               PMT37360
                               PMT37370
                               PMT37380
                               PMT37390
                               PMT37400
                               PMT37410
                               PMT37420
                               PMT37430
                               PMT37440
                               PMT37450
                               PMT37460
                               PMT37470
                               PMT37480
                               PMT37490
                               PMT37500
                               PMT37510
                               PMT37520
                               PMT37530
                               PMT37540
                               PMT37550
                               PMT37560
                               PMT37570
                                     202

-------
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   STABILITY CLASSES D,E, AND F
15 PX=0.5*X*X/DX
   DPDX=0.5*X*(1.+DX)/(DX*DX)

   ALL STABILITY CLASSES EXCEPT C
20 TX1=1.+0.5*BA*X
   TX2=1.+.0002*X
   TX3=1.+.0004*X
   QX=1.+DX*TX2/(TX1*TX3)
   DQDX=(-.0002*DX*TX1+0.5*BA*TX2*TX3)/((TXl*TX3)**2)
   ALL STABILITY CLASSES

25 FX=PX*QX-R
   FPRIMX=PX*DQDX+QX*DPDX

   RETURN
   END
   SUBROUTINE ROOT(X,XSTAR.EPS,NSTOP,IEH)
                    SUBROUTINE ROOT  , PART OF PEM-2 (VERSION 84130)


   THIS SUBROUTINE FINDS THE ROOT OF A POLYNOMIAL EQUATION
   F(X) = 0, USING THE NEWTON-RAPHSON ITERATION METHOD.
   THIS SUBROUTINE IS CALLED IN SUBROUTINE AUTGRD TO
   DETERMINE THE DOWNWIND DISTANCE TO MAXIMUM GROUND-LEVEL
   CONCENTRATION FROM AN ELEVATED POINT-SOURCE PLUME.

   X = ROOT OF EQUATION F(X)=0. (OUTPUT)
   XSTAR = INITIAL GUESS OF VALUE OF X (INPUT)
                                    INPUT)
                                    TEPS  (INPUT)
EPS = UPPER BOUND OF ERROR IN X
NSTOP = MAXIMUM NO.OF ITERATION
IER = ERROR MESSAGE (OUTPUT)
    = 0  NO ERROR
    = 1  NO CONVERGENCE AFTER NSTOP ITERATIONS
    = 2  FPRIM GOES TO ZERO AT SOME ITERATION STEP

PEM-2 PROGRAM DEVELOPMENT: JANUARY 1984
K. SHANKAR RAO
NOAA-ATDL, P.O. BOX-E
OAK RIDGE, TENN 37831
   COMMON/PARM2A/HAS,KSC,AA,BA,CA

   INITIALIZATION
   IER=0
   X=XSTAR
   R=XSTAR*XSTAR
   XO=X
   CALL FUNR(XO,R,F,FPRIM)
   XOF=100.*EPS

   START ITERATION LOOP
   DO 16 1=1.NSTOP
   IF(F) 11,16,11

   EQUATION  IS NOT SATISFIED BY X
11 IF(FPHIM) 12,18,12

   ITERATION IS IMPOSSIBLE
12 DX=F/FPRIM
   X=X-DX
   XO=X
   CALL FUNR(XO,R,F,FPRIM)

   TEST ON SATISFACTORY ACCURACY
   XO=EPS
PMT37580
PMT37590
PMT37600
PMT37610
PMT37620
PMT37630
PMT37640
PMT37650
PMT37660
PMT37670
PMT37680
PMT37690
PMT37700
PMT37710
PMT37720
PMT37730
PMT37740

PMT37750
PMT37760
PMT37770
PMT37780
PMT37790
PMT37800
PMT37810
PMT37820
PMT37830
PMT37840
PMT37850
PMT37860
PMT37870
PMT37880
PMT37890
PMT37900
PMT37910
PMT37920
PMT37930
PMT37940
PMT37950
PMT37960
PMT37970
PMT37980
PMT37990
PMT38000
PMT38010
PMT38020
PMT38030
PMT38040
PMT38050
PMT38060
PMT38070
PMT38080
PMT38090
PMT38100
PMT38110
PMT38120
PMT38130
PMT38140
PMT38150
PMT38160
PMT38170
PMT38180
PMT38190
PMT38200
PMT38210
PMT38220
PMT38230
PMT38240
PMT38250
PMT38260
                                      203

-------
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    XABS=ABS(X)
    IF(XABS-1.)  14,14,13
 13 XO=XO*XABS
 14 IF(ABS(DX)-XO)  15,15,16
 15 IF(ABS(F)-XOF)  17,17,16
 16 CONTINUE
    END ITERATION LOOP

    NO CONVERGENCE AFTER NSTOP ITERATION STEPS ERROR RETURN
    IER=1
 17 RETURN

    ERROR RETURN IN CASE OF ZERO DENOMINATOR
 18 IER=2
    RETURN
    END
    BLOCK DATA
                          BLOCK DATA ,  PART OF PEM-2 (VERSION 84130)
C
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C

C

C

C

C
    THIS SUBPROGRAM INITIALIZES VARIABLES IN COMMON/PEMCOM/

*** PEM MODIFICATIONS BY M.M.STEVENS,
    NOAA-ATDL.  P.O.BOX-E, OAK RIDGE,  TENN 37831
    DECEMBER 1982
*** PEM-2 MODIFICATIONS BY K. SHANKAR RAO,
    DECEMBER 1983


    COMMON/PEMCOM/CONC(50.50.2).SDF(50,50,2).TT(20).
   1 XP 300),Yp7300),EP(300,2),te7300),DP(306),VP(300),TP(300),
   2 XA 50) YA(50),EA(50.2) SIZE(50),
   3 WD 24),WS(24),TA(24).HMIX(24),DtDZI(24),
   4 AZ 6),BZ(6),CZ(6),P(6),SCLAB(6),DTDZ(2i,SECTAN(16),
   5 XSWC,YSWC,GRID,LX,LY,A(2),B(2T,POLNAM(3,2),CALNAM(7S2),
   6 ITA,IRD.IWR,IDSK.D80.D47,08047,D1ST,DELTA.HPRIME,
   7 ESH(2),PEAK,IBUOY,IRISE,IDWN,EFF,XS,UINV,WVEC,
   8 NAS.NPS,INDEX.IGRID,IAV.ISCEN,IWDOPT,IWD,ISC.IPS,
   9 NTOPT.NWDOPT,NWSOPT,NWPOPT,NSCEN,NLIST,NARRAY,NTAPE,NCSOPT,
   * NMAX,NSTDWN,NPRISE,NINPEN,INTER,NPRINT.NGPR.NBID


    DATA INDEX,NAS,NPS/0,0,O/
    DATA ITA,IRD,IWR.IDSK/1,5,6,8/
    DATA SCLAB/2HA ,2HB  ,2HC ,2HD  .2HE ,2HF /
    DATA P/0.15,0.15,0.2,0.25.0.3,0.3/
    DATA AZ/.24..24..20,.14..08,.087
    DATA BZ/.OOl,.001,0.,.0003,.0015,.0015/
    DATA CZ/.001..001.0..0.,0.,0./
    DATA SECTAN/0...39270,.78540.1.17810.1.57080.1.96350.2.35620,
   1 2.74890,3.14159,3.53429,3.92699,4.31969,4.71239,5.10509,
   2 5.49779.5.89049/

    END
    SUBROUTINE XINTEG(XL,XU,EPS,NDIM,FCT,Y,IER,AUX)
                   SUBROUTINE XINTEG , PART OF PEM-2 (VERSION 84130),
      REAL*8 FCT
    FOR UNIVAC-1100
    REAL*8 XL,XU,X,Y

    DIMENSION AUX(l)
PMT38270
PMT38280
PMT38290
PMT38300
PMT38310
PMT38320
PMT38330
PMT38340
PMT38350
PMT38360
PMT38370
PMT38380
PMT38390
PMT38400
PMT38410
PMT38420

PMT38430
PMT38440
PMT38450
PMT38460
PMT38470
PMT38480
PMT38490
PMT38500
PMT38510
PMT38520
PMT38530
PMT38540
PMT38550
PMT38560
PMT38570
PMT38580
PMT38590
PMT38600
PMT38610
PMT38620
PMT38630
PMT38640
PMT38650
PMT38660
PMT38670
PMT38680
PMT38690
PMT38700
PMT38710
PMT38720
PMT38730
PMT38740
PMT38750
PMT38760
PMT38770
PMT38780
PMT38790
PMT38800
PMT38810
PMT38820
PMT38830

PMT38840
PMT38850
PMT38860
PMT38870
PMT38880
PMT38890
PMT38900
PMT38910
PMT38920
PMT38930
PMT38940
                                      204

-------
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THIS SUBROUTINE PERFORMS NUMERICAL INTEGRATION OF AN EXTERNALLY
PMT38950
PMT38960
DEFINED FUNCTION OVER A FINITE INTERVAL USING THE TRAPEZOIDAL RULEPMT38970
WITH ROMBERG EXTRAPOLATION. THIS ROUTINE IS CALLED IN THE MAIN
PROGRAM FOR NUMERICAL INTEGRATIONS W.R.T. X FOR AREA SOURCES.

XL = LOWER LIMIT OF INTEGRATION INTERVAL. (INPUT)
XU = UPPER LIMIT OF INTEGRATION INTERVAL. (INPUT)
EPS = UPPER BOUND FOR RELATIVE ERROR BETWEEN SUCCESSIVE
APPROXIMATIONS TO THE INTEGRAL. (INPUT)
NDIM = MAXIMUM NO. OF BISECTIONS OF INTERVAL (XL.XU). (INPUT)
FCT = EXTERNALLY DEFINED INTEGRAND FUNCTION. (INPUT)
Y = BEST POSSIBLE APPROXIMATION OF INTEGRAL. (OUTPUT)
IER = ERROR MESSAGE (OUTPUT)
= 0 NO ERROR
PMT38980
PMT38990
PMT39000
PMT39010
PMT39020
PMT39030
PMT39040
PMT39050
PMT39060
PMT39070
PMT39080
PMT39090
= 1 SPECIFIED ACCURACY CANT BE REACHED DUE TO ROUNDING ERRORSPMT39100
= 2 IMPOSSIBLE TO CHECK ACCURACY (IF NDIM<5) OR SPECIFIED
ACCURACY CAN'T BE REACHED. NDIM SHOULD BE INCREASED.
AUX = AUXILIARY STORAGE ARRAY WITH DIMENSION NDIM. (INTERNAL)

PEM-2 PROGRAM DEVELOPMENT: DECEMBER 1983
K. SHANKAR RAO
NOAA-ATDL, P.O. BOX-E
OAK RIDGE, TENN 37831


PREPARATIONS FOR ROMBERG-LOOP
AUX(l) = .5*(FCT(XL)-hFCT(XU))
H=XU-XL
IF(NDIM-l) 8,8,1
1 IF(H) 2,10,2

NDIM IS GREATER THAN 1 AND H IS NOT EQUAL TO 0.
2 HH=H
EPSREL=EPS
EPSA=1.0E-10
DELT2=1.E06
P=l.
JJ=1


DO 7 1=2, NDIM
Y=AUX(1)
DELT1=DELT2
HD=HH
HH=0.5*HH
P=.5*P
X=XL+HH
SUM=0.


DO 3 J=1,JJ
SUM=SUM+FCT(X)
3 X=X+HD
AUX(I)=.5*AUX(I-1)+P*SUM

A NEW APPROXIMATION OF INTEGRAL VALUE IS COMPUTED BY MEANS OF
TRAPEZOIDAL RULE.

START OF ROMBERG EXTRAPOLATION METHOD.
Q=l.
IM1=I-1
DO 4 J=1,IM1
II=I-J
Q=Q+Q
Q=Q+Q
4 AUX(II)=AUX(II+1)+(AUX(II+1)-AUX(II))/(Q-1.)
END OF ROMBERG-STEP
FINAL VALUE OF AUX(II)=AUX(1) WHICH CONTAINS VALUE OF
INTEGRAL FOR THIS APPROXIMATION.
PMT39110
PMT39120
PMT39130
PMT39140
PMT39150
PMT39160
PMT39170
PMT39180
PMT39190
PMT39200
PMT39210
PMT39220
PMT39230
PMT39240
PMT39250
PMT39260
PMT39270
PMT39280
PMT39290
PMT39300
PMT39310
PMT39320
PMT39330
PMT39340
PMT39350
PMT39360
PMT39370
PMT39380
PMT39390
PMT39400
PMT39410
PMT39420
PMT39430
PMT39440
PMT39450
PMT39460
PMT39470
PMT39480
PMT39490
PMT39500
PMT39510
PMT39520
PMT39530
PMT39540
PMT39550
PMT39560
PMT39570
PMT39580
PMT39590
PMT39600
PMT39610
PMT39620
PMT39630
PMT39640
205

-------
      TESTS FOR CONVERGENCE





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5
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8
9

IF
IF
IF
IF
IF
Y.GT.EPSA) DELT2=ABS(Y-AUX(1))/Y
Y.LE.EPSA) DELT2=0.
1-2) 7,5,5
DELT2-EPSREL) 10,10.6
DELT2-DELT1) 7,ll,ll
JJ=JJ+JJ
END LOOP ON APPROXIMATIONS


IER=2
Y=H*AUX(1)
RETURN
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      GO TO 9
 IER=1
 Y=H*Y
 RETURN
 END
 SUBROUTINE D01AJF(F,  A,  B,  EPSABS,  EPSREL,  RESULT,  ABSERR.WORK,
* LWORK, IWORK,  LIWORK,  IFAIL)
                SUBROUTINE D01AJF ,  PART OF PEM-2 (VERSION 84130).

 MARK 8 RELEASE. NAG COPYRIGHT 1980

 D01AJF IS A GENERAL PURPOSE INTEGRATOR WHICH CALCULATES
 AN APPROXIMATION TO THE INTEGRAL OF A FUNCTION OVER A FINITE
 INTERVAL (A,B).  THIS ROUTINE CAN BE USED WHEN THE INTEGRAND
 HAS SINGULARITIES, ESPECIALLY WHEN THESE ARE OF ALGEBRAIC OR
 LOGARITHMIC TYPE.  D01AJF IS AN ADAPTIVE ROUTINE, USING THE
 GAUSS 10-POINT AND KRONROD 21-POINT RULES.   THE ALGORITHM
 INCORPORATES A GLOBAL ACCEPTANCE CRITERION TOGETHER WITH
 EPS-ALGORITHM TO PERFORM EXTRAPOLATION.  THE LOCAL ERROR IS
 ESTIMATED.

 THE GENERAL PURPOSE INTEGRATOR D01AJF INCLUDES THE FOLLOWING:
 SUBROUTINES (1) D01AJF,  (2) D01AJV, (3) D01AJX, (4) D01AJY,
 (5) D01AJZ, INTEGER FUNCTION P01AAF, DOUBLE PRECISION FUNCTIONS
 (1) X02AAF, (2) X02ABF,  (3) X02ACF, AND SUBROUTINE X04AAF.
 THE PROGRAM LISTINGS FOR THESE SUBROUTINES AND FUNCTIONS, COPIED
 HERE FROM ORNL - NAG LIBRARY, FOLLOW.  THESE ARE DEVELOPED BY
      NUMERICAL ALGORITHMS GROUP (NAG)
      1131 WARREN AVENUE
      DOWNERS GROVE, ILLINOIS 60515
 WHICH HOLDS THE COPYRIGHT (NAG FORTRAN MINI MANUAL, MARKS, 1980).
 THESE PROGRAM LISTINGS ARE INCLUDED HERE WITH THEIR KIND
 PERMISSION.  THEY ARE RELEASED BY
      COMPUTER SCIENCES DEPARTMENT
      OAK RIDGE NATIONAL LABORATORY  (ORNL)
      OAK RIDGE, TENNESSEE 37831
 EXCLUSIVELY FOR USE IN THE PEM.  THESE LIBRARY SUBROUTINES AND
 PROGRAMS SHOULD NOT BE USED FOR ANY OTHER PURPOSE WITHOUT PRIOR
 APPROVAL FROM NAG AND ORNL.
 D01AJF ITSELF IS ESSENTIALLY A DUMMY ROUTINE WHOSE FUNCTION IS
 PARTITION THE WORK ARRAYS WORK AND IWORK FOR USE BY D01AJV.
 WORK IS PARTITIONED INTO 4 ARRAYS EACH OF SIZE LWORK/4.
 IWORK IS A SINGLE ARRAY IN D01AJV.
TO
PMT39650
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PMT39670
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PMT39800
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PMT39830
PMT39840
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PMT39860
PMT39870
PMT39880

PMT39890
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PMT40070
PMT40080
PMT40090
PMT40100
PMT40110
PMT40120
PMT40130
PMT40140
PMT40150
PMT40160
PMT40170
PMT40180
PMT40190
PMT40200
PMT40210
PMT40220
PMT40230
PMT40240
PMT40250
PMT40260
PMT40270
PMT40280
PMT40290
PMT40300
PMT40310
PMT40320
PMT40330
                                     206

-------
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   ..  SCALAR ARGUMENTS ..
   DOUBLE PRECISION A, ABSERR,  B,  EPSABS,  EPSREL,  RESULT
   INTEGER IFAIL,  LIWORK,  LWORK
   ..  ARRAY ARGUMENTS ..
   DOUBLE PRECISION WORK(LWORK)
   INTEGER IWORK(LIWORK)
   ..  FUNCTION ARGUMENTS  ..
   DOUBLE PRECISION F

   !'.  LOCAL SCALARS . .

   DOUBLE PRECISION SRNAME
   INTEGER IBL, IEL, IER,  IRL,  LIMIT
   ..  FUNCTION REFERENCES  . .
   INTEGER P01AAF
   ..  SUBROUTINE REFERENCES  . .
   D01AJV

   EXTERNAL F
   DATA SRNAME /8H D01AJF  /
   CHECK THAT MINIMUM WORKSPACE REQUIREMENTS ARE MET
   IF (LWORK.LT.4) GO TO 20
   IF (LIWORK.LT.LWORK/8+2)  GO TO 20
   LIMIT = UPPER BOUND ON  NUMBER OF SUBINTERVALS
   LIMIT = LWORK/4
   SET UP BASE ADDRESSES FOR WORK ARRAYS
   IBL = LIMIT + 1
   IEL = LIMIT + IBL
   IRL = LIMIT + IEL
   PERFORM INTEGRATION
   CALL D01AJV(F,
                                                    PMT40340
                                                    PMT40350
                                                    PMT40360
                                                    PMT40370
                                                    PMT40380
                                                    PMT40390
                                                    PMT40400
                                                    PMT40410
                                                    PMT40420
                                                    PMT40430
                                                    PMT40440
                                                    PMT40450
                                                    PMT40460
                                                    PMT40470
                                                    PMT40480
                                                    PMT40490
                                                    PMT40500
                                                    PMT40510
                                                    PMT40520
                                                    PMT40530
                                                    PMT40540
                                                    PMT40550
                                                    PMT40560
                                                    PMT40570
                                                    PMT40580
                                                    PMT40590
                                                    PMT40600
                                                    PMT40610
                                                    PMT40620
                                                    PMT40630
        XL D01AJV(F, A, B, DABS(EPSABS), DABS(EPSREL), WORK(l),WORK(IBL)PMT40640
        WORK(IEL). WORK(IRL), LIMIT, IWORK, LIWORK,RESULT, ABSERR,  IER) PMT40650
        ' (IER.NE.O) GO TO 40                                            PMT40660
   IF
   IFAlL = 0
   GO TO 60
   ERROR 6 = INSUFFICIENT WORKSPACE
20 IER = 6
40 IFAIL = P01AAF(IFAIL,IER,SRNAME)
60 RETURN
   END
      SUBROUTINE D01AJV(F, A, B,
     * RLIST, LIMIT, 	  	
                              EPSABS, EPSREL, ALIST, BLIST.ELIST,
                  IORD, LIORD. RESULT, ABSERR, IER)'
                  SUBROUTINE D01AJV ,  PART OF PEM-2 (VERSION 84130),
   MARK 8 RELEASE. NAG COPYRIGHT 1979
   BASED ON QUADPACK ROUTINE DQAGS (FORMERLY QAGS)
   **********************************************************

      PURPOSE
         THE ROUTINE CALCULATES AN APPROXIMATION
         /RESULT/ TO A GIVEN DEFINITE INTEGRAL   I =
         INTEGRAL OF /F/ OVER (A,B), HOPEFULLY
         SATISFYING FOLLOWING CLAIM FOR ACCURACY .
         ABS(I-RESULT) .LE. MAX(EPSABS,EPSREL*ABS(I)).

        CALLING SEQUENCE
         CALL D01AJV (F,A,B,EPSABS,EPSREL,ALIST,BLIST.ELIST,
                      RLIST,LIMIT,IORD,LIORD,RESULT,ABSERR,IER)
      PARAMETERS
          F
- FUNCTION SUBPROGRAM DEFINING THE INTEGRAND
  FUNCTION F(X). THE ACTUAL NAME FOR F
  NEEDS TO BE DECLARED EXTERNAL
  IN THE DRIVER PROGRAM

- LOWER LIMIT OF INTEGRATION
 PMT40670
 PMT40680
 PMT40690
 PMT40700
 PMT40710
 PMT40720
 PMT40730

.PMT40740
 PMT40750
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 PMT40810
 PMT40820
 PMT40830
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 PMT40850
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 PMT40870
 PMT40880
 PMT40890
 PMT40900
 PMT40910
 PMT40920
 PMT40930
 PMT40940
 PMT40950
 PMT40960
 PMT40970
 PMT40980
 PMT40990
 PMT41000
 PMT41010
 PMT41020
                                      207

-------
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B
- UPPER LIMIT OF INTEGRATION
EPSABS - ABSOLUTE ACCURACY REQUESTED

EPSREL - RELATIVE ACCURACY REQUESTED

ALIST,BLIST,ELIST,RLIST
       - WORK ARRAYS (FUNCTIONS DESCRIBED BELOW)

LIMIT  - UPPER BOUND FOR NUMBER OF SUBINTERVALS

IORD   - WORK ARRAY

LIORD  - LENGTH OF IORD (AT LEAST LIMIT/2 + 2)

RESULT - APPROXIMATION TO THE INTEGRAL

ABSERR - ESTIMATE OF THE MODULUS OF THE ABSOLUTE ERROR,
         WHICH SHOULD EQUAL OR EXCEED ABS(I-RESULT)

IER    - IER   = 0 NORMAL AND RELIABLE
                 TERMINATION OF THE ROUTINE.
                 IT IS ASSUMED THAT THE
                 REQUESTED  ACCURACY HAS BEEN
                 ACHIEVED.
       - IER   .NE. 0 ABNORMAL TERMINATION OF
                 THE ROUTINE. THE ESTIMATES
                 FOR INTEGRAL AND ERROR ARE
                 LESS RELIABLE. IT IS ASSUMED
                 THAT THE  REQUESTED ACCURACY
                 HAS NOT BEEN ACHIEVED.
             = 1 MAXIMUM NUMBER OF SUBDIVISIONS ALLOWED
                 HAS BEEN ACHIEVED. THE USER CAN
                 ALLOW MORE SUB DIVISIONS BY
                 INCREASING THE DIMENSIONS OF THE
                 WORK ARRAYS WORK AND IWORK.
                 HOWEVER, THIS MAY
                 YIELD NO  IMPROVEMENT, AND IT
                 IS RATHER ADVISED TO HAVE A
                 CLOSE LOOK AT THE INTEGRAND,
                 IN ORDER TO DETERMINE THE
                 INTEGRATION  DIFFICULTIES. IF
                 THE POSITION OF A LOCAL
                 DIFFICULTY CAN BE DETERMINED
                 (I.E.  SINGULARITY,
                 DISCONTINUITY WITHIN THE
                 INTERVAL) ONE WILL PROBABLY
                 GAIN FROM  SPLITTING UP THE
                 INTERVAL AT THIS POINT AND
                 CALLING THE INTEGRATOR ON THE
                 SUB-RANGES. IF POSSIBLE, AN
                 APPROPRIATE SPECIAL-PURPOSE
                 INTEGRATOR SHOULD BE USED
                 WHICH IS DESIGNED FOR
                 HANDLING THE TYPE  OF
                 DIFFICULTY  INVOLVED.
             = 2 THE OCCURRENCE OF ROUNDOFF
                 ERROR IS DETECTED WHICH
                 PREVENTS THE REQUESTED
                 TOLERANCE   FROM BEING
                 ACHIEVED. THE ERROR MAY BE
                 UNDER-ESTIMATED.
             = 3 EXTREMELY BAD INTEGRAND BEHAVIOUR
                 OCCURS  AT SOME  INTERIOR POINTS OF THE
                 INTEGRATION INTERVAL.
             = 4 IT  IS PRESUMED THAT  THE REQUESTED
                 TOLERANCE CANNOT BE  ACHIEVED,
                 AND  THAT THE  RETURNED RESULT
                 IS  THE  BEST WHICH CAN BE
                 OBTAINED.
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PMT41400
PMT41410
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PMT41440
PMT41450
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PMT41500
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PMT41590
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                                      208

-------
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                     = 5 THE INTEGRAL IS PROBABLY DIVERGENT.  OR
                         SLOWLY CONVERGENT.  IT MUST BE NOTED
                         THAT DIVERGENCY CAN OCCUR
                         WITH ANY OTHER VALUE OF IER.

 **********************************************************
 ..  SCALAR ARGUMENTS ..
 DOUBLE PRECISION A, ABSERR, B, EPSABS, EPSREL, RESULT
 INTEGER IER, LIMIT, LIORD
 ..  ARRAY ARGUMENTS ..
 DOUBLE PRECISION ALIST(LIMIT), BLIST(LIMIT), ELIST(LIMIT),
* RLIST(LIMIT)
 INTEGER IORD(LIORD)
 ..  FUNCTION ARGUMENTS ..
 DOUBLE PRECISION F

 !!  SCALARS IN COMMON ..
 INTEGER JUPBND

 !!  LOCAL SCALARS ..
 DOUBLE PRECISION Al,  A2. ABSEPS. AREA12. AREAl, AREA2, AREA, Bl,
* B2,CORREC, DEFAB1, DEFAB2, DEFABS, ORES, EPMACH, ERLARG,ERLAST,
* ERRBND, ERRMAX, ERR012, ERROR1, ERROR2, ERRSUM.ERTEST, OFLOW,
* RESAflS, RESEPS, SMALL, UFLOW
 INTEGER ID, IERRO, IROFFl, IROFF2, IROFF3,  K, KSGN, KTMIN.LAST1,
* LAST, MAXERR, NRES,  NRMAX, NUMRL2
 LOGICAL EXTRAP. NOEXT
 ..  LOCAL ARRAYS ..
 DOUBLE PRECISION RES3LA(3), RLIST2(52)
 ..  FUNCTION REFERENCES ..
 DOUBLE PRECISION X02AAF, X02ABF, X02ACF
 ..  SUBROUTINE REFERENCES ..
 D01AJX, D01AJY, D01AJZ

 EXTERNAL F
 COMMON /AD01AJ/ JUPBND

        THE DIMENSION OF /RLIST2/ IS DETERMINED BY
        DATA /LIMEXP/ IN SUBROUTINE D01AJY 7/RLIST2/
        SHOULD BE OF DIMENSION (LIMEXP+2) AT LEAST).

 EPMACH = X02AAFQ
 UFLOW = X02ABFO
 OFLOW = X02ACF()

        LIST OF MAJOR VARIABLES
       ALIST     - LIST OF LEFT END-POINTS OF ALL SUBINTERVALS
                   CONSIDERED UP TO NOW

       BLIST     - LIST OF RIGHT END-POINTS OF ALL SUBINTERVALS
                   CONSIDERED UP TO NOW

       RLIST(I)  - APPROXIMATION TO THE INTEGRAL OVER
                   (ALIST(I),BLIST(I))

       RLIST2    - ARRAY OF DIMENSION AT LEAST LIMEXP+2
                   CONTAINING THE PART OF THE EPSILON TABLE
                   WHICH IS STILL NEEDED FOR FURTHER
                   COMPUTATIONS

       ELIST(I)  - ERROR ESTIMATE APPLYING TO RLIST(I)

       MAXERR    - POINTER TO THE INTERVAL WITH LARGEST ERROR
                   ESTIMATE

       ERRMAX    - ELIST(MAXERR)

       ERLAST    - ERROR ON THE INTERVAL CURRENTLY SUBDIVIDED
PMT41730
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PMT41860
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PMT41890
PMT41900
PMT41910
PMT41920
PMT41930
PMT41940
PMT41950
PMT41960
PMT41970
PMT41980
PMT41990
PMT42000
PMT42010
PMT42020
PMT42030
PMT42040
PMT42050
PMT42060
PMT42070
PMT42080
PMT42090
PMT42100
PMT42110
PMT42120
PMT42130
.PMT42140
PMT42150
PMT42160
PMT42170
PMT42180
PMT42190
PMT42200
PMT42210
PMT42220
PMT42230
PMT42240
PMT42250
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PMT42270
PMT42280
PMT42290
PMT42300
PMT42310
PMT42320
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PMT42340
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PMT42370
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                                      209

-------
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                  (BEFORE THAT SUBDIVISION HAS  TAKEN PLACE)

      AREA      - SUM OF THE  INTEGRALS  OVER THE SUBINTERVALS

      ERRSUM    - SUM OF THE  ERRORS OVER THE SUBINTERVALS

      ERRBND    - REQUESTED ACCURACY MAX(EPSABS,EPSREL*
                  ABS(RESULT))

      *****!    - VARIABLE FOR THE LEFT INTERVAL

      *****2    - VARIABLE FOR THE RIGHT INTERVAL

      LAST      - INDEX FOR SUBDIVISION

      NRES      - NUMBER OF CALLS TO THE EXTRAPOLATION ROUTINE

      NUMRL2    - NUMBER OF ELEMENTS CURRENTLY  IN
                  RLIST2. IF  AN APPROPRIATE
                  APPROXIMATION TO THE  COMPOUNDED
                  INTEGRAL HAS BEEN OBTAINED IT IS
                  PUT IN  RLIST2(NUMRL2) AFTER NUMRL2
                  HAS BEEN INCREASED BY ONE.

      SMALL     - LENGTH OF THE SMALLEST INTERVAL CONSIDERED
                  UP TO NOW,  MULTIPLIED BY 1.5

      ERLARG    - SUM OF THE  ERRORS OVER THE INTERVALS LARGER
                  THAN THE SMALLEST INTERVAL
                  CONSIDERED  UP TO NOW
      EXTRAP    - LOGICAL VARIABLE DENOTING THAT THE
                  ROUTINE IS  ATTEMPTING TO PERFORM
                  EXTRAPOLATION.  I.E.  BEFORE
                  SUBDIVIDING THE SMALLEST INTERVAL
                  WE TRY TO DECREASE THE VALUE OF
                  ERLARG
      NOEXT     - LOGICAL VARIABLE DENOTING THAT EXTRAPOLATION
                  IS NO LONGER ALLOWED(/TRUE/ VALUE)

      FIRST APPROXIMATION TO  THE INTEGRAL


LAST1 = 1
IER = 0
IERRO = 0
CALL D01AJZ(F, A, B, RESULT,  ABSERR, DEFABS, RESABS)

      TEST ON ACCURACY

ORES = DABS(RESULT)
ERRBND = DMAX1(EPSABS,EPSREL*DRES)
IF (ABSERR.LE.1.0D+02*EPMACH*DEFABS  .AND. ABSERR.GT.ERRBND)IER
IF (LIMIT.LT.2 .AND. ABSERR.GT.ERRBND)  IER = 1
IF (IER.NE.O  .OR. ABSERR.LE.ERRBND) GO TO 320

      INITIALIZATION
      ALIST(l)  = A
      BLIST(l)  = B
      RLIST(l)  = RESULT
      RLIST2(1) = RESULT
      ERRMAX =  ABSERR
      MAXERR =  1
      AREA  = RESULT
      ERRSUM =  ABSERR
      ABSERR =  OFLOW
      NRMAX = 1
      NRES  = 0
      NUMRL2 =  2
 PMT42430
 PMT42440
 PMT42450
 PMT42460
 PMT42470
 PMT42480
 PMT42490
 PMT42500
 PMT42510
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 PMT42530
 PMT42540
 PMT42550
 PMT42560
 PMT42570
 PMT42580
 PMT42590
 PMT42600
 PMT42610
 PMT42620
 PMT42630
 PMT42640
 PMT42650
 PMT42660
 PMT42670
 PMT42680
 PMT42690
 PMT42700
 PMT42710
 PMT42720
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 PMT42750
 PMT42760
 PMT42770
 PMT42780
 PMT42790
 PMT42800
 PMT42810
 PMT42820
 PMT42830
.PMT42840
 PMT42850
 PMT42860
 PMT42870
 PMT42880
 PMT42890
 PMT42900
 PMT42910
 PMT42920
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2PMT42940
 PMT42950
 PMT42960
 PMT42970
 PMT42980
 PMT42990
 PMT43000
 PMT43010
 PMT43020
 PMT43030
 PMT43040
 PMT43050
 PMT43060
 PMT43070
 PMT43080
 PMT43090
 PMT43100
 PMT43110
 PMT43120
                                     210

-------
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   KTMIN = 0
   EXTRAP = .FALSE.
   NOEXT = .FALSE.
   IROFF1 = 0
   IROFF2 = 0
   IROFF3 = 0
   KSGN = -I
   IF (ORES.GE.(0.1D+01-0.5D+02*EPMACH)*DEFABS)  KSGN

         MAIN DO-LOOP
                                                        = 1
   IF (LIMIT.LT.2) GO TO 220
   DO 200 LAST=2,LIMIT

         BISECT THE SUBINTERVAL WITH THE NRMAX-TH LARGEST
         ERROR ESTIMATE

      LAST1 = LAST
      Al = ALIST(MAXERR)
      Bl = 0.5D+00*(ALIST(MAXERR)+BLIST(MAXERR))
      A2 = Bl
      B2 = BLIST(MAXERR)
      ERLAST = ERRMAX
      CALL D01AJZ(F, Al, Bl, AREA1, ERROR1, RESABS, DEFAB1)
      CALL D01AJZ(F, A2, B2, AREA2, ERROR2, RESABS, DEFAB2)

         IMPROVE PREVIOUS APPROXIMATION OF INTEGRAL
         AND ERROR AND TEST FOR ACCURACY

      AREA12 = AREA1 + AREA2
      ERR012 = ERROR1 + ERROR2
      ERRSUM = ERRSUM + ERR012 - ERRMAX
      AREA = AREA + AREA12 - RLIST(MAXERR)
      IF (DEFAB1.EQ.ERROR1 .OR. DEFAB2.EQ.ERROR2) GO TO 40
      IF (DABS(RLIST(MAXERR)-AREA12).GT.0.1D-04*DABS(AREA12) .OR.
  *   ERR012.LT.0.99D-)-00*ERRMAX) GO TO 20
      IF (EXTRAP) IROFF2 = IROFF2 + 1
      IF (.NOT.EXTRAP) IROFF1 = IROFF1 + 1
20    IF (LAST.GT.10 .AND. ERR012.GT.ERRMAX) IROFF3 = IROFF3 + 1
40    RLIST(MAXERR) = AREA1
      RLIST(LAST) = AREA2
      ERRBND = DMAX1(EPSABS,EPSREL*DABS(AREA))
      IF (ERRSUM.LE.ERRBND) GO TO 280

         TEST FOR ROUNDOFF ERROR AND EVENTUALLY
         SET ERROR FLAG

      IF (IROFF1+IROFF2.GE.10 .OR. IROFF3.GE.20) IER = 2
      IF (IROFF2.GE.5) IERRO = 3

         SET ERROR FLAG IN THE CASE THAT THE NUMBER OF INTERVAL
          BISECTIONS EXCEEDS /LIMIT/

      IF (LAST.EQ.LIMIT) IER = 1

         SET ERROR FLAG IN THE CASE OF BAD INTEGRAND BEHAVIOUR
         AT INTERIOR POINTS OF INTEGRATION RANGE

      IF (DMAX1(DABS(Al),DABS(B2)).LE.(0.1D+01+0.1D+03*EPMACH)*
  *   (DABS(A2)+0.1D+04*UFLOW)) IER = 4
      IF (lER.NE.O) GO TO 220

         APPEND THE NEWLY-CREATED INTERVALS TO THE LIST

      IF (ERROR2.GT.ERROR1) GO TO 60
         ALIST
         BLIST
         BLIST
         ELIST
            LAST) = A2
            MAXERR) = Bl
            LAST) = B2
            MAXERR) = ERROR1
 PMT43130
 PMT43140
 PMT43150
 PMT43160
 PMT43170
 PMT43180
 PMT43190
 PMT43200
 PMT43210
 PMT43220
 PMT43230
 PMT43240
 PMT43250
 PMT43260
 PMT43270
 PMT43280
 PMT43290
 PMT43300
 PMT43310
 PMT43320
 PMT43330
 PMT43340
 PMT43350
 PMT43360
 PMT43370
 PMT43380
 PMT43390
 PMT43400
 PMT43410
 PMT43420
 PMT43430
 PMT43440
 PMT43450
 PMT43460
 PMT43470
 PMT43480
 PMT43490
 PMT43500
 PMT43510
 PMT43520
 PMT43530
.PMT43540
 PMT43550
 PMT43560
 PMT43570
 PMT43580
 PMT43590
 PMT43600
 PMT43610
 PMT43620
 PMT43630
 PMT43640
 PMT43650
 PMT43660
 PMT43670
 PMT43680
 PMT43690
 PMT43700
 PMT43710
 PMT43720
 PMT43730
 PMT43740
 PMT43750
 PMT43760
 PMT43770
 PMT43780
 PMT43790
 PMT43800
 PMT43810
 PMT43820
                                      211

-------
   60
         ELIST(LAST) = ERROR2
         GO TO 80
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  140
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  160
ALIST
ALIST
BLIST
RLIST
RLIST
ELIST
ELIST
MAXERR) =
LAST) = Al
LAST) = Bl
MAXERR) =
LAST) = AR
MAXERR) =
LAST) = ER
   CALL SUBROUTINE D01AJX TO MAINTAIN THE
   DESCENDING ORDERING IN THE LIST OF ERROR
   ESTIMATES AND SELECT THE SUBINTERVAL WITH
   NRMAX-TH LARGEST ERROR ESTIMATE (TO BE BISECTED
   NEXT)

CALL D01AJX(LIMIT, LAST,  MAXERR, ERRMAX, ELIST, IORD.LIORD,
 NRMAX)
IF (LAST.EQ.2) GO TO 180
IF (NOEXT) GO TO 200
ERLARG = ERLARG - ERLAST
IF (DABS(Bl-Al).GT.SMALL) ERLARG = ERLARG + ERR012
IF (EXTRAP) GO TO 100

   TEST WHETHER THE INTERVAL TO BE BISECTED NEXT IS THE
   SMALLEST INTERVAL

IF (DABS(BLIST(MAXERR)-ALIST(MAXERR)).GT.SMALL) GO TO 200
EXTRAP = .TRUE.
NRMAX = 2
IF (IERRO.EQ.3 .OR. ERLARG.LE.ERTEST) GO TO 140

   THE SMALLEST INTERVAL HAS THE LARGEST ERROR.
   BEFORE BISECTING DECREASE THE SUM OF THE ERRORS
   OVER THE LARGER INTERVALS(ERLARG) AND PERFORM
   EXTRAPOLATION

ID = NRMAX
DO 120 K=ID,JUPBND
   MAXERR = lORD(NRMAX)
   ERRMAX = ELIST(MAXERR)
   IF (DABS(BLIST(MAXERR)-ALIST(MAXERR)).GT.SMALL) GO TO 200
   NRMAX = NRMAX + 1
CONTINUE

   PERFORM EXTRAPOLATION

NUMRL2 = NUMRL2 + 1
RLIST2[NUMRL2) = AREA
CALL D01AJY(NUMRL2, RLIST2, RESEPS, ABSEPS, RES3LA, NRES)
KTMIN = KTMIN +1
IF (KTMIN.GT.5 .AND. ABSERR.LT.O.1D-02*ERRSUM) IER = 5
IF (ABSEPS.GE.ABSERR) GO TO 160
KTMIN = 0
ABSERR = ABSEPS
RESULT = RESEPS
CORREC = ERLARG
ERTEST = DMAX1(EPSABS,EPSREL*DABS(RESEPS))
IF (ABSERR.LE.ERTEST) GO TO 220

   PREPARE  BISECTION OF THE SMALLEST INTERVAL
    (NUMRL2.EQ.1) NOEXT =
    "IER.EQ.5) GO TO 220
MAXERR = IORD(1)
ERRMAX = ELIST(MAXERR)
NRMAX = 1
EXTRAP = .FALSE.
SMALL = SMALL*0.5D+00
ERLARG = ERRSUM
.TRUE.
PMT43830
PMT43840
PMT43850
PMT43860
PMT43870
PMT43880
PMT43890
PMT43900
PMT43910
PMT43920
PMT43930
PMT43940
PMT43950
PMT43960
PMT43970
PMT43980
PMT43990
PMT44000
PMT44010
PMT44020
PMT44030
PMT44040
PMT44050
PMT44060
PMT44070
PMT44080
PMT44090
PMT44100
PMT44110
PMT44120
PMT44130
PMT44140
PMT44150
PMT44160
PMT44170
PMT44180
PMT44190
PMT44200
PMT44210
PMT44220
PMT44230
PMT44240
PMT44250
PMT44260
PMT44270
PMT44280
PMT44290
PMT44300
PMT44310
PMT44320
PMT44330
PMT44340
PMT44350
PMT44360
PMT44370
PMT44380
PMT44390
PMT44400
PMT44410
PMT44420
PMT44430
PMT44440
PMT44450
PMT44460
PMT44470
PMT44480
PMT44490
PMT44500
PMT44510
PMT44520
                                     212

-------
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         GO TO 200
  180    SMALL = DABS(B-A)*0.375D+00
         ERLARG = ERRSUM
         ERTEST = ERRBND
         RLIST2C2) = AREA
  200 CONTINUE
          SET  FINAL RESULT AND ERROR ESTIMATE
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220 IF (ABSERR.EQ.OFLOW) GO TO 280
    IF (lER+IERRO.EQ.O) GO TO 260
    IF (IERRO.EQ.3) ABSERR = ABSERR + CORREC
    IF (IER.EQ.O) IER = 3
    IF (RESULT.NE.O.D+00.AND .AREA. NE.O.D+00) GO TO 240
    IF (ABSERR.GT.ERRSUM) GO TO 280
    IF (AREA.EQ.O.D+00) GO TO 320
    GO TO 260
240 IF (ABSERR/DABS(RESULT).GT.ERRSUM/DABS(AREA)) GO TO 280

          TEST ON DIVERGENCY

260 IF (KSGN.EQ.-l .AND. DMAX1(DABS(RESULT),DABS(AREA)).LE.DEFABS*
   *0.1D-01) GO TO 320
    IF (0.1D-01.GT.(RESULT/AREA) .OR. (RESULT/AREA).GT.O.1D+03.0R.
   * ERRSUM.GT.DABS(AREA)) IER = 6
    GO TO 320

          COMPUTE GLOBAL INTEGRAL SUM

280 RESULT = O.D+00
    DO 300 K=1,LAST
       RESULT = RESULT + RLIST(K)
300 CONTINUE
    ABSERR = ERRSUM
320 IF (IER.GT.2) IER = IER - 1
    lORDjl) = 4*LAST1
    RETURN
    END
    SUBROUTINE D01AJX(LIMIT, LAST, MAXERR, ERMAX, ELIST, IORD.LIORD,
   * NRMAX)
                   SUBROUTINE D01AJX , PART OF PEM-2  (VERSION 84130)

    MARK 8 RELEASE. NAG COPYRIGHT 1979
    BASED ON QUADPACK ROUTINE ORDER
          PURPOSE
             THIS ROUTINE MAINTAINS THE DESCENDING ORDERING
             IN THE LIST OF THE LOCAL ERROR ESTIMATES
             RESULTING FROM THE INTERVAL SUBDIVISION
             PROCESS. AT EACH CALL TWO ERROR ESTIMATES
             ARE INSERTED USING THE SEQUENTIAL SEARCH
             METHOD . TOP-DOWN FOR THE LARGEST ERROR
             ESTIMATE,  BOTTOM-UP FOR THE SMALLEST ERROR
             ESTIMATE.

          CALLING SEQUENCE
             CALL D01AJX
             ( LIMIT , LAST , MAXERR, ERMAX , ELIST, IORD , LIORD , NRMAX)

            PARAMETERS (MEANING AT OUTPUT)
             LIMIT  - MAXIMUM NUMBER OF ERROR ESTIMATES THE  LIST
                      CAN CONTAIN

             LAST   - NUMBER OF ERROR ESTIMATES CURRENTLY
                      IN THE LIST. ELIST (LAST) CONTAINS
PMT44530
PMT44540
PMT44550
PMT44560
PMT44570
PMT44580
PMT44590
PMT44600
PMT44610
PMT44620
PMT44630
PMT44640
PMT44650
PMT44660
PMT44670
PMT44680
PMT44690
PMT44700
PMT44710
PMT44720
PMT44730
PMT44740
PMT44750
PMT44760
PMT44770
PMT44780
PMT44790
PMT44800
PMT44810
PMT44820
PMT44830
PMT44840
PMT44850
PMT44860
PMT44870
PMT44880
PMT44890
PMT44900
PMT44910

PMT44920
.PMT44930
PMT44940
PMT44950
PMT44960
PMT44970
PMT44980
PMT44990
PMT45000
PMT45010
PMT45020
PMT45030
PMT45040
PMT45050
PMT45060
PMT45070
PMT45080
PMT45090
PMT45100
PMT45110
PMT45120
PMT45130
PMT45140
PMT45150
PMT45160
PMT45170
PMT45180
PMT45190
PMT45200
 PMT45210
                                      213

-------
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                     THE  SMALLEST  ERROR  ESTIMATE.

            MAXERR -  MAXERR POINTS TO  THE  NRMAX-TH LARGEST  ERROR
                     ESTIMATE  CURRENTLY  IN THE  LIST.

            ERMAX   -  NRMAX-TH  LARGEST  ERROR ESTIMATE
                     ERMAX = ELIST(MAXERR)

            ELIST   -  ARRAY OF  DIMENSION  LAST CONTAINING
                     THE  ERROR ESTIMATES

            IORD   -  ARRAY CONTAINING  POINTERS  TO ELIST SO
                     THAT IORD(1)  POINTS TO THE LARGEST
                     ERROR ESTIMATE,....IORD(LAST) TO THE
                     SMALLEST  ERROR ESTIMATE

            LIORD   -  DIMENSION OF  IORD

            NRMAX   -  MAXERR =  lORD(NRMAX)

   ##*###************************************************

   ..  SCALAR ARGUMENTS ..
   DOUBLE PRECISION ERMAX
   INTEGER LAST, LIMIT,  LIORD, MAXERR,  NRMAX
   ..  ARRAY ARGUMENTS ..
   DOUBLE PRECISION ELIST(LAST)
   INTEGER IORD(LIORD)

   '. '.  SCALARS IN COMMON . .
   INTEGER JUPBND

   !!  LOCAL SCALARS ..
   DOUBLE PRECISION ERRMAX, ERRMIN
   INTEGER I, IBEG, IDO,  ISUCC, J, JBND, K

   COMMON /AD01AJ/ JUPBND

          CHECK WHETHER THE LIST CONTAINS  MORE  THAN
          TWO ERROR ESTIMATES

   IF (LAST.GT.2)  GO  TO 20
   IORD(1} = 1
   IORD(2) = 2
   GO TO 180

         THIS PART OF THE ROUTINE  IS ONLY  EXECUTED
         IF, DUE TO A DIFFICULT INTEGRAND, SUBDIVISION
         INCREASED THE ERROR ESTIMATE. IN  THE NORMAL CASE
         THE INSERT PROCEDURE  SHOULD START AFTER THE
         NRMAX-TH  LARGEST ERROR ESTIMATE.

20 ERRMAX = ELIST(MAXERR)
   IF (NRMAX.EQ.l) GO TO 60
   IDO = NRMAX - 1
   DO 40 1=1,IDO
      ISUCC = IORD(NRMAX-1)
      IF (ERRMAX.LE.ELIST(ISUCC))  GO TO 60
      IORD(NRMAX)  = ISUCC
      NRMAX = NRMAX - 1
40 CONTINUE

         COMPUTE THE  NUMBER OF ELEMENTS IN THE  LIST TO
         BE MAINTAINED IN DESCENDING ORDER. THIS NUMBER
         DEPENDS ON THE NUMBER OF SUBDIVISIONS  STILL
         ALLOWED

60 JUPBND = LAST
   IF (LAST.GT.(LIMIT/2+2)) JUPBND = LIMIT + 3  - LAST
   ERRMIN = ELIST(LAST)
PMT45220
PMT45230
PMT45240
PMT45250
PMT45260
PMT45270
PMT45280
PMT45290
PMT45300
PMT45310
PMT45320
PMT45330
PMT45340
PMT45350
PMT45360
PMT45370
PMT45380
PMT45390
PMT45400
PMT45410
PMT45420
PMT45430
PMT45440
PMT45450
PMT45460
PMT45470
PMT45480
PMT45490
PMT45500
PMT45510
PMT45520
PMT45530
PMT45540
PMT45550
PMT45560
PMT45570
PMT45580
PMT45590
PMT45600
PMT45610
PMT45620
PMT45630
PMT45640
PMT45650
PMT45660
PMT45670
PMT45680
PMT45690
PMT45700
PMT45710
PMT45720
PMT45730
PMT45740
PMT45750
PMT45760
PMT45770
PMT45780
PMT45790
PMT45800
PMT45810
PMT45820
PMT45830
PMT45840
PMT45850
PMT45860
PMT45870
PMT45880
PMT45890
PMT45900
PMT45910
                                     214

-------
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          INSERT ERRMAX BY TRAVERSING THE LIST TOP-DOWN
          STARTING COMPARISON FROM THE ELEMENT
          ELIST(IORD(NRMAX+1))

    JBND = JUPBND - 1
    IBEG = NRMAX + 1
    IF (IBEG.GT.JBND) GO TO 100
    DO 80 I=IBEG,JBND
       ISUCC = IORD(I)
       IF (ERRMAX.GE.ELIST(ISUCC)) GO TO 120
       lORD(I-l) = ISUCC
 80 CONTINUE
100 lORD(JBND) = MAXERR
    IOHDCJUPBND) = LAST
    GO TO 180

          INSERT ERRMIN BY TRAVERSING THE LIST BOTTOM-UP

120 lORD(I-l) = MAXERR
    K = JBND
    DO 140 J=I,JBND
       ISUCC = IORD(K)
       IF (ERRMIN.LT.ELIST(ISUCC)) GO TO 160
       IORD(K+1) = ISUCC
ooo
140
160
K = K
CONTINUE
IORD(I) =
GO TO 180
IORD(K+1)
SET
LAST
= LAST
MAXERR AND
ERMAX
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  180 MAXERR = IORD(NRMAX)
      ERMAX = ELIST(MAXERR)
      RETURN
      END
    SUBROUTINE D01AJY(N, EPSTAB. RESULT, ABSERR, RES3LA, NRES)
                   SUBROUTINE D&1AJY , PART OF PEM-2 (VERSION 84130),

    MARK 8 RELEASE. NAG COPYRIGHT 1979
    BASED ON QUADPACK ROUTINE EPSALG
          PURPOSE
             THE ROUTINE TRANSFORMS A GIVEN SEQUENCE OF
             APPROXIMATIONS, BY MEANS OF THE EPSILON
             ALGORITHM OF P. WYNN.

             AN ESTIMATE OF THE ABSOLUTE ERROR IS ALSO GIVEN.
             THE CONDENSED EPSILON TABLE IS COMPUTED. ONLY THOSE
             ELEMENTS NEEDED FOR THE COMPUTATION OF THE
             NEXT DIAGONAL ARE PRESERVED.

          CALLING SEQUENCE
             CALL D01AJY (N, EPSTAB, RESULT, ABSERR, RES3LA, NRES)

          PARAMETERS
             N      - EPSTAB (N) CONTAINS THE NEW ELEMENT IN THE
                      FIRST COLUMN OF THE EPSILON TABLE.

             EPSTAB - ONE DIMENSIONAL ARRAY CONTAINING THE
                      ELEMENTS OF THE TWO LOWER DIAGONALS OF
                      THE TRIANGULAR EPSILON TABLE.
                      THE ELEMENTS ARE NUMBERED STARTING AT THE
                      RIGHT-HAND CORNER OF THE TRIANGLE.
                      THE DIMENSION SHOULD BE AT LEAST N+2.
 PMT45920
 PMT45930
 PMT45940
 PMT45950
 PMT45960
 PMT45970
 PMT45980
 PMT45990
 PMT46000
 PMT46010
 PMT46020
 PMT46030
 PMT46040
 PMT46050
 PMT46060
 PMT46070
 PMT46080
 PMT46090
 PMT46100
 PMT46110
 PMT46120
 PMT46130
 PMT46140
 PMT46150
 PMT46160
 PMT46170
 PMT46180
 PMT46190
 PMT46200
 PMT46210
 PMT46220
 PMT46230
 PMT46240
 PMT46250
 PMT46260
 PMT46270
 PMT46280

 PMT46290
 PMT46300
 PMT46310
-PMT46320
 PMT46330
 PMT46340
 PMT46350
 PMT46360
 PMT46370
 PMT46380
 PMT46390
 PMT46400
 PMT46410
 PMT46420
 PMT46430
 PMT46440
 PMT46450
 PMT46460
 PMT46470
 PMT46480
 PMT46490
 PMT46500
 PMT46510
 PMT46520
 PMT46530
 PMT46540
 PMT46550
 PMT46560
 PMT46570
 PMT46580
 PMT46590
 PMT46600
                                      215

-------
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          RESULT - RESULTING APPROXIMATION TO THE INTEGRAL

          ABSERR - ESTIMATE OF THE ABSOLUTE ERROR COMPUTED FROM
                   RESULT AND THE 3 PREVIOUS /RESULTS/

          RES3LA - ARRAY CONTAINING THE LAST 3 /RESULTS/

          NRES   - NUMBER OF CALLS TO THE ROUTINE
                   (SHOULD BE ZERO AT FIRST CALL)

 ******************************************************
 ..  SCALAR ARGUMENTS ..
 DOUBLE PRECISION ABSERR, RESULT
 INTEGER N, NRES
 ..  ARRAY ARGUMENTS ..
 DOUBLE PRECISION EPSTAB(52), RES3LA(3)

 '.'.  LOCAL SCALARS . .
 DOUBLE PRECISION DELTA1, DELTA2. DELTAS, EO, El, ElABS, E2.  E3,
* EPMACH.EPSINF, ERR1,  ERR2, ERR3, ERROR, OFLOW,  RES,  SS, TOL1,
* TOL2,TOL3
 INTEGER I, IB2, IB, IE, IND, Kl, K2, K3, LIMEXP, NEWELM, NUM
 ..  FUNCTION REFERENCES ..
 DOUBLE PRECISION X02AAF, X02ACF
        MACHINE DEPENDENT CONSTANTS
        /LIMEXP/ IS THE MAXIMUM NUMBER OF ELEMENTS THE EPSILON
        TABLE CAN CONTAIN. IF THIS NUMBER IS REACHED, THE UPPER
        DIAGONAL OF THE EPSILON TABLE IS DELETED.
 DATA LIMEXP /50/
 EPMACH = X02AAF()
 OFLOW = X02ACF()

       LIST OF MAJOR VARIABLES

       EO     - THE 4 ELEMENTS ON WHICH THE
       El       COMPUTATION OF A NEW ELEMENT IN
       E2       THE EPSILON TABLE IS BASED
       E3                 EO
                    E3    El    NEW
                          E2
       NEWELM - NUMBER OF ELEMENTS TO BE COMPUTED IN THE NEW
                DIAGONAL
       ERROR  - ERROR - ABS(E1-EO|+ABS(E2-E1)+ABS(NEW~E2)
       RESULT - THE ELEMENT IN THE NEW DIAGONAL WITH LEAST
                ERROR

 NRES = NRES + 1
 ABSERR = OFLOW
 RESULT = EPSTAB(N)
 IF  (N.LT.3) GO TO 200
 EPSTAB(N+2) = EPSTAB(N)
 NEWELM = (N-l)/2
 EPSTAB(N) = OFLOW
 NUM = N
 Kl  = N
 DO  80 1=1,NEWELM
     K2 = Kl - 1
     K3 = Kl - 2
     RES = EPSTAB(Kl+2)
     EO = EPSTAB(K3)
     El = EPSTAB(K2)
     E2 = RES
     ElABS = DABS(El)
     DELTA2 = E2 - El
     ERR2 = DABS(DELTA2)
PMT46610
PMT46620
PMT46630
PMT46640
PMT46650
PMT46660
PMT46670
PMT46680
PMT46690
PMT46700
PMT46710
PMT46720
PMT46730
PMT46740
PMT46750
PMT46760
PMT46770
PMT46780
PMT46790
PMT46800
PMT46810
PMT46820
PMT46830
PMT46840
PMT46850
PMT46860
PMT46870
PMT46880
PMT46890
PMT46900
PMT46910
PMT46920
PMT46930
PMT46940
PMT46950
PMT46960
PMT46970
PMT46980
PMT46990
PMT47000
PMT47010
.PMT47020
PMT47030
PMT47040
PMT47050
PMT47060
PMT47070
PMT47080
PMT47090
PMT47100
PMT47110
PMT47120
PMT47130
PMT47140
PMT47150
PMT47160
PMT47170
PMT47180
PMT47190
PMT47200
PMT47210
PMT47220
PMT47230
PMT47240
PMT47250
PMT47260
PMT47270
PMT47280
PMT47290
PMT47300
                                     216

-------
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   20
   40
   60
       TOL2  =  DMAX1(DABS(E2),E1ABS)*EPMACH
       DELTAS  =  El  -  EO
       ERRS  =  DABS(DELTAS)
       TOL3  =  DMAX1(E1ABS,DABS(EO))*EPMACH
       IF (ERR2.GT.TOL2 .OR.  ERR3.GT.TOL3) GO TO 20

          IF EO,  El AND E2  ARE  EQUAL  TO WITHIN MACHINE
          ACCURACY, CONVERGENCE IS ASSUMED
          RESULT =  E2
          ABSERR =  ABS(E1-EO)+ABS(E2-E1)

       RESULT  =  RES
       ABSERR  =  ERR2  + ERRS
       GO TO 200
       E3 =  EPSTAB(Kl)
       EPSTAB(Kl) = El
       DELTA1  =  El  -  E3
       ERR1  =  DABS(DELTAl)
       TOL1  =  DMAX1(E1ABS,DABS(E3))*EPMACH

          IF TWO ELEMENTS ARE VERY CLOSE TO EACH OTHER,  OMIT
          A  PART OF THE TABLE BY ADJUSTING THE VALUE OF N

       IF (ERR1.LT.TOL1 .OR.  ERR2.LT.TOL2 .OR. ERRS.LT.TOL3) GOTO 40
       SS =  0.1D+01/DELTA1  +  0.1D+01/DELTA2 - 0.1D+01/DELTA3
       EPSINF  =  DABS(SS*E1)

          TEST TO DETECT IRREGULAR BEHAVIOUR IN THE TABLE.  AND
          EVENTUALLY  OMIT A PART OF THE TABLE ADJUSTING THE VALUE
          OF N

       IF (EPSINF.GT.0.1D-03) GO TO 60
       N = I + I - 1
       GO TO 100

          COMPUTE A NEW ELEMENT AND EVENTUALLY ADJUST
          THE  VALUE OF RESULT
C
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       RES = El + 0.1D+01/SS
       EPSTAB(Kl) = RES
       Kl = Kl - 2
       ERROR = ERR2 + DABS(RES-E2) + ERRS
       IF (ERROR.GT.ABSERR) GO TO 80
       ABSERR = ERROR
       RESULT = RES
 80 CONTINUE

          SHIFT THE TABLE

100 IF (N.EQ.LIMEXP)  N = 2*(LIMEXP/2) - 1
    IB = 1
    IF ((NUM/2)*2.EQ.NUM) IB = 2
    IE = NEWELM + 1
    DO 120 1=1,IE
       IB2 = IB + 2
       EPSTAB(IB) = EPSTAB(IB2)
       IB = IB2
120 CONTINUE
    IF (NUM.EQ.N) GO TO 160
    IND = NUM - N + 1
    DO 140 1=1,N
       EPSTAB(I) = EPSTAB(IND)
       IND = IND + 1
140 CONTINUE
160 IF (NRES.GE.4) GO TO 180
    RESSLA(NRES) = RESULT
    ABSERR = OFLOW
    GO TO 200

          COMPUTE ERROR ESTIMATE
 PMT47310
 PMT47320
 PMT47330
 PMT47340
 PMT47350
 PMT47360
 PMT47370
 PMT47380
 PMT47390
 PMT47400
 PMT47410
 PMT47420
 PMT47430
 PMT47440
 PMT47450
 PMT47460
 PMT47470
 PMT47480
 PMT47490
 PMT47500
 PMT47510
 PMT47520
 PMT47530
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 PMT47550
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 PMT47570
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 PMT47590
 PMT47600
 PMT47610
 PMT47620
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 PMT47660
 PMT47670
 PMT47680
 PMT47690
 PMT47700
 PMT47710
•PMT47720
 PMT47730
 PMT47740
 PMT47750
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 PMT47770
 PMT47780
 PMT47790
 PMT47800
 PMT47810
 PMT47820
 PMT47830
 PMT47840
 PMT47850
 PMT47860
 PMT47870
 PMT47880
 PMT47890
 PMT47900
 PMT47910
 PMT47920
 PMT47930
 PMT47940
 PMT47950
 PMT47960
 PMT47970
 PMT47980
 PMT47990
 PMT48000
                                     217

-------
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  180 ABSERR = DABS(RESULT-RES3LA(3))  + DABS(RESULT-RES3LA(2))  +
     *DABS(RESULT-RES3LA(1))
      RES3LA(1) = RES3LA(2)
      RES3LA(2) = RES3LA(3)
      RES3LA(3) = RESULT
  200 ABSERR = DMAX1(ABSERR,5.0D+00*EPMACH*DABS(RESULT))
      RETURN
      END
 SUBROUTINE D01AJZ(F, A, B, RESULT, ABSERR, RESABS, RESASC)
               SUBROUTINE D01AJZ  , PART OF PEM-2  (VERSION 84130)

 MARK 8 RELEASE.  NAG COPYRIGHT  1979
 BASED ON  QUADPACK ROUTINE QUARUL
 ******************************************************

       PURPOSE
          TO  COMPUTE I  = INTEGRAL  OF  F  OVER  (A,B), WITH  ERROR
                        ESTIMATE
                    J  = INTEGRAL  OF  ABS(F) OVER (A.B)

       CALLING  SEQUENCE
          CALL  D01AJZ  (F,A,B,RESULT,ABSERR,RESABS,RESASC)
       PARAMETERS
          A

          B
- FUNCTION SUBPROGRAM DEFINING THE INTEGRAND
  FUNCTION F(X). THE ACTUAL NAME FOR F NEEDS
  TO BE DECLARED EXTERNAL IN THE
  CALLING PROGRAM

- LOWER LIMIT OF INTEGRATION

- UPPER LIMIT OF INTEGRATION
 C
 C
 C
 C
          RESULT - APPROXIMATION TO THE INTEGRAL I.
                   RESULT IS CALCULATED BY APPLYING
                   THE 21-POINT GAUSS-KRONROD RULE
                   (RESK),  OBTAINED BY OPTIMAL
                   ADDITION OF ABSCISSAE TO THE
                   10-POINT GAUSS  RULE (RESG).

          ABSERR - ESTIMATE OF THE MODULUS OF THE
                   ABSOLUTE ERROR, WHICH SHOULD NOT
                   EXCEED ABS(I-RESULT)
          RESABS - APPROXIMATION TO THE INTEGRAL J

          RESASC - APPROXIMATION TO THE INTEGRAL OF
                   ABS(F-I/(B-A)) OVER (A,B)

 ******************************************************
 ..  SCALAR ARGUMENTS ..
 DOUBLE PRECISION A, ABSERR, B, RESABS, RESASC,  RESULT
 ..  FUNCTION ARGUMENTS ..
 DOUBLE PRECISION F

 '.'.  LOCAL SCALARS ..
 DOUBLE PRECISION ABSC,  CENTRE, DHLGTH, EPMACH,  FC,  FSUM,  FVAL1,
* FVAL2.HLGTH,  RESG, RESK,  RESKH, UFLOW
 INTEGER J
 ..  LOCAL ARRAYS ..
 DOUBLE PRECISION FVl(lO),  FV2(10), WG(10), WGK(ll), XGK(ll)
 ..  FUNCTION REFERENCES ..
 DOUBLE PRECISION X02AAF, X02ABF


        THE ABSCISSAE AND WEIGHTS ARE GIVEN FOR THE
        INTERVAL (-1,1)  . BECAUSE OF SYMMETRY ONLY THE
PMT48010
PMT48020
PMT48030
PMT48040
PMT48050
PMT48060
PMT48070
PMT48080
PMT48090

PMT48100
PMT48110
PMT48120
PMT48130
PMT48140
PMT48150
PMT48160
PMT48170
PMT48180
PMT48190
PMT48200
PMT48210
PMT48220
PMT48230
PMT48240
PMT48250
PMT48260
PMT48270
PMT48280
PMT48290
PMT48300
PMT48310
PMT48320
PMT48330
PMT48340
PMT48350
PMT48360
PMT48370
PMT48380
PMT48390
PMT48400
.PMT48410
PMT48420
PMT48430
PMT48440
PMT48450
PMT48460
PMT48470
PMT48480
PMT48490
PMT48500
PMT48510
PMT48520
PMT48530
PMT48540
PMT48550
PMT48560
PMT48570
PMT48580
PMT48590
PMT48600
PMT48610
PMT48620
PMT48630
PMT48640
PMT48650
PMT48660
PMT48670
PMT48680
 PMT48690
                                      218

-------
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        POSITIVE ABSCISSAE
        WEIGHTS ARE GIVEN.
                           AND THEIR CORRESPONDING
C
C
C
C
C
C
C
C
C
C
C
c
 c
 c
 c
 c
        XGK
        WGK
        WG
                                  21-POINT GAUSS-KRONROD RULE
                                  ...  ABSCISSAE OF THE 10-POINT
ABSCISSAE OF THE
XGK(2), XGK(4),
GAUSS RULE
XGK(l), XGK(3), ---- ABSCISSAE WHICH
ARE OPTIMALLY ADDED TO THE 10-POINT
GAUSS RULE
WEIGHTS OF THE 21-POINT GAUSS-KRONROD RULE
WEIGHTS OF THE 10-POINT GAUSS RULE,
CORRESPONDING TO THE ABSCISSAE XGK(2),
                                    T
XGK(4),
TO ZERO.
                      XGK
                             WG(1), WG(3),
                                               ARE SE
 DATA XGK(l), XGK(2)

*6.9739065285171717200779640'121D+00,
*0.9301574913557082260012071801D+00,
*0.8650633666889845107320966884D+00,
*0.7808177265864168970637175783D+00,
*0.6794095682990244062343273651D+00,
*0.56275713466860468333900009930+00,
*0.43339539412924719079926594320+00,
*0.2943928627014601981311266031D+00,
*0.14887433898163121088482600110+00.0.ODO/
PMT48700
PMT48710
PMT48720
PMT48730
PMT48740
PMT48750
PMT48760
PMT48770
PMT48780
PMT48790
PMT48800
PMT48810
PMT48820
PMT48830
                                   XGK(4),  XGK(5).  XGK(6),  XGK(7) ,XGK(8)PMT48840
                                   . 9956571630258680807355272807D+00 ,    --------
                                                                   PMT48850
                                                                   PMT48860
                                                                   PMT48870
                                                                   PMT48880
                                                                   PMT48890
                                                                   PMT48900
                                                                   PMT48910
                                                                   PMT48920
                                                                   PMT48930
                                                                   PMT48940
      T\J • JL^ W*J i TT«J*J*J»-/U J.\J*J ±t-t J. \J w *-t^i~J£j \J\J\J J* J.U ' \J\J j \J * \J U\J /                          LLI iTC w^JTV/
      DATA WGK(l), WGK(2), WGK(3), WGK(4),  WGK(5), WGK(6),  WGK(7),WGK(8)PMT48950
     *0
   WGK(9). WGKflOl. WGK(ll) /O.1169463886737187427806439606D-01,
*U.32558162307964727478818972460-01,
*0.5475589657435199603138130024D-01,
*0.75039674810919952767043140920-01,
*0.93125454583697605535065465080-01,
*0.1093871588022976418992105903D+00,
   1234919762620658510779581098D+00,
   1347092173114733259280540018D+00,
*0.1427759385770600807970942731D+00,
*0.1477391049013384913748415160D+00,
*0.1494455f	 "
 DATA WG(i;
  _-_x.-»

*0.
*0.2190863625159820439955349342D+00', 0. ODO;
*0.2692667193099963550912269216D+00,0.ODO,
*0.2955242247147528701738929947D+00/
 EPMACH = X02AAFQ
 UFLOW = X02ABF()

       LIST OF MAJOR VARIABLES
         .
       ATA WG(1), WG(2), WG(3), WG(4),  WG(5),  WG(6),  WG(7),  WG(8),WG(9)
       WG(10) /O.000,0.66671344308688i3759356880989D-01,0.6oO,
       .14945134915058059314577633970+00,0.ODO,
       CENTRE - MID POINT OF THE  INTERVAL
       HLGTH  - HALF LENGTH OF THE  INTERVAL
       ABSC   - ABSCISSA
       FVAL*  - FUNCTION VALUE
       RESG   - 10-POINT GAUSS FORMULA
       RESK   - 21-POINT GAUSS-KRONROD  FORMULA
       RESKH  - APPROXIMATION TO  MEAN VALUE OF  F  OVER
                (A.B), I.E. TO I/CB-A)

 CENTRE = 0.5D+00*(A+B)
 HLGTH = 0.50+00*(B-A)
 DHLGTH = DABS(HLGTH)
       COMPUTE THE 21-POINT GAUSS-KRONROD APPROXIMATION TO
       THE INTEGRAL, AND ESTIMATE  THE ABSOLUTE  ERROR
       RESG
       FC  =
      = 0.00+00
      F(CENTRE)
 RESK = WGK(11)*FC
 RESABS = DABS(RESK)
 DO 20 J=l,10
    ABSC = HLGTH*XGK(J)
                                                                    PMT48960
                                                                    PMT48970
                                                                    PMT48980
                                                                    PMT48990
                                                                    PMT49000
                                                                    PMT49010
                                                                    PMT49020
                                                                    PMT49030
                                                                    PMT49040
                                                                    PMT49050
                                                                    PMT49060
                                                                   .PMT49070
                                                                    PMT49080
                                                                    PMT49090
                                                                    PMT49100
                                                                   .PMT49110
                                                                    PMT49120
                                                                    PMT49130
                                                                    PMT49140
                                                                    PMT49150
                                                                    PMT49160
                                                                    PMT49170
                                                                    PMT49180
                                                                    PMT49190
                                                                    PMT49200
                                                                    PMT49210
                                                                    PMT49220
                                                                    PMT49230
                                                                    PMT49240
                                                                    PMT49250
                                                                    PMT49260
                                                                    PMT49270
                                                                    PMT49280
                                                                    PMT49290
                                                                    PMT49300
                                                                    PMT49310
                                                                    PMT49320
                                                                    PMT49330
                                                                    PMT49340
                                                                    PMT49350
                                                                    PMT49360
                                                                    PMT49370
                                                                    PMT49380
                                                                    PMT49390
                                      219

-------
         FVAL1 = F(CENTRE-ABSC)
         FVAL2 = F(CENTRE*ABSC)
         FV1(J) = FVAL1
         FV2(J) = FVAL2
         FSUM = FVAL1 + FVAL2
         RESG = RESG + WG(J)*FSUM
         RESK = RESK + WGK(J)*FSUM
         RESABS = RESABS + WGK(J)*(DABS(FVAL1)+DABS(FVAL2))
   20 CONTINUE
      RESKH = RESK*0.5D+00
      RESASC = WGK(11)*DABS(FC-RESKH)
      DO 40 J=l,10
                                                                  PMT49400
                                                                  PMT49410
                                                                  PMT49420
                                                                  PMT49430
                                                                  PMT49440
                                                                  PMT49450
                                                                  PMT49460
                                                                  PMT49470
                                                                  PMT49480
                                                                  PMT49490
                                                                  PMT49500
                                                                  PMT49510
         RESASC'= RESASC + WGK(J)*(DABS(FV1(J)-RESKH)+DABS(FV2(J)-RESKH)PMT49520
     *   )                                                              PMT49530
   40 CONTINUE                                                          PMT49540
      RESULT = RESK*HLGTH                                               PMT49550
      RESABS = RESABS*DHLGTH                                            PMT49560
      RESASC = RESASC*DHLGTH                                            PMT49570
      ABSERR = DABS((RESK-RESG)*HLGTH)                                  PMT49580
      IF (RESASC.NE.O.D+00) ABSERR = RESASC*DMIN1(0.1D+01,(0.2D+03*     PMT49590
     *ABSERR/RESASC)**1.5DO)                                            PMT49600
      IF (RESABS.GT.UFLOW/(0.5D+02*EPMACH)) ABSERR =DMAX1(EPMACH*RESABS*PMT49610
C
C
C

C
C
C
C
C
C
C
C

C$P 1
     *0.5D+02,ABSERR)
      RETURN
      END
INTEGER FUNCTION P01AAF(IFAIL, ERROR, SRNAME)
                 FUNCTION P01AAF ,  PART OF PEM-2 (VERSION 84130)

MARK 1 RELEASE.  NAG COPYRIGHT 1971
MARK 3 REVISED
MARK 4A REVISED, IER-45
MARK 4.5 REVISED
MARK 7 REVISED (DEC 1978)
RETURNS THE VALUE OF ERROR OR TERMINATES THE PROGRAM.
INTEGER ERROR, IFAIL, NOUT
      DOUBLE PRECISION SRNAME
C     TEST IF NO ERROR DETECTED
      IF(ERROR.EQ.O) GO TO 20
C     DETERMINE OUTPUT UNIT FOR MESSAGE
      CALL X04AAF (O.NOUT)
C     TEST FOR SOFT FAILURE
      IF (MOD(IFAIL,10).EQ.l) GO TO 10
C     HARD FAILURE
      WRITE (NOUT.99999) SRNAME, ERROR
C     STOPPING MECHANISM MAY ALSO DIFFER
      CALL WAUDIT
      STOP
C     SOFT FAIL
C     TEST IF ERROR MESSAGES SUPPRESSED
   10 IF ?MOD(IFAIL/10,10).EQ.O) GO TO 20
      WRITE (NOUT,99999) SRNAME, ERROR
   20 P01AAF = ERROR
      RETURN
99999 FORMAT (1HO, 38HERROR DETECTED BY NAG LIBRARY ROUTINE
     * 11H - IFAIL = , I5//)
      END
                                                        A8,
C
C
C

C
C
C
C
C
C
DOUBLE PRECISION FUNCTION X02AAFQ
                 FUNCTION X02AAF  , PART OF PEM-2 (VERSION 84130)

NAG COPYRIGHT 1975
MARK 4.5 RELEASE

* EPS *
 PMT49620
 PMT49630
 PMT49640

 PMT49650
 PMT49660
 PMT49670
 PMT49680
 PMT49690
 PMT49700
 PMT49710
 PMT49720
 PMT49730
 PMT49740
 PMT49750
 PMT49760
 PMT49770
 PMT49780
 PMT49790
.PMT49800
 PMT49810
 PMT49820
 PMT49830
 PMT49840
 PMT49850
 PMT49860
 PMT49870

 PMT49880
 PMT49890
 PMT49900
 PMT49910
 PMT49920
 PMT49930
 PMT49940
 PMT49950
 PMT49960
 PMT49970

 PMT49980
 PMT49990
 PMT50000
 PMT50010
 PMT50020
 PMT50030
 PMT50040
 PMT50050
 PMT50060
                                     220

-------
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UNIVAC DOUBLE PRECISION VERSION

RETURNS THE VALUE EPS WHERE EPS IS THE SMALLEST POSITIVE
NUMBER SUCH THAT 1.0 + EPS > 1.0

FOR ICL 1900
X02AAF = 2.0**(-37.0)

FOR IBM 360/370
X02AAF = 2.0DO**(-52.0DO)

DOUBLE PRECISION Z

FOR IBM-3033
DATA Z/Z3410000000000000/

FOR UNIVAC-1100
DIMENSION ZZ(2)
EQUIVALENCE (ZZ(l).Z)
DATA ZZ /0171410000000,0000000000000/
X02AAF - Z
RETURN
END
DOUBLE PRECISION FUNCTION X02ABFQ
                 FUNCTION X02ABF  , PART OF PEM-2  (VERSION 84130)

NAG COPYRIGHT 1975
MARK 4.5 RELEASE

* RMIN *

UNIVAC DOUBLE PRECISION VERSION

RETURNS THE VALUE OF THE SMALLEST POSITIVE REAL FLOATING-
POINT NUMBER EXACTLY REPRESENTABLE ON THE COMPUTER

FOR ICL 1900
X02ABF = 2.0**(-257.0)

FOR IBM 360/370
X02ABF = 16.0DO**(-65.0DO)

DOUBLE PRECISION Z

FOR IBM-3033
DATA Z/Z0010000000000000/

FOR UNIVAC-1100
DIMENSION ZZ(2)
EQUIVALENCE fZZ(l).Z)
DATA ZZ /OOOOllOOOOOOO.OOOOOOOOOOOOO/
X02ABF = Z
RETURN
END
DOUBLE PRECISION FUNCTION X02ACF()
                 FUNCTION X02ACF  , PART OF PEM-2  (VERSION 84130)

NAG COPYRIGHT  1975
MARK 4.5 RELEASE

* RMAX *

UNIVAC DOUBLE  PRECISION  VERSION
 PMT50070
 PMT50080
 PMT50090
 PMT50100
 PMT50120
 PMT50130
 PMT50140
 PMT50150
 PMT50155
 PMT50160
 PMT50170
 PMT50175
 PMT50180
 PMT50185
 PMT50190
 PMT50200
 PMT50205
 PMT50210
 PMT50220
 PMT50230
 PMT50240
 PMT50250
 PMT50260
 PMT50270

 PMT50280
 PMT50290
 PMT50300
 PMT50310
 PMT50320
 PMT50330
 PMT50340
 PMT50350
 PMT50360
 PMT50370
 PMT50380
 PMT50390
 PMT50400
 PMT50410
 PMT50420
 PMT50430
.PMT50440
 PMT50445
 PMT50450
 PMT50460
 PMT50465
 PMT50470
 PMT50475
 PMT50480
 PMT50490
 PMT50495
 PMT50500
 PMT50510
 PMT50520
 PMT50530
 PMT50540
 PMT50550
 PMT50560

 PMT50570
 PMT50580
 PMT50590
 PMT50600
 PMT50610
 PMT50620
 PMT50630
 PMT50640
 PMT50650
 PMT50660
 PMT50670
                                      221

-------
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   RETURNS THE VALUE OF THE LARGEST POSITIVE REAL  FLOATING-
   POINT NUMBER REPRESENTABLE ON THE COMPUTER

   FOR ICL 1900
   X02ACF = (2.0 - 2.0**(-36.0))*2.0**254.0

   FOR IBM 360/370
   X02ACF = (1.0DO-16.0DO**(-14.0DO))*16.0DO**63.0DO

   DOUBLE PRECISION Z

   FOR IBM-3033
   DATA Z/Z7FFFFFFFFFFFFFFF/

   FOR UNIVAC-1100
   DIMENSION ZZ(2)
   EQUIVALENCE (ZZ(1V,Z)
   DATA ZZ /0377777777777,0777777777777/
   X02ACF = Z
   RETURN
   END
   SUBROUTINE X04AAF(I,NERR_)
                  SUBROUTINE  X04AAF
  PART OF PEM-2 (VERSION 84130.)
   MARK 7 RELEASE.  NAG COPYRIGHT 1978
   MARK 7C REVISED  IER-190 (MAY 1979)
   IF I = 0,  SETS NERR TO CURRENT ERROR MESSAGE UNIT NUMBER
   (STORED IN NERR1).
   IF I = 1,  CHANGES CURRENT ERROR MESSAGE UNIT NUMBER TO
   VALUE SPECIFIED  BY NERR.

   *** NOTE ***
   THIS ROUTINE ASSUMES THAT THE VALUE OF NERR1 IS SAVED
   BETWEEN CALLS.  IN SOME IMPLEMENTATIONS IT MAY BE
   NECESSARY TO STORE NERR1 IN A LABELLED COMMON
   BLOCK /AX04AA/ TO ACHIEVE THIS.

   ..  SCALAR ARGUMENTS ..
   INTEGER I, NERR

   '. '.  LOCAL SCALARS . .
   INTEGER NERR1

   DATA NERR1 /6/
   IF (I.EQ.O) NERR = NERR1
   IF Q.EQ.l) NERR1 = NERR
   RETURN
   END
   SUBROUTINE WIND(UA,PWR.HQ, UPL)
                SUBROUTINE WIND
PART OF PEM-2 (VERSION 84130)
SUBROUTINE WIND DETERMINES THE WIND SPEED AT SOURCE HEIGHT
 ACCORDING TO THE WIND PROFILE POWER LAW.

  UA = ANEMOMETER WIND SPEED (M/S)
  PWR = EXPONENT OF POWER LAW WIND PROFILE
  HQ = SOURCE HEIGHT (M)
  UPL = OUTPUT WIND SPEED AT SOURCE HEIGHT (M/S)
  HA = ANEMOMETER HEIGHT (M)
  HMIN = WIND SPEED HELD CONSTANT BELOW THIS HEIGHT (M)
  HMAX = WIND SPEED CONSTANT ABOVE THIS HEIGHT (M)
  UMIN = WIND SPEED NOT ALLOWED LESS THAN THIS VALUE (M/S)

  IUFLG = WIND SPEED FLAG INDICATOR
PMT50680
PMT50690
PMT50700
PMT50705
PMT50710
PMT50720
PMT50725
PMT50730
PMT50740
PMT50745
PMT50750
PMT50755
PMT50760
PMT50770
PMT50775
PMT50780
PMT50790
PMT50800
PMT50810
PMT50820
PMT50830
PMT50840

PMT50850
PMT50860
PMT50870
PMT50880
PMT50890
PMT50900
PMT50910
PMT50920
PMT50930
PMT50940
PMT50950
PMT50960
PMT50970
PMT50980
PMT50990
PMT51000
PMT51010
PMT51020
.PMT51030
PMT51040
PMT51050
PMT51060
PMT51070
PMT51080
PMT51090
PMT51100
PMT51110
PMT51120
PMT51130

PMT51140
PMT51150
PMT51160
PMT51170
PMT51180
PMT51190
PMT51200
PMT51210
PMT51220
PMT51230
PMT51240
PMT51250
PMT51260
PMT51270
PMT51280
PMT51290
PMT51300
                                     222

-------
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   0  -  NORMAL COMPUTATION
   1  -  WIND SPEED SET AT VALUE AT HMIN
   2  -  WIND SPEED SET AT VALUE AT HMAX
   3  -  WIND SPEED SET AT UMIN VALUE
 COMMON/PARM7A/HA,Pi(6)
 COMMON/WND/HMIN,HMAX,UMIN,IUFLG

DEFAULT VALUES FOR HA, HMIN,  HMAX, AND UMIN WERE SET
IN SUBROUTINE INMOD AS 10., 10., 200., AND 1. RESPECTIVELY,
UNLESS DEFINED ON THE INPUT CARD #7.

 IF(HQ.LT.HMAX) THEN
 IF(HQ.GT.HMIN) THEN
 UPL=UA*((HQ/HA)**PWR)
 IUFLG=0
 ELSE
 UPL=UA*((HMIN/HA)**PWR)
 IUFLG=1
 END IF
 ELSE
 UPL=UA*((HMAX/HA)**PWR)
 IUFLG—2
 END IF
 IF(UPL.LT.UMIN) THEN
 UPL=UMIN
 IUFLG=3
 END IF
 RETURN
 END
PMT51310
PMT51320
PMT51330
PMT51340
PMT51350
PMT51360
PMT51370
PMT51380
PMT51390
PMT51400
PMT51410
PMT51420
PMT51430
PMT51440
PMT51450
PMT51460
PMT51470
PMT51480
PMT51490
PMT51500
PMT51510
PMT51520
PMT51530
PMT51540
PMT51550
PMT51560
PMT51570
PMT51580
PMT51590
PMT51600
PMT51610
                                      223

-------
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   0  -  NORMAL COMPUTATION
   1  -  WIND SPEED SET AT VALUE AT HMIN
   2  -  WIND SPEED SET AT VALUE AT HMAX
   3  -  WIND SPEED SET AT UMIN VALUE
 COMMON/PARM7A/HA,PI(6)
 COMMON/WND/HMIN,HMAX,UMIN,IUFLG

DEFAULT VALUES FOR HA, HMIN,  HMAX,  AND UMIN WERE SET
IN SUBROUTINE INMOD AS 10.,  10., 200., AND 1.  RESPECTIVELY,
UNLESS DEFINED ON THE INPUT CARD #7.

 IF(HQ.LT.HMAX) THEN
 IF(HQ.GT.HMIN) THEN
 UPL=UA*((HQ/HA)**PWR)
 IUFLG=0
 ELSE
 UPL=UA*((HMIN/HA)**PWR)
 IUFLG=1
 END IF
 ELSE
 UPL=UA*((HMAX/HA)**PWR)
 IUFLG-2
 END IF
 IF(UPL.LT.UMIN) THEN
 UPL=UMIN
 IUFLG=3
 END IF
 RETURN
 END
PMT51310
PMT51320
PMT51330
PMT51340
PMT51350
PMT51360
PMT51370
PMT51380
PMT51390
PMT51400
PMT51410
PMT51420
PMT51430
PMT51440
PMT51450
PMT51460
PMT51470
PMT51480
PMT51490
PMT51500
PMT51510
PMT51520
PMT51530
PMT51540
PMT51550
PMT51560
PMT51570
PMT51580
PMT51590
PMT51600
PMT51610
                                     223

-------
                                  Date
Return form to;

James M. Godowitch
Meteorology and Assessment Division (MD-80)
U.S. Environmental Protection Agency
Research Triangle Park, NC  27711
I wish to receive future revisions to the
PEM-2 User Guide.
Name
Organization
Address
City/State

Zip Code
Additional Optional Information;

Phone (   )    -	

Computer system

-------