EPA 905-73-001
Water Quality Model Of The
Lower Fox River, Wisconsin

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                                  ABSTRACT





     A mathematical  model  describing the interrelationship  between  the



dissolved  oxygen  concentration of a river and its various sources  and sinks



has h2f:n adapted  for use in a study of the Lower Fox River  in  Wisconsin.



Th; analysis  Assumes steady-state conditions and describes  the longitudinal



di-t.'-ib"i;ion  of dissolved  cxygen in the river from Neanah-Menasha  to Green



j?,y, a distance of  aporoximately ^0 milss (64.4 km).



      .~h2 mo^c-1 was  verified f'O'- various conditions of waste loading, river



tri^-c'tur: .  -nc!  river  flow.   The rnouel w^s then used to evaluate  the effect



CP WF.V..- au-ility  o-.r imnlementing interim bsst practicable control  technol-



ogy :ff"i,,ent  linji^.ticns for industrial dischsrners and  90  percent  SOD re-



r.^vr I frrvn iTn^iicir-al  '\dSbe ^ciirces, as fin sstiMi\-Lt. of levels  of treatment



required jy th= 1972 Amsndner.ts to the Federal  Hater Pollution Control Act



v*-fluGnt limits will  result in a



si^Tifinrit -irMprcvomont in water quality in lih? Lr'v^r Fax Pover.  A daily



average dissolved oxygen concentration of 4 to 5 mg/1 will  be  maintained



under most flc-w conrjitions.   During an extrpma Inw flow  and high temperature



sitmtian, trie dissolved nxyqsn cr-n--:;itr \ticn cnip'1 drop to Z  to 3  mg/1.

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                             TABLE OF CONTENTS



                                                                         PAGE
LIST 0!-' 1ABLES                                                             i



LIST OF FI3URES                                                           ii



NOMENCLATURE,                                                             iii



INTRODUCTION                                                               1



MODEL PEi/ELOPMENT                                                          4



     Theory                                                                4



     Initial Conditions                                                    7



     Atmospheric Reaeration                                                B



     Biochemical Oxygen Demand                                             fl



          Carbonaceous BOD                                                 fl



          Mitrogencus BOD                                                 1°



     PhutGsynthdsis and Respiration                                       12



     Benthic Oxygen Demand                                                15



     Raaeration Over Dams                                                 18



     Physical Parameters                                                  15



     Sieche Effect                                                        20



     Survey Data                                                          23



     Proposed Effluent Limitations                                        24



RESULTS                                                                   27



      Mod2! Verification                                                  27



      Model Sensitivity                                                   32



      Water Quality Prediction                                            32



                nf Occurrence Below Given Dissolved Oxygen Levels         43

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                                                                       PAGF



SUf-WARY                                                                 44



ACKNOWLEDGEMENTS                                                        45



REFERENCES                                                              46



APPENDIX                                                                4fl



     Prugratn Listing



     Documentation



     Input - Output

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                               LIST OF TABLES.

TA3LE                                                                  £AGE_

   '1     Ratio of Ultimata  to  Carfaanv:c:t;ns LsHD                          10

   Z     Spatial Variation  cf  Alcjc.1  Oxygen Pt">c'uctirn and
            Respiration                                                  15

   3     P.eijerLtinn 0/or Dam:                                            19

   4     Physical Parameters                                             21-77.

   T     'i'.irimary of V'ste Discharges                                    25

   5     Node"! V?n"f:cctiort Ss^sltr-'Hy                                 33

   7     Summary nf Medal Input  !'Ht?                                    37

   a     Mod^l Prediction Sensitivity                                   40

   9     Frequency of Occurrence Ralow Given Dissolved Oxygen
         Levels at Mile Point  7.3                                       43

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                               LIST OF FIGURES

FIGURE                                                                  PAGE

   1     Map of the Lower  Fax  River                                      2

   Z     Mass Balance  of Total  Nltrorjei                                 ^

   3     Model Verification, Au"i-rt T1, T°7i                            2B

   4     Model Verification, Ou*e 20-21, 19?2                           29

   5     Model Verification, J-j'y S-G, 1?7?                             30

   6     Model Verificatfcin, J-ily I*  >~72                              31

   7     Model Prediction,  197.?                                         35

   B     Comparison of 1978 P^e'V-Tti".; Cnnditions to
         June, 1972 Survey  n?,ta                                         3S

   9     Sensitivity to Benthi<; w'-.i  • '••"vt:.d                           ^^

  ID     Sensitivity to Algal  Oxj-'jc'i •  "

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                                 NOMENCLATURE
     n   =   coefficient nf dam rtaeration
     A   =   river crass-sectional area
     c   =   concentration of dissc'i/cd oxygen
    ca   =   dissolved oxygen s^ove : de-.i
    C[]   =   dissolved raxygen helo.v -j darn
chl-a   =   concentration of Chlorophyll-a
    cs   =   saturation  value of Jiri.nin/yj oxygen
     D   =   deficit  af  dissol"ed oxygen
    Da   =   deficit  of  dissolved uxvg^n above a dam
    D[,   =   deficit  of  dissolved oxygen below a dam
    DQ   =   initial  dissolved cxygen deficit
     F   =   percent  of  the  ri.'.'" hot'-o i cry^red by sludge deposits
     H   =   average  river depth
   Hj   =   height through  which water falls ovur a dam
   K    =   reaeratinn  coefficient
     a
   K[j  =   deaxygenation  coEfficient
   KP  =   first order NBOD decay  ccefficient
   Kr  =   first artier CB(]D decay  r-oafficicnt
    L  =   carbonaceous  EDO (CP0.9)  distribution
t                                       'i
   LG  =   initial  carbnnacec;:?  ROP
    N  =  nitragenous 3CD  (r»rO;l)  liistMliutii/o
    P  =   gross photosynthatic  di:.solv-ir|  n<\rjc!ii  production
    p  =  period of algal  photosynthesis,  i.e.,  period af daylight
  Pav  =  average d^ily photoiyr.tl'jjli c  oxygen  production
          river flew rate
 q  =
 R  =
 5  =
Si  =
 T  =
 t  =
 u  =
Wd  =
 x  =
 algal  dissnlvsd n^;">r.~
 bEnthi c  O'.ygsn  .'P'"' ^ '
 bentnic  oxyGcii  u.'i.-i t? c
 rivar  teiiiff-M-atur?
 ti.'O of  ' .MVC i
 dvai-igc  i-j-,jr v::   i !•;
 dissol v'-ri ov; ; :n ~. •   '

spat-a I  ,'--^K.-
                                                     -  tributary
                                                                        (ft2)
                                                                        (mg/1)
                                                                        N/D
                                                                        (mg/1)
                                                                       (mg/1)
                                                                       (mg/1)
                                                                       M/l]
                                                                       (mg/1)
                                                                       (rag/1)
                                                                       (decimal)
                                                                       (ft)
                                                                       (ft)
                                                                       (I/day)
                                                                       (I/day)
                                                                       (I/day)
                                                                       (I/day)
                                                                       (mg/1)
                                                                       (mg/1)
                                                                       (mg/1)
                                                                       (mg Dz/l-ddy)
                                                                       (days)
                                                                       (mg/l-day)
                                                                         (mg 02/l-day)
                                                                         (gra Oz/m2-duy
                                                                         (mg az/l-day)
                                                                         (°C)
                                                                         (days)
                                                                         (ft/sec)
                                                                      (mi IBS)

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                                     -  1  -

                                 INTRODUCTION

      Gross water pollution has  existed in the  Lower  Fox  River  and  Green
Bay,  Wisconsin for  a number  of  years.  Concentrated  in this basin  are
eight urban areas and nineteen  pulp  fnd  naner  tnnufacturers that make  in-
tensive USE of the  river  far  disposal  and assirnlation of wastes.  The
lower river,  approximately 40 miles  (69.4 km)  in  length, flows  in  a north-
easterly  direction  through a  series  of 18 locks and  dams used  for  navi-
gation and hydroelectric  purposes.   The  drainage  area  of the basin is  419
square miles  (1QB5  sq. km).   (See figure 1)
      Because  of the continuing  gross water pollution in  the river, the U.S.
'Environmental Protection  Agency (EPA) and the  Wisconsin  Department of
Natural Resources (DNR) initiated a series of enforcement actions against
the various industrial and municipal waste dischargers in the  Lower Fox
River basin.  The Wisconsin DNR has  issued orders requiring municipal waste
sources ta remove 90% of  the  biochemical ox-p-n demand contained in their
waste influents.  The 1972 Amendments to the FeJ..;vqi Water Pollution Control
Act provide that municipalities sh^ll provide,  as  * minimum,secondary treat-
ment)  and  industries shall achieve "best practicable  control technology"
(BPT) by no later than 1977.   Under  the Act, E7'ft  is  required to define final
effluent guidelines representing BPT by Qctob^- 1973.  The effluent limits
for industrial dischargers used in this ropnrt and summarized  in Table 5
ware derived from interim guidelines ;-' IT.' !-v - ""•. in early 1973 which were
dGvaln[)2d in anticipaticn of the 1973 A'-,MV'  .-    The cc-mbination of 90%
BOD removal  for municipalities  and *!v. uvv.' n -. 1  limitations  in Table 5 are
referred throughout this  report as '..!•• " MI-----!  -vffluent limitations."  The
1972 Amendments  alsn require that, in  JiiJ.:o-i   tj ^peting the municipal and

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 "f   « "* ?*  '1 * ? J 
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                                     -  3  -
 industrial  guidelines, the water  quality standards must be met.   For  the



 Fox  River upstream  nf the upper dam at Appletonjthe water quality standards



 provide  for all water uses including fish and  aquatic  life and  recreational



 use.   These uses require among other parameters that the dissolved oxygen



 shall not be lowered tn  less  than 5.D mg/1  at  any time.  The Fox  River  from



 i'he  upper dam  at Appleton downstream to tii2 Village of Wn'ghtstown shall meet



 all  standards  except that the dissolved oxygen shall  not be lowered to



 less than 3.Q  mg/1  during any consecutive 8 hours of  a 24-haur period nor



 to less  than 5.0 mg/1 fcr the remainder of the day.   The Fox River below the



 Village  of  Wrightstown downstream to the mouth shall  meet all  standards except



 that the dissolved  oxygen shall not be lowered  to less than Z.D mg/1 at  any time.



     In  1969,  the engineering firm of quirk,  Lawler,  and Matusky  (QLM)  developed



 a mndal  of  the river for the  Wisconsin DNR.  The data base used far



 verification of this model was not as complete as that presently  available.



 Extensive river surveys  performed during the summers  of 1971 and  1972 have



 accumulated  enough  new data to al^ou1 a better  estimate of certain parameters



 and thus permit the development of an updated model for the Lower Fox River.



     The purpose of the work  presented here was to evaluate the effect on



 the water quality of the Lower Fox River of implementing the proposed effluent



 limitations for industrial and municipal sources and  to evaluate  if these



 control  levels would achieve  existing water quality standards.



     The scope of the study was  limited to developing a steady-state, one-



 dimensinnal  model  based on availehl? ^at^ and using an existing computer pro-



 gram.  A discussion of the theoretical  background is  presented  first, followed



hy a description  of the development 
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                                   - 4 -



                             MODEL DEVELOPMENT




Theory


     The dissolved oxygen concentration of a natural  water system indicates


the general "health" nf a stream, and its ability,  or inability,  to  main-


tain a diverse population of fish and aquatic life.   The conservation of


mass farms the basis for the fundamental relationships which describe the


temporal and spatial distribution of dissolved oxygen in the natural  water


system.  Both the net flux into and the effect of various sources and sinks


within a unit volume of water determine the change in dissolved oxygen con-


centration with time.  For a fresh water river  such  as the Lower Fox,


the advcctive component of the flux is much more significant than the dis-


persive component.  Hence, the dispersive term was  neglected in the


development of the model.


     An understanding of the overall effect of the  complex interactions among


the system parameters can be gained by modeling the interrelationship


between the various sources and sinks and the dissolved oxygen  concentration


in the river.   The specific equation is developed by  a mass balance  employing


the continuity equation and takes the following form:   (Thmnann,  1972)
             l£ = - 1 3(^1 - KdL -  W + Ka  (Cs-c)
             at     A  ax


                  - S^x.t)  + P(x,t)  -  R(x,t)  + Ka(Ca  -  cb)
in which


     A  = river cross-sectional  area  (ft2)


     C  = concentration  of  dissolved  oxygen  (Do)  (mg/1)


     ca = dissolved  oxygen  above a  dam  (rrg/1)

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                                   - 5 -






     Cfa = dissolved oxygen below a dam (mg/1)



     Cs = saturation value nf dissolved nxygen {mg/1)



     Ka = reaeration coefficient (I/Hay)



     Kd = denxygenatinn coefficient (I/day)



     Kn = first order NBOD decay coefficient (I/day)



     L  = carbonaceous BDD (CBDD) distribution (mg/1)



     N  = nitrogenous BOD (NBOD) distribution (mg/1)



     P  = gross photosynthetic dissolved oxygen production (mg/l-day)



     Q  = river flow rate (cfs)



     R  = algal dissolved oxygen respiration (mg/l-day)



     S1 = benthic nxygen uptake coefficient (volumetric) (mg/l-day)



     t  = time (days)



     x  = distance downstream (miles)





     In equation (1), the concentration of dissolved oxygen is assumed to



be uniform in the lateral and vertical planes.   The sources and sinks may



be functions of their own concentrations or the concentration of another



substance.



     It is usually more convenient to  introduce the dissolved oxygen



deficit into the equations since all  values will  then be referenced to a



zero dissolved oxygen deficitj the saturation value of dissolved oxygen.



If D, the dissolved oxygen deficit (I>CS-C) is  substituted into equation



(1) and if steady state conditions ar-? assumed  (i.e., no change in paint



source waste loadings with time), the  solution  is as follows,  given the



appropriate boundary conditions (D=n0  at x=o)  (Thamann,  1972):

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                                     -  B  -
                     D(x) =  (Wd  +  DD)  exp( - Ka x/u)                       Ua)

                             Q



                                                                            (Zb)
                                   [EXp( - Kn x/u) -  EXP(  - Ka x/u)]       (Zc)





                          "        [1  - exp( - Ka x/u)]                     (Zd)




                          + |     [1  - exp( - Ka x/u)]                     (Ze)
                              Q




                          + |     H  - exp{ - Ka x/u)]                     (Zf)
                            lva


                          - {Da  -  Db) oxp[ - Kfl(x -  xd)/u]                (Zg)






where


     Da =  deficit of dissolved  oxygen above a dam  (mg/1 )


     D^ =  deficit of dissolved  o.cyo^n he low a d^n  (mg/1)


     Kr =  first order CBOD decay  co zf «r.i.- "; (LMay)


     Sl =  benthic oxygen uptake rn-j' .--;ji.;iu •'•< '• ' .".'fric) (mg/l-day)


     Wd =  dissolved oxygen input  fro.,i wjst-: 3 .1 rce  or  tributary  (Ibs./day)


     Xj =  spatial location of a >-'*r; (f.ilos)




The various  parts of the solutioti a-1.-; intei'.'ir .i-,d as:


     (Za)  paint source of DO,  '^-jj  rc-'i ir:ir. i  >'i!ue  of  DO deficit,  Dn


     (2b)  deficit d'je to point •J'rjr.;: -f \   1


     (2c)  d2ficit due to f.dint 5 ••>••-:'  ;--f '


     (?d)  deficit due to distri'-..   '. li'--"1- '   ••  jsynth--?sis


     (2e)  distributed hlj..! -.'e;,.j . -• ' ic.i •-.  -./.


     (Zf)  distributed be:ithic  ox >•.•-.'! ci_,:!-i'-: - "f-ict


     (Zg)  deficit change due to  •-  •  ;-ati>n '>•• .• spillways over darvs

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                                   - 7 -

     A detailed discussion  af each of  the model  components  shown in
Equation (Z) is presented in the  following  sections.   In these sections
a discussion nf the assumptions used in  describing  the component model
is presented along with a summary of the values  of  the parameters selected
for use in the verifications and  predictions.  The  model  is structured  so
that each of the input parameters may  be varied  spatially in the river.
Initial Conditions
     Values for initial conditions of  dissolved  oxygen,  carbonaceous BOD,
and total nitrogen in the Neenah-Kenasha Channel were obtained either from
recently available river survey data,  or from  the results of an extensive
statistical analysis of dissolved oxygen and carbonaceous BOD data presented
in the report prepared by Quirk,  Lawler, and Matusky, Engineers.
     Generally, the initial concentration of dissolved oxygen was at or above
saturation at Neenah-Menasha due  to phntosynthetic  activity of the aquatic
plants {QLM, 1969).  For the model vo^i-Mcations, observed  values of dis-
solved oxygen (all abova saturati '•?-.} ,-j..'"2 .r.,H.  F';r  the rondel predictions,
the saturation value was used,
     Where available, initial carb',.r);u*i*c.js  BOD values, measured by the  Wis-
consin HNR, were used.  In  trie"; ru:"i i,.-1 .r n+~ t^e  analyses, an initial  value
of 6 mg/1 was chosen based  on tf _ •,.;'. ,nr,:: n; ">s.-t:t.ryl in the  QLM study
(QLM,  1969).
     Relatively few measurements  r.r' i.oi,-«'i oxidizable  nitrogen were available
for use in  the analysis.   A re-'—. • cf  i if- n istlng  data  suggested that  the
/alue  of 1.0  rng/1  was a rsasonat.-i-  ,, •

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                                   - a -

Atmospheric Reaeration
     The atmospheric reaeration coefficient,  Ka, was  calculated using
O'Connor's formulation  (Dobbins and O'Connor,  1958),

                      Ka  (I/day) =lzV^_                            (3)
                                     H3/2
in which,
                      y = average stream velocity  (ft/sec)
                      H = average der>th  (ft)
     The O'Connor equation forms a reasonable  basis for  estimating  the
reaeration coefficient for a wide range nf  depth and  velocity  conditions
(average depth ranging from about 1 foot to 30 feet [0.3 m  to  9.1 m] and
average velocities in the range frorc 0.5 to l.fi ft/sec [0.15 m/sec  to
0.49 m/sec]) encountered in the Lower Fox River.
     The effect of temperature on the reaeration coefficient has  been
experimentally determined to be representr-l by
far T in degrees centigrade.
Biochemical Oxygen Demand
     As shown in Equation (2), tfi- •-:- "-s a 'hi unction rnado between the
oxygen demand of the carbonaceous •• -   -i--l {: • l) in a w^ste effluent, and
the nitrogenous oxyg°r, dt'Windn'j ( • -.- .'.:V:. (.'••  0 of tns effluent.
Carbonaceous BOD
     The removal rate of carbon -.cro •••  nr^nr ,-uLter, expressed as Kr> is

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                                   - 9 -




a result nf oxidation and physical settling nf the organic materials.



Far oxidation alone, as might result from a soluble organic waste, the



reaction rate is expressed as Kj — the rate nf oxidation nf the organic



substance.  The two reaction rates, Kr and Kj, associated with the decay of



CBDD are shown in Equation (Zb).



     Previous studies have shown that the primary mechanism for CBDD



removal is the oxidation of organic matter (QLM, 1969).  Although settling



of the suspended matter does occur, the rate of removal via this mechanism



is small compared to oxidation.  Far the analysiss the removal rate, Kr,



was assumed to be essentially equal to the oxidation rate, Kj.



     Values for the CBQD coefficient, !C|, were taken directly from the



qL&M report.  In that study, K, was reported to be a function of river flow



between about 1,000 cfs (1,699 cu m/min) and 4,OOD cfs (6,797 cu m/min) for



the area from Appleton dam (mp 32.1) to D« Pere dam (mp 7.3).  For flows



greater than 4000 cfs (6,797 cu tn/vnin) the rate coefficient was considered



constant.  Beyond DE Pere dam, K^ was •independent of river flow and was



assumed constant at 0.12/day.



     For the present study, observed flows of about 2,000 cfs (3,398 cu m/min)



to 2,500 cfs (4,24B cu m/min) resulted in corresponding deoxygenation



coefficients of about 0.2 to 0.3/day.



     Long term (20-day)  CBOD measurements were available at several  places



in the river.   From these measurements,  the ratio of ultimate to 5-day BOD



was calculated.   This ratio varied from  1.29 to 2.36,  as shown in the



following table.

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                                  - ID -
                                  Table  1
                        Ratio nf Ultimate to 5-Day
                             Carbonaceous ROD

Location

Segment 1-13
Segment 14-18
Segment 19
Segment 20-25
Segment Z6-3Z
Segment 33-40
Segment 41-45
Ratio
CBODu/CBQDg
qLM Report (1969)
l.Bfl
2.19
1.B9
1.56
1.89
2.36
1.29
Wisconsin DNR (1972)
(Menasha Channel ) 1.B1



(Rapide Creche Dam) 1.95
(DePere Dam) Z.35

Source:  Quirk, Lawler, and Matusky, Engineers, 1969

Nitrogenous GOD
     The assumption of a first-order kinetics model to describe the  process
of nitrification is a simplification of a rather complex set of consecutive
reactions.   In reality, organic and ammonia nit^agen are oxidized through a
series of reactions, shown below, to nitrite and nitrate nitrogen.   This
oxidation process draws on the oxyqer. rc.-'^.«s T.es nf the river and is  included
as a component in the model .
     The ammonia formed from organic ni^ n •-)?,-• ,  together with direct  dis-
charges nf  arrcnonia frcm vaste sources,  '-. .  ;^> . '':^d tn nitrite by Nitrospmonas
bacteria, as follows:
           (NH4)++ OH
                                                    ZH20

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 Thr.  >^:u:tion  requires  3.43  pounds  of nxygen fa1* each pound of aTr,mnnia
 .litrci^en oxidized  to nitrite.
     TIM nitrite formed  is  then oxidized ta nitrate by Nitrohacter as
 Fc I 'I ov.'s :
            NGjf + 0,5Q2 bacteria
                irm requir&s 1.14 pounds of sxj.gt!n for one pound of nitrite
nit. •;,'•••• P oxidize'! to  nitrate.
     The total  oxygen consumption  in the nitrification process is 4.57 pounds
nf  oxycjsn for  each  pound  of ammnnia nitrogen.   Thus, the nitrogenous BOD (NBQD)
is  enj-il to ^-.57 times,  the concentration of total  axidizable forms of
nitrogen (ammonia + organic nitrogen).
     In the present analysis,  active nitrogenous oxidation is assumed tn
ccFiiTvsrice in the first segment  in the Neenah-Menasha channel.  This assumption
i;-  considered  valid on  the basis of high concentrations of algae and related
nutriants entering  the  Lower Fax River from Lake Winnebago.
     The rate  cc=ff iclent,  Kn,  is  dependant on rivor temperature and the
cnncer+ratiDn  af dissolved oxygen.   Under conditions of law dissolved oxygen,
nitrificEticn  is inhibited ands at  values belnw 1.5 mg/1 dissolved oxygen,
nitrification  ceases.   The maximum rate of nitrification at high levels of
dissolved oxygen was  O.T43/day (QLM,  1963).
     Ths efT^ct of  temperature  on  tha reaction rate af nitrification is
given by
for tei,-ipera-»ures greater than 10aC.  At river  temperatures  nf less than 10DC,
m'trif icrati an is suppressed.

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                                  - 12 -
     Estimates nf point source loadings nf total oxidizable nitrogen
 (NH^-N + nrganic-N) were applied tn industrial and municipal  dischargers.
A comparison of observed total nitrogen values for July 14, 197ZjWith a
computed mass balance of total nitrogen,is shown in Figure 2.
Photosynthesis and Respiration
     Lake Winnebagn contributes large concentrations of algae to the Lower
Fax River in the summer months.  The algae and rooted aquatic plants,
through the processes of photosynthesis and respiration, serve both as a
source and a sink of dissolved oxygen in the river.  In the steady state
model presented herein, the complex interactions involved in photosynthesis
and respiration are simplified by relating the chlorophyll - ^concen-
tration in the river to an oxygen source term, Psand a sink terms R.
     Chlorophyll - admeasurements at various locations in the river were
available from recent surveys by Sager and Wiersma.  Estimates of the gross
oxygen production and respiration due to algae concentrations were made by
using the empirical relationship between chlorophyll - ^concentration and
maximum oxygen production established by Ryther and Yentsch and reported by
Di Toro (1963).  This relationship is:
     P = D.Z5 chl - a                                                    (6)
where
     P = gross photosynthetic dissolved oxygen production
         (mg D2/l-day)
     chl  - a. = chlorophyll  - £ concentration (vig/1)
     The relationship between the algal  respiration rate, R,  and chlorophyll
- a  concentration is:

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                   Jllass           gsf  Till!  Nitronn
   2.00
   1.60
tafl
E
tu
1.20
   0.00
   0.40

0 Obsarved Dita

0 r
j-


i

, _H '
	 	 	 r-1
0
)

River Flow: 2141 CFS
River Temp: 23 °C
iurvey Date: July 14, 1
Jata Source; Sipr & 1

o


172
^iarsma
Q
/^ • . 	 i 	

nl
G

   0,00
      40
                      30                  20
                       Miles from Green lay
10
0
                                                                            Figure 2

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                                  -  14 -





     R = 0.025 chl - a.                                                  (7)



     The average daily rate of photosynthetic dissolved oxygen production,



Pav, is given by:



     Pav - P 2p/TT                                                       (8)



Where



     p = fractional period of sunlight in a day



     The unfortunate implication is that a constant ratio of P/R = ID exists



for all algal populations.  This is not true, since the ratio is known to



vary considerably.  Howevera  comparison of results from this empirical



relation and data presented in the QLM report from light and dark battle



measurements agree reasonably well and so lend confidence in the empirical



relation used in the analysis.



     Table 2 shows the spatial variation of maximum grnss algal  oxygen



production and respiration used in preparing twn verifications of survey



data and a prediction of 197B conditions.

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                                               TABLE   2
                            SPATIAL  VARIATION OF ALGAL OXYBEN PRODUCTION
                                    AND  RESPIRATION  (mgOz/l-day)
July ZB, 1971
Segment
1-11
12-28
Z9-33
34-4D
41-45
P R
3S.O 3.50
23. 7a z.aa
21.25 2,13
16.25 1.63
11.25 1.13
June 20-21, 1§73
Segment
1-14
15-22
23^27
2B-45

P R
21.3 2.13
21.3 2.13
12.5 1.Z5
12.5 1.25

1S7B Prediction
Segment
1-14
15-22
23-27
2fl-4i

P R
14.0 1.4
11.0 1.1 «
LTl
B.D D.8 ,
6.0 D.G

Source:  Sager and Wiersma,  1972
         (197B Prediction conditions are estimates)

-------
                                  - 16 -



 Benthic  Oxygen Demand


      The continuous  discharge nf settleable waste material from municipal and


 industrial sources for many years has resulted in the formation of sludge


 banks  throughout the river.  The bottom conditions in the river vary from


 rather thick  deposits nf sludge to relatively shallow deposits of decaying


 organic  material from natural sources such as dead algae.  The surface layer


 of sludge, in direct contact with the water, undergoes aerobic decomposition,


 during which  dissolved oxygen resources are depleted from the overlying water.


 Assuming that the river is vertically well mixed, this benthic or sludge oxygen


 demand (SOD)  is the  distributed sink of dissolved oxygen shown as 5 in


 Equations (1) and (2).


      Values for 5 were orginally taken from the literature.  Thomas (1970)

                                         n
 reported SOD  values  of up to 2.3 mgs 02/m -day in unpolluted sections of the


 Willamette River in Oregon.  For sections of the river covered with fresh


 paper  mill sludge deposits, values as high as 19.5 mgs Q^/m^-day were


 reported, with the average uptake rate in the range from 3.6 to 9.B mgs


 0,2/n£-day.  McKeown  (196B) reported a range of 1.5 to 5.0 mgs D^/m^-day


 for sludge deposits from pulp and paper mill wastes at various locations.


 Review of other literature (Thomann, 1972) indicates a range of 4 to 10

mgs 02/m^-day SOD for cellulosic fiber sludge.


     Both Thomas and McKeown describe a rapid decrease in sludge oxygen


 demand as the sludge agas.  According to  Thomas,  within  90 days  after de-


 composition,  the SOD had dropped to half of the maximum value at the time


of deposition.  McKeown  reported a decrease to  about one-third of the


maximum SOD within  flD days of deposition.

-------
                                  -  17  -



     Based on the above infnrmatinn, a maximum SOD of 5.0 mgs  O^/m^-day

                                                                         n
was utilized far mast analyses presented herein.   A value of 2.5 mgs Dz/m -


day was used far predicting future conditions in anticipation  of decreased


loadings of settleablematerials to the river and of aging of the existing


sludge deposits in the river.


     Although the average value far the benthic oxygen demand  will  be about


2.5 mgs D^/m^-day, it possibly will be higher than this at a few locations.


Sludge deposition in the Lower Fox River was recently studied  by Springer


(1972).  Under most flaw conditions, significant sludge deposition was found


to occur in segments B to 11 and 2fl to 45.  Since fresh sludge deposits may


well settle in these locations in the future, the benthic uptake rate could


be higher than that assumed in the present analysis.


     Subsequent to the development of the present model, the Wisconsin DNR


conducted laboratory measurements of the benthic oxygen uptake due to sludge


deposits taken from the river.  These studies indicated an uptake range of


2.5 to 3.2 mgs Dz/mZ-day for areas having relatively little sludge.   In more


grossly polluted areas, SDD values of 6 to 20 mgs D2/m -day were measured


(Wisconsin DNR, 1973).   Results of the Wisconsin  DNR  studies support the SflD


values taken frnm the literature and used far the Fox River analysis.  The

                                     ^
measured range of 2.5 to 3.2 mgs  Oz/m -day for areas relatively free of


sludge deposits supports the assumption made in evaluating future conditions


that the average SOD will  be near these values after installation of adequate


treatment.


     Effects of river temperature on the benthic  oxygen uptake rate  can be

-------
                                  -  IB  -

approximated in the 10° to 30D range by

     (S)T = (S)ZO (1.065)(T-ZQ)                                        (g)
where T is river temperature in degrees centigrade.

Below 10DC, the rate decreases mnre  rapidly than indicated  by Equation  (9)

and approaches zero in the range nf  D°  to 5°C.

Reaeratinn Over Dams

     The reaeration occurring at dams along the river is  similar to  the

natural phenomenon of atmospheric reaeration and always  drives the dissolved

oxygen concentration of the water toward  the saturation  value.   In the  Lower

Fax River, the major sources of continuous artifical  reaeration are  the

watsrfalls over dams located at De Pere (mp 7.3),  Little  Rapids (mp  13-1),

Rapide Croche (mp 19.18), and Upper  Appleton (mp 32.1).   Although there are

19 dams located gn the river, these  four  dams were considered to be  the

significant sources of reaeratinn based on observations made by the  Wisconsin

DNR during recent field studies and  as  clearly  indicated  in  the data shown  in

Figures 4 and 5.

     For the Mnhawk River and Barge  Canal  in New York State,  Mastropietro

(Mastrnpietro,  1972) developed an equation similar to the following  for

reaeratinn over dams:

                          Da - Dfa =  <*Hd Da                            (1°)
     Da = dissolved oxygen deficit above  dam (mg/1)
     D   = dissolved oxygen deficit below  dam (mg/1)

     Hj = height  through which the waterfalls (ft.)

      a = empirical  coefficient for  dam reaeratinn

-------
                                   -  19  -





     Mastropietro used an a value of 0.037 in his work.  However, for the



Lower Fnx River, coefficients determined frnm field data were substituted



in describing reaeration aver dams.  A summary nf the dam heights and



coefficients is presented in Table 3.





                                  TABLE 3





                           REAERATION OVER DAMS



        DAM                MILEPDINT          HEIGHT (FT.)            a



De Pere                       7.30                9.8         .      0.037



Little Rapids                13.10                6.1               0.115



Rapide Crache                13.18                9.4               0.037



Upper Appleton          .     3Z.10                B.O               0.065




Total dissolved oxygen transferred at the various dams could be as high as



4 to 5 mg/1 if the dissolved oxygen concentration at the dam headwater is



at, or near, zero.



Physical Parameters



     Geometric characteristics of the river, such as average depths, widths



and crass-sectional areas are necessary to determine the assimilative



capacity nf the river since these parameters combined with the river flow



rate determine velocity.   Each of the terms in Equation (Z) is a function of



river velocity.



     Average widths and depths were obtained directly from the QLM report.



Cross sectional areas in the river were then readily computed from this



information.  River segments used in  the model   presented in this reportj

-------
                                  -  20  -






were those used in the qLM study.  Table 4 presents the average depths, widths,



and crass-sectional areas used in the analysis.



     In the development of the model, the Menasha Channel  was arbitrarily



considered as a tributary to the main branch of the Lower Fox River entering



at river mileptrint 37.24 in Segment 6.  River flow from Lake Winnebago was



proportioned between Menasha and Neenah Channel by a consideration of the



respective dam spillway dimensions and current measurements taken during



stream surveys.  Flow in Menasha Channel  was calculated by qLM to be 0.54



of the total river flow, with the flow in Neenah Channel  being the



difference, or D.46  of the tntal river flow.



Seiche Effect



     Green Bay, at the mouth of the Lower Fox River, is sufficiently large



tn be subject to a phenomenon similar to  oceanic tides.  This phenomenon,



the seiche effect, will cause long period oscillations in the river similar



to the waves caused by tides in a coastal estuary.  Neither amplitude,



current, nor dye tracer measurements of any detail were available to fully



evaluate the effect of the seiche in Green Bay nn the Lower Fox River.



     Aerial photographs obtained during a recent study of (EPA, 1972) thermal



discharges in Lake Michigan clearly indicate current reversals at about 1.3



miles from Green Bay near the confluence  of the East River and the Lower



Fnx.   Contrary to the conclusion presented in the QLM report, it is evident



that  longitudinal  backmixing does appear  tn significantly alter the dis-



tribution of pollutants in the river below De Pere at certain times.   The



effect of backmixing can be seen in the results of a recent river survey shown



in Fiqure E,

-------



Segment
No.
1

2
3

4

5

E

7

B

9

ID

11

12

13

14

15

IE

17

IB

19

ZD

Zl

22

23




Depth
(fEEt)
Z

Z.S
3

2

2

4

4.5

5.5

9

9.E

E.E

4

4.5

l.fi

5.H

6.7

3.3

6.7

6.4

Z.B

S.3

6.D

E.D




Width
Ifeet)
4BB

l.fiOH
2.326

305

355

2.915

3,Z5Z

Z.739

1.033

1,045

556

41?

444

3fl7
-
GZ9

6ZE

BOB

580

1.D3D

533

553

15D

150

- 21 -
TABLE 4
PHYSICAL PARAMETERS

Cross -Sectional Ml'le
Area (sq.ft.)
976 38.63

40ZO 33.1
6978 37. 6Z

£10 3S.1H

712 37.92

1166 37. Z4

14634 36. B3

15D65 36.0

9H37 34. B

1QD3Z 34.3

367D 33.96

1576 32.1

199B 31.65

619 30. B

364S 3D. 56

4194 Z9.73

Z66D 27.24

4556 Z£.S

B592 26.4

1492 25.6

34S4 ZS.l

sna 23.93 -

9Dn 23.2




Points

- 3H.1

- 37. 6Z
- 37. Z4

- 37.92

- 37.24

- 36. B3

- 36. Q

- 34. B

- 34.3

33. SB

- 3Z.1

- 31.65

- 30. H

- 30.56

- 29.73

- 27.24

- 26. B

- 26.4

- 25. 6

- 25. 1

23.33

23.2

22.5




Location ''

NeEnah Dam - BErgstrnn
Paper (Seen ah Channel)
Bergstrom PapEr -
Kimberly-Clark (Lakeview)
KimhErly-Clark -
James Is.
Men ash a channel -
John Strange Paper
John Strange Paper -
James Is.
James Is. -
Men as ha Luck (Main River)
Henasha Lock -
Menasha (9th Strest)
Menasha (9th Street)
StrnbE Is.
Strobe Is. -
Mud CrEek
Mud CrEek -
Grignnn Rapids Channel
Grignnn Rapids Channel -
Dam, Wis --Mich. Power
Wis-Hich. Power -
Dam, Fox River Paper
Fox River Paper -
Dam, Forninst Dairies
Dam, Fnrmnst Dairies
Consolidated Paper
Cnnsolidated Papsr
Appleton Sewage Plant
Appletnn Sewage Plant
Kiirberly-clark (Kim.)
Kimberly-Clark (Kim.)
Little Chute (Jefferson St
Little Chute - Guard
Lock, LittK' Chute
Guard Lock, Little Oiure -
Dam, Contined Lacks Paper
Camhined Lacks Paper -
Sanitarium Road
Sanitrrium Raarf -
LaftillEtte Part,Kaukauna
LaFnllettc Fark.Kaukauna -
Tiiilrnany Paper
Thil.iiany Paper
Lagonns

-------
                                       - 22  -
                                       TABLE 4  (Cpn't)
                                  PHYSICAL PARAMETERS
_ 	
" No!
24
25
Z6
Z7
ZB
29
30
31
32
33
34
35
36
37
38
33
40
41
42
43
44
«
Depth
(flBtJ
4.7
7.5
4
I.fl
7.7
1.5
5
5.7
10,3
3.4
fi.6
7.4
5.6
5.6
g
13
Zl
13
ZD
13
16.5
13
Hidth
(feet)
•. 	 	 • 	
l,3Bfi
627
§05
snz
575
.319
1,629
1.7K3
303
1,431
1,540
1,160
2,083
2,711
1,338
1,154
BIB
fl4S
§34
765
850
93S
Cress -Sectional
6514
4703
242D
2312
4421
5D55
B145
10146
9301
4B89
ioaz4
BSH4
11661
15ZD4
1204Z
15002
1Z978
1ED55
11880
§945
14025
12194
Mile Paints
22.5
21.0
If.lB
17.4
15.0
13.1
12.6
12.1
10.4
7.3
6.37
6.25
5.7
4,8
4,0
3.7
Z.63
1.3
1.0
0.7
0.33
0.14
- 21.0
- li.lH
- 17.4
- 15.0
- 13,1
- 1Z.fi
- 12.1
- 10.4
- 7-3
- i.§7
- 6.25
- 5.7
- 4.8
- 4.0
- 3.7
- 2.63
- 1.3
- 1.0
- D.7
- 0.33
- 0.14
- O.D
Location
Lagoons - nils
point 21.0
Mile point 21. 0
Rapide Croche.Qam
Rapide Croche Bam -
Plum Creek
Plum Creek - Apple
Creek
Apple Creek - Dam
Little Rapids
Dam, Little Rapids -
Lpst Dauphin State Park
Last Dauphin State Park -
Hickory Grove Sanitnrium
Sam" tori urn - uld Plank ftd.
DePere
Old Plank M, DePere -
Dam, DePere
Dam, DtPere - U. s.
Paper Mills
U.S. Paper Hills -
DePere Sewage Plant
DePen Sewage Plant -
AsHwaubenon Creek
Ashwaubennn Creek -
Dutchman Creek
Dutchman Creek -
Refiners Meat Products
Reimers Meat Products -
Fort Howard Paper
Fort Howard Paper •
Pnrlier Street firesn Bey
Pnrlier Street - East
River
East River - Charmin
Paper CD.
Charmin Paper CD. -
Green lay Packaging
Green Bay Packaging -
Reiss Coal CD.
• Reiss Cnal CD. -
Sreen Bay Yacht Club
Green Bay Yacht Club
Green Bay
Source:  (Quirk, Lawler and Mitusky Engineers,  meg)

-------
                                  - 23 -






     Because nf the backmixing effect, the distribution nf pollutants is



altered such that the concentration nf dissolved oxygen occasionally



tends tn increase belnw De Pere, rather than decrease, as would be



expected due to the magnitude of the waste loads discharged into the river.



     Since the observed phenomena are similar to tidal effects in a coastal



estuary, the effect of current reversals, i.e., a seiche, can be accounted



fnr in the model by the addition of a term describing the mass flux due to



longitudinal dispersion in Equation (1).



     Data were not available to permit evaluation af the effect nf current



reversals on water quality predicted by the present model.  Since the



seiche phenomena is not a continuous occurrence, as are estaurine tides, the



integrity of the model reported herein is not affected for situations in which



the effects of dispersion are negligible.



Survey Data



     Two recent sources of extensive data greatly facilitited construction



of the model.  Sager and Wiersma's 1971 and 1972 study of water quality in



the Lower Fox River and Green Bay provider! temperature, dissolved oxygen



and chlorophyll - a_measurements at ten Iccations in the river.  In



addition, the Wisconsin DNR conducted stream surveys on the Lower Fox River



throughout the summer of 1972, the results of which were made available to



the EPA.



     Sager and Wierma's data is a result of a single surface grab sample



taken at locations where the river was considered to be well  mixed.  The



data furnished by the Wisconsin DNR represents several measurements af



dissolved oxygen across the width of the river at numerous locations on the



river.

-------
                                   - Z4 -

      Observation  of the  data  indicates  the  existence  of a rather signifi-
 cant gradient  in  the lateral  and  vertical planes of the river, demonstrating
 that the river is not truly a completely mixing system as is assumed in
 a one-dimensional model.
      Despite the  apparent  lack of complete  mixing in  some portions of the
 river,  the  computed profiles  of dissolved oxygen do agree sufficiently well
 with the observed data to  validate  the  assumption of  an approximately
 uniform concentration of dissolved  oxygen in the lateral and vertical planes
 in each segment of the river.
 Proposed Effluent Limitations
      The 1972  Amendments to the Federal Water Pollution Control Act changed
 the major emphasis  of water pollution  control from water quality standards
 to effluent limitations, regulating  the  amount nf pollutants discharged from
 specific point sources.  The  1972 Amendments required that EPA define the
 "best practicable control  technology currently available" for various
 categories  of  industrial operations  and determine maximum allowable effluent
 limitations.   The Act requires  that  all dischargers provide at least this
 level of treatment  and meet existing water  quality standards no later than
 July, 1977.
      "Best  practicable control  technology currently available" effluent
 limits  are  in  the process of being defined  for the pulp and paper industry.
 These limitations will be expressed in terms of pounds of CBQDg,  suspended
 solids,  and other materials allowed to be discharged per ton of product and
 are  being established  for the numerous specific operations  in the pulp and
 paper industry.  These limits  were not completed at the time of this  evaluation;
therefore, previously developed "interim" guidelines  (Table  5)  were used.

-------
                                   - 25 -





These compare very closely to the initial  draft of the guidelines being



developed for the type Df papermills located an the Fnx River.



     Also, the various municipal waste facilities in the basin  are required



by Wisconsin DNR orders to achieve a minimum of 3Q percent removal of



influent BOD.  These requirements compare closely with the minimum Federal



requirements nf secondary treatment for municipalities as defined in the



promulgated regulations  (40 CFR 133).



     The proposed effluent limitation represented by 90% BQD removal at



municipalities and the interim guideline limitations shown in Table 5 are



the basis for the water quality predictions  made in this report.



     A location map indicating the study area,  municipal and industrial



waste sources, and river segmentation,  and the  dams considered  to be



significant sources of reaeration is shown in Figure 1.  Table  5  lists



the various pnunt sources in the river by  identification number,  segment



and river milepoint.   It also gives estimated waste loadings assuming



implementation of estimated effluent limitations for industries and for



municipalities.



     Non-point sources of BDD and other pollutants, primarily from urban and



rural runaff, were not evaluated in detail in this report.   At  certain



times of the year,  these sources may contribute significant amounts nf waste



loads to the river,  although the extent of this contribution has  not been



established.

-------
                                                                                             TADI.E  s
                                                                                   SUMMARY  DF HASTE DISCHARGES
                                                                                 Juris 2D-Z1,  1372  Effluent  Levels
                                                                                                                                                         Proposed Effluent Li rotations

r
2.
3.
4.
5.
6.
7.
B.
9.
ID.
11.
1Z.
13.
14.
15.
16.
17.
IB.
19.
ZD.
21.
Z2.
23.
24.
25.
2E.
Z7.
Source
KlniErly -Cldrlr (Neenah)
Kimberly-Clark (Badger Globe)
BErgstnrn Paper
Kimberly- Clark (Lakevfew)
Gilbert Paper
John Strange
Neenah-Kenasha STP
George Whiting
Menasha Sanitary District 14
Riverside Paper
Forernst Foods
Consolidated Paper
AppleXcr. 1TF
Kir-ici-Iy- Clark (Kinterly]
rirberly STP
Lit'le C-^tB STP
Appletnn Papers
Kav.ks.ina STP
Thi lirany Paper
Nicalet Paper
U.S. Paper
De'ere STP
Fort Howard Paper
Charmin Paper
Green Bay Packaging
Anerlcan can
Green Bay Metro STP
TOTAL liiSTE L3AD
Segment
2
2
Z
3
5
5
6
7
B
14
14
IE
IB
17
17
IB
2D
Z4
24
33
34
35
39
42
43
44
45
River mile point
4D.1
39. 3
39. B
39.2
39. B
35, B
37. S
38.7
36. D
33.3
30. B
3G.1
30. n
29.11
27.0
ZE.H
27. D
23.1
23. D
7 D
E.B
E.Z
3.7
1.0
D.7
D.3
D.I
Flow (mgd)
1.7
D.7
5.0
5.4
2.5
2.D
15.2
n.5
D.E
2,4
1,3
17.9
1D.D
11. D
n.4
D.4
B.3
1.1
27.1
3.3
D
1.7
15.2
13.7
Z.E
35.9
13.5
CBDDj'Ibs/dayl
55
263.
2DD57
E4D
D
7ED
3470
ZDD
273Z
1SD5
Z99
5Z4D5***
Z15D***
1749D
90
167
30695
144
20542
43B
D
11BD
5285D
473B5
17DD
BB4BB***
254 Bl*"
371B3D
NBDD Ilbs/Javl
55
46
22DD
4EG
n
D
3ZB7
IE
3JO
Z3fl
D
EBBD
3363
1B2B
ZE5
13D
53 D
B54
25EB
D
D
1GZB
a
3EE7D
137
112
5E31
_ E7234
Flow (mgd]



3.E

l.D
24 .0
a. 4
0,6
D.4
1.3
IB. a
14.2
11. D
D.E
D.B
B.3
1.2
19.2
3.Z

Z.2
22. B
6. a
l.B
5.4
39. a
CBDD^lbs/day)
TO NEENAH-HENASHA STP
•
II
550
TO NEENAH-MENA5HA STP
10DD
7DDD
1DD
535
9D
ED '
4900
4139 '
1E5B
1QQ
100 ]
ZQDD <
232
42ED ,
945 ',
TO DE PERE STP
1543
B5DD i
7DDD
3150
4Z15
14EDO v
E7D77
NBDD (Its/day)



4EE

D
3ZB7
IE
33D
Z3B
D
EBBQ
3353
i
zfise* Si
Z65
130
53D
B54
ZBZB*
4953*

1E2B
2157*
131E**
15Q*
510**
5631**
379 9 a
*  Reoresents infnmatinn frqm  HpnES  pprmits                                                                                                                                 '
** EitiTated in anticipatinn  nF  f'jtu"E  ciirdit-'cis
•"Values  For vtsstewater diSchargES far these  facilities were  takEn  from the  Refuse Act Permit r-ogrim ap.ill catinns and,  thEreFnre, rerresent iverage daily CDnditinns. not those for June ZD-21, 1972.

-------
                                  - Z7 -





                                 RESULTS





      The fallowing analysis demonstrates a reasonable degree nf correlation



between observed data and computed results for varying conditions of river



flow, river temperature and waste loadings.



Model Verification



      Figures 3 through 6 depict the comparison between the observed data and



the computed profiles of dissolved oxygen for the river survey data that



was analyzed.



      Comparisons were made for river flow rates varying from 1,340 cfs



(2,277 cu m/min) to 2,25Q cfs (3,823 cu m/min) and river temperatures ranging



from 21D to 25°C.



      The comparison shown in Figure 5 for the data collected on July 5 and E,



1972 is of particular significance since several of the pulp and paper mills



were shut down for the Fourth of July holiday.  The observed data and the



computed profile both show a significant improvement in water quality as a



result of decreasing some of the waste loads  to the river.   The good agreement



between the computed profile and this particular set of data lends confidence



in the ability of the model  to predict future water quality conditions as a



result of implementing the proposed  effluent  limitations on the Lower Fox



River.



      Also of interest is the observed data shown in Figures 4 and 5.  The



survey data indicate  rather high concentration gradients of dissolved oxygen



in the lateral  and vertical  planes  at certain locations on  the river, most



notably near the Menasha Channel, Applaton Papers,  below the Rapide Croche Cam-



and near the mouth of the river  at Green  Bay.   Despite the  vertical



stratification  of dissolved  oxyrnn  due to benthic deposits  and the apparent



lack of complete mixing near waste  outfalls,  the agreement  between the observed

-------
Lower  Fox River Mel  Verification
                                      River Flow
                                      River Tern
            2235 Gfs
            24J5°C
                                                 August
                                                 Slier I Wiersma
Survey
Dati Sourc
0 Observed Data
      3D                  20
       Miles from Green Bay
                                                                            I
                                                                            ro
                       Figure 3

-------
- ze -
                                                tog
                                               BU
                                               u
                                               >_

                                               U3
                                               LSI
                                              _OJ



                                              2E

-------
                                           1Z
lower Fox  River Made! Verification
      30                 20
       Miles  From Green Bay
                                                                             I
                                                                             Ul
Figure 5

-------
                           Fox  River  Mode!
C£>
B:-—
OJ
tifl
>n
>S
C3

ts
03
 in
 C>O
C3
                                                       Rivar Flow: 2141CFS
                                                      Rim Temp; 23 Df]
                                                      Survey Datcriify
                                                      Data Source: Sigkr i Wiersma
                          3D                   2D
                           Miles  from Green Bay
                                 o  Observed  Dati
                                                                                 Figure

-------
 data  and the computed profile, which assumed an average, and uniform
 concentration, is good.  The observed data shawn in Figures 3 and 6 do not
 demonstrate significant gradients since only nne sample (assumed to be
 representative of a completely mixed system) was taken at each location.
      The observed data for July 14, 137Z shawn in Figure 6 possibly
 demonstrate the backmixing  'interaction between the mouth of the Lower Fnx
 River and Green Bay.  Because of this effect, the distribution of pollutants
 is  altered so that the concentration of dissolved oxygen occasionally tends tc
 increase below De Pere.  The backmixing effect, similar to estuarine tidal
 effects, was not considered in the development of this model, since the
 phenomenon is nnt a continuous occurrence.
 Model Sensitivity
      Using August 10, 1971 actual conditions, the sensitivity of the model
 to  the benthic oxygen demand, the carbonaceous BOD decay coefficient and the
 nitrogenous BQD decay coefficient were evaluated.  Table 6 presents the sensi-
 tivity of the model to these parameters at t:>.reE critical locations on the
 river.  The analysis indicates that the water quality is most sensitive to
 the benthic oxygen demand and the rate of CHOD deoxygenation.  The model is
 relatively insensitive to the variations in die maximum rate coefficient for
 nitrification,  as can be seen in Table 6.   If further refinement of this model
 is to be obtained, additional field work is iiaeded tn, in more detail, evaluate
the spatial  distribution of sludgE deposits, the resultant oxygen uptake rat:,
and the rate cf CBQD utilization.
Water quality Predictions
      The preceding analysis demonstrated  die ability of the model  to
reproduce observed dat?  for varying cond-Itiu ~.:  of flow,  temperature, and waiU

-------
                                  -  33  -

                                  TABLE 6

                      Model Verification Sensitivity

                       Survey Date - August 10, 1971
       Parameter
.a.  35. D
m. p. 15.0
m.p. q.q
Bcnt/iic Uptake Rate
                                     Dissolved oxygen (mg/1)
S = 2.5 g/m2-day
*5 •- 5.0 g/m2-day
S - 10.0 g/mZ-c'ay
CLO'u Decay Rate
,j = e.!5/d*y
-'•/' -- 0.30 /day
Kd = u.6C!/doy
NBOD Decay Rate
*Kn = 0.14/day
Kn = 0.28/day
Kn = 0.55/day
4.75
C.23

4.7B
3.24

3.24
2.7B
2.07
2.53
0.80
0.0

2.79
C.BO
n.c

0.80
0.62
0.49
if

o.o
0.0
P'-.O
- - - -
0.0
0.0
0.0
m.p. = mile point from mnuth
* Value used in verification

-------

-------
                                  - 34 -

 loadings  in  the  river.  The  verified model was  then  used  to  evaluate  the
 improvement  in water  quality as  a result  nf  implementing  the proposed
effluent  limitations.
      Figure 7 depicts the average response  of water quality tn implementation
of the required  effluent limitations for  all waste sources on the river.
      Conditions assumed for the prediction  represent  a fairly extreme
summertime condition with a  7-day ID-year low-flow of  1,1Z7  cfs (1,915  cu
m/min), a stream temperature  of Zlnc, and relatively low  algal populations
in the river.  The daily average concentration  of dissolved  oxygen  is about
6 mg/1, falling  significantly below this  in  the region past  De Pere (mp 7.3),
although still above 4 mg/1.
      The profile shown in Figure 7 is not mea^t to  be a  precise forecast
of future water  quality conditions in the Lcwer Fox  River; rather the analysis
indicates a significantly improved water  quality as  a result of implementing
the projected effluent limitations for puiot :;::urces.
      The shaded area in Figure 7 approximates  the average diurnal variation
to be expected from algal photosvntfxi :s  .1 .•••-.! respiration, and other periodic
fluctuations in parameters such as I^'-.hv, uptake rate anij natural background
conditions of water quality.   Thy variation  in  dissolvad  oxygen due
to algal  activity  has,  in  the p.\<;t,  ,;verage«.i about 1 tng/1  with a range from
1 to 3 ing/1 above and below thi daily -:veraga concentration  as measured by
tha Wisconsin Department of Natu.'rH  Reioi:rc~:S automatic monitors.   It is
assumed that diurnal  variations will  occur uridar future conditions, yet it is
di rn--ult ,o foracast the magnitude of si'-J.\ ? fluctuation for future

-------
                                H *«*.
     3
C9
 eu
 tafl   fl
 1/1
I   4
    2
    0
      40
V ^
*\^J

liir-r Flaw: 1127
• , - ,_ ^i_» _.| J N ^ . ^-,\ ,|l|
nT ""! ' "^"^ I**'^TT1T*1I1 Hi*
tiii&J!i*£il^*H«*jltiJti U I .



'*>,. ....... :rM- _*«—

:FS
5 !•-'•*». "''TIC




J
Initial Condit
DO; 9.
NBOD: 4.
Slurip Uptake 2




vj\
ons
0 mi/1
D me/1
57 me/I
50 g/m2-day
AvcragR
diurnal
variation
ao                       20
 ?,ti!2s from Grasn  Day
10
                                                                                                             Ln

                                                                                                             1
0
                                                                                               Figure  7

-------
                                  - 3G -

     The predictions are based on the assumption of a linear system.   The
 terms in equations 1 and 2 assume that the biological systems can be
 modeled by linear functions.  However, it is realized there exist some
 nonlinear biological feedback mechanisms.  For example, the improvement
 in dissolved oxygen in the future may provide more suitable conditions for
 nitrifying bacteria, and the predicted profile may be slightly less than
 that shown in Figure 7-  The effect of reduced waste discharges on algal
 growth and the resultant effect on water quality may also alter the pro-
 jected profile shown in Figure 7, but the extent of this alteration is
 uncertain.
     The prediction shown in Figure 7 represents the best estimates
 available for ths various significant input parameters with consideration
 given to the effects of decreased waste loading to the river upon each of
 the parameters.   A summary of the values used in the prediction analysis
 including an approximate occurrence frequency for each parameter and the
 renga of values  reported in'the literature is shown in Table 7.
     Further evidence nf the effect of reducing waste loads and the
 resultant improvement in water quality is shown in Figure a.  In this
 figure, the survey data and model verification for June 20-21, 1972 (Figure
 4) is superimposed on a model prediction that uses the flow and temperature
 conditions that  occurred on the survey date.   Thus, the prediction in
 Figure a indicates what the average dissolved oxygen would have been  had
 the proposed effluent limitations been in effect as compared to existing
 loading Isvels.   Clearly,  there will  be a marked improvement in average dis-
sol"ed oxygen levels  in the river,  and existing water quality standards should
be achieved.

-------
           TABLE   7
SUMMARY OF PARA3SETEt« USED IN STREAM ANALYSIS
- — - 	 	
rARAMJTER
,. J.1K
f SYMBOL)
Flow (OJ
cfs
Sludges Uptake
(5] gms fl2/m2-day
Algal
Productivity
(r*nm) mg/l-day
MOB decay
(Kit) I/ day
Temperature
(T) "C
N'BOD decay
fKn) I/day
Initial CBOD
|iaf/l
Iritial NBOD
rog/1
Initial D.U,
mg/1
Industrial-Mutiici
pal Loadings
Us/day
VALUE USED i
FDR VEMFICATIQM FOR PREDICTION
As measured daily by
u.s.c.s.
5.0
As measured by
Sager
AS rsportcd in QLM.
Measured values
varied with flow.
	 ' 	
As measured an
survey date
0 . 14 maximum
As reported in f|LM
As measured nr
6.D
Usually 4.6
As measured on
survey date
As reported tn WDNR
or EPA
1127
2254
2,5
14 maximum
0.15
B. 124 below
DsPere Dan
21°C
2S°C
D . 14 maximum
6,0
4.6
C , the saturation
value
EPA production
guidelines
PREDICTION
VALUE
OCCURRENCE
, FREQUENCY
7 day, 10 year
low flew
2,5 js literature
value for unpolluted
treams
Median valua of
available data
Lowest cbserved
bscause D£ low
floh
SEE Tamp. - FltW
'Sarrslation
Not available
5D to BD* a£ values
are <_ 6.0
About 50%
7D to 90% of the
values are greater
than Cs
«^ —
REPORTED VALUES
FDR FOX RIVER FROM LITERATURE
--
2.5 to 20
2.D to 41
D.124 - 0.6
n - 31
D.14
1 to 9
2.3 to 11.2
Cs -* SIR/I
"
--
1.5 to 13
--
n,l - o.fi
without settling
--
D.I to 0.6
—
—
—

SENSITIVITY
AT MILE POINT
0,0
from 1127 tn 2254
AD. d. = +1.9S
from 2,5 to S.Q
AD.O. = -4.04 wg/1
from 7 to 14
AD.D. = +2.86 rag/1
from D.IE" tn 0.3
AD.O. = -a. 58 mg/l
from 21 to 2S
AD. D. = -1.5D Biff/l
from n.14 to O.fi
&D.O. = -D.3I IBri/1
from 3.0 to fi.o
AD. a. = -Q.SS wg/l_
from 4.6 tc 9.2
AD.D. = -0,17 ng/1
for initial D.r. =
Cs-2, &D.O, 
-------
u:
rj
WJ
     0
IK 	 j--
t,|
\ f*
~T\- ! 1
1 ; i
^

fl
|1 J
~r M ("1
§
4 T 1


NT '
X J
£#
}
V
5 Average
Minimum •
-
"-


1
*,W£m
t


"V
\
c

s
)

X.I
!
?


,
,>, -5
,x
c
,
i
r
J
pmji-^^qjj P
i •J^'ufc'.'jw n
t"J"3^flliad (
i\

j
\

1
*»
)
\
\
r*'-i-*r
Dito S
Survey
•!V'2T Jcaslltiafis far
• Jv!:^nt LiRiitstioiii
>. f \
\
in
\iFV
" N
1 (
y»««j- 2">KQ CFS ^
FiRip: 21.Q°C s
lurce; Wisconsin H c
Date: lune 23-21,1972 1
                                        30
10
0
                                         l>sil^^ fivf^t I*,-.-,,, l^.i
                                         i.Hi'i^ U-..J(  .41 -tvli *'-.]
                   Figure  B
                                                                                                                                                    CXI

                                                                                                                                                    i

-------
                                   -  39  -





     A sensitivity analysis was performed on the model prediction to



demonstrate the range of response to be expected for various combinations



nf reasonable ranges of the parameters.  The results nf the analysis are



shown in Table fl for three critical river milepoints.  Inspection of Table



8 would indicate that the Lnwer Fox River is most sensitive to the following



parameters (shown in decreasing order of sensitivity):  benthic oxygen



uptake rate, algal photosynthesis, river flow, temperature, and deoxygenation



rate for CBOD.



     Sensitivity of the prediction to the benthic oxygen demand is shown



in Figure 9.  As stated in the previous discussion on benthic oxygen demand,



all evidence indicates that the average value will be nearer to 2.5 than



to 5.D gms 02/nr-day, once the sources of the sludge deposits are controlled.



This is due to the rapid lowering of the uptake rate as the sludge ages.



Hence, an average oxygen uptake rate for sludge of Z.5 gms 02/nr-day was



used in the prediction.



     Figure ID shows the sensitivity of the model  prediction to variations



in gross  algal oxygen production.   The middle profile, which is the same



as that shown in Figure  7,  uses average algal oxygen production values



estimated from the chlorophyll-^ data provided by  Sager and Wiersma.   For



comparison purposes, profiles  equal to double and  one half the calculated



algal  c-xygen production  values were utilizer!.  These profiles do nnt



represent c normally expected  situation, but are included to show the



ri,ng3  oi"  sensitivity ta  algal  oxygen  production.

-------
                             - an -



                             TABLE B

                 Model Prediction Sensitivity

                     ta Parameter Changes
Parameter m.
Benthic Uptake Rate
* 5 = Z.5 g/mz-day
S = 5.0 g/mz-day
Algal Productivity
P - 1/2 P'mg/l-day
- p = P1nig/l-day
P =ZP1ms/l-d&y
CBuD Decry Rate (Kr = K,j)
••- K,j - 0.15/day
1 ^ = Q. 'j/di'.y
Kn ~ 0. a/day
NEC"1 [/at?;- Rats
* K-i = 0.14/day
Kn = 0.3/day
Kn = CW'Jay
Initial C30D
Cr.OD = 5.C mg/i
J "EDO1 - 6.0 mg/1
CBuD1 = 9.D mg/1
Initial NBOD
i NBQD1 = 4.6 mg/lm
N30D1 - 9.Z mg/1
Riyir Flov;
* Q = 11Z7 cfs
0 = 2254 cfs
~lt'Ks.i sture
* "• - 21 °C
1 - ZS=C
p. 35.0

7.53
5.35

5. 50
7.53
11 . 60

7.53
5.91
3.39

7.53
6.77
5.89

8.49
7.53
E.55

7.53
7.23

7.53
6. 87

7.53
6,07
m.p. T5.0

5.74
4.55

F.3S
6.74
9.44
.-
5.74
5.2A
f.43

5.74
5.48
C.4E

'.24
6.74
G.Z4

6.74
6.62

5.74
,-.«

5-7a
5.40
m.p. 0.0

4.09
0.05

1.Z3
4.09
g.fll

4.09
3.51
2.40

4.09
".07
3.73

4.68
4.0D
3.49

4.09
3.92

4.09
6.07

4. as
2.49
'i Li DPT:
 5  - -.3 q/Tiz-day
y  - j.i?,'day
                      cBOD1 =  e.a  i,,.]/i
                      NBG3' =  4.:.  nc/1
                          P -  14.0 .,gC2/l-aa>'
                               9 np 23.03

-------
                         fax  Oliver Msitel Sensitivity
   10
=•  a
    s

    2
   0
^ /\
u
i x
i \ !
4 **
V"
River Flow: 1121 CF
Rivsr Ts^p: 21 °C
Conditions: frapos
Variable Paramet


>XK
^^^-^.
h
V
\
X
V
vx-^
-^.
"""^
\
ad Effluent Limits
er: Sludge Uptake Rate

Cliiftva iintabp ~ *J F
- Sludge Uptake = 5.0

— \
K
	 _ |\
X I \
v^ \
V
\
\
X
x
initial Cunditiuns
DO: S.D me
CQQD: B.D mg
N3DD: 4.57 m
g/m2-daif
g/m2-diif
^
^SJ N.
^ \
S \
\ V
\
\
\
\
\
V
'x ^
^
\
/I
/I
I/I
     40
30
2D
ID
                              from Green Bay
                            Figure  i
0
                                                                                       .p.
                                                                                       I

-------

=r 3
\
u
s
&fl n
S S
0
OI
a-
a
1 4
2
a
/ s
*jft | |
/ " ^"~\ Lawer Fai River Kiaiiel Sensitifiti
» I j/ V
f
/
\ ^^
fy_/
\ j""^\
\ i
•>..-.•-•
iii«r Flow: vat i.r
iilver Te.'np: 21° C
Tiiiis: luni. D;
Conditions: pf02«
VarisSHs Psraactaf
«• ^*"
v^


X' . 	 .
t
iiy Averse
2tians
: Chlorophyll A
t"«»
fi
r^
^
r- -^ i \
•j \
\
Initiil Cnndilini
DO: l.O
r.BGD' 5 0
I3D: 4.5"
CHI: 51.1
tii of Cfciariplqll A
1-1
	 .1:1
s^l \L
, K\ •
'Nl V
\
s \
mi/I \
rsa/l \
mgf i \
•I/I
4fl
30                   20
 Miles from Green Diy
10
0
                                                                                                  I

                                                                                                 ro
                                                                          ftgun 10

-------
Frequency of Occurrence Below Given Dissolved Oxygen Levels
     Although the set of parameters chosen to generate the prediction
shown in Figure 7 represent fairly extreme sumiiertime conditions, it  is
recognized that other combinations of low-flow and high temperatures
would result in lower dissolved oxygen profiles.  In order to approximately
determine haw often lower dissolved oxygen profiles would occur as a
result of various extreme combinations of low-flow and temperature, 10
years of daily data from 1961 to 1371 were analyzed.  The results of  this
analysis are shown in Table 9 for the normally critical point just above
De ?erE Dam at mile point 7.3.  The table shov.'s the number of days when
extreme combinations of flow and temperature,, if used as input parameters
in the model, would have resulted in a daily average dissolved oxygen
concentration of less than a given oxygen level.
                                  TABLE 9
               Frequency of Occurrence Below Given Dissolved
                      Oxygen Levels at Mile Point 7.3
Daily Average
DO level
(mg/1)
5
4
3
Average Number cf Occurrences
Below Given Level
(days/yr)
35
B-9
0
Anticipated Range of
Observed Below Given Level
(days/yr)
2-71
D-32
D

-------
                                   - 44 -
                                  SUMMARY

     The effect nf the various wastewater inputs on water quality in the
Lower Fox River can be modeled in a rational quantitative manner.  Such
a model was used to evaluate future water quality in the river assuming
implementation of a proposed effluent program consisting of "best
practicable control technology currently available" (interim estimates)
for industrial waste sources and 90 percent BOD removal for municipal
waste dischargers as required by the 1972 Amendments to the Federal
Hater Pollution Control Act and by Wisconsin State Orders.   The approach
presented herein has been shown to offer a reasonable basis for estimating
the effects on water quality of implementing the proposed effluent
program in the Fox River basin.  The results of the study indicate that
if the effluent limitations are implemented, there will  be a significant
improvement in water quality, and a daily average dissolved oxygen con-
centration of 4 to 5 mg/1 will be maintained in all  areas under most
conditions and will not fall below 4 ing/!  ir-ors than 2%  of the time.   During
extreme low-flow and high temperature situations,  the dissolved oxygen
concentration could drop to about 2 to 3 ng/1.

-------
                                  -  45  -
                             ACKNOWLEDGEMENTS

      The cooperation and assistance of numerous persons is acknowledged
as having been invaluable in preparing the material presented in this
report.
      Professors James H. Wiersma and Paul E. Sager of the University of
Wisconsin at Green Bay provided much of the data used in the analysis;
Mr. Jerry McKersie and Mr. Ralph Berner of the Wisconsin Department of
Natural Resources provided data and invaluable cooperation and advice;
Messrs. Dale S. Brysnn, Glenn D. Pratt, Howard lar,  Walter L. Redman,
Norbert Jaworski, William Richardson, and Robert Hartley, all of the United
States Environmental  Protection Agency, furnished critical  review and
comments on drafts of this report that contributed significantly to the
final report;  Merlin Diepert and EPA staff personnel of the Automatic Data
Processing Branch provided technical assistance; members nf the Graphics
Branch prepared the artwork presented in this report.

-------
                                   - 46 -


                                  REFERENCES
  1.  DiToro, D.M.   "Predicting  the  Dissolved  Oxygen  Production  nf Plank-
     tonic Algae",  notes  for Manhattan  College Summer Institute in Water
     Pollution  Control, Manhattan College,  Bronx,  New York,  1969.

  2.  MastropiEtro,  as  cited in  "Addendum  tn Simplified Mathematical Modeling
     of Water Quality", prepared by Hydrascience,  Inc.  sub-contract with the
     Mitre Corporation and the  U.S. Environmental  Protection Agency, May
     1972.

  3.  McKeown, J.J.  ejt jil_.  "Studies on  the  Behavior  nf Benthal  Deposits nf
     Paper Mill Origin",  Technical  Bulletin No.  219,  National  Council
     af the Paper Industry for  Air  and  Stream Improvement,  Inc., New York,
     New York,  September  1968.

  4.  O'Connor,  D.J. and Dobbins, W.E.   "Mechanism  of Reaeration in Natural
     Streams",  Trans,  ftner. Snc. Civil  F.ngrs., Vol.  1Z3,  195EI,  p.  655.

  5.  Patterson, Dale,  "Results  of a Mathe-.'aii-;al Water Quality  Model of
     the Lower  Fox  River, Wisconsin, " W1' seisin  Department  of Natural  Re-
     sources, March i 1973.

  6.  Quirk, Lawler  and Matusky  Engineers   "Development nf a  Computerized
     Mathematical System  Model  of thp Lowe"1 rax  River from  Lake Winnebaga
     tr Green Bay", a  report to the !/i scons'/1 Oopartment  af  Natural Re-
     sources, Madison, Wisconsin. Avojsi  l?b.9

  7.  Khyther, J.H.  "The  Measurement of '"'"  "-.ry  Productinn", Contribution
     Ho. 825 from the Woods Hole Oc^aiog-^fi'-  . 'r'.stitution,  Woods -Hole,
     Massachusetts, 1957.

  B-  Sager, P.E. and Wiersma, J.H.  "Nutrient Discharges  to  Green  Bay,
     L-?ke Michigan  from the Lower Fax River", presented at the  Fifteenth
     Annual Conference on Great Lakss Rei-?a-c'n,  Madison,  Wisconsin, April
     1D7Z.

 9.  Springer, A.M.  "Investigation of  ths  environmental  Factors Which
     Affect the Anaerobic Decomposition of  -ibrnus Sludge Beds  an  Stream
     LJottnms", Ph.D. Thesis, Lawrence University and  the  Institute of
     Paper Chemistry, Appleton, Wisconsir -  .\'ne  1972.
10.   Thci.'igrins, R.V.  Systems Analysi'?. and  -'risr Quality  Management,  En-
     vironnsntal Science Services Dili's*! an, 'vn^ironrnsntal  Research  and
     Ape 11 cations, Inc., New Ynrk, Hev/ vcrk.  .37?.

11.   Thongs, rJ.A.  "Sediment Oxygen nena-u! >•'-::• ciyafions  of tha  Williamette
     %-•  ,-_r  Pir eland, C^Ggon", U.S. rsDar-.iT:;-  I -)•" -die Interior,  Federal
     i>l£!;..r 7TUu":icn "ortrol Administration, '.'t'cicnal Field Investigations
     !'i-.: ,er, Cii-ci-.nati, Ohio, February "!?70.

-------
12.  U.S. Department of the Army, Corps nf Engineers,  U.S.  Lake Survey
     Chart No. 72Q  "Lake Winnehago and Lower Fox River",  Edition  of
     1969, corrected to May Zfl, 1971.

13.  U.S. Department of the Interior,  Federal  Water Pollution  Control
     Administration, Great Lakes REgion "A Comprehensive Water Pollution
     Contra!  Program—Lake Michigan Basin--Green  Bay Area",  Chicago,
     Illinois, June 1966.

14.  U.S. Environmental Protection Agency,  Office of Enforcement "Report
     on Remote Sensing Study of Thermal Discharges  to  Lake  Michigan",
     National Field Investigation Center,  Denver, Colorado  and Region  V,
     Chicago, Illinois, September 197Z.

15.  U.S. Environmental Protection Agency,  Office of Permit Programs
     "Interim Effluent Guidance for NPDES  Permits", Washington, D.C.,
     Miy 3,  1973.

16.  Wisconsin Department af Natural  Resources, Water  Quality  Evaluation
     Section   "The Fax River, Summary  Report an Water  Quality  and  Waste
     Hatar Discharges  During the Summer nf 1972", Madison,  Wisconsin,
     November 1972.

17.  Hi sconsin Department of Natural  Resources, personal communication,
     February 1973.

-------
                             - 4fl  -
                       APPENDIX
PROGRAM    LISTING

-------
FSRTRUN IV G LFtf£L   21                  MAIN              DATE - 721U    '      19/31/SB              PAGE ODOl
             c                      •
             C                        DISSOLVED OXYGEN STREAM MODEL
             C
             C      PROGRAMMMED  AT HYDH03CIENCE «  IMC. I'rfESTWOQD, NJ«1967)
             C      MODIFIED  BY  ANDREW STODDAHD.  E^A* HEGIQN S  I19?Z)
             c                                                              ' '     ........
             C                             DISCUSSION Or MODEL
             C
             C      THIS PROGRAM DESCRIBES THE INTERRELATIONSHIP  BETWEEN  THE  DISSOLVED
             C      OXYGEN IN A STREAM AND ITS VARIOUS SOURCES  AND  SINKS  SUCH AS
             C      ATMOSPHERIC REAEHATIDN AND THE OXIDATION  OF BDD.  THE  MODEL
             C      EVALUATES THE DAILY AVEHAGC. ONE-D I HENSIONAL  SPATIAL  PROFILE OF THE
             C      CONCENTRATIONS OF DISSOLVED OXYGEN AND BDU  UNDER  STEADY-STATE CONDITIONS.
             C      IN THIS MODEL THE DI5PEH5IVE COMPONENT UF THE MASS  FLUX IS CONSIDERED
             c      INSIGNIFICANT. THE MODEL isi THEREFDHE.ADVECTIVE  AND  PREDICTS THE
             C      LONGITUDINAL QI5TNIHUTION UF DISSOLVED HXYEEN AND BDD DUE TD THE EFFECTS
             c      OF THE VARIOUS POINT SOURCES OF ^ASTEWATE*  UISCHAHGESI  TKISUTAWIESI AND
             C      BACKGROUND MATER QUALITY CCUDITIDNS  IN THE  SEGMENT  UNDER  CUNSIDEHATI UN.
             C      THE CONCENTRATION PROFILES AHE COMPUTED ALONG THE LONGITUDINAL AXIS
             C      UF THE RIVER  AND AHE ASSU'-'ED TO HE  UNIFORM IN  DEPTH  AND  KIOTH IN EACH
             C      SEGMENT.  THE CONCENTRATION AT THE UPSTREAM END OF  A  SEGMENT IS DETERMINED
             C      BY A MASS BALANCE EQUATION. IN THIS  EVALUATION  THE  MODEL  USES A NUMBER OF
             C      BIOLOGICAL* PHYSICAL! AND CHEMICAL CHARACTER IS T I C5  1VHICH  AHE UNIQUE TO  .
             C      THE STREAM Ul;D£P INVESTIGATION.
             C
              C                                                   "
              C     jOUkCtJ AUD SINKS COr^I CE«FD  IN EVALUATING PROFILE OF DISSOLVED OXYGEN
              C
              C      " CA^ab.\'AC£D"US BOD
              C       NITROGENOUS BOD
              C       flEMTHIC OXYGEN DEMAND
              C       ALGAL RESPIRATION AND PHOTOSYNTHESIS
              C       ATK05PHE.PIC HEAEHftTION
              C       HEAEHATIQN OVER DAMS
              C       INPUT FROM WASTE SOURCES  AND/OR  TRIBITAHIES          •
              c                                           "               •
              C                              INPUT  PARAMETERS
              C                                                        ,''
              C          VARIABLE NAME                                         UNITS
              C                                                     .
              C     5T*EAM= NAME AND LOCATION  OF  STREAM
              C    'RUrJDES= DESCRIPTION OF PARTICULAR  SET DF DATA
              C     SEGID= LOCATION UF SEGMENT  BY  LANDMARKS AND NUMBER
              C     CQ= INITIAL CONCENTRATION  r,F  DISSOLVED  OXYGEN             MG/L
              C     FLDLD= INITIAL CAHSONACEDUT. BDD  (CfiUD)                     MB/L
              C     FLUND=INITIAL NiT^aGENCTJS  nOD   (N5UD)                     MG/L
              C     XTDT-T INITIAL '••rLSPOINr  GF  S^WflA1,  M07EL                   XILHS
              C     .,C . '.-  •   ~.  . N.rE.Al. ING  ll^:-.PC.i'«i
              C     XCJDii-  0  h^R D£CKc.ASIf;G  "ILi'PO  VT

-------
FDRTPiAr« IV G L£"IL  H
                    MAIN
DATE = 73141
19/'31/'5fl
PAGE ooaz
  0001

  ODDS
             C
             c
             c
             c
             c
             c
             c
             c
             c
             c
             c
             c
             c
             c
             c
             c
             c
             c
             c
             c
             c
             c
             c
             c
             c
             c
             c
             c
             c
             c
             c
             c
             c
             c
             c
             c
             c
             c
             c
             c
             c
             c
NTOT= TOTAL NUMBER OF CEKKENTS  IN  SYSTEM
'.iC= 00 FROM WASTE LOAD AND/DH TRIBUTARY
WL= CBOD 5 FROM WASTE SOURCE AND/OR  TRIBUTARY
KN = N30n FMQH WASTE LOAD A\D/OH  TRIBUTARY
00= H1VER FLOW UPSTREAM LlF  SEGMENT BOUNDARY
QA= FLOW OF WASTE SOURCE AND/OH TRIBUTARY
HR= ALGAL RESPIRATION RATE
PMM= ALGAL PHDTDSYNTHETIC OXYGEN SOURCE
DELTA= INTERVAL OF COMPUTATION  IN  SEGMENT
FLENG= LENGTH OF SEGMENT
CON5T= *l FDR CONSTANT CKD55 SECTIONAL AHEA
          IN SEGMENT
     = H FOR LINEARLY INCREASING AREA IN
          SEGMENT
AREA= CROSS SECTIONAL AREA  FOR  CONST=*1
SLOPE= SLOPE OF LINEAR AKEA FUNCTION FOR
      CDNST=D
FINT= INTERCEPT OF LINEAH AREA  FUNCTION AT
      UP5THEAM BOUNDARY
FL= RATIO OF ULTIMATE CB.'JQ  TD 5 DAY  CBOD
FN= RATIO OF ULTIMATE NBuO  To 5 DAY  NHDD
TEMP= STREAM TEMPERATURE
cs= SATURATION VALUE  OF DISSOLVED  OXYGEN
hDAM= HEIGHT OF A DAM IN  SEGMENT
ALpHA=COEFFICIENT FDR HEAEHATION OVER DAMS

C&£FrIClENTS FOR BRITISH  0AM REAERATlaN EQUATION
A=  1.25 —CLEAR TO SLIGHTLY  POLLUTED  WATER
  =  1.00 — POLLUTED WATE«
  =  0.30 — SLV.AGE EFFLUENT
3-~  1.0D--WEM ^ITH FREE FALL
  -  1,30 —STEP WEIRS  OR CA'JCAOES

F~  FRACTION OF SLUDGE  COVER ON  BOTTOM
FL(MH= CBDD REMOVAL  CDEFK  AT 20 C
FLaNrf= cynD DECAY COEFF  AT  20  c
FLOKN= NQOD DECAY RATE  AT  zo c
S=  OXYGEN  UPTAKE  HATE  FHar-l  BENTHIC DEPOSITS
DEPTH  =  AVERAGE  DEPTH IN  SEGMENT
                    LBS/DAY
                    LHS/DAY
                    LBS/DAY
                    CFS
                    MED
                    MG/L-DAY
                    MG/L-DAY
                    MILES
                    MILES
                     SO.  FT

                     SQ  FT/MILE

                     SB  FT
                     DEE  CENTIGRADE
                     MG/L
                     FT
                     DECIMAL
                     I/DAY
                     I/DAY
                     I/DAY
                     GM/SQ METER-DAY
                     FT
 DlMtNSION DI30I iFLOLI301 , FLDN13D) iC|3D)iXXI30liFOFXI3D)i
1STKEAMI2QI iSEGlD 120) iHUN'JES IEOI
 NCHUN=3
 NCHIIN=1  AS INITIAL COUNTER FOR SEGMENT SYSTEM OF STREAM MODEL.
 ANALYSIS FOR LOrfEH FOX RIVER USED NCHUN=3 DUE TO SEGMENT SYSTEM
 IN QLH REPORT. IN EPA ANALYSIS MENASHA CHANNEL WAS  CONSIDERED  AS  A
 TRIBUTARY TO LOWER FOX RIVEH . THIS DELETED SEGMENTS 4-5 USED  IN
 OLM MODEL I1S69I ,
  0003
  DQD4
  D035
 READ(=.]25DI (STPEAMIKI
                        .-:•.-? iz 01

-------
FORTRAN IV 6 LEVEL   Zl
                          MAIN
DATE = 731U
                                                                                        = »'5F  B5C3
 0006
 DD07
 OQCB
 0009
 DD10
 0011
 OD1Z
 0013
 nou

 0015
 UD16

 DD17
 001B
 DD19
 DDja
 ODZ1
 OD22
 D023
 0024
 D025
 D02&
 DD27

 QOZB
 0029
 0030

 DD31
 CD 32
 0033

 OD34
 D035
 OD3&
 0037
  0039
  DD39
  D040
  0041
  UD4Z
  D 043
  OD44
  0045
      FORMAT(3F1D.2)
      WHITE lib. 1300 I (STREAM IKIiK=li20|
 13DO  FORMAT I1H1i//p20A4,//l
      WPITE (6i1Z55I IRUNOES IKI »K = 1i2DI
 1255  FORMAT l/,2UA4i/»                            "        "  —-  _
  910  READ I5i12031 CQ,FLdLO,FLONO,XTOTiXCDDEiNTOT
 1203  FOHKATCJFlO.ZiIIDI
      WHI1E |b, 12121
 1212  FDHMAT l/i i <»o«»a««*«a«i/i2QA4,/i4DX»'INPUT',/]

      RE4D 15 i 1201 )  DELTA,FLENr., CONST, AREA » SLOPE i F INT i HD AM p DEPTH
      KE4D I5i 1201 I  FLiFNiFLDKR(FLOKD»FLC)KN»SpF
      PEiUI5,lZD2)  PHMiRRiArBiALPHA

 l.'tf?  FORMAT I/.i3X»*WC' »BXp 'WL1 i3X,» >WN" iflXt iQO« ,BXp ' QA ' iBXi ' CS • i 6X1 'TEMP'
     1)                                              "
      WHITE 16 i 1Z01! VIC,WLpWNpCO,QA,CSiTEMP
      WRITE IS,1EU9I
 120B  FDflMATI/p5XpiDELTA'»5Xf'FLENG"p5Xi«CONST'16X1'AREA1p5X»'SLOPE1r6Xi
     1'FINT'1fiX,'HDAHi,5Xi 'DEPTH'1
      WRITE Ifi i 121)1) DELTAiFLEKO^DNST.AREApSLDPEpFINTiHDAMiDEPTH
 1209
     iqKr'F">
      WRITEI&.1ZOM FLpFNiFLOKH,FLDKDiFLDKNiSpF
      WRITE 16.12lni
 1210 FOHMAT 1/.7X, iPMM'.BX.'Rk'.SXi'A'iSX.'B'.SX,'ALPHA')
      WHITE 16,1Z02I PMM.RR iA,t) > ALPHA

 C     COMPUTATION  DF  ATMDSPHEHIC REAERATION RATE  JFLDKA)
    ,  FLOKA = 1Z.9»I(a3/AREAI*«(.5l l« I IDEPTH!•«(-1,5)I
      WMITEI&.1211IFLOKA
 1211 FORMATI/)5X. 'FLDKA1 i/iFlD-Zl
 1206 FORMAT l/i4UX, •OUTPUT'p/l
      WRITE 16,1205)
 1202 FDHMATI4F10.Z,F10.31
 l.-:03 TO J"AT 1/pllXp 'MP'ilXp >D FICIT'iSX; 'TERM! ':-3r, iTCRM2't3Xi iTERMJi i

-------
                                                         GAlt = 7-JlM
                                                                              19/31/33
0046
0047
UQ4B
0049
0052
0053
0054
OB55
cuss
0057
D 050
0059
OOfiO
D061
OQS2
UHS3
0 D &A
OOf-5
0067
oo&a
 D07D

 QD71
 D072
 DD73


 QP74


 r: •> 7'.
            c
            c
            c
            c
             C
             C
                  ADJUSTMENT OF KATE REACTIONS  TQR STREAM TEMPERATURE
                               1 .DZ4«* ITEMP-20.I
                               ,.04^* i fEM^-so..)
                               ,04*«(TEMP-ZD.)
                  FL[)KiJ=FLOKN«loOfl*»(TEMP-2D.>
                             •ITENP-20.1
                  MASS BALANCE COMPUTATION  AT  UPSTnE/'.M END OF .SEBMENT
                           WASTE SOURCE  FLCtf  IN MOD TO CFS
                  QA=UA»1.54723
                  WN=WN/5.4

                  Cl= (JQ»CG*WCI/Ql
                  Dl=CS-Cl    .                   • •
                  FLOL1=IQD»FLDLa*WLI/Ql
                  FLDM=[QG»FLONa»WNI/Ul

                  TE5T FOH CROSS  SECTIONAL  AREA FUNCTION
                  IF(CONSTI2.2»3
                                                             •««»»«««««•«»»«»««««« «»•»••••«»«•
                   CONSTANT CKOSS SECTIONAL AREA
                 3  1 = 1
                   FLOJA = - [FLOl
-------
                J|-.  ^i                  MAIN               3'

                   ')rFK>7 OUE Ta POINT SOUR"-: np nj^;-.W,V~V  0?
             r
             C      'J-TICIT DUE T0  ALijAl  K1-;' IRATItM  AND  PHOTOSYNTHESIS
                   T>~r,Mb~( IRR~(PHN*c., -.5/^«l- I' ' VFI.C1:;:,/ V . -LXFifXOJ.VM I

                           CUE TO  rtEAErTVTiCN 0<;T:;- A  0AM
             r      TOTAL DEFICIT  UF  DISSOLVED OXYGEN
, ;7':               :j'.i)= TEr?Ml + TERHE*TERM3*TERM'.
L'Dt«'J               C(1I=CS-D III
^ , " 1               IF ( C ( J ]  ! 3 I] ? '* 0 i 4 0
OL  ••;            jo cm =0-
             c
             C      COMPUTATION OF  CBOD AND NflaC1 D. ^T/IItU'VIOM
                40 FLQLUI=FLLLl»EXP(rLOJR-XI
                   FLONIII=FLDN1-EXP(FLOJN«XI
             C
             C      TEST FOR  INCREASING OR DECREASING  RiVEF? KILEPOINT
                   IF IXCQDEI560i56Di55G
               55D XX(II=XTDT+X
Qof.7               Gb TO 551
:OUB           56C XX(1I=XTQT-X
•JHB;           551 CONTINUE

                   TEST FOR  END  OF SEGMENT
                   IF  <-FLENG|4,Si50J
                 •'• '. = X> DELTA
                  iFLQL II I irLONdl i C ll>
              i'jCO FOH^AT l5XillFBi2l  --  -•
                   1 = 1 -1
                   60  TD  6
               5-'0 X = FLENG
DT"?               GQ  TO  6
0090             5 WRITE lbil TEFW i TERMS i TERM& »
                  1FLDL III iFLDNIII rCll)
             C
             C     REINITIALIZATION OF BOUNDARY CONDITIONS AT  UPSTREAM cfio Or  SEGMENT
                   FLOLU = FLDLHI
0101               FLDNU=FLDN|J|
CID2               XTDT=XXIIJ
             C
           . C     TEST FQR  FINAL SEGMENT  IN  RIVER SYSTEM
DIPS    -          . NCHUN=NCHUN*1
DID*               IFINCHUN-NToTlliliZO

             C
             C     LINEARLY  INCREASING AREA WITH CONSTANT
0105    - '        Z 1 = 1
D10&               XQ=F ..NT/SLU?!:'
DID?               i- . ,..;,- -  ,-.••..* S-. ^c •.-•   '-  •)

-------
FORTRAN IV G LEVEL  21                 MAIN

                   FLOJN=-(FLOKN*Sl.OPE/Ca/i& ,4!

                 9
01 OB
0109
0110
Dill
0112
0113


0114
0115
Ollb

OUT
U11S

nil?
0120
1121




0122


0123


0124


D125


0126


0127


C12B
012S
013D
D131


0132
D133


0134
0135
D13b
0137






C
C



C


C



C
C
C
C

C
C

C
C

C
C

C
C

C
C

C
C




C
C


C
C
•



                                          DATE = T3U1
       I = FLOJN«FDFXII)
    XjR=FLnjR»FOFXII)        -              __         ___

    TEST FDR DAM REAERATION EQ TO USE
    IF IHUAM-15. I 3DOi3Q0.3ni
300 IF! rEMP-?5.>3»2i3D2,301
302 IF nEMP-2D.)3Dl i3D3»3D3
    COMPUTE DEFICIT USING MOHAWK R  EQUATION
303 DEF&=ALPHA«D1«HDAM
    GD  TD 305
    COMPUTE DEFICIT USING BRITISH ED
301 Z6=I1.*(D,11*A*B*HDAMI«<1 . *G . 046«TEMP I I «« 1-1.0)
    DEFn= Dl«ll.-26)
305 CONTINUE

    COMPUTATION OF COMPONENT SQURCEs'AND  SINKS OF DD DEFICIT

    DEFICIT DUE TO POINT SOURCE  OF CBUO
    TEKM1=IFL»FLOKD«FLDL1/IFLDKA-FLDKN) >MEXP (XJRJ -EXP (XJAI J
                                                            19/31/SB
PAGE 0006
DEFICIT DUE Tn POINT SOURCE OF NBQD
TERM2= (FN*rLDKN«FLOMl/
                                        ) « !E,XP I X JN \ -EXP I XJA) )
    DEFICIT DUE TO DISTRIBUTED  9ENTHIC  DEMAND
    TERHJ=lS/FLOKA)«ll,-EXP|XJA) )

    DEFICIT DUE TO POINT SOURCE OF  DISSOLVED OXYGEN
    TE«H4=DI«EXP 1XJA)

    DEFICIT DUE TD ALGAL RESPIRATION  AND  PHOTOSYNTHESIS
    TEHM5=l IRR-IPMM»2.».5/3.1416) ) /FLDKA I « 1 1 . -EXP (FLDJA'XJ I

    DEFICIT DUE TO REAERATION  QVE«  A  DAM                   .
    TEHHb=-DEF6« (EXP IXJAI!                                „
                                                       i   r
    TOTAL  DEFICIT UF  DISSOLVED OXYGEN
    T (11=  TERM 1«TERMZ«TERM3*TERM4« TERMS »TERM6
    CII]=CS-DIII
    IFICIl) 150,60,60
 SO C[II=0,

   • COMPUTATION  OF C3DD AND  NQOD DISTRIBUTION
 GD FLUL(I)=FLOL1«EXP IXJRI
    FLDNIII=FLON1*EXPIXJNI
    TEST  FDR  INCREASING  OR  DECREASING RIVER MILEPOINT
    IF IXCCIDE) 66D ,66Di65D
650

-------
FORTRAN IV G LEVEL  l\                 MAIN              DATE =  73141          11/31/5B              PAGE nOO?

 Cir,»          i':51 CONTINUE
             c
             C     TEST FOR END OF SEiMENT
 0139              IF IX-FLEN6) Ui5»501
 0140           10 K=X*DELTA
 GIU              WniTE(&tl*OHlXX!I) .OUI iTERHl»TERM2iTERM3iTEHH*iTERHSiTERMii
                  1FLULID  .FLDNIDiClI)                                                      •^•~
 DH2              1 = 1*1
 D143              CO TO  9
 0144          5D2 X=FLENG
 D145              GQ TO  9                                                               *
 01*6           211 CONTINUE
 0147              STOM 9999
 D14S              END

-------
DOCUMENTATION

-------
                                                  TABLE 2

                                         DATA IOTUT REQUIREMENTS

                                                  COLUMN
Card
1

2
3
4,
5
6
7
a
i-10
STREAM 	

RUKDES----
CO
SEGID- 	
we
DELTA
FL
PMM
11-20



FLDUQ

WL
FLENG
FN
RR
21-30



FLDNO '

WN
CONST
FLDKR
A
31-40
f i pi rl 1 -

f i nl A 1-____ _,
XTQT
Fi E.1 ril-_ ______
QO
AREA
FLOKD
1
41-50 51-60 61-70 71-BD



XCODE NTOT

QA CS TEMP
8LDPE FINT HDAM DEPTH
FLOKN S F
ALPHA
Nates;
(a)  Repeat  cards four through eight for tntal numter  (NTOT) of segments
(b)  STREAK, RUNDES, and SEGTD are alpha-nunerlc  variablEs with 20A.4 fatmat, -da^ta entete'd(  col.  1-iO
(c)  NTOT ts an integer  variable with 12 format in col, 59-60
(d)  ALPHA is a floating point variable  with F1Q.3 format
(a)  All other variables are  floating point with F10.2 format

-------
                                  SAMPLE INTUT CARDS
                                STREnfl
                                 re;-; ,%jvz?
                                                   TD 'jREEH BAY
                                            -"; 2'J-2: • I-??:.   44I3C BFif
'[ TLD      TL
j. ?        1!
                                             0. C'
                                                               HTDT
          SEGMENT 1
                     SEC ID
                   tft» -  EES'Go:! i\'0c1  PnPER  CD
-, c
6,0
LCL1 A

ci.'ss"

ft
1 , 83

FMM
:-:.3
i
UL
0.0
FLEtlG

6.53"
I
FH
1.0
i
RR
a. 13
1
it: i
0. 0
CONST

i.o
i
FLDKR
6.3
1
A
b.

re
1020.3
ftRCft

976.0

FLDKD
0.3
i
B
b.

I •*'
0.0
SLOPE
>
0.0
1
FLDKH
d. 14
i
ALPHA
* ft I)
0. 0
j
CS TEF1P
9.2 20.0
ii
»4
FIHT " " HDAM " " DEPTH
• * i - * i * #
0.0 0.0 2.0

S F
5,0 6.5




                                 SECID
          SEGMENT £   BEHGHROil PAPER  CD - KH1I1PLV
>. 1.7
           ML
                      no
DA
                                                        C£
                                                        TEMP
                                                        20.
                                                          i)
                                     ,i ,. .    •, . • i1« ,. i i'.  • :• " . ;l .«ii •! n t! >i »• i: 11 ti ti i' >i ij d n u n 11 it <  '
                                  i' f f : [ •' ' ' j M I ,' I  r H I H I I I f M 1 I !1 H I 11 i II M 1 I I I 1 I  II'
                                  • :  . .  :'  ' •"  ?  •  ,"'.'.   ;" .-2 • 11  \ i:: .• j:: ?, . • •

-------
SAMPLE     OUTPUT

-------
       *.UH>,- ' G/'T, •
1C

•1
Q
1
z;
FL
CV FU 1.0
SEGMENT 1
'•1C KL
.0 3,U
I,TA FLcN?
.53 0.53
rL FN
,-S 1 ,,00
t-',- " RR
.3C 2 11
CA'
'i a
( LC.MD XT!5T XCOPE NTDT
l 1 . {•'. ', 3D. 63 O.D 4S
INPUT
Hi! DO QA CS TEMP
Q,|] 10£i.3D OnU 9oE^ i"93Cl»
CONST AREA ^LOPt FIN" ' HDAM DEPTH
l.DO 97fiL00 n.r 0.0 D.O 2.53
FLOKR FLDKD FLOKN S F
0,30 0.30 0 ,. 14 Sp.BD 053Q
A 3 ALPHA
0,0 D.O D.D

                         OUTPUT
TfHHZ   TERH3
                                          TERMS    TE~,M6    CSOCl
-•J.CO     0,0      D.D      0,,8     -5i,80     0.0      0,0.   >  6.00   iX-60    XO.OO
-1.57     0,IU    0«,05     (i,12    -D,!T.9   -0*13    0=.D      5.95   11.fi     S.77
                          INPUT
   VC         WL
61.70   2C375.GS

rr i        ' f-  TI
 0 . ' -       •'  4 'I
             WN
        2301. Oil

          CCMST
      QD
 1328.30
   DA
 T.'-n

51 n~r-"
  CS
9^0
 TEMP
23.00
                                                     o.o
                                               ?.r-r-

-------
         F.-J
         0 0
                      "LOKR
         Rfi
       1*25
                       c.o
                            i! .0
                     TERM?,
                                TE,?
if ,33
" * I A-
                      o.o
                             o,r-
                             O.U5
                                        ,0?    6 05
                                           i .
                                           O.i1;
                                            0,0
                                                                  is
                                                                  4-3,
                          t.^41
 SEGMENT
                                 INPUT "
    >c
112.uO

 DELTA
  0.1'
12.50

FLOKft
 0.12
          V.'L
           Fi-ENO
            D .14
1,00

  R*
1.25
     WN
3131.00

  CONST
   1*00

  FLOKR
   0.12
                  o . c
                       ao

                     AREA
                                  B . n
                                      SiOPI
                                       J.C
  C5


FiNl


   S
5 C C
 TEf-'P
2 D „ P 9

 HP AM
                                                               F
                                                            i,oc
                                                                     L'Ef^TIi
                                 OUTPUT
        MP  DEFICIT   TERKI    TERKE   TE^.MS   TC-TW-    vcsas
                                                                   caco     waoo
0.14    6.21     0.0
0,00    6,29     D.1S
           O.Q
                          O.Q
                          0 ., fl 6
                                          6, IK
                                                       0,0     G-.3
                                                      -Oi.12    (1 . B
                                                                  20.63
                                                                                 a»T«J
                                                                                 B«7i
                                                                                    H.9S

-------