440/9 73-003
             AUTO-QUAL MODELLING SYSTEM
                                  \
                          March 1973
               U.S. ENVIRONMENTAL PROTECTION AGENCY
                  Office of Air and Water Programs
                Monitoring and Data Support Division
                      Washington, D.C. 20460

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AUTO-QUAL MODELLING SYSTEM

            by
      Robert L.  Crim
            and
    Norman L.  Lovelace

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ERRATA:
P. 67    4 statements below statement no. 20 should
         read;

            READ(NRD,30) I,X(J),Y(J)

p. 82    statement no, 50 should read;

            50 ALPHA(J,2)-Z(J)*A(J)/XLEN

p. 154   4 statements below statement no. 20 should
         read;

            READ(NRD,30) I,X(J),Y(J)

p. 166   2 statements below statement no. 150 should
         read;

            IF(DT.GE.24.0)DT-24.0

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                        TABLE OF CONTENTS
                                                               Page
  I.  INTRODUCTION                                               i
 II.  MODEL DEVELOPMENT                                          1
      A.  Channel Representation                                 2
      B.  Hydraulic Developemnt                                 10
      C.  Quality Development
          1.  Conservative Substances                           16
          2.  Non-Conservative Substances                       19
              a.  Carbonaceous Oxygen Demand                    20
              b.  Nitrogenous Oxygen Demand                     22
              c.  Dissolved Oxygen                              23
      D.  AUT0SS Solution Technique                             27
      E.  AUT0QD Solution Technique                             31
III.  APPENDIX A (AUTOSS-PROGRAM DESCRIPTION/OPERATING
                 INSTRUCTIONS)                                  35
      A.  Program Logic                                         35
      B.  Data Description                                      40
      C.  Entering DAta                                         47
      D.  Output Description                                    50
      E.  Data Codes                                            53
      F.  Running Tips                                          54
      G.  Control  Card Example                                  55
      H.  Variable Glossary                                     56

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                                                                           1  A
     I.  Subroutine Descriptions                             58
     J.  Program Listing                                     60
     K.  Example Problem                                     95
         1.   Problem Statement                               95
         2.   Data Deck                                       98
         3.   Program Output                                 103
IV.   APPENDIX B (AUT0QD-PROGRAM DESCRIPTION/OPERATING
                INSTRUCTIONS)                                133
     A.  Program Logic                                      133
     B.  Data Description                                   134
     C.  Entering Data                                      135
     D.  Output Description                                 139
     E.  Data Codes                                         140
     F.  Running Tips                                       140
     G.  Control  Card Example                                141
     H.  Variable Glossary                                  142
     I.  Subroutine Descriptions                            145
     J.  Program Listing                                    148
     K.  Example Problem                                    190
         1.   Problem Statement                              190
         2.   Data Deck                                      191
         3.   Program Output                                 198

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 V.  APPENDIX C (APPLICATION, VERIFICATION & SENSITIVITY)   266



     A.  Application Principles                             266



     B.  Calibration Principles                             267



     C.  Sensitivity Analyses                               268



     D.  Verification Principles                            299



VI.  REFERENCES                                             300

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INTRODUCTION
     The planning requirements contained in sections 303(e) and 208
of the recently passed Public Law 92-500 (Amendments to the Federal
Water Pollution Control Act), have underscored the need for easily
operated and accurate water quality planning tools.  This report
describes two mathematical models that have been designed to meet
the specific needs of Federal, State or local planning agencies.
     These two models are subsets of a large and complex system of
models known as the "Comprehensive Modelling System" (CMS)[1].   It
was recognized early that the CMS programs were essentially experi-
mental tools for scientific investigation.  As such, they did not lend
themselves to easy operation by the general engineering community.
     At the same time it was recognized that the field of water
quality simulation was becoming self sufficient and that models were
being developed for which no one had any real use.  Large amounts of
resources were being spent attempting to modify old programs to
handle different conditions in different geographical areas.
     It seemed the proper course to develop, from anew, a set of
planning tools that incorporated the lessons learned from the CMS
programs, yet were designed with planning needs in mind.  The result
of this effort is the AUT0-QUAL set reported on here.
     The AUT0-QUAL set is designed specifically for water bodies where
widths are small  relative to their length.   Most freshwater streams
and tidal tributaries to estuarine bays fit that description.  These

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are waters whose net hydraulic circulation  patterns  are  essentially
unidirectional.
     Compatibility with the ST0RET [2]  system,  the GPSF  [3]  system
and the AUT0MAP  [4] project has been  designed  in  by  the  use  of  a
river mile index (RMI) for positioning  inputs  and diversions as well
as geometric data and physical features.  This  should  facilitate  the
storage and retrieval of the data  required  by  the models and more
closely tie the  modelling activities  to the planning process.
     The notion  of a fixed point in a freshwater  system  or a free
flowing system may seem foreign initially.   Specifically, it may  be
difficult to reconcile the transfer from the Lagrangian  framework,
best exemplified by the venerable  Streeter-Phelps [5]  equations to
the Eulerian system used in the AUT0-QUAL set.
     The reader  should recognize that the classic biochemical oxygen
demand (BOD) equation:
                                -K,t
                      L   =  L e  '
     where,           L   = BOD at any  time
                      LQ  = BOD at t=0
                      t   = time
                      ki  = deoxygenation rate
                      e   = naperian  log  base
is the integrated (with time) form of the standard first order  decay
equation i
                      dT=-kiL

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                                                                     m
which is a gross simplification of the mass transfer equation:
                                      2
                      |k =   |k  _ E 3L  + sources _ Slnks
                      3t     8x       3X2
          where;      x = distance
                      u = velocity of flow
                      E = dispersion coefficient
                      and the sink term is -kiL.
     Essentially the Streeter-Phelps equation as commonly used assumes
that all physical features are constant along a stream bed, that the
water particles do not intermingle, and that only time and decay rate
(ki) determine the resulting BOD concentration.
     There is no good reason to cling to those assumptions.  A section
of this report compares the results of the AUTO-QUAL set and the
Streeter-Phelps equation under identical conditions.  Those compari-
sons demonstrate the validity of the Eulerian framework in free flowing
streams.

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MODEL DEVELOPMENT
     The development of AUT0SS and AUT0QD has been broken Into sections.
Because the two models have many of the same properties, a general
development is given first.  The last two sections will  deal  with each
model separately and discuss the particular solution techniques used.

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CHANNEL REPRESENTATION:
     The first problem to be resolved in a model development is how
to represent the stream or estuary being modelled in terms that can
be mathematically described and represented on a digital  computer.
The method of representation used in these models is called the
"channel-junction" method.  Essentially this method consists of
dividing the natural channel into a finite number of sections (See
Figure 1).  Each of these sections contains a finite volume of water.
These sections (discrete volumes of water) are assumed to be uniform
at a given instant in time in all their properties.  This assumption
is generally referred to as the "fully mixed assumption".  Thus, any
property of this volume of water, for instance, a constituent concen-
tration, represents the average value for that volume.  This average
value has a point value at the center of the volume.  These discrete
volumes of water are referred to as junctions.
     Generally the system being modelled is not static.  There will be
flow and movement of water in the system.  Thus, the problem of repre-
senting flow and the consequential transfer of properties from one
junction to another has to be dealt with.  For this reason the concept
of channels is introduced.  Physically a channel may be thought of as
the interface between two junctions.  Computationally the channel  fs
treated as a uniform, rectangular channel between junction midpoints.
Water properties are not associated with channels.  Channels are used
(computationally) for the transfer of properties from junction to
junction.

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                                                                       3
     Various properties are associated with either a channel  or a
junction; the properties of a channel  are:
          1.  Flow (ft3/sec)
          2.  Velocity (ft/sec)
          3.  Dispersion coefficient (ft2/sec)
          4.  Cross-sectional  area  (ft2)
          5.  Depth (ft)
          6.  Width (ft)
          7.  Length (ft or miles)
     The  properties of a junction are:
          1.  Volume (ft3)
          2.  Surface  area (ft2)
          3.   Constituent concentrations (ppm)
          4.   Temperature (°C)
          5.   Evaporation - rainfall (in/month)
          6.   Inflows  (ft3/sec)
          7.   Diversions  (ft3/sec)
          8.   Reaeration  rate  (I/day)
          9.   Photosynthesis - respiration rate (gr 02/m2/day)
        10.   Sediment uptake rate (gr 02/m2/day)
        11.   CB0D decay rate  (I/day)
        12.   NB0D decay rate  (I/day)
                                       3
        13.   Constituent masses (ppm-ft )
        14.   Inflow concentrations (ppm).

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Some of the junction properties are computed from channel  values.
For instance, junction volumes are computed by using the channel
depths and widths on either side of the junction.
     The system of channels and junctions used in a model  is commonly
called the "network".  This network can be visualized as a system  of
pots (junctions) connected by hoses (channels).   The network is
established automatically in AUT0SS and AUT0QD.   However,  some basic
information is required:
          1.  Starting river mile
          2.  Ending river mile
          3.  Number of sections.
     Thus far in the network representation the  following  assumptions
have been made:
          1.  The natural channel can be accurately represented by
              a system of discrete volumes
          2.  Within each junction all  water properties are uniform
              (fully mixed assumption)
          3.  Junction values have point values  at the center of a
              junction.
These assumptions should be kept in mind when applying the models.
Experience has shown that in most applications these assumptions are
valid.   However, some caution must be exercised  in such cases as heavily
stratified estuaries or impoundments.
     The following example demonstrates how the  network is established:

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*•      1
                                       FIGURE 1
                                                          Mil* 4.0
     Mil* O.O
                     Mile-
 Mil* O.5     Mil* 1.5

           I             f
Channel  |  |  Channel 2  I  Channel 3
Mil* 2.5     Mil* 3.5      Mil* 4.5
                                                                         Channel 4

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                                                                       6
          Given the basic data:
              starting mile      =0.0
              ending mile        =4.0
              number of sections = 4
The network shown in Figure 1 would result from the above information.
     The starting and ending miles are the midpoints of the first and
last junctions, respectively.  The distance from junction interface to
junction interface is equal  to the length of the segment (ending  mile
minus starting mile) divided by the number of sections.   This  distance
is referred to as the channel length.   In AUT0SS and AUT0QD the channel
lengths are constant throughout the network.  The first and last  junction
will actually extend one-half of a channel  length outside the  defined
segment.  The stream and/or estuary being modelled is referred to as the
segment, and the term "channel" is used  as it pertains to the  network.
     At this point all  that has been done is to define the network, the
junction boundaries, and the channel lengths.   The physical  properties
(width, depth, etc.) have not yet been determined.  Most of these physi-
cal characteristics are read as input  to the program.   Those values that
are not read are computed internally on  the basis of data that has been
read.   The input data for these models is referenced to river  miles.  Once
read the input data is either interpolated to define values over  the entire
segment, or in the case of point value data (such as inflows)  it  is assign-
ed to the closest junction.
     For example, if in the network shown in Figure 2, widths  were read
in as follows:

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            FIGURE 2
700-
500-

400-

300-

200-

100-
           DATA POINT
                          DATA POINT
   0.0
T~
1.0
—I	
 2.0
 RIVER
—T"
3.0
4.0
                            MILE
     MILE 0.5 - CHANNEL I; width = 600.0ft.
     MILE 1.5- CHANNEL 2; width = 483.3ft.
     MILE 2.5- CHANNELS: width = 366.7ft.
     MILE 3.5- CHANNEL4; width = 250.0ft.

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                                                                     8
            (3  mile  0.5         width = 600.0 ft.
            @  mile  3.5         width = 250.0 ft.
The program would  assign the values of width as shown  in  Figure 2.
The interpolating  procedure, shown in Figure 2, is  used for all
physical data  (see operating instructions for definition  of physical
data) whether  it be a channel or junction parameter.
     As a general  example of how some of the internal  computations
on physical  data are done, consider the following general network:
    CH
let       d.   =  mean depth of channeT j  (ft)
           J
          As.  =  surface area of junction j  (ft2)
           J
          W.   =  width of channel j (ft)
           J
          V.   =  volume of junction j (ft3)
           J
          L   =  channel length (constant)(ft)
W. is an input to  the program, d. is computed  on  the basis of flow
 J                             J
and L is defined in  the network construction.   The remaining are
computed as follows:

                    A<;  =  (]il  + W   ^ I  (ft^-}
                    Hi-    VH. T W. -, ; L VTt )
                                            L (ft3)

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The first and last junction's values are given by:
     Last junction (nj):
                        Asnj ' VlL -
     First junction (1):
                        A$1 = W, L (ft2)
                        V] = W^ L (ft3).
In general, when values are assigned to channels and they are needed
to compute a junction parameter, the channel values on  either side of
the junction are averaged and that average value is used in the
computations.

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                                                                     10
HYDRAULIC DEVELOPMENT:
     The hydraulic solution used in AUTOSS and AUTOQD consists  of
two parts:
     1.  Determine the flows in each channel.
     2.  Determine the depths in each channel. •
The solution represents a net, steady state situation.   No attempt
is made in these models to solve the equations governing tidal
flow, storm surges, or any unsteady flow condition.   That is  why
AUTOQD is called a quasi-dynamic model.   The quality equations;  are
integrated with time using net, steady state flows.   The implicit
assumption in this approach is that the hydraulic response to
changes in flow is instantaneous, while the quality  response  lags
in time.  This assumption is acceptable in most instances.
     The first part of the solution is a simple application of  the
principle of continuity.   Consider the following situation:

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          where (h * flow rate in channel j (ft /sec)
Isolating junction j;
                                                                     11
              qout
                            evap.  _(+)
0)
let;
      j * Inflow to junction j (ft /sec)
          diversion from junction j (ft /sec)
  evap- * net evaporation minus rainfall  at junction j
      J   (inches/month)
     CF a conversion factor, to convert in/mo*  to ft/sec
                                       2
    As. * surface area of junction j (ft  )
      «l
Q. , will be given by;
 j ~ •
                                         o
   Q. .j » -Q. -qin. +qout. +evap.As.CF (ft  /sec)
The signs appear to be wrong in the above  equation,  this  is because
the sign convention used is: a flow from upstream to downstream is
defined as negative. The above procedure is  followed for  all channels
in the network, starting at the upstream end and working  downstream.

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However, the first and last junction aire computed*differently'
because 4aeJ» has only one channel connected to it.
junction (nj);
                                                                      12
               qoutnj
         Vl
          Qni_l wil1 be given by;
              (note sign convention)
Taking the first junction (1);
                qin
        QOUT
                            evap1
                                                 . if
                                                    qout,

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                                                                     13
           QOUT  (-QI) will  be given by;
 (3)          QOU   _  _      .    .qou*  -evap,As,CF (ft3/sec)
                              '       '       '   '
A  positive QOUT-.  indicates a flow out of the segment at the downstream
end. A negative QOUT, represents an inflow and its absolute value
is referred to as QIN, .
     After the above procedure has been completed, flows will have
been established in all the channels. The second part of the solution,
determining depths may proceed;
          let di = mean depth of channel i  (ft).
Depth can be given tyan equation of the form;
(4)           "l-*l.l.
           where A, ., A9 ., and A, .  are emperical constants.
                   I » •   £ 9*       3 9 *
The coefficients of equation (4) (A-, • , A9 ., A- .) are entered as
                                   l»l   *- 9*    ^ » '
point inputs and interpolated over the segment. These coefficients
may be determined from stage/discharge curves when  aval liable. In
some special cases they may be computed. For  example, assume the
Manning Equation is applicable (a special case). The coefficients
could then be determined as follows:
          U = L^§i R2/3sl/2 (ft/sec)    Manning's Formula [6]
        where;
          U = velocity (ft/ sec)
          n = Manning's coefficient
          R = hydraulic radius (ft)

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                                                                     14
          S = water surface slope (ft/ft)
Assume the channel is wide compared to its depth, then R = d.
For uniform steady flow S = slope of channel bottom (S ). Letting
                                            o
B = channel witdh (ft) and Q = flow rate (ft /sec), the Manning
Formula may be written as;
            Q    1.486  ,2cl/2
                   rT~  d bo
         solving for d,
                          0.6  0.6
         d = [    "      ]    Q
         which corresponds to;
                A
         d = AQ * + A
                      3
         with,
                           0.6
          Al =
            1
               1.48685
          A2 = 0.6
          A3 = 0.0
     In an estuary the depth of flow may be essentially invariant
with the flow magnitude. In that case A-j equals 0.0 and A3 represents
the estuary depth at mean tide level.
     There has been no distinction made between estuaries and  free
flowing streams in the hydraulic development.  Since the models use daily
average or net flows, the hydraulic differences between estuaries
and streams may be represented in the coefficients of the depth

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                                                                    15
equation. It is possible to link together the stream and estuary

in these Models.

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                                                                     16
QUALITY DEVELOPMENT
     The quality solutions used in AUT0SS and AUT0QD are based on
the mass balance equations.   A general  development is given first
and then the equations and solution techniques for AUT0SS and  AUT0QD
are given separately.
GENERAL QUALITY EQUATIONS:
CONSERVATIVE SUBSTANCES:
Isolating junctions j-1,  j,  j+1,  and channels j+1, j, j-1, j-2
Taking junction j
                    evapj   (+)
                                             qirij

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                                                                      17
          Let   C. = constituent concentration (ppm) at junction j
                 J


              C.-l =      "            "         "          "    j-1
              Cln. = Inflow concentration (ppm) at junction j

                 J   (associated with qin.)
                                         J

                V. = volume of junction j (ft3)
                 v)


Writing a mass balance for junction j



          Mass  in (during At) - [QjC.+1 + qin.Cin.] At(ppm ft3/sec)



          Mass out (during At) = [Q*_-|C. + qoutmCm] At(ppm ft3/sec)



          (Note sign convention on flows)



         AM. - Mass in - Mass out
         — i.
         At
             = -Q.^      j..    ^j -     ..
          "d • vjcj and


         AMj • V.
           J    «J
         At       At


(5)      AC. = (-QjCj+1 + qinjCin.. + Q^C.. - qout..C..) / V..(ppm/sec)
         At


If the flow were in the opposite direction the above equation would


appear as:


(6)      AC. = (Q^-iC. , - Q.C. - qout.C. + qin.Cin.) / V.(ppm/sec)
           J     J~IJ"*I    J J       \IJ      J   J     J

         At


     The flows used in equation 5 are used for further developments.


Equations 5 and 6 are applicable to purely adyective systems.  However,


in general there are exchanges due to tidal oscillations (in estuaries)

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                                                                     18
and/or turbulent dispersion (in estuaries and free flowing streams).
These exchanges are not included in equations 5 and 6,  To express
these changes, an analogy is made with Fourier's law of heat
conduction [7]
                 = -kfj-
where
              6q = the heat flow across 6A (BTU/hr)
              6A = elemental cross sectional  area (ft2)
               k = thermal conductivity (BTU/°K-ft)
               T = absolute temperature (°K)
              3j_ = derivative of temperature  in the direction of
              3n   the outward normal  n (averaged over 6A).
Integrating over A and considering the x direction
               Q - -W §
The equation says that the heat transfer per  unit time is proportional
to the temperature gradient.  The analogy is  drawn that the  mass
transfer per unit time is proportional to the concentration  gradient.
(7)            8M       9£
               at " ~LA ax
The constant of proportionality (E) is called the dispersion coefficient.
It is considered a channel property and is an input parameter.   The
dispersion coefficient is important in both models, particularly in
tidal bodies.  This feature is now added to the mass balance
equation (5):

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                                                                     19
(8)      AC. =[-0.^., + Q, |C. - qout.C. + qln-Cin-]/ V.
         	j.     j j^«    j '  J      j j      j   j    j
         At
                                                    Vppro/sec)
where
          A. = cross-sectional  area of channel  j  (ft2)
           J
          E. = dispersion coefficient in channel  j  (ft2/ sec)
           J
          L  = channel length (ft)
If qin and qout are zero and a  uniform channel  is assumed,  the above
equation reduces to the familiar form [8]:
(9)       4=Ei!c.u|£   (U = velocity)
          at     3x       x
when the limit of  L-»0  is taken.
                   MO
Equation 8 is the basis for the solution of conservative constituents.
NON-CONSERVATIVE SUBSTANCES
     The formulation for conservative substances  also apply to non-
conservative substances, however, the reactions of  the  substance with
the environment and/or other substances must  be added.
     Three non-conservative substances are  considered in these models:
          1.  CB0D - first stage (carbonaceous) Biochemical Oxygen
              Demand (BflD)
          2.  NB0D - second stage (nitrogenous) Biochemical Oxygen
              Demand (B0D)
          3.  D0   - Dissolved  Oxygen

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                                                                     20
     The oxidation of organic waste will  be broken into three stages:
          1.  Oxidation of oxidizable carbon compounds
          2.  Oxidation of ammonia (to nitrite)
          3.  Oxidation of nitrite (to nitrate)
The oxidation of the carbon and nitrogen  constituents will  be considered
separately.
FIRST STAGE OXYGEN DEMAND (CB0D)
     Theoretically this term represents the ultimate oxygen demand  of
the organic carbon compounds, (carbonaceous B0D).   It has  been reported
that this term has a theoretical value of 2.67C  [9], where  C is the
organic carbon content.  Realistically, this term  represents the oxygen
demand of inorganic compounds (chemical oxygen demand) as  well  as the
oxidation of organic waste.  To determine its value, various factors
have been developed to be applied to 5-day B0D values to obtain the
ultimate first stage oxygen demand.   These factors may vary from 1.10
to 2.40, with 1.45 being the most common.  CB0D  may be obtained from
B0D values as follows:
          Determine the deoxygenation rate K  (I/day) with  no
                                            C
          nitrification taking place.  Then using BOD5, again
          assuming no nitrification.   CB0D will  be given as:
(10)                              B0D
                        CB0D =
                              (1.0 -e   c)
          Note that if K  =0.23 (a common literature value)  then
                        C
          CB0D = 1.45 B0D5.

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                                                                     21
             If B0Dn Is known CB0D would be given as
                                   B0Dn
 (11)                    CB0D =        n
                               (1.0-e-nkc)
     The behavior of CB0D in the natural waterway is described by
the first order reaction [10]
(12)
where Kc is the deoxygenation rate in the waterway.  The complete
equation for CB0D may now be written
     let      C- = CBflD concentration in junction j (ppm)
               J
            Cin. = CBflD inflow concentration at junction j (ppm)
               J
(13)        AC.
                                                         / Vj
                                                      J/Vj
The deoxygenation rate Kc- is the rate in the stream.   K  is entered
                         J                              c
as input to the program.  The value entered is assumed to be the value
at 20°C.  Stream temperatures are also entered and K  is then corrected
                                                    \f
according to the equation [11]
(14)          K 0T°C = (K020°C) (1.047)(T"20)
               C         C
     The oxidation of the organic carbon compounds (CB0D) is assumed
to be independent of the dissolved oxygen concentration.   This assumption,
naturally, limits the application of these models to aerobic systems.

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                                                                  22
SECOND STAGE OXYGEN DEMAND (NB0D)
     This constituent represents the ultimate oxygen demand of all
the oxidizable nitrogen fractions.  The oxidations of ammonia, nitrite
and organic nitrogen are lumped together in this term.  Organic nitrogen
is included because it is generally assumed that organic nitrogen first
hydrolyses to ammonia nitrogen and the oxidation occurs.  The ultimate
NB0D may be given by [12]
(15)                NB0D = 4.57 TKN + 1.14 (NOz -N)
where TKN Is the Total  Kjeldahl Nitrogen (Organic N + Ammonia -N) and
NO? is nitrite nitrogen.  The above relationship assumes that all the
TKN and NO* -N is oxidizable.  If this is not the case an appropriate
reduction factor, as determined by laboratory studies, will have to
be applied.
     It is assumed that the oxidation of the various nitrogen fractions
(referred to as nitrification) can be characterized by one gross rate
K  (I/day).  This rate  is primarily a function of the nitrifying bacteria
populations and temperature.   Specifically, Nitrosomonas for the oxida-
tion of ammonia to nitrate and Nitrobacter for the oxidation of nitrite
to nitrate.  Despite the laboratory B0D test results, it is reasonable,
in most cases, to assume that the populations of Nitrosomonas and
Nitrobacter are sufficient, in the stream, to bring about significant
oxidation of the nitrogen fractions immediately upon their introduction
to the natural stream.   The nitrification rate K  is entered as input
to the model.   A commonly used literature value is 0.103 (I/day).  [13]
NB0D is handled in the  same way as CB0D.
(16)                   3NB0D = -K NB0D
                       ~~     n

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                                                                     23
The complete equation for NB0D is identical to the one for CB0D
except that K  replaces K.  As with K , K  is temperature corrected
             ii           c            en
according to the equation  [14]
(17)                    Kn@T°C = (Kn@20°C)(1.017)T"2°
     Nitrification is assumed to proceed independently of dissolved
oxygen in AUT0SS.  In AUT0QD, when D0 drops below 5% of the air
saturation value the nitrification rate is set to zero.
DISSOLVED OXYGEN
     Dissolved oxygen is the most complex constituent considered.  Many
factors enter into the DO budget, some of which are well  understood,
others of which very little is known.  Below are the factors in the
D0 budget considered here:
              Oxygen Gain                        Oxygen Loss
     1.  Atmospheric Reaeration         1.  CB0D
     2.  Photosynthetic Production      2.  NB0D
                                        3.  Sediment uptake
                                        4.  Biological  respiration
                                        5.  Evaporation
Some of the factors are considered as constant sources  or sinks for a
particular junction, while others are computed, such as CB0D and NB0D.
The DO budget for junction j  is written in equation form as:

-------
                                                                    24


(18)      AD0.
                           L                     L


                    CB0D. - KN NB0D.  + K2 (D0sat.-D0.)

                   j    J     j    J      j       J   J

                                As.

                -KP.-R.-Sedmt.) -rfL .  CV -evap.$0,CF/V.
                   J  J      J*4          J    J    J



where


     1.  D0j = dissolved oxygen concentration at junction  j  (ppm)


     2.  D0in- = dissolved oxygen input eoncenttrortfon  at junction  j  (ppm)


     3.  Kp CB0D. =  the rate of oxygen usage by CB00
          *•» -J   J

     4.  KN NB0a =  the rate of oxygen usage by HB0D


     5.  K2 (D0sat.-D0.) =  the rate  of the addition of  oxygen due


         to atmospheric reaeration.  K2  (I/day) is  the  reaeration

                                       j
         coefficient for junction j.   D0sati is  the  oxygen saturation
                                           J

         concentration in junction j.   Both K2   and/or D0sat. may  be


         entered as input or they may be computed within the program.


         If the computing option is chosen, the  following  methods


         are used:



        D0sat  is computed  by the  equation   [15]



               D0sati  = 14.62 -  0.367T. + 0.0045T2.(ppm)
                    J                  J           J

        where  T. is the water  temperature  (°C) at junction j.
               J

        Note:  This equation assumes  a salinity  of 0.0 parts


               per  thousand.   Equation 19  is a  simplication


               of the following  equation:

-------
                                                                     25
                    D0sat = 14.6244 -  0.367134T +  0.044972T2
                           - 0.0966S + 0.00205ST
                           + 0.0002739S2
          where S is the salinity concentration in parts per thousand
          (°/oo)- K2 is  computed  by  the Dobbin's O'Connor equation   [16]
(20)                                 12.9U *lz
                           K2 @20°C = ~~~TFr~
                             j          ffj -U
          where H  = hydraulic radius   (ft)
                 J
          and  u. = velocity  (ft/sec)
          H.  is assumed to be equal  to  the depth.
           J
          K2  is computed in the  channels and then averaged
          to obtain junction values.
          K2  is also adjusted for temperature:   [17]
(21)           K2?T°C = (K2 020°C)(1.024)T"20-°(l/day)
          With relatively minor  program changes, other equations for
          computing the reaeration  rate may be incorporated into the
          model  to replace the above equation.  The reader is referred
          to "Trtcer Measurement of Stream Reaeration" [18] and
          "Characterization of Stream Reaeration Capacity" [19]
          for  information on other  methods for determining or computing
          the  reaeration rate.
     6.    P. -  R.  (Photosynthesis - Respiration Rate) = the net
           J     J
          difference between the  production of oxygen and the usage
          of oxygen  by  biological activity other than CB0D, NB0D and
          sediment uptake.   It is a daily and volume averaged value

-------
                                                                    26
          and has the units gr.  02/m2/day.   in reality,  these terms
          are difficult to evaluate.   The reader is referred to avail-
          able literature for further information.
     7.   Sedmt.=  the net oxygen uptake of the sediments.   It is
               3                                      2
          entered as input and has the units gr. 02/m /day.   As with
          P-R this term is difficult  to accurately  evaluate.  Various
          literature values have been presented. One method for
          obtaining field measurements is presented in  "An  In-Situ
          Benthic Respirometer."  [20]
     8.   CV and  CF are units conversion factors.   The  other terms  in
          equation 18 have been  previously defined.
     The dissolved oxygen solution presented here should be  viewed as
an approximation.  For most applications most of the important sources
and sinks of oxygen have been accounted for in some form.   In many
applications the  user may find many of the terms may be  neglected.

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                                                                    27

AUTiSS SOLUTION:



   For the steady state condition the time  derivatives  of equations


(8), (13) and (18) are set to zero.  The quality  equations are written


as:


          1. Conservative Constituents.


             0 = [-QjCj^ + Qj^Cj  -  qoutjC.  +  qin^.] / Vj


(22)                   r _r                C  -r
                         •-.               U-,.  i
                                               J"'      v
                                                       v
                _
                   j      L         j-lj-V   L           j


          2. Carbonaceous Oxygen Demand  (CBOD)


             0 = [-Q.CBOD. ,  +Q. ,CBOD.  -qout-CBOD. +qin.CBODin,] / V.
                    J    JIJ*™1     J       J    J     J      J     J


                       CBOD. -CBOD. .,             CBOD. -CBOD.  ,


                           J      -1                        i-1
(23)            -


                    CBOD.
          3.  Nitrogtnous Oxygen Demand  (NBOD)


             0 = [-Q.NBOD.  ,  +0. ,NBOD.  -qout-NBOD. +qin.NBODin.] / V.
                    J     J'J*"'    J      J    J     J      J     J



                       NBOD. -NBOD..,             NBOD. -NBOD.  ,

(24)            -[EjAj (    V    J*1) Hj.^., (    JL    -H)] / Vj



                -KN NBOD.




          4.  Dissolved  Oxygen (DO)


             0 = [-QjDOj,,  ^..,00.,  -qoutjDOj ^I^DOIn,,] /  Vj



                       DO. -DO..,            DO. -DO.
(25)
                -Kr CBOD.  -Kw NBOD,  +K9  (D0sat,-D0,) -evap.CF-DO./V-
                  ^j    J    "     J    ^       J   J       J     J  J
                +(P,-R .-Sedmt . )As -CV/V,
                   J   J       J   J     J

-------
These equations are based on the same flow condition from which
equations  (8), (13) and (18) were derived. As before, all the
remaining  derivations are made on the basis of this flow condition.
Derivations for the other flow possibilties are left to the reader.
The models were designed to handle any flow possibility.
     The set of equations for a constituent now appear as a set of
linear equations with the junction concentrations as the only
unknowns. Taking the conservative equation for junction j and
solving for C. gives;
             *J
                a. o    a,- i        a.
 (26)      C  = - J'   - "J*  C    -  J
 Ub;      Cj    Bj      Bj    J-l   Bj
       where;
           8j = Wj-l - <">Utj -E/j/L    .-
         aj,l = Ej-lAj-l/L
         °J.2 = -Qj +E/J/L
         "J.3 = "1njC1nj
The coefficients for the ffrst and last junction are:
       Last junction (nj);
           3nj= -"outnj -Enj-lAnj-l/L +Qnj-l
         anj,l= Enj-lAnj-l/L
         anj,2=0
         anj,3= ^"nj01"^
       First junction (1);
           B1 = -qout] -E^^L
         al,l =0
         al ,2 = El VL +Ql

-------
The  equations for  the first and last junction are written as;
                          1 tZ *.
                            ~
 (28)      C  = -i   .      . c
           nj   Pnj      Bnj    nj  '
The coefficients for the other constituents are determined in the same
 manner as for the conservative constituents.
     The basic solution technique used in AUT0SS is called the "Gauss-
 Seidel Iterative Method "[21]. A relaxation factor has been added to the
 method to increase or decrease the rate of change. The algorithm for
 this method is decribed as follows:
          Given the system of equations;
                    al 3   al 2
             C1"3^-B^C2
             r      "2.3   "2,1 P   a2,2 ,.
                " '      "
             c  .-.
              '                  '
                    ci • •»   01 • ^
             C  . -  "J.3    n],1 ,
              "J    6             Cnj-l
          1. Assign initial values to the junction concentrations, these

-------
                                                          30
   values are approximations.
2. Starting at the first junction, compute  a  new concentration.
   Compute the difference between the old and new concentration;
      6C = Cj,new " Cj,old
   Compute and store the new concentrations as;
      Cj = Cj,old + W6C
      where w is a relaxation factor.
   Repeat this procedure for junctions 2, 3,  4,	,  n j.
3. If all the 6p's computed in step 2 are within a specified
   limit (convergence criteria) then the solution is
   complete, if not, return to step 2 and repeat. Every  time
   step 2 is repeated it is referred to as  an iteration.  The
   maximum number of iterations has been set  at  1000  (see
   MAXCYC in Subroutine S0LVEX), this value may  be changed by
   the user, if desired. The convergence criteria and u>  have
   been set at 0.001 and 1.00 respectively  (see  DELMAX and
   RELAX in S0LVEX), these may also be changed.

-------
                                                                    31

AUTPQD SOLUTION:
     The AUT0QD solution 1s naturally more complex than the steady


state solution. TN equations to be solved are essentially the  same


as those derived In the basic development, except they are left in


terms of mass changes:


          1. Conservative Constituents


             AM.

             AT ' -Vj+1 ^injCinj +Qj-lCJ  -VutjCj


(29)                     C.-C.+1              C.-C. ,
                   _r A { J  J '  \  -F   A    ( J   J M
                    E            ;   fcA            ;
          2.  Carbonace«as Oxygen Demand  (CBOD)


             AM.
                 * -Q.CBOD.+1  +qin.CBODin.  +Q._1CBOD.  -qout.CBOD.
                         CBOD. -CBOD. .,            CBOD. -CBOD.

                   _r A (    J      J  M  -E   A    (    J     J
(30)                EjY    L        J   hj-lAj-r     L



                   -1C CBOD.V.
                     Uj    J  J
                      J



          3.  Hitrogtnous  Oxygen  Demand  (NBOD)


             AM
                   -Q.NBOD.  ,  -Kjin.NBODin, +Q.  ,NBOD. -qout.NBOD.
                     w    J'     J      w   w "" '    J      \l    \/
                         NBOD. -NBOD..,            NBOD. -NBOD.
(31)                -E  A  (   J     J+l) _F   A    f    J     J
^U                 tAi             J  LA-l
                   -1C,  NBOD.V.
                    ^,-   J J
                     J


           4.  Dissolved Oxygen  (DO)


              AM.

 (32)          -I = -Q.DO.+1 ^..,00. -qoutjDOj ^qin.DOin.j

-------
                          DO.-DO. ,             DO. -DC
                         (  J   3 h -E   A   f  J
                                   '  h-A-
                    -Kr CBOD.V. -KM NBOD.V. +IC (DOsat .-DO.)V.
                      ^4    J J   MJ    J J   ^j      J    J   J
                    +(P.-R. -Sedmt.)As.CV -evap.DO.CF
     The method of integrating these equations may be called a
modified Euler Predictor-Corrector Method [22], A simplified example
of the method is:
          Gi ven ;
            let
                  A = Vl
           then,
            and,
                  Vl '  yn + I [ ^Vl/Z^n+l/g) + f (xn'yn)
     To demonstrate how this procedure is done in the program,
consider the CBOD, NBOD and DO equations. In AUT0QD, CBOD and MBOD
must be solved for concurrently with DO to yield a solution.
          Given initial conditions CBOD0., NBOD0., and DO0, and  an
                                       J      J        J
          integration step At;
          1. Compute initial constituent masses at each junction;
             CMAS? = CBODjv.
             NMAS? = NBOD°.V,
                 J       J J
             DMAS" . oojvj
          2. Compute and store mass slopes at time t;

-------
                                                            33
   ACMAS.
   -ft	J- = [equation (30)] = SC1


   ANMAS,
   •ft	>L= [equation (31)] = SN1


   AOMAS.
   •ft	1 = [equation (32)] = SO-j


3. Compute new junction concentrations at time t + At/2;


   CBODt1/2 = [SC,(At/2) + CHAS?] / V.
       j         i             J     J
   NBOD
'T    = [SMAt/2) -«• NMAS?] / V.
\|          '             J     J
     DOT1/2 = [SO,(At/2) + OMAS^] / V.
       J          I             J     J


4. Using concentrations computed in step 3, compute new mass


   slopes;


   SCp, SN2, and SOp



5. Average mass slopes at times t and t + At/2;


   SC = [SC] + SC2] / 2


   SN = [SN1 + SN2] / 2


   SO = [S0] + S02] / 2


6. Compute new masses and concentrations at time t + At;



   CMAsJ = CMAS? + SCAt
       J       J



   NMAS1. = NMAS? + SNAt
       J       J



   DMAS1, = OMAS° + SOAt
       J       J



   CBOD! = CMAS] / v.
       J       J    J

-------
             NBOD! = NMAsl / v.         '                             34
                 j       j    j
               DO! = DMAS! / v.
                 J       J    J
          7. Return to step 2, and repeat until  run is complete.
     The integration  method is the same as the  above for all  the
constituents.
     As with many integration schemes the problem of instability
can arise.  The time step (At) is the most sensitive parameter  in  the
solution. A time step that is too small  will increase the operation
cost and also increase numerical mixing. One that is too large will
result in instabilities in the solution. The most stable time  step to
use is;
(33)      At * [ L/u ]„„„,„,„,
          where; At = time step (sees)
                  L = channel length (ft)
                  u = channel velocity (tidal in estuaries and net in
                      free flowing streams) (ft/sec)
The time step as determined above will not necessarily be the  same for
all channels.
     The program will compute its own time step  based on the above equation.
The user may bypass this option and specify the  time interval  if  desired.
In some cases, the user may have to experiment to find the best time
step.

-------
                                                                     35

APPENDIX A

AUTPSS - PROGRAM DESCRIPTION/OPERATING INSTRUCTIONS

GENERAL:
     Program AUT0SS is written in ANSI FORTRAN and has been success-
fully run on the IBM 370 operating system (NIH - Bethesda, Maryland).
The program requires no input/output devices other than a card reader
and line printer.  The read and write unit numbers are presently set
at 1 and 6 respectively. These are variable and may be easily changed
(see program listing—Main program, variables NRD & NWR).  Machine
storage requirement is 105K.  A typical running time is 1.1 sees.
(compute time) per steady state solution with 150 sections.  These
times and their respective costs will vary with the computer used and
the network used.
     The program is written in a modular framework.  This type of
program construction is easy to understand and facilitates changes.
The user has a wide degree of flexibility in the use of the program because
of its construction and the input setup.   It is possible to make multi-
problem solutions within the same computer run.

PROGRAM LOGIC:
     The program is controlled by the use of "program control  cards".
These cards are read as input and consist of a word code, starting in
column 1, punched on the card.  Each control  card causes the program
to execute some function.   Usually data cards follow each program

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                                                                    36

control card.  The program control cards and their respective functions

are as follows:
     Program Control Card
      (Columns 1 thru 4)


          DATA
          FL0W
          CB0D
          NB0D
          D0
          HALT
          Any four letter
          word except one
          of the above
              Function
Directs the program to read in or replace
existing physical data.  Data cards follow.

Directs the program to read in flow data,
and compute flow related physical constants.
Data cards follow.

Directs the program to read inflow CB0D and
then to compute the steady state CB0D con-
centrations.  Data cards follow.

Directs the program to read inflow NB0D and
then compute the steady state concentrations.
Data cards follow.

Directs the program to read inflow D0 and
then compute the steady state concentrations
based on the previously run CB0D and NB0D
concentrations (if any).  Data cards follow.

Tells the program the run is complete.
Program terminates.  No data cards follow.

The program assumes this is the name of a
conservative constituent.  The program
reads the inflow concentrations and then
computes the steady state concentrations.
Data cards follow.
     These cards are the basis for the program operation.   Through their

proper use it is possible to run any number of problems  under  any number

of different conditions within one computer run.   Following is a  flow

chart showing how these cards are handled in the  program:

-------
               J&JT0SS  - GENERAL  FLOW CHART
37
Read Program
Control
Card
        No
                   Yes
                   Yes
                                           (Program\
                                           Terminates/
                                         Read  Data
                                         Code  Card

-------
    AUT0SS - GENERAL  FLOW CHART (Continued)
                                        38
No
 No
 No
Read in
Flow Data
             Read
             Inflow
             CB0D

             Compute
             Solution
  Read
  Inflow
  NB0D

              Compute
              Solution
                              Print out
                               Flows

-------
            AUT0SS - GENERAL FLOW CHART (Continued)
                                        39
       No
                  Read
                  Inflow
                  DP

                  Compute
                  Solution
                  Print out
                    Solution
Read inflow
Conservative
Constituent
Concentrations
Compute
Solution
, Print out
   Solution

-------
                                                                    40
DATA DESCRIPTION
     The data for AUT0SS are all referenced to river miles (statute).
The channel section being modelled is described by a beginning down-
stream and ending upstream mile.  The input data for the program is
divided into physical data and computational data.  For physical data
the values are read in (at river mile X, the parameter has a value Y)
and are interpolated to assign values over the entire river section.
If a parameter is constant over the river section only one value at
any river mile need be read in.  Computational data input values are
also referenced to river miles.  However, they are not interpolated
since they are considered point values.   The program may move them
slightly or in some cases combine them to conform to the channel-
junction concept used in the model.  It is important to keep in mind
that input data will be interpolated linearly between points, and
sufficient physical data points should be entered to adequately define
the channel geometry.
     The physical data associated with the stream and/or estuary being
modelled can be assembled without regard to the starting mile and
ending mile that define the section.  A data deck describing an entire
river length may be prepared and used in AUT0SS even if only very
small  portions are to be studied in any particular run.
Physical Data:
     The following is a list of the parameters that may be entered.
These values are entered under the program control card "DATA":
          1.  Al, A2 and A3:  The coefficients for the depth of flow
              equation (d=aiQ32 + a3).   They may take on different

-------
                                                           41
    meanings depending on the nature of the channel being
    modelled.  (See model development.)
2.  Width (ft):  The channel width.  Width Is assumed to
    be independent of depth.  Average widths for the flow
    condition to be run should be entered.  For instance,
    in the case of estuaries one would usually enter the
    width at mean tide level.
3.  Tidal Velocities (ft/sec):  The average tidal velocity
    (regardless of direction).  These values are usually
    only entered in the case of estuaries.  If a fall line
    is specified, the program sets the tidal velocities to
    zero above that point, regardless of what is entered.
    Velocities are used only to compute the reaeration rates
    (if that option is selected).  If no tidal  velocities
    are specified, or they are zero, the net velocity is
    computed in the flow computations.
4.  Water Temperatures (C°):  The average water temperatures
    for the condition being run.  If no values are  entered,
    the temperature is assigned a constant value of 20°C.
    Water temperatures are used to adjust the various rates
    and to compute the saturation dissolved oxygen  concen-
    trations (if that option is selected).
5.  Evaporation - Rainfall (in/month):  The net (evaporation
    rainfall) for the period being modelled.  A rainfall  is
    negative, while an evaporation is positive.

-------
                                                          42

6.  (Photosynthesis - Respiration Rate) (gr.02/m2/day):
    This represents the net production or usage of dissolved
    oxygen by biological activity, (excluding CB0D, NB0D,
    and sediment demand).  Many meanings can be attached to
    this value.  For instance, it may represent algal  decay
    downstream from a bloom.  This value represents a  24-hr.
    average and is not temperature corrected.
7.  Oxygen Uptake of Sediments (gr.02/m2/day):  The net usage rate
    of oxygen by the sediments.  It may also be used to repre-
    sent a non-point source oxygen demand.   This value is not
    temperature corrected.
8.  Dispersion Coefficients (ft2/sec):  One of the most
    important parameters in estuaries.  Tidal mixing is
    represented with this term since net flows are used. In
    tidal bodies it may have values as high as 6000 (ft2/sec).
    In free flowing systems it is generally much lower,
    100 (ft2/sec).  These values are determined by the  user.
9.  CBJ9D Decay Rates (I/day):   The first stage (carbonaceous)
    BOD decay rate or deoxygenation rate.   The program assumes
    the value entered is for 20°C, and the  rate is corrected
    to the specified temperatures according to the equation:
    K_@T=(K_<320°C)( 1.047)(T"2°).   Note that if no value is
     \f     L»
    entered for temperature the entered K  rates will  remain
    unchanged because temperature defaults  to 20°C.  If it
    is desired to change the temperature during a run  and

-------
                                                           43
     correspondingly change the rates, it is necessary to
     enter both temperature and the rate again.
10.  NB0D Decay Rate (I/day):  The second stage (nitrogenous)
     BOD decay rate or deoxygenation rate.  It is handled the
     same way as the CB0D rate except its temperature correc-
     tion equation is given as:
     (Kr|erc)=(Kn@20°C)(1.017)(T"20)
11.  Reaeration Rate (I/day):  This term represents the atmos-
     pheric reaeration rate.  It is handled the same way as
     the CB0D and NB0D decay rates except its temperature
     correction equation is given as:
     (K20T0C)=(K2»Z00C)(1 -024) ^^ -
     The user may choose to have this rate computed by the
     Dobbin's-01Connor formula.  If this rate is to be computed
     in the program and it is desired to change the temperature
     and correspondingly the computed rate, it is necessary to
     enter the flow condition again as well as the temperature.
12.  Oxygen Saturation Concentration (ppm):  The saturation
     concentration of oxygen for the conditions being run.   An
     option is available to have this computed by the equation:
     D0sat=l4.62-0.367T+0.0045T2
     where T is the  temperature (°C)
13.  Initial  Dissolved Oxygen (ppm):  The initial  estimate  of
     the DO concentrations.  It is not necessary to have values
     here to obtain  a solution, but reasonable initial  estimates

-------
                                                                    44
              will allow the solution to converge more rapidly.
         14.  Initial CB0D Concentrations (ppm).
         15.  Initial NB0D Concentrations (ppm).
         16.  Initial Conservative Constituent Concentrations  (ppm).
              The program will  only handle one set of initial  concen-
              trations for a conservative parameter at one  time.   If
              more than one conservative constituent is to  be  run it
              will be necessary to enter initial  concentrations  for
              each constituent  successively.   If  this is not done the
              initial concentrations will  remain  the same (a possible
              alternative in some cases).
     Some parameters are computed on the basis of the above inputs.
Junction surface areas are computed using the width input and  section
lengths.  When the flows are entered the depths and velocities (for
non-tidal areas) are computed as well  as cross-sectional  areas,  junction
volumes and reaeration coefficient (when the  compute option is used).
Computational Data:
     Under this category the following data are read in:
          1.  Inflows and flow  diversions (cfs).
          2.  Inflow concentrations (input concentrations)
              of the particular constituent to be run (ppm).
          3.  Boundary conditions (constituent concentrations
              at fixed points)(ppm).

-------
                                                                     45
Network Data:
     The data required to establish the computational network
(channels and junctions) is as follows:
          1.  Starting river mile.
          2.  Ending river mile.
          3.  River mile of fall line.
          4.  Number of sections.
     The fall line is the point above which there is little or no tidal
action.  When an estuary is being modelled the fall line will be at or
above the ending river mile, otherwise the tidal velocities which are
entered will be zeroed above it.  When a combination of an estuarine
and a free flowing system is being modelled the fall line will lie
somewhere in between the starting and ending mile.   When a free flowing
system is being modelled the fall line will be at the starting mile or
below it (See Figure Al).  The fall line is important since entered
tidal velocities will take precedence over the competed net velocities
downstream of the fall line.  Since velocities are only used in the
reaeration rate computation, if the reaeration rate is entered rather
than computed it is unimportant where the fall line is placed.
     The starting and ending river miles of the section being modelled
are self explanatory.  The number of sections determines the number of
channels and junctions in the network.  The maximum number of sections
as programmed is 249.  The length of the segment is divided by the
number of sections.  The points along the channel  separated by this
length represent the midpoints of the junctions.  Thus if 10 sections
are specified there will  be 11 junctions and 10 channels in the network.

-------
                  FIGURE Al
                                                                   46
                  ESTUARY ONLY
                          Fall    Ending Mile
                          Line
                                         Starting Mile
Ending Mile
                  COMBINED STREAM/ESTUARY
      Fall Line
                             Starting Mile
Ending Mile
                  STREAM ONLY
Starting
Mile
Fall  Line

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                                                                    47

ENTERING DATA
     All data Is entered under the direction of a program control card
except the run title and network data.  Before any variables are
entered or computed they are set to default values.  It should also
be noted that once a variable is entered or computed it will retain
that value until it is, re-entered or recomputed, except CB0D and NB0D
which are zeroed after each DO run.
  I.  Run Title Card
          1.  The first card of the data deck.   On this card is
              punched a title or description of the run being made.
              (Cols.  1-80)
 II.  Network Card
          1.  The second card of the data deck.  Its format is:
               Starting River Nile - cols.  1-10, include a
                                     decimal  point
               Ending River Nile   - cols. 11-20, include a
                                     declaal  point
               Nile of Fall Line   - cols. 21-30, include a
                                     decimal  point
               No.  of Sections     - cols. 31-40 (Right hand
                                     justify),  no decimal  point
III.  Entering Physical  Data
          1.  The program control  card DATA precedes the data cards.
          2.  The next card will contain the  type of data  (see data
              codes)  being entered and the number of cards to be
              entered with this  data.   The formt for this card is:

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                                                                  48
                   Data code -  starting  in  col.  1  (Left  hand  justify)
                   No.  of data  points  -  cols  12-15 (Right  hand  justify,
                                        no  decimal  point)
         3.   Next are the actual  data  cards;  there has to  be  exactly
             the number of cards  as  specified on the data code card.
             The format for these cards  is:
                   Card no.                - cols.   1-5  (Right  hand
                                              justify, no  decimal  point)
                   River mile of            - cols.  11-20  (include a
                   data point                 decimal point)
                   Parameter value         - cols.  21-30  (include a
                                              decimal point)
         4.   If other physical  data  are  to  be entered repeat  steps
             2 and 3.   There is no required order  for entering  physical
             data.  If  no other physical  data is to  be entered, a  card
             with the word ST0P punched  in  the first 4 columns, is
             placed in  the deck.
IV.   Entering Computational Data
    A.   Flows
         1.   The program control  card  FL0W  precedes  the  data  cards.
         2.   Next are the data  cards in  the following format:
                   River mile of  data  point - cols.  11-20  (include a
                                              decimal point)
                   Inflow (cfs)            - cols.  21-30  (include a
                                              decimal point)
                   Diversion (cfs)         - cols.  31-40  (include a
                                              decimal point
         3.   After the  data cards, a card with ST0P  punched in  the
             first 4 columns is placed in the deck.

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                                                               49
B.  Carbonaceous Oxygen Demand (CB0D)
     1.  The program control card CB0D precedes the data cards.
     2.  Next are the data cards in the following format:
         Note:  If it is desired to fix (establish a boundary
                condition) the concentration of a point, the
                word FIXED is punched in the first 5 columns
                of that data card, otherwise these columns
                are left blank.
         River mile of data point - cols.  11-20 (include a
                                    decimal  point)
         Inflow at data point     - cols.  21-30 (include a
                                    decimal  point)
         Inflow concentration     - cols.  31-40 (include a
                                    decimal  point)
         Fixed concentration      - cols.  41-50 (include a
         at data point (if          decimal  point;)
         desired)
     3.  After all  data cards are entered  a  card with ST0P punched
         in the first 4 columns is placed  in the deck.
         Note:  If the river concentration at a point other than
                an inflow point is to be fixed the corresponding
                inflow,simply has a value  of zero at that point.
C.  Nitrogenous Oxygen Demand (NBOfl)
     1.  The program control  card NB0D precedes the data cards.
     2.  Next are the data cards, the format and procedure are
         the same as for CB0D.

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                                                                   50

     D.  Dissolved Oxygen (D0)
          1.  The program control card D0 precedes the dati cards.
          2.  Next are the data cards, the format and procedure is
              the same as for CB0D.
     E.  Conservative constituents
          1.  The program control card with the constituent name
              precedes the data card.
          2.  Next are the data cards, the format and procedure
              is the same as for CB0D.
After all the data has been entered the HALT program control  card is
placed in the deck.
OUTPUT DESCRIPTION
     The output for AUT0SS is controlled by the program control cards.
The output is referenced to river miles as well as channel  or junction
numbers, depending on the variables.
     The first output in a run is the title and a listing of  the
general network data.  Included is the run title, mile of upstream
end, mile of downstream end, mile of fall  line, and the number of
sections.
     Each time physical data is entered  the data is printed  out
under the heading "Estuary/Stream Data".
     When a flow condition is entered two groups of information are
printed.  Under the heading "Depth or Velocity Dependent Variables"
are printed:

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                                                                    51
          1.  Cross*-sectional areas
          2.  Channel depths
          3.  Channel velocities (tidal or net)
          4.  Junction volumes
          5.  Computed reaeration rates (if this option was chosen)
     Under the heading "Steady State Flow Conditions" the inflows,
diversions, and channel flows are printed.  Channel flows may have
a negative sign due to the sign convention used.  Again, a flow
from upstream to downstream is defined as negative.
     When a constituent control card is encountered, two other groups
are printed.  Under the heading of "Steady State (Constituent Name)
Input Values" the inflow concentrations are printed.  Under the
heading of the program title card and the constituent name, the steady
state concentrations are printed and a graph of the concentrations versus
river mile is plotted.
     In addition to the regular output just discussed, there are a
number of error statements the program may issue.   These are printed
only if mistakes were made in entering data.  They are:
          1.  DATA CODE (	) DOES NOT EXIST - PROGRAM TERMINATES
              This can occur when inputing physical data.   An undefined
              data code has been entered,  the program terminates.
              User action: Correct mispunched card or misordered deck.
          2.  AN INFLOW WAS READ IN AT JUNCTION (—) (RIVER MILE XX.XX)
              IN THE QUALITY INPUT, BUT NOT IN THE HYDRAULIC INPUT,
              PROGRAM TERMINATES.

-------
                                                         52
    This message is self explanatory.
    User action: Check inflows and quality inputs for
    correspondence and correct errors.
3.  ZERO DIVIDE AT JUNCTION (---)
    A divisor formed in the steady state equations is
    zero.  This occurs when insufficient data  has been
    entered or the flow solution has determined  that  a
    junction has no flow entering or leaving and
    dispersion in the surrounding channels is  zero and
    the decay rate or volume is zero.
    User action: Check run data for completeness.
4.  ZERO DIVISOR IN (Constituent Name)  SOLUTION  MATRIX  -
    PROGRAM TERMINATES
    This follows message 3 and tells you which constituent
    has the zero.
    User action: see #3.
5.  ZERO AREA IN CHANNEL (	)
    DEPTH OR WIDTH IS ZERO PROGRAM TERMINATES
    This error occurs when the channel  cross-sectional  area,
    as computed using width and depth of flow  is zero
    Channel  widths have been entered incorrectly or a
    channel  flow was zero and the A3 flow equation coefficient
    was also zero.
    User action: Check channel flows and flow  equation
    coefficients.  Check that widths have been properly entered.

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                                                                     53
DATA CODE FOR PHYSICAL DATA
CODE (starting in col. 1)
SEDI

DISP
CDECAY
NDECAY
REAER
SATD0
INITCB0D
INITNB0D
INITD0
INIT (4 letter word of
     conservative parameter)
C-SATD0

C-REAER
DATA TYPE
                                 The coefficients for
                                 the flow equation
Channel widths (ft)
Tidal velocities (ft/sec)
Net evaporation - rainfall (in/mo)
Net photosynthesis - respiration
rate (gr.02/m2/day)
Oxygen uptake rate of sediments
(gr.02/m2/day)
Dispersion coefficients (ft2/sec)
CBOD decay rate (I/day)
NBOD decay rate (I/day)
Reaeration rates (I/day)
Oxygen saturation concentration (ppm)
Initial CBOD concentrations (ppm)
Initial NBOD concentrations (ppm)
Initial DO concentrations (ppm)
Initial conservative concentrations (ppm)
Instructs the program to compute
saturation D0 concentrations,
no data cards follow
Instructs the program to compute
the reaeration rates, no data
cards follow

-------
                                                                    54
 RUNNING TIPS
      The  purpose of this section is to bring together and Clarify the
 operating procedure for AUT0SS.  The example presented at the end of
 this appendix should also serve to clarify any remaining questions.
      As already stated, the program control cards direct the program
 to do some function.  Generally these cards act independently of each
 other; however, some general rules should be followed:
      1.  DATA should be the first control card in the deck.  This is
          because the other control cards (except HALT) use physical
          data of some kind in their respective functions.  DATA may
          be called again later in the deck to either add or replace
          physical data.
      2.  FLOW should be the second control card.  This is because the
          quality control cards use flows and values computed using
          flow in their functions.
      3.  CB0D and/or NB0D should be run before D0 if it is desired
          to consider their effects on the D0 budget.  If only CB0D or
          NB0D are to be considered only that constituent would be run
          before D0.
      4.  Subject to the above general rules the control cards may be
          arranged in any desired order to yield the desired solution(s)
A general  example of the control  and  setup is given below to demonstrate
these principles (see the end of this  appendix for  a  specific example
problem).

-------
                                                                     55
Problem Statement:
     Run IDS, CB0D and D0 under flow condition 1, then run CB0D, NB0D
and 00 under flow condition 2, then change the water temperatures (and,
correspondingly, the decay rates) and run CB0D, NB0D and D0 under flow
condition 3.
               The arrangement of the control cards would be:
Enter basic data-DATA - enter original physical  data
                 /'FLOW - enter flow condition 1
Solution 1
Solution 2
Change basic
  data
Solution 3
  TDS  - enter inflow TDS and  boundary conditions -
         compute solution
  CB0D - enter inflow CB0D and  boundary conditions -
         compute solution
  D0   - enter inflow D0 and boundary conditions -
         compute solution
 "FLOW - enter flow condition  2
  CB0D - enter inflow CB0D (these may be different than
                          the  first time)
  NB0D - enter inflow NB0D
 kD0   - enter inflow D0
- DATA - enter new temperature  and also enter decay rates
         and all  other temperature dependent variables
  FLOW - enter flow condition 3
  CB00 - enter inflow CB0D
  NB0D - enter inflow NB0D
  D0   - enter inflow D0
 k.
  HALT

-------
                      AUT0SS  VARIABLE GLOSSARY
                                56
Variable
  A(N)
  A2(N)
  A3(N)J
  ALPHA (J,K)
  AS(J)
  C(J)

  CB0D(0)
  CB0DI(J)

  CIN(J)

  CS(J)

  DECAY(L)

 .DELMAX
  DEPTH(N)
  DKl(J)
  DK2(J)
  D0S(J)
  DVD(J)

  EVAP(J)

  IPLT(I)
                Definition
cross-sectional area oT channel  N
flow equation coefficients at
channel N
K=l,3 elements of solution matrix
for junction J
surface area of junction J
concentration at junction J, not
associated with a particular parameter
CB0D concentration at junction 0
initial CB0D concentration at
junction 0
input concentration at junction J, not
associated with a particular parameter
initial conservative concentration at
junction 0
temporary storage variable used in
computations
closure criteria for solution matrix
depth of channel N
CB0D decay rate at junction J
NBJ8D decay rate at junction J
oxygen saturation at junction J
divisor in solution matrix for
junction J
net evaporation - rainfall at
junction J
temporary storage variable used in
computations and output routines

-------
                                                                  57
RMFR
RMJ(J)
RMUP

RN(I)

SEDMT(J)

TEMP(J)
V(N)
V0L(J)
WIDTH(N)
X(D

XLEN
XMIL
XNpD(J)
XN0DI(J)

Y(D

Z(N)
river mile of fall line
river mile of junction J
river mile of upstream end of
segment
temporary storage variable used
in computations and output routines
sediment oxygen uptake rate at
junction J
temperature at junction J
velocity at channel N
volume of junction J
width of channel N
temporary storage variable used in
computations and output routines
channel length in feet
channel length in miles
NB0D concentratioaat junction J
initial NB0D concentration at
junction J
temporary storage variables used in
computations and output routines
dispersion coefficient for channel N

-------
                                                                   58
 SUBROUTINE DESCRIPTIONS
      Following is a brief description of each subroutine in AUT0SS.
 MAIN  BRANCH:  The main program.  Its primary function is to direct
 program functions and print out the heading.  The basic network data
 is read in here.
 SETUP:  Two things are done in this subroutine.  The network of channels
 and junctions is established, and arrays are set to their respective
 default values.
 NETDAT:  This is one of the most important routines in the program.
 All data (except flow and quality data) is read in here.  The data is
 read  and interpolated over the entire network, and values are assigned
 to the channels or junctions.
 FLJWS.:  The flow inputs are read.  Once read, the flow inputs (or outflows)
 are distributed through the network.
 FJJ5CMP;  Called from FL0WS.  The depths of flow and channel velocities are
 computed.  Tidal velocities, if specified, take precedence over velocities
 computed,  Once depths of flows are computed, the various physical para-
 meters, depending on depth, are computed.  (Cross-sectional areas, junction
 volumes, depths, velocities).  In addition reaeration rates are computed
 if this option is specified.
 pjJAJ-IN:  The quality inputs are read in.  Once read in the inputs are
 assigned the proper junction.  If more than one input is read in for  a
 junction, they are balanced accorddng to their respective flow?; and
 concentrations.  According  to the equations:  qin=zq  and  cin=~^—, it is
                                                             Zq
also possible to fix mile points  at  a  specified  concentration.

-------
                                                                   59
QALCMP:  The elements of the quality matrix are determined.  CB0D,
NBflD and conservative parameters are done.
D0CMP:  The elements of the quality matrix for dissolved oxygen are
determined here.
S0LVEX:  The quality matrix is solved by the Gauss-Sidel iteration
method with a relaxation factor.  The maximum number of iterations
is assigned as 1000 with a closing criteria of 0.001  ppm and a relax-
ation coefficient of 1.00 (These may be changed if desired).
INTER:  Called from NETDAT.  The routine arranges an array of input
data in order according to river mile and assigns data values for
each junction or channel.
TABU:  Called from INTER.  TABU performs a linear interpolation to
obtain a data value at a specified point.
0UTG0:  An output routine.  It prints out data in tabular form.
DIVCK:  Checks for zero divisors in the quality matrix.   If a zero
divisor is found, the error message is printed out and the program
terminates.
JKFND:  Determines the junction number for a corresponding river mile.
QAL0UT:  An output routine for quality data.  A heading is printed
followed by the data listing.
GRAPH:  Constructs and prints  a graph of the quality solution.   It is
called from QAL0UT.

-------
                                                                   60
PROGRAM LISTING:
Following is a listing of program AUT0SS:

-------
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                                  MAIN  PROGRAM  (Can't.)
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-------
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-------
                            MAIN  PROGRAM (Con't.)


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-------
                             SUBROUTINE  SETUP
                                                                                      65
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                                                                            66
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                                                                                   69
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                                                                                         70
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-------
SUBROUTINE FL0WS (Con't.)
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-------
                           SUBROUTINE  FL0CMP


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                          SUBROUTINE FL0CMP  (Con't.)

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-------
                           SUBROUTINE QUALIN
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-------
                              SUBROUTINE  QUALIN  (Con't.)

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-------
                               SUBROUTINE QALCMP
                                                                                      80
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-------
           SUBROUTINE  QfllLCMP (Con't.)
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                            SUBROUTINE  D0CMP


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                              SUBROUTINE  0UTG0

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EXAMPLE PROBLEM
Given the following river/estuary
                                                                  95
                         ,500 cfs


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     mile 100.0
mile 75.0
mile 50.0
mile 0.0
and the following information:
     1.  Number of sections = 49
     2.  Fall  line at mile 50.0
     3.  Width at mile  0.0 = 10,000.0 ft
         Width at mile 40.0 =  5,000.0 ft
     4.  Dispersion coeff.  at mile    0.0 =  5,000.0 ft2/sec
         Dispersion coeff.  at mile    50.0 =   100.0 ft2/sec
         Dispersion coeff.  at mile   100.0 =    50.0 ft2/sec
     5.  Tidal  velocities  = 1.5 ft/sec
     6.  Temperature = 25.0 °C
     7.  Evaporation - rainfall  =0.0 in/mo
     8.  Photosynthesis -  respiration rate @ mile   0.0 = 1.5 gr 02/m2/day
         Photosynthesis -  respiration rate @ mile  50.0 = 0.5 gr 02/m2/day
         Photosynthesis -  respiration rate @ mile 100.0 = 0.0 gr 02/m2/day
     9.  CB0D  decay rate =  0.23 at 20 °C
    10.  NB0D  decay rate =  0.12 at 20 °C

-------
                                                                   96
11.  Sediment oxygen uptake rate at mile  0.0 = 1.0 gr 02/m2/day
     Sediment oxygen uptake rate at mile 50.0 = 0.5 gr 02/m2/day
     Sediment oxygen uptake rate at mile 75.0 = 1.0 gr 02/m2/day
     Sediment oxygen uptake rate at mile 80.0 = 0.0 gr 02/m2/day
12.  Al at mile 100.0 =  0.02
     Al at mile  51.0 =  0.05
     Al at mile  50.0 =  0.0
13.  A2 at mile 100.0 =  >0.6
     A2 at mile  51.0 =  0.6
     A2 at mile  50.0 =  0.0
14.  A3 at mile 100.0 =  0.0
     A3 at mile  51.0 =  0.0
     A3 at mile  50.0 = 15.0
PROBLEM STATEMENT
Run IDS (conservative) with mile 0.0 fixed  at 20,000.0 ppm and the
above conditions.  Then, using computed  reaeration  rates and the
following inputs:
     Mile 100.0 (5000 cfs)    CB0D =  6.0 ppm
                             NB0D =  6.0 ppm
                             D0   =  6.0 ppm
     Mile  75.0 ( 500 cfs)    CB0D = 20.0 ppm
                             NB0D =20.0 ppm
                             D0   =2.0 ppm
run CB0D, NB0D and D0.

-------
                                                                    97
     Next, run IDS with the flow at mile 100.0 changed  to 1000.0 cfs
and the same downstream boundary condition.   Initial  concentrations
are assigned as follows:
     CB0D and NB0D    =      3.0 ppm
     D0               =      7.0 ppm
     IDS at mile  0.0 = 20,000.0 ppm
                 50.0 =    100.0 ppm
The data deck for this problem follows:

-------

-------

-------

-------

-------
                                                                 102
Several things should be noted:
     1.  CDECAY and NDECAY are entered after temperature.  Had they
been entered before the temperature, they would not be corrected since
the temperature would have had its default value (20°C) at that time.
     2.  The order of entering physical data makes no difference except
temperature dependent values should be entered after the temperature.
     3.  When a value is constant over the entire section, only one
value need be entered - at any river mile.
     4.  CB0D and NC0D were run before D0, because the D0 solution
uses the CB0D and NB0D solutions.
This problem was run on the IBM 370 system at the National Institutes
of Health facilities at Bethesda, Maryland.  The total time was 4.39
seconds (excluding compile time) at a cost of $6.62 (excluding compile
cost).
The output for this problem follows:

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                                                                133

APPENDIX B
AUT0QD - PROGRAM DESCRIPTION/OPERATING INSTRUCTIONS
GENERAL
     AUT0QD and AUT0SS are very similar in their construction and
their method of use.  Only the main differences in operating procedure
will be discussed.  The reader should read the AUT0SS operating  instruc-
tions first.  The main differences in the operation of the models  lie
in the entering of computational  data.
     AUT0QD is written in the same language as AUT0SS and  requires
the same input/output devices.  Machine storage requirement is 115K.
Typical  running time is 0.15 second (compute time) per day of simu-
lation for a 150 section network.  These times will  vary depending on
the computer used, the network used, the constituents being modelled,
and the integration step.
PROGRAM LOGIC:
     AUT0QD is also controlled by "program control cards".   Their  format
is the same as in AUT0SS.  The program  control  cards and their respective
functions are:
     Program Control Card                       Function
     (Cols. 1  thru 4)
           DATA                      Same as AUT0SS
           FL0W                      Same as AUT0SS
           CB0D                      Directs the program  to read  in
                                     the input CB0D values and  then
                                     compute CB0D for the specified
                                     period.  Data  cards  follow

-------
                                                                134
     Program Control Card                          Function
     (Cols. 1 thru 4)

            NB0D                      Directs the program to read the
                                      input NBjDD values and compute
                                      NB0D for the specified period.
                                      Data cards follow.

            D0                        Directs the program to read input
                                      CB0D, NB00 and 00 values and then
                                      compute CB0D, NB0D and D0 for the
                                      specified period.  This; is differ-
                                      ent from AUT0SS, because CB0D and
                                      NB0D are done simultaneously with
                                      D0.  Data cards follow.

            HALT                      Same as AUT0SS

     Any 4-letter word                The program assumes this is the
     except the above                 name of a conservative parameter.
                                      Input values are read, and the
                                      concentrations are computed for
                                      the specified period.

DATA DESCRIPTION

     The data for AUT0QD have the same characteristics as the data for

AUTjBSS.  The physical and network data is identical for both programs.

The computational data is the same except additional information is

needed for time keeping:

     1.  Beginning and Ending data of period (day-month-year), e.g.

         (1-10-1971).

     2.  Print period (days):  This number specifies the number of days

         between quality print outs.  If a period consists of 50 days

         and the solution is to be printed every 5 days, the print

         period would be 5.  If the print period is omitted the program

         will assign a value of 1 day.

-------
                                                                135

     3.  Integration time step (hours):  This is the integration step
         used in the program.  It must be less than or equal to 24
         and an even divisor of 24.  If no value is entered the program
         will compute its own time step.  (See model development,  AUT0QD
         solution.)
     The meaning of initial  concentrations changes slightly in AUT0QD
In AUT0QD they are considered as starting concentrations.   Since
continuous simulation can be done with AUT0QD the starting concentra-
tions are updated every integration step (time step).   Concentrations
at the end of one period become the starting concentrations for next
period.
ENTERING DATA
     Data is entered under the direction of a program control  card,
except the run title and network data.   As in AUTJ9SS variables are
zeroed or set to default values before data is entered or  computed.
       I.  Run title card
               Same as AUT0SS
      II.  Network card
               Same as AUT0SS
     III.  Entering physical  data
               Same as AUT0SS
      IV.  Entering computational  data
           A.  Flows
               1.   The program control  card FL0W precedes  the  data
                   cards.

-------
                                                            136

     2.  Immediately after the program control  card Is the timing
         card which specifies the dates of the  flow period to  be
         entered:
         Beginning month number:   cols.  1- 2 (right hand  justify,
         (1-12)                              no decimal point)
         Beginning day number  :   cols.  4- 5 (right hand  justify,
                                             no decimal point)
         Beginning year        :   cols.  7-10
         Ending month number   :   cols. 16-17 (right hand  justify,
                                             no decimal point)
         Ending day number     :   cols. 19-20 (right hand  justify,
                                             no decimal point
         Ending year           :   cols. 22-25
     3.  Next are  the data cards  in the following format:
         River mile of data point:   cols.  11-20 (include a decimal
                                                point)
         Inflow (cfs)            :   cols.  21-30 (include a decimal
                                                point)
         Diversion (cfs)         :   cols.  31-40 (include a decimal
                                                point)
     4.  After the data cards a card with ST0P  punched  in  the  first
         4 columns is placed in the deck.
B.  CB0D
     1.  The program control card CB0D precedes the data cards.
     2.  Immediately  after the program control  card is a  card
         which specifies the dates of the period, the print
         interval, and the integration step (optional):

-------
                                                      137
    Beginning month number


    Beginning day number


    Beginning year


    Ending month number


    Ending day number


    Ending year

    Print interval
    (optional)

    Integration step
    (optional)
cols.  1- 2 (right hand justify,
            no decimal point)

cols.  4- 5 (right hand justify,
            no decimal point)

cols.  7-10 (right hand justify,
            no decimal point)

cols. 16-17 (right hand justify,
            no decimal point)

cols. 19-20 (right hand justify,
            no decimal point)

cols. 22-25

cols. 31-35 (right hand justify,
            no decimal point)
              »
cols. 41-50 (include a decimal
            point)
3.  Next are the data cards in the following format:

        (Note: If it is desired to fix (establish a boundary
        condition) the concentration of a point, the  word
        FIXED is punched in the first 5 columns of that data
        card; otherwise, these columns are left blank.)

    River mile of data point:   cols. 11-20 (include a decimal
                                           point)
    Inflow at data point
cols. 21-30 (include a decimal
            point)
    Inflow concentration at :   cols. 31-40 (include a decimal
    data point                             point)
    Fixed concentration at
    data point (if FIXED
    option is chosen)
cols. 41-50 (include a decimal
            point)
4.  After all data cards are entered,  a card with ST0P punched

    in the first 4 columns is placed in the deck.

-------
                                                            138
C.  NB0D
    1.  The program control card NB0D precedes the data cards.
    2.  The rest of the cards have the same format as CB0D.
D.  Conservative constituents
    1.  The program control card with the constituent name on it
        precedes the data cards.
    2.  The rest of the cards have the same format as for CB0D.
E.  D0
    1.  The program control card 00 precedes the data cards.
    2.  The next card is the same as CB0D.
    3.  Next are the data cards in the following format:
         River mile of data point
         Inflow at data point

         CB0D inflow concentration
         NB0D inflow concentration
         00 inflow concentration
         CB0D fixed concentration
         (if desired)
         NB0D fixed concentration
         (if desired)
         D0 fixed concentration
         (if desired)
cols. 11-20 (include a decimal
            point)
cols. 21-30 (include a decimal
            point)
cols. 31-37 (include a decimal
            point)
cols. 38-44 (include a decimal
            point)
cols. 45-51 (include a decimal
            point)
cols. 52-58 (include a decimal
            point)
cols. 59-65 (include a decimal
            point)
cols. 66-72 (include a decimal
            point)
4.  After all data cards are entered a card with ST0P punched  in the
    first 4 columns is placed in the deck.

-------
                                                                   139
After all the data has been entered the HALT program control card is
placed  in the deck.
OUTPUT  DESCRIPTION
     The output for AUT0QD is also controlled by the program control
cards and is referenced to river miles as well as to channels or junctions.
     The first items printed are a title and listing of the general net-
work data.  Included here is the run title, mile of upstream and downstream
end, mile of fall line, and the number of sections.
     Each time physical data is entered, it is printed out under the
heading "Estuary/Stream Data".
     When a flow condition is entered two groups of information are
printed.  Under the heading "Depth or Velocity Dependent Variables for the
Flow Period Month, Day, Year thru Month, Day, Year", the following are
printed:
              1.   Cross-sectional Areas
              2.   Channel  Depths
              3.   Channel  Velocities
              4.   Junction Volumes
              5.   Computed Reaeration Rates (if the compute option is used)
     Under the heading "Flow Conditions for the Period Month, Day, Year,
thru Month,  Day,  Year" the inflows,  diversions and  channel  flows are
printed.  The same sign convention is used  as in AUT0SS.
     When a  constituent control  card is encountered, two  other groups are
printed.  Under the heading (Constituent Name) "Input Concentrations for
Month,  Day,  Year  thru  Month,  Day, Year: the input concentrations for the

-------
                                                                140
period are printed.  The solutions are printed under the heading of
the run title and (Constituent Name) "Concentrations for the Period
(Month, Day, Year) thru (Month, Day, Year)" at interval  specified.
     In addition to the regular output, error messages may be printed.
These are the same as AUT0SS except there are no zero divisor messages.
DATA CODES FOR PHYSICAL DATA
     Same as AUT0SS
RUNNING TIPS
     The same general rules apply to AUT0QD as in AUT0SS;  however,
there are some differences due to the different types of solutions.
         1.  DATA should be the first control card for the same reasons
             as for AUT0SS
         2.  FL0W is the second control card.  The dates entered under
             the FL0W card have no computational  significance; they are
             for the user's reference.  A flow condition will  continue
             to be used in the program until it is replaced.
         3.  CB0D and/or NB0D are run simultaneously with D0.   They can
             be run separately if desired, however, they will  have  no
             effect on the DjJ budget if they are.
         4.  The starting (initial) concentrations for a constituent
             are updated every integration step.
     A general example of control card setup is given below (see the end
of this appendix for a specific example problem)

-------
                                                                  141
PROBLEM STATEMENT
     Given flow condition 1, which represents flow from 1/01/72 to
2/01/72, and flow condition 2, which represents flow from 2/02/72 to
3/01/72.  Run TDS with 4 downstream boundary conditions (1/01/72-
1/15/72, 1/16/72-2/01/7?, 2-02/72-2/15/72, 2-16/72-3/01/72) print out
values every 2 days.  Run CB0D, NB0D and D0 with 4 different input
conditions (same dates as TDS) print solutions every day, and let the
program compute the time step.
The arrangement of the control cards would be:
               DATA  -  enter physical  data
                     -  (1/01/72 - 2/01/72)
    =«*=
    o
    •J3
    •»—
    •o
    o
    o
                    (1/01/72 - 1/15/72)  Print interval  = 2
                    (1/01/72 - 1/15/72)  Print interval  = 1
                    (1/16/72 - 2/01/72)  Print interval  = 2
                    (1/16/72-2/01/72)  Print interval  = 1
                    (2/02/72 - 3/01/72)
§          TDS   -  (2/02/72 - 2/15/72)  Print interval  = 2
E        j
'•5       <  D0       (2/02/72 - 2/15/72)  Print interval  = 1
                    (2/01/72 - 3/01/72)  Print interval  = 2
                    (3/16/72 - 3/01/72)  Print interval  = 1

-------
                                                                 142
                      AUT0QD VARIABLE GLOSSARY
Variable
  A (N)
              Definition
  CBDIN(J)


  CBPD(J)

  CIN(J)


  CS(J)


  DELT

  DELT2

  DELTD

  OKI(J)

  DK2(J)

  D0S(J)


  EVAP(J)


  IDAYB

  I DA YE

  IM0B

  IYRB
cross-sectional area of channel N


flow equation coefficients at
channel N


surface area of junction J

concentration at junction J,
can be any parameter

CB0D input concentration at
junction J

CB0D concentration at junction J

input concentration at junction J
can be any parameter

conservative constituent concen-
tration

timestep (sec.)

half timestep (sec.)

timestep (hrs.)

CB0D decay rate at junction J

NB0D decay rate at junction J

oxygen saturation concentration
at junction J

net evaporation minus rainfall
at junction J

beginning day

ending day

beginning month

beginning year

-------
                                                                 143
IYRB
IYRE
K2FL

LALPHA(K)
MFS(K.I)

NBEG
NC
NDAYS
NEND
NFS(K)
NJ
N0JFX
NPRT
NQCYC
NRD
NSES
NWR
0XIN(J)

0XY(J)
PH0T0(J)

Q(N)
QIN(J)
Q0UT(J)
beginning year
ending year
flag to tell if reaeration rates
are to be computed
run title
Ith fixed parameter at Kth fixed
junction
period beginning day number
number of channels
number of days in a period
period ending day number
K   fixed junction number
number of junctions
number of fixed junctions
print interval
number of timesteps per day
card reader unit number
number of sections
line printer unit number
D0 input concentrations at
junction J
D0 concentration at junction J
photosynthesis minus respiration
rate at junction J
flow in channel  N
inflow at junction J
diversion at junction J

-------
                                                                144
REAIR(J)

RMC(N)
RMDUN
RNFR
RMJ(J)
RMUP
SEDKT(J)

TEMP(J)
V(N)
VJBL(J)
WIDTH(N)
XCMAS(J)
XLEN
XMASS(J)
XMIL
XNDIN(J)

XNNAS(J)
XN0D(J)
X0MAS(J)
Z(N)
reaeration coefficient at
junction J
river mile of channel N
downstream river mile
river mile of fall line
river mile of junction J
upstream river mile
sediment uptake rate at
junction J
water temperature at junction J
velocity in channel N
volume of junction J
width of channel N
CB0D mass in junction J
channel length in feet
constituent mass in junction J
channel length in miles
NB0D input concentration at
junction J
NB0D mass in junction J
NB0D concentration at junction J
D0 mass in junction J
dispersion coefficient in channel  N

-------
                                                                   145
SUBROUTINE DESCRIPTIONS
Following is a brief description of each subroutine of AUT0QD
MAIN BRANCH
     Same as AUT0SS
SETUP
     Same as AUT0SS
NETDAT
     Same as AUT0SS
FL0WS
     Same as AUT0SS, except the dates of the period are also read in
FL0CMP
     Same as AUT0SS
VAULIN
     The dates of the quality period, the print interval  and time step
     (optional) are read.  In addition, the quality inputs are read
     and assigned to the proper junction.  D0 is not considered here.
     If more than one input is read in for a junction, they are combined
     according to their respective inflows and concentrations.   Junctions
     may also be fixed.  Conservative constituents, CB0D  and NB0D, may
     be entered here.
VALCMP
     The quality equations are integrated over the period specified in
     VAULIN.   The concentrations are printed at the specified  intervals
     (print interval).

-------
                                                                   146
CDERIV
     The quality derivatives are evaluated.   This routine Is called
     from VALCMP.
VD0IN
     The period dates, print Interval  and time step are read,  as  in
     VALCMP.  The input CB0D, NB0D and D0 concentrations are read.
     The D0 title for this quality output is printed.
VD0CP
     The CB0D, NB0D and D0 equations are integrated over the period
     specified in VD0IN, and the solutions are printed  at the  specified
     interval.
PDERIV
     The CB0D, NB0D and D0 derivatives are evaluated.
JKFND
     Same as AUT0SS
SERIAL
     Converts a date (month, day, year) into a corresponding day
     number.
TABU
     Same as AUT0SS
INTER
     Same as AUTflSS
CALEN
     Converts a day number into a corresponding (month, day, year).
0UTG0
     Same as AUT0SS

-------
                                                                  147
PROGRAM LISTING



Following is a listing of program AUT0QD:

-------
                                       MAIN  PROGRAM
                                                                                                    148
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-------
                                        149
MAIN PROGRAM (Con't.)

-------
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-------
                               MAIN PROGRAM  (Con't.)                        151
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-------
                                SUBROUTINE  SETUP
                                                                                       152
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                             SUBROUTINE SETUP  (Con't.)
                                                                          153
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-------
SUBROUTINE NETDAT
                                            154
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                       SUBROUTINE  NETDAT  (Con't.)
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-------
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SUBROUTINE FL0WS (Con't.)
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                              SUBROUTINE  FL0CMP
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SUBROUTINE FL0CMP (Con't.)                 165

-------
                           SUBROUTINE  FL0CMP  (Con't.)
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SUBROUTINE VAULIN
                                             167
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SUBROUTINE VAULIN  (Con't.)
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                            SUBROUTINE VAULIN  (Con't.)
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-------
                          SUBROUTINE VALCMP

                                                                                170
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-------
                            SUBROUTINE  VALCMP  (Con't.)

                                                                               171
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-------
                   SUBROUTINE VALCMP  (Con't.)

                                                                  172
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-------
                          SUBROUTINE CDERIV

                                                                                173
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-------
                         SUBROUTINE VD0IN

                                                                                174
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-------
                        SUBROUTINE VD0IN  (Con't.)
                                                                                 175
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-------
                               SUBROUTINE  VD0IN  (Con't.)
                                                                                            176
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-------
                             SUBROUTINE  VD0IN  (Con't.)

                                                                                        177
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-------
SUBROUTINE VD0CP
                                             178
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-------
                          SUBROUTINE  VD0CP  (Con't.)
                                                                                  179
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-------
                        SUBROUTINE VD0CP  (Con't.)
                                                     180
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-------
                                                                  190
AUTgQD EXAMPLE PROBLEM
The stream/estuary system used  in the  AUT0SS  example  is used  for  this
example.  The input data is the same except for  the flow at mile  100.0
(River Flow) and the TDS (Total Dissolved  Solids)  boundary condition
at mile 0.0.
PROBLEM STATEMENT
Using the steady state values obtained  in  the AUT0SS  example  problem
(5000 cfs at mile 100.0), as initial values,  run the  same constituents
(TDS, CB0D, NB0D, D0) for a continuous  20  day period  (January 1-20, 1973)
using the following inflows and downstream TDS boundary conditions:
     Jan.  1- 5   Flow Q mile 100.0 =   6000 cfs
                  TDS  @ mile    0.0 =   18000 ppm
     Jan.  6-10   Flow @ mile 100.0 =   8000 cfs
                  TDS  @ mile    0.0 =   15000 ppm
     Jan. 11-15   Flow 9 mile 100.0 =   6000 cfs
                  TDS  @ mile    0.0 =   18000 ppm
     Jan. 16-20   Flow @ mile 100.0 =   5000 cfs
                  TDS  @ mile    0.0 =   20000 ppm
CB0D, NB0D and D0 inflow concentrations will  remain the same  for  the
entire period.  Have the program compute its  own time step and print
out qualities every day.
The data deck for this example  is as follows:

-------

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                                                                   198






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                                                                  266
APPENDIX C
APPLICATION, CALIBRATION. VERIFICATION, AND SENSITIVITY
     In the past much effort was spent in the planning effort
evaluating alternative water qaulity management schemes.   It was
this type of analysis that stimulated the use and growth  of mathe-
matical techniques.  Little or no effort was spent determining the
reliability of the individual  models in predicting absolutes.
     It was then considered that the ability of a model to reproduce
nature was secondary to its ability to predict differences between
alternatives consistently.   Considering the defined problems of that
time, it was certainly proper to take that viewpoint.
     Since that time, water quality standards have been introduced.
These standards are absolutes in terms of defined quantities of
that may be present in the receiving waters.  Plans and proposals  must
now be weighed not only against each other but ultimately against  the
"standards".  Plans which will not allow the receiving water quality
to be at or above standards must be rejected as infeasible on the
basis of standards.
     The introduction of water quality standards, and  the civil  and
criminal penalties for their violation, adds a new dimension to
mathematical modelling for water quality planning.  The model  user
must now be concerned with the accuracy of a technique  as well  as
its consistency.

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                                                                267
MODEL CALIBRATION:
     There are constants and coefficients of functions inherent
in the AUT0-QUAL set that can not be directly determined or
measured.  For example, there are no methods for making direct
field measurements of dispersion coefficients (E). The reader may
recognize these quantites as being:
          1. Dispersion coefficients (E)
          2. CBOD decay rate (Kc)
          3. NBOD decay rate (KN)
          4. Reaeration rate (K2).
     While techniques exist  for the determination of KC and KN, the
wide range of values obtained in the tests of the replicate
samples preclude considering KC and KN as "knowns".  Similarly,
field measurements for the determination of the reaeration rate
(Kg) show a wide range of values.  The Dobbin's - O'Connor formula
is currently the most common function used, and as such it is
considered to be the standard form.
     Dispersion is probably the most obvious calibration coefficient
in the above group. The elimination of tidal effects in the flow
computations demands that some mechanism be incorporated in the
model to represent the smearing of the quality profiles by the
tides (See Model  Development).
     Those inputs to the model  that can be directly measured
or determined with good reliability are considered as knowns.
Since the calibration process consists of matching a predicted
profile (or profiles) to an observed profile by means of adjusting

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                                                               268
the calibration constants.  Any errors in the knowns will  be
incorporated into the calibration constants.
     The primary knowns and their sources are:
          1. Flow - from streamflow gages operated by State or
                    Federal agencies or direct  field measurements.
          2. A-], Ap. A- - from stage/discharge  records maintained
                    by State or Federal agencies or direct field
                    measurements.
          3. A- (in estuaries) - nautical charts or field measurements.
          4. widths - charts, maps or direct measurements.
          5. Q  .  (amount and location) - diversion records.
          6. Q.   (amount and location) - waste water records  or direct
                    measurement (direct measurement is preferable)
          7. Water temperature - direct field measurements or  existing
                    records.
          8. Tidal velocities - current tables  or direct  measurements.
          9. Sediment uptake of oxygen rate - direct measurements  or
                    existing records.
         10. Photosynthesis-Respiration rate -  direct field measurements
                    or existing records.
     Where field measurements are indicated, they must be made at  the
same times as the observed  profiles.  To do otherwise is  to assume
that those inputs are in fact constant.  The above list may, of course,
be tailored to the particuliar constituents under considerartion.

SENSITIVITY:
     The following figures  illustrate the sensitivity of  the AUT0-QUAL
set to normal variations in the magnitudes of the important varibles.
The reader should study the figures and experiment with his own systems
to get a better feeling for the effects of the  different  factors.

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                                                                 269
     AUT0SS was generally used to compute the sensitivity
profiles. The effects are identical in AUT0QD. Figure C16 shows
the convergence of the AUT0QD solution, over time, to the AUT0SS
solution. Since natural streamflow and waste sources are rarely
constant for the period of time required for a body of water
to reach a steady state condition in water quality, AUT0QD should
be used in the calibration process. The calibration coefficients can
then be transferred to AUT0SS for the planning runs.

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          FIGURE Cl

SCHEMATIC DIAGRAM OF  ESTUARY/STREAM
USED IN SENSITIVITY ANALYSES
270
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                                                                   271
     The following data values were assigned to the example

stream/estuary system:

          Mile of upstream end      150.0
     Mile of downstream end

     Mile of fall line

     Number of sections

PHYSICAL DATA;
          Ar>
             Miles 0.0 thru 48.0
             @ mile 50.0
             § mile 150.0
                                      0.0

                                     50.0

                                     150
                                   A,=0.0
                                   A,1 =0.040
                                   A=0.025
             Miles 0.0 thru 48.0
             0 mile 50.0
             Miles 50.0 thru 150.0
                                   A=0.0
          A3;
             @ mile 0.0
             @ mile 50.0
             Miles 50.1 thru 150.0

          Widths;

             @ mile 0.0
             @ mile 50.0
             Miles 50.0 thru 150.0

          Tidal Velocities;

             @ mile 0.0
             3 mile 25.0
             @ mile 50.0
             Miles 50.1 thru 150.0

          Dispersion Coefficients;

             @ mile 0.0
             @ mile 10.0
             @ mile 20.0
             @ mile 30.0
                                   A=20.0
                                   Width=21200.0 ft.
                                   Width=l000.0  ft.
                                   Width=l000.0  ft.
                                   V.=1.2 fps
                                   V^=0.8 fps
                                   V:>0.6 fps
                                   V^=0.0 fps
                                   E=5000.0 ft£/ sec
                                   E=4300.0 f
                                   E=3500.0 ftp/ sec
                                   E=2200.0 ft /sec

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                                                                  272
             (a mile 40.0                E=1200.0 ft?/sec
             @ mile 50.0                E=400.0  ft«/sec
             @ mile 55.0                E=100.0  ftf/sec
             Miles 55.0 thru 150.0      E=100.0  ftVsec
When point values are specified, the program will  interpolate
linearly between the points for intermediate values.
     These values will remain the same for all  the runs  on the
example stream/estuary, except where changes are specified.  The
other inputs are specified for each run.

-------
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                             FIGURE C2

                    EXAMPLE RUN WITH ONLY CBOD INPUTS
                             (AUT0SS)
                                                               273
10.0-


9.0-


8.0-


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6.0-


5.0-


4.0-


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 1.0-
                 DISSOLVED OXYGEN
                 FIRST STAGE BOO  (CBOD)
        10   20  30   40
                                50  60   70  80   90   IOO   110  120  130 140  ISO

                                        RIVER  MILE
     INPUT DATA:
     TEMPERATURES:
     @ mile 0.0  T=28.0°C
     g mile 25.0 T=25.0°C
     & mile 75.0 T=20.0°C
     Miles  75.0 thru 150.0 T=20.0°C

     CBOD DECAY RATE = 0.23(l/day)

     NBOD DECAY RATE = 0.1 03(1 /day)

     SEDIMENT UPTAKE;
                                          COMPUTED REAERATION RATES

                                          COMPUTED OXYGEN SATURATION
                                          CONCENTRATIONS

                                          INFLOW DATA:

                                          @ mile 150.0
                                            2000.0 cfs * «!• «-°e)20.0p|m CBOD »

     PHOTOSYNTHESIS-RESPIRATION RATES       ?                   O.Oppm DO
     Miles  0.0 thru 30.0   P-R =-0.2(gr.02/mp/day)
     @ mile 35.0           P-R =-1.0(gr.O«/m /day)  ml'e 45.0
     @ mile 50.0           P-R = 0.0(gr.b,/m,/day)  200-° cfs PSO.Oppn
     Miles  50.0 thru 150.0 P-R = O.Ofgr.O^/m /day)              O.Oppm DO

-------
                          FIGURE C3

                  EXAMPLE RUN WITH CBOD AND NBOD INPUTS
                          (AUT0SS)
                                                         274
Q.
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 .*x
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                            %       ..
                            j»       • •
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         0   10  20  30  40  50   60  70  80  90  100  110  120  130  140  150

                                     RIVER  MILE


     SAME INPUT DATA AS FIGURE C2 WITH THE FOLLOWING INFLOWS:

         & mile 150.0
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         @ mile 145.0
           150.0 cfs eiOO.Oppm CBOD &  50.0ppm NBOD & O.Oppm DO

         @ mile 65.0
           50.0 cfs  @12Q.Oppm CBOD &  GO.Oppm NBOD & O.Oppm DO
           mile 45.0
           200.0 cfs @50.0ppm CBOD & SO.Oppm NBOD & O.Oppm DO

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                             FIGURE C4


                   BASE CONDITION FOR SENSITIVITY RUNS

                             (AUT0SS)
                                                            275
&
O.
I
UJ
u

I
10.0



 9.0



 8.0



 7.0



 6.O-i



 5.0



 4.0



 3.0



 2XH




 1.0
DISSOLVED OXYGEN

FIRST STAGE BOD  (C BOD)

SECOND  STAGE BOD  (N BOD)
                             A       A
                             /:-.xx.^ j
                            / : •    •'   \
                           ' :  '•  •'    i
                         / .-'   —     :
          0   10  20   30  40   50  60   70  80  90   100  110  120  130  140  150

                                       RIVER MILE
     INPUT DATA:


     TEMPERATURE * 20.0°C


     CBOD DECAY RATE = 0.30(l/day)


     NBOD DECAY RATE = 0.10(1/day)


     SEDIMENT UPTAKE =0.0 (gr.02/m2/day)


     (P-R> = 0.0 (gr.02/m2/day)


     REAERATION RATE = 0.30(l/day)


     COMPUTED OXYGEN SATURATION CONCENTRATIONS


     OTHER INPUT DATA IS THE SAME AS FIGURE C2
                                       INFLOW DATA:


                                       SAME AS FIGURE C3

-------
                                FIGURE C5
                                                                276
2
Q.
O.
10.0-




9.0-



8.0-



7,0-



6.0-



5.0-



4.0-



3.0-



2.0-



1.0-
                    EFFECT OF CBOD DECAY RATE (KC)


                               (AUTJDSS)
                 Kc = 0.lO( '/day)

                 Kc = 030('/day)

                 Kc = O.SCX'/day)
          0   10   20  30   40   50  60  70   80   90  100   110  120  130  140  ISO

                                         RIVER  MILE
                     INPUT AND  INFL0W DATA IS THE SAME AS FOR FIGURE C4,

                     EXCEPT THE CBJDD DECAY RATE HAS BEEN VARIED

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                                FIGURE C6



                      EFFECT OF NBflD DECAY RATE (Kp)



                                (AUT0SS)
                                                               277
a
a
10.0-




9.0-



8JO-



7.0-




6.O-




5.0-



4JO-




3.0-



2.0-




 1.0-
              	Kn = 0.10 ('/day)

              	Kn= 0.20 ('/day)
          O   10   20  30   40  SO  6O  70   80  90  IOO  IIO I2O  130  I4O  ISO


                                         RIVER MILE
                INPUT AND INFL0W DATA IS THE SAME AS FOR FIGURE C4,

                EXCEPT THE NB0D DECAY RATE HAS BEEN VARIED

-------
                                 FIGURE C7



                      EFFECT OF  REAERATION RATE (K2)



                                 (AUT0SS)
                                                                   278
a
a
10.0-




 9,0




 8.0-




 7.0»




 6.0-




 5.0-




 4.0-




 3.0-




 2.0-
                  K2=0.2{'/doy)

                  K2= 0.3 (^day)


                  K2=0.4('/day)
              10  20   30  40   50   60  70   80  90   100  110  120  130  (40  150
                                        RIVER  MILE
                 INPUT AND INFL0W DATA IS THE SAME AS FOR FIGURE C4»

                 EXCEPT THE REAERATION RATE HAS BEEN VARIED

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                         FIGURE C8



                 EFFECT OF SEDIMENT UPTAKE



                         (AUT0SS)
                                                                   279
a.
a
10.0-



 9.0
 7.0-




 6.0-




 5.0-




 4.0-




 3.0-



 2.0-




 1.0
                 •S«diiMf)t = 0.0 (gr O2/m2/doy)


                 S«dim«nf = 1.0 (gr O2/m2/doy)

                 S«dim«nf = 2.0(gr O2/m2/day)
        10  20   30  40   SO  60   70  80  90  100  110  120  I3O  140  ISO


                                 RIVER  MILE
        INPUT AND  INFLOW DATA IS THE SAME AS FOR FIGURE  C5,

        EXCEPT THE SEDIMENT UPTAKE  HAS BEEN VARIED

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                                FIGURE C9

                EFFECT OF PHOTOSYNTHESIS - RESPIRATION RATE

                                (AUT0SS)
                                                             280
a
a
O
a
lO.O-i

 9.0

 8.0-

 7.0-

 6.0-

 5.0-

 4.0-

 3.0-

 2.0-

 1.0-
               	CP-R) = -l.Otgr 02/roVday)
               -(P-R)  =0.0{gr O2/m2/doy)
               .-(p-R)  = * l.0(gr 02/m2/day)
         0   10  20   30  40   50  60  70  80  90   100   110   120  130  140  !50
                                      RIVER MILE
              INPUT AND  INFL0W DATA IS THE SAME AS FOR FIGURE C4,
              EXCEPT THE PHOTOSYNTHESIS-RESPIRATION RATE HAS BEEN VARIED

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                              FIGURE CIO

                        EFFECT OF TEMPERATURE

                              (AUT0SS)
                                                              281
      11.0-

      IO.O-


      9.O
Q.
a
o
o
ao-

7.0-

6.0-

5.0-

4JO-

3.0-

2.0-

1.0-

  0

                 T=IO.O*C
                •T=20.0*C
                •T = 30.0*C
              10   20  30   40  50   60  70   80  90  IOO  110  120  130  I4O  ISO

                                       RIVER  MILE
               INPUT AND  INFLJDW DATA IS THE SAME AS FOR FIGURE C4,
               EXCEPT THE STREAM TEMPERATURE HAS BEEN VARIED
               Note:

               D.0.  Saturation Concentrations
                                        10°C = 11.4  ppm
                                        20°C =  9.08 ppm
                                        30°C =  7.52 ppm

-------
                                   FIGURE Cll

                           EFFECT OF DISPERSION COEFFICIENT

                                    (AUT0SS)
                                                                 282
a
a
O
o
10 -

 9 -


 8 -

 7 -


 6 -


 5 -

 4 -


 3 -

 O w


 I  -

 0 -
E='/2Eo
E = Eo
E = 2Eo
                i    i    i     i    i     i    i     I     i    i     I     r    i     I     I
                10  20  30  40  50   60   70  80   90   100  110   120  130  140  ISO
                                         RIVER MILE
                INPUT AND INFL0W  DATA IS THE SAME AS FOR FIGURE  C4,
                EXCEPT THE DISPERSION COEFFICIENTS (E) HAVE BEEN
                VARIED.  E0 ARE THE DISPERSION COEFFICIENTS SPECIFIED
                IN FIGURE C4.

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                          FIGURE C12

             EFFECT OF DISPERSION COEFFICIENT

                          (AUT0SS)
                                                                283
P
a
a.
                                20          30         40

                                  RIVER  MILE
          INPUT AND INFL0W DATA IS THE SAME AS FOR FIGURE C4,
          EXCEPT SALINITY IS BEING RUN WITH THE DOWNSTREAM END
          FIXED AT 15000 ppm.   THE DISPERSION COEFFICIENTS ARE
          VARIED AS SHOWN WHERE E_ ARE THE DISPERSION COEFFICIENTS
          SPECIFIED IN FIGURE C4.   ONLY THE ESTUARY  PORTION IS
          SHOWN BECAUSE THE SALINITY CONCENTRATIONS  WERE NEGLIGIBLE
          IN THE FREE FLOWING SECTION.

-------
                                                                 284
     To demonstrate the use of AUT0QD a run was made on the same
hypothetical stream/estuary that was used for the AUT0SS examples.
A hypothetical hydrograph and downstream boundry condition (salinity
concentration^ were chosen for this example (see Figure CIS).  Notice
that the hydrograph and the downstream concentration are represented
in a stairstep fashion.
     The same general input data used in AUT0SS has been used for
AUT0QD.  A steady state solution (AUT0SS) for the 2000.0 cfs flow
condition was used for starting concentrations.  A time step of 1
hour was specified for the run.  Figures C14 & C15 show the results
of the model run, only the estuary portion was shown because the "
salinity concentrations were negligible in the free flowing portion.

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                             FIGURE CIS
                                                                 28D
      9000-
ui

I

"o
Q.
a


o
 •
o

UJ
16000



14000



IZOOO



10000



8000



6000



4000



20OO-
               I    I
                  JANUARY  1-31
                                       FEBRUARY 1-28

-------
P
a.
Q.
Z
                               FIGURE C14


                  AUT0QD RUN RESULTS  - SELECTED POINTS
286
                             MILE  0.0  - FIXED BOUNDRY CONDITION
                      JANUARY 1-31
                                          DAY

-------
                        FIGURE CIS



             AUT0QD RUN RESULTS - SELECTED DATES
     287
P
a
a
         0 -i
                              .JAN. I

                                 ,JAN. 10
                                 ,JAN. 15
                                      JAN. 20
                                            JAN. 25
                                              JAN. 30
                      10
40
5O
                                  RIVER  MILE

-------
                                                                   288
      Figure C16 shows a comparison of the AUT0SS steady state
 solution and the AUT0QD solution as it approaches steady state.
A  condition with a total fresh water inflow of 2300.0 cfs
 (2000.0 cfs river flow and 300.0 cfs total for inputs 1, 2 & 3),
 and the downstream concentration fixed at 15000.0 pprn, was chosen
 for this example. The starting concentrations for AUT0QD were
 purposely chosen not to coinicide with the AUT0SS steady state to
 better see the two solutions converge. The inputs for these runs
 are the same as for Figure C4.

-------
            FIGURE C16
COMPARISON OF AUT0SS AND AUT0QD
WHEN RUN UNTIL STEADY STATE
289
 (ONVSnOHl M3d SlUVd) AilNHVS

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                                                                   290
     For the next set of runs a uniform, free flowing stream
was selected. The charateristies of this stream are defined  as
follows:
          T—	'	~	•	'	•—'	"—•	—I
           I                                                 i
           i                                                 l
           i                                                 '
      mile 100.0                                       mile 0.0
          Mile of downstream end        0.0
          Mile of upstream end        100.0
          Mile of fall line             0.0
          Number of sections          100
     PHYSICAL DATA;
          A^ 0.04
          A2= 0.60
          Width = 1000.0 ft.
          CBOD decay rate = 0.6@20.0°C (I/day)
          DO Saturation = 10.0 ppm
          Reaeration rate = 0.4@20.0°C (I/day)
     All other physical data assumes their respective default
     values.
     INFLOWS;
          @ mile 100.0     1000.0 cfs at 10.0 ppm CBOD &
                           10.0 ppm DO
     All runs have these values as inputs, except for the stated
variations.

-------
                                                                291
     By using a uniform stream it is possible to make comparisons
between the model solution and an analytical solution. For these
comparisons the integrated forms of the Streeter-Phelps DO sag
equation are used [23];
          „       r
                  c
          D .
           c   KA
          x^=
       where;
          D = dissolved oxygen deficit (ppm) (saturation concentration
              minus stream concentration)
          I* in stream BOD (ppm) at X=0, for this application L =10.0
           0  ppm at river mile 100.0 (X=0)                     °
          KD= deoxygenation rate (I/day), corresponds to CBOD decay rate
          K.= reaeration rate (I/day)
          X-= distance to location of maximum deficit (miles)
          U = stream velocity (miles/day)
          DC= maximun DO deficit (ppm)
These equations are resticted to the case where the initial deficit
(@ X=0) is zero, which is the condition specified in the runs.
(DO saturation = 10.0)

-------
                          FIGURE C17

                        EFFECT OF A!

                           (AUT0SS)
                                               292
2
Q.
Q.
         9 H
         8 H
         7 H
         6 H
         3 H
         2 H
                                              o
	A, = 0.02

	 A, =0.04
	A, = 0.06
O    Streeter — Phelps Equation - Computed Sag
                               Point.
                  T
                 10
20   30
                    1
                    40
50
 I "
60
 I
70
 I
80
90    100
                                  RIVER  MILE

-------
                             FIGURE CIS
                            EFFECT OF A2
                              (AUT0SS)
o.
a.
O
o
10

 9 -

 8 -

 7 -

 6 -

 5 -

 4 -

 3 -

 2 -
              O
A2 = 0.4
A2=0.6
A2 = 0.8
Streeter —Phelps Equation — Computed Sag
                         Point.
                  I     i^    III1     i     I      I     l
            0    10   20   30   40   50    60   70   80    90   100
                                  RIVER MILE

-------
                 FIGURE C19

  EFFECT OF Ai  WITH COMPUTED REAERATION RATES
294
                  (AUT0SS)






5
a
a
O
0






10-
9-

8-
7-
6-


5-

4-

3-

2 -
1 -
•
n-

^****^^;- •••-.. .••'']
NX"^
X^ts//

xd




A- n r\?
| — \J.\JC.
A 	 f\ f\ A
M | — U.VJ*f
	 A ,= 0.06
O Streeter — Phelps Equation — Computed Sag
Point.


0     10    20   30   40   50    60    70   80   90   !00
                       RIVER  MILE
        Ai HAS BEEN VARIED AND REAERATION  RATES
        HAVE BEEN COMPUTED RATHER THAN SPECIFIED
        AT 0.4 (Vday).

-------
                            FIGURE C20

             EFFECT OF A2 WITH COMPUTED REAERATION RATES

                            (AUT0SS)
                                                     295
          10
a.
Q.

O
O
9-


8-


7-


6-


5


4-


3-


2-


 I-


0
                 O
A2 = 0.4

A2=0.6
A2=0.8

Str««t«r — Phdps Equation — Computed Sag
                          Point.
                 10   20   30   40   50   60   70   80    90   100
                                   RIVER  MILE
                   A2 HAS BEEN VARIED AND REAERATION RATES
                   HAVE BEEN COMPUTED RATHER THAN SPECIFIED
                   AT 0.4 (Vday)

-------
                     FIGURE C21

               EFFECT OF  INCOMING LOAD

                      (AUT0SS)
                                                             296
c>
ci
4.0


30 -


20 -


 1.0 -


 0
                                                       O
             	 L0 = I2.5ppm (+25<%)

             	 LQ = 10.0 ppm

             — — — • LQ = 7.5 ppm (-25<#»)

               Q   STREETER-PHELPS EQUATION-COMPUTED  SAG  POINT
           i
          10
                  20    30
 I      1      I
40    50    60

 RIVER  MILES
 I
70
 I
80
 1
90
100
              THE INCOMING CB0D  CONCENTRATIONS
              AT MILE 10Q.O (LQ) HAVE  BEEN VARIED.

-------
                     FIGURE C22

                 EFFECT OF FLOW RATE
                                             297
50 -


40 -


30 -


20 -


 10 -
 0 -
   LEGEND

   •••• QlOO = 1250cf» (+25«7b)

       QIOO = lOOOcfs

	Q|00 = 750cfs (-25*%)

       STREETER-PHELPS  EQUATION-COMPUTED SAG  POINT
          i      I      r     r     i     i      i      i      i      i
          10    20    30    40    50   60    70    80    90    100

                            RIVER   MILES
           THE  INFLOW AT MILE 100.0 (Q100) HAS BEEN VARIED-

-------
                           FIGURE C23

                      EFFECT OF NETWORK SIZE
                                                   298
£L
a
o
0
10


 9 -


 8 -


 7 -


 6 -


 5 -


 4 -


 3 -
10 SECTIONS (L= 10 MILES)
50 SECTIONS (L- 2 MILES)
100 SECTIONS (L=l MILE)
200 SECTIONS (L= V2 MILE)
Str««t«r - Phelps Analytical Solution
         I  -
           0
         r
         10
    i
   20
30
 r
40
SO
 I
60
 I
70
 I
80
 I
90
100
                                 RIVER MILE
                    THE SAME  INPUT DATA HAS BEEN USED
                    AND THE NETWORK SIZE HAS BEEN VARIED.

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                                                                  299
 MODEL VERIFICATION:
     As stated under Model Calibration, errors in the known quantities
will be absorbed by the calibration coefficients. The model verification
process should indicate the amount of such errors and give a measure
of their effect on the model's prediction of other conditions.
     The verification procedure requires that the same amount of
information that is required by the calibration step be collected
and used as input to the model (AUT0QD).  The computed or predicted
quality profiles are then compared to the observed profiles.
     The two sets of profiles should be in close agreement. If they
do not agree within the normal range of laboratory errors, some
investigation should be made into the nature of the problems. All of
the major inputs to the model should be checked for errors under
bothethe calibration conditions and the verification conditions.
     In most cases the source of the errors will  be found in the
input data. The use^s knowledge of the prototype system and the model's
sesitivities will be the most valuable guides.
     In some cases it may be desirable to recalibrate the coefficients
using both observed data sets. The user must be cautioned, however,
that in such cases he will not have a verified model, and another
verification period must be monitored, predicted and compared.
     Common sense Indicates that extreme conditions, such as periods
of heavy algal blooms, drought conditions, or winter temperatures should
not be used for either the calibration or verification steps. The
various rates and functional  forms incorporated in the AUT0-QUAL
set are not generally adequate to describe extreme conditions.

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                                                                        300
                                    REFERENCES

      1.   Crim5 Robert L.,  "A System of Mathematical Models  for Water
          Quality Management," Technical  Report  51, U. S.  Environmental
          Protection Agency,  Region  III,  Annapolis  Field Office,,
          January 1972.

2,.3, 4.   ST0RET, CPSF and  AUT0MAP are  components of the Water Quality
          Information System  operated by the Monitoring and  Data Support
          Division of the Office of  Air and Water Programs,  U. S.
          Environmental Protection Agency, Washington, D.  C.

      5.   Streeter, H. W. and E.  B.  Phelps,  "A Study of the  Pollution and
          Natural Purification of the Ohio River, Part III,  Factors
          Concerned in the  Phenomena of Oxidation and Reaeration/ U. S,
          Public Health Service,  Public Health Bulletin 145,  1925.

      6.   Henderson, F. M., "Open Channel Flow." Macmillan Company,
          New York, p. 69,  1966,

      7.   Hansen, A. G., "Fluid Mechanics," John Wiley and Sons, New York,
          p.  121, 1967.

      8.   Thomann, Rovert V., "Systems  Analysis  and Water  Quality
          Management," Environmental Research and Applications, Inc.,
       .   New.-York, p.- 129, 1971.

      9.   "Effects of Polluting Discharges on the Thames Estuary," Water
          Pollution Research, Technical  Paper No. 11, Dept.  of Scientific
          and Industrial Research, Her  Majesty's Stationery  Office,
          London, p. 216, 1964.

     10.   See Reference # 5.

     11.   See p. 96 of Reference # 8.

     12.   See p. 221 of Reference #  9.

     13.   See pp. 218-219 of  Reference  # 9.

     14.   See p. 219 of Reference #  9.

     15.   Hyer, P. V., C. S.  Fang, E. P.  Ruzecki, and W. J.  Hargis, Jr.,
          "Hydrography and  Hydrodynamics of Virginia Estuaries, Part II,
          Studies of the Distribution of Salinity and Dissolved Oxygen
          in  the Upper York System," Special Report in Applied Marine
          Science and Ocean Engineering Number 13,  Virginia  Institute
          of  Marine Science,  Gloucester Point, Virginia, p.  41, August  1971.

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                                                                 301
16.  O'Connor, D. J. and W. E.  Dobbins, "Mechanism of Reaeration
     in Natural Streams," Transcript American Society of Civil
     Engineers, Vol. 123, 1958.

17.  See p. 8 of Reference # 8.

18.  Tsivoglou, E. C., "Tracer  Measurement of Stream Reaeration,"
     Federal Water Pollution Control Administration, U.  S.  Department
     of the Interior, Washington, D. C.,  June 1967.

19.  Tsivoglou, E. C. and J. R. Wallace,  "Characterization  of Stream
     Reaeration Capacity," Project No.  16050 EOT,  Office of Research
     and Monitoring, U.  S. Environmental  Protection  Agency,
     Washington, D. C.,  October 1972.

20.  O'Connell and Weeks, "An In-Situ  Benthie Respirometer," CB-SRBP
     Technical Paper No.  6, Federal  Water Pollution  Control Admin.,
     Middle Atlantic Region, U. S. Department of the Interior,
     Washington, D. C.

21.  McCalla, T. R., "Introduction to  Numerical.Methods  andJF0RTRAN"
     Programming," John  Wiley and Sons, New York,  pp.  180-185,  1967.

22.  See pp. 310-313 of  Reference #  21.

23.  "Simplified Mathematical Modeling  of Water  Quality," Hydroscience,
     Inc.,  Environmental  Protection  Agency, p. 72, March 1971.

-------