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                                                        evision No.  0
fluctuations can be calculated by simplified analytical approximations,

as summarized earlier in Table 2-2.



      Time-variable approaches to eutrophication problems are sometimes

 employed when a time-variable data base exists (or can be developed)

. to calibrate tbe model dynamically over a range of conditions.  Models

 such as SECSXV II and WASP are constructed to be run in the time-

 variable mode.  When using these models, the computation can be

 continued, using constant input values, until a steady-state condition

 is reached. (QUAL II can be used in this mode as well.)


      A general guideline for decisions regarding  the appropriateness

 of a steady-state versus a  tiae-variable approach is as follows:
                                                                      •

         • If phytoplankton  chlorophyll concentrations are relatively
           constant over a tiae period  of 1  or 2 weeks,  then  a  steady-
           state approach is  justified.  Where DO  levels are  the water
           quality feature of interest, periods of  this  length,  during
           the  critical  season in terms of stream flow and  temperature
           are  those usually  selected for investigation.  Where  they
           exist,  spatial variations in algal  biomass  can be  handled  by
           spatial averages over appropriate river reaches.

         •  Where the principal water quality issue is  biomass levels,
           longer tune periods  (covering one or more seasons) are
          unually selected.  On. such a time scale, expected  changes
          are large, and time-variable eutrophication models are the
          most appropriate modeling approach.


3 •! .4  Kiaec ie Form lag ions

     As indicated by Table 3-1, the steady-state SRSIK model can ad-

dress nutrient/eutrophication effects only to the extent.that it can

-------
                                                                         , Q
  incorporate gross photosynthetic oxygen production mnd Algal respir-

  ation valuer (P-R) in the disaolved oxygen calculation.  Since the

  model contains no elements for chlorophyll and nutrients, it has no

  capability for evaluating hov P-R and hence streaa DO effects would

  change,  based on nutrient control.  This aodel would be applicable

  when:
          • Dissolved oxygen response to BOD loads  is the primary water
            quality problem of  interest.

          • Algal  effects  are a minor component  of  the dissolved  oxygen
            concentration  dynamics.

          • The point source discharge being studied  is a minor con-
            tributor of  the total nutrient  load  causing the  algal DO
            effects,  or  for some other reason is not  the  subject  of a
            Hutrient Haste Load Allocation.
                                               •     •

      Models providing  detailed kinetic formulations  (such  as QDAL II,

 EZCZIV II or WASP listed in Table 3-1)  are most appropriate when:
                          •

        .• An important vater  quality concern is the magnitude and
            temporal  or  spatial variation in phytoplankton biomass.

         • Algal effects  are a significant  element of  the dissolved oxygen
           resources.

         • The complexity and  significance  of the environmental effects
           warrant the magnitude of  the  resources (both data collection
           and analysis) which arc implied  by the uae of such models.

         • An assessment of the impact of nutrient load reductions is
           desired.


Since the  introduction of complex kinetic «utrophication models by

Chen (JO)  in 1970 and Di Toro,  at ml.,  (6)  in 1971, these models  have

undergone  continuing improvement and refinement.  It is important that

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                                                         Revision No.  0


 the  analyst  use the most current  version of the kinetic  femulations,  in

 addition,  such  models  are sufficiently  complex that  it is  important to

 perform a  baseline  check of  the model program to ensure  that  it  is coa-

 puting correctly, either by  checking results against analytical  solu-

 tions or against manually calculated results covering several integra-

 tion steps.



 3.2  MODELING PROCEDURE



     The most appropriate modeling procedure to adopt in a particular

 case will depend on the situation being addressed.  One of the following

three general situations will usually apply to the ease at hand.
        Situations where the photosynthetic effects on DO are
        relatively minor compared with other "influences, or where
        nutrient allocations are not being considered for whatever
        other reason.   In such cases, the analyst may seek only to
        quantify the algal component of the DO response so that this
        effect can be -factored into calculations to determine appro-
        priate allocations for CBOD and/or NBOD.  Appropriate tech-
        niques for this situation are discussed in Section 3.2.1 below.

        A WLA analysis  that requires an allocation of nutrient loads
        because algal effects on DO in a stream are substantial.
        represents a situation1 requiring an increased level of detail.
        For  stream situations where these effects can be examined with
        * steady-state  modeling framework. Section 3.2.2 below reviews
        approaches which are appropriate.  Nutrient/phytoplankton DO
        interactions form the basis for nutrient WLA's which are
        geared in stream D.O. effects.

        Circumstances that require detailed evaluation of phytoplankton
        population dynamics in response to nutrient•inputs and other
        environmental factors may require the use of complex kinetic
        eutsophication  models.   These may be appropriate where the
        receiving water system is complex, where longer-term (seasonal)
        changes  in algal population are important,  and/or population
        levttls per se .are' important.  A situation of this type is not
        covored  by that manual.
                               3-10

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                                                          Revision /»o, u
 3.2.1  Set Algal Effects on Stream D.-O.

    .  Where the WLA analysis requires only the contribution of algal
 effects to the net average dissolved oxygen concentration at a streac
 station,  and an estimate Of the magnitude of the diurnal D.O. variation,
 the necessary calculations may be performed using either the simplified
 equations presented in Table 2-2, or a model such as SNSIM^.

      In either case,  an estimate of photosynthetic oxygen production ard
 respiration  is required as an input for the calculation.   The necessary
 estimates can be  derived from several different  types of  field monitor-
 ing data,  including

      e  Light  and  dark bottle studies (or Benthic chambers.)
      •  Diurnal dissolved  oxygen observations
      •  Chlorophyll concentrations

Section 4 of  the manual  discusses the analysis and interpretation of
such  data to develop  the inputs  required  for  model calculations.  These
values then provide a  constant input  for  the  model,  similar  to the way
sediment oxygen demand  is  incorporated.

     In most cases  where a net algal  effect on 9.0.  is to be superim-
posed on the results of an analysis of CBOD and NBOD impacts,  the
analyst will have no sound basis  for modifying the value of  P-R derived
from survey data.   It should nevertheless be  recognized that the proce-
dure does not consider the following points:

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      •    Projections for minimum design flow conditions  (e.g. 7Q10)
           oust consider that algal activity night be different than
           under more average simmer flow conditions, during whiph
           surveys may have been conducted.  Travel time increases under
           lower flows, providing a greater opportunity for phytoplankton
           to reach their maximum population potential.  Stream nutrient -
           concentrations may be either higher because of reduced dilution
           or lower because of reduced nonpoint source loads.  Water clari;
           might not be the same under, average summer flow, and minimus  -
           flow conditions.

      •     Nutrient discharges stimulate growth of populations which are
           present in the stream at the point of discharged  The tacit
           assumption made when a constant P-R component for algal
           effects, developed  from survey data, is transferred- to low
           flow conditions, is that the upstream contribution of such
           populations remain  essentially unchanged.


 3.2.2  Effect  of  Nutrient Levels on Stream P.O.



      For  situations  in which  phytoplankton impacts on  stream D.O.  are

 large enough to warrant  reduction  in nutrient  levels as  a  means of  '

 supressing these  effects,*analysis procedures  are required'which  first

 calculate  the  effect  of modified nutrient  levels  on phytoplankton  popu-

 lations, and then the  effect  of  the  modified phytoplankton level  on

 stream  dissolved  oxygen.



      QUA!  II and WASP  (Table  3-1)  are models which are able to  address

 this  situation.   la addition, a  simplified  "desk  top" analysis  is

 described* below, and illustrated by  example is Section 5.   In most cases

 the formal computerized models Identified above will provide  a  more

accurate analysis, given the  availability of adequate data.   For some

users they may also provide a more convenient analysis»  *
                             3-12

-------
                                                            rvc » i 4 i wii  itw.
        The presentation of the desk top analysis procedure however.

  provides an  effective way of illustrating the following:





       *    Xf~cions"a  ^ ^  Cr*aSl*"d la"  Che  "«"~T  **««•  f=r


       •    The type of system responses: which  occur.

       •    The type of insights that can be  derived froo  a
            analysis, and the perspective obtained which can
            tailed analyses which may follow."



       One example of the latter is the concept of "short" versus "long-

  streams.   Because nutrient limiting concentration, are ,o low,  there may

 .be  situations in which even substantial  reductions in nutrient  dis-

  charges will  not influence the levels  of phvtoplankton or the D.O.

  effects,  in a  stream reach of concern.


            •                                                           *

 3.3  D2SK TOP ANALYSIS PROCEDURE.                                  '




 3*3>1  Nutr*«*C and Phvtonlinkten Distributions - "Short" Streaas




      A. previously stated, residence time i, an important  factor in

 determining if maximum  phyetplaakton growth will occur. Streams with

 inadequate residence time  for m«im«m growth are referred  to  a.  "short"

 streaas.   Growth  relationship, in  the,, streams are diseuas.d in this

 ••etion.   Relationship, for utream,  with reaidenc.  time, in exce,,  of

 that needed for maximum growth ("long"  stream,)  are discussed  in section

3.3.2.
                           3-13

-------
      In short streams, maximum potential algal populations will not


 occur because the required travel times in the streams to achieve thec


 are often greater than the actual travel times.  For test cases, a


 simplified model can be constructed for the limiting inorganic nutrient


 concentrations and the phytoplankton (chlorophyll a,) concentration — so


 long as th« nutrient is in excess of phytoplankton growth-limiting


 concentrations.  For purposes of determining "short" streams, a defini-


 tion that nutrients are in excess if they are greater than five times


 the Michaelis concentrations (5 ug/1 inorganic phosphorus, 25 ug/1


 inorganic nitrogen)is'adopted.  Therefore,  inorganic phosphorus and


 nitrogen will be considered in excess of phytoplankton growth-limiting


 concentration if their instream concentrations are greater than 0.025 mg/1


 «nd 0.125 fflg/1,  respectively.
                                                                     9


     •                                    "

   •  As  shown in Figure 3-2, both inorganic phosphorus  and nitrogen


 instream concentrations at the outfall  are in  excess  of the Michaelis


 concentrations for various degrees of treatment when  the  effluent  flow


 exceeds  one percent of the total  stream.flow.  The  indicated  relation-


 ships apply for  POTW's, since  they are  based on typical effluent concen-


 trations for municipal discharges.  The flow ratios which produce a


 nutrient excess may be quite different  for industrial discharges if
          .                                   '

 typical effluent nutrient  concentrations are higher or lower  then the


municipal data used for the illustration.  For example, pulp  and paper


effluents generally contain much lower  nutrient concentrations than do


POTW discharges.
                                 3-14

-------
                        Activated Sludge
                        Effluent
                                             Activated Sludge
                                               P-removal
       0.01
          0.001    0.005  0031      0.05  0.1

                RATIO, EFFLUENT FLOW/TOTAL RIVER FLOW
2   €  10-°
f\ A JB_
23
SMS
§83
        "H
       0.1
                                                   Frew ««f. (23)
                 NITROGEN
                       Activated Sludge
                       Effluent
                                            Activated Sludge
                                              N-removaJ
                                   0.125 mg/C N
                    T
         0.001     0.005 04)1     0.05 0.1        OJ  1J3

                RATIO, EFFLUENT FLOW/TOTAL RIVER FLOW
        Figure 3-2. Inorganic phosphorus and nitrogen at outfall for
                  different ratios of effluent flow to total river flow.
                               3-15

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                                                           Kev3.so.on.iNo. u
        Ihomann and Mueller (23)  describe a simplified  set  of  differencial
    equation* for chlorophyll a and inorganic phosphorus and nitrogen under
    a  steady state condition:
                                                       CM)
                            G A
                                        (3-3)
    where:
A
P,N

t*
X
u
a_
concentration  of  chlorophyll  a.
concentrations of inorganic phosphorus
and nitrogen
travel time in stream  (« X/u)
distance downstream of effluent
stream velocity
phosphorus:chlorophyll ratio
(0.001 mg p/vg A)
nitrogen:chlorophyll ratio
(0.007 mg N/yg A)
phytoplankton  net growth rate
6  - D  « 	
              H
      phytoplankton growth rate  (r^ « 1.0)
      phytoplankton death rate
      phytoplankton net settling velocity
      average stream depth*
yg/J
mg/1
days
miles
miles/day
mg/yg
mg/yg
   -1
                                               ,-1
                                               -1
                                                                day
                                            day
                                            ft/day
                                            ft
     In thesis equations, inorganic phosphorus is assumed not to settle
and is not recycled from respired algae.

-------
Solutions .of equations 3.1 through 3.3
                                                are:
                  St*
          A » A_ e n
            * po " ~^»	' '*     - 1 ), for p > 0.
   and    N « N  -
                                                                  (3.4)
                                     P > 0.025 mg/1      (3.5)




                                 for N > 0.125.mg/1      (3.6)
                                        .  A(). % Md    „.
      *.»  that  th.se  ecuations  ire enly


      «. in «=.ss  cf phytopiankton growth


      instrew concentrations of chl6rophyll .


      (»g/i) «d inorganic nitrogen (mg/1) lt the outfall Ut.r aixing of the

     upstreaa »„ .«ltten£ floHs.'  „„ CWU ^ ^ ^ ^^^ ^ ^



     scre^'.h.r. nutrient, begin to significantly affect the phytopiankton


     growth rat, can be  calcuiated  fro. Eouation 3.5 or 3.6 by substituting p


     - 0.02S *g/l for  inorganic  phosphorus and  0.125 ^/l for organic nitro-
     gen:


where:    tj. tj . travel times to stream  locations where  Inorganic

                                 n?1?'09en concentrations  begin to
                                 I1n.1t phytoplankton growth  (days)
                  6  A,
                                             (mg/l)

-------
                                                            revision no. u




     In summary, "shore"  streams are defined as those screams where


actual travel times are less than t*  or c* as calculated from


Equations 3.7 and 3.8.  For such streams, phytoplankton vill vary
                                                                    '""•'        »

exponentially according to Equation 3.4 and are essentially independent


of nutrient concentrations (which arc in excess of growth-limiting


concentration's).  Nutrient removals.at a point source will reduce the instrean


concentrations p  and/or  K  and will decrease the travel  times  t* and/.or
                o         o                                     p

t.*  If t* or t* becomes less than the actual stream travel time, peak
 W      P -    «*

chlorophyll concentrations vill be reduced.
     For small streams,  10 to 20 miles long with velocities of 0.5 to 1.0


ft/sec  (8 to  16 miles/day), resulting travel times are from 1 to  2.5


days. • If a high rate activated sludge (HRAS) plant.flow with p • 5 ag/1


(752 of which is available for.uptake) mixes with an equal upstream flov


with p - 0.02 mg/1 — and P  - 25 ug/1, C  « I/day, G  - 0.5/day, t*
                           o            .             n             p

will equal approximately 7 days-.  If phosphorus removal were instituted


and the effluent were reduced to 1 mg/1, t* would become approximately 4


days.  In both cases, t* exceeds the actual travel time and'the strean
                       P

would be classed as a "short" stream, with phytoplankton concentrations


varying exponentially throughout its length.
     The following procedure for analysis is suggested:





     1.  Determine the limiting nutrient- {.Inorganic phosphorus or


         nitrogen).  Include aa estimate for the fraction of the


         inorganic nutrients available for uptake (say 0.75).
                                 3-18

-------
                           •          —


    2.   For present  conditions,  estimate C ,  c,  D  and  v  using
                                          n      p      c .    *



        observed  phytoplankton  data  and empirical relationships.




    3.   Calculate t*   or  t* for  present conditions from Equation  3.7  or




        3.8.
• If t* (or t*) is greater than the actual travel tiae



  in the stream reach under c



  nutrients are in excess and
            in  the  stream  reach under  consideration  (t*),  then
                          A     « A  e
                            max    o
             If tj or t* is less than t*, nutrients have  the potential to



             limit at z* or t*  and
                                           °r
    4.  Under projected conditions and future removal programs, repeat



        steps 1 through 3.  If the new t* (or c*) is greater than the



        new t*t nutrients would still be in excess.
   An example of this ealculational procedure is presented in Section 5.1,



 has been assumed in this example that the limiting nutrient has



ready been calculated to be inorganic phosphorus.
                             3-19

-------
 3.3.2  Nutrient and Phytoplankton Distribution - *Long"  Streams




      For those streams whose lengths are such'that nutrients are not  in

 excess over the entire length,  the preceding analysis framework  is  only

 valid up to t* ot  t* at which point nutrients begin to affect the phyto-
              " •.              '          
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                                                                       II  (2)
                                                                       Revision ho.  0
  §
  i
                    ?  If
                 .•   •   1C
                 a  l£  i&    •
       i
                                            •

                                            &
                                                                 .
                                                                 o •
                                                                                  |

                                                                                  1
                                                                                  «5
                                                                                  £'
                                                                                  e
                                                                                   e>
                                                                                   £
      O
      i
      e
           6
           |
§
 <
*I«  <
         f  :.
            §•
                   K K
»   <

*
v>
                                                                                   8

                                                                                   O
                                   91
     K


1     *r
       •
                                                *   <
                                                I
                                                                                  •>
                                                                                  i
-------
1.  The differential equations for chlorophyll a, (Equation 3.1 ) and
    inorganic phosphorus (Equation 3.2) are rewritten as:

           A1 « ex A                              '     *             (3.
           P1 » B A                                                 (3.-

      where:  A* and p1 are the derivatives  (slopes)  Of  the A  vs.  t-
              and p vs. t* curves
              6  « G    . r.  . rN  (no longer  a  constant  since  rN
                    max    L    N  decreases with  distance downstream)
              •»
              rN
              B  - -ap  6
                                                                 '  (3.1
 2.   'The  chlorophyll  a. and inorganic phosphorus derivatives (slopes)
      are  calculated at location i using the known concentrations AI
      and  p:
       Note that 6  • 6max • rL .

  3.   Predicted values of chlorophyll a. (A") and  inorganic  phosphorus  f
       are calculated tt location 1+1:
                      - A  + ft At*                                 (3.1J
                              B1
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                                                           II  (2)
                                                           Revision No. 0
  4..   Predicted slopes of both concentration curves are calculated at

       location i+1:


                 "                                                 (3.17)


                                                                   (3.18)
       Note that 6  « 6mav . r.
                       max    t
                                   inp


  5.    Corrected values of both concentrations are calculated at i+1
     An  example  of  the  procedure  for a  "long" stress is presented  ir.

Section  5.2  using  the  DESIGN  conditions  of.th«"short" streao  analyzed

in Section 5.1.




3'3'3  Algal Effect on  Daily Average Dissolved Oxygen




     Presuming that a spatial  distribution  of algae  is known  in terms of

chlorophyll £, a relationship  between chlorophyll £  and the average

daily photosynthetic (P^) and respiration  (R) rates is required for use

in the simplified oxygen equation [Table 2-2  (e) and  0. for every microgram of  carbon synthesized,  estimate

that there are approximately 2.67 micrograms. of oxygen produced (23).
-------
 This ratio is slightly different than the value of 2.67 which would be


 derived from the stoichiometry suggested by Stumun and Morgan (6)


 presented in Section 2.2.4.  Algal stoichiometry is not precise and


 somewhat different relationships, based on other studies or local data,


 may  be preferred by knowledgeable analysts.  However, using the ratio


 selected above:
 where ao and a£ are the stoichiometric ratios of oxygen and carbon to '



 chlorophyll £.   Since ag ranges from 50 to 100 micrograms of carbon



 synthesized per microgram of chlorophyll £ produced (23),
                                            •     «

                                                                    »


                         ao - 2.67 X (50 to 100)




                         AO - 133 to 266 ug oxygen/ug Chi £





                  or'     AO - 0.133 to 0.266 mg02/yg Chi ±.






With  the  rate of chlorophyll £ production equal to  G'A,  where  C is the



daily averaged  growth rate of  algae and A is  the phytoplankton



chlorophyll £,  the  daily average rate of oxygen production  (P.«)  is
                                                             J% V

simply,





                             PAV *  *o  C A                    ^3-21>





Similarly, the  daily average rate  of  oxygen uptake by viable algae  is


given by,
                                   Dp A                     (3.22)
-------
                                                           Revision Ho.  0
 where  Dp  is  the  death rate (endogenous respiration rate)  of the



 phytoplankton.   In both cases,  through knowledge of the algal kinetic



 rates  (C  and Dp)  and  the chlorophyll £ (algal)  concentrations,  the  daily



 average photosynthetie  oxygen production  rate  (?Ay)  and the respiration



 rate (R)  can be estimated.








      It may be noted  that  spatial variation in  the  chlorophyll  a implies



 spatially varying rates  of photosynthesis and respiration.  Since the



 simplified algal-oxygen  solution (Table 2.2) is developed for spatially



 constant values of PAV and R. streams with varying rates can be



 segmented with representative values of P   and R constant for each .
                                          ^fc V


 segment.   An  example of the calculation of the spatially varying P   and
                                                                   f\ V

 R  values  — as well"as resulting dissolved oxygen deficits - is given



 in Section 5.3  for the "long" stream discussed in the example in



 Section 5.2,  under DESIGN conditions.







 3.3.4   Algae  and Maximum/Minimum Daily  Dissolved Oxygen







     With  no  sunlight  throughout the night,  respiring algae  will



 diminish dissolved oxygen concentrations to  their lowest levels  in the



 predawn hours.  As solar  radiation increases throughout the  day,  the



 rate of oxygen production increases, peaking in  the  early afternoon with



maximum dissolved  oxygen  concentrations  occurring  shortly thereafter.
                              3-25
-------
                                                         II (2)
                                                         Revision No. 0
 Estimates of these maximum and minimum daily dissolved oxygen '
 concentrations may be obtained through use of the time variable  portions
 of  the  siaplified  algal-dissolved oxygen equation in Table 2-2.
 Specifically,  the  time variable boundary condition (a), the diumal
 fluctuation  ,(g) and the  spatial transient (h)  are used to calculate
 fluctuation  about  the daily average  dissolved  oxygen concentration
 discussed  in the preceding  section.

     For streams and  rivers with spatially varying phytoplankton
 concentrations, the portions of the  simplified equations  (a,  g.  h) are
applied piecewise to  each stream segment  having a  representative value
of the oxygen production rate  (?ffl) constant over" its  length.  Concen-"
tration* of  the 'diurnal dissolved oxygen  deficits  withia  and  at  the end
of a given stream segment can be  calculated from Equations  (a),  (g) and
(h), expressed is the following  form:
              D(t)  -  DQ(t)  * D^t) + D2(t)
                                   -K  At*
   .where:     Dn(t) « Dn(t  - At*) e  *
                                dn MS 6n *
                                 n      n.t
                                         d • cos e_ «. v
                                    n-1    n      n.ttx
(3.23
(3.24
(3.25

(3.26
                               3-26
-------
     and  D(t) •      • time variable dissolved oxygen deficit
                       concentration in a segment, mg/1

          D0.  Dr  D2 • the components of the deficit in  the segment
                       due to photosynthetic oxygen production
                       upstream of the segment (Dn), and production
                       within the segment (^  and 82),
          t          «  time of day,  in days

          At*         «  travel  time through the  segment,  in  days


                       =. -toy*'*
                                                                 •      (3.27)
         en,t *  (2im/T)(t-ts-f/2) - tanim/Oc), radians           (3.2S)
         en.t.x " en.t ' 2m At*/T, radians                      '     {3>29)
      The  first  component  DQ(t)  of the  total  deficit  is  equal  to  the

 deficit at  the  upstream face  of the  segment, phase-shifted by the  travel

 time  within the segment At* and reduced by reaeration [exp <-K   At*)].

 The second  component D^t) is the diurnal deficit variation, due  to the

 oxygen production rate  (PJ vithin the segment. It is a function of the

 time within the day t,  the photoperiod' f and the reaeration rate K  and


 is independent  of the location  within the segment.  The third component

 of the deficit  D2(t) is due to  the abrupt beginning of the segment-

 specific production rate at the upstream face of the segment.   It is a

 function of  t.  f. and K^). as well as a function of the travel time

within the  segment. At X - 0 (At* - 0), the values of the first  and

third terms are at a maximum;  for locations in a segment, having  travel

times greater than 4/K^, these terms are negligible.              . : •


                              3-27
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                                                           Revision No.  0
                                               *
       In the general case of an arbitrary upstreaa boundary and spatially.
  varying phytoplankton, the" tines of day when the maximum and minimum
  deficits occur cannot be expressed analytically.  Thus, the procedure  is
  to-calculate deficits throughout the day on a sufficiently short time
  interval so that  maximum and minimum values can be determined, to the
  accuracy required.   This procedures is computationally tedious,  and
  development of appropriate  computer software is recommended.   For the
  case where  phytoplankton concentrations are uniform over a sufficiently
  long reach  of  stream (>4U/K  ). the  boundary condition  D (t) and  the
                            *                            o
  spatial  transient D2(t)  are negligible  and  diurnal  deficits are  given by
  the, diurnal fluctuation  D2
-------
                                                            Revision
                               SECTION 4

                        TECHNICAL CONSIDERATIONS



 4.1   PROCEDURES FOR DIRECI KEASDSZHENT OF PHOTOSYNTHITIC OXYGEN
      PRODUCTION AND EZSPIIATION


 4.1.1  Light and Dark Bottle Technique

      This  section emphasizes the analysis  and interpretation of data

 developed  by standard light/dark bottle technique described by Standard

 Methods  (25).   As shown  in Figure 4-1,  clear glass  (light) and foil-wrapped

 glass (dark)  bottles  are stationed or  suspended at various fixed

 .depths is  a  river and filled vith vater collected at  their respective

 depths.  Usually, as  atteapt is made  ia deep rivers to  suspend the
                                                                       •'
 bottles  at least to the  depth of the  euphotic rone, takes to be the 12

 light penetration depth.   From the exponential relationship describing

 light attenuation vitb depth which vas  presented earlier  (Figure

 2-2c), the depth  to 11 remaiaiag light  can be estimated as 4.6/ke.

 Sisce ke i. approximated by  1.6/Secchi  depth, the approximate depth

 of the euphotic  zone  is  2.9  x Secchi depth.


      Dissolved oxygen measurements arc made at regular time intervals,

vith  the light bottles, which  receive the  solar radiation, measuring

set pbotosyathetic oxyges production (P-l), and the dark bottles is

the absesce of light measuring gross respiration (K) as shown is

Figure 4-1.


     It should be noted that:  .
        • Only the pbotosyathetic activity of the algae is the vater
          column (phytoplankton) is measured by this technique.  If
                                4-1
-------
                                                              II  (2)
                                                              Revision  No.  0
                   LIGHT
                   •OTTLES
                            c

                            o
                                           DARK
                                           •OTTLES
  12

S"1
s  ,.
                                      12


                                   9 10


                                   1 .
         10 •  12
                                             10    12
                                                              4    •
               TIME
                                                     TIMC
  gXAMFLg CALCULATION ttef »» bofftal
  (1) Sloe* of Ii0n Mts« DO «m
      «?«-«. *g. a .^^
      • hr

Q)Skx»*
                 OOi
    •^S!.^:.^.^^
OIR •«««••(
(41 f • Slaw «f U^t
    ^•324*1.4
                      1*1.4
     U.B.C. Ol*«
                                           I
                                             o-
                    Figure 4-1.  Light »nd dark bottle audio.
-------
                                                              &*vis ion No. Q
            there are sigaificaat attached algae or rooted pints. BO
            aeasureaeat of their photosyatbetic coatributioa i. aide.

          • The estimate of respirstioa (£) made from the dark bottle
            studies iacludes .both algal re.piratioa aad bacterial
                             °Xid*tien °f ^boaaceou. .ad attrogeaous
          • Both P aad £ are temperature dependent.  Since they are
            ...eatiall, expresses of grovch rate aad respiration rate
            » oxygea eqmyaleats,  the temperature rate relatioaships
            discussed earlier ia the report for grovth aad respiration
                                                                •

      As a practical matter  ia perfomiag  light/dark bottle tests, it

 is i-portaat that the light bottle, aot be allowed to progress to the

 poiat where saturatioa is exceeded.  Losses of DO duriag sample head-

 ling atteadiag the aaalytical measureaeats would introduce errors into

 the test results.  Figure 4-2 has beea developed, based oa the pbyto-

 plaaktoa dissolved ozygea productioa relatioaships which have beea

 preseated,  aad  caa be  used to estimate appropriate sampliag iatervals

 aad maziaua  duratioa of  light bottle aeasureaeats .


      The productivity vs.  depth  relatioaship  developed froa the light  '

 aad dark bottle test data,  ohowa ia  Figure 4-1, provides a  determi-
                   •
 B-tioa of the depth-averaged primary productivity.  The exteat to

which it is  ti.. averaged depeads oa the period of the day  covered by

 the aeasureaeats.  Because of the sigaificaat variatioas ia P with

depth .ad tia, (illustrated previously by Figure. 2-4, 2-9), care must

be takea that light .ad dark bottle test results are iaterpreted

correctly.                       .
                                  4-3
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                                                            Revision No.  0
-a


f
i

i
z
I
X
•taximim Algal Growth Rm • 2LO/day

Cwtoen/Chli-50
     0.4-
                                                100    .120     140
                           CHLOROPHYLL i (MB*)
              Baus for retationMhip •hown •:


              Maximum hourly
                                            2.17
                                    CM&
                                   1000-24
            Figurt 4-2.  Expected maximum hourly

                       DO in •jrfaa light bactfe.
                                           in
                          4-4
-------
                                                             revision no.  o
        If  light  and  dark bottle te.t.  are being performed to provide
  input value, for the analv.i. procedure, de.cribed  in  thi. .anual,
  an understanding of the following productivity factors  and
  their relationship to light and dark bottle test results is    '   ..
  required.
                       ,a  £he                 
-------
                                                            Revision.NO.  0
 PB and substantially "more than Pay.   In some cases,  appropriate extra-
 polations oust be made to derive the values  used in  the  analysis.  An
 example of such a correction to the  measured rate is presented in
 Table 4-1.
 4.J..2   Benthic  (Sediment)  Chamber
     This  method  is  similar  to  the  light and dark bottle technique,
 'but  instead  of  measuring the productivity of the algae in the water
 column,  a  clear plexiglass "benthic  chamber" is used to measure the
 productivity of the  attached algae on the bottom (periphyton) and any
 rooted  aquatics.  A  covered  (dark) benthic chamber measures the
 community  respiration of the'algae,  bacterial and animal components of.
 the  benthos.  The benthic  chamber is used to measure productivity
 and  respiration at various points across a stream cross-section to
 estimate the areally.averaged flux terms, since water depth and
benthic population can'vary  substantially.

     The rate of oxygen production measured with a benthic chamber,
PBC  faS/1/day)• is related to the volume of water contained by the
chamber  (V^) and the surface area of the stream bed covered by
the chamber  (A^).  An area-averaged photosynthesis rate is calcu-
lated from the average of  the individual rates (Pg.) determined by
repeating the test at equally spaced locations across the.stream sec-
tion.  The rate of production (P) is derived from the light and dark
                                  4-6
-------
                                                             Revision ho.  0
  Table 4-1.  CONVERSION OF MEASURED PHOTOSYNTHESIS RATE Tp AVERAGE
              DAILY RATE
                                           Light Bottle Measurements:

                                             t. & t. • beginning and end
                                            .           of test with respec:
                                                       to time'of sunrise

                                             P* • observed average
                                                  production  rate betveer.
                                                  t, and t2
             HOUR
Conversion of Measured Rate to Aversee Dailv  Rate
          AV
                                - cos(irt2/f)
for the special case where t.


         P   - T- n 2f/T   • P*f
         'AV   r  x i-(-i)    i
                                0  (sunrise) and t, « f  (sunset)
Example
                                                        •
     As in Tig. A-l, light bottles aeasured fron 10 a.m. to 4 p.mi

     (t^ - 4, t2 • 10) give a photosynthetic production rate of

     30.05 ag/l/day.  Assuaing a 12 hour photoperiod beginning at

     6 a.m., the daily average rate would be estimated as:
         PAV - 30.05 mg/l-day
                                      2 (10-4/24)
                                  cos (w x 4/12) - cos(ir x 10/12)
             -11.0 mg/l/day
     The maximum daily rate would be:   -

            - *T/2f «.PAV - w-24/2-12 • 11.0 - 34.6 m»/l/day
-------
                                                             II  (2)
                                                             Revision  No.  0
 chamber data,, using the same calculation shown for light and dark

 bottles in Figure 4-1.  Then:
                          •    (P^ * ( PBC)2 + ----- (PBC)n ]



 and, area-averaged photosyntbetic production for a benthic population is


           P (gm/m2/day) . Fg  - J£
                            BC   *BC

 This surface loading rate is converted to a concentration basis  by

 dividing by the average depth (E)  of the stream:


       .    P (ng/l/day) - FBC •  -M - 1
                                 Ow
                                                                       s>

 4.2   IOT12ZCT METHODS  OP DETZSMIHING PHOTOSTHTHSTIC OZICEK P20DDCTION
4»2^  The Pelt* Method of T.^^.f-jng Oxygen Production
                                         •              .           t
     PhotosTnthetic oxygen production (P)  can be estimated froa site

data on diurnal fluctuations in dissolved  oxygen concentration.  The

rationale is based on a theoretical analysis by BiToro (21).  The

principal factors that influence 'the characteristics of a photosyn-

thesis-induced diurnal oxygen variation  (the amplitude and shape of

the curve) am:


        • the photopcriod (f) - daylight fraction of the day.

        • the rate of photo synthetic oxygen production (P). based on
          the temperature, light and nutrient regime for the study
          location.
-------
           • xhe  s-reasi Tearation rate  Cka)  of  the  stream  segment
             being  studied.  The reaeration-rate modifies  the  amplitude
             of the dissolved oxygen variation  by influencing  the rate
             at which DO is replenished at low  points in the diurnal
             swing, and by influencing amounts  lost to the atmosphere
             when DO concentrations exceed saturation values.


      Using parts (g) and (h) of the water quality model summarised in

 Table 2-2, multiple analyses were performed using algal oxygen production

 (P) inputs such as illustrated by Figure 4-3(a).  The relationship showr.

 would represent the variation in depth-averaged P over the course of a day.
                                                       *
 Figure 4-3(b)  illustrates the solution .for a range of values of reaera-

 tion coefficient  (Kfi),  based on the indicated set of input conditions.

 The-significant  damping  effect  of high reaeration rates  is evident.   As

 reaeration rates  decrease,  the  magnitude  of the diurnal  swing A
 *
 (DO max)  - (DO min)  approaches a  constant  value.

                                                                          •

      Repeating the  process  described- above  for  a  range of reaeration

 coefficients and  photoperiods,  provided the  information  for  developing  the

 relationship between P,A, kfl and  f,  shown in Figure 4-3(c).   Note that  for

 Ka< 2  (day" ), A/Pffl is essentially  independent  of Kg  and  is  a  sole function

 of  the photoperiod  (f).  This relationship-can  be'used to:



     •  Estimate  Pffl when A is determined from analyzed survey data,
        f  is known, and Ka has  been calculated  or estimated.

     «  Estimate  A when Pffl is estimated using chlorophyll  a data
        (discussed subsequently), f is known, and K. is calculated
        or can be estimated.                                         .   -


It is presumed that reasonably  constant phytoplanktcm populations exist

over a sufficiently long reach  of stream, since the above analysis

assumes a spatially constant photosynthetic rate.
                                  4.9
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                          II  (2)
                          Revision  No.  0
                                    •o
                                    I M

                                    2^
                                    " 5
                                    £.=
                                    S u
                                    It
                                    « >
                                    £• X
                                    « o

                                    n
                                    r
                                    ^
         NOIJLVkUNiONOO
NidAxo aiAiossta NI
-------
                                                                i a
  4-2.2   Determining Oxygen Production  from Phvtop lank ton  Kinetics  and
         Cell  Stoiehiometry                                - - — — —


      Utilizing  the ph>toplankton  kinetic  equations  presented  in Section  '

  2.2.2 and values  commonly found in  the  literature for the various  co-

  efficients, maximum saturated photosynthetic oxygen production, P

  can be estimated,  since P& is essentially the product of algal growth
                                                  »
  rate and algal biomass.   From a knowledge of ambient phytoplahkton'

  chlorophyll  concentrations and water temperature,  Pg can be  estimated

 using Figure 4-4 (b) reproduced from Figure 2-4,   if the average water

 depth and the extinction coefficient of the water CK ) are known. . K

 can be  estimated from Secchi depth (SD) measurements or suspended  solids

 concentrations,  as described in Section 2 of the manual.




      As  an  example, for a  river at 25°C and an  ambient chlorophyll a   '

 concentration  of 20 ug/1.  daily average oxygen production (Pav)  can be

 estimated as  follows.   If  the  carbon/Chi a ratio is  assumed  to be  50, the

 saturated productivity  (pj  can  be estimated using Fig. 4-4 (a).
                     Ps/chla «  0.37
                     PS " 0.37 x 20 « 7.4 mg/l/day




High and low bound estimates of the carbon/Chi a, ratio, provide a range

for this estimate 'of 4 to 9.4 mg/l/day.




     If the photoperiod is 14 hours, average light intensity for the time

of year (Ia) is 600 LY/day, and organism saturated light intensity is

taken to be 350 LY/day.
-------
                                                          II (2)
                                                          Revision  No.  0
(a)
      1.0

      O.fl

      0.8


 ^   °-7


 8   "
 ^   US -



 I'-
 .1   0.3
 •r
      0^

      0.1
                                             Mo iMirwnt limitniafl
              »    I
         0   10  12  14   16  1§  20  22  34  X  28  »  32

                       WATER TEMP€RATUHE (*C)
(b)
         01234  S   •   7  t  •  10 11 12 13 14  15  16
       Ffeun 4-4. Enimcting alg*! productivity from eMarophylt
                 eonocntrationc and sown oondrtiom.
-------
                    .   •  ."                      .           Revision Ho. 0


                        lf * Ia/f « 600/0".S8 « 1050

                        If/Is - 10SO/350-3.

 If the' river depth is 10 ft, and secehi depth measurements made at the

 time chlorophyll samples were taken yield a secehi depth SD • 4 ft, the

 light extinction factor can be estimated


                        Ke « 1.6/SD « 1.6/4 « 0.4 ft"1 /

                        KftH * 0.4 x 10 « 4
      From the estimates of If/I- and K H, Figure 4-4 (b) provides an

 estimate of the light limiting factor (r, ) .



                        Rt • PAV/PS ' °-32
                                    - •

      This ratio,  and the value of P  estimated earlier, provides the

 estimate of average daily production rate.          •


                       fAV » 0.32 • Ps « 0.32 « 7.4 » 2.4 mg/l/day

 the  range in values for PS translates into a. range of estimates for

 PAV  of 1.3 to 3.0 mg/l/day.
  .3    EFFECT OF PHTTOPLANKTON ON THE NTTOGENOUS DEOXYGESATIOX RATE
       AND BOD TEST RESULTS
4-3.1  Nitrogenous Deoxygenation Rate Considerations

     Nitrogenous deoxygenasion races (KQ) art usually calculated for a

receiving stream using the conservative assumption that the loss of

ammonia is a result of nitrification.  As such, the calculated K  may be

higher than the actual rate because ammonia sinks that do not consume

oxygen are not considered in the calculation.  When the algal biomass is

     » the calculated K  based on the loss of ammonia may significantly
                                 4-13
-------
                                                          >\ev
  overestimate the K  race,  in these situations, it is recommended that
  an estimate of these losses be incorporated into the K  calculation, or
                                                        n
  that K  be determined based on an increase in nitrate rather than the
  loss of ammonia.                                         •

  4.3.2  Corrections to BOD Test for Presence of Phyteplankton
       When a sample is collected from a .receiving water, the presence of
  algae in the sample can have a significant effect on unfiltered C30D
  measurements and the resulting calculation of the carbonaceous deoxy
  genation rate (K.).  Since CBOD is a measure of the oxygen depleted in &
 . sample volume,  if algae are present in the sample, the consumption of
  oxygen due to algal respiration is also measured 'in addition to the
  consumption of  the so-luble organic material.  Additionally,- since the
  samples are stored in the dark,  no photosynthesis occurs;  hence,  in
,  addition to continual respiration, death takes place and the bacterial
  decomposition of the dead algae  also consumes oxygen.

      The effect  of phytoplankton in standard BOD tests depends on the
 chlorophyll concentration of the vater sample, the algal respiration
 rate, and she bacterial oxidation rate of cellular material from dead
 algae.  From stoichiometric. relationships and information or estimates
 of the oxygen utilization rates,  the contribution of algal cells to
 measured BOD values can be determined.

      The phytoplankton contribution to ultimate carbonaceous BOD is:
-------
      vhere:

        PO  "ambient phytoplankton chlorophyll a concentration

                        livi?!!?^1 ratio for *l8*1 cel1'-  Xt «  th«
     The corresponding contribution of phytoplankton to  a  5-day  test

is (22):                      '                    •

     (CBOD-)  * a   p M.F '
         5 p    o   ov'  rc-
                       ao
     where:
        Fc  -  temporally  averaged value of the fraction of the initial
             phytoplankton  that are viable over the tesr duration.

       kr -  "bottle rate" bacterial deoxygenation of organic matter-

       Dp * *l*al respiration rate (equation 2.7),
   •The first term in the above equation represent, decomposition of dead

    algal cells;  the second t.ra represent, oxygen utilization by

    endogenous  respiration of viable algal  cells.


         The  non algal  (NA)  component of  the BOD measured in ch. field i.




                     (CBOD.)   - CBOD.  - (CBOD.)
                          S NA       *         5 p


        Figure 4-5 summarise, the relationship,  de.cribed above and .hov.

   the effect of  chlorophyll concentration, on CBOD,. test results for a

   range of possible value, for respiration and deoxygenation  rate.
                              4-15
-------
 4.4   SUGGESTED MINIMUM  SAMPLING  REQUIREMENTS

      Table -U2 presents a list of suggested minimum monitoring re-
 quirements.  This table is'a slightly modified version of a similar
 table presented in Chapter 1, vhich deals wich BOD/DO impacts in
'streams and rivers.   The modifications introduced reflect the ad-
 ditional requirements for situations where eutrochication effects are
 of major concern.  The general  considerations  with regard to the num-
 ber and location  of  sample stations,  which were discussed in the other
 chapter,  also  apply  to eutrophication situations.

     The  only  additional considerations  likely to  be  specific  for -euwo-
phication situations  is  that  location  of-at least  some'of the  sampling
stations"should be guided by  the  presence  of conditions that would tend
to enhance algal productivity.  Such conditions would include  open,
well-lighted segments'with longer residence time.
                               4-16
-------
                                                         Revision No.  0
                                               0.1
       0   10  20  »  40  K  «  70  iO  W 100


         . PHYTOPLANKTON CHLOROPHYLL t. fcifl/8)
5"   2-
     1-

6
e
              0.1      &2      0.3     0.4


             OEOXYGENATION MATE K,
 0.100
                                              •0.075   «
-0.060
                                               OJQ5
                                                     £
     Fifura 4-5. Al^i oomporMnt of BOOs
                             4-17'
-------
     CX.95AT.UL (I)  - 3
     Fable 4-2.  SW.TE57EP M2C1««1 SttffllNG REQITRS^KTS
    Variable0
    Dissolved ttcygen

    pH
    CcnductivitY or
     Chloride "
   CBO^
   n?
   Crsznic-N
  Organic Phosphorus
  Inarsanic Fhosphoms
  Flow
  Tisu of Travil
  Velocity and Depth
  Re«erationd
 Bottoa Demandd'J
 light & Dark  lottles
 Diurnal
 Nitrifier Countsd
 Phytoplanktoo
  chlorophyll a
Periphyton
  chlorophyll  a*
D0?robl«ns
All Probleas
All Problans
All Problss
All Problos
All FroblcBS
All Probleas
CBOD & NBO)
CBOD & NBCD
CBCD & NBQD
CBCD & KBGD
Eucrophication
All Problens
All ProbloBS
All Problcns
All Problem
All Problos
Eutrophication
NBCD
Eutrophication
SUraticmc'b
of Survey
—•— ^— — -^—_
. 2 Days
2Days
1 Day
2 Days
2 Days
—
2Days
2 Days
2Days
—
2 Days
2 Days
2 Days
—
2 Days
—
l.B*
iDay
—
2 Days
Nunbcr of*
™^~— — — — —
2/Day AK/PM1 '
2/Dayg
1/Dayg
1/Dayg
1/Dayh
Onceh
1/Dayh
1/Dayh
I/Day
Ooc*
1/Dayh
1/Dayh
1/Oayg
Once/now
I/Day
. Once
Once
.GKC
I/Day
^^••••Miaii^^
Station
— •— •___
. IOCS
100:
10B
10GC
so:
so:
50-100:
100:
iocs
25:
50-100:
50-100:
1 Station
100Z
100B
10GE
IOCS
so:
yz
SCR
XXX
Butrqphication      —
                                                       251
    ,
 Replicates
-------
                                                              Revision ito. Q
                                  SECTION 5
                              EXAMPLE PROBLEMS

       A set of example computations is presented in this  section to illus-
  trate the  use of the  desk top  analysis procedures  described  in  Section  3.3.

       Sections 5.1 and 5.2 illustrate  procedures to develop estimates of
 maxnmum chlorophyll a. concentrations  which result  from nutrient discharges
 Section 5.3 illustrates procedures for converting  either estimates or obser-
 vat!ons.of phytoplankton  chlorophyll  a  concentrations, to estimates of  daily
 average dissolved concentrations.  Section 5.4  illustrates procedures for
 estimating diurnal dissolved oxygen variations.

 5.1   PHYTOPLANKTON ANALYSIS FOR "SHORT" STREAMS        '
                                                                        •
      A -short" stream  is defined as one in which nutrients  are in excess
 of growth  limiting concentrations over the entire length  of interest.
 The  analysis procedures illustrated.describe  the computational  basis'for
 estimating  the maximum chlorophyll  a. concentration  anticipated  under
 future design  conditions.   This concentration becomes  an  input  in
 subsequent  computations (Sections 5.3  and .5.4)  which illustrate  the
 estimation  of  stream dissolved  oxygen  impacts of nutrient waste  load
 allocation  decisions.

     The example problem scenario is summarized  by  Figure 5-1, which
 summarizes pertinent data  for both present conditions and future  condi-
 tions on which design  1s to be  based.   Using  this information, the"
objective 1s to estimate the maximum chlorophyll a  concentration  in the
downstream reach of.the tributary.  The assumption  1s made that phosphorus
has been determined to  be the controlling nutrient.    '•
                                   5-1
-------
                                                    Revision  No.  0
FIGURE  5-1.   ANALYSIS CONDITIONS  FOR SHORT STREAM
      I W(STP)
      1  	^/Tributary
                   20 miles
'Main Stem
Condition
Item
Flow - Upstream
- STP

- Combined Downstream Flow
Stream - Depth (H)
-•Velocity (u1)

-• Water Temperature (T)
Sunlight - Daily Solar Radiation (Ia)
- Photoperiod (f)
- Light Extinction Coef. (K«)
- K. - H
- If - Ia/f
- Is (saturated light intensity
for phytoplankton)
- If/Is
Inorganic Phosphorus Concentration
- Upstream
- STP Effluent
Chlorophyll a. Concentration
-.Upstream (x < 0)
- Downstream (x « 20 ml )

cfs
MGD
cfs
cfs
ft
fps
mi /day
•c
langley/day
, .
ft'1





mg/1


ug/i


Present
20
0.25
0.39
20.39
3.0-
0.5 •
8.2
23
600
0.5
0.33
1.0
1200

300
4.0

0.02
5
•
25
65
Design
12
0.30
0.49
12.49
*
• 2.2
0.4
6.56
25
600 .
0.5
0.33
0.73
1200

300
4.0

0.02
1

25

                         5-2
-------
                                                                    No.
      Analyze Present Conditions to Establish Relationships to be
           Used in Projections for Future Design Conditions


 (1)   Estimate  net pnytoplanktor, growtn  rate  (GN).



      •   Use observed chlorophyll  a. data at X « 0 and X « 20 miles  and

         assume an exponential  increase.



      •   Travel  time  for reach    t* *  20 mi/8. 2 mi/day * 2.44 days



      •   Chlorophyll  a_ at end    '  A « A   •  EXP(G  •  t*)


                                  65 « 25 • EXP(Gn  •  2.44)



      •   Net growth rate          Gn « (:n  (65/25)) /2. 44 «  0.391 day"1



(2)   determine algae  population dynamics rate factors.


  .    V  6n'G-  Dp. vs/H                            •



         G  • Gmax  ' rL  '  rn


         0  • O.K1.08)23"20 -.0.126 .day"1 .-(Equation 2.7)
                                    •                            »


     *  Gmax ' 1-8(1.066)23"20 « 2.18 day"1  (Equation 2.1)



     *  rn * ^'Q  ("Initially assume excess nutrients)
                                   (-4(£XPO.O))) -
           • 0.287    (Equation 2.3)
     •  6 * G    • r,  « r_
             max    L    n
            (2.18) •  (0.287) -'(1.0) - 0.626 day"1
                                 5-3
-------
                                                           Revision  No.  0
              H(G  -  Dp - Gn)
             3.0(0.626 -  0.126 -  0.391) «  0.327 ft/day
     •  Summary of population dynamics rates:
             Actual Growth Rate
             Respiration Loss Rate
             Settling Loss Rate
             Net Growth Rate
                           G * 0.626
                           Dp «  0.126
                           VS/H  « 0.109
                           G. «  0.391
day
   -1
(3)  Check assumed nutrient Tiirritation.
        Evaluate factor p  used in equation 3.7.
                   ao • s • Ao
        a  « phosphorus/chlorophyll ratio * 1.0
         p
        A  « initial chlorophyll concentration (at X « 0)
A'  -  0) ' (0-     • (25) .
 0   .
                                              yg p/1
                                              vg K/ i .
        Compute initial phosphorus concentration resulting from blending
        of discharge and stream (W/&Q)-
 -- (2°
  •
                               ('39 ' 5)
          (20 + 0.39}
                                            0 115 ma/1
                                            °*115 mg/1
     wg/1
     •  Compute travel time (t*) to reach point of nutrient limitation
        on growth rate.
                           A!  +p -  0.025
                                               (Equation 3.7)
                                 5-4
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                                                  II.(2)
                                                  Revision No.  0
dsr:««(y*jj'-a)  .3.
                                              01
      th. Preeedjn9 •„,,„,. 1§  ,                     on occurs
                                           futur,
 Assume phytoplinkton settling rate t»  } .»- ^
 coefficient (K ) w-m M* ^        $)   ^ 119nt """ction
            (V will not change under future design conditions.

Using -design- conditions su^narized in Figure 5-1  and
Pertinent relationships defined earlier (part A  *
factors  for populated  dynamics become:
          Limiting Factor      ,    . 0. 236 day'1
    Nutrient Limiting Factor   P    . !  n MMM.I
                              rn     i.u unltial assunsption)
          firowth R,M        G    . 0.585 d
    »«sp1ration Uss Rate      D    . fl  U7
    Settllnj loss Rate        VjP/H . O.'l49
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                                                            II (2)
                                                            Revision No. 0
  (5)  Check travel times.
       .•  Actual travel time
               t* * 20 ml/6.56 ml/day « 3.05 days

          Travel  time to point where nutrient concentration  begins  to  limit
          growth  (assume upstream  chlorophyll  (AQ)  unchanged).
*;
                                    CD
                         (0.585)
                         (0.289;
(25)
                                                       50.6
D « 02 . 0.02) + (0.47 .
•            (12 * 6.47)
                                             ._
                                             56*6
                                                      days
      •  Since, actual travel time (3.05 days) 1s greater than travel  time
         to reach point of nutrient limitation on growth rate (1.68 days),
         tht phytoplankton growth rate will  t* less than the exponential
         rate assumed where nutrients are not limiting — or at down-
         stream distances greater than 1.68  days x 6.5fi ai/day) 11  miles.

(6)   Estimate maximum pnytuplankton chloropnyll a. concentrations.

     •   An  upper  bound  1s  provided  by assuming that growth  rate over
         the entire reach remains  exponential,  and nutrient  limitations
         do  not  taHs  effect.  Chlorophyll  concentration at »1le 20
         (t* » 3.05)  Is:
             A.AQe
               * 25 • EXP(C.289 • 3.05)*- 60 ug/1
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                                                               II (2)
                                                               Revision No.  0
          •   A  lower  bound  is  provided  by an  estimate of concentrations
             reached  at  the  travel time to the point where nutrient limita-
            poin  I                                 P   K68
                                                                   s
                         Gn t*
                 A « A  e n  P
                      0

                   - 25 .  EXP{0.289 - 1.68) - 41  Ug/1

         •  Since growth  continues even  when nutrients  are present at concen-
            trations which  are  less than limiting levels,  the  conclusion  at
            this  point  1, that  under future design conditions, and with an
            erfluent phosphorus concentration of  1.0 mg/1,  the maximum
            chlorophyll a concentration  in  the 20 mile  stream reach would be:
                At  least 41 yg/i
                Not more than 60 ug/1

   (7)     The proposed reduction in effluent phosphorus has converted the
           stream from a  "short" to a "long" stream.   Refinement of the
           estimate  of maximum chlorophyll  concentration could be made using
           the procedures  described for  "long"  streams  in  the  following
           section.
5.2 ' PHYTOPLANKTON ANALYSIS FOR LONG STREAMS

     In a "long" stream, phosphorus concentrations are reduced by algal
uptake to levels which Impose a limitation on growth rate.  The future
design conditions from the previous section are used, but the stream
length is extended to 45 miles to illustrate computations for estimating
the shape of the chlorophyll a and inorganic phosphorus profiles 1n river
reaches where nutrient limitations exist.
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                                                          II (2)
                                                          Revision No. 0
         Actual Growth Rate       G     «  0.585 day'1
         Respiration Loss Rate    Op    .  0.147 day'1
         Settling Loss Rate       VS/H   -  0.149 day'1

        Note that actual  rate 6 was based on G    and
                   fact.,  In «« «„„,,, JgC              to
                                        9rowt" rate
(1)   Estlnitt growth r«M for nutrient Uniting situations.

       Nutrient Limiting Factor  r,  .  _J^     (EquaMon ,.,„
                                           K
            whert
                 Ktop *  0.05 mg/1 « 5 yg P/l

       Actual  Growth Rat?        G « G    . r  •  ^
                                     max   rL   rn

                                  -   ' '
                                  • 0.585 •

      Net Growth Rate           G|1  . G -  Dp - VS/H
                                                          - 0.149

                                                  - 0.296
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                                                       II  (2)
                                                       Revision No.  0
                       .„„

Select an mni.l  inerawntj,             ,».„..
«* stream 1nto snort        over 1 r-he         ** *
                                       ' nu
                                   over       -he
       procedure will be appUed ,„ d«, , .      ' nuwn"'
       (A) M inoramc        '  ??      eStlMte *"* Cf
                                  tp) «-*«»«« .« t« . 0.3
(3)
      t* » 0.5 days.
   •  Slopes at i (f» « 0)
          A1 * 25 ug/1; Pj « 56.6  ug/l
          G  » 0.585
          «.-«.• 0-538  - 0.296 . 0.242       (EquatJon ,.,„
         .«.-V -'•«•-«• -0.538        (Equation 3.,2,

         A) • Vl •  0.«2 •  25  -  6.05 u9/Vday  (Equat1on 3
         Pi • Vl ' -0.538  . 25 . .,3.45  B9/1/day  (£quation J>]4)
    -"-.dieted  concentrations ,t , + ,  (t.  . 0_5
                                  X
        ^1+1 • A, +  Aj 4f . 25 * (6.05 •  0.5) . » ug/1
        Pi*] ' P," +  PJ «• . 56.6  - tU.*i •  0.1) - «,.,'„„
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                                               I1
                                               Revision No. 0
Predicted slape at 1
        - 0.532-0.296- 0.236/day

     O • -0.532/day


                           •• a- «.«.
                                           „,„*,
              _
        ',*.  ' «,*,
                                                        3.,;,
                   - -».* • 28 . .„.„ u9/1/day  tEquatfon3i3)

       concentrations at 1* 7
             25 +  (ii2L*L«i\ nc   .
                   V      2      -05 • 28'
                                           (Equation 3.19)
           - 56.6 ^3.45 - 1*  on\
                  V      2       / -°5 ' 49'5
  herefore,  it t* « a
                                            (Equation 3.20)

                    tedious
««• 0"  Persona, computers
                                     """'" 1s  Stra19ht-
                                        be progranme, for
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                                                          i:  (2)
                                                          Revision  No.  0
TABLE 5-1.  EXAMPLE OF PHYTOPLANKTON COMPUTATION FOR LONG STREAMS
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                                                              II (2)
                                                              Revision No. C
       (5).  Figure 5-2 presents a graphical summary of chlorophyll a and
            phosphorus concentration profiles derived from the computations.

            Also  shown,  for informational  purposes,  are the concentrations
            computed  from equatioos  3.1  and 3.2,  for the short stream examole
            At  tj » 1.63  days,  chlorophyll  a. concentration using  a constant
            net growth rate  is  41 ug/l compared with 37 yg/1  from use of
            nutrient  limited growth  rates.   The peak chlorophyll  a is
            44  ps/1,  approximately 10* higher than the  41  ug/l estimated
            using  the constant net growth rate at t*
                                                  P


 5.3   EFFECT OF PHYTOPLANKTON  ON DAILY AVERAGE DISSOLVED OXYGEN CONCENTRATION

      Using  the chlorophyll  a and phosphorus concentration profiles  developed
 1n the previous  section  (5.2).  the  objective  is  to  estimate  the  dissolved
oxygen deficit profile along the stream due to dally average algal  photo-
synthesis and  respiration rates.

     (1)  The following conditions apply for the example  calculation.

               G « 0.585 '>N            H • 2.2 ft
               Dp • 0.147     •          y - 0.4 ft/sec
               f  « 0.5                  T » 25°

          Estimate stoichometric oxygen  ratio

               *op *  °.133 mg O./ug  Chi  a
         Assume that Initial chlorophyll concentration  (25  ug/l)  1*
         constant for many iles upstream of point source discharge.

         Initial phosphorus concentration in stream after discharge is
         P • 56.6 ug/l.   .
                                   5-12
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                                                    DIJ
                                                    •^vision No.  o
\   Oil i (linear, p •
             TRAVEL TIME, t'
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                                                       II  (2)
                                                       Revision No. 0
C2)    Calculate PAV  - R at t* . r
       AV


r- * v D. - . .  56-s
                                  1  0.3^3



          G  -0-585.  rn- 0.585. 0.926. 0.542/day

          PAV • VG'A • (0.133) •  (0.542)(25) .  1.80


         P  . ~Z  .  a     IT  •  1
          m    2f     AV   2-6.5" *  L80 . 5.66 me


         R  -*0  Op A.  (0.133) .  (0.147)(25).0.49/day


         PAV  - R • L80 - 0.49 . 1.31 mg 02/l/day
          segments.                ' °  «"<«•«"• «m tta re^in ng


            D1ss0,v,d 0V9en Def,c,t at f . o.S
  *" iWtl   terms  (,) and  M  f            ** exp8nen«"
                                                ™  to
       °0 "      K
                 a
                i • n-024)-20 - 2.84
                          5-U
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                                                   II  (2)
                                                   Revision No.  o
         TABLE §-2(a).  EXAMPLE OF P
                               AV
o.oo    25
                              fl-542
 *-**   2f.ll 41. S
                                                             /•37
 Z.oo
 2.25
 2.50
2.15 |  4-3,*
3.00
3.Z5
4.7S
               11.*
                3.*   *.31S
        «-*63 I  2,
        0.444-
0-744 |  o.43S | 7^?
        0.331
0.5541  0.323
      Jo.4*
      21.*
                                     /.rr
                                              7.41
                                              7.10
                                              5.15
                                                    6.10
                                                              /.71
               (b).  DEFICIT COMPUTATIONS
                                                             o.4»9
                                                              *'
                                                              *
                                                            •o.S7
                                                           -0.5S
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                                                              II (2)
                                                              Revision No. 0
         •  Then, at X - 0 (t* - 0) initial deficit, neglecting the small
            dilution due to treatment plant flows is:
                                       V1
            The effect of the algae on the daily average D.O.  at the end of
            a  segment with a  constant value of PAV -  R,  is:
                          EXP(-K
                                         -
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                                II  (2)
                                Revision  NO.  0
TRAVEL TIME, t*
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                                                               II  (2)
                                                               Revision Ho. 0
    Photosynthesis rate occurs  at , travel time
    day upstream of the mx1mm chlorophy ,"
    Plankton growth rate (S) has been
    The ,hytop,ankton contribu   0 5^0 0
   concentrations  from  f . 0 C to Vc
                              of o
       added to
»urc, C800. «BOO and deficit
-- and comparison of resultin
                            '
       are of conce.i,.  „
                                                         ippr-1-t"> "»
                                                          "here the
                                                          di"0'ved
                                                              beyon
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                                                        II (2)
                                                        Revision No.  0
0)
                    4?r/f
                                      *
                                                                 (5.1)
          I. limit
                f * 0.5
  g^r (cos  »f/T)
  f1—	
.Hf(l/f-4f)
  with:
                  0.0725140

                  0.01647.10
 Also:
      Jl.t * 2n - 2.71708


      92.t " 4n ' 4.49012
                                          '  0.5/1) . 0.212207
                                                              (5.2)
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                                                         II  (2)
                                                         Revision No. 0
       where pnotoperiod f . 0.5 days., a    is  in radians, end t is in
       days.
            6n,t,x  *  en.t  '  "» «w"                              (5.3)

       and


            6l,t.x " 2n ' 5.85867 (for At* « 0.5 deys)

            92,t,x " 4irt - 10-7733 (for At* - 0.5 days)


(2)-   Estimate diurnal dissolved  oxygen deficit  variation at stream
      location t* « 0.


      From previous example  computations,  the following conditions
      apply:

           Kfi  - 2.84/day

           Pm  - 6.13 mg/l/day (at X < 0).

           Pm  - variable at X ^ 0

           f   » 0.5°day                              -

    also   t « 0 is equivalent to  sunrise


     Exclude PAy - R since it has been  considered previously.  There-
     fore, with a long upstream distance with constant photoplankton
     concentration  (Chi a  .  25 Wg/l.  ^ .  6.13 mg/l/day). the oxygen
     deficit at K - 0 is given by D,(t)  in equation 3.25.
             -6.13  [0.0725140 cos(2n - 2.71708)

             * 0.0164710 cos(4wt - 4.49012)1


             -0.445 eos(2n - 2.71708) - 0.1010 cos(4n - 4.49012)
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        0.427
                                                     II  (2)
                                                     Revision No. 0
                           d1urnii
                 aiurn,i  Defic^ lt t. . „
1
2
3
4
5
6
C.413
0.355
0.258
0.118
-0.042
-0.205
7
8
9
10
11
12
-0.351
-0.457
-0.515
-0.516
-0.469
-0.383
13
14
15
16
17
13
-0.275
-0.163
-0.058
0.030
0.102
0.161 .
19
20
21
22
.23
24
0.213
0,265
0.317
0.368
0.409
0.427
(3)
Estimate diurnal deficit variations at tv. 0.5 days.
                                                          of

*"1ch Pm , 5.97 mg/1."	""'.   'nereTort- At* - 0.5,  over
    D0(t) -. -0.383 EXP(-2.84  ..0.5) - -0.093 mg/1
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                                                       II (2)
                                                       Revision No. 0
           -0.383 is the deficit at f « 0 at r  . 12 hours.   sisrt-
     larly. at f « 1 hour:

          D0(t) - -0.275 EXP(-2.84 -  0.5)  .  -0.666 mg/1

     Tabulated solutions for all  components  of deficits at the ends
     of segments  1 and  2 are presented in Tables -5-3 and 5-4.

(4)  Repeat the analysis for all stream segments.

     The computations are performed, as above, for all  segments,  and
     the maximum and minimum deficit at each  stream location is
     Identified.  These results may then  be tabulated,  as  in Table
                   2e the d1fference  betwecn *****and •*"—
    *4,„   .I     L                max    rain'* "- cawn stream  loca-
    tlon.   Also shown  on  this  table are values of A estimated usfng
    the  approximation  presented  in Section 4.of the report.

    Figure  5-4  presents a spatial plot of chlorophyll  a.  P ,  and
    dissolved oxygen deficit .at locations along the l«gthV the
    stream.  The approximation, shown by the dashed line,  is
    obtained by computing * . 0.155 ?„,,  and then  estimating:
        Dmax " °avg "

         min * ^avg *


  SNH1T tlW •PPn>Xlrat1on 1s Sl19"*'y conservative y1e,d,ag
  slightly  mn posltl¥t ^i,.^ .„,„ the yi]ues pr8
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II (2)
Revision No.
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     TABLE 5-4.
                                                      II (2)
                                                      Revision No. 0
Ct)  -  4.57  .
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                                                               I!  (2)
                                                               Revision No. 0
           TABLE 5-5
    t*
   (days)
    0.0
    0.5
  .  1.0
    1.5
    2.0
    2.5
    :.o
   3.5
   4.Q
   4,5
   5.0
   5.5
   6.0
   6.5
Diurnal 0.0. Deficit
fmo/n
Hin
-0.52
-0.50
-0.56
-0.61
-0.66
-0.66
-0.57
-0.33
-0.11
-0.03
-0.01
0.00
0.00
0.00
Max
0.43
0.41
0.47
0.51
0.55
0.55
0.47
0.26
0.08
0.02
0.01 '
0.00
0.00
0.00
Aili
1.05
0.91
1.03
1.12
K21
1.21
1.04
0.59
0.19
" 0.05
0.02
0.00
0.00
0.00
Approximate
    0.95
    0.93
    1.02
    1.11
    1.20
   1.21
   1.07
   0.66
   0.23
   0.06
   0.01
   0.00
  0.00
  0.00
0)  From computations illustrated in this  section.
(2)  Approximation  from:   4 «  0.155 P
                                     m
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1
m
3


H)-
4G-
X-
20-
10-
0
1
 a
                                                             •wvision No.  0
                        2       3       4


                          TRAVEL TIME, t*
                                   Daily Deficit
                         5-26
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                                                             II (2)
                                                             Revision NO. o
                                   REFERENCES
   3-   H»I'.M.  s.M.   Rlv.r
                               of
 7.  Au.r. M.T. and ». ?.
«-  e
-------
                         •                                 II (?)
                                                          Revision No.  £


   13.  WToro. »•«•«* J.F.  Connolly  (1980). Mathematical Model, of

            £M^                    - "• «••• «••. »A.
1*.  DiToro, D.M.  .
                            ."Optic, of Turbid  E,t«arine Water,:.

  16.
  17.  Hydro.ci.nce. Inc.. (1976)  "Eutrophication Analysis of  Lake

           Living,ton Re.ervoir." for I«a. Wat.r Quality BoarJ.


  18.  O'Connor. D.J  .nd D.M. DiToro, "Photo.ynth.si, and Oxygen

           Balance in Streao,." ASCE. JSED. V96, SA2  -    - "8


  19.  ****.£ H  :^oto.ynth..i. m the OcMn a, .
 20-
 *
23.
25.
                   2
                                        of Ec81oglcal

                                                             =«
                                    to Numerical Math«natic,«. Acadenric
                            6-?
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                                                      II (2)
                                                               a0. 0
  26.   DiTore. D.M..
                    Thoaann
27..  O'Connor. D  T
          Mw* • w.j.t
    DiToro  and .
29.
    Thoaann and Seeura  "n«.  ^
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1
.V
-------