United States               EPA-600/7-82-037b
                Environmental Protection
                Agency                  May 1982
vvEPA       Research  and
               Development
               VERIFICATION AND TRANSFER OF

               THERMAL POLLUTDN MODEL

               Volume IL User's Manual for

               Three-dimensional Free-surface Model
               Prepared for
               Office of Water and Waste Management

               EPA Regions 1-10
               Prepared by

               Industrial Environmental Research
               Laboratory
               Research Triangle Park NC 27711

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                 RESEARCH REPORTING SERIES


Research reports of the Office of Research and Development, U.S. Environmental
Protection Agency, have been grouped into nine series. These nine broad cate-
gories were established to facilitate further development and application of en-
vironmental technology. Elimination  of  traditional grouping was consciously
planned to foster technology transfer and a maximum interface in related fields.
The nine series are:

    1. Environmental Health Effects Research

    2. Environmental Protection Technology

    3. Ecological Research

    4. Environmental Monitoring

    5. Socioeconomic Environmental  Studies

    6. Scientific and Technical Assessment Reports (STAR)

    7. Interagency Energy-Environment Research and Development

    8. "Special" Reports

    9. Miscellaneous Reports

This report has been assigned to the INTERAGENCY ENERGY-ENVIRONMENT
RESEARCH AND  DEVELOPMENT series. Reports in this series result from the
effort funded  under  the 17-agency Federal Energy/Environment Research and
Development Program. These  studies relate to EPA's mission to protect the public
health and welfare from adverse effects of pollutants associated with energy sys-
tems. The goal of the Program is to assure the rapid development of domestic
energy supplies in an environmentally-compatible manner by providing the nec-
essary environmental data and control technology. Investigations include analy-
ses of the transport of energy-related pollutants and their health and  ecological
effects; assessments of, and  development of, control technologies for energy
systems; and integrated assessments  of a wide range of energy-related environ-
mental  issues.
                       EPA REVIEW NOTICE
This report has been reviewed by the participating Federal Agencies, and approved
for  publication. Approval does not signify that the contents necessarily reflect
the  views and policies of the Government, nor does mention of trade names or
commercial products constitute endorsement or recommendation for use.

This document is available to the public through the National Technical Informa-
tion Service, Springfield, Virginia 22161.

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                                        EPA-600/7-82-037b

                                        May 1982
              VERIFICATION AND TRANSFER
              OF THERMAL POLLUTION MODEL
   VOLUME II:  USER'S MANUAL FOR THREE-DIMENSIONAL
                  FREE-SURFACE MODEL
           Samuel S. Lee, Subrata Sengupta,
              S. Y. Tuann and C. R. Lee
         Department of Mechanical Engineering
                 University of Miami
             Coral  Gables, Florida  33124
          NASA Contract No. NAS 10-9410

        NASA Project Manager:  Roy A. Bland

  National Aeronautics and Space Administration
               Kennedy Space Center
       Kennedy Space Center, Florida  32899
     EPA Interagency Agreement No. 78-DX-0166
      EPA Project Officer:  Theodore G. Brna

   Industrial  Environmental  Research Laboratory
Office of Environmental  Engineering and Technology
  Research Triangle Park, North Carolina  27711
                  Prepared for:

      U.  S. Environmental  Protection Agency
        Office of Research and Development
            Washington, D. C.  20460

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                               PREFACE
     This volume presents the description and program documentation of
the three-dimensional, free-surface mathematical mode! for thermal  pollu-
tion  analysis and prediction for shallow  water bodies,  for example, lakes
and  coastal  waters.  The program  was developed by the Thermal Pollution
Group at the University of Miami,  and was successfully verified through
application to several sites.  This  success was made possible by funding
and  technical assistance provided by the National Aeronautics and  Space
Administration  (NASA)  and the Environmental Protection Agency (EPA).

     The model is time  dependent, and the leap-frog and DuFort-Frankel
schemes are adopted for solving the predictive equations  based on the
conservation principles  of mass, momentum and energy.  The model has
been developed with minimal physical  and  site restrictive  assumptions,  and
its algorithm has sufficient generality to allow for different boundary con-
ditions specified at open boundaries.  The program  shows both the tem-
poral and spatial variations of the surface water height.  It computes
three-dimensional velocity  and temperature fields.  The model can  serve
as an effective means for hydrothermal analysis  and prediction.  Plotting
programs  employed for  representing the numerous results are also in-
cluded.

     The volume is intended as a user's manual  and, as such, presents
specific instructions regarding data preparation  for  program execution.
To illustrate further, an  example case is included here with its input
data, hard  copy printout and plots.  The complete listing of the program
and  its accessories is also included.
                                   ii

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                              ABSTRACT
     A mathematical model that can  be used for the analysis of thermal
discharge from power  plants into tidal estuaries and coastal waters is
described.  This transient, free-surface, three-dimensional model  can
be applied to  predict the water temperature as a function of time  and
position in a specified region.

     In situations of practical relevance, the specified coastal  or off-
shore region will be a water body of  irregular bottom  topography  with
possible islands or keys.  The user specified the boundary and boundary
conditions, as well as  the water  depth distribution. Semi-diurnal  tide is
considered in  the model.   Hourly weather data is needed for wind stress
calculation and heat exchange between water and the atmosphere.   The
ambient temperature is assumed of a sinusoidal  form of 24-hour period.
The  ambient turbulence is included  by an eddy viscosity and diffusivity
formulation.  The appropriate values  are to be calibrated  against mea-
sured currents.
                                  Hi

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                              CONTENTS
Preface  [[[     .1!
Abstract  ... [[[     '"
Figures  [[[     v
Tables  ........................ . .................................     vi
Symbols   [[[    ^11
Acknowledgments  ................................................    v'"

     1 .  Introduction  ............................................     1
     2.  Recommendations  .................................... ...     **
     3.  Program  Description and Flow Chart for Main Program
         (ANCMN)  ..............................................     5
              Description of program algorithm ...................     5
              Flow chart ........................................     7
              Subroutine descriptions  ...........................     11
     4.  List of Program Symbols of Main Program  ...............     18
              Description of main variables  .......... . ...........     18
              Marker matrices  ...... . ............. . ..............     21
              Depth matrix and its  derivatives  ........... « ......     25
              Dimensions of  subscripted  quantities   ..............     25
              Other program symbols ............................     26
     5.  Preparation of  Simulation Run   ..........................     30
     6.  Input Data  .............................................     34
     7.  Plotting  Program ... .....................................     38
              Description and flow chart for plotting program  ...     38
              Subroutines .......................................     39
              Input data ........................................     *3
References
Appendices
     A.   Example Case  ..........................................     *7
              I ntroduction   ......................................     **7
              Problem statement  .................................     *9
              Calculation of parameters and input data  ..........     51
              Execution deck  ....................................     56
              Sample output  ... ..................................     62

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                              FIGURES


Number                                                         Page

   1   Flow  chart for calculating  program ANCMN  and its
       subroutines	    8

   2   Relative position and designation of the variables  	   19

   3   Space-staggered grid system  -  plan  	   20

   4   MAR  (i, j) matrix  	   22

   5   MEX  (i, j) matrix  	   22

   6   MEY  (i, ]) matrix  	   23

   7   MX (i, j) and MY (i, j) matrices  	   24

   8   Flow  chart for plotting program PLOTMN and- its
       subroutines	   40

   9   Anclote Anchorage location in the state of Florida   	   48

  10   Grid  work for the Anclote Anchorage 	   50

  11   Semidiurnal tide for June  19-20, 1978 at south end of
       Anclote Key   	   54

  12   Surface velocity, Anclote Anchorage by modeling   	   71

  13   UW velocity, Anclote Anchorage by  modeling   	   72

  14   VW velocity, Anclote Anchorage by  modeling   	   73

  15   Surface temperature, Anclote Anchorage by modeling  	   74

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                             TABLES






Number                                                      Page



   1   Governing Equations  	    5



   2   Subroutines of ANCMN  	    9



   3   Symbols Used in the Program  	   21



   4   Size of the Matrices 	   25



   5   Input Data for ANCMN  	   34



   6   Subroutines of PLOTMN  	   «



   7   Input Data for PLOTMN  	   M
                                vi

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                               SYMBOLS
 V

!h
B
9

h

H
H«

I

J

K

K.
L
P
t
       Vertical_eddy  viscosity,
       cm2 sec
       HorizontaJ eddy diffusivity,
       	•>	~ i
                              T
                              T
cm* sec
Vertical_eddy diffusivity,
cm2 sec             ,
Coriolis factor,  sec
Relative humidity in fraction
of unit
Acceleration of gravity,
cm sec
Local  water depth with re-
spect to mean sea level, cm
Total  water depth,  cm
Gross solar radiation,
BTU ft"2  day"1
Node  index in the direction
of the x-axis
Node  index in the direction
of the y-axis
Node  index in the direction
of the z-axis
Surface heat exchange  co-
efficient,  BTU ft'1* day"1
deg F~'
Reference  length,  cm-
Pressure,  dynes cm"
Time, sec
                                ave
                                    u
                                    w
Water temperature, deg C
Air temperature, deg  F
Average of air and dewpoint
temperatures, deg  F
Dewpoint temperature, deg F
Equilibrium temperature,
deg F
Ambient surface tempera-
ture,  deg  F
Component of water velocity
along x-axis, cm sec
Wind speed, mph
Component of water velocity
along the y-axis, cm sec"
Component of water velocity
along the z-axis, cm  sec"
Displacement of the free
surface with respect to the
mean water level , cm _ _
Water density, gm  cm
Nondimensional vertical
fluid velocity
Nondimensional vertical
coordinate
                                    VII

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                        ACKNOWLEDGMENTS
     This work was supported by a contract from the  National  Aeronautics
and Space Administration (NASA-KSC) and  the Environmental Protection
Agency  (EPA-RTP).

     The authors express their sincere gratitude for the technical and
managerial support of Mr.  Roy A.  Bland, the NASA-KSC project manager
of this contract, and the NASA-KSC remote sensing group.  Special thanks
are also due to Dr. Theodore G. Brna, the EPA-RTP project manager, for
his guidance and support of the experiments, and to Mr.  Albert W.  Mor-
neauit from Florida Power Company (FPC),  Tarpon Springs,  and his data
collection group  for data acquisition.  The support of  Mr.  Charles H.
Kaplan of EPA was extremely helpful in the planning and  reviewing of
this  project.
                                  viii

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                              SECTION  1

                            INTRODUCTION
     The analysis of thermal discharges is important in order to minimize
the environmental impact and to manage efficiently and safely the waste
heat problems.  The study of  technological  solutions to the problems of
heated water disposal involves complicated relationships,  such  as the
location, geometry  and types of the discharge outlet,  the flow condition
and  temperature of the receiving water body, the meteorological conditions
of the site, the waste heat output of  the  power plant, etc.  A  thorough
understanding  of the thermal effects and  physical processes of heated
water dispersion to the environment is an essential  part of serving the
rapidly growing demand for electrical  energy, while reducing the possible
impact on the receiving  ecosystem.

     The thermal effluent  from  a power plant will have variable conse-
quences  on the aquatic life of  a receiving water  body and the adjacent
environment depending on the temperature rise.   Therefore, the  prime
objective of the heated water discharge system is to bring the discharged
water into thermal  equilibrium  with the surrounding water by bringing
thermal outfall  to the mainstream of the water body, whereby the mixing
and  convective processes will increase the surface heat transfer to the
atmosphere.  Thus, the temperature rise  within the tolerance of natural
environmental conditions is very important on the disposal system de-
sign and the standards for regulating  thermal effluent.

     Under limited  circumstances, in-situ  measurements can serve for
diagnostic and  monitoring  purposes for meeting the  need  of analyzing
thermal impact  on receiving water body.   However,  to provide a priori
information  about the nature and extent of thermal impact for site selec-
tion  and discharge  system design, numerical modeling  for simulating hy-
drothermal behavior of the water body is  imperative.

     During the past years, many numerical  models  have  been developed
for hydrothermal studies.   Dunn  et al.  (1975) gave  a presentation of
different models developed up  to  then.  They applied  those models  to
the Point Beach Nuclear Power Plant and compared the performance of
various models  in predicting a  standard data base.  A general conclusion
that  can  be made from their analysis is that  though some models may
perform  well under certain  conditions,  a generalized model which accounts
for wind, current,  tide, bottom topography and diverse  meteorological
conditions is yet to be developed.

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     Since 1974 the Thermal Pollution Group at  the University of Miami
has endeavored to  develop  a mathematical package for hydrothermal  studies.
The  primary motivation behind the effort was to develop a series of models
which make minimal site restrictive assumptions  enabling application  to
diverse basin and discharge configurations.  Two separate formulations
were made, one with the rigid-lid approximation and  the other with  the
free-surface included.  The details of the package and  formulation are
presented  in a number of reports by Lee et al.   (1978).

     The  present report  concerns the UM's free-surface model  and its
application to the Anclote Anchorage in Florida  for waste heat discharge
from a power plant.  The features of the model are:   a) three-dimensional,
b) nonlinear, c) time-dependent, d)  irregular topography, e) driving
forces including wind,  tide, heat and mass flux, f)  graphical represen-
tation of results of velocity and temperature fields, g)  prediction of
temporal and  spatial variation of water surface.

     The  descriptions of the main  program  and  its subroutines, main
algorithm  and flow  chart, program symbols, input data  and logic para-
meters, as well as  the  description of associated plotting programs, are
contained herein for the  ready  access of the computer program  package
to the user.  A preliminary review on existing  three-dimensional free-
surface models, basic concepts  of the present model,  assumptions,  ap-
proximations, governing  equations,  initial  and boundary conditions,
finite difference implementation and  numerical solution methods is pre-
sented in Lee et al.  (1979)  and  Carter (1977).

     The  report also contains a  plotting  program which  is used to analyze
the results of the  main calculation.   A subroutine to compare the calcu-
lated temperature field with that obtained  by IR scanning is presented in
the program.  Note that  the IR  temperature is  interpreted by hand from
the mosaic film  and then read  in for isotherm plotting and comparison.

     The  model has been tested for  its adaptability.   That is,  the model
allows for program  modifications so that  different initial  and  boundary
conditions could be considered.  The main  program  has  several flag
statements which make different usage of same  program  possible.  Any
program modification for the purpose of model transition should be made
with care, and  the new program should  be validated by sample runs to
assure that the effect of the modification is as  desired.    The same is
also applicable to the plotting  program.

     The program  therefore contains two parts. Part 1 is primary and
performs  calculations; Part 2 is  secondary  and  is for analyzing and plot-
ting the results of Part  1.   ANCMN  is the  driving program of Part  1.
The input contains parameters,  geometrical and  initial data,  or  tape  which
stores intermediate results; output contains printout of results  at preset
time intervals,  in both hard copy  and tape form.  The  hard copy printout
provides  the base  for analysis,  upon which decisions and choice of the
plots needed  for further analysis and detailed  comparison with measured

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results can be made.  PLOTMN  is the driving program of Part 2.   The
tape output from Part 1  is the main input.   In addition, control cards
assigning choice of plot, plot size, simulation  hour and measured result
for comparison are also required.  Output is in printout and plot tape.
The latter is used for plotting by CALCOMP  plotter.

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                              SECTION  2

                          RECOMMENDATIONS
     The mode! can  be enlarged  to handle any passive  constituent, dis-
solved or suspended,  possessing arbitrary decay characteristics.  The
formulation of the constituent transport is based on the convection-
diffusion equation, which is analogous to the  thermal transport equation
in the present model.   The enlarged model would then  be an ideal tool
to study the ecological response of aquatic biota to the thermal effluents
of the power plant.

     The model can  be modified to include bouyancy effects caused by
fresh water/salt water  sensing by including a salinity-dispersion equa-
tion.   This equation will be of similar form to the energy equation.

     The code is written for a constant grid size.  Modifications can  be
made to incorporate a  coarse grid for the complete field in comparison
with a fine grid near  the discharge location.  This will allow a more
accurate prediction of plume behavior in the near field.  A  penalty in
computational  cost will  be incurred.

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                              SECTION 3

PROGRAM DESCRIPTION AND  FLOW CHART FOR MAIN  PROGRAM (ANCMN)


DESCRIPTION OF PROGRAM ALGORITHM

     The governing  partial  differential equations are given in Table 1;
the symbols and definitions are referenced  in Nomenclature.  The problem
is set up as an initial-boundary value problem, so values of  dependent
variables are assumed known initially and prescribed on  boundaries.
Values at  successive  time steps are obtained by  using a  true explicit
scheme.  The leap-frog finite difference format is  used  to calculate sur-
face elevation n and two horizontal velocity components,  u and v, at
time n+1,  where n is the present time step.  The variables at times n-1
and n are all known.  The  sequence  in which calculations are performed
is as follows:

1.  Integrate the surface elevation equation using  central-time central-
    space  (CTCS) differencing.  That rs,  n   ,  n" and  un,  vn  and h.
    Note that h is independent of time while the present water depth H
    = h+n  is needed in tfyts calculation.   In the subroutine BETA, not
    only n    but also  Q     (i, j,  k),  the  modified vertical velocity in
    transform  (a)  plane, is accomplished immediately after the n compu-
    tation .

2.  The next task in the sequence is  to calculate the nonlinear inertia
    terms  that appear in the horizontal momentum equations.   Here, two
    subroutines are  involved:  BNRT1A is

                   TABLE 1.   Governing Equations

Continuity Equation*:

                      3Hu
                                          **• -rr- = 0
                      ox.    ay      ct a   3t

u Momentum Equation:
                                                 ,  3 u 3 n
                                              + a)  — — - fvH
                      p 3x

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v Momentum Equation:
                  = .H |p    „ (a|H  +|a, H-Av|iv_
                      p 3y   3  *  3y    3y'   H   3 a2
Energy Equation:
               3HT  . 3HuT  , 3HvT .  u  3 flv .  M  .  ,  3T 3 n
               TT   TIT" + "FT" + M~+u  +  cr)TTJt
*  This equation is vertically integrated to yield a) prognostic equation
for y, and b) synoptic equation  for ft; they are
                                ro f9Hu  +	
                                      x    3  y
                    0  _ a  3ji   1   f0
                    "  ~ H  3t   H aj


The  latter,  upon transformation, yields  the actual vertical velocity
               w =
    for interior  points, while ABNR3 is  for open  boundary points.   Note,
    for the Anclote Anchorage sample problem, the open boundaries are
    at j = 1 and j = 14,  and the imposing tides are applied at points
    immediately outside these open boundaries.  Therefore,  program
    modification  is needed  if different open boundary conditions are
    employed .

3.  Following the inertia terms computations, which may be  skipped if
    the Rossby Number is  very close to  zero, new  values of u and v
    at n+1  are computed for all points in the grid.   Again,  the leap-
    frog and central-space  scheme is used, but DuFort-Frankel differ-
    encing is applied to  the vertical momentum diffusion terms.  Two
    subroutines  are  called  here,  BVEL for interior  points and ASAF3
    for open boundary points.  Since velocity at  all points is calculated
    without distinction, a subroutine GIVENU  is  needed to specify  the
    given discharge or flowrate at particular points, that is, to replace

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    calculated velocities at those  points with known values.

     Steps 1, 2 and  3 are calculations for surface elevation, modified
vertical velocity and  horizontal velocity components; they constitute the
V-calculation.  Whether the V-calcuIation is -to be carried out or not
depends on flagged statement  KVEL = 1  or 0.  The next group  of calcu-
lations is for thermal transport, or T-calculation, and  it involves the
energy  equation only.  Similarly, this group is to be flagged by state-
ment whether KTEMP is unity  or  zero.

1.  The convective term in the energy equation is calculated next,  using
    either a  given  velocity field,  in the  case of KVEL  =  0, or the pre-
    sently known velocity  field at n+1, in the  case  of  KVEL  = 1.  The
    subroutine for  this purpose is CONV.

5.  The energy equation itself is then integrated  over time to obtain T
    at  n+1.  The forward-time, central-space (FTCS) and DuFort-Frankel
    differencing for the vertical diffusion  term are  used  in  the  calcula-
    tion.   The subroutine involved is TCOMPT.   Since temperatures at
    all points are computed  without distinction as to whether the points
    are with given  temperatures or not,  subroutine GIVENT  is needed to
    respecify the temperature  at  the given points.

     Clearly, Steps 4 and 5 make up the T-calculation.  In either of V-
or T-calculations,  vertical velocity  w is  involved.   Instead of w, the
rate of  change of surface  elevation, -r-n / is used  for convection in ver-
tical direction.

6.  The actual vertical velocity,  w, is computed when  It is .needed for
    printout.  The subroutine is  WCAL,  and instead of un   and vn
    which  are defined at half J and half I respectively,  the interpreted
    velocities at center of grid cell are used in this calculation.  Since
    a space-staggered scheme  is  used, the water  level and vertical  velo-
    city are  described at the center of grid cell,  while the  horizontal
    velocities are described  at the edges of cells.

7.  The real time  (or simulation time) is checked  and Steps 1 through 6
    are repeated;  that  is, the above procedure is repeated  for  n+2  using
    values at n+1 and n.

     Reference to  the flow  chart  presented in  Figure 1 will  clarify  the
description of program algorithm.

FLOW CHART

     Figure  1 shows  the main  flow chart  of the three-dimensional, free-
surface program applied to the Anclote Anchorage.   In the flow chart,
the subroutines and their  functions are described briefly.   Table 2 lists
the subroutines called in the main-program, ANCMN.

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          Read Data Card (17)
                                     Yes
          First Run?  (LN  = 1 ?)
                     ,  No
                                            BAYBOT
                                            BAYINI
Preliminary Data
Initialization
          READT - Read Tape for
          Data of Previous Run
          Card to Reaffirm DT,
          EST  &  Tide Conditions
          Hourly Climatical Data
BETA
BNRTIA
ABNR3
BVELS
ASAF3
GIVENU
          Compute ETA (n) and OM
          Compute RX, RY at Interior  Point
          Compute RX, RY at Boundary Point
          Use RX, RY & Others to do  U, V
          Do the Same for Boundary Point
          Specify  U,  V at Discharge Point
CONV   - Compute Convection Terms for T
TCOMPT - Continue to Compute T
GIVENT - Specify T  at Discharge Point
WCAL   - Convert OM  (n) to W
ANCPR  - Continue Printout at Chosen Points
                                    No
          Enter a  New Hour?
                       Yes
TPRLOK - Prints Out Hourly Results
STORET - Store Results & Data  in Tape
                                    No
          Time Up?   (End of NCY?)
                       Yes
          Put Another EOF on Tape
Figure 1.  Flow chart for calculating program ANCMN and its subroutines

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   TABLE 2.  Subroutines Required in Main Calculating Program ANCMN
No.
 Name
         Description
Remark
      BAYBOT
      BAYINI
      READY


      1RREAD
      EQTEMP


      BETA



      BNRTIA



      ABNR3
10
11
      BVELS
ASAF3
GIVENU
             Reads in bay bottom sounding
             (H)  and various grid book-
             keeping matrices, calculates
             depth matrices accordingly.

             Initializes the dependent
             variables such as U, V, W, T,
             ETA,  RX, RY  also set  10s to
             values outside the calculation
             region.

             Reads in stored data from
             tape  for continuing run.

             If required, it reads in IR
             data  as  initial  temperature;
             thus  it replaces T input
             from  READT.

             Calculates the  equilibrium
             temperature over  that hour.

             Calculates surface elevation
             ETA  and vertical  velocity
             OM
Calculates inertia terms of
momentum eq. for boundary
pts.

Calculates inertia terms of
momentum eq. for boundary
pts. on north and south
exit of the anchorage.

Calculates velocity at in-
terior pts. - main part of
velocity calculation.

Calculates velocity at boun-
dary pts. along north and
south boundaries.

Specifies velocity at control
pts., such as discharge,  in
take and river head.
                               Skip if LM=1,  depends
                               on problem and grid
                               work, data file AMATN
                               preferred.

                               Also depends on probelm
                               and run conditions.  RX
                               RY  are inertia terms.
                               Skip if LN=1.
                               No need if T-calcuIation
                               began with ambient
                               temperature.
                               Number of hour is NCY.
                               Mandatory in
                               V-calculation.
                                           Skip if ROSSBY = 0.
                                           Skip if ROSSBY = 0.

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   TABLE 2.  Subroutines Required in Main Calculating Program  ANCMN
                               (Continued)
No.
        Name
                     Description
                                     Remark
12


13

14


15



16
CONV


TCOMPT

GIVENT


WCAL



ANCPR
17
TPRLOK
18
STORET
19
ZZ1
20
21
AMATN
C2007
Calculates convective terms of
energy equilibrium.

Calculates temperature.

Specifies temperature at dis-
charge outlet.

Converts the OM (n) vertical
velocity to physical  vertical
velocity W.

Prints  surface elevation,
velocity (mag. with  dir.) and
temperature at 4 chosen loca-
tions after completion of
marching of DT, i.e. printout
after each time  step.

Prints  out the velocity  field,
water depth, surface elevation
and temperature field after
one hour of simulation time.

After TPRLOK for printout,
the same data and relevant
parameters are stored onto
tape,  either for later plotting
or for  continued calculation.

A  subroutine called  by ANCPR
and TPRLOK; it is for  finding
velocity dir.  based on U and
V  components.

Is a data  file containing all
grid matrices and bottom depth
matrix to  be  read in BAYBOT.

Climatical  data used in  the
run; the data is on  hourly
basis.
                                                 Depends on run condi-
                                                 tion.
                                                 Locations are  to be
                                                 chosen by user.
                                                 Skip if KSTORE = 0.
                                                 Same data  could be in
                                                 card  form, inserted
                                                 after TIN IT card.

                                                 Could also be in  card
                                                 form.
                                    10

-------
SUBROUTINE DESCRIPTIONS

     This section describes  the subroutines used in ANCMN, in order of
their appearance.

BAYBOT

     It  reads the marker matrix MAR; the elevation matrix ELEV which is
changed to depth matrix H by adding a constant STAGE; then four more
marker  matrices, MEX, MEY, MX  and MY.   it interpolates H according
to marker MEX, MX and MY to find  additional depth matrices,  called HB,
HU and HV, respectively.

BAYINI

     It  initializes most of the variable matrices.   Since the initial condi-
tion for velocity is a  quiescent condition, U1, U2,  U3, VI, V2, V3,  RX,
RY, ETA1, ETA, ETAS,  UB, VB, OM, W  and TC are  set to zero.   The
quiet bay is assumed  to have a constant temperature TINIT to begin with,
so Tl,  T2, T3 and TB are set to TINIT.

READT

     This subroutine  reads  in input parameters,  physical quantities
and intermediate results stored on tape.

IRREAD

     It  reads in in-situ measured or  IR scanned  temperature as an  alter-
native  initial condition to temperature calculation.  This temperature is
interpolated by hand  and  stored  in the form of matrix Tl.

EQTEMP

     It  calculates the equilibrium temperature T  and surface heat  ex-
change  coefficient  K  of a natural water surface^   The procedures  for
these calculations are as follows:

1.  T ,  = T  -  (14.55 + 0.114 T ) (1-f) -  [(2.5 + 0.007 T ) (1-f)]3
     Q    3                   Q                       a

    where T .  = dewpoint temperature in °F
          T   =• air temperature in  °F
          f   = relative humidity in fraction of unit

2.  3 = 0.255  - 0.0085 T    + 0.000204
    where T     = i(T   + T .) ,  and 6 is an intermediate step
          T     = ambient surface temperature in  °F

3.  f(u)  = 70  +  0.7 u2, and u  is wind speed in mph


                                    11

-------
4.   K  = 15.7 + (g * 0.26) f(u)
     5
    where K  = surface heat  exchange coefficient in BTUy(ft2 day °F)
           5  H

5-   Te = Td+r
    where T  = equilibrium temperature in °F
          He = gross solar radiation  in BTU/(ft2 day)

Note:  The T  , f, u, H  and T  are climatological  data;  however,  care
must be taken3 for the hourly da^ta TAIR,  HUMID, WIND,  SRAD  and TSURF
are in  metric units.   Therefore, in the above calculations, the basic data
must first be transformed into English units, then the final results,  T  and
K  , must again be transformed back to metric units.  T  (TEQ)  and K
     are used in subroutine  CONV for T-calculation.
BETA

     Computes  nn+  (ETAS) and fln   (OM) by using central differencing
from the continuity equation.  The vertical integration  is done using
Simpson's rule.  The following symbols are used:

DR = depth at  half-integer j point  on  right edge, i  + 1, of the cell.

DL = depth at  half-integer j point  on  left edge, i, of the cell.

D2 = depth at half-integer i  point on  upper edge, j + 1,  of  the cell.

Dl  = depth at half-integer i  point on  lower edge, j,  of the cell.

DHUX =
DHVY  =

AH - total depth at  the center of the  cell, a half-grid  point.

BNRTIA

     It computes the sums of the nonlinear inertia  terms,  RX and RY,
in the x and y momentum equation at  each interior point of  the domain.
Note that RX  (i, j,  k) =  RY (i, j, k)  =0 for k  =  KN.   The following
symbols are used, in their order of appearance:

AH = depth either at u-point or at v-point
DHUUX =                          DHUVX =
          o X
                                    12

-------
DHUVY =     .                    DHVVY =

D2 = depth at forward half-grid point  in either x or y direction.

D1  = depth at backward  half-grid  point in  either x or y direction.

UBAR2 = average u at forward half-grid point.

UBAR1  - average u at backward half-grid  point.

VBAR2 = average v at forward half-grid point.

VBAR1  = average v at backward half-grid  point.

E2  = averaged n at (i, j  + 1)  or (i + 1,  j)

E1  = averaged n at (i, j)

D2 = depth at (i, j + 1)  or (i + 1, j)

D1  = depth at (i, j)

DUOMS = |^S-                     DVOMS = %&-
         3 a                                3a

DUS « |H.                         DVS = f*
       oO                                do

      3Huu   3Huv   u  3ufl   ,,     ,  3u  3 TI
    _ .__  + ___ + H  j^- + n  + a) — aTT
RY -       4. 3Hvv   u  3vn   M    ,  3v 9
RY -    ~ +     "        ~   (    CT)
ABNR3

     It computes RX and RY for points on boundary.  The tide heights
at half-grid points outside  the north and  south boundary are computed
first.  Since the open boundary is in x-direction, that is, only the v-
point appears,  RX = 0 and RY  is given by
    - 9Huv + 9Hvv + u 3ufl    M    , 3v  3 n
    ~ 3  x  + 3~T" + H 3T~ + (1 + a) FaTT

In the computation, it  is assumed:

D2 = depth at half-grid point  just outside the boundary
   =  HV (i, JN) +  North Tide Height, if D2 is HB  (i, JN)
   =  HV (i, 1} + South Tide Height,  if D2 is HB (i,  0)

VBAR2 = v at half-grid point  just outside the boundary
       = V2 (i,  JN, K) if it  is north boundary
       = V2 (i,  1,  k)  if it is  south boundary
                                   13

-------
BVELS

     It calculates u""*"1  (U3)  and vn+1  (V3) at interior points by central
time differencing and DuFort-Frankel  scheme.   Note that  the  horizontal
diffusion of momentum is  neglected in the model.

     The equations for u and v are

                         -  fv - a IJL + ^  32"   . i Rv
                         ~fv   g ^ + 73 FT   HRX
                                        n    a


                  HTT—-*•-»#•+ Jp IT-BRY
                                         n    a

where RX and RY are the nonlinear inertia terms.

The following  symbols are introduced  for briefness.

A2  = Coriolis term

     «? *i^^     ^y  o\/
       OJ\        Ci i

A5  = i RX or 1  RY

A6  = the rest  of  vertical  diffusion term.

ASAF3

     This calculates  vn+1 (V3) at the v-points on the south  (j = 1)
and  north  (j =JN) boundaries.  It is similar to ABNR3.  The tide heights
at imaginary half-grid points just outside the south and north boundary
are computed first.  The term j^ is  calculated at v-point at both j = 1
and  JN, with tide height  at  outsfde half-grid point and n at inside  half-
grid point.  Since the u  velocity on these boundaries are assumed zero,
the Coriolis force term  B2 is set to zero.  Symbols B4, B5 and B6 stand
for pressure,  convection  and diffusion terms  respectively.

GIVENU

     It specifies velocities at cooling  system outlet  and  intake.  These
velocities are determined  from power  plant flowrate.  The river flowrate
is also simulated  by  imposing velocities at river entry point.

CONV

     It computes  the  sum of the convective terms in the energy equation
at each point.  Note that T  is designated at half-grid points/ The follow-
ing symbols are used in this subroutine:

AH = depth at point (i, j) where TC  (i,  j, k) is to be calculated,


                                   U

-------
DR  = depth at forward u-point

DL  = depth at backward u-point

D2  = depth at forward v-point

Dl  = depth at backward v-point

                              3T
DTZ (i, j) =  temperature slope  -r-  at the surface

UR  = forward u but at T-Ievel

UL  = backward u  but  at T-!eveI

DHUTX = |~y!

VR  = forward v but at T-level

VL  = backward v  but  at T- level

DHVTY = |^I
         3 y

The convection term TC is written for

              _r _ 3HuT . 3HvT .  „ 3flT ,  M  ,  , 3T  3 n
              TC - TT~ + TT~ + H ?T~ + (1  +  a) ~c  ft

TCOMPT

    This subroutine computes  temperature T    (T3) for  each  point in
the domain.   The equation is

               1  3 HT _ fy 3 'T  . _  .3 'T  . 32T, 1 __
               Hat   ~       " + Bl" +   "J~  TC
where TC is the convection term obtained  from  subroutine CONV.  The
boundary condition on solid boundary is adiabatic, but on open boundary,
T is assumed known.  There  are three different formulas for computing
the f'^j   although the same DuFort-Frankel  format is used  throughout.
This is because the surface temperature slope is DTZ (i, j) and the bottom
is adiabatic.  The symbols here are

          D2TX=JLL-
                 3x                       3y^

G1VENT

     It specifies  the temperature of cooling system discharge water and
river delivery.
                                  15

-------
WCAL

     This subroutine calculates vertical velocity w  (i, j,  k)  from modified
vertical velocity JJ  (i, j,  k)  by using cr-transformation  formula.  The fol-
lowing symbols are used:

          DEX =  JL               DEY =  JL
          DAHX = ~              DAHY = ~
                  3x                       3y
ANCPR
     It prints continuous records of elevation, velocity and temperature
at certain particular  points.

     All data are printed on a single line, with the first item on the
line  being the total simulation  time TTOT in  sec.   Items for each point
are:  surface elevation, resultant velocity, direction in which the velocity
vector points (deg positive clockwise from North), and temperature,  in
that order.

TPRLOK

     This subroutine performs the major printing tasks.   The following
variables are printed hourly, or controlled by printout interval  TPRT:

AYR = resultant velocity,  cm/sec

ANG = direction in which the velocity points

W = vertical  velocity, cm/sec

ETA = surface elevation, cm

T2 = temperature, deg C

After TPRLOK is executed,  the main program ANCMN prints out the total
depth,  H = h + n, at each point.  Thus, the hourly printout of the  rele-
vant variables  is completed.  In this subroutine,  there are two  flags,
KUV and KPROF.  If both are zero,  it skips the printing  of velocity
components u and v  either presented in layers  (k = 1, KZ) or in cross
section along x-direction (j  =1, JM).  These two flags are flipped only
by interchanging the statements in the subroutine.

STORET

     It records  all the relevant data  and results of the preceding  simula-
tion hour.  STORET  puts one EOF on tape after each block, while the
main program ANCMN puts another EOF after the last block of data is
recorded.


                                     16

-------
ZZ1

     This subroutine  finds the direction of the resultant horizontal velo-
city.
                                   17

-------
                              SECTION  4

           LIST OF PROGRAM SYMBOLS OF MAIN  PROGRAM
     This section presents the program  symbols and their  definition in
alphabetical order.   In many cases,  the symbols are described with the
aid of diagram  to show the definition.

DESCRIPTION OF MAIN VARIABLES

     The relative position  and  designation of variables are shown in
Figure 2.  The water  depth, h,  is described in integer  values of i and
j;  the u-component is  described  at half-integer value of j  and integer
values of i and k;  the v-component at half-integer value of  i and integer
values of j and k;  the w-component at integer  value of k  and half-
integer values of i  and j;  the  surface elevation,  n, is described at half-
integer values of i  and j;  and  the temperature, T, is  described  at half-
integer values of i, j  and  k.   The modified  vertical velocity, fl, is de-
scribed  at  the same place  as w-component.  Figure 3 shows  the  space-
staggered grid system in horizontal.projection.

     Table 3 lists all the symbols used for dependent  variables appearing
in  the program.  Since three levels of time  step are used, same variable
at  different level is assigned with different  symbols.   The rule for
symbolizing the dependent variables  is:  for variable F(iAx,  jAy, kA a,
nAt), Fl(i, j, k) is used  to denote the value of variable at  n-1; F2(i,
j,  k)  is the present value; while F3(i, j,  k) is the value  at n+1 thus  to
be computed;  and  FB(i, j,  k)  is  the interpreted value of  F2(i, j, k) at
a set of  grid points differing from where  it is  designated.
                                    18
                                T

-------
Figure 2.  Relative position and designation of the variables
                             19

-------
               all  points on
               these columns
               have same
               subscripts
                          I
                         I    all points  in  this
                             square have same
                             subscript i,j


                                   all points on
                                   these rows have
                                   same  subscript j
                              water  level (71)
                              z velocity (w)

                              depth  (h)

                              x velocity (u)

                              y velocity (v)
                                 x(i)
Figure 3.   Space-staggered grid system - pfan
                  20

-------
               TABLE  3.  Symbols used in the program
          Symbols
Argument
      Description
U1, U2, U3,  UB

V1, VI, V3,  VB

T1, T2, T3,  TB

ETA1,  ETA2, ETAS

TIDE1N, TIDE2N, T1DE3N


TIDE1S, TIDE2S, TIDE3S


DTZ


RX; RY; TC


W;  OM


WAT
 (i, j,  k)

 (i, j,  k)

 (i, j,  k)

  (i, j)

    0)


    (i)


  0, j)


 (i, j,  k)


 (i, j,  k)


  (i, j)
u-component

v-component

Temperature T

Surface Elevation r\

Tide Outside North
Boundary

Tide Outside South
Boundary

Heat Exchange  at Water
Surface

Convection Terms  in u;
v; T equation

w-component; Non-dimen-
sional Q

Total Water Depth or
h + n
Note:  In the program ANCMN,  ETA2 is labeled as ETA and ETX; the
former is used for calculation while the latter for  printout.

MARKER MATRICES

     The following integer-valued matrices are introduced to describe the
grid system and to distinguish boundary from interior.

MAR (i,  j)

     MAR (i,  j) identifies nodes in  the  full-grid system, i.e.

     MAR =0, (i, j) outside of boundary, hence no calculation

     MAR =1, (i, j) inside or on a boundary, as  shown in Figure 4.
                                    21

-------
',
" '
10 '.

'

10 ;
i '
1





I
1


I



1

1





1
1


1



1

1





1
1


1



1

1





1
1
/ r s s / / sr /


1



1

1





1
i ;
> — -1


o



1
y(j)
i i





i
0
                                                              xCi)
                     Figure 4.  MAR (i,  j) matrix
MEX (i, j)
     MEX (i, |)  provides marker to the half-grid system with reference
to the y-direction boundaries, i.e.

     MEX =0,  (i, j)  outside of y-boundary,  or exterior

     MEX = 1,  (i, j)  just inside  an east boundary

     MEX = 2,  (i, j)  just inside  a  west boundary

     MEX = 3,  (i, j)  nowhere near  to y-boundary,  or interior,  as shown
                     in  Figure 5.

/
' /
^
/

s




i







3







3







3







2




I
I
r
• i
i
' i
?
S f / ^ J f > f *'
\
                      Figure  5.  MEX  (i,  j) matrix
                                       22

-------
MEY (i, j}

     MEY  (i, j)  provides marker to the half-grid system with reference
to the  x-direction boundaries, as shown in Figure 6.

     MEY  =0,  (i, j)  outside of x-boundary,  or exterior

     MEY  =1,  (i, j)  just inside  a  south boundary

     MEY  = 2,  (i, j)  just inside  a  north boundary

     MEY  = 3,  (k,  j) nowhere near to  x-boundary, or interior






2


3
3
1
0

S t S S f / { f/.
2
3
1
i
i
i
0

\ 	
/
; o
2
i



f S


                                                         -»» X
                     Figure 6.  MEY (i, j) matrix

MX (i, j)

     MX  (i, j)  provides  marker to u-points, as shown in  Figure 6.

     MX  =0,  (i, j) outside of y-boundary,  or exterior

     MX  = \,  (i, j) on east boundary

     MX  =2,  (i, j) on west  boundary

     MX  = 3,  (i, j) nowhere near to y-boundary
                                     23

-------
MY (i, j)



     MY  (i, j)  provides marker to v-points, as also  shown in Figure 6.



     MY  =0,  (i, j) outside of x-boundary, or exterior



     MY  = 1,  (i, j) on south  boundary



     MY  = 2,  (i, j) on north  boundary



     MY  = 3,  (i, j) nowhere near to x-boundary








^
/,





/
/
/
/
/
/
/
/

«•
^
/
M
C
1
	 1
f

j s y

]

>»t\





-1



- 1
.

Y
1


/
! /
/
rx^/
3


"",


2
. *


j



L


1
	 1
^""n
r

i
1
i
c
\




r


" 3
i


-3
1

/



^


B
}




!



!



L

















-3

f
f
f~2 ~
?
f
f
r-*,,i ,
















-3

I
i
1-0

1
















-3

i x
i /
-o -»
l x
j 	 _^;
















-3



- 1


















-3



- 3 M

'/v/v /'
               Figure  7.  MX (i, j) and MY (i, j)  matrices
                                     2U

-------
DEPTH MATRIX AND ITS DERIVATIVE
     The bathymetry of the area of interest is given by the matrix ELEV
(i, j) designated at full-grid  points.  The values in feet are positive for
lake  or inland waters as elevation above MSL.  However, for coastal
water, the depths are read from the survey chart and  are designated by
positive values.   For certain  periods of the year,  the water level may
differ from MSL; a stage (STAGE!) is added to the  ELEV  (i, j)  to obtain
the actual depth matrix  H  (i, j).   Note  that the values of H  (i,  j) are in
cm.  To facilitate the calculation, the matrices HB (i, j), HU (i,  j) and
HV (i, j)  are derived from H (i, j), and  are  for depths at half-grid
points,  u-points and v-points, respectively.   Thus, the following real-
valued matrices  are introduced.

     ELEV (i, j) elevations of the  bottom  with respect to MSL

     HB (i, j) depth at half-grid points,  in accordance  with MEX/MEY

     HU (i, j) depth at u-points, in accordance with MX

     HV (5, j) depth at v-points, in accordance with MY

SIZE OF THE MATRICES,  OR DIMENSIONS OF SUBSCRIPTED QUANTITIES

     Let the grid work consist of IN x JN x KN nodes, i.e.  IN  nodes  in
x(i)  direction, JN nodes in y(j)  direction, and KN levels in a(k) direction.
Then there  are  IM = IN -  1 half-grid points in x-direction,  JM  = JN - 1
half-grid  points in y-direction,  and  KZ  = KN  - 1 layers in a- direction.

     The  values IN, JN, KN, IM and JM are the parameters to  be specified
at the beginning of the program and are  determined by the  grid  used.
Therefore, the  dimensions of the matrices are given in terms of these
parameters.  Table  4 shows the  size of  the matrices already defined.

                    TABLE  4.   Size of the Matrices
Symbol
Ul, U2, U3
VI, V2, V3
Tl, T2, T3, TC, TB
UB, VB
W, OM
Least Size
(IN, JM, KN)
(IM, JN, KN)
(IM, JM, KZ)
(IM, JM, KZ)
(IM, JM, KN)
Given Size
(IN, JN, KN)
(IN, JN, KN)
(IM, JM, KN)
(IM, JM, KN)
(IM, JM, KN)
                                     25

-------
                   TABLE  4.   Size of the Matrices
                             (Continued)
Symbol
RX, RY
ETA1, ETA, ETX, ETAS
WAT, DTZ
ELEV, H
HB
HU
HV
TIDE1N ... TIDE3S
AYR, ANG
MAR
MEX, MEY
MX
MY
Least Size
(IM, JM, KZ)
(IM, JM)
(IM, JM)
(IN, JN)
(IM, JM)
(IN, JM)
(IM, JN)
(IM)
(JM)
(IN, JN)
(IM, JM)
(IN, JM)
(IM, JN)
Given Size
(IN, JN, KN)
(IM, JM)
(IM, JM)
(IN, JN)
(IM, JM)
(IN, JN)
(IN, JN)
(IM)
(JM)
(IN, JN)
(IM, JM)
(IN, JN)
(IN, JN)
AYR and ANG are used to facilitate  printout of velocity and angle re-
spectively.

OTHER  SYMBOLS OCCURRING  IN  PROGRAM ANCMN

ALREF:  Reference horizontal length L in cm.

AY:   Vertical  eddy viscosity, estimated by  means of
              A  = 0.0018 H    ,  H in  cm,  A  in cm2 sec  .
                v              '            v

BH:   Horizontal  eddy diffusivity,  estimated by means of
                                                      -1
               Bh = 0.0018  L    , L  in cm, BH in cm2  sec   .

BY:   Vertical eddy diffusivity,  estimated by the same formula as
                                      26

-------
     thus  turbulent Prandtl No. is one.

DHR:  Time increment in  hour as simulation  continues.

DTX:  As a check on when to printout.

DS:  Increment in cr-direction, in fraction of unit.

DT:  Time step in second.

DX:  Increment in x-direction,  in cm.

DY:  Increment in y-direction,  in cm.

DUMS:  2DS.

DUMX:  2DX.

DUMY:  2DY.

EST:  Eastern standard time in the day of simulation.

FCOR:  Coriolis factor =  2Wg  sin (latitude), sec'1.

        W  = earth's angular rate of rotation.

G:   Earth's gravitation = 980  cm sec   .

I:   Index for x-axis.

ICO:  Flag.  Set as 1 initially; it changes to 0 when the calculation be-
       comes unstable.

IM:  Maximum number of  half-grid point in x-direction.

IN:  Maximum number of  full-grid point in x-direction.

J:    Index for  y-axis.

JCTR:   Index for simulation hour.

JM:  Maximum number of  half-grid point in y-direction.

JN:  Maximum number of  full-grid point in x-direction.

K:   Index for craxis.

KN:  Maximum number of full-grid point in o-direction.

KZ:  Maximum number of half-grid point  in a-directton.
                                     27

-------
KSTORE:  Flag.  Set as  1 to store hourly result on tape.

          Set as 0 if no store is needed.

KVEL:  Flag.  Set as 1 If velocities are to be calculated,  otherwise set
        as 0.

KTEMP:  Flag.   Set  as 1 if temperature is to be calculated, otherwise
         set as  0.

LN:   Set as 1 for  1st run of present  case; set as n for subsequent n
      run.

MBLOK:  Data block number which is to compare with data block NBLOK
         which  is to be  read  in.  Used only when  LN  > 1.

NBLOK:  Index  for data  block.

NCASE:  Case number.

NCY:  Number  of hours  to be simulated in this run.

QQ:   37.3,  used for changing from deg to rad.

ROSSBY:  Rossby number.

RR:   Water  density, = 1.

RWEX:  Number of hours between ciimatological input data,  = 1.

TABN:  Ambient water temperature outside of north entrance.

TABS:  Ambient water temperature outside of south entrance.

THETA:  Angle  between  north and y-axis, clockwise positive.

TINIT:  Water temperature at initial instant before the waste heat dis-
        charge  start.

TPRT:  Time between printouts,  in sec.

TTOT:  Total simulation  time, in sec.

TZ:   Record of  time for  hourly printout.

TZERO:  EST hour at the beginning of present simulation run.

     The following symbols are used to specify tidal condition.

AMPLIT :  Tide amplitude, in cm.
                                    28

-------
DPHASE:   Phase lag per Ax, in hour.

PERIOD:  Tide period,  in hour.

PHASE:  Phase difference between tides at north and south entrance.

STAGE:  Difference in cm between daily mean level and short-term
         (weekly) average sea level.

STAGE!:  Difference in cm between  short-term (weekly)  average sea
          level  and long term average level (MSL).

TSHIFT:  Time shift for adjusting tide  with EST,  in hour.

     The following symbols are used to  specify the hourly climatological
conditions.

TAIR:  Ambient air  temperature, deg C.

HUMID:  Relative humidity,  fraction.

WIND:  Wind speed, cm sec  .

WDIR:  Direction from  which wind is coming, deg measured clockwise
        from North.

SRAD:  Gross solar radiation, in BTU/(ft2 day).

TSURF:  Surface water temperature, deg C.

     The following symbols are related to climatoiogical data and appear
in the calculation of wind stress, equilibrium ambient temperature  and
heat exchange at surface.

EPSLON:  Direction  to which wind blows, in rad.

WPR:  Wind speed in m sec'1.

CTEN:  Empirical constant appears in wind stress  formula.

TAU:  Wind stress  T.

TAUX:  x-component of wind stress  T .
                                   J\

TAUY:  y-component of wind stress  T .

TDEW:  Dewpoint temperature,  deg C.

TEQ:  Equilibrium temperature,  deg  C.

SK:  Surface heat exchange coefficient in cal/(cm2 sec °C).
                                    29

-------
                             SECTION  5

                 PREPARATION  OF SIMULATION RUN


     This section describes the preparation work needed  for ANCMN run.
The  flow chart and the associated subroutines  in Figure  1 and Table 2
are referred to in the following description.

1.  Specify number of full-grid points, IN, JN, KN and  number of half-
    grid points, IM, JM, in PARAMETER  statement.  Although the domain
    of solution under consideration is  usually smaller than the rectangular
    space of IN x JN x KN,  the  marker  matrices will assure that the grid
    points outside of domain  skip the calculation.   To have a clear  print-
    out, the variables at off domain point have been set  to 10 .   This
    value is beyond  the capacity  of the computer printout in  printing real
    numbers (F format) so that stars  will be printed and show  the  off
    domain area.

2.  Specify run number by input data LN, card #2:

         For LN = 1, i.e.  first run, data  file or card deck of AMATN
          is needed.

         For LN > 1, i.e.  subsequent  run, tape with previous result
          is needed.

    Specify flag for  storage by KSTORE, card #3:

         For KSTORE = 0,  desire no storage.

         For KSTORE = 1,  tape must be provided for storing results.

    Specify flag for  velocity  calculation by KVEL, card 14:

         For KVEL = 0, no V-calcuIation,  thus thermal dispersion only.

         For KVEL = 1, do V-calcuIatSon,  thus circulation included.

    Specify flag for  temperature  calculation by KTEMP, card  #5:

         For KTEMP  = 0, no  T-calculation, thus only a hydrodynamic
          model.

         For KTEMP  = 1, do  T-calculation, a complete hydrothermal model.
                                    30

-------
    Specify data block  number MBLOK, to make sure the data read  in
    from  tape is correct, card #6.

    Specify number of  hours to be simulated in this run by  NCY, card #7.

    Specify the time between  successive printouts by TPRT,  card #8.

    Specify grid size by input data DX, DY,  DS, card #9.

    Specify time step DT and tide  data STAGE, AMPLIT, PHASE, DPHASE,
    PERIOD, TSHIFT by input data, card #10.

    Specify Coriolis factor FCOR and stage STAGE1 by data, card #11.

    Specify the angle between North and the  y-axis of grid  system  by
    THETA, card #12.

    Specify reference length ALREF and Rossby  No.  ROSSBY, card #13.

    Specify number of  hours between weather observations RWEX, card #11.

    Specify TZERO, the Eastern Standard Time when the simulation starts,
    card  #15.

    Specify water density, vertical eddy viscosity, vertical eddy and
    horizontal eddy diffusivity, RR, AV, BV,  BH, card #16.

    Specify initial temperature TIN IT, a constant  for whole domain,  card  #17.

3.   In general, the first run  of present case  has:

      LN = 1,  KSTORE = 1,  KVEL = 1, KTEMP = 1, MBLOK = 0.

    Then the subroutines BAYBOT and BAYINI are used to  initialize
    the calculation.  This includes  reading matrices,  MAR, ELEV, MEX,
    MEY, MX,  MY,  by  BAYBOT  from data file AMATN.  The same sub-
    routine calculates the derivative height matrices, HB,  HU and HV.
    The initialization of various variable matrices  is done in  subroutine
    BAYINI and in the  main program itself.

4.   In general, the continued n    run has  the same NCASE  with:

            LN = n, KSTORE = 1, KVEL  = 1, KTEMP = 1.

    MBLOK = index number of the  data block  which is to be read in;  the
    calculation will continue thereafter.  In fact,  the data  being  read  con-
    tains  all the information needed to continue the run.  However, to
    allow  for the freedom of matching tide of different amplitude,  period
    and phase  shift, an additional  card (#18)  specifyinq NBLOK, TTOT,
    DT, EST, AMPLIT,  PHASE,  DPHASE,  PERIOD and "TSHIFT is needed.
                                   31

-------
    The data may be same as those contained  in the tape or different
    from  them so  that the calculation  goes on  to follow another tide
    format.   In accordance with this change of tide, the NBLOK,  TTOT,
    DT, EST may be reset.

5.   The main loop in the main program ANCMN !s  the hourly simulation
    loop, which is started with hourly climatoiogicai data card containing
    TAIR, HUMID, WIND, WDIR, SRAD and TSURF.  The wind  stress
    and equilibrium temperature are then computed and held thereafter
    as  constants throughout that hour.

    The main part of the hourly loop  is an internal  loop for At  increment,
    In  which the main calculation is done in the order of (n,  &),  (u, v),
    T,  W, then a printout of elevation, surface velocity and surface
    temperature at certain chosen  half-grid  points.

6.   The V-calcuIation  controlled by flag  KVEL consists  of  subroutines
    BETA,  BNRTIA, ABNR3, BVEL, ASAF3 and GIVENU.   BETA  computes
    TI and ft.  BNRTIA and  ABNR3 compute the convection terms,  RX and
    RY, for the momentum equations; this computation is decided  by
    whether ROSSBY is zero or not.  The  (u, v)  calculations are  done  by
    BVELS  and ASAF3.   The given velocities  at control points are re-
    specified by  GIVENU.  The BNRTIA and BVELS are for interior
    points while ABNR3 and ASAF3 perform the same purpose except for
    normal  velocity  points along open boundaries,  where the water eleva-
    tion is  specified as a function of  time.

    The T-calcuiation  controlled by flag  KTEMP consists of CONV, TCOMPT
    and GIVENT.   CONV computes the convective term TC,  then  TCOMPT
    computes T,  and GIVENT  respecifies T  at discharge points.

    After the completion  of marching  forward  to (n+l)At,  the variables are
    relabeled and UB  and VB  are  computed  as the horizontal components
    of  velocity at centers of (1, J) blocks.  Finally,  before the printout
    of  newly obtained variables at fixed  locations  to serve as flow  develop-
    ment at fixed point,  the surface velocity and  temperature at a critical
    point are compared with preset values to  see whether  an instability
    has developed.  If instability  does occur,  the program terminates after
    producing a  hard  copy of the latest  result.

7.   The subroutine ANCPR produces  step-by-step  records of surface
    elevation, surface velocity  and surface temperature at certain  chosen
    points.   These  points are selected because of the variables  that are
    believed  to undergo the most  change, as they are close to open
    boundaries, river exit and discharge outlet.

    The hourly loop included subroutines SOTRET and  TPRLOK too;  the
    former  stores the hourly results as well as all  pertinent data  onto
    tape for  later uses, and the latter produces a  printout of resultant
    horizontal velocities, vertical velocities, temperatures  at four  levels
                                     32

-------
    and elevation of free surface.  In addition, the main program ANCMN
    itself does the calculation and printout of total water depth, H  = h +
    n,  before starting next hourly loop.

8.   ANCMN performs  the hourly loop NCY a  number of times.
    Therefore,  NCY number of climato log Seal  data cards are needed to
    provide the  necessary  data.
                                    33

-------
                            SECTION  6

                            INPUT DATA


    The input cards for running ANCMN are given in Table 5 below.
Note that the data  symbols  have  already been defined in the previous
section; however, the following remarks  should be considered.

*  Free format is used  for ail data input.

*  Distinction must be made for integer and real  number.

*  The order of  these cards must be followed.

                  TABLE 5.  Input Data for ANCMN
Input
#1
#2



#3



#4



#5


#6
Card
Content
1
1



1



1



1


1
Symbol
NCASE
LN



KSTORE



KVEL



KTEMP


MBLOK
Definition /Value
= Case No.
= 1, if it is first run then data file
or card deck AMATN is needed in
#18
= n, if it is n run
= 0 no store, then there are no
continued runs
= 1 store intermediate results on tape
for plotting or next run
= 0 no V-calculation, i.e. dispersion
of T by given (u, v) field
= 1 do V-calculation, so momentum
is under dispersion
= 0 no T-calculation, i.e. hydrody-
namic only
= 1 i.e. hydrothermal model
= No. of latest hour of last run

-------
TABLE 5.   Input Data for ANCMN
           (Continued)
Input
#7
#8
#9


#10






#11

#12
#13
Card
Content
1
1
3


7






2

1
2
Symbol
NCY
TPRT
DX
DY
DS
DT
STAGE
AMPL1T
PHASE
DPHASE
PERIOD
TSHIFT
FCOR
STAGE1
THETA
ALREF
Definition /Value
= Number of hours intended for
simulation in this run
= 3600 seconds, hourly loop
= x-direction grid size in cm
= y-direction grid size in cm
= a-direction grid size in nondimen-
sional unit
= T;me,ffi(^,seAcY)folIOWS
J 29hmax
~ Average level of tide-MWL, in cm
= Amplitude of tide, in cm
= Phase lag of the north tide behind
the south tide, in hr
= Phase lag in east-west direction,
in hour per Ax
= Period of tide at entrances, in hr
= Time shift (in hr) for tide to agree
with EST time
= Corjolis factor = 2W sin(Iat), in
sec e
= MWL-MSL (datum for sounding) ,
if MWL * MSL, in cm
= Clockwise angle from North to the
y-axis of grid work, in deg
= Horizontal reference length, in cm
                  35

-------
                  TABLE 5.   Input Data for ANCMN
                            (Continued)
Input
 Card
Content
Symbol
           Definition /Value
 #14



 #15

 #16
 #17


 #18



 #19
                      ROSSBY
   1

   4
 RWEX



TZERO

  RR

  AV


  BV

  BH

 TINIT
= Rossby No. which controls whether
  advection is  needed  to account for
  in the equations of motion,  zero or
  nonzero

= Number of hours between climatical
  data, generally it agrees with hour-
  ly loop

= EST when the simulation run starts

= Density of water = 1.0

= 0.002  (AHREF)4/3, AHREF = refer-
  ence depth in cm

= Same value as A

= 0.002  (ALREF)4/3

= Initial temperature,  a constant for
  the  whole domain
   A deck of cards or data file,  called  AMATN, to specify
   matrices MAR,  ELEV, MEX, MEY, MX and MY.   It is  re-
   quired only if  LN  =1.
            NBLOK

            TOTT


              DT

             EST

            AMPLIT

            PHASE

           DPHASE

            PERIOD
            = To reset data block  number

            = To reset total time in sec if
              necessary

            = To reset time step AT if necessary

            = To reset EST

            = If tide changes

            - New phase lag

            = New phase lag per AX

            = If tide has different period
                                    36

-------
                  TABLE 5.  Input Data for ANCMN
                             (Continued)
Input
 Card
Content
Symbol
Definition /Value
                      TSHIFT
                       = Time shift of the new tide
 #20
   A deck of NCY cards, each card contains  six hourly
   weather data:
                       TA1R

                       HUMID

                       WIND

                       WDIR


                       SRAD

                       TSURF
                       - Air temperature,  deg C

                       = Relative  humidity in fraction of unit

                       = Surface wind speed, cm/sec

                       - Wind direction, from which direc-
                         tion wind is blowing

                       = Gross solar radiation,  BTU/Cft2 day)

                       = Ambient  surface water temperature,
                         deg C
                                   37

-------
                              SECTION  7

                         PLOTTING PROGRAM
     This section presents the descriptions of main plotting program
PLOTMN and its subroutines.  As  mentioned  earlier,  the plotting and
analyzing of the results constitute Part 2 of  the  three-dimensional, free-
surface model.   Here, the tape containing the hourly results of simulation
is  the  main  input. The control data cards help the user to choose the hour,
the plot and the comparison.   The output is  in a plot tape which is used
by a CALCOMP plotter to generate plots.

DESCRIPTION AND FLOW CHART OF PLOTMN

     The purpose  of  PLOTMN is to read in the measured and for calcu-
lated temperature  fields and to plot the isotherms.  In  addition, the cal-
culated velocity field  is plotted in  crplanes (craxis), in certain x-cross
sections (y-axis) and in y-cross sections (x-axis), and the surface
elevation  field is plotted in contour plots.

     Since the main input  is the data block from Part 1, the symbols
and their dimensions  agree with those that appear in ANCMN.  In order
to store the IR scanned surface temperature  at  four  tidal stages  for later
comparison  with calculated results,  a TIR (IM, JM,  4)  matrix is added.
It  is to be  noted that temperature fields are interpolated at half-grid
points  from the mosaic IR  images by hand.   Several data cards contain-
ing the quantities to  be used in plot caption are read in as well as con-
trol cards which assign the data block to be used  (NPLOUT) and  the  plot
to be done  (IPLOT).   A flag NSTAND is  to assign which measured tem-
perature  field is to be compared with the calculated.  The algorithm for
PLOTMN is  simple and  straightforward since  no complicated calculation
is  involved. The only calculation  is to compute  average deviation of
calculated temperature  field from measured temperature  field at the same
tide stage.  The average deviation is given by

                        .Z. (TB(i,  j,  1) - TIRfi, j))2
                   X2 = LJ	.	;	
                                  Z (i, j)
                                 • *
                                 M

where  TB is the calculated temperature while TIR is the measured  tem-
perature by infrared, and .£.(i, j)  is the number of surface half-grid
points in the  domain.      ''
                                      38

-------
     The isotherms of TIR and TB are the plots of main concern, as one
is to be compared with the other in order to assess  the accuracy of the
model in predicting the hydrothermal dispersion of waste heat.  Occasion-
ally, the water surface contour,  the surface current and the velocity
profile are also of interest, as they depict the circulation set up by the
tide and the wind in  conformity with the configuration and bathymetry
of the  waters.  The surface  elevation contour is done  by the subroutine
ECHKON which is also used for plotting isotherms, but care  must be
taken to assign the contour values, since the surface  elevation  changes
with tide; thus,  the hard  copy printout of surface elevation  ETA must
be consulted in order to choose the right contour values.  The surface
current is done  by PLOTUV,  while  the velocity profiles in ](y)-cross
sections and i(x)-cross sections are plotted by PLOTUW and  PLOTVW,
respectively.  It  is noted  that the velocity scale for horizontal components
is different  from  that  for vertical component.  The ratio is to remain the
same as the ratio of horizontal to vertical length  scale.  Therefore, the
velocity profiles are exaggerated in vertical direction;  however,  since
the horizontal velocities of the top level  (a = 0) are plotted  right on the
water surface, they show  free-surface profiles too.  Note that the j-sec-
tions and i-sections are fixed by given I- J- values.   They  are chosen
by  the user's concern about  the  effect of plan-form  configuration and
bathymetry  on currents.

     The flow chart for the main program PLOTMN is presented in Figure
4, and the subroutines are listed in Table 4 for quick reference.  It is
to be noted  that  several CALCOMP subroutines are also listed.

SUBROUTINES

ECHKON

     This subroutine  calls subroutines  CONL1N and ENDER.   This  program
was developed by the National Hurricane center for map contouring using
CALCOMP or MILCO-type plotter.  ECHKON is the entry point for the
package.  It scans the rectangular  gridded  scalar field, such as surface
temperature or surface elevation,  to determine where to start a new con-
tour.   Each contour is done  in a loop.  Inside the loop the subroutine
CONLIN is called to do the interpolation and drawing,  and ENDER  is
called by CONLIN to  label each contour of the same contour  value.  The
exit of contour loop in ECHKON is made when the final contour value
increased by increment has reached the specified maximum.   Here,
ECHKON is  used  for contouring TlR(i, j,  N = 1,  4), TB(i,  i,  1) and
ETAfi, j).

PLOTUV

     It computes  the  horizontal resultant  velocity from  components  u and
v at each level.   In general,  there  are four levels corresponding to k  = 1
to 4.   However,   for the present  problem,  only the surface current is  of
interest; therefore, KPLOT is set to 1.
                                     39

-------
         Read IPLOIR, IPLOCM, NIR, KPLOT, NCY
         Read Contour Values for TIR and  Caption Data
         Read Control Vectors 1PLOT, NPLOUT,  NSTAND
         Read Contour Values for ETA and Plot Size XL (in)
                       IPLOIR = 0
N1R Loops
                                     Yes
No
  ECHKON:  Plot Isotherm for Measured Temperature at  Each Stage
                       IPLOCM = 0
NCY Loops
                                     Yes
             READT:  Read in Data  Block from Tape
             Check Whether NPLOUT = 0 and NSTAND = 0
                        No
  Point by Point Comparison of Computed T with Measured T
                      IPLOTH) = 1
                                     Yes
                        No  ,:
                      IPLOT(2) = 1
                        No
                      IPLOT(3) = 1
                        No
                      IPLOTC4) = 1
                        No
                      IPLOT(5) = 1
                        No
           *  PLOTUV:  Do UV Plot
           *  PLOTUW:  Do UW Plot
                                                     J
              PLOTVW:  Do VW Plot
              ECHKON:  Do r\ Contours
                                                     T
              ECHKON :  Do T Contours
Figure 8.  Flow chart for plotting program PLOTMN and its subroutines

-------
TABLE 6.  Subroutines Required in Main Plotting Program PLOTMN
No.
1
2
3
4


5

6



7

8

9

10
11
12

13

U
15
16

Name
FACTOR
PLOTS
PLOT
ECHKON


READT

PLOTUV



PLOTUW

PLOTVW

CAPTN 1

CAPTN2
CAPTN 3
CAPTN 4

CAPTN 5

CAPTN 6
CAPTN 7
CAPTN 8

Description

Are CALCOMP Subroutines

Subroutine for plotting isotherms
and contour of surface elevation;
also draws the domain
Same as READT in ANCMN, for
read in- stored data from tape
Plot U, V on different layer, to
select the layer one can choose
KPLOT value; normally it is the
surface layer
Plot U, W on chosen J sections
west-east across the bay
Plot V, W on chosen 1 sections
south-north across the bay
Write common heading on each
diagram
Write title for UV Plot
Write title for IR-T isotherms
Write deviation of calculated
temperature from IR-T
Write tidal stage on the
diagram
Write title for UW plot
Write title for VW plot
Write title for surface eleva-
tion contours
Remark

In UCS * ACALCOMP
of UNIVAC 1100

Calls subroutines ENDER,
CONLIN, OUTLIN



Calls subroutine OUTLIN



J section once chosen
is fixed
I section once chosen
is fixed

-------
TABLE 6.  Subroutines Required in Main Plotting Program PLOTMN
                          (Continued)
No.
17
18
19
20
21
22
23
24
25
Name
CAPTN9
ENDER
CON LIN
OUTLIN
FIT
VECT
AROHD
NUMBER
SYMBOL
Description
Write title for calculated surface
isotherm
Write contour value to label
contour
Called upon to draw individual
contour
Called upon to draw outline of
the computational domain
Fit a parabola to three point
used in PLOTUV to interpolate
water depth
Calculates the velocity and
calls AROHD to draw the vector
Are CALCOMP subroutines,
called upon in various sub-
routines used in PLOTMN
Remark

Subroutine of
Subroutine of
Subroutine of
and PLOTUV
Subroutine of
Subroutine of
In library file
ACALCOMP of
1100

CONLIN
ECHKON
ECHKON
PLOTUV
PLOTUV
UCS *
UNIVAC

-------
PLOTUW

     It  computes the resultant velocity based on  components u and w.
As mentioned, the vertical and  horizontal components cannot be made to
the same scale;  therefore, the velocity profiles are distorted.  The j-cross
sections on  which the velocity is computed and plotted  are  preassigned in
the subroutine itself.   For the  present problem,  plots are drawn  for j  =
4, 8, 12.   All three plots are done on the same sheet.

PLOTVW

     It  computes the resultant velocity based on  components v and w,
and  plots  the velocity vectors on  the vertical cross  section along  y-
direction.   The  i values are likewise preassigned in the subroutine.
Here plots are drawn for i =  4, 8,  12 and are on one sheet.

INPUT DATA

     Table 7 lists the data to for PLOTMN.  Free format is used  generally.
The  total  input  consists of data cards and data files, but in the  list,
the input  data have been numbered in the order  of their appearance,
regardless of whether card  form or file form is used.
                                   43

-------
TABLE 7.  Input Data for PLOTMN
Input
#1





#2
#3
#4
#5
#6
#7
#8
#9
#10
#11
#12
Card
Content
5





N1R
NIR
NIR
NIR
NIR
NIR
NIR
NIR
NIR
1
5
Symbol
IPLOIR

IPLOCM
NIR
KPLOT
NCY
TL(I)
TH(I)
TI(1)
TAI(I)
QUD
Q2(i)
Q3(I)
Q4(I)
Q5(I)
Q6
IPLOT(l)
; Definition/Value
= 0, if no isotherm of IR obtained tempera-
ture is desired
= 1, otherwise
= 0, if no isotherm of computed temperature
is to be plotted
= 1, otherwise
= Number of IR obtained temperature fields
= Number of the o-leve! to be plotted
= Number of simulation hours
= Array of min. contour values for TIR
= Array of max. contour values for TIR
= Array of increment values for TIR con-
touring
= Array of ambient temperature, assigned
to out-domain points
= Array of EST time, for caption
= Array of wind speed values, for caption
on TIR plot
= Array of wind direction values, for cap-
tion on TIR Plot
= Array of air temperature for caption on
TIR plot
= Array of discharge temperature for cap-
tion on TIR plot
= Discharge flow rate, for caption in general
= Array of integers to assign the plot desired
                 44

-------
TABLE 7.   Input Data for PLOTMN
           (Continued)
Input
#13
#14
#15
#16
#17
#18
#19
#20
#21
Card
Content
NCY
NCY
NIR
NIR
NIR
1
2
Data File
Data File
Symbol
NPLOUT(I)
NSTAND(l)
ETAL(I)
ETAH(I)
ETAINT(I)
XL
DX, DY
1, J
TIR(I,J,N)
Definition /Value
= Array of integers to assign the hour de-
sired to be plotted
= Array of intergers to assign the TIRto
be compared with
= Array of min. contour values for ETA
= Array of max. contour values for ETA
= Array of increment values for ETA
contouring
= Plot size in x-direction (in)
= Spacing in x- and y-direction (cm)
= The (i, j) value of boundary nodes, used
for drawing domain's boundary
= To read in the IR measured temperature
fields of different tidal stage, files like
HDATA, EDATA, LDATA, FDATA
                45

-------
                            REFERENCES
Carter,  C. V.  The Hydrothermal Characteristics of Shallow Lakes.  Ph.D.
     Thesis,  Department of Mechanical  Engineering,  University of Miami,
     Coral Cables, Florida.  December  1977.

Dunn, W.  E., Policastro, A. J. and  R. A. Paddock.  Surface Thermal
     Plumes:   Evaluation of Mathematical Models for the Near and Com-
     plete Field.  Part One and Two.  Energy and Environmental Sys-
     tems  Division,  Great Lakes Project,  Argonne National Lab., May
     1975.

Lee, S.  S. and S. Sengupta.  Three-dimensional  Thermal Pollution Models
     Volume I = Review.  Department of Mechanical Engineering, SEA,
     University of Miami, Coral Cables, Florida, 1978.

Tuann,  S. Y., Lee, S.  S., Sengupta,  S.  and C. R. Lee.  Application
     of  Three-dimensional, Free-surface Model to  Shallow Tidal Waters.
     Proceedings of the Third International Symposium on Computer
     Methods for  Partial Differential  Equations, Bethlehem.  June 1979.

-------
                             APPENDIX A

                            EXAMPLE  CASE
 INTRODUCTION

     The present model  has been successfully applied  to thermal disper-
 sion study at Anclote Anchorage.  The Anchorage is located on Florida's
 Gulf coast and north of St. Petersburg (Figure 9).   It is  a  relatively
 shallow passage between the mainland and the Anclote Key.  A  series of
 barrier islands separates the anchorage from the Gulf of Mexico.  Through
 natural channels to  the north and  south of the Keys,  the  Anchorage has
 an  unrestricted exchange of water with the  Gulf.

     The Anclote  power plant operated  by the  Florida  Power Corporation
 has two  515 MW, oil-fired,  electrical  generating units.  Once-through
 cooling water is drawn from the Anclote River  through a man-made  canal.
 The six  pumps delivering a total of 1,990,000 gpm  (125.6 m3 /sec) are
 designed to raise the  water temperature 2. 8°C  above the ambient.   The
 heated water is discharged  back into the Anchorage through the dis-
 charge canal with a  dredged submarine extension.  The designed  total
 flowrate  is approximately 53 times the long-term average flowrate of the
 Anclote River.  At present, only Unit  1 is operative while Unit 2 is
 still pending permission.  That is, the present flowrate is  62.8 m3/sec
 (995,000 gpm).

     The principal driving  mechanism for current circulation is  tidal
 flux at the north  and south entrances  of the Anchorage.   The tide  is
 predominantly semidiurnal with mean  range of 2 feet.  Earlier measure-
 ments  of temperature and salinity indicated the currents flow in and out
 through  both  entrances; however,  the  exchange appears to be stronger
 in the south  than in the north, or the currents generally  flow north
 during flood  tide and  south during ebb tide.  Moreover, the wind plays
 an  important part too.  The surface  current  direction  depends on wind
 blowing at wind speeds exceeding 15 mph.

     The model as applied to the Anclote Anchorage shows its capacity
of considering the effects of geometry and bathymetry, spatio-temporal
 variation of the free surface, various boundary conditions, including
tides of different phase and range,  surface  heat transfer based on  equi-
 librium temperature  concept, and changing meteorological conditions.  In
addition,  turbulence has been considered by  using the eddy  transport
concept,  and the effects of  baroclinicity have been  included.  Again, the
user should refer to Tuann  et  al. (1979) for the general review, mathe-


                                     47

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                                         Jacksonville
                                              Daytona Beach
           Anclote
           Anchorage
Anclote R.
Tarpon Springs

Tampa
                                                   Melbourne
GULF OF MEXICO
                       .JWest
                         Palm
                         Beach
                       /
            Lauderdale *1

                       •|  Miami
  Figure  9.  Anclote Anchorage location in the state of Florida

-------
matical formulation, finite difference implementation and numerical method
of solution.

     The finite difference grid work is three dimensional and  is designed
to cover the area of interest.  The grid  size Ax  x Ay x Aais that the
least number of vertical  layers is four.   That is,  a Mayer, 5-level,
vertical partition is a reasonable choice for the present generation of
computer.  The grid work is  allowed to orient away from north-south,
east-west system,  but in general,  the x-axis of the grid system  aligns
with west-east,  and y-axis  with  south-north.  Thus, the subscript i
increases eastward, while j  increases northward.   The z-axis  is chosen
upward from mean water surface, while the subscript k increases down-
ward from the water surface.  That is, the  k = 1 level is the free
surface which is continuously changing,  while k =  5 is always the bottom.

     For the study of Anclote Anchorage, the grid is 16 x  14 x  5 with
five levels,  each with  224 nodes  for a total of 1120 nodes.   The  grid size
used isAx=Ay = 417m.   Depths off the natural coastal line are read
from the Coast and Geodetic Survey chart.  The maximum depth is 4
m  at the south end of Anclote Key.  It was  found that  gravity waves
were the dominating consideration  with regard to the maximum allowable
time step  At.  A 15 second magnitude of At was  found to work  well for
the present grid system.

     Numerical results were obtained with the University of Miami Com-
puting Center UNIVAC 1100 computer. The time histories of  the three
velocity components,  (u, v, w), the surface elevation,  n/  and the tem-
perature, T, for a 24-hour simulation period were obtained  with  about  90
minutes of computer time in most cases.  This is a time ratio of about
16:1 (the ratio of real time to computer time).

PROBLEM STATEMENT

     Florida  Power Corporation has a  fossil fuel power plant situated at
Tarpon Springs on the Anclote Anchorage.  The discharge  rate is 62.8
m3/sec of water at temperatures, in general, 2. 8°C above the ambient
water.   On  June 19-20,  1978, a  team carried out an in-situ data acquisi-
tion mission  to gather field  data  on temperature and current.   At the
same time, four flights by  NASA/KSC were undertaken  to obtain tempera-
ture by remote  sensing  method.   These four flights were intended to cover
four different tidal stages  in  the Anchorage.  The remotely sensed data
were processed  into digicolor film.  The  in-situ measurement of surface
water temperature at the time when the airborne IR data was  undertaken
provides a reference  for IR temperature.  With this reference, the  iso-
therms were drawn from the digicolor film.  The in-situ  current  measure-
ment data were  used  in  plotting  current  of different depth.  The ground
measured  temperatures  were used to draw surface and subsurface  iso-
therms.

     Once the model has been verified for its versatility and its  capacity,

                                     49

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U1
o
             II
            1O
                \
                                    Figure 10.  Grid work for  the Anclote Anchorage
                                                          10    i

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 and in  particular,  to the prediction  of hydrothermal development in well-
 mixed shallow coastal waters,  the model was run with actual tidal and
 meteorological data as input, but the initial temperature condition either
 could be  that of uniform state, that is to assume  the  power plant start
 impulsively,  or  could be that of an IR temperature field, that is using
 IR  data as the initial temperature field.  The demonstrative runs were
 carried out to simulate the hydrothermal situation for several days.  The
 predicted current fields are verified against the in-situ measured currents,
 and the predicted isotherms are verified against the  IR-obtained surface
 isotherms and the in-situ measured subsurface isotherms.

 CALCULATION OF PARAMETERS AND  INPUT DATA

     In this  section, the specification grid system, reference and physi-
 cal parameters,  tidal and meteorological data, discharge and intake  velo-
 cities,  ambient and  discharge  temperatures  will  be presented.   The actual
 calculation of some input data quantities is  carried out in detail for the
 purpose of demonstration.

 Grid System

     The  map indicating the exact locations of power plant,  intake and
 discharge outlets, and  the  sounding of the  Anchorage was  used to deter-
 mine the  size of the domain,  the grid system  to cover it, and the arrange-
 ment  of intake and discharge points  in the  system.  So, a  domain of
 about 6 km x 5 km covering most of the Anchorage was used.  A grid
 system  of 16 x  14 was  selected in the horizontal plane.  The size of the
 grid cell is Ax = Ay =  416.7 m; this size and the grid orientation has
 made the  intake  and discharge outlets  to the open water fall in with
 nodes respectively,  and the intake and discharge channels  have 45° and
 315° orientation  respectively.  The depth was specified according to
 sounding  chart.  There are five nodes in the vertical direction.  This
 gave  a  total  of 16 x 14 x 5 nodes.   The coordinate system  and grid
 work  are  shown  in Figure 10.   The MAR matrix, bottom elevation matrix
 and four additional marker  matrices are stored in  data file AMATN.

 Reference Quantities

 L:  Reference length = ALREF  = Maximum Length  = 6  km

 BH:  Horizontal eddy diffusivity = 0.002L4/3  =
      0.002 x (600,OOQ)4/   = 100,000 cm2/sec

 BV:  Vertical eddy diffusivity = 0.002H4/3 (H = maximum depth) =
      0.002 x (360)H/J  = 6  cm2 sec

     For shallow  well-mixed tidal water about three times the calculated
value was found  suitable.   Here, we use BV = AV  = 20 cm2/sec, i.e.
Turbulent Prandtl No.  = 1
                                     51

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RR:   Density  of water = 1.0

THETA:   0, since the grid system orients along North-South

RWEX:  1.0

ROSSBY:   0.0, that is,  based on test run,  it was shown that the nonlinear
           inertia  terms  can be safely neglected to save computation

TIN1T:  Initial uniform temperature or reference temperature =  20 deg  C

Calculation of Time Step, DT

     In order to determine the time step,  DT, the stability criterion  has
to be followed, which is done as follows.
                   DT <
                          DX
                                   41760
                                            = 50 sec
                        'J 2gH  " j 2x^9 80X360

About  1/3 of this value is reasonably safe to use.  Here we  use DT = 15 sec.

Calculation of Intake and Discharge Velocities

1.  Flowrate = 995,000 gpm (from power plant physical  data)
             = 62. 8 m3/sec
                        o
             = 62. 8 x  10  cm3/sec

2.  Both intake and discharge canals are at 45° from N, therefore

    31.4 x 10  cm3/sec is crossing the Ax  and Ay at the point  of
    intake  and discharge.

3.  The average depth at intake and discharge is approximately 4' or
    122 cm, and  the width is Ax = Ay  = 41760 cm,  so the cross-sectional
    area is 41760 x 122 cm2.
4.  The  average velocity is:
                  ave    ave
                                31.4x10
                               41760x122

5.   The velocity profiles are assumed as  shown.
                                         = 6.163 cm/sec
         1

         2

         3

         4

         5
                                              7.0 cm/sec
                                     52

-------
6.   To allow  for canal storage during tide change we assume the  intake
    and discharge velocities to be  sinusoidal,  i.e.

    Intake:   V3(14, 4,  k)  = 7 -  3 x cos[y|~(EST - 7.625)]

             U3(15, 3,  k)  = V3(14, 4, k)  for k = 1,  2,  3,  4

    Discharge:  V3(14, 8, k) = 7 - 3 x cos[~%EST - 7.5)]
                                           I ^« J
                U3(15, 8, k) = -V3(14,  8, k)  for k = 1, 2, 3, 4

    where 7. 625 and  7. 5 are taken to be the phase shift which takes
    into account the time to travel from the south end of Anclote Key
    to the concerned point.

Calculation of Tide on June  20, 1978

     Simulated diurnai tide is shown in  Figure 11, where

1.   Period = 12. 5  hr

2.   Stage = short  term  average sea level - MSL = 48 cm

3.   Amplitude = f short term average tide range = 65 cm

4.   Time shift = 7.125 hr

    i.e. at 7.125 a.m., June 19, 1978, the tide at the south end  of
    Anclote  Key was  zero.

5.   W - E lapse = 0.014 hr/DX

    Wave propagation speed  C = J2gh = J2x 980x360 =  850 cm /sec
    (H = 360 cm is the  maximum depth of the  Anchorage.)

    The time needed  to travel one  grid  distance is

                     DX   41760
                     C    850
                                =  50 sec = 0.014 hr.
    We use 0.014 hr per DX for phase shift in W - E direction  and the
    imposing  tide at the south entrance is


           n   = 48  + 65 sinfr—rfEST - 7.125  -  0.014(1 - 1)]
           5               I £*• D

    I  - grid  no. in W - E  direction.

6.   S -  N lapse = 0.15  hr.

    Distance  from south entrance to  north entrance is about 543,000 cm,
                                     53

-------
U1
                                •Tide at south end of Anclote Key
                                 Simulated tide for calculation  n= 48 + 65 x sin
                                                           Average Level
                     Figure 11.   Semidiurnal  tide for June 19-20,  1978 at  south end of Anclote Key

-------
    Time  for wave  to travel  this distance is   300° = 0.18 hr.   We take
    0.15 hr as phase difference between the south and the north boun-
    daries;  there,  the imposing tide at  the  north  entrance is


         r,  = 48 + 65 sin[T|^r(EST - 7.125 - 0.15 - 0.014(1 -  1)]
          n               I &• o

Calculation of Anclote River Flowrate and Temperature

1.  The distance traveled from South Anclote Key to Tarpon Springs  is
    20 DX.  We estimate a time lapse of  0.5 hr to account for  the re-
    tardation due to buffering effect of river storage and Anclote River's
    natural  outflow.

2.  The average current  is estimated to  be  20 cm/sec,  therefore, we take


               U3(16, 1,  k)  =20  costJrVEST -  7.625)]
                                     I Z* D

              V3(15, 1,  k)  = -20 cos[y~(EST - 7.625)]

    for k  = 1,  2, 3,  4.

3.  The surface elevation at Tarpon Springs is to be calculated.

4.  To  be in accordance with given velocities at Tarpon Springs, the
    temperature there is also assigned  and its value has a 24 hr period
    instead  of 12.5 hr.  This temperature is


             T3(15,  1, k)  =26.9 + 0.5 sin[-~(EST  -  12)]


    where the 12 hr shift is to make the peak temperature occur at 1800.
    Thus, the water in and out at Tarpon Springs has  a  temperature
    ranging from 26. 4 (before dawn) to 27.4 (late afternoon).

Discharge Temperature and Gulf Water  Temperature

1.  On  June 19-20, 1978,  the recorded discharge temperature at daytime
    is in the range of 29.3-30.3.   To account for  the further drop of
    discharge temperature due to  cooler ambient temperature at nighttime,
    we assume a sinusoidal variation of discharge  temperature with diurnal
    period.

2.  Discharge  temperature is estimated


             T3(14,  8, k) =29.4-1-0.4 sin[|j(EST  - 12)]


    therefore,  the highest discharge temperature of  30. 3°C occurs at
                                    55

-------
    6 p.m. and the lowest  (29. 3°C) at 6 a.m.

3.   The Gulf water outside the Anciote  Anchorage as well as the atmos-
    phere is sink to the heat disposal from the power plant; therefore,
    the boundary condition on temperature at the north and south en-
    trance is not considered as adiabatic as in normal case of far-field
    thermal pollution problem.  Instead,  we specify the outside-anchorage
    ambient temperatures.  Again, they are 24 hr periodic and their
    values should be in accordance with the measured  temperature in the
    same neighborhood.  Here in compliance with measured data, we use

                 Tgb  = 27.0 + 0.2 sin[||(EST - 12)]


    for both ambient temperature outside the south and the north boun-
    daries.

EXECUTION DECKS FOR CALCULATION AND  PLOTTING RUNS
                                                                    i

     The  following execution  decks are  for use in UNIVAC 1100 computer
at  the University of Miami.  These may  have to be  modified if a different
computer  is  used.   The programs  and subroutines used in these runs are
all compiled and stored in the file.

Calculation Run

First  Run—
1.   0 ASG, A  FILENAME.
    The file 'FILENAME1 is  assigned for the run.

2.   0 ASG, T  8., 16N, TAPENAME1
    A tape file names '81  is being assigned.   The tape is  9-track, and
    the reel number is TAPENAME1.1 ~

3.   0 PRT, S  FILENAME.ANCMN
    The main program  'ANCMN1 is  printed.

4.   0 PACK  FILENAME.
    'FILENAME' is packed  together, eliminating the  space  left by deleted
    elements, and thus, condensing the file.

5.   0 PREP FILENAME.
    Prepare an entry point table for the 'FILENAME.'

6.   0 MAP, S
    Combines relocatable elements to form an  executable absolute element.

7.   IN FILENAME.ANCMN

8.   LIB FILENAME.
                                    56

-------
 9.   END

10.   9 XQT

11.   3
     Case number  (NCASE).

12.   1
     First run (LN).

13.   1
     Store the calculation  results on to tape 'TAPENAME11 (KSTORE).

14.   1
     Calculate velocities (KVEL).

15.   1
     Calculate temperatures (KTEMP).

16.   0
     Specify numbers of the latest hour of the last run (MBLOCK).

17.   13
     Number of hours to be simulated (NCY).

18.   3600.
     Print the results at each 3600  seconds  (TPRT).

19.   41760., 41760., 0.25
     Grid sizes in x-,  y-  and cr-direction  (DX, DY,  DS).

20.   15.0, 0., 60., 0.08,  0.005,  12.5, 7.125
     Specify time step,  the difference of average tidal level and mean
     water level,  amplitude of tide, north-south phase lag, east-west
     phase lag per DX, period of tide, and  time shift  (DT, STAGE,
     AMPLIT,  PHASE,  DPHASE,  PERIOD,  TSHIFT).

21.   0.66E-4,  48.8
     Coriolis factor and the difference of  mean water level and mean sea
     level (FCOR, STAGED.

22.   0.
     The y-axis  coincides with North (THETA).

23.   8.E5, 0.
     Horizontal reference  length  and Rossby number (ALREF, ROSSBY).

24.   1.
     Number of hours between climatic data  (RWEX).
                                    57

-------
25.   7.
     Simulation run starts at EST  0700  (TZERO).

26.   1.026,  20., 20., 50000.
     Specify water density,  vertical eddy viscosity, vertical eddy diffu-
     sivity,  horizontal eddy diffusivity  (RR, AV,  BV, BH).

27.   27.0
     Initial water temperature (TINT).

28.   0 ADD  FILENAME. AMATN
     Input data  file  'AMATN1 for specifying grid matrices and initial
     water depth.

29.   @ ADD  FILENAME.FDATA
     Input data  file  'FDATA' for initializing temperature distribution.

30.   @ ADD  FILENAME.C2007
     Input data  file  'C20071  of climatic data.

31.   @ FIN
     Terminate this calculation  run.

Sebsequent Run—
1.  @ ASC,  A FILENAME.

2.  @ ASC, T 7.,  16N, TAPENAME1
    A tape File named  '7' is  being assigned; the reel  number is 'TAPE-
    NAME!.'   This tape was  used  in the first run for storing the hourly
    calculation results for 13 hours in 13 blocks.

3.  @ MOVE  7.,  12
    Move TAPENAME1  to the 13th  block which is the  last hour result of
    the first run and is going  to be used as input data for this subse-
    quent run.

H.  @ ASC,  T 8.,  16N, TAPENAME2
    A new tape  named 'TAPENAME21 is  assigned to store the calculation
    results of this run.

5-13.  Same as the cards 3-11  of the first run.

14.   2
     Continuing run (LN).

15-17.  Same  as the cards 13-15 of the first run.

18.   13
     The  last hour of the First  run is 13.

19-29.  Same  as the cards 17-27 of the first run.
                                     58

-------
30.   Same as the card  20 of the first run.   If new tidal data is needed,
     this card has to be changed.

31.   9 ADD  FILENAME.FDATA
     If different I'R temperature distribution is  needed,  FDATA has to
     be changed.

32.   @ ADD  FILENAME.C2007
     The data file C2007 has  to be changed  since the weather condition
     will be different from the first run.

33.   ©FIN

Plotting Run

1.  9 ASG,  A FILENAME.

2.  9 ASG,  T 7.,  16N,  TAPENAME1
    A tape file named '71 is being assigned.   'TAPENAME1'  stored the
    results of the calculation run.

3.  @ ASG,  T 11., 16,  TAPENAME2
    A tape file named 'IT  is  being assigned. The tape  is 7-track,  and
    the reel number  is  TAPENAME2.1  This  is used for  plotting tape.

4.  9 PRT,  S  FILENAME.PLOTMN

5.  9 PACK  FILENAME.

6.  9 PREP  FILENAME.

7.  9 MAP,  S

8.  IN FILENAME.PLOTMN

9.  LIB FILENAME.

10.   LIB UCS*ACALCOMP.
     Call 'CALCOMP1  plotter  library.

11.   END

12.   @ XQT

13.   1,  1, 1, 1, 6
     Plot IR isotherms and computed  isotherms;  only  one IR  temperature
     field  is to be  plotted.   Plot isotherms on the surface level only,
     and run for 6 simulation hours (IPLOIR, IPLOCM, NIR, KPLOT
     NCY).

14.   27.5


                                   59

-------
     Minimum contour value for IR plot  (TL).

15.   30.0
     Maximum  contour value for IR Plot (TH).

16.   0.75
     Increment of contour value for IR plot (TI).

17.   27.0
     Ambient temperature (TA1).

18.   13.
     EST for caption (Q1).

19.   358.0
     Wind speed in cm /sec for caption  (Q2).

20.   110.
     Wind direction for  caption  (Q3).

21.   29. 4
     Air temperature for caption (Q4).

22.   29.5
     Discharge temperature for caption  (Q5).

23.   62.7
     Discharge flowrate in cm3/sec for caption  (Q6).

2*.   1,  1,  1,  0,  1
     Plot UV,  UW,  VW velocities and isotherms (IPLOT).

25.   0,  0,  0,  0,  0,  1
     Plot the results at the 6th hour  (NPLOUT).

26.   0,  0,  0,  0,  1,  1
     Compare  the deviation  of computed temperature from IR tempterature
     (NSTAND).

27.   0.0
     Minimum contour value for surface height  (ETAL).

28.   0.0
     Maximum  contour value for surface height (ETAH).

29.   0.0
     Increment of contour value for surface height (ETAINT).

30.   6.
     6"  plot size  in  x-direction (XL).
                                    60

-------
31.   42000.,  42000.
     Grid size (cm) in x- and y-direction (DX, DY).

32.   9 ADD  FILENAME.APER1
     Specify  boundary nodes for plotting the boundary.

33.   @ ADD  FILENAME. ED AT A
     Input data file 'EDATA;1  specify IR temperature  distribution at
     ebb tidal stage.

34.   @ FIN
     Terminate this plotting run.

     The input data file AMATN,  FDATA, C2007, APER1 and EDATA
are listed in  the Appendix  B.   If these data are not stored in the
'FILENAME,1  card decks have  to be substituted.
                                    61

-------
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-------
SAMPLE PLOTTING
         TIHEUUNE 20,  1978):
         HIND SPEEDCCM/SEC):
         HIND OIRECTIQNCDEG/NJ:
         RIR TEMPERRTUREtDEG-C)*
         DISCHRRGE TEMPCDEG-C):
         D1SCH FLOWRRTECCUM/SEC):
         LENGTH SCRL£UCri= X CflJj
         VELOCITY SCRLE(CM/SEC):
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358.0
110.
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29.5
62.7
41339.
52.49
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                                               «..   V
           f
           \
  Figure 12.  Surface velocity, Anciote Anchorage by modeling
                          71
-------
  TIHEUUNE 20.  1978Js
  HIND SPEEO(CM/SECJi
  WIND DIRECTIQN(DEG/NJ:
  RIR TEMPERRTUREtDEG-CJs
  OISCHRRGE TEMP(DEO-C):
  DISCH FLGHRRTECCUM/SEC)s
  LENGTH SCRLE(1C«= X CM):
  VELOCITY SCHLECCM/SEC):
13.0
358.0
no.
29.4
29.5
62.7
41339.
52.49
                                               J= 12
                                               J= 8
                                               J= 4
  EBB  TIDE
Figure 13.  UW velocity, Anclote Anchorage by modeling
                      72
-------
     TIME(JUNE 20. 1978J*
     HINO SPEEDtCM/SECJ:
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110.
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29.5
62.7
41339
52.49
                                                  1=  12
                                                  1=  8
                                                  1=  4
     EBB  TIDE
Figure 14.  VW velocity, Anclote Anchorage by modeling
                      73
-------
       TIHEUUNE 20. 1978 Js
       HIND SPEEDtCM/SEC)»
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13.0
358-0
110.
29.4
29.5
62.7
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52.49
       DEVIRTIQN FROM IR TEMP
       EBB  TIDE
0.410
Figure 15.  Surface temperature, Anclote Anchoraqe by modeling
-------
                            APPENDIX  B

                FORTRAN SOURCE PROGRAM LISTING


LIST OF SUBROUTINES OF THE MODEL

Calculating Part

1.   Main Program

    ANCMN

2.   Subroutines Called (in order)

    BAYBOT:   Reads grid matrices and bottom topography

    BAYINI:  Specifies initial conditions

    READT:  Reads data from tape for continuing run

    IRREAD:   Reads 1R data  as  initial temperature distribution

    EQTEMP:   Calculates equilibrium temperature

    BETA: Calculates surface elevation and vertical velocity in
           xya coordinates

    BNRTIA:   Calculates inertia  terms in momentum eq. at interior points

    ABNR3:   Calculates inertia terms  in momentum eq. on the north and
             south boundaries

    BVELS:  Calculates interior velocities

    ASAF3:  Calculates north and  south boundary velocities

    GIVENU:   Specifies velocities at discharge point  and river  mouth

    CONV: Calculates convective terms in energy eq.

    TCOMPT :  Calculates interior temperatures

    GIVENT:   Specifies temperature at discharge point
                                   75
-------
    WCAL:   Converts vertical velocity in  xya coordinates into xyz
            coordinates

    ANCPR:  Prints surface  height, velocity and temperature at four
             locations at each time step

    TPRLOK:  Main printing  program

    STORET:  Stores calculating results onto the tape

    ZZl:  Finds  the current  direction

3.   Data  Files

    AMATN:  Specifies marker matrices and elevations

    APER1:   Specifies outline of interest  area

    C2007:   Climates data on June  20, 1978, start at 0700

    HDATA:  High  tide data  from  IR

    ED AT A:  Ebb tide data from IR

    LDATA:  Low tide data from IR

    FDATA:  Flood  tide  data from IR

Plotting Part

1.   Main  Program

    PLOTMN

2.   Subroutines  Called  (in order)

    PLOTUV:  Plots U, V  velocities on different levels

    PLOTUW:  Plots U, W  velocities at different j sections

    PLOTVW:  Plots V, W  velocities at different 5 sections

    ECHKON: Plots surface  isotherms and  surface height

    ENDER:  Subroutine in ECHKON,  for labeling

    CONLIN:  Subroutine in  ECHKON, for contouring

    CAPTN1:  Writes captions  on the  plot

    CAPTN2:  Writes captions  on the  plot
                                     76
-------
    CAPTN3:  Writes captions on the plot

    CAPTN4:  Writes captions on the plot

    CAPTN5:  Writes captions on the plot

    CAPTN6:  Writes captions on the plot

    CAPTN7:  Writes captions on the plot

    CAPTN8:  Writes captions on the plot

    CAPTN9:  Writes captions on the plot

    FIT:   Fits a paraboiar to three points

    VECT:   Establishes the components of  a  vector

    OUTLIN:  Draws the  outline of interest area

*  The plotting subroutines PLOTS, PLOT, AROHD, NUMBER,  SYMBOL
are existing in  UNIVAC 1100, University of Miami,  CALCOMP file.
                                 77
-------
SUBROUTINE  LISTINGS


*FLOW( 1J.ANCMN FOR  CREATED ON 1H DEC 79  AT  10:11:39
 I      £*****»«»* »«i>«»»»**»-a**»,Vl(IN,JN,KN»,
 0           CV2lI*,JN,KfJ),V3,H  ,HB { I « , JM ) ,ELE V t IN.JN),
II           CUe(If,Jf,KN),V6(I«,J«,KN) ,HU ,MEX (IM,JM»,
12           CMEYt I",JM)
13            OI."EKSION Tl»TM,JM,KNJ,T2ei«,JM,KN),T3(IM,.JM,XN),TC(IM,JMtKNI
11            OIMESSION AVR( J«) , ANG< JM1 ,OTZ(IM,JM}, TEMM, jMtKN)
IS            OIMEOS10N ETXI IK,JM>,TIOE3Nf IM),T1CE2NUMI .TIDE1NUM)
16            OIMEKSION UATJI*,JM},TIOE3Sf lM),TID£2S(IMI,TIOElS
13      C
19      C**1**CASE  MO UNDERTAKING, FOR  LABELLING PURPOSE
20            READ  2, NCASE
21      C
li      C*»2**LM=1  FIPST RUM OF PRESENT  CASE;  M SU8SEQUEWT  RUN
2T            READ  2, LN
21      C
25      C**3**KSTOKE=Q NO STOPEtTEST RUNJ,  =1  STORE ON TAPE
Z-b            READ  2, KSTORE
27      C
2?      C**i?**KVEL:0 MO V-CALCULATION,  =1  00 V-CALCULA TION
2"            READ  2, KVEL
3C      C
31      C**5**KTEHF=0 NO T-CALCULATI ON ,  -1  00  T -CALCULATION
32            READ  2, KTE^P
33      C
3D      C**6**TO  ASSURE MBLOK CONTINUE,  THUS «S  COUNTER  OF  SIMULATION HOUR
31-            READ  2, MBLOK
3*      C
37      C**7**THIS  RUN WILL 00 NCY*TPRT/3iOO HOURS OF SIMULATION
3?            READ  2, NCY
39      C
HO      C**6**FOR  1-OURLY CYCLE TPRT = 36QO;  OTHERWISE CLIfDATA  DO  LIKEWISE
41            READ  2, TPRT
12      C
1,3      C**9**DX.D1 GRIT S17E IN  CM; OS  SPACING  IN SE.6MA DIRECT ION I . 25 1
IK            READ  2, OX.OY.CS
x**      C
Uf-      C**lu**Tll'ESTEc,MWL-TrHPOOAL KWl , «Kf>L I T , M-S PHASE  DIFFERENCE,
17      c**10**e-V  PHASfc. DIFF PER OX,  TIDEPERTOO, TIDE SHIFT  IN  HOUR
1?            READ  2, OT, STAGE, AMPLIT, PHASE, DPHASE , PERIOD TTSHIF T
i»c      C
5C      C«*ll**FCOFrCORIOI IS F A CTOR , TEMPORAL MUL-ANNUAL  MULIREF. FOR  SOUNDING!
51            READ  2, FCOR.STAGE1
5?      C
53      C**12**THE TA=ANGLf PETUEEN NORTH  rNO OF HOURS BETWEEN  WEATHFR  OBS tRVA T IONS ( IN  GENERAL HOURLY)
kr            READ  2, R»EX
61      C
63      C**15**TZECO=EST. OF THE DAY  HHEN THE SIMULATION  RUM  STARTS
6'            READ  2, TZCPO
6"      C
6=      C**16»*OENSITY,VERT EDDY  VI S COS IT Y , VEPT  t HORI EDDY  OIFFUSIVITY
66            READ  ?, Rfi,AV,8V,9H
67      C
fee      C*»17**IM TIAL TEMP FOR TKE  »HOLE.  COMPUTATIONAL  DOMAIN
t0            SEAO  2, TI-JIT
7-3      C
71            WRITnt.,321 ^CASE
7?            WRITE (6, 3) LN
7?            IFIK STORE. EO.OJ V-R I TF { fc , 1 30 )
7"            IF IK STORE .GT.CH W<» ITE < fc , 1 1 1 >
7=         13C FORM M ( IX, 'DATA NOT RECORHt" ON TAPE*)
76         131 FORM tti IX, 'DATA RCCCSPID  ON  TAPCM
77            WRITE»6,m NCY
7R            WfiITE(6,5) OX,OY,nS,DT
                                            78
-------
 79            HRITE(6,2'M STAGE ,A"PL IT , PHASE ,PPHASE .PERIOD , TSHI FT
 £C            WRITE«6,7J FCOR
 81            WRITEtfa.lCU) THETA
 S2            WR1TF.J6.151 ALPEF
 8T          IS FORM*Tt 1X,'ALR£F=',F12.C, '    CM')
 ga            URITE(6,72J TZERO
 6"!            WRITE<6,73) RR,AV,BV,BH
 66            WRITE<6,8C6) RWFX
 87        806 FORMATUX,*RWEX = » .F10.2J
 *t            WRlT£<6,3Sq) TINIT
 S3        381 FORM*T( IX, 'TINIT=* ,F10 .2 >
 9P          72 FORMAT! IX, *TZERO=' , Fid. 21
 91          73 FORMATUXr'RRr*,Fia.2,'    AV=',F10.2,'    BV=*,F10.2,'  BH=*,F10.2>
 92            G = 98C.
 93            00=51.3
 9u            xz=Kft-i
 95            IGOri
 9*            THET*=THETA/CQ
 97            DUMX:2.*DX
 98            DUHY:2.»OY
 9<3            DUMS:2.*OS
               IFCLN.GE.2J GO TO  1
               EST=17ERO
1C2            TAUX:0.
1C?            TAUY:0.
ICf            TTOTrO.
105            NBLOKZQ
1 C6            CALL  !)AYBOTriN,JN,KN,IHf JM , U 1 ,U2,U 3, V 1 , V2, V ?,H ,OH ,£TA 1 f CTA ,ETA 3,
107           rRX,Rl,HX,MY,M*R,H,HB,ELEV,UB,VB,HU,HW,MEX,MEY,
1G^           COUMX ,DUMY,DU«S,OX ,OY,DS,OT,FCOR , TA UX , T AUY ,G ,NCAS£ ,N8LOK,TTOT,
1C9           CSTAGE1)
110      C
111      C**18*«A  DECK  OF AMATN  CARDS OR  FILE AMATN  IS NEEDED  H£RE,(ONLY  IF LN=1>*«*

113            CALL  BAYIN'ItlN,JN,KNtlHfJM,Ul,U2,U3,Vl,V3,V3,VfOHf€TAlfET*,ETA3»
1 14           CRX,RH,MX,MY,KARtH,HP,ELEV,UB,Vb,HU,HV,MEX,MFY ,
1 15           CDUMX ,OU«Y,OUK$,OX,OY,OS,OT,FCOR,TAUX,TAUY,C»,NCAS£,l
         c*******«M «IN LOOP IN HOURCY-STEP,  WITH HOUKLY  CLIK&TICAL DATA
1 14.0      Cn<«*o**B»«t <4*n->»«jina»4i>*a*»»**oi>»i»*»i«***'»*4jj»*»4»*«
II"             DO  1 CO JCTRrl.NCY
1ST      C
151      C*»2C*«A  DECK OF MCY CLIf.ATICAL DATA CARDS FOLLOWS
IS"5      C»*20**EACl-  CARl/ RECORDS  AIP  TEMP , HUMID I TY , WSPEEO , WO IR , SORAO , SURFACE  TEMP
IS?             READ  2, TAIR, HUMID , WIND, UOIRfSRADfTSUHF
1 Sf      C
lSr             «RITE(6,328» TAIR , HUMID, WIND ,VOIR , SRAD.T SURF
156        328  FOR)»/T( IX, • TA IR , HUH ID , WI ND , WO IR ,SR AO , T SURF • ,6F 10. 2 J
157             CB=2.
                                              79
-------
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3 X,_J  *(J3*»#UJ     *   *—   vOO   V»OO   Ut   «t  *>-*— »>-Q:  »>-»--*X   _J  ••>-    U.  »>-*~*XUI      •   >  **   S.  »-IL|     II M II •-* M M M It — *- ** *•      IK)  »M^-*N,«—


y >~»2r HH 21 ^-*— r*» uicx.     »?f-*fr~*rt     TJ(V   ui   tr  ••*/) m ••cj'*'^- owtf- Jeer  *o    *c.»"Q vit— o y   uj   (j*   *~  *-i3 ^?   oc~  »«-«  *"—«'-'fM~3*o TT™ *r^^ x 3* ~3 ~>~3

    131 —Dl M X>-.JIia
Q.O.U.U.U.    O**«X   U.   «tff!U,*lX^D'«t^"Z)tMiXO«*xr» «Sf— 3 *-»S;«—OO O*~*fvJ *-*f\iO OOO U O *-* f*JO
                                                                                  - «X OO OICS1^. OUIO *—«tOO   *-«    OZJt—OXOO  OOUIUltiJOO O33 > >O OOQ *-^Q^— *~ 13
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                                            *
                                          oo     o  o                                                        ooo
                                                                                                                » ir»\or^ a.'tr o»-»M^' rru^-o^ ft'f l_>•-«rJ^- ar u- »c f
                                                                                                               JUJUlJlJt-Jtj*Mm-»*-^»-*-M«-» »«»-«^< CJTN)(VJ IN fxi
                                                                                                                f-J fNJf^fM f^f>lfN* fMCMIV l\lrvf^ t^CMrj CJ f^fMCMfMC'JTJ rjCNJ f JOJTM 
-------
237             VB(I ,J.K ) = (V2(I,J,Kl«V2tllJ«l,KI)/2.
23F        201  CONTINUE
23?        203  CONTINUE
21C      C
2H1             DTXrlPRT-T?
212             CALL  UCAL«IN,JN,KN,IM, JH,U1,U2,U3,V1 ,V2,V3,W,OMfETAl,ETA,ETA3,.
211           CRX,RY,MX,MY,HAR,H,HB,ELEV,UB,va,HU,HV,f!EX,MCY,
211           CDUHX ,CUMY,OUHS,DX,DYtOS,DT,FCOR,TAUX,TAUY,GfNCASE,N8LOK,TTOT>
215             IFS,PX,Oir,OS,OT,FCOR,TAUXtTAUY,G,NCASE,N8tOK,TTOT,
2S«           CKVEL ,KTEVP,AVR,ANG»THETA)
255             GO TC 1COC
256        361  CONTINUE
257             lFtT2.LT.TPRT> GO TO  702
258      c**********************************
259        600  CONTINUE
26"             WRITE(6,607) EST , T AIR ,TEQ ,TABN , TABS ,TAUX ,TAUY
261        6Q7  FORMAT
26?             00 313 I=ltIH
263             DO 3«3 J=lfJM
261             IF(MEX(I,J).EO.OJ GO  TO  313
265             DO 311 K=1.KH
266             IFfK.ES.H TS(ItJ,K) = T2fI,J,KJ +
267             IF(R.EQ.KK) TB (I , J , K J = T2 II , J. K- 1>
26?             IFH K.NS.U.ANO.IK.NE.KN )) T8«I,J
2£ GO  TO  131
29=             END FILE 6
2<,f,             WRITE(6,308 )
2
;C"           7 FORM»T( IX, 'FCORr' ,ElS. 7,"   PEP SECM
3C^          32 FORf*;T(lX, t>JCA5E = I,If I .
3C6          33 FCR"iT(lX, 'START  ST  £S Tr • ,F 6 . 2 , '   CASE fJO.r',11,'   HBLOKr«,lm
3C7          31 FCRl- JT1 IX, 'STAGE, AMP, M-S PHASE, E-W PH ASE ,PE R , TSHI FT ' ,6F7. 3 )

3C?         7Q3 FORi* JTJ IX, 'COMPUTATIONS  BEING  STOPPED  BECAUSE  OF  INSTABILITY')
31r        1011 FORM {TI IX , 'THET4' ,F10. 1, *   HEG'1
311        10CP STOP
31?             END
                                            81
-------
*FLOU< U.SAY6QT  FOR CREATED ON  «  PEC 79 AT 09:4-Xf«Y,HARfH,H8,ELEVfUB,VB,HU,HV,HtX,MEYf
 i            CDUHX ,OUMY,OUMS,nx»OY,DS,DT,FCOR ,TAUX , TAUY ,G ,NC ASi ,N8LOK , TTOT ,
 7            CSTAGE)
 3             OIMCkSION U1(IN,JN,KN> ,U2d»l, JN,KN),U.3(IN»JM,KN>f VldN,JS,KN»,
 <>            CV2(I*,JN,KN> ,V3ClN,JN,KN) ,WdN,JM,KN) ,OM I IM . J« ,X N > ,ET A H I". , JM J ,
JQ            CETA(l«,JM),FT«3d1<,JH),RX{I>l,JNtKN),RY(IN,Jfl,KNlfMXdN,JN>,
H            CM Y(I N.vIN) .CAR (JK, JN),H»IN,JN) ,HP(IM,JM),ELEV(IN,JN),
12            CUB (I ^, JM ,KN >,VB(I«,JM,KN> ,HU(IN,JN ) ,H V t IN , JN) ,KEX  ,J=1 ,JNJ
:u             l,PITE(b,3C) I, (FLEVrl, JJ ,J
2?          37 CONTINUE
26             00 ICO 1 = 1, IN
Z~>             DC 1 CT J=1,JN
2a             IF
29          52 FCR" JTi IX , •'•EX MATRTX'J
to             DC s: 1=1
Ml             RCA.O 2, <^EX(I , JJ ,jri , J
«2             WRITE(6,60) I, (MEX{'I,J )
M'          53  CONTINUE
ft             WRIT E(£>T5tt>
qs          si  FORH;T( ix , «MEY MATRIX*)
Mft             DO 55 I=ltlf
i*7             READ 2, (KEY(I.J) ,J =
u?             WRITE(6,60) I, tM£
4<)          55  CONTIVUC
5C             WSITE(fc.l >
51           1  F ORM «T ( IX, 'VX  MAT"IX«J
5?             00 8 ;6 1 = 1, IN
5T             READ 2, (CX (I, J) , J=1,JK»
5<»             ^PITE{6,6C) I, IKX d,J) ,J=.l, JM)
5?        826  CONT INUE
56.             WRITE J6 ,3 J
57           3  F QKK *T ( IX, 'f Y  KATRIX'I
5°             00 "*C2 1 = 1, IM
= "             RE40 ', (HY« I, J) , J = l, JM
b^             WPITf(6,62) I, (MY d ,J) ,J=1, JN)
tl        4C2  COMT l';UE
62             DO 1C1 1=1 ,IM
6T             DO 1C1 J=1,JP
6U             IFCMEXC I ,JJ .EO.C)  GO  TO 101
6=             H8(I,J) = (Hd,J)+Hd + l,J)»H(
fc6        1CJ1  CONTINUE
6'             DO 1C2 1 = 1,1 H
65             00 1C2 J=1,JM
6"             IF«f XI ,J > .EC.O)  GO  TO  102
7"             HUd ,J) = IHCI ,J)+Hd ,J« 1) 1/2.
7!        i02  CONT ]NUC
7?             001C3I=l,If
7T             00 1 C3 J^l tJN
7 'i             iF .EO.OJ  r,c  TO  IQJ
71!             HVI I ,J) =(Hd,J) *Hd + l, J) 1/2.
76        1G3  CONTINUE
77             u KITE (6 ,109 )
7?        1C9  F CRM 'T ( 1 X, 'MB  MATRIX')
                                             82
-------
79            DO  1 JO  1 = 1
8C        110 USITEI6,3C)
31            URITE16.111J
82        111 FOBH*T(lX,'HU MATBIXM
83            00  1 12  1=1, IN
80        112 WRITEI6,3C) I, (HU (1 ,J J ,J=1 , JM )
35            WRITCC6.113I
E6        113 FORfmlX,*HV MATRIX')
87            00  1 IM  1 = 1 ,1H
88        lit URITE(6,30> I , t HV 1 1 ,J > , J= 1 , JN )
89          2 FORf*T  (  }
9f         3C FQRMiTt 1X,'I = ' ,It ,15F8 .11
91         31 FO«fiT< JX, •WATE'? DEPTHS, CM'/)
9?         10 FORM«T(lX,'rr',TH,15E3.2)
93         HI FCRf *T« IX, 'ROTTOH SLOPES, CH/.CMVI
91         51 FORMiTUX, *MAR MATRIX1/}
95         60 FCRMfT(lX,*I = *,m,iaX,15I<»)
96         61 FORHAT{1X.»ST«GE=',F10.2»
97        250 FORM4T ( "1M
9
-------
31
32
T T
37
70
39
1C
"1
12
<4'
qu
<*«;
UP
(40
sr
51
5?
53
57
50
               OIME^SION Ul(IN,JN,KN>,U2tIM,JN,KNJ,U3(IN,JN,KN)fVUlN,JN,KN),
              CV2IIN,JN,KN),V3HH,JNfKN),«(lM,JM,KNJ ,OM ( I M , JH ,K N ) ,fTA 1 ( IM , JMI ,
              CETA( I",JM),ETA3JlM,JH),RXUN,JN,KNJ,RY{INfJM,KN)MXCIMJN»
   CETA(
   rMYIINtJM,M«R(IN
       (If,
                                 JN>,HUN,J«M ,H6 t IM , JM) ,EU£ V I IN , JN )
   CMEYf ]M.JM),TPfIK
    DIMEKSION TltIMf
*FtOW{ 1 I .BAYINI FOP CREATED  ON « DEC 79  AT  09:<«5:2<»
 1       £#****#*»******» ***<$*****#****** ****#*$ 9*4 $****J*********##** ,T2 «!•• , JM ,KN ) ,T 31 IH , JK, KN» , TCf I« , JM , KN )
           ICC
            1=1,IN
            J=ltJN
            K = 1,KN
           ,K =0.
              = 3.
              = 0.
    V1CI ,J,K =C«
    V2II,J,K =C.
    V3«I ,J,K -C.
    RX(I ,J,K =0.
    RY(I ,J,K =0.
    CONT INUE
    DO  2CO 1=1,I«
    DO  2CO J=1,JM
    CTA1fI,JI=Q.
    ETAJ 1,J)=0.
    ETA3 =C.
    van ,J,K 1=0.
               U2«I ,J,K
               U3(I ,J,K
         ,J,K)=3.
    Tltl.J.KJ  —•
    T2(I ,4,K)
    T3(I ,J,KJ
    TC(I ,J,K I=Q.
    TRtI ,J,K1 = TIN1T
	 CONTINUE
iaa CONTINUE
        5CG
        <»CU
    DO tea  1=1,IM
    DC ICC  J=1,JH
    I F {f E X I I , J ) . fit
    E TA1 (I,JJ = ABJ
    EIA( I,J)rA3J
    ETA3 (I,J ) = APJ
    DO SCO  K=1,KN
    T9(I ,J,K JZA3J
    U(I,>,K1=< ~ '
    CONTINUE
    CONTINUE
    REfUFN
    END
                              .0)  GO TO <*C1O
                                              84
-------
 »FLOW(1
 1
 2
 3
 4
 c
 6
 7
 p.
 9
 10
 II
 1?
 11
 1»
 IS
 It
 17
 1?
 1°
 2C
23
21
<*
Zfr
27
2"
2"
T H
31
32
33
).RtAOT FOR CREATED  ON 7 OFC 79 AT  10:08:01
 C********* *************************************** ******************* ****
 C  READS lt> HOURLY  PESULT STORED IN  TAPE  FOR CONTINUE  RUN  OP PLOTTING
 £*******»* <* ************* *****************v4**4*************************
       SUBRCUTIHE  PEAC.TUN,JN,KN,IM,JH,U1FU2,V1,V:,W,ETA1,T1,T2,TB,
      CETAjfY.MY.MaR^.H^.DB.VB.HU.HV.MEX.PEY.NCASEfNeLOKtT
      CTIOE IN, TIDC2N.TIDE3V.T IDE IS ,TIDE2S , TIOE3S , STAGE, E ST.
      CAMPL 1T,PHASE.DPHASE,PERIOO»
       DIMENSION Ul (IH.JN.KN) ,U2 C IN , JN .KN ) ,V1< IN. JN,KNI . V2 « I M , JN ,KN J
      CU{IM,JH,KN),ETAl(I'«,JMjr£TA(if»,JMJ .Jx (IN , JN J , M Y I I N, JN > J»Al5 tlN
      CH«IN,JN),HP(IM,JM>,UBf IH,JM,KN» ,«B (IM,JH,KN I,
                 MVtIN,JHJ,HEXtj
                     ,,,,,,t,
                  f IK, JM,KN> , T IDE IN C I* I , T IDl !2N I IM J , T IDE 311 (IM )
                  fIH,J%KN),T10£lSCI»)tTIDE2S(IM),TIDt3SaH>

                  l» N8LOK
                   U1(I,J,K> , K = l ,KN ) , J=l , JN » ,1 = 1 , IN J ,
                                   fl = l,I
                  ,H = l,KNIf J = l,JN»,l:l,IN),
                  ,K=lfKN),jri,JNJ,I=l,IN),
                  =l,JNI,I=l,IN)l
                  1,JN),I=1,IN),
                  l,JN),I=lfIN),
                  1,JN) ,1 = 1, IN I ,
                  l, J,M1 ,1-1, 1NJ ,
                  ,JN),I=l,INJ
                                      .
              CJ (H13 (I,J), J=l, JP) ,1 = 1, IM1
39
M?
Ml
12
M?
<•«
i»e
<»6
M?
<«?
H9
5C
51
5?
5-5
5«
55
 C(TIDF.1NII ,1 = 1, IK
 ciriDE2N
     W3ITE»6,2»
     FCRMiTJIX,*NO  EOF
   £. rvwrr^iiiAf
     N8LOK=-1CO
     GO TC  1000
 SOC CONTl'^UE
     WRITE(6,112)  TTOT.NCASE.rJBLOK
 112 FORMfTCIX,'DATA  READ FROM T«PE,    TTOT = *,F10.0 ,
    f.'   CASE N8R = ',I5,'   BLOK NBR=',I5)
1C30 RETUPN
     END
                                               85
-------
*FUOV( D.IRRESO  SY^ CREATED ON  6  DEC 79 AT 09j<«7:52
 1
 ?      C   IN  THE CASE OF STARTING  FROM GIVEN  T-FItLD, READS IN THE  IR-TE"P
 3      C**ft***4ttft4tt**ft**ft*4**««***«*«**»**a**********«************************
 1             SUBROUTINE IfiPE*0 U^,JM,KNt T1,T?)
 S             OIHEHSION Tl CIH,J1,KN1 ,T2tIM,JM.KNI
 k      c*****DATA READ FPOM  ONE  OF THE IF ,H ,E,«. JOA T A BY
 7             00 5JO J=1,JM
 3      550    READ 2, ( T1(I,J,U,1=1,IM)
 9      2      FORMJT( )
in             DO 5ES J=I,JM
11             00 555 Irl.IH
12             00 553 K=2,KN
17      553    TUI ,J,K ) = T1 (I ,J, 1J
i<»             OQ 5!1 K = 1,KN
IS      354    T2«I ,J,K) = T1(I,J,1J
1*      555    CONTINUE
17             RETURN
18             END
                                               86
-------
*FLOwm.£QTEHP SYf CPEATFD  ON  12 DEC 79 ST 20:36:54
 2      C  COMPUTES EQUILIBRIUM  T  AND SURFACE HEAT EXCHANGE  COEFFICIENT  SK
 J      C********«4******tt********************ft********************************
 «            SUBROUTINE EQTEPPCTAIR.HUHIQ.UIMO.wOia.SRAO.TSURF.TOEU.SX.TEO)
 =            TAIR ] = TAIR*9./5.*32.
 6            TSURF1=TSURF*9./S.«T2.
 ?            HIND 1=UINO/H'».7
 ,»            SRAO ]=SPAO*mtO.
 9            TDEWl = (lH.55*.im*TAIRlJ*(l.-HU»'IO)
10            TDEW < = ({2.5 + .CQ7*TAIRl)*(l.-HUMIDJ J**3
1»            TDEW:TAIR1-TDEW1-TOFU2
17            TFIfrtTSUSF l»THE«)/2.
13            BfTAr.2S5-.OC85*TFILM+.C00201*TFILM**2
in            FCNUi7d.».7*ulN01**2
]=            SK=l£.7*fBETA».26l*FCNU
16            TEQ=1DEM+SRA01/SK
17            SK=S«*.00000564
IP            TEO= (TEO-32.)*S./9.
1"            RETUFN
2C            END
                                              87
-------
 "5
 6
 7
 P.
 Q
1C
11
12
1*
1<»
15
16
17
n
19
2C
21
22
23
2"
25
26
27
23
2-»ETA(I,j)!/2.
20C

    100
        DO ICO K=1,KZ
        OHUX:(OR*U2( I«1,J,KJ-OU*U2(I,J,KJ)/DX
        DHVY:(02*W2(I,J*1,K)-01*V2II,J,K11/DY
        F CK) :DHUX-»CHVY
              (l ) + d.*F (2J»2.*F
        DET= •13S*SU?>
        ETA3fT,J}=ETAUI,JJ«A8C*OET
        AH5=He< I ,J J+ETA3(I,J3
        IF(A hJ.GT.C. 1 SO  TO 200
        ETA3II,J)r{iC.»*( -6 » ) -HB ( I , J)
        OETr«ETA3{I,JI-ETAHl, JM/ABC
        CONTINUE
          =Hf 
-------
*FLOW(l>.eNRTIA  FOP  CREATED ON « DEC 79  AT  09:48:40
 1      c»******»* **»******************************'                    „_, ,,
 2      C  COMPUTES  NONLINEAR TER»S RX/RY  AT  INTERIOR HALF-GRID  U-/V- POINTS
 I      r ****************************** ********* ***********************«*****•-
 14             SUBROUTINE PNRTTA fl*l, JN,KN , IM ,JM,U 1 ,U2 ,U3 , V 1 , V2, V 3,W,OM,£T Al ,
 •5           CETA.£TA3,RX,RY,MX,HY,MAR,H,HB,El.EV,U8,tf8,HU,HV,MEX,HEYf
 6           COU«X,OUMY,OU?S DX OYJOS.DT FCOR,TAUX,TAUY,G,NCAS£,N3LOK,TTOT,CB1
 7             DIMENSION U KIN, JN,KNJ,U2t IV, JN,KNJ,U3( IN, JN, KM, VltIN.JN.KNI .
 •           CV2irK,JN,KNJ,V3h«IjN,KN»,«fIM,JMtKN) ,OH(IM,J",KNI.ETAlf JM.JMl,
                                 '
12
n             KZ=K»-I
It             ABC=CB*OT

16      C***»*CCMPt?ES*RX6AT INTERIOR  u-POINTS*****
17             00  ICO I=2fIH

1°             IF(MX(l,J)lNE'.3> GO TO  103
2?             AM=HL(I,JJ*(ETA{I,J)+ETA(I-l,J>l/2.

22             DET=KTA2a!j!-ETAl(I,J)*ETA3(I-l,J»-ETAltl-l,JI»/ABC/2
2T             oo  i ia K=I,KZ
                      i
25             D1=HE{I-1,J>«ETAJI-1,J)
'7             UeAR:rCU2(I,JtK)«H2U-lfJtK»/2.
2P             OHUU»=«02*(UfiAR?»*2l-01*CU8ARl**2) )/DX
               IFtl* Y1I.J) «EO.D SO TO  10M
 -             E2z(ETA(I-,J*n+eT»(I,J*l)*ETA(I-lfJJ*ETAa,JM/1.
31             El = (£TA(I,JMETA(I,J-lJ*ETAII-l,J-lJ*ETA(I-l,J))/'».
3?             D2=H (I ,J + l)+£2
23             D1=H(I,J1*?1  .
31             D1 = APAX1 (01 t I« »
25             02 = Af^Xl fOZ.l. )
3ft             UPAR;rro;*U9AR2*VBAR2/OY
4"         106  CONTINUE

I?             i^lffrilK^.^OM^l'.J.K-l.^OHir-UJ
5?             Ai=o;«i,j'K*n»(OMfr,j,K-»n*cmi-ifj
5'             OUC."C=< A 3-« 1 J/CUMS
SM             OUS=(UZ(I,J
55             GO  TC  108
eo             OUQK 'r { 3.*43-<» .*A2**1 J /OU"S
6"             OLS: n.*U2a,J.l>"'».»02«I,J,2»«U2tl,J,31)/DUKS
61         108  S IG^ -OS*FLP« T(K -1 >
62             RXtl ,J,H J=OHUUX+OHUVY^AH*OUOMS»«I.*SISI*OUS*OET
6T         110  CCMT IN'Ut

65      C  *°*  *°»r*N*Ca a**********************
6fc      C*«*»»CC«PLTES  RY AT INTERIOR  V-PO INT S**»**
67             00  2CP I:l,TM
ba             DO  2CH J=2»Jf
(,"•             IF (M Y( I ,J ) .HE .3 J  GO  10 2dC
7T             AH=HV(J,J)»lETAfI,JJ*ETA«ItJ-H'/2.

72             0£T= (ET«3(l"jl-ETAUI,Jl»ETA3(I,J-l>-ET«l(I,J-m/ABC/2
7^             00  2 13 K=l ,K Z
7«            ,02rHE( I ,JI *ETA 1 1, J I
75             01=HMI,J-1 )*FTA( I, J-l >
7«>
77
7"
                                              89
-------
  7°             IFIMMI, Jl .co.II  GO  TO  2d<»
  57             01=H(T,JI+E1
  P«             Dl=AfAXlf01,l.l
  §5
  I?
  P
 51             GO TC 206
 9?         20t CONTINUE
 If             Ei^JAjIt^lTO^l.JJ'ETAa + UJ-IMETAfl.J-l )!/<».
                OHUV):D2*UBAR2*V8AR2/DX
           206  CONTINUE
                IFfK.ITO.il GC TO ?C7
lcc!
}"             D«S:(V2
-------
»FLOW<1J.ABNR3  FCR  CREATED ON 6 OFC  79  AT  10:20:22
 1       C******»4* 44******************************X
 ?       C  AT VELOCITY POINTS ON THE OPEN  BOUNDARIES, COMPUTES  RX  ON Y-
 7       C  BOUNDARY,  COMPUTE RY ON X-BOUNOARY:  RX t RY ARE NONLINEAR TERMS.
 "       C  TIDE HEIGHT JUST OUTSIDE  THE  OPEN  BOUNDARY HOST ?E GIVEN
 5       C****»**»*<***********»«****************************»***|« **************
 6             SUBROUTINE ABNR3< IN ,JN ,KN,1^,JM,U1,U2,U3,V1,V2,V3,W,OM,ETA1,ESTt
 7            CETA,ETA3,RX,PY,MX,MY,MAR,H,HB,ELEV,UB,VB,HU,HV,MEX,MeY,
 S            CDUMX ,DUMY,DUMSIOX ,OY,DS,0T,FCOR,TAUX,fAUY,G,NCASE,N8LOK,TTOT,CB,
 °            CT10E IS,TIDE2S,TIDE35,TinElN,TIDE2N,TID£3N,STAGE,
1C            CAHPl IT,PHASE,PPHAS£,PERIOD,TSHIFT)
11            rOIMOSIQN..UJ(I>^N,KNI,y2(IN,JN,.K!^h,U3iINJJN,KN>,yinNtJN,KN>;


la            CMYII ^,JN1 ^ARtlNtJNIiHlINiJMitHSUMijMlteLEVCINtJNIt
15            CUB(If,JH,KN),VB«I'4,JMrKN>,HU(IN,JNl,HVIIN,JNJ,MEX»IK,JM),
16            CMEYflM.JM),
17            CTIDE INtIM»,TIOE2N, TIDE 3SCIHJ
1°            C,SOM(5»
20             K2=K^-l
21             A3C=CB*OT
2?             ACE= 10.**(-6)
2^             0011 I = 7, 15
2t»             TIDE 'N{I)=STAGE«AMPLIT*SIN(6.2S3/P£RIOO*» C EST- TSHIFT) -PHASE
21            C-OPH/SE«(I-1)))
2*       11    CONTINUE
27             DO  12 1=2,11
2"             TIDE 2SII )rSTAGE*AMPLIT*SIN<6.283/PERIQO*«EST-TSHlFT»
2°            C-CPH4SE*fI-l) 1J
If       12    CONTINUE
31       C«****CCMP».T£S RY CN NORTH BOUNDARY  OF  THE ANCHORAGE*****

3'             DO  ICO  1=3,15
31             AHZHXd, J) + (TIOE2N(I1*ETA)/ABC
«r             AHi = mi,jj»Tiof2NtT.j
41             SOH(Hl=tSIG/AHl)*D£T1
M?       SCO   CONTI'JUE
M3             DO  2 10  K=l ,K2
MU             02=HV(I, Jl •» TIDE2N tl )
HT             01=HHI ,J-1 »«ETA(T,J-1 -

47
               V3AR ] = (V2{I,J,K) + V2fI,J-l,K JJ/2.
               DHVVYr(02*«veAR2**2l-01*(VB«Rl**2JJ/OY
i*1?             DHUV>=O.
5"             IFtK .EO.l J  GO TO 207
«!             A3=V2fl,J,K-l)»»SOM»K-lJ+OMrOHUVX*OH VVY J AH*OV OMS*< 1 . «SIG J *0 V S
i"        21C  CONTINUE
t*!      10u    CONTINUE
ifc      C*****COMPITES  RY ON SOUTH  BOUNDARY OF  THE ANCHORAGE*****
67             J=l
6?             DC  3 fP ir?, 11
i°             AH = H\,
7"             OiTI:(T10£3S(I)-TIDElS«I))/»BC
lf.             AHlTtvc I,JMTICE2S(I>
7f>             SOMI K) = ( SIG/iHll*OETl
77      60C    CONTINUE
T>.             00  3 11 K = l ,K2
                                              91
-------
 7"            C2=HVtI,J»+TIDE2S(I>
 sn            D 1=HF(I,JJ+ETA
 81            VHAR»V2tI,J»l,KM/2.
 3?            DHVVirioi*(V8ARl*»2l-Oi*tVB«R2**2M/DY
 a«            CHUV»=C.
 a*            1F(K ..TQ.ll  GO TO TO?
 36            A3 = V2!I,J,K-n* = CHUVX+QHVVY*AH*OVOMS*»l««SIGl*OVS*OET
 9
-------
*FLOU<1 J.BVELS  FOR CPEATED  ON  H  DEC 79 A7 09:51:16
 j      £**»***»** 4 ************ *************** *********************************
 2      C   COfPUTEJ U3/V3  AT  1NTE°IOR HALF-GRID U-/V- POINTS

 tt        *    SUBPCUTINE 9vrLSARriN,JN>,HIINtJNi,HB(IHf JMI ,eLEV(tNtJN)»
17            CU3(I^»JMtKN|,VB(I^,JMtKN) ,HIM If, ,JN J ,H V (IN ,JN I ,MEX (IH, JM 1 ,
\u             KZ=Kf-l
               ABC=CB*OT
16             ACE=
17      C*****COKPIT£S U3  AT  INTERIOR U-POINTS*****
1"             DO ICO 1=2, IM
lJ/
If             U2tl ,JtKl = Al*(Gl*UHI,4,K)*S2*Aec*tA2-A'»-AS»A6»
37             GO TC 101
3S         102  CONT IMUE
               Ab=2.*AV*(U2 .ME. 3)  150 TO 20C
m>             AH=H V«I tJI«<£TA(I,J)+ETA(I,J-l»)/2.
146             AHrA HX1 (AH, ACE J
er             AHl=l-V*<£T«lU,J»«ETAlU,J-lM/2.
51             AH3Z*-V(I,JI + tET»3(I,UJ*ETA3tItJ-l)>/2.
53             C1 = AH/AH3
£3            .G2iA^/AH3
511             DEFr «%C*4V/« OS»*2 J/«H3/AH
5=             A 1 = 1 ./(I .*DEF»
56             OEYr IcTAd ,J J-ETA<1 ,J-U J/OY
57             StrGOtY
CP             DO 2C! K=l ,K?
6r             B5=RXI,J,K I /Ah
i 1             IF
bti             GO TC 201
ke         202 CONT IMUE
                                               ) /2 . *AH» T»UY*TS / AV ) / t AH*DS I *»2
67             V3II ,J,K ):41*JGI*V1 (1, J.,K )«ri2*APC*(P2-Bii-B5+86)l
6"         201  CONTT'IUE
6-J         2CC  CONT IMJE
71             RETUFN
72             E\'0
                                               93
-------
*Ft_OW( D.ASAF3 FOR CREATED ON  12  PEC 79 AT 13r<47:21
 1      C ********* ********************* ******* ************* ********************
 2      C   COMPUTES TIDE HEIGHT  AT  POINTS JUST OUTSIDE  OF  OPEN BOUNDARIES,  THEN
 ?      c   COMPUTE; THE NORMAL  VELOCITIES AT BOUNDARY  POINTS.
 u      C**********************************************************************
 •5             SUBROUTINE ASAF3tIN,JN ,KN,1*,JH,U1,U2,U3,V1,V?,V3,V,OM,ETA 1,
 6            CETA, fTA3,RX,RY,MX,PY,MAR,H,H9,ELEV,Ub ,ve,HU,HV,M.EX,*£Y ,CB,
 7            CDUMX ,DUMY,0UHS,OX,CY,DS,QT,FCCR,TAUX,rAUY,G,NCASE,NBLOK,TTOT,
 •            CTIDE IS,TIDE2S,TIDE3S,EST,STAGE,AV,
 9            CTIOE lN,TIDF2N,TIO£3N,AMPLIT,PHAS£,GPHASE,PERrOO,TSHTFTJ
If             OIH^SION Ul(IN,JN,KNJ,U2»I»l,JN,KN»,U3CIN.JM,KNI,VlfIN.JN,KN).

1'            CETA( 1M, Jli) .ETAld'^JKI rRX(IN,JN,Kt* ) ,H Y (IN, JK,K N i , MX f IN , JN J \
13            CMYtl*,JNJ,M4R(IM,JN),HtIN,JNJ,HP{IK,JH),ELEV(IN,JNJ,
16            CTIOE 1N(IM),TIDE2N(IM),TIDE3NCIH),
17            CTIDE JSeiM),TIOE2SU«n,TIOE3S(!M!
1°             KZ=K^-l
19             ABCrCB*OT
2?             DO 1 1 Ir3,15
21             TIDE 3M(I>=STA(5E+AMPLIT*SIN(6.287/PCRIOO*((EST-TSHIFT)-PHASE
2?            C-DPHAS£*(I-1I) J
23       U     CONT IMUE
2''             DC 12 1=2,11
25             TIDE 2StI)=STAGE+AfPLIT*SINC6.283/PERIOD*t tEST-TSHIFT)
26            C-DPHASE*«I-1 I!)
27       12     CONTINUE
28       C**»**CCMP ITES V ON  NORTH  BOUNDARY*****
29             J=iu
30             DO 3CO 1=3,15
31             AHl = HV(I,J) + (TIPElNfI)ȣTAHI,J-l))/2.
32             AH=HUI,J)»«TIOE2NtII+ETA{I,J-l))/2.
33             AH=A fAXl (AH, 10. **(•«] >
3"             AH3:^V(ItJ)*{TIDE3N(I}«ETA3fI,J-lJ)/2.
35             G1 = AH/6H3
36             G2=Ah/AH3
27             DEY= ITIOE2N{I)-€TA(!,J-1) J/DY
3"!             DEF: «eC*AV/(OS**2)/AH3/AH
3°             Al = l ./I l.»OEFl
11             DO  3C1 K=1,KZ
t2             S2=n.
<»3             BS=R Yf I ,J,K I /AH
"•"             IFjK .EQ.l ) GO TC  3C2
                          ,J.K + ll-VUI,J,K)+V2fI.J,K-lM/**2
50             V:iI,J,K)=Al*(Gl*Vl(I,J,K)+G2*APC*(82-B'»-R5*B6])
51        301  CONTINUE
5?        iOC  CONTINUE
«?      C** ***UPCA 1ES TIDE HEIGHT*****
51             DC  1: 1=3, 2C
55             TIDE !1( I J = TIDE2M(I >
56      13     TIDE 2N(I ) = TIOE3N(T)
r?      c**«**COMPlT£S V ON SOUTH  BOUNDARY*****
5 S             J = 1
S"5             DO  ICC 1:2,11
6"             AHl=hV(I,J»«ITlDElSfI)+ETAl(lfj)»/2.
6!             At-=M\i(I,Jl-»(TTOE2S(n-i'CTA(ITJt>/2.
6?             AH=ACJX1 tAM,10.**{-6) i
fc?             AH2=r-
6"             61 = «H
66             OEY= «ETAf I ,J)-TTOE2SII J J/DV
67             DEF:i^C*AV/f 0$**2I/«H3/AH
f             A 1=1 ./ t 1 .
7T             00  «C1 K=l ,K2
71             B2 = C.
7?             B5:R *( I , J,K J/AH
7T             IF (K .EQ. 1 ) r,Q TO  10?
7U             B6=AV*/2.*AH*TAUY*nS/AV>/*»2
-------
7"            V3«I ,J,K>=Al*+02*A9C*tP2-B«l-«5+B6n
              CONTINUE
SI      ICQ   CONTINUE
fi?      C*****UPOA 1ES TIDE HEIGHT*****
8?            DO 1« 1=2,11
9<»            TIDE 1S(I »=Tinr2SU J
as      in    Tio£asm-noe3s
-------
*FLOU

 2
 6
 7
 8
 9
10
11
15
16
17
(li.GIVENU SYf CREATED  ON  m  SCP 7° AT 17:M7:<»3
   C*****SP£C 1FY VELOCITY  AT  D ISCHARRE t INT AKF. , AND  PIVER  HEAD*********
         SU8f?CUTlNE GIVENU(IN,JN,KN,IHtJM,Ul,U2 ,U3,Vl,V2,W3,Tl,T2,T3,
        CESTJ
         OIMe^SION  «1{IN,JN,KN),V2(IN,JN,KN),V4{IN,JN,KN),
        n HI I",J.«,KM>,TZ(IM,JM,KN> ,T3< IM,JM,KN»
        CtUK IN, JN.KN) tU2(IN,JN,KNI,U3(IFltjr. ,KN)
         DO
     C3 K —1 K Z
     '"-   =-10.«COS(6.2832/25.0*(EST-5.OJ)
         U3H t,l,K
         V3(l 1»«tK
         U2ti;,3,K
   100
           =10.*COSt6.2t32/25.0*«EST-5.CII
           =5.-2.*COSJ6.2a32/12.5*(CST-7.62SIJ
           :5.-2.»COS(6.2332/12.S*(EST-7.625J)
           =5.-2.*COSl6.2332/12.5*«tST-7.5))
CONTINUE
RETUFN
END
                                              96
-------
*FLOWIU.CONV FOR  CREATED  ON It DEC 79 AT  10:13:57

 2      C  COfPUTES  TC-THE CONVECTIVE TERMS OF  T-EQN,  AT T-POINTS.
 3      c********* *************************************************
 0            SUEPCUT1NE  CONV(IN,JN,KNtIM,JM,OX,OY,QS,DT,OUf«X,OUMY,OUPS,
 5           CSK,RR,BV,U2fU8,V2tVB,T2,IC,HB,hU,HV,OM,ETAl,ETAt£TA3,Ce,MEX,
 6           CMEY,U?DT2,TEO)

 I?
 9
                              I, JHI,MEYf IM,JMI,OTZUM,JMI
 DIMENSION U2(IN.JN,KN),V2(IN,JNfKN1,UB(IM,J»,KNJ,VB(II,JM,KN),
CT2tIC,JM,K«ll ,HBtIH,JMJ ,HU(IN,JN) ,HV « I U, JN 5 , Of «1H , JM,KN ) ,
CETAl(IH,JM|f£TAtIu,JM),ETA3(IH,JMI,TC(IM,JH,KN>,ttClMtJM,KNl
 DIM»:>SION H£X(IM,JMI.MEYIIM,JM|,OT2JIH,JMI
11
12
13            HK = S f /(RR»«*V J
11            00 1 CO  1 = 1 ,IM
15            00 ICC  J=1,JH
16            IF(M-EX(I ,J).E0.01 GO TO  100
17            AHZHeU.JJ+ETA II, JJ
18            DET= (ETA3tI,J)-ET»lfl ,JJ)/ASC
1*ETA{IfJ})/2.
2C            IF(^EX(I,J1 .E0.21 OP=HU(I + 1,J I+ETA (I ,J»
21            OL = H(.(I,J! + (ETA(I-l,Ji«eTA(IfJ»/2.
22            IF(HEX(frJJ ,E0.1 1 DL=HU:(OR*UP*TR-QL*UL*ILJ/OX
36             VRr«»2tI,J*l»K)*V2(IfJ+l,K»l»/2.
2'             VL=( V?(I,J,K J+V2I I,J,K*1) J/2.
3°             TR=T;«I.J,K»
3"             IFiMfYJl ,JI.HE.2J TRrf T2(I,J,K )*T2(I, J+l.K M/2
40             Tl=T2(I,J,KJ
14 !             IF(MEY«I,J>.NE.l 1 TL-(T2CI,JtKI-*T2(It J-l
M?             OHVT'»:(02»VP*TR-D1*V,L*TL)/OY
t^            IFtK.NE.ll  TR=(T2lIfJ,H)*T2«I.J»K-l) 1/2.
46            IFCK.EO.l)  TRrT2(T,J,K )«(OS/2. J*OTI( I ,J1
M7            IF(K.NE.K2> TLi(T2IIi JfK >+T2CItJfK+llJ/2
48            IF
-------
is
17
13
ii
26
26
27
2"
2"
7"
31
22
33
3«
te;
35
37
50
1 1
<*2
<*«•
16
47
*FLOWU>.TCOPPT  FOR CREATED cv  i  APR  eo AT m:29:3a

 |       C   COHPUTF.J T3 BY CTCS+OUFORT-FRAMKEL SCHEKE*TO*INTEGRA TE***EON'

 <«             St'BRCUTIIMf^TCOKPT (IN, JN1KN, TM..1".

 6
 7
 S
 9

11
12
i:
 K Z — K ^ ™*
 ABC=CT
 DQ ICC 1=1, If
 DO ICO J=1,JP
 IFlffvH fj J.EC.2)  GO TO 100
 AH=HEn,JJ»ET*(I,J)
 AH1=I-B(I,J)+ETA1 tl,j)
 AH3 = ^t^lI,J)+ETA3(T^J^
 AACrgV/AH/ «DS**2)
 ACC=EH*AH
 D£F=3./fl.+AeC*BV/AH3/AH/.£0.1 >02TYr(T2II,J«ltK>+TABS-2.*T2f I,J,K)J/
 IF(Ya,j).E0.2)02TY=(T2(I,J-l,KHTA3h.-2.*T2(i;jtK)I/
    IF(K
            J GO  TO  51
           ,,ft,,-
 BARrc-TC(I,J,K}+AaC*BARl+ACC*(D2TX»02TYJ
 T3(I,J,K):CEF*(AH*T2{I,J,K)»A8C*BAR2I/AH3
 GC TC 200
 CONTINUE
 BARl:T2U,J,K + l)-TlfIfj,K)/?.«oS*OTZ(I,JJ
 BaR2:-TC(i,J,K}»AAC*BARl + ACC* J02TX «02 TY )
 7 3(1 ,J,K )=OEG*(*H*T2(I ,J,K)«A8C*BA|52)/AH3
 GO TC 200
 CONTINUE
 8ARl:-Tl{I,J,K]/2.+T2f ITJ,K-1I
 BAR2:-TCII,J,K)+AAC*BAR1+ACC*(02TX«D2TYI
 T3(I,J,K):OEG*(AH*T2(I,J,K)+ABC*BAR2)/AH3
 CONTINUE
 CONTINUE
 SETUPS
 END
                                             98
-------
*FLOW(ll.C-IV£NT  SYP CREATED ON  6  DEC 79 AT  10:22:11
        c*****SF|CIfY TEMPER ATU«»E  AT DISCHARGE  AND  RIVER HEAD*****************
               SL'BPCIITINE GIVEN! t IN, JH,KN, IH , J" ,U 1,U2 ,U3 , V 1 , V 2, V 3,Tl , T2t T3,

 5             O^ME^SION VI (IN.JN.KN) ,V2»IN, JK,K^4),« 3(IN,JN,KN»,
 5            CT1U I'.J'-.KN) .T2tI",JH,KN) ,T3«IM,JH,KN \
 *            CtUK lN,JI*,KNjtU2lIN,JN,KNI,U3flM,JNTKNl
 7             00  2CO K=1,KN
l'      200
11            RETURN
1?            END
                                             99
-------
1"             00  9CO 1=1,IM
15             00  9CC J=1,JH
16             IFfMEXII,J) .EO.OJ GO  TO  9CQ
17             DET:»ETA3(I,J)-ETAl(ItJH/2./OT
IS             AH=H8fI,J>*ETA(T,J)
1"             IFtHEXlI ,JJ.EQ.31 GO  TO  15
2C             IMME*«I,4> .EC.1> GO  TO  1
21             IF(H£X(I,J).EG.?I GO  TO  2
2?          15  CONTINUE
23             OEX= lETAU«l,J)-ETAfI-l,JM/OUMX
21             DAHXrtHB(I+l,JJ*ETA(I»I,J)-H8(I-l,JJ-ETACI-1,J)I/DUMX
25             50  TC  3
26           1  DEX= IETA (1 + 1 ,J»-ETAH,JI I/OX
27             E2=(ETAII«l,JJ+ET4tt.JI»/2.
21?             DAHX:(HU-ETA(I-l.J})/DX
3?             E2 = E1A/2.
3*             DAHX rcHUJI ,J)+E2-HU«I-if J J-FH/DX
35.             GO  TC 3
36           3  CCNTl'JUE
37             IF-£TAtI,J-l! )/OUHY
<«?             OAHY KH8 (I ,J*1 I«£TAM tJ-»ll-HB            H  OEYr (ETA (I ,J + l 1-ETAd, J) )/DY
46             E2 = t ETA( I, J+ 1)+ET«( I, J »/2.
46             E1=EUII,J+11-1.5*(ETA(I,J*1J-ETA(I,J1)
<»7             OAHY r(HV ( I , J«l !+E2-HV<
IS             GO TC 6
49           5  OEYr (ETA(I.JJ-ETAfI.J-1))/QY
5C             Et-tI*11tJ-l)*J.5*(ETA{I , J)•"
51             El = t ETA(I,J-l»*ETA
-------
*FLOWU>.ANCPR  FOB  CREATED ON 3 DEC 79  AT  20:i6:<46
 i      c ********* *************«**********»****#«*#«********•*******«**********
 2      C  PRINTS  ETA,  RESULTANT VELOCITY,  AND  T  »T  «« FIXFO LOCATIONS  CnuTINU-
 3      C  OUSLV,  THUS  SHOWS THE FLOW AND  TEKPERATUKE DEVELOPMENT AT THESE  PTS.
 U      C«*******« J
 ?            U=UB(6,1,1J
 o            V = USI6,1,1)
10            X 1 = SCPTIU*"»2«V**2 J
11            CALL  2Z1(U,V,ZED»
12            ZlrQ*«TH+ZEO J
1?            IFtZl.LT.O.I n=21«360.
11            Sl = £(6,l)
15            TH1=T2(6,1,1 1
16            U-UBU2,<»T1>
17            VrVSI^,"*,!!
18            X2=SCRT(U**2*V**2I
1°            CALL  221tU,V,2EDJ
2C            ?2=0»(TH+ZED)
21            IF(?<.LT.C.I 72=22*360.
22            S2=E(12,'H
2?            TM2-T2(12,1TH
2»            U=U8 (3,12,!)
25            V = V6 (fl.12, 1 J
26            X3 = SC"T
-------
*FLOWfl).TPRLOK  POP CHEATED ON  1  DEC 79 AT Ur31:18
 2       (;**«**«*** ******** ******************** *********************************
 2       C  PRINTS  CUT HOURLY RESULTS OF HORIZONTAL  RESULTANT VEU,  W-VEL, AND T
 3       t  AT  «»  LEVELS, *ND THE  SURFACE ELEVATION ETA

 5              SUBPCUTINE TPRLOK (I*',JN,KN,IM,JMtUl,U2,U3,Vl,V2,V3,W,OM,ETAl,
 6            CETA,£TA3,RX,RY,«X ,KY ,M AR ,M ,H8 ,EL£ V ,U8 , VB , HU ,HV ,MeX,NE Y ,T2,
 ?            CDUKX ,DU1Y,OUPS,[?X,aY,DS,DT,rcCR,TAUX,f AUY,G,NCAS£,N6LOK, TTOT,
 fl            CKtfEL ,KTEMP,VR,ANG»THETA»
 9              0 IME hSION Ul(IN..lN,KMtU2fIN,JN,KN»,U3,
11            CETAI IH,JMI ,ET«Z(I«'tJM) ,RX tIN, JN.KN ) ,R Y (IN ,JN,KN> ,MX(IN,JNI ,
I?            rMYm,JNl,«»P«IN,JNI,HtIN,J»M,H9tlP,.JM),ELEVtIN,JN»,
IT            CU?(I >,J*,HN) ,V6Uf»,JM,KNJ ,HUtIN»JN J,HV ,J=1,JM)
5?           1  CONTINUE
53             VRITF(6,505>
51             DO 6 1= 1,1-
55           6  WrtITf(6,5CSI  I,(ETA(I,J) ,J=l,JM)
56             IF(KFSOF.£0.0>  GO  TO  ICO
57             WR1TE(6,5C8I
5"             CO 1C J=l , JM
59             WRITE»6,6C?I  J
k"             CO 1C K=l,Kr
tt             ViRITE(6,5C7)  K,«US(I,J,K I ,I = ltlH;
62          10  CONTINUE
65             URITEI&.5Q91
61             00 2C 1=1,1"
65             UR1TE(6,6C1I  I
66             00 2C K=l,KZ
67             W«ITE(6r5a7)  K , (VR
-------
 7°        552 FORHfTt lX,*I = ',Ii», •    TEMP:* , 1MF7 .2// )
 S?        551 FORH*T(lX,»I=«tlU,«    TEHP=*,I5F7.21
 81         31 CONTINUE
 S2         S9 CONTINUE
 
 91        508 FCRK*TI1X, 'VERTICAL PROFILES  OF U VELOCITIES')
 92        509 FORM*T<1X, -VERTICAL PROFILES  OF V VELOCITIES')
 9J        fcCC FORMJTt •!')
 91        601 FORH*T{lHO,»Tr',I!t//)
 95        6C9 FORMfTflHC, ' J-*,IH//l
 96        700 FORM/TUX, 'RESULTANT  VELOCITIES  AND OIRS,    K = ',I<»/)
 97        701 FCRM*T( 1X,'I = ',II»,'   VRES = ',15F7.1 )
 9P        702 FORMiT(lX,12X,15F7.0/l
 9°            RETURN
100            END
                                              103
-------
3!
7 J
33
3"
3"
39
10
11
1?
13
11
1C
16
17
5C
*PLO«C1 ).STORET  FOR  CREATED OK' H DEC 79  AT  11:22:36
 1
 ?
 3
 i
 5
 6

 a
 Q
1C
U
12
13
11
IS
16
17
1"
!«•
2C
21
22
23
2"
25
26
27
2°
C  STORES  I-OURLY  RESULT ONTO TAPE FOR  LA
C***************************************
      SUBROUTINE  STOfiET(IN,JN.KN,IM,JM,U
     CETA, *X,MY,yAR,H,H?,t'e , VP,HUf HV.MEX
     CTIOE IN,TIDE2N,TICK 3N,TIDE IS,TIOE2S
     CA*Pl. n,PHASE,nPHA§E,P£RIOO)
      DIMENSION  Ul IIN.JN.KNJ ,U2(IN,JN,KN
     Cw fI" ,JM,KNI,ETA1cIM,JM J,ETA(IM,JM »
     CH UN ,JNI ,HS ( If , JM ) ,UB ( IK, JP. ,KN) ,VB
     CKUl^.JN),HV«IN,JN),MEXIIH,JH),fEY
      DIME^SI0^4  Tl (IK,JM,KN) , TIDE IN (I" I ,
      0 IfENS I ON  T2(IM,JM,KN),TIOElS{IMlt
      N3LOKrNBLOK+l
      WRITE  13)  N8LOK
      WRITE  (8J  (( (Ul (I , J,K) ,K = 1,KN),J=1,
                                    *******************
                                    IER  RUN  OR  PLOTTING
                                    :**********************
                                    1,U2,V1,V?,W,ET»1,T1,T
                                    ,HE Y,NCASr,N'BLOK,TTOT,
                                    ,TIDE3S,STAGE,E.ST,
                                                                       ,T2,TP,
                                                                         QT ,
                                                  I,Vl(IN,J*l,KNt,V2IIN,JN,KN),
                                                  ,KX ( IN , JN >,MY , TIOE3S(If 1
             CI((VKI,J,K),Krl,KN),J = l,JN),I = l,IM,
             Cl t  III  Uri,J,K) ,K = 1,KN),J=1,JH1,I=1,IMI ,
         fJ=lfJM1,1=1.IfJ
         (VE(I,J,K)fK=l,KN),J=l,JM),!=!,IK)
         (THI,J,K),K=1,KN),JS1,JK1,1=1,IK)
         (T2(1,J,K),K:i,KN),J = l,JM),!=!,If!
         {TE(I,J,K)fK=l,KN),j:l,JM),I=l,IM)
Cl
Cl
ri
C(
ci
ci
Cl
Cl
ct
Cl (HE _. .  .
C{TIDE1NII) ,1 = 1,IH
                   HI, Jl ,J = 1 , JM
                   XI ,U) ,J = I ,JN
                      ,JJ ,J = 1,JH
                         ,1=1,11),
                         ,1 = 1, 1M),
     CITIDF3N(I),I=1,IH
     CITIDEISCI) ,r=l,IM
     C«TIOE2SIIJ,I=1,I
     CtTIDE3SfI),I=I,I
      WRITE  (8)  TTOT,NC*SC,DT, STAGE, £S T , AMPLIT .PHASE ,OPHASE ,
     CPERI CD
      END  FILE  8
      URITE(6,1121  TTOTfNCAS£,NBLOK
      FCRM iTt 1 X, 'DATA RECORDED ON  TAP^,    T TOT= • , F10 .0 ,
     C*    CASE  *BP=*,IS,*   6LOK NBRi',15)
      RETUfN
      END
                                              104
-------
•FLOWC11.ZZ1 FOR CHEATED ON <» DEC 79  AT  11:39:05
 1       C*****0£TERMIN£S THE ANGLF OF RESULTANT  VELOCITY ******
 2             SUBROUTINE ZZ1 (U t V,?ED )
 3             IF(«FS(V).LT.. 00011 GO  TO  10
 5            GO TC 1QG
 6         10 CONTINUE
 7            IFtU.GT.O.) ZFO=1.571
 a            IFtU.tE.O.I ZEO-^.713
 0        IOC RETURN
10            END
                                            105
-------
*FtOUf ll.AKATN SY* CREATED ON 25 SPR 79 AT
1 3,0,0*1*1. 1,1, 0,0,1, 1,1,0, U
2 1,1,1,1,1, ,1,1,1,1,1,1,0,0
0
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it
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61
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, 11., 8. C, 8. 0,3. 0,3. 0,5. 0,5. 0,3
, 8. C, 9. C, 10. ,13., 6. 0,3. 0,8. 0,o
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9. 0,9. 0, 8. C, 8. 0,9. 0,8. 0,9. 0,8. 0,8
7. 0, 7. U, 7. C. 7. 0,7. 0,6. 0,3. 0,8. 0.9
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,2.0, l.C, 1.0, 1.0, 3. 0,2. 0,5. 0,7
, 1.0, l.C, 3. 0,1. 0,2.0,2. 0,2. 0,6
, C. C, 3. C, 3. 0,3. 0,1. 0,1. 0,2. 0,3
, 3. 0, 3. C, 3. 0,3. 0,0. 0,1. 0,2. 0,6
,3.0,3.C,5.0,C.C,O.C,C.O,b.O,2
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,3,3,3,2,3,3,3,3,3,1,1
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,3,3,3,2,3,3,3,3,3,3,3
,3,3,3,2,3,3,3,3,3,3,3
,3,3,3, 2,3,3,3,3,3,3,3
,3,3,3,2,3,3,3,3,3,3,3
,3,3,3, 2,3,3,3,3,3,3,3
,3, 3, 3, 2, 3,3,3,3,313,3
,2,3,3,2,3,3,3,3,3,3,3
,0,3,2,2,3,3,3,3,3,3,3
,1,2,0,C,2,3,3,3,3,3,3
,2,0,0,C,0,2,3,3,3,3,3
,C,0,C, C, 3,0, 2 , Z, 2, 2, 2
,0,1 ,3, Z, 0,0,0,1,2,0,0
, 3,3,3, 2,3,3,3,3,2,0,0
,3,3,3,2,3,3,3,3,3,3,2
,3,3,3, 2,3,3,3,3,3,3.2
,3,3,3, 2,3,3,3,2,3,3,2
,3,3,3, 2,3,3,3,3,3,3,2
,3.3,3, 2,3,3,3,3,3,3,2
,3,3,3,2,3,3,3,3,3,3,2
,3,3,3, 3,3,3,3,3,3,3,2
,3,3,3, 2,3,3,3,3,3,3,2
,3,3,3,2,3,3,3,3,3,3,2
,0,1,3,2,3,3,3,3,3,3,2
,1,2,C,C,1,3,3,3,3,3,2
,2,0,0,C, 3,1,1,3,3,3, 2
,G,C,.C,C,0,0,1,3,3,3,2
,0,1,1,1,0,0,0,1,1,0,0
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,3,3,3, 2,3,5,3,3,3,1,1
,3,3,3, ,3,3,3,3,3,3,3
,3,3,3, ,3,3,3,3,3,3,3
,3,3,3, ,3,3,3,3,3,3,3
,3,3,3, ,3,3,3,3,3,3,3
,3,3,3, ,3,3,3,3,3,3,3
,3,3,3, ,3,3,3,3,3,3,3
,3,3,2, ,3,3,3,3,3,3,3
,3,3,3, ,3, ,3,3,3,3,3
,2.3,3, ,3, ,3,3,3,3,3
,1,3,2,2,3, ,3,3,3,3,3
,5,2,0,Cf2, ,7,3,3,3,3
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                                            107
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*FI_OWf 1I.C20C7 SYH CREATED ON  20  JUN  80  AT 11:13:26
 r      25.0,.82,3!7.6,90.0,."5,26.6
 ?      26.1,.76,357.6,90.0,.20, 26.7
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                                             109
-------
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t*FLQW{ 1 I ,£u ATa  SYM C«EA ICO 0,4 IP JAN  80  *T  33:2C:£C
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 7       i7.u,r7.C,27.C,27.C,27.Qt?7.0,27.C,27.J,27,],27.7,,?6.7,2t.9,29.n,2y.i,29.6
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113
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 7<>      3      CONTINUE
 80             IFdFLOIR.EO.O) GO  TO  7
 8!             00  1C Nrl.NIR
 82             P1 = 01(M>
 87             P2=CJ(NJ
 att             P3=C2
 87             ZLIT:TL
 9?             0011 J=1,J"
 93             0011 1=1,1*
 91      11     E TAC J,J»=TIR(I ,J,N>
 9S             CALL  5CHKON«ETA,I«,dM, 1,1*, 1,JM, 1.8, 5.6, .Ot.SAHCON, TINT,
 96            CRGRIC,IM,JMt2HT,Z8IG,C.,a.,0.,C.,C;,0,.C7,l.,NPLT,IN,JNfKN,
 97            CNCN,CX,DYfXSCALE,YSCAL£,COSFfSINFrXX,YY)
 9«             CALL  CAPTN1             IFC»EX
1«1           5 CONTINUE
1«2             KC=1«INT   .
1H3      C*****PLOT? RF.SULTAMT  VEL  OF TJ ">[. V ON  NEARLY HORIZONTAL  SIGKA PLANE
100             IFU FLOTC1 ) .iO.fl)  GO TO 1GQ1

la«.            CXX,YY,AKN,PCL?J?PRH,ARKIN,ARMAX ,CO SF JsiNF , K 0 JHB.UOUMI ,
1U7            CUCUf,XL,UM4X,OX,DY,MMAX,WPLT,KPLOT,
IIP            CX SCt tc. ,YSC«L£,Z?CALf,USCALE..VSCAL£,USCALE, STARE, ETAJ
11^             CiLL CAPTMfTl ,P2,P3,PM,P5,Q6,XSC,USC)
15C             CALL CAPTH5(N.MlDEW)
151             CALL CAPT?i?»N»
15?             CALL PLCT tO.,0.,3>
i='3             CALL PLOT i ia. .0.,-31
icu      c*****PLOT< RESULTANT  Vc-l  CF U ?C W CM  £ -«  VERTICAL  SECTIONS
155      10C1   IF (I FLOT(; ) .EO.OI  r,0 To 100-
15ft             CALL PLOTlJ'J(If.',JN,KV, I f , J" ,MF ,-,K2 ,DX ,OY,DS,
157            CPLOTt-T,HMAX,UMAX,WF'AX,KEX ,HU , AR"I N , AHMAX , XL ,COSF , SINF , HR ,M AP ,
                                              115
-------
ISP
15"
160
16!
               CNPLT ,XSC ALE, YSC ALE, ZSC ALE, USC ALE, V SCALE, WSC ALE, STAGE, ETA, MX »
               CALL  CAPTNUPl,P2,P?,P«»,P5,Ob,XSC,USC)
               CALL  CAPTN5fN,MIOEW)
               CALL  CAPTN6IN)
               CALL  PLOTCO. ,o. ,3)
16?
16".
               CALL  PLOT(10.,D.,-3)
         C*****PLQTJ RESULTANT VEL OF
         1002
                                       V £ W ON N-S  VERTICAL SECTIONS
17!
172
17?
176
177
17P
179
ISC
131
It?
183
ISt
18=
186
1?7
191
19?
195
         998
197
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199
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205
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2C7
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2C°
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211
212
         591
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         101
                IFUFLOT<3».£O.CJ GO TO 1303
                CALL  PLOTVV(IN.JN,KK,IH,JM,V8,U,KZ,DX ,DY,OS ,
               CALL  CAPTNS
               CALL  CAPTN71N1
               CALL  PLOTID. ,0.,3 >
               CALL  PLOT<10.,C.,-3)
               2LIT:ET»L(NGJ
               ZFIG^ETAHt NG)
               SAMCCNrZLIT
                                                  CONTOU(? VALUES MUST 9E SIVEN  INOIV
               CALL ECHKCN
               CALL
               CALL
               CALL
               CALL
                     CAPTNM(SUM)
                     CAPTN9(N)
                     PLOT (C. ,0.,3 J
               CALL  PLOTf 10.,C.,-3I
               FORM /T( IX, 15F8.21
               FORM4T(F8.2, •   DEVIATION
               CONTINUE
               CALL  PLOT(C.,0. ,999)
               STOP
               END
                                         y.B.T. IR TEMP  AT', 15,"  IS (OEG-C 1 * ,F1 2.5 1
                                              116
-------
»n.OW( 1 I.PLOTUV FO F CREATED  0*1  7 DEC 79 AT  1C:C5:19

 2      C   TO PLOT RESULTANT  OF  U t V ON SIGMA  PLANE K=KPLOT
 7      £444444444 4444 44*444444444444444**444444444444444444<
 1             S'UBRCI.'TIME PLOTUVfl'l, JN,KN,IK,JM,U6,Vb,MEX,PEY,NCNf XX, YY.AKN,
 e            COELZ ,ZPPR,ARMIN,ARMAX,COSFfSINF,KC,HB,UDUM1,UDUM,XL,UMAX,OX,OY,
 k            CHMAX ,NPLT,KPLOT,
 7     '       CXSCAlE,YSC*LE,ZSC4LF.,USCALE,VSCALE .KSCALE .STAGE.E.T A}
 f             DIMENSIOfJ UP(IM,JM,KN) ,V8(IH. JM,KN1.MEX(IM,JM> ,MEYtIH,JHl ,
 9            CXXfNtN) , YYCNCN1 ,HPtIHf JM I ,£TA (I*«,JKJ
IP             URITF(6,32)
11          22 FORM«TIIX,'UV  PLOTS')
1?             A l = CX*XSCALE/2.
13             M=KPLOT
11             IFCM .GT.1J GO  TO  20
15             DEPTI-=0.
16             00 3C 1=1,IM
17             00 3C J=1,JK
I"             IF(MExtI,J) .EQ.O)  GO TO 30
1"             AI=FIOAT(I-1)*OX*XSCALC
2T             AJ=FLOAT(J-lI*GY*YSCALE
21             AAl=/T*UB(I,JtMJ*USCALE
2?             AAJ=AJ+V3(I,J,H»*VSCALE
2?             CALL VECT(AI,AAI,AJfAAJ,ARHINfARMAX,COSF,SINF I
21          3C CONT 1NUE
25             GO TC 8
27          20 CONTINUE
2a             OEPTh:OELZ*FLOAT(H-l)
2"             DO M r 1=1,1"
2C             DO. 1 C J = 1,JM
21             IFCM EXII ,JJ .EC.CJ  GO TO MO
3?             AH=HEfI ,J)+ETA II, J)
3?             IF(DEPTH.GE.AH1  GO TO HC
31             DQZ=»H/AKN
3^             L 1=1 
65             CALL "LOT! Al ,A 1 ,-3 )
66             NPLTrtJPLT* 1
67             •3lTE«>.iaJ  NPLT.OEPTH
6=          19  FOR" £T( IX, 'PLOT  N<>R = ',I6f'  COMPLETED.   DE PTH=« , F 10. 0 , •   C»*)
6C          13  CCNT ]NUt
7n        5CG  CONTINUE  '.
71      2      FORM«T( )
72             RETUPN
7T             END'
                                              117
-------
*FLOU<1 J.PLOTUW  FOR  CREATED ON 19 DEC 79  AT  1?:12:<46
 1      C ******************************************** ************ **************
 ?      C  PLOTS RESULTANT OF U t W ON SELECTED  E-W  CROSS SECTIONS
 7      C ****** ************ ****************«***4«**************** **************
 »            SUBROUTINE  PLOTUW(IN,jM,KK,TM,.JM,Ue.U,KZ,nx,OY.OS,
 c           CPLOTt-T,HMAX,UMAX,U«*X,HEX,HU,AR»'lN,ARMAX,XL,CO$F,SlNF,HP.,MAP,
 6           CNPLT ,XSCALE,YSCALE,7SCALE,USCALE,VSCALE,USCALF,STAGE,ETAfPX)
 7
              DIME JSION U8            IF(HEX(I,JJ.EC.O} GO TC 70S
2?            AI=FLOAT fl-l )*CX*XSCALE
21            AH=H£U,JI+ETA<1,JI
2?            DC  7CS  K=1,KZ
23            AK=(JTAGE«ETA(I,J>-FLOATCK-1J*DS*AHJ*2SCALE
2«            AAI=*I+UB(I,J,K>«USCALL
2*5            AAK=AK + W tl ,J,K J*WSC3LE
26            YW=. J*SQPT { «AAI-AI I »*2« C A AK -AK ) **2 J
27            YUrA>AXl tA3HIN,AMINl (YW, ARHAX > J
2?            CALL  «ROHO(AI,AK,AAI,AAK ,YU,a.O,12>
2"        7C6 CONTINUE
2C        705 CONTINUE
31      C*****03AWS BOUNDARY  OR BOTTOM OF  THE  CROSS  SECTION
32            CALL  PLOT<-A1,C.,-3J
2?            NN=0
3"            DO  7 10  1=1, IN
3^            IF(K>(I, J) .CO.G) SO TO 710
36            ^^^=N^ + l
27            IF(N».GT.l >  CO  TO 711
3S            AlrFlOAT ( 1-1 J*OX*XSCALE
39            AK=( $TAGE»ETAJ I,J) )*ZSCALE
t"            CALL  PLOT(AI,AK,3 J
M            AK = -2SCALE*«HUU,JJ-STAGE1
12            CALL  PLOTUI.AK ,2)
f?            GC  TC 712
<*<*        711 CONTINUE
4?            A IrFLOAT tl-! )*OX*XSCAL£
46            AKZ-iSCALEitHUd .Jl-STAGEJ
»7            CALL  PLOTCAI.AK ,2)
«'            IC=I
1°            AID=*I
5n        712 CONTINUE
SI        713 CONTINUE
S'              IF( I.LT.IN> GC  TQ 707
ST              AKr (STAGE+a.OI*ZSCALE
S«t              GO  10  7G£
55        707   AK= (STAGE*ETA II ,JM»ZSCAL£
56        7C3   CALL PLO T t A ID , AK ,2 )
57            WPITEI6.77JJ
5P         77 FCSM «T< IX, • J=* ,m J
59            FJ=FIOAT(J)
6T            CALL  SYMBOL(S.i,-n.7,. l,2HJ=,G. ,2)
6!            CALL  MU«"3E5I5.7,-D.7, . 1,FJ,P.,-1>
fc?            CALL  PLOTt Al,C.,-3)
67        13CC CCNf 1NUE
6"            C4LL  PLCT(0.,-<4.5,-3)  '
S?            NPLT :.'JPLT*1
6*            URITE(6,I6I  NPLT
67         13 FCRM*T(1X,»PLOT  N8fi',I1,'    COMPLETED*)
6°            RETURN
6?            END
                                              118
-------
*FLOW« U.PLOTVW FOF CREATED  ON  19  DEC 79 AT 12J1G:<»1

 J       C   PLOTS RESULTANT OF  V  £  U  ON SELECTED N-S CROSS SECTIONS
 .7       C ********* *************************************************************
 t             SUBPCUTINt PLOTVW (INtJM,KN,IM,JM,V6,y,Kr,DX,DY,OSt
 *            CPLOTJ-T,HHAXtUMAX,UHAX,MEX,HV,AHMIN,ARMAXtXL,COSF,SINF,HP,MAPf
 fr            CNPLT,XSCALE,YSCALE».'SCALE,USCALEtVSCALE,USCALf,S J AGEt E TA , M Y I
 7             DIMENSION MAR(IN,JNJ,H3•IM,JfI,FfA(IM,JK»,HY(IN,JN)
 9             DIMENSION VS**2«IAAK-AK)**2>
 27             YVrAfAXlfASKIN,AMINHYH,ARMAXJ}
 2"             CALL ARCHD(AJ,AK,4AJ.AAK,YU.Q.Q.IZ)
 2"         803 CONTINUE
 3D         802 CONTINUE
 3!      C*****ORAWS BOUNDARY  OR  BOTTOM OF THE CROSS SECTION
 32             CALL PLOT(-A1,Q.,-31
 3T             NN=C
 31             DO 8 10 J = 1,JN
 3r             IF(MY(I,JJ.EQ.OJ  GO TO 810

 37             IFtNk.GT.ll GO  TO  811
 3s             AJ=FIOAI(J-1)*CY*Y
-------
*Fl.OWC ll.OUTLIN FOC  CSEATFD ON 10 DEC 7-3 *T  11:23:23
 1      c** ******* <«a* ****************************************,*****************
 ?      C  DRAWS OITLINE/SOUNOARY OF THE INTEREST  AKEA
 ^      C ********* ****** a******************************************************
 "            SUBIUUTINE  OUTLINtlK, JN,KN,NCN,DX,DY,XSCAtE ,YSCALEtCOSF,
 *>           CSINF.XX.YY)
 6            DIH^SION XX{NCN1,YYCNCNJ
 7            001!  NC=1 ,NCN
 <•            A=XX (NC)*OX*XSCALE
 t            B=YY INC)*OY*YSCAU€
1C            KV=2
11            IFJNC.EO.l I
1H         15 CiLL  PtOTtX, Y,KV)
15     •       RETURN
16            END
                                            120
-------
 **-LOWyUcU(S5ARtNuiNttDcD«

12      C     ANY  FECTANGULAR GRIOCEO  SCALAR FIELD  CAN BE CONTOURED ON HUGO
|,?      C     0"? CJLCOPP TYPE PLOTTER  BY  SETTING UP PROPER CALLING ARGUMENTS AND
1|!      C        PPOCEDURES AS  INDICATED  BELOW AND  THEN CALLING ECHKON.

1*      C            ------ CALLING  STATEMENT IS  AS  FOLLOWS ------

\l      C     CALL ECHKO'JCHH,IN1,TN2,NEX1,NEX2,N£Y1,NEY2,HI,WIO,PLTINC,SAMCON,

\l      i    ij^i^xL^E0^^^

22      C               --- DESCRIPTION  OF CALLING ARGUMENTS ---

|2      C     HH IS ARRAY CONTAINING GRID DATA TO BE  CONTOURED. ITS DIMENSIONS
H      C        APE INI AND IN2. DIMENSION1  HHC I Nl , 1N23 .  POINT 1,1 IS LOWER LEFT
                             ^-™51^ IN  X «"ECTIO«'*NO IN2 I
         C                                                              IN2 IS
              CX  INCREASES FROM WEST TO EAST AMD Y INCREASES  FROM  SOUTH  TO NORTH3

 2;       C      NEX1, NCX2, NEY1, AND NEY2 DETERMINE THE PCPTION  OF HH  GRID TO
 \\       C         M. ."H^'TFSJ 4N2 NEX2 A°E THE fIRSTCLEFTMOST3 AND LAS TCRIGHTMOST]

 |f       c         SIlir?S  B! SIE«!EDcTllg!MS?0sg!TT!«aR§rTllS «SS2P85ET833  ANO  LASTCTO
 -2       C             FOR  FULL GBin---
 ~*       C                         NEXi > 1
 ||       C                         NEX2 > INI
 37       c                         wen > !
 3^       C                         NEY2 5 IN2

 f?       C      HI  IS HEIGHT IN INCHES OF CONTOUR MAP BETWEEN  LIMITS NEY1 ANO NEY2
 *i       c      wio  is  WIDTH IN INCHES OF CONTOUR MAP BETVTEEN  LIMITS NEXI AND NEX2

 MI       C      PLT^C  IS STPAIRHT  LiNE PLOT INCREMENT IN INCHES  TO BE  USED
 11 2       C         ALONG CONTOUR. GOOD VALUE IS .CM, BUT CAM t>£ VARIED  UP 0» DOWN.
 1,       c      SI"f?  LARGER VALUES CAUSE ff>0&9AH T0 RUN A LITTLE  FASTER,  IDEAL  VALUE
 I*       c         is LARGEST THAT  WILL STILL GIVE SMOOTH LOOKING CURVES.
 H       <•          CO  SOME  EXPERIMENTING WITH TT. START WITH  .03 OR .0$  ANO INCREASE.

 *°       C      SAMCCN  IS ANY SAMPLE CONTOUR VALUE.  IT IS USEP AS t STARTING POINT
 |j       C        FCR  COUNTING UP  AND DOWN TO GET OTHER CONTOUR VALUES.

 |<       C      CCNIM  IS CONTOUR INTERVAL TO BE USED.

 12       C      RGRIt IS AN  TMTEGER«2  STORAGE APRAV  USED INTERNALLY IN  PROGPAM
 |f       C        00  PJEED  NOT 3t  IMTIALI7EO.  IT IS INCLUDED AS ARGUMENT  IN ORDER -
 l|       C        J?cJ5rEr?PM.NJAG- OF V*RIABLE DIMENSIONS. DECLARE AS INTEGER*2
 ' '       *-        otrUKcCALLING«
fi      C        INK f-UST pr  /IT  LFAST  AS  IAPGE  AS  NEY2-^'EY1<1
°'^      C         CTHUS RGRID MUST  BE  AS  LARGE  AS  PORTION OF DATA ARRAY HH BEING USEDT
o ^      C                          »

.6"      c     ZLIT  ^NO ZBIG ARE  LOWER"  AND UPPFS CONTOUR CHECK LIMITS. NO CONTOUR

65      C        MrIiLi^-?F,,05AUS0S£t°V V5LUF OF ^LIT OR A90VE VAL|JE OF 2BIG.
£*      C         CUStFUL TO PREVENT DRAWING FOR  ANY COHPLETELY WILD DATA]

I*      c     ANO^IH, ASOUTH, AEAST, AND  "WEST  CAN BE USED TO ELIMINATE ANY
|°      C        NlfbER OF INCHES FROf  ANY SIDE OF FINAL DRAWING.

ll      £        r« fULL DRAWING WITH  HEIGHT > HI ANO WIDTH ) Win,
J|      C           TNITIALI7t ALL "I OF  ABOVE *RGL"ENTS TO ZERO.

Z2      £        FCR EACH OF THE ABOVE  WITH POSITIVE VALUE, THIS MANY INCHES
ll      C         VTLL 3P ELIMINATCO ON SIDE TO WHICH II JPPLItS.
4°      C         THIS ALLOWS US TO FIT ANY RECTANGULAR GPIO TO ANY  MERCATOR
I'                 OR OTHER MAP  LIMITS  WITHOUT  ACTUALLY ADJUSTING THE GRID.
                                            121
-------
 7"      C      NCASI-H  AND NOASHU CONTROL  TYPE  OF  CON TOURS rSOLIO  OR  DASHED LINES]
 80      C         IF EITHER OR BOTH ARE ZERO  OR  LESS, CONTOURS  ARE SOtIO LINES.
 31      C
 8?      C       IF  PITH APE POSITIVE, CONTOURS WILL BE DASHED AS  FOLLOUS—--
 ST.      C
 8"      C         PEN  DOWN SECTION LENGTH >  N0«SHD*PLTINC   CPLTINC  IS INCREMENT LENGTH.'
 PS      C          PEN UP SECTION LENGTH >  NDASHU*PLTINC
 86      C             CTHUS LENGTH OF DASHES  AWO  SKIPS IS FULLY  VARIABLE!
 87      C
 2?      C         XIASEL CONTROLS LABELING OF  CONTOURS. LINES ARE LABELED
 8"      C           ONLY IF XLAREL GREATER  TH«N  ZERO. VALUE OF  XLABEL
 9r      C             IS HEIGHT IN INCHES OF  L»BEL NUMBERS. LINES ARE  LABELED
 91      C             WITH NEAREST WHCLE  NUMBER  VALUt OF CONTOUR. IF SPECIAL
 92      C             LABELING TO INCLUDE ONLY PART OF NUMSE? OR  TO  INCLUDE
 "3      C             DECIMALS IS DESIRED, SUBROUTINE ENOEP MUST  8E  CHANGED.
 90      C
 ?•?      C         SCOOTH IS 4 CONTROL FOR VARYING CONTOUR SMOOTHING.
 96      C           INITIALIZE SMOOTH TO SOME VALUE BETWEEN 0.25 AND  7.5
 97      C          CANY VALUE OUTSIDE THIS RANGE  IS SET INTERNALLY TO  1.03
 9R      C             LARGER VALUES GIVE  SUOOTMER CHART WITH LESS DETAIL, WHILE
 9"      C              SMALLER VALUES GIVE LESS  SMOOTHING AND MORE DETAIL.
1C"      C         OORMAL VALUE FOP HOST  RUNS  SHUD BE ABOUT 1.S3
1C1      C         A^YTHI^G LESS THAN ABOUT Q.fn  CR LARGER THAN  ABOUT 3. IS
13,7      C          PROBABLY NO GQOO. BEGIN WITH  1.5 AND EX°EPIM£NT UP  OR DOWN
1C?      C         TC OETEP"IN£ MOST DESIRABLE  VALUE FOR YOUR NEEDS.
1C"      C        CmPUT GRID DATA VALUES  ARE  NOT  ALTERED IK THIS  SMOOTHING]
1C5      C
ic*      c         IFECCY is PLOT TAPE RECO°D  COUNTER. INITIALIZE  TO  NUMBER
107      C           OF PLOT RECORDS WRITTEN  BEFORE FIRST CALL  TO CONTOUR SUBROUTINE.
1C"      C
1C9      C       ALL OF THE ABOVE ARGUMENTS EXCEPT ARRAY RtRIO MUST BE  DEFINED.
110      C         ARGUMENTS ARE NOT ALTERED  WITHIN PROGRAM, AND  RETURN INTACT.
Ill      C
112      C          PLOTTER BUFFER SPACE MUST  BE  SET UP AND C»LL  TO PLOTS
m      C           MADE B£pORE FIRST CALL  TC THIS SUBROUTINE.

115      C           PLOT TAPE MUST BE CLOSED  OUT AFTER FI'-'AL CALL.
116      C
117      C          /NY ^4U^•SER OF SUCCESSIVE  CALLS CAN BE MADE TO  CONTOUR
11"      C          SUBROUTINE fCHKON. EACH MAP BECOMES A SEPARATE PLOT RECORD.
11?      C          NO  INTERNAL MAP SPACING IS  °ROVID£0, WITH PEN  RETURNING TO
12C      C          ORIGINAL ORIGI'ICLOWER  LEFT  CORNER] AT COMPLETION  OF KAP.
121      C      C THU < IT IS SIMPLE TO PUT  MORE  THAN ONE SET OF CONTOURS ON SAME MAP3
12?      C         AfY  SPECIAL "ARKfNDS OR LAPELS  THAT ARP. PESIRED MUST BE DOME
12?      C          rtJTSIDE THIS SUBROUTINE.  THIS  SUbSOUTINF DRAWS CONTOURS ONLY
121      C         WITH INCOMING ORIGIN BEI'iG  LOWER LEFT COPNF.R  OF CONTOUR CHART.
12^      C
12<,      C	
i27      C	'	'	
1 2"      C
1 2"             SUSR CUTIN'E ECHKON fHH, IM ,IN7,NEXl,NCX2fNEYl,NFY2,HI,W10,PLTIMC,
13D            ?SAMCCM,CONINT,RSRin,JN3,IN«»,ZLIT,ZeiG,ANORTH,ASOUTH,AEAST,AWESTf
131            JNCASI-l.fJOASHU.XLASEL.'MOOTH.IRECCY.IN.JNtKN,
13?            CNCN,CX,OY,XSCALE,YSCALE,COSF ,S1NF , XX , YY >
123      C
Ija      c          SEE ABOVE COMMENTS FOR DESCRIPTION AND USE OF  ABOVE ARGUMENTS
1 3S      C
126             CTMMCN  X:TRCON/SMHI.SMWlrX,Y,XGRIO,YGRID,CUTOF,SCHI,SCWI,TMAX,XPP,
127            2YPP,CGIG,U,V,f!Xl!X ,JDOO,NUVX ,MUVY,YCPTH,SOUTH,eAST,W£ST,CLIT,CBIG,
13"            3LCLX,LCLY,INCRCS,OI"C,CLOSIT,PVAL,PVOL,NEKTER,HINU«,NMXltNKYl,
13°            IN-XINN-YII.MOSINC.VALLIN.HINC.MAXCRO,WHAT,LDASH I,LOASH2.0ASHEPt
!•»?            5DCLAfS,OUTS
IM             CCMMC'J  /Q£NOEC/HIXE'.1,WCOE,HOGH,XXLAST,YYLAST
in?             LCGIC&L DASHER .DOLABS., OUTS
l
-------
j!o          m2FCR"/T(/!5x^7CH?HT 2BIG  ANORTH ASCUTH AEAST  4UEST MOASHO NDASHU  X
16C           >LA6£l  SMOOTH IRECCY,//,2X, 2F12. 3, MF10. 1,216, 2F10. 3,16, /»
161            MAXCFO=0
162            WHATs-99.
its            CQNi!>c::coNiNT
16«            IFtC CNINC.»!E.a.)GO  TO  3

Ifel           2 FCRjjT{/^2X,3HMAP,l3,lMH  2ERO INTERVAL)
167            GO  TC  120
Ifa?           3 1REC J=IPECCY«1
2?
17T             LDAS»-2=NOASHU

17'             IF(LCASH2.GT.6.ANO.LDASHl.GT.a)OASHER=.TRUE.
173             HINU*=XLABE:L
171             OCLAES=. FALSE.
17"!             IFIHINUM.GT.C. )OOL«PS = .TRUE.
176             IF«CCNINC.LT.O.)CONINC=-CONINC
177             PVCL :.005*CONIf«C
17s             MOSI^C=a
171?             V »LL ]N=-98989fi .9
16C             NUVX :NEX2-NEX1«I
}"             jnNLVxIIf!3!Ko.MUVX.LE.IN3.ANn.NUVY.GT.3.ANO.NUVY.l.E.IN«»)60  TO  8
If             WRIT£f6,7)N'CXl,fJEX2,NUVXfM£Yl,NFY2,NU«Y      ,T,n,,nY itini
IgU           7  FOR" tT«/,iax,23HBAO  ARRAY  LIMITS. SKIP . / 10X ,31 ID/ XDX, 3 110 I
1SC             GOTC120
Igf,      C        SKIP IF NUVX OR  NUVY  LESS THAU 1
1=7           8  YOrtTI-THl-ANORTH
                £AST:'4IC-AEAST
19?             WEST=AW£ST
191             IF(UEST.LT.O. JWFST=r.
19?             IF(E AST.GT .Win JEASTrwIO
IS'             IFtSCUTH.LT.G. JSOUTHrQ.
15U             IF«YCRIH.GT.HI)YORTH=HI
196             UCOE rtAST-WEST
197             HOGHrYCRTH-SQUTH
15"             XXL4ITC99.
150             YYLAST=99.
2CP             QINC:PLTINC
201             CUT :Q1N'C/1.99
  2             C8IG:QIMC/2.
  T             TMAX :t ,C*< YOPTH-SOt'TH + t AST-WEST)
  «             XCRI C^'.ID/FUOATfKUVX-l)
 C"             YGRIC=HI/FLOAT«NUVY-1)
 C6             HINC:XGf?IO
2C7             IFT(XGRID*XGeiO*YGRIO*YGPID) + .Gl
21'             CLOS 1T = .Q«»
21-5      C      CLOS IT IS VALUE FOR  CLOSED CONTOUR CH£CK
21 =
216             NMX1 l=f.
217             HPYl irtJHYl-1
221      C        NEXT OFTFPKtNE  MAX.AND MIN VALUES IN  SCALAR FIELD
                    rHH(NEXl,NEYl J
i t, I             £.-lN-£., »A
22"             DO 31 I=N£Xl,NtX?
                00 3 C J=KEYl,NtY2
                IF(MKI, J) .''T.rXAXl/MAXrMHII ,J)
                IF CHU 1 , J> -L T.i^IM)ZKIH = HHlT , Jl
22s          3G CONTINUE
22°             IF IZMX.GT .20IG)Z"AXrZEIG

231       C         M?XT*DETfpHlME  BOTTOM STARTING  VALUE  FOR CONTOUR LOO"

2J!          32 IF(PVAL.GT.?MIfJ)GO TO  Jn

23«             GO TC 32
236          3<» IF(P \AL-CCNINC.LT.2'«r.M JGO TO 35
                                              123
-------
237             PVAL=PVAL-CONINC
                GO TC 31
21C          35  XPPrC.
211             YPP=C.
212             NlrNlVX-1
213             N2=KLVY-1
211      C
215      C      CONTCUR LOOP STARTS BELOW  AT STATEMENT  36
216      C       THIS LOOP DETERMINES  fcHERE TO START A  NEW  CONTOUR,  THE" CALLS

I?*      g       ALL^MuRl £«ETETD'.nRAW EACH CONTOUR-  CXIT  IS  MADE UHEN
? (1 Q      /•

25?      C      THERE ARE 2 SCAMS FOR  EACH CONTOUR VALUE. FIRST kITH VAPIABLE OUTS  AS
251      C       FALJE SELECTS ONLY CONTOURS ENTERING GRID  FROH OUTSIDE EDGES.
2|2      C        SECOND SCAN yiTH OUTS  TPUE SELECTS REGAINING INNE" CONTOURS.
2|-      C       STARTING POINT CLOSEST  TO PLOT  PEN POSITION  IS SELECTED IN EACH CASE.

255      C
256.          36  IF(PliAL.GE.2MAX JGO TO  110
257             OUTS:.FALSE.
25*             DO 31 1=1,Ml
259             0037 J=1,N2
26C          37  RGRICd ,J)=0
2S1          38  OZT9S9999.
2t2             DO ICO 1 = 1, Ml
2fcT             DO ICO J=1,N2
261             IF«OITS)GO TO 6?0
265             IF
27C             DO ICO K=l,1
27*             IF(A5S=PVAL-PVOL
27°        <»CO  CONT INUE            ,
2Sr             IF(OITSIGO TO 250
2S1 •            NENN:I
2??             IF(I.EO.l.AVO.HEN(1».GT.PVAL.ANO.HENC2).LT.PVAL1GO  TO 6T1

2?1             IF(I I?0 .Nl .AND.HEN{3J .GT.PVAL.AND.hEN{i»J .LT.PVADGO  TO 601
235             NENNri
2E6             IF(J .TO.LAND.HENfD.GT.PVAL. AND.HEN( 1) .LT.PVADGO  TO 601
2£7             NENN:J
2??             IFI J .EO.N2. AND. HEN(2J.GT.PVAL.A»IO.HEN(3) .LT.PVADGO  TO 601
28'             GO T C 6Q2
25"        25C  DO 1 10 Krj , 11

29?             I2:K«1
29?             IFIK .EC.1J12 = 1
29'«             IFCHEMtl 1 > .GT.PVAL.AND.H£N'30  TO 610
299             11=RC"IO(I,J»/10
320             I2=RC°ID(I,JI-10*I1 *  .
3C1             IFU 1.EO.NENH.OR.I2.EO .NENNJGO TO ICC
3C7        610  GO TC«3n,3l2,3l1 ,316) .NENiN
3CT        602  IFCRCPIO(I,J).EC.0)PGRID(I,J)=1
3C1             GO TC ICO
3Cr        310  Y = YG K10* (FLOAT (J-l I «(PVAL-HEN ( 1U/(HENt 2J-HEN ( 1J J J
3Cf>             x :XGCIU*FLOAT 11-1)
3C7             GOTC4S
3C"        312  XrxGKT0*tFLCAT U-l J « J P VAL-HEN ( 2 ) }/ t HE N t 3 )-HEN I 2 11)
3C9             Y=YGPTD*FLOf.TCJ)
31"             GO -TC 15
311        311  Y=Y6FTC»/(H£N<3J-HENC 111 J
31?             X=XG SIC1 -»FLOA T (I )
311             GO TC 15
311        316  XrXGSIU* CfLOAT (T.-1 IMP VAL-HEMt 1 I >/IHENIU)-HENt 1) J »
315             Y=YGSIO*FLOATCJ-l)
-------
316         <»5 0 = IX -XPP j*(X-XPP)+tY-YPP»*«Y-YPP)
317            IFID.GE.OZJGO TO 100
31«            02=0
                        .
323            LCLXrl
321            LCLYU
322            XTTrx
327            YTTrY
32«        IDC CONTINUE
32e            IF(07. GE. 999990. IGO TO 105
326            IF(PC!?lD{LCLX,LCLYJ.EO.O>RGRIDaCLX,LCLY>=l
327            XZXT1
329      C
33:             W5ITEI6,101IPVAL.OOLABS,OUTS

33?      C IQ1   ORH*EXTXCALL*luBROUTIN£ CONLIN  TO  ACTUALLY DRAW CONTOUR WITH  VALUE  PVAL

331             CALL  CONLINCHH.INl ,IN2,RGRin»IN3,IN1>
235      C
336      C       NOW  GO  BACK TO INNER LOOP TO  SEE  IF  THERE ARE OTHER PVAL  CONTOURS
337      C       To  EE DRAWN.
33?      C
339             GC  TC 33
3in        105  IFCOITSIGO TO 612
31!             OUTS:.TRUE.
312             60  TC 33
31"*        612  PVAL :P«AL*CONINC
3H      c         INCREMENT CONTOUR AND GO TO TOP  OF  LOOP FO" NEXT CONTOUR
315             GC  TC 36
316        11C  CALL  PLOTtQ.,0.,-3)
317      C
31"      C       NOV TO  DRAW THE OUTLINE OF INTEREST  APEA PY CALLING OUTLIN
319      C
351             Al=DX4XSCALE/2.
351             CALL  PLOTI-ni,-Ai ,-3>
35?             CALL  OUTLlNfIN,JN,KV,NCN,DX,DY,XSCALE,YSCAL£,
25?           CCOSF ,SIUF,*X ,YY)
351             CALL  PLOT!*1,A1,-3J
356             I3ECCY=!R£CCY+1
357             W?ITgf6,ll5)IMAP,IReCltIRECCY
3SR        115  FCR^JTI/ , 10X , 11HCONTOUR HAP,I3,2«»H  BEGINS  UTTH PLOT RECORD ,13, 1 1H
359           2AND  ENDS  WITH. I?)
36C             WB1TFC6, 116IKOSIM C , VALL IN ,MA XCRP, WH* T
361        116  FORH«T(12X,21 HMOST LINE INCSEKENTS  ,I5,12H O'J CONTOUR ,F1C.2,/,12X
36?           Z,12Hr-OST  SaUAP£StT1,12H ON CONTOUR  ,F10.2,/J
363        120  RF.TUBN
361
                                            125
-------
>FLOV( i). CONLIN  en  CREATED ON 27 AUG 79 «T sujssae
 1        '•   SUBROUTINE  CONLIN (HH.IM ,IN2,PGOIO, IN j. INI )
 2            COMHCN  /STRCON/SMHI,SM*-I»X,Y,xGRID,YCRID,CU70F,SOHI,SOWI,TH«X,
 3           2YPP, CG IG,U , V, NX UX.JTOO, NU VX ,NUVY,Y OR TH, SOUTH, EAST ,UEST ,CLIT,CBIG
 M           3LCLX ,LCLY,INCROS,OINC, CLOSIT.PViL, PVOL,NENTER,HINUH,NHX1 ,NPYJ,
 5           »N>«XlI,f.fmi,MOSINC«VALLIN,HINC,MAXCRQ,WHAT,LDASHl ,LDASH2 .DASHER,
 5           5DOLA?S,OUTS
 7            OIMEHSION HHtIM,TN2) ,CIDE«1,2» .XXPLO T « 27S »2J ,HAX ( 4 1 ,LEXE( « ) ,
 ?           2CORO C<4Ca,2>,HIPPSmOOl
 •>            INTEGER  RGRioiiN3,iNS, DASHER, CLOS, OUTS, OASHIX

12      C            THIS  SUBROUTINE IS CALLED TO DRAW  EACH INDIVIDUAL CONTOUR

1°      C         IF  DOLA9S ENTERS AS TRUE, LABEL CONTOURS  WITH HEIGHT HINUM
15            0*SH JXiOASHER
16            LABL JTr9
17            IF(OCLABS)LABLITzO
18            INCS:. FALSE.
I1?            YM»X:-9.
2?            X^AXr-9.
21            N£NST=NENTE&
22            IOPLCT=2
2?            NHARCTLDASH1
2<»            NSOF1=LDASH2
25            NUGGra
24            XX=X
27            YY=Y
28            XHIGrXX
2"            YSIG:YY
3C            LZX=ICLX
21            L?Y=LCLY
33           'XG=0.
3"            YO=C.
35            TCT=C.
3fi            HYPTCTrQ.
27            NCQPC=C
3P            CLOSt. FALSE.
3"»            GO  TC MOO
«C      C
II      C    END  SfTUP.  BEGIN LOOP THAT PICKS EXACT  STRSIGHT LINE SEGMENTED  TRAVERSE
«2      C
M3        250 IFINCORO.LT.MOQ1GO TO 252
"»a            USITEffe, 251 JK'COPD.PVAL
1?        251 FORK «Tt/ ,2X,IS,1MH =HYPE
5«            CORD             XPIG:XIf>0
75
7 'i        <)00
                F«Q >I .LT.7. )OX t=T.
77             IF(0>!.CT.XGRID>OXi:XRf,ID
JO             OYl=>ieiG-YGI?IO*FLOAT(L2Y-l>
                                              126
-------
1C6
1C?
 79             IFCOM.LT.O. >OY1=0.
 £C             IFCOH.GT.YGRIO)OY1=YGRIO
 81             I=L2X+NMX11
 32             J=LZY»NMY11
 83      C
 fid      C         START  EXIT POINT LOOP
 85      C
 86             HAX( H=HHt I,J)
 87             HAX( ZJlHHC I.J+1 J
 88             HAX« :)=HHII+1,J*1)
 89             HAX( «lI=HHei + l,J»
 9*             oa  in  n=i»i
 91             IFCA EStHAXtm-PVALI.GE.PVOLlGO  TC  HOI  '
 92             IF JMm II) .GE.PVADHAX  .GT.PVALIGO TO  120
                G3  TC 135
           120  NUMOlT=,MimOUT*l
1C*             1F{NI»OUT.E0.1 INN1=III
1C9             IF(NlfOUT.E0.2 JNN2=III
in             GO  TCf'»22,'»2l,H26,128> ,111
111        122  OY2= MPVAL -HAX (1 M / fH AX t 2 » -MAX ( 1 H )*YGRIO
112             OX2=C.
113             GO  TC 13D
111        (I21  0X2= UPVAL-HAXI2JI/fHAX(3 )-HAX{2> > )*XGRID
II1;             OY2=fGRIO
116             GO  TC 130
117        If26  OY2= HPVAL-HAX tl) »/ CHAX C 3 > -HAX 11 » J»*YGRIO
118             OX2=XGRIO
119             GO  TC 13G
120        128  0X2= HPVAL-HAXim/tHAXID-HAXm ) )*XGRID
121             OY2=C.
122        13C  CIOE GO TO 132
12"7             NEXE1=NN1
12*             GO  TC 115
Ii9        132  IF(Nl»OUT.EQ.2JGO TO 138
130        131  WRIT£tfaT136 JL2X ,L?Y,NUMOUT,PVAL,XB IG ,YBIG
131        136  FORM JT t/,2X, 10HNO WAY  OUT , 5X , 31 1 0 » 3F1 u. 2 , / )
U2             GO  TC SCO

131      C      BEGIN SECTION  THAT  DETERMINES  PROPER PATH THRU GRID SQUARE
12r      C       CONTAINING HYPERBOLIC  CONFIGURATION.  C2 ENTRY AND  2 EXIT SIOES3
136      C
127        138  IFtPEPtOtL?X,L2YI .GT.l JGO  TO  112
13°             X10=CIDE (MM ,1 1-0X1
13°             Y1D=CIOE(N>.'1,2»-OY1
ItO             D fiA=JQRT (XID*XIO+YID*YID)
111             X IO=CIDEINN2,1 >-OXl
IM?             YIOrCIOE (MN2,2)-OY1 '  .
113             c?3= ;QRT (xin*xir«YiD*Yio)
11"             IM06? .LT.OAA)GO TO 11C
115        139  OX2=CTOE INN1 ,1 )
]M*             OY2 = C!OE (Nf = 1
157             IF(I l.GT.G.»Nn.I2.GT.O.ANC.Il.NE.I2.ANO.NENTER.GT.C)GO  TO 117
                                              127
-------

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-------
237             H=Q.
23?             DO 7f3 I=1,NCORD
229             jrNCC^D-I+1
210             IFCH'MIPPSCJJ.GE.HAVOGO  TO 755
2M1             H=H«HPPS ( JJ
2«2             XP=XE-CORO( J,l)
2«3         753 Ye=YF-CORDIJ,2)
2t«             GO TC 757
215         755 X = (H/>SC-H)/HIPPJ(J)
216             X8=XP-X*COROIJ,1I
217             Y9=Y?-X*CORO
251             IF(HYP£.LT..C001 JGO  TO 7 17
252             SINB *C=YYSC/HYPE
253             CCSB              S ArS IN I A }
256             CA=CCS(A)
257             SENTrSINBAC*CA-»COS3AC*SA
25"             C£NT:COSSAC*CA-SIN3AC*SA
25"             E\TI P=ATAN2(SENT,C£NT)
260             SSEN1=SENT
261             CCENTrCENT
262       C
26^       C           ENTER IAIN CURVILINEAR INTERPOLATE AND PLOT  LOOP
26«       C
265             00 8 C? LUPEzl.NRIMC
26«.             IFIL IPE."JE .NPTNC JGO  TO 762
267             IF(CLOS)GO TO 760
26°             SOUTrSANG
269             CCUT^CAKG
27C             60 TC 200
271         760 SOUT^SSENT
27?             CCUTZCCEVT
273             GO TC 200
27«         762 XINO:XX
27^             YINOrYY
276             ZANC :HANC*FLOAT(LUPE+1)

27?             00 76M Irl.MCORO
273             IF{H
•>0:             IFlXENO.LT.WEST.OP.XENO.GT.rAST.OR.YENO.LT.SOUTH.OR.YENO.GT.YnRTH)
3CT            ?GO TC  793
3C1             IF(I^CS)GO  TO MI46
|Cr             INCSr.TSUC.
3C.S             CALL  PLOT(XBEG-WEST,YB£G-SCUTH,3)
3S7         i»i»6 IzIPE"
30P
3C°
3C°      C     CALL  PLaT(yENO-UEST, VEND-SOUTH, I)
3 1C            NUGG rr.'UGG* 1
311            TOT=10T+HYP
31?            GO  TC  79'J
313      C
31"      C  .   BEGI>  SNAKE  INTERPOLATION FOR
                                             129
-------
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-------
39?             IFOT.CLOS.OR..N'OT.OCLABS.OR.YMAX.LT..01 JCO TO 501
44!             XPPr X"AX»W£ST
44?             YPPr V'AX + SCUTH
443             CSLL  ENDER(XKiX, YMAY,PVAL,2I
444        501  IFt. NOT.CLOS.AND.LABLI T.EO.l JCALL  ENOER f XUX ,YUY ,P V AL t 1 1
445             IFINISG.LE .^OSIMC JGO TO 502
44f             MOSINC=NUGG
447             V4LL1W=PVAL
44"        502  RETUPN
449             END
                                             131
-------
*FLOW( 1 I.ENDEP  ELT  CREATED ON 8  MY  79  AT 10:17:51
 1            StSRCUTINE ENDER«X,Y,PVAL,ICQ)
 "•            CCMPCN /CENOEQ/HONUf ,UC.OE ,HOGH,*LAS ,YLAS
 ?            DIMENSION 013)
 «      C
 e      C         TUS SU8POUTINE  IS  CALLED TO LABEL  CONTOURS

 7            OM = SC!M :48S (Y-HORHI
11            012) :43S (X-WOOE)
17            K=l
I"            or
15            00  1C 1=1.3
16            IFtD «I).6£.Of )GO  TO  10
17            DM=0 + X            CALL  PLCT{X,Y,3)
37            XLASiX
 ^            Y^Y
39         25  RfTUFN
M"        10Q  X AO=-.75*HCNU«
MI             IF(PVAL.GE.9.5.0R.PVAL.L£.t-.5))XADrXAO-MOM(f
"»3             IFCPVAL.GE.999.5.0R.PVAL.LE. t -99.5 ) ) X AO=X AO-HONUM
MU             IFII ,EC.2>XAO=.S*XAO
«5             GO  TC  20
t6             END
                                          132
-------
*FLOW(U.FIT ?Q1 CPEATED  ON  1  DEC 79 AT 10:02s3<»
 1      C •**********:»»**:»»****«*****:* ****************************** **************
 t      C  FITS A  FARAQOUA  TO  THREE POINTS, USED IN MAKING  PLOT.

 M            SUBSCUTINE  FIT{21,Z2,Z3,El,.T2,E?,A,e,C!
 ?            0:|Zl**2>*«?2-Z3J-2!*<22»*2-Z3**2>«23*tZ2**2)-72*(Z3**2)
 6            A = (El*(Z2-Z3l-Zl*(E2-E3)«E2'»Z3-'-3*Z2)/D
 7            B = ( t Z1*«2J*(E2-F.3>-E1*(Z2**?-Z3**2)+E3*«Z2**2)-E2*»?3**2» )/0
 "            C:((7t**2l*(Z2*E3-Z3*E2)-Zl*(E3*(22**2l-C2*(Z3**2IJ-»El*JZ3*C22**2)
 "           C-22* «?3»*2UJ/0
in            ff£TU(=N
11            END
                                           133
-------
*FLOWf D.VtCT FOR  CPEATEO ON 14 DEC 7S  AT  lltS^Si?
 1       C*****TO OPAW  VELOCITY VECTOR  BY  CALLING CALCOMP  SUBROUTINE
 2             SUBROUTINE VECTJAT, SAI ,AJ,AAJtAf>MIH,Af?MAX,COSFiSINFI
 ^             Y«=. Z
 5            BIrA I*COSr -«AJ*SINF
 6            8J=
 0            BBJ=-AAI*SINF»AAJ*COSF
 -5            CALL  IROHOCBI.BJ.gBI.BBJtYk^C., 12)
10            RETUFN
11            END
                                            134
-------
      D.CAPTN1 ELI  CREATED ON in SEP 79 »T 10:2S:2M
 1            SIJBRCUTIME  CAPTV1 (Pl,P2,P3,Pt,P5,Pb,Q7,08)
 ?      C******HRI1E  COMMON' HEADING FOR EACH "LOT WHETHER  TEMP  OR  VELOCITY******
 ?      C*****C (MONTH  DAY,  YEAR)} NEEDS RESET*****
 0            CALL SYMPOLC0.8,6.7CI,0.10,25HTI»E (JUNE 20,  1978»:       ,0.0,251
 e            CALL NUMBERfM.C,&.7r,0.10,P!,G.n,+l>
 *            CALL SYneoL<0.8,6.5P,0.10,25HWI»)D SPEED (CM/SEC I s       ,0.0,25)
 7            CALL NUMBERS.o,6.sc.o.10,P2,n.o,*i)
 9            CALL SYMeoL(C.8,6.30,0.10,25HUI»fO OIRECTIONfOE6/N):    ,0.0,25)
 0            CALL NUM8ERCH.O,6.3'Jta.ia,P?,a.n,.»G)
10            CALL SY."BOLt3.S,6.10,0.la,2<;HAIP TEHpEBATUREfOEG-C) :  ,0.0,25)

1?            CALL SYHSOLtoTeJs^9d!criol2^HDis2HARGE TEMProGG-CIs    ,0.0,25)
13            CALL MUMPERS.0,5.90,0.10,P5,0.0,»l)
If            CALL SYM80L(Q.6,5.70,0.1C.a^HDISCH FLOWRATE (CUM/SEC)J  ,O.C,25I
IS            CALL NUMBERS.0,5.70,0.10»P6,0.0,»1)
16            CALL SYM80Lf0.6,5.50,a.lO,2^HLEMGTH SCALEUCMr X  CM):  ,0.0,25)
17            CALL NU*BER«<».0,5.50,a.ia,Q7,O.C,-»OJ
1"            CALL SY«t80L(0.8,5.30,0.10,25HVELOClTY SCALE (CM/SEC)S  ,0.0,25)
1'            CALL HUMBERIf.C,5.3C',0.10,C8,0.0,«2J
2C            RETUPN
el            END
                                             135
-------
*FUO««11.CAPTM2 SYf CREATfD  ON  II  SEP 79 AT 2Z:29j52
 t            SUBROUTINE  CAPTN2(N)
 •>      C*****UBITE PLOT  TITLE  ON  BOTTOM OF DIAGRAM FOR CALCULATED UV****
 3            CALL SY»«eOL( l.C,-1.8, .:
-------
*fLOWtl J.CAPU'3 SYf CREATE6 OW  n  SEP  79  AT  22:31:55
 1            SU8RCU7INE CAPTN3(NI
 ?.      C****BRITE PLOT TITLE ON BOTTOM OF  DIAGRAM AND PLOCK IT****
 3            CALL SYHBOLf1.0,-2.Qt.11.29HFIG        TEMPEPATURC F"OM
 <4            CALL PLOT«-l.Q,-2.5,3)
 S            CALL PLOT«-1.0f»7.5,21
 ft            CALL PLOT(+6.5,+7.5f2J
 7            CALL PLOT«*6.5,-2.5f2>
 a            CALL PLOT(-1.0,-2.5,2»
 9            RETURN
10            END
Ifi,0.0,Z9J
                                          137
-------
*FLOUt1J.CAPTNU src CREATED  ON  11  SEP 7? *T 22:36:39
 1            SLBRCUTINE. CAPTNMSUM)
 2      C**** WRITE DEVIATION VALUEfFROM IR> ON ISOTHERM PtOT  *******
 •»            CALL SYMBOL  C0.8,-a.5,.13t23HD£VIATION FROM  IR TEHP:,0.,23l
 »            CALL MUMBEt?m.Ct-0.'5,.10f SUMtO. ,»3)
 s            RETURN
 6            END
                                   138
-------
*FLOU(1 J.CAPTNS SY* CREATED  ON 11 SEP 79 AT 22:39rH9
 1            SU8RCUTINE  CAPTNS(N,MIDEW)
 2      C*****WRITE TIDAL STAGE  AT THAT TIME*****
 3            DIKENSJON  MIDEW<<»»
 S            CALL  SYHBOLf0.8t-.7fa. 1D,IBCO,0.,<«)
 6            C«LL  SYMBOLtl.3t-.7fC. 10,i»HTIOE,0. ,t
 7            RETURN
 8            END
                                   139
-------
*FLOHI1I.CAPT16 SYP CREATED ON  tl  SEP  79 *T 22s
 «            CALL SYMBOLf 1.0,-.?.?,. 11,29HANCLOTE ANCHORAGE BY MODEL ING » .0,29 I
 5            CALL PLOT«-l.G,-2.5,3»
 6            CALL PLOT(-1.Q,»7.5,^J
 7            CALL PLOT(»6.5,»7.5,2)
 9            CALL PLOTl*6.S,-2.5,2>
 o            CALL PLOT«-l.C,-2.5.2)
1C            RETURN
11            END
-------
*FLOW{ 11.CAPTM7  SYf  CREATED ON 11 SEP  79  AT  22:«(3:36
 1            SUBROUTINE, CAPTNTfN!
 2      C*****wRIT£  PLOT TITLE ON BOTTOM  OF  DIAGRAM FOR CALCULATED  VU****
 3            CALL  SYMBOLf l.C.-U",. 1M ,:9HFIG      V» VELOCI TY , .0 , 19 I
 *            CALL  SYMBOL< 1.0,-2.?,. 1<< , 29HANCLQT E ANCHORAGE BY  MODELING , .0,29 )
 5            C4LL  PLOTC-1,0,-2.5,3»
 6            CALL  PLOTI-1.0,»7.5,^J
 7            CJLL  PLOT{*6.5,*7.5,2»
 B            CALL  PLOT(*6.5,-2.5»2)
 9            CALL  PLOT{-l.Q,-2.5,2i
10            RETURN
11            ENO
-------
*FLOW< 1) ,CAPT«8 SY" CREATED ON 11 SEP 79 »T 22s«»5:H3
 1            SUBROUTINE CAPTN8CNI
 2      C*****W=?ITE PLOT TITLE ON BOTTOM OF DIAGRAM FOR CALCULATED ELEVATION****
 3            CALL SYM80LU.C.-1.S,.1'»,25HFI&     SURFACE ELEVA T10N, .0,25 J
 1            CALL SYfSOL(l.a,-2'.2t.m,29HANCLOTE ANCHORAGE BY MODEL ING , .0129 )
 5            CALL PLOT(-1.0,-2.5,3l
 6            CALL PLOT{-1.0,«7.5,21
 7            CALL PLOT{*6.5,»7.5,2J
 f            CALL PLOT(*6.5,-2.S,*>

i?            i^
11            ENO
                                        142
-------
*FLOWt 11.CAPTN9 SYt> CREATED ON  II  SEP  7<5 AT 22:S2:
 2       C*****WR1TE PLOT TITLE  ON  BOTTOM OF DIAGRAM FCR CALCULATED TEMPERATURr****
 *             CALL SYVBCLn.C,-l.P,.l<»,27HriG      SURFACE TEMPERA TU9E , .0,27 J
 t             CALL SYMBOL! l.C,-2.2,.1M.29HANCLOTE ANCHORAGE BY MODEL ING,. C,29 |
 5             CALL PLOT{-1.0,-2.5,3)
 6             CALL PLOTt-l.Q,«7.S,2I
 7             CALL PLOT!»6.5,+7.5,2)
 a             CALL PLOT{«6.5,-2.5,2>
 "             CALL OLOTl-1.0,-2.S,2>
10             RETUFN
11             END
-------
                            TECHNICAL REPORT DATA
                      (Fleast read Inunctions on the reverse before completing)
 REPORT NO.
EPA-600/7-82-037b
                        2.
                                                3. RECIPIENT'S ACCESSION NO.
 T,TLEANDSUBT,TLE  Verification and  Transfer of
 Thermal Pollution Model; Volume II. User's
 Manual for Three-dimensional  Free-surface Mode
                                               5 REPORT DATE
                                                May 1982
                                               6. PERFORMING ORGANIZATION CODE

                                               1
 AUTMOR  s.S.Lee, S.Sengupta,  S.Y.Tuann, and
          C.R.Lee
                                                B. PERFORMING ORGANIZATION REPORT NO.
 PERFORMING OROANIZATION NAME AND ADDRESS
 The University of Miami
 Department of Mechanical  Engineering
 P.O. Box 248294
 Coral Gables, Florida   33124
                                                10. PROGRAM ELEMENT NO.
                                               11. CONTRACT/GRANT NO.
                                                EPA IAG-78-DX-0166*
 3 SPONSORING AGENCY NAME AND ADDRESS
 EPA, Office of Research and Development
 Industrial Environmental Research Laboratory
 Research Triangle Park, NC  27711
                                               13. TYPE OF REPORT AND PERIOD COVERED
                                                Fina 1 ? 3/78-9/80	.
                                               14. SPONSORING AGENCY CODE
                                                 EPA/600/13
 5. SUPPLEMENTARY
           NOTES IERL-RTP  project officer is Theodore G.Brna,  Mail Drop
61, 919/541-2683.  (*)  IAG with NASA, Kennedy Space Center,  FL 32899,
subcontracted to U.  of Miami under NASA Contract NAS 10-9410.
16.ABSTRACT The six-volume  report:  describes the theory  ot  a  tnree-dimen-
 sional (3-D) mathematical thermal discharge model and a related one-
 dimensional (1-D) model,  includes model verification at two sites, and
 provides a separate  user's manual for each model. The 3-D model has two
 forms: free surface  and rigid lid. The former, verified at Anclote An-
 chorage (FL), allows a  free air/water interface and  is  suited for signi
 ficant surface wave  heights compared to  mean water  depth? e.g., estu-
 aries and coastal regions. The latter, verified at Lake Keowee (SC), is
 suited for small surface  wave heights compared to depth (e.g., natural
 or man-made inland lakes)  because surface elevation  has been removed as
 a parameter. These models allow computation of time-dependent velocity
 and temperature fields  for given initial conditions  and time-varying
 boundary conditions. The  free-surface model also provides surface
 height variations with  time. The 1-D model is considerably more econo-
 mical to run but does not provide the detailed prediction of thermal
 plume behavior of the 3-D models. The 1-D model assumes horizontal
 homogeneity, but includes area-change and several surface-mechanism
 effects.
17. KEY WORDS AND DOCUMENT ANALYSIS
a DESCRIPTORS
Pollution
Thermal Diffusivity
Mathematical Models
Estuaries
Lakes
Plumes
13. DISTRIBUTION STATEMENT
Release to Public
b. IDENTIFIERS/OPEN ENDED TERMS
Pollution Control
Stationary Sources
19. SECURITY CLASS (This Report)
Unclassified
20. SECURITY CLASS (Thiipoft/
Unclassified
c. COS ATI Field/Croup
13B
20M
12A
08H,08J
21B
21. NO. OF PAGES
152
22. PRICE
f PA Form 2220-1 (••73)
                                   144
-------