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TITLE: Technical Guidance Manual for Performing Wasteload Allocations,
       Book IV: Lakes, Reservoirs, and Impoundments-
       Chapter 2: Eutrophication

EPA DOCUMENT NUMBER: EPA-440/4-84-019                DATE: August 1983

ABSTRACT

As part of ongoing efforts to keep EPAs technical guidance readily accessible to water
quality practitioners, selected publications on Water Quality Modeling and TMDL Guidance
available at http://www.epa.gov/waterscience/pc/watqual.html have been enhanced for
easier access.

This document is part of a series of manuals that provides technical information related to
the preparation of technically sound wasteload allocations (WLAs) that ensure that
acceptable water quality conditions are achieved to support designated beneficial uses.
The document presents methods for WLA analysis to control eutrophication in lakes,
where water pollution control strategies are often directed towards qualitative objectives
such as improvement of a lake's trophic state. Water quality improvements have often
been used as the measure of success instead of attainment of specific numerical water
quality criteria.

WLAs for lake eutrophication are generally designed to reduced nutrient inputs under the
presumption that the nutrient is a significant factor limiting the rate of growth and
subsequent population of phytoplankton (algae). It is also presumed that reducing
phytoplankton population will control undesirable water quality situations such as algal
blooms or low hypolimnetic dissolved oxygen concentrations. In general, these WLAs
therefore focus directly on nutrient reductions and only indirectly on phytoplankton and
dissolved oxygen conditions resulting from overstimulation  by nutrients.

The document first presents the nature of lake eutrophication processes and their
relationship to water quality effects, and then describes and discusses three classes of
models - from simplified techniques to complex, sophisticated analysis procedures - that
that can be used  to perform WLAs for lake eutrophication. It also provides guidance on the
nature and extent of monitoring  programs that may be required to support eutrophication
analyses.

KEYWORDS: Wasteload Allocations, Nutrients, Eutrophication, Dissolved Oxygen,
              Phytoplankton, Impoundments, Lakes,  Reservoirs, Water Quality Modeling

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  Technical Guidance Manual for
Performing Waste Load Allocations
Book IV Lakes and Impoundments

      Chapter 2 Eutrophication
               August 1983
               Final Report
                  for

      Office of Water Regulations and Standards
        Monitoring and Data Support Division,
              Monitoring Branch
        U.S. Environmental Protection Agency
      401 M Street, S.W. Washington, D.C. 20460

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                    UNITED STATES ENVIRONMENTAL PROTECTION AGENCY
MEMORANDUM
     SUBJECT:
     FROM:
     TO:
               Technical Guidance Manual for Performing Wasteload
               Allocations Book IV, Lakes and Impoundments,
               Chapter 2, Eutrophication

               Steven Schatzow, Director
               Office of Water Regulations and Standards  (WH-551)

               Regional Water Division Directors
               Regional Environmental Services Division Directors
               Regional Wasteload Allocation Coordinators
     Attached,  for  national  use,   is   the  final  version  of  the
technical guidance manual  for  performing wasteload allocations Book
IV,  Lakes  and  Impoundments,   Chapter   2,  Eutrophication.  We  are
sending  extra  copies  of  this  manual  to  the  Regional  Wasteload
Allocation  Coordinators  for distribution  to  the  States  to use  in
conducting wasteload allocations.
     Modifications
draft include:
             o
                   to sections 1, 2,  3.1,  and  3.2  of the March 1983
               Increased  emphasis  on  reasons  why  nitrogen  control
               alone  is  generally  not effective  for eutrophication
               control.
             o  Expanding the model  selection  and use considerations
               to include the possibility  of  controlling a nutrient
               so that it becomes limiting.
             o  Listing   septic   tank  and  other   on-lot  disposal
               discharges as non-point sources.
             o  Adding a  discussion  relating the detail  of analysis
               with the anticipated cost of nutrient removal.
             o  Explaining the variability  of  trophic boundaries and
               allowing  other water quality conditions  as  a target
               condition.
             o  Including  caveats about  using nitrogen:  phosphorus
               ratios for determining limiting nutrients.

The remainder of the report is unchanged from the March 1983 draft.

     If  you have  any questions  or  comments  or desire  additional
information please contact  Tim  S. Stuart,  Chief,  Monitoring Branch,
Monitoring and Data Support Division  (WH-553)  on (FTS) 382-7074.

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            TECHNICAL GUIDANCE MANUAL FOR
          PERFORMING WASTE LOAD ALLOCATIONS
                         by
John L.  Mancini (Mancini and DiToro Consulting, Inc.
    Gary G. Kaufman  (Woodward-Clyde  Consultants)
  Peter A. Mangarella  (Woodward-Clyde  Consultants)
 Eugene  D.  Driscoll (E.D. Driscoll and Assoc., Inc.)
               Contract No. 68-01-5918
                   Project Officer
                  Jonathan  R.  Pavlov
      Office of Water Regulations and Standards
        Monitoring  and  Data  Support  Division
                  Monitoring Branch
        U.S. ENVIRONMENTAL  PROTECTION AGENCY
                   401 M  STREET,  SW
               WASHINGTON,  D.C.  20460

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                          ACKNOWLEDGEMENTS

The contents of this section have been removed to comply with
current EPA practice.

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                                 CONTENTS

ACKNOWLEDGEMENTS 	 i

FIGURES	v

TABLES	vi

SECTION 1.0 INTRODUCTION 	 1-1

  1 . 1  PURPOSE  	1-1
  1.2  RELATION TO OTHER BOOKS  AND CHAPTERS  	 1-1
  1 .3  SCOPE  OF THIS  CHAPTER	1-3

SECTION 2.0 BASIC PRINCIPLES 	 2-1

  2 . 1  GENERAL  	2-1
  2 .2  BASIC  PROCESSES  	2-6
   2.2.1 Loads	2-6
   2.2.2 Nutrients	2-9
   2.2.3 Phytoplankton	2-12
   2.2.4 Transport	2-21
   2.2.5 Bottom Processes 	 2-25

SECTION 3 . 0 MODEL SELECTION AND USE	3-1
  3.1  INITIAL  CONSIDERATIONS 	 3-1
   3.1.1 Limiting Processes 	 3-1
   3.1.2 Availability of Nutrients 	 3-4
   3.1.3. Estimating Loadings 	 3-8
  3.2  SIMPLIFIED LAKE  NUTRIENT MODELS  	 3-15
   3.2.1 Nutrient Mass Balance Model 	 3-15
   3.2.2 Use of Phosphorus as the Limiting Nutrient	3-17
   3.2.3 Total Phosphorus Sedimentation Rate 	 3-18
   3.2.4 Alternate Form of Mass Balance Equation	3-19
   3.2.5 Comparison of Steady-State Mass Balance Equations 	 3-21
   3.2.6 Other Nutrient Formulations 	 3-23
   3.2.7 Determination of Allowable Phosphorus Discharges 	 3-23
   3.2.8 Calculation Procedure 	 3-32
   3.2.9 Comments on Limitations and Applicability 	 3-35
   3.2.10 Preliminary Nitrogen Allocation 	 3-40
  3 .3  TIME VARIABLE  MASS  BALANCE  MODELS 	3-44
   3.3.1 Formulations	3-45
   3.3.2 Example Problem	3-48
   3.3.3 Range of Parameter Values 	 3-52
   3.3.4 Model Calibration 	 3-53
   3.3.5 Applications and Limitations of Residence Models 	 3-54
  3.4  NON-LINEAR EUTROPHICATION MODELING 	 3-57
   3.4.1 General	3-57
   3.4.2 Formulations and Ranges of Coefficients 	 3-58
   3.4.3 Calibration and Verification 	 3-76
   3.4.4 Supplemental Calculation Procedures 	 3-77
   3.4.5 Example Problem	3-78
   3.4.6 Vertical Dissolved Oxygen Analysis 	 3-82
   3.4.7 Example Problem	3-86
  3.5  AVAILABLE LAKE EUTROPHICATION  MODELS  	 3-89
  3 . 6  MODEL  SELECTION  	3-102

SECTION 4 . 0 DATA REQUIREMENTS	4-1

                                    iii

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  4 . 1  INTRODUCTION 	4-1
  4.2  GENERAL  CONSIDERATIONS 	  4-1
  4.3  SPECIFIC CONSIDERATIONS IN DETERMINING DATA REQUIREMENTS 	  4-3
   4.3.1 Problem Identification/Description 	  4-3
   4.3.2 Model Operation  (Including Calibration/Verification) 	 4-10
   4.3.3 Simple Mass Balance Models	4-12
   4.3.4 Time Variable Mass Balance Models	4-13
   4.3.5 Non-Linear Eutrophication Models 	 4-15

REFERENCES	R-l
                                     IV

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                                 FIGURES

Figure 2-1.  Trends in concentration in relation to lake
            eutrophication	2-3
Figure 2-2.  Nutrient cycle mechanisms for  nitrogen,  phosphorus and silica
            in the water column	2-11
Figure 2-3.  Specific growth rate versus substrate concentration	 2-14
Figure 2-4.  Nutrient absorption rate as a  function of nutrient
            concentration: comparison of Michaelis-Menton theoretical
            curve with data from Ketchum	2-16
Figure 2-5.  Normalized rate of photosynthesis versus light intensity . 2-17
Figure 2-6.  Use of algal bioassays to determine the limiting nutrient in
            stream or lake waters	2-19
Figure 2-7.  Grazing rates of zooplankton versus temperature 	 2-22
Figure 2-8.  Formation of baroclinic motions in a lake exposed to wind
            stresses at the surface:  (a) initiation of motion,  (b)
            position of maximum shear across the thermocline,  (c) steady-
            state baroclinic circulation	2-24
Figure 3-1.  Problem framework and nutrient sources 	 3-9
Figure 3-2.  Relationship between impervious area and runoff-to-rainfall
            ratio	3-12
Figure 3-3.  Test of trophic state indicators 	 3-26
Figure 3-4.  The relationship between chlorophyll a and total phosphorous
            concentrations in northeastern U.S. lakes and
            reservoirs	3-27
Figure 3-5.  Effect of point source control on trophic status, sample
            problem	3-36
Figure 3-6.  Total nitrogen loading plot 	 3-41
Figure 3-7.  Phosphorus mass balance for completely mixed lake	3-46
Figure 3-8.  Mass balance equations for horizontally or vertically
            separated completely mixed segments	3-51
Figure 3-9.  Effect of density gradient on  vertical dispersion
            coefficient	3-61

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                                   TABLES

Table 1-1.   ORGANIZATION OF GUIDANCE  MANUAL FOR PERFORMANCE  OF	 1-2
Table 3-1.   VALUES OF P/W for Ks = VS/Z  and Ks =  -Jp  USING EQUATIONS  3-10
             AND 3-15	3-22
Table 3-2.   CHARACTERISTICS OF SELECTED LAKES IN SIMPLIFIED  EUTROPHICATION
             ANALYSIS DATA BASE	3-38
Table 3-3.   MAXIMUM (SATURATED) GROWTH  RATES AS A FUNCTION OF
             TEMPERATURE	3-65
Table 3-4.   HALF-SATURATION CONSTANTS FOR N, P,  AND Si UPTAKE (pM)
             REPORTED FOR MARINE AND F RESHWATER PLANKTON ALGAE (After
             Lehman, et al. ,  1975)	3-66
Table 3-5.   MICHELIS-MENTON HALF-SATURATION CONSTATNS  (Ks) FOR UPTAKE OF
             NITRATE AND AMMONIUM  BY C ULTURED MARINE  PHYTOPLANKTON AT 18°C
             Ks UNITS ARE  jiMOLES/LITER (After Eppley,  et al.  1969) .... 3-70
Table 3-6.   MICHAELIS-MENTON HALF-SATURATION CONSTANTS FOR NITROGEN A ND
             PHOSPHORUS  (From DiToro,  et al., 1971) 	 3-71
Table 3-7.   VALUES FOR THE HALF-SATURATION CONSTANT IN MICHAELIS-MENTON
             GROWTH FORMULATIONS	3-72
Table 3-8.   SUMMARY OF FORMULATIONS FOR FACTORS CONSIDERED IN NON-LINEAR
             EUTROPHICATION MODELS  AND ESTIMATES FOR RANGE AND INITIAL
             VALUE OF COEFFICIENTS  INITIAL VALUE OF COEFFICIENTS	3-79
Table 3-9.   DESCRIPTION OF CHAPRA'S TIME VARIABLE PHOSPHORUS  MODEL... 3-91
Table 3-10.  DESCRIPTION OF LARSEN'S TIME VARIABLE PHOSPHORUS  MODEL... 3-92
Table 3-11.  DESCRIPTION OF WATER ANALYSIS SIMULATION PROGRAM	 3-93
Table 3-12.  DESCRIPTION OF WATER ANALYSIS SIMULATION PROGRAM  AND ADVANCED
             ECOSYSTEM MODELING  PROGRAM	3-94
Table 3-13.  DESCRIPTION OF CLEAN PROGRAMS 	 3-96
Table 3-14.  DESCRIPTION OF LAKECO AND ONTARIO MODELS 	 3-99
Table 3-15.  DESCRIPTION OF WATER QUALITY FOR RIVER RESERVOIR  SYSTEMS 3-100
Table 3-16.  DESCRIPTION OF GRAND TRAVERSE BAY DYNAMIC MODEL	 3-101
Table 3-17.  NON-TECHNICAL CRITERIA  APPLIED TO CLASSES OF
             EUTROPHICATION MODELS	3-105
Table 4-1.  BASELINE LIMNOLOGICAL MONITORING PROGRAM 	 4-6
Table 4-2.  DATA NEEDS FOR DIFFERENT MODEL TYPES	4-11
                                      VI

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                             SECTION  1.0

                            INTRODUCTION
1.1 PURPOSE

     This chapter is one in a  series  of  manuals  whose  purpose is to
provide   technical   information   and  policy   guidance   for   the
preparation  of  Waste   Load   Allocations   (WLAs),  which   are   as
technically  sound  as  the  current  state  of the  art  permits.  The
objectives  of  such  load  allocations are  to ensure  that  quality
conditions that protect designated beneficial uses  are achieved. An
additional  benefit  of  a  technically  sound WLA  is that  excessive
degrees  of  treatment,   which  are  neither necessary  nor result  in
corresponding  improvements  in  water  quality,  can be  avoided.  This
can result in a more effective  utilization of available funds.

     This  chapter  addresses  Nutrient/Eutrophication  impacts   in
lakes.

1.2 RELATION TO OTHER BOOKS AND CHAPTERS

     Table  1-1  summarizes  the  relationship  of  the various "books"
and "chapters"  that make up the set of guidance manuals.

     These  technical  chapters  should be  used  in  conjunction  with
the  material  in   Book  I,   which   provides  general  information
applicable  to  all  types  of water  bodies  and  to  all contaminants
that must be ad-dressed by the  WLA process.
                                 l-l

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Table 1-1.     ORGANIZATION OF GUIDANCE MANUAL FOR PERFORMANCE OF
               WASTE LOAD ALLOCATIONS
BOOK I         GENERAL GUIDANCE
               (Discussion of  overall WLA process,  procedures,  and
               considerations)

BOOK II        STREAMS AND RIVERS
               (Specific technical guidance for these water bodies)

               Chapter   1 - BOD/Dissolved Oxygen Impacts
                         2 - Nutrient/Eutrophication Impacts
                         3 - Toxic Substances Impacts

BOOK III       ESTUARIES

               Chapter   1 - BOD/Dissolved Oxygen Impacts
                         2 - Nutrient/Eutrophication Impacts
                         3 - Toxic Substances Impacts

BOOK IV        LAKES, RESERVOIRS, AND IMPOUNDMENTS

               Chapter   1 - BOD/Dissolved Oxygen Impacts
                         2 - Nutrient/Eutrophication Impacts
                         3 - Toxic Substances Impacts
Note:     Other water bodies  (e.g.,  groundwaters,  bays,  and oceans)
          and other contaminants  (coliform  bacteria  and virus, TDS)
          may subsequently  be incorporated  into  the manual  as the
          need for comprehensive treatment is determined.
                                 1-2

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1.3 SCOPE OF THIS CHAPTER

     The processes that, are  significant  in  eutrophication of lakes
are  complex,  and  technical  understanding is  incomplete  from  both
the  qualitative  and quantitative  standpoints.  The  expected  result
and  level   of  confidence  associated  with  waste  load  allocations
addressing  eutrophication  in lakes  will  reflect  this  degree  of
complexity and incomplete knowledge.

     It  is  not   unusual   to  consider   implementation   of   water
pollution  control  strategies  for  lakes  that  are  directed  toward
such relatively  qualitative  objectives as  alterations of  a  lake's
trophic  state  from  eutrophic to  mesotrophic.  This  type  of  waste
load  allocation decision  has  a  different   basis  than  a  typical
dissolved  oxygen  waste  load  allocation, which   sets  a  numerical
target for dissolved oxygen  (for  example,  five  mg/1).  Historically,
there have been  essential  differences in the results  expected  from
waste load allocations for control  of lake  eutrophication and those
for  dissolved  oxygen.   When  eutrophication is  considered,   water
quality improvements have often been  used as the  measure of success
rather  than  attainment  of  specific  numerical   values  of   water
quality variables.

     Waste load  allocations  for  control  of  eutrophication  in lakes
are  generally  designed  to reduce  nutrient  inputs. This  strategy
presumes  that  the  nutrient  to  be   controlled   is  a  significant
factor,   limiting  the rate  of growth  and subsequent population  of
phytoplankton.  It
                                 1-3

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further   presumes   that   reducing   the   population   level   of
phytoplankton  will  provide  the   desired  control  of  the  complex
process  of   eutrophication  and/or  eliminate   undesirable   water
quality  situations such  as algal  blooms  or  low dissolved  oxygen
concentrations  in  the   hypolimnion.   It,  therefore,   should  be
recognized  by  the  analyst  and  by  the   decision  maker  that,  in
general, waste  load  allocations to control  eutrophication  in lakes
focus   directly   on  nutrient   reductions   and   indirectly   on
phytoplankton  and  dissolved  oxygen  conditions  that  result  from
overstimulation by nutrients.

     These  waste   load   allocation  procedures  do   not   consider
ecological factors such  as  fish populations and  species,  growth of
macrophytes,   and  species diversity.  The  quantitative  knowledge  is
not   presently  available   to  address   water  quality   problems
associated with macrophytes  (rooted aquatic plants).

1.4 ORGANIZATION OF THIS  CHAPTER

     The remainder of this  chapter is organized into three parts
summarized below.

     Section  2.0  discusses   the   nature   of   lake   eutrophication
processes and  some factors  that influence the performance  of a WLA
analysis  and  the  interpretation  and  evaluation  of   results.  This
section  also   identifies  and  discusses  the basic  processes  that
determine the  rate and magnitude of the water  quality effects,  and
which are incorporated in the  models that  will  be used to  perform a
WLA analysis.
                                 1-4

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     Section 3.0 describes and discusses models  that  can be used to
perform  WLA's  for  lake  eutrophication. This  section  covers  three
classes  of models  ranging  from  simplified  techniques  to  complex
sophisticated  analysis  procedures.   Example  problems  are presented
to illustrate  the  use of  the  simplified models. This  section also
discusses  factors  that  must  be  appreciated  and  given  careful
consideration  in   the   application  of  the  models   and  in  the
interpretation of the resulting calculations.

     Section 4.0 provides  guidance  on the  nature and  extent  of the
monitoring  programs   that  may  be  required   for  eutrophication
analyses.  Data  requirements  for  both   problem  identification  and
model  operation   (calibration/verification)   are   discussed.   Some
simple   statistical   procedures   for  predicting   the  statistical
significance   of   the  data   collected  from  proposed  monitoring
programs are presented.
                                 1-5

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                            SECTION 2.0

                          BASIC PRINCIPLES
2.1 GENERAL

     Two  time  scales  are of  interest  in  the  evaluation of  lake
eutrophication.  The  first  time  scale  is  long  and  considers  the
period over which a lake  exists and may  extend for  hundreds  or even
thousands of years. The second period  is the  annual cycle  when lake
chemistry and  biology  respond  to  the  annual  temperature,  flow,  and
solar radiation  (light) cycles.

     Lakes are considered to undergo a process of "aging"  which has
been  characterized  by three qualitatively  defined conditions.  The
initial condition of  a lake  is  termed oligotrophic and  is normally
associated with  deep  lakes,  where the waters at the bottom  of the
lake  are  cold  and have relatively  high  levels  of  dissolved  oxygen
throughout the  year.   The waters  and  bottom  sediments  of the  lake
usually contain  only  small  amounts of organic matter.  Productivity
in terms  of  the  population  levels of  phytoplankton,  rooted  aquatic
plants, zooplankton,  and  fish is  usually low.  Species diver-sity is
often quite high and chemical water quality is good.

     The  eutrophic condition of  a lake  represents  the  opposite end
of  the aging  process. Eutrophic  lakes   may  be  either  shallow  or
deep.  They  are  characterized  by high concentrations of  suspended
organic matter in the  water column  and by relatively  large sediment
depths with high organic  contents particularly  in  the  upper  layers
of the  sediment.  Biological  productivity is  high and the  diversity
of biological populations  may be somewhat limited.
                                 2-1

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Coarse  (non-game) fish may predominate  due  to  elevated bottom water
temperatures  and/or  depressed  water   quality.   Dissolved  oxygen
concentrations  of  bottom  waters  are  usually  depressed  and  in
extreme  cases  of  eutrophication  may  reach  zero  during  summer
periods.  Generally  water   quality  is  low  and   can   result  in
impairment of beneficial water usages  such  as  water supply,  contact
recreation,  and/or boating.

     A  third  lake  condition is mesotrophic  which is  defined  as  an
intermediate  state  between  oligotrophic and  eutrophic.  Mesotrophic
lakes have  inter-mediate  levels  of biological productivity  and can
have  some  reductions in  bottom  dissolved  oxygen levels. Lakes  in
this  category generally have  water quality  which  is adequate for
most beneficial  uses but  may be deteriorating toward  the eutrophic
state.

     Figure  2-1  is  a  representation  of  a  transition  in  lake
condition as  a  function  of  time.  The  progression from oligotrophic
to eutrophic  is  shown  on  the figure as  a  concentration  "C"  varying
as a  function of time. The  concentration  could  represent any  of  a
number  of   constituents  such  as  phosphorus,  chlorophyll,  organic
carbon,  etc.  The figure illustrates that  there   is  a  general  trend
of changing — usually  increasing — concentration as  a  function  of
time.

     The  boundaries  between  the  three  stages  are  not  rigidly
defined and may  vary with regions of the nation  and with beneficial
uses  of lake  waters.  For  lakes  in  the north  temperate zone the
following   relationship    between    water    quality    and    lake
classification has been suggested.  However,  it should be
                                 2-2

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  Concentrition
  of Substance
      "C"
                   Oliflotrophic
Mesotrophic
Eutrophic
                                               Inset {itow up ielowj
                                       TIME {Decades)
                                        Inset Blowup
                                       TIME (years)
Figure  2-1.  Trends  in concentration  in  relation  to  lake
               eutrophication.
                                         2-3

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noted  that  a  number  of  other  trophic  classification schemes  have
been developed  (3, 4, 5).
     Water Quality

Reference
Total phosphorus

Chlorophyll (jig/i;

Secchi  depth (m)

Hypolimnetic
(%saturation)
                          Variable    Oligotrophic  Mesotrophic   Eutrophic
                  oxygen
                             <4

                            >3.7

                            >80
10-20

4-10

 2-4

10-80
                                                     >20
<2
(1)

(2)

(1)

(1)
     Some  lakes  in the  southern  part  of  the  country  are  often
perceived to have  higher  recreational value where  chlorophyll  a. and
total  phosphorus   levels  are   substantially  higher  than   those
indicated above. As an illustration,  the  state of Texas employs

               Total Phosphorus     =     0.4 mg/1
               Orthophosphate       =     0.2 mg/1
               Inorganic  Nitrogen  =     1.0 mg/1
               Chlorophyll a.        =50  |ig/l

as  alert  levels  of  concern  for  lake  water  quality.  Lakes  and
reservoirs   in   the  southwestern   region   of   the   country   have
considered  levels  of  concern  ranging  from  20  to  40  |ig/l.  In
addition,  low  availability  of  nutrients  in  areas  with  high  clay
content  soils  entering  lakes  and  reservoirs  have  result-ed  in
acceptable  water  quality even  with  total  phosphorus  loadings  and
in-lake  concentrations   in  excess  of  those  indicated  above.  In
summary,   judgment  is  required   in establishing  target  levels  of
total  phosphorus,   chlorophyll  a.  or  other measures of  lake  water
quality.

     As  shown in  the inset  in  Figure  2-1 there are  often  very  large
short-term  yearly variations   which  characterize  the   gradually
increasing  concentration.  The  large  year-to-year  variations  are
related  to hydraulic
                                 2-4

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and climatic conditions and may be  particularly  marked for small to
moderate size lakes. Therefore it is  often  difficult  to discern the
basic pattern of  concentration increases. Further, the  large year-
to-year variations  make it difficult  and in some  cases impossible
to identify  the  effects of remedial  actions such  as  reductions in
nutrient inputs.

     The annual cycle  in  lakes is driven by the seasonal interplay
of  temperatures,   density,  and  wind.  For  temperate   zone  lakes,
waters are cold  in the winter and  may be near  the maximum density
of water at 39.2°F  (4°C) .  During  this  period, biological activity is
low   due   to   the   reduced   temperatures   and   stable   density
stratification can be present. In spring, diurnal  heating and winds
tend to promote vertical  mixing  which results in  a spring turnover
where  water   quality   tends  to   be  vertically  uniform.   Light
transparency can be high, and  solar radiation and  temperature begin
to  increase.  The  levels  of  nutrients  available  to  biological
systems are usually elevated as a result  of  the  accumulation during
the winter period  of low  biological activity.  These factors combine
to  yield  conditions  that can  support high levels  of  growth  and
biological activity.

     As  spring   yields  to   summer,   the   surface  waters  become
progressively warmer and  less  dense.  A stable vertical structure is
established which  is characterized by a surface   layer  of uniform
temperature   and    water   quality,    and  an   intermediate   layer
(thermocline)  which has  significant   gradients  in temperature  and
water quality and provides a barrier to vertical transport of
                                 2-5

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dissolved  substances  such  as  dissolved  oxygen.  The bottom  waters
(hypolimnion)  are usually cool with  decreasing  water quality  as the
products of  active biological  productivity  in the  surface  waters
settle  and begin  to  accumulate  below  the  thermocline.  The  late
summer  is  the  usual   time  when  high  surface  chlorophyll and  low
hypolimnetic  dissolved   oxygen  levels   are  observed.   Nutrient
limitations,  settling, outflow,  and  light usually  combine to limit
growth  of  phytoplankton.  If  the dissolved  oxygen  in the  bottom
waters drops to zero,  release of  nutrients  from the sediment  can be
significant.  The  vertical  structure during  the summer  period  will
vary  from  year  to year  due to differences  in solar energy,  wind,
and flow.

Cooling  of surface  waters  in the fall  leads to a  uniform vertical
structure  for   both   temperature   and   water  quality.   Reduced
biological productivity is  associated with  lower  water  temperatures
and reduced solar radiation.
2.2 BASIC PROCESSES
2.2.1 Loads

     Nutrient levels in lakes  are  controlled  by external sources to
the  lake  and  in-lake  processes.  External  sources  of  nutrients
include  municipal  and  industrial  point  sources,  stream  inputs,
atmospheric  sources,  urban   drainage,   groundwater,   agricultural
drainage, and other  non-point  sources  surrounding  the  lake.  In-lake
processes  include   sediment   release,   biological  recycling,   and
nitrogen fixation.

     Municipal  and  industrial  point  sources  may  discharge  both
nitrogen  and phosphorus  directly  into  lakes  or  to  streams  that
eventually drain into
                                 2-6

-------
lakes.  Existing monitoring  data  should be  used  or  a  monitoring
network developed to provide  reliable  estimates  of nutrient inputs.
Source  strength of  municipal  discharges  can  vary  diurnally  and
seasonally. Total municipal load usually tends  to  increase over the
years due to population growth.

     Stream inputs are  the  most significant source of  nutrients  to
most  lakes.  As  such,  these  inputs  should  be  carefully  estimated.
Estimates  can  often be  obtained by  sampling  on  two  to  four  week
intervals  and  during major storm  events.  It  should  be  noted  that
significant  increases   in  nutrient   inputs  may  occur  during  wet
weather flows.  Consequently,  it is necessary  to  collect  sufficient
dry weather flow and concentration data, so as  not to  overestimate
load  contributions  during dry-weather  periods.  Nutrient  input  can
then be estimated by multiplying average flow by  the  flow-weighted
concentration,   or by a regression  equation of phosphorus  input  on
flow. The  availability  of these nutrients would depend  on upstream
activities responsible for the  nutrient  concentrations. Most  of the
phosphorus, though,  is probably not available for immediate uptake.

     Atmospheric  sources  to  lakes  include precipitation and  dry
deposition;  these  sources  are  frequently   considered  together  as
bulk  precipitation.  Because  nutrient  forms  in precipitation  are
generally  soluble and  those in dry  deposition  generally  insoluble,
the  availability of  nutrients  from  bulk precipitation varies  from
year-to-year,  site-to-site,  and storm-to-storm.  Nutrient  quantities
also vary with  respect to these parameters.  Because nutrient  inputs
from  bulk precipitation  are  generally  small,  literature  values,
despite   their   limitations,    are   frequently  used   for  loading
estimates.
                                 2-7

-------
If   literature   data  indicate   bulk  precipitation   inputs   are.
relatively large, a sampling program may be necessary.

     Sampling  for  nutrient  loads from  the runoff  of urban  areas
during storm  events  using automatic  samplers  can  provide  estimates
of both  combined sever overflow  (CSO)  and urban  runoff inputs.  If
sampling, which  is  the most desirable and  most  costly approach,  is
not  possible,  a  number   of  literature   sources  can  be  used  to
estimate inputs  (6, 7,  8).

     Making  reliable  estimates  of  groundwater nutrient  input  to
lakes  is  difficult.  A  monitoring  system  to  measure  rates  of
groundwater   flow   with    seepage   meters    and   to   determine
concentrations  of  phosphorus  in  wells  has been  demonstrated  (9) .
Such a system might  be necessary in  a lake impacted  by septic  tank
discharges. Because  of the  spatial  and seasonal  non-uniformity  of
groundwater   nitrogen   and   phosphorus   concentrations,   it   is.
necessary to  catalog potential sources  of  nutrients  to surrounding
groundwaters.  The  nutrient  forms reaching  lakes  from groundwater
sources  would,   of  course,  be soluble  and  readily   available  for
phytoplankton incorporation.

     Agricultural drainage may contribute  significantly to  the  lake
nutrient  budget.  In most  cases,  agricultural drainage  would  be
estimated as  part  of  the  stream  input.  Estimation of agricultural
drainage from lands  immediately  adjacent  to the lake  would  use the
same sampling techniques used  for measuring stream input.  It  may be
useful to utilize literature values to initially
                                 2-i

-------
estimate  loads.  If  these loads  are relatively  small,   a  sampling
program may not be necessary.

     Sediments release nutrients  in  soluble  forms  readily available
for  algal  uptake,  although  the  density  structure  of the  lake  may
hinder  immediate  uptake. Although  this  release  from sediments  is
not  well  understood,  laboratory  and  field  investigations  have
produced numerical estimates  of  nutrient loss which  can  be used to
compare  sediment  release to  other  lake  inputs.  If  the  release  is
relatively high a sampling program may need to be undertaken.

     Biological decomposition occurs  throughout  the water column to
make  the  nutrients   locked  in  organic  detritus  available  for
phytoplankton.  In  addition,   phytoplankton  and  zooplankton secrete
and excrete soluble and insoluble nutrient forms.

     Nitrogen  fixation may  be a  significant  source  of  nitrogen  in
lakes  with  limiting  concentrations  of  nitrogen.  During  nitrogen
fixation, blue-green  algae  and  some macrophytes are  able to reduce
molecular nitrogen to nitrogen  at the  ammonia  oxidation  level.  The
ability  of  selected  algae   and  macrophytes  to   fix  nitrogen  is
frequently cited as  one  of  the  reasons  phosphorus  and  not nitrogen
is considered to be the limiting nutrient in most lakes.
2.2.2 Nutrients

     As mentioned  above,  the two nutrients of  greatest  concern are
nitrogen   and  phosphorus.   In   addition   to  these   nutrients,
phytoplankton  require  carbon dioxide and  a host of  minor elements
(potassium,  sodium)  and  trace  elements  (iron, manganese,  cobalt,
copper, zinc, boron, and molybdenum) and organic
                                 2-9

-------
growth factors.  Silica  is  an important nutrient  for  diatoms,  as it
forms the basis for their skeletal structure.

     Phosphorus in  lake  inputs  and the lake itself can  be  found in
dissolved inorganic and/or  organic  and particulate forms;  Dissolved
inorganic forms  include  the free orthophosphates  and the  condensed
phosphates  (pyro,  meta,  and poly).  Orthophosphate  is  immediately
available  to  phytoplankton  growth.   Dissolved  organic  phosphorus
includes  nucleic   acids,   nucleotides,   and  phospholipids,   among
others.  The  phosphate part  of  these  molecules  must  be cleaved by
exoenzymes to  release phosphorus  for  uptake. Particulate phosphorus
includes  algae,  bacteria,   detritus,  and  silt,   etc.  A  schematic
diagram  of phosphorus cycling in lake waters is  shown  in  Figure 2-
2.

     Analytical  testing  for   phosphorus   in   water   can   identify
orthophosphate, dissolved and particulate  condensed phosphates,  and
dissolved and  particulate  organic  phosphorus.  Total phosphorus is
just the  sum of  all phosphorus species. Levels  of total phosphorus
in lakes  can range from as  low as a  few  |ig/l  to as high  as  a  few
mg/1.  These  levels are  usually reported  for  elemental  phosphorus;
in some  instances  data  are  reported  as phosphates  and appropriate
conversion   is  required.   Levels   of   dissolved   orthophosphate
expressed  in  terms  of elemental   phosphorus   range   from  below
detection limits to a few hundred |ig/l.

Nitrogen  can exist in  several  different  forms  in lakes and  their
inputs.  Nitrogen in  its  most reduced state  is  found  in ammonia  and
various  organic  nitrogen   forms   such  as  purines,  pyrimidines,
nucleic acids,  etc. Ammonia  is
                                2-10

-------
TOTAL
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                   \
                 DIATOMS
                              RESPIRATION
   TOTAL
   NONACCESSIBLE
   SILICON
SILICON
DETRITUS"
                                                 SILICON
               ZOOPLANKTON
                           EGESTION
  SEDIMENTS
                                               Source: Canale (10)

Figure  2-2. Nutrient cycle mechanisms  for nitrogen,  phosphorus
             and silica in the  water column.
                                   2-11

-------
immediately  available  for  phytoplankton  uptake.  Organic  nitrogen
forms  (both  dissolved  and participate) may  need to be  broken down
to ammonia for  uptake.  Some amino acids  are  immediately available.
Other common nitrogen  forms include  the more  oxidized  and soluble,
nitrate  and  nitrite. Nitrate  is  immediately  available  for  uptake
but  requires  the  organism to  expend  more  energy  to   employ  this
source of nitrogen than for utilization of ammonia.

     Measurements  of nitrogen  compounds  are  usually   reported  in
terms  of elemental  nitrogen.  In  lakes,   the  sum  of  the  oxidized
forms of nitrogen and ammonia may  range from  10 |ig/l and above.  The
concentration of  organic  nitrogen may  range  up to  several mg/1.  A
schematic  diagram  of  these  nitrogen  forms  as  well  as   their
interactions   is  also   shown   in   Figure   2-2.  A  pathway  for  the
utilization of silica by diatoms  is also shown in Figure 2-2.
2.2.3 Phytoplankton

     The specific growth rate of phytoplankton  is  controlled by the
levels  of  important  nutrients,   light  and  temperature.  Overall
phytoplankton  growth in  an  area  is  controlled  by this  specific
growth  rate  and  the  effects   of  death,   respiration,   settling,
zooplankton grazing,  and vertical and horizontal transport.

     Phytoplankton are  one  of two main primary producers  found in
lakes. Primary producers  are  able  to utilize light,  carbon dioxide
and nutrients to  synthesize new organic material.  The other primary
producers are  the rooted or floating aquatic plants (macrophytes).
These   plants    are   generally   restricted  to   shallow   waters.
Phytoplankton are free-floating  and transported
                                2-12

-------
by currents.  In most cases,  phytoplankton are more  important  than
are rooted  aquatic  vegetation in  the  basic food production  of the
lake ecosystem,  although their  relative  importance depends  on the
specific characteristics of the pond/lake in question.

     Phytoplankton can  be  characterized in terms of  species,  size,
composition,  growth  rates,  and  pigmentation,  among  others.  Groups
of phytoplankton species  include  diatoms,  green  algae,  nitrogen-
fixing  blue-green  algae and  non-nitrogen-fixing blue-green  algae.
The standing  crop of phytoplankton in  lakes has  been characterized
in terms  of overall cell  counts,  individual  species  counts,  mass,
and  chlorophyll  a..   These   quantities   are   usually   expressed
volumetrically,  that is, per  unit volume.  Enumeration and counting
can be  performed using  a  microscope  equipped with  a hemocytometer
for  nano-plankton  counting  or  with   a  Sedgwick-Rafter  cell  for
enumeration  of  larger  species.  Phytoplankton mass  has   also  been
characterized  after  drying,  ashing,  and  weighing.  A  problem  with
this determination   is  that  all  biomass  in   a  lake  water  sample,
including bacteria,   detritus  and zooplankton,  will  also be measured
as  phytoplankton.   The   characteristic   algal  pigments  include
chlorophylls  (a, b,  c) , xanthophylls,   and  carotenes.  Chlorophyll  a.
is   the   pigment    typically  used    to   quantify   phytoplankton
populations.      Chlorophyll       a.      is     measured      either
spectrophotometrically or fluorometrically.

     The effect  of phosphorus  on phytoplankton growth is  frequently
described in  terms of an equation  attributed  to Michaelis-Menton to
describe  enzyme kinetics.   As shown  in Figure  2-3,   this equation
expresses  the  specific growth  rate  as  a  function  of  phosphorus
concentration and two coefficients,
                                2-13

-------
                                               Rtgion of "zero-ordtr kintties"
a,
tu

K
I

O
ec

o
u.
U
a.
                                               [S] decreases with time but
                                                  remains essentially
                                                 constant.
                                  Region of mixed (first-tnd zero-order)
                                  kinetics, but the dependency of |i upon
                                  IS} i» stilt experimentally obwrvable.
                         Region of ipproximatt "first-order kinetics."
                         As [Sj cffCftasts, ft decreasts proportionately.
                      SUBSTRATE CONCENTRATION  [S]
         Michaelis-Menton Kinetics
     = Hrr
            Km
              where  iamax = Maximum specific  growth rate
                        u =  Specific  growth rate
                        S =  Substrate concentration
                        Km = Substrate  concentration at  which
                                  JJjnax =
                                   2
                                                            Source: Rich  (11|
Figure  2-3.  Specific  growth rate  versus substrate  concentration
                                     2-14

-------
the  maximum growth  rate  coefficient,  |imax  and  the  half-saturation
coefficient, Km.  A plot illustrating the similarity between nutrient
uptake data and  the  Michaelis-Menton  formulation is  shown in Figure
2-4.  Growth rates  of individual  phytoplankton  have  traditionally
been  measured  in terms  of  mean doubling  times. The  mean doubling
time  is  simply  the  natural  logarithm of two  divided  by the maximum
specific growth rate.

     The  growth  rate  variation  of phytoplankton  as  a  function  of
nitrogen  concentrations  can  also  be modeled using  the  Michaelis-
Menton  formulation.  An  example of  the  close  correlation  between
this  formulation and  real  data  is  shown  in  Figure  2-4.  Similar
correlations  have  been   found when  ammonia and  various  organic
nitrogen compounds are the substrate molecules.

     Phytoplankton  growth  rates  vary  with  temperature   and  light
intensity. Examples  of the  rate of photosynthesis as  a function  of
light    intensity    are   shown    in    Figure   2-5.    Mathematical
representations   of   light    dependent   growth  are   discussed   in
subsequent  sections  of  this  report.  It  can  be observed  from  the
data in  Figure 2-5 that an optimum light level exists.

     Other processes  affecting  phytoplankton  levels  are respiration
and  death.  Respiration  is   a  biochemical   process  that  occurs
continuously  day  and night  and  results  in consumption of  some
portion  of  the  photosynthetically  fixed  carbon  in  the  system.
Hydrolysis of the phytoplankton cell follows  death.

     Factors affecting phytoplankton  growth  in  a  particular volume
include   advective   and   dispersive   transport,   settling,   and
zooplankton grazing.
                                2-15

-------
                                       ISO     200    25{>    300
                                                    50    60
                                       Source:  Manhattan College  (12]

Figure 2-4. Nutrient absorption  rate as a function of nutrient
            concentration: comparison of Michaelis-Menton
            theoretical curve with  data from Ketchum
                                 2-16

-------
           P/P$
     V)
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                                             Chterophyta
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           23456
                                            10
                     123456789   10
                                              789   10



                       LIGHT INTENSITY (foot candles x 103)



                                                  Source: Manhattan College (12)



Figure 2-5.  Normalized  rate of  photosynthesis versus light

              intensity
                                      2-17

-------
Transport  is  the  gain  or  loss  of plankton  from  the  system  as  a
result   of  water  movement.   Settling  results   in   a   loss  of
phytoplankton from the  euphotic  zone.  Settling occurs  even  though
the  density  difference  between  phytoplankton  and water  is  very
small. Zooplankton grazing  provides another check  on  phytoplankton
populations.

     As  mentioned above,  there  are a  number  of  factors  that can
limit  phyto-plankton growth.  For  the  purposes of  modifying  the
productivity of  a lake,  it  is important to identify  those  limiting
factors which can  be controlled.  Very  little  can be done to control
the  intensities   or  concentrations of  light,  temperature  and the
various  trace elements  and  organic  growth  factors.  Because  some
control  can be  exerted  over the  concentrations  of  nitrogen and
phosphorus in lakes, considerable  effort has  been exerted to  define
the  effects  of  these nutrients.  While nitrogen  contributions  from
point  sources are controllable,  the greater  solubility  of  nitrogen
compounds  in non-point sources makes control  difficult.  The ability
of  blue-green  algae to  fix nitrogen  from   the  atmosphere  also
reduces the importance of nitrogen  control. In addition,  control of
nitrogen  alone  may cause a shift  from  green  to blue-green  algae,
thereby   reducing  the   effectiveness   of  control.  As  inorganic
phosphorus compounds are  much less soluble than inorganic  nitrogen
compounds  and tend  to   adsorb  onto  natural   surfaces,   control  of
phosphorus point sources can be more effective.

     One  method   to  determine the  limiting nutrient  is the  algal
bioassay.  In  this procedure  lake water  samples  are   spiked  with
incremental additions  of the nutrient(s)   being investigated   (see
Figure 2-6). A number of samples
                                2-18

-------
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     + Tr«ee tiwnaou, and
                                 Actual I*kf
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             TIME (days)
                                                   I      I       I
                                                  14     16     18
                                                                Source: Thornton  (19)
Figure  2-6.  Use of  algal bioassays to determine  the  limiting

               nutrient  in stream or lake waters
                                          2-19

-------
with  different  levels  of  nutrient(s)  are  then  incubated in  the
laboratory   for   a  specified  period   of  time   under   specified
conditions (13).  These samples may also be incubated in-situ.

     Considerable  controversy  still  exists over the role  of rooted
aquatic plants in  eutrophication  dynamics. The  area of controversy
revolves  around   the  origin  of  nutrients used by  these  primary
producers. Bole  and Allan  (14) reported  levels of phosphorus  that
control  the   source  (sediment or  water)  of  nutrient  uptake  by
aquatic weeds. In  addition macrophyte growth was  found to increase
in   response   to   steadily   increasing   nitrogen  and  phosphorus
concentrations in  waters  of  the  Goczalkowice  River   (15) . On  the
other hand, Carignan and Kalf  (16) showed that  mobile  phosphorus in
sediments closely matched the phosphorus uptake by macrophytes.

     Other  investigations  have  found  that   aquatic   plants  were
limited only by light and  space requirements.  For  instance, Sheldon
and Boylen (17)  found  that the density of  aquatic  plants  decreased
linearly  as  the  depth  of the  sampling  location from  the  shore
increased.   Jupp    and   Spence   (18)   found   that  wave   action,
phytoplankton competition, and grazing by waterfowl had more effect
on macrophyte biomass than other factors.

     Zooplankton,   including protozoa,  rotifers and Crustacea,  form
the next  link  in  the  lake food chain. These  primary macroconsumers
provide the  link  between the primary producers  (phytoplankton)  and
such  secondary consumers   (carnivores)   as predaceous  insects  and
game  fish.  As such,  zooplankton  provide a  primary  constraint  on
phytoplankton  growth.  The  basic  mechanism by  which  zooplankters
feed is by filtering the surrounding water and clearing it
                                2-20

-------
of whatever  phytoplankton and  detritus  is present.  This  filtering
rate varies  as  a function of the temperature,  the  concentration of
phytoplankton,  the  size of  the phytoplankton cell  being  ingested,
and the amount of particulate matter present.

     Zooplankton  growth rate depends  on temperature,  the  quantity
of  food  ingested,  and  the  rate  of  predation  by higher  trophic
levels.  Grazing rates  as  a  function  of  temperature  are  shown in
Figure  2-7.  At  high  phytoplankton  concentrations,   the zooplankton
do not metabolize all  the phytoplankton  that  they graze,  but rather
excrete a portion of  the food  in undigested  or  semi-digested form.
At  low   phytoplankton  concentrations,    zooplankton   utilize   the
ingested  food most  efficiently. For  example, at low phytoplankton
concentrations  the  ratio of zooplankton organic  carbon produced to
phytoplankton  organic  carbon  consumed  has  been  estimated to  be
about 63 percent  (21).
2.2.4 Transport

     Horizontal  transport  is  affected  by  inflows,  outflows,  and
wind action.  Incoming  waters  may be at  different  temperatures than
the  lake  waters.   If  inflows  are  warmer  than   lake  waters,  the
incoming  waters  would tend to  spread  out  over  the lake  surface.
Mixing  would  occur as  temperature  differences   were  reduced.  If
inflow is  colder  than  lake waters,  the  inflow would  drop  below the
surface to  a  depth  where the  density of the  lake  and inflow waters
are equal.

     A  wind  blowing  over  a   lake  exerts  a  stress on  the  water
surface.  Under some wind conditions,  there is movement of  water in
the epilimnion, resulting
                                2-21

-------
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                                                             ,.....*
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                          TEMPERATURE (°C)
                                               Source: Manhattan  College  (12]
Figure  2-1.  Grazing rates  of  zooplankton versus  temperature
                                   2-22

-------
in  an  inclination  in   the  water   surface   (wind  setup)   and  a
counterflow in  the  hypolimnion.  As illustrated in  Figure  2-8,  such
motions  can  cause  significant  horizontal  as  well  as  vertical
transport in both the epilimnion and the hypolimnion.

     Heat input and depth  are two  important factors determining the
thermal  structure  of  lakes.  Insolation  heats the  water and  this
energy  is  distributed  over  an  upper  mixed  layer.  During  any
particular period,  the difference between  the heat  input  from the
sun   and  heat  losses   through  back    radiation,   evaporation,
convection,   and outflow   determines  whether  the  lake  surface  is
heating or  cooling.  Heating during the  spring and  summer may  lead
to  stratification  in  some  lakes.   Stratification  in  extremely
shallow  lakes   is not  expected  because  wind-induced  turbulence  is
large  enough  to mix  lake waters  to  the bottom.  In lakes  that  do
stratify, the  depth of stratification  is  determined by  the amount
of  energy causing  turbulence,   which is  related  to surface  wind
stress  and  the temperature  differences  between  upper  and  lower
layers.

     The  turbulence found  in  the  epilimnion may  be important  in
keeping  phytoplankton  and  zooplankton   in   suspension.   At   the
thermocline,   which  is  an  area  of  extreme  stability,   vertical
transport between  the  epilimnion  and the  hypolimnion  is  limited.
Internal seiches in the thermocline may cause  spatial  and temporal
variations in  the  location of  the thermocline, but  probably do not
increase transport across  the thermocline.
                                2-23

-------
Figure 2-i
              "•-,»
             (ci
                                            Fischer (21)

Formation of baroclinic  motions in a lake exposed to
wind stresses at  the  surface:  (a)  initiation of
motion,  (b) position  of  maximum shear across the
thermocline,  (c)  steady-state  baroclinic circulation

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Most  calculation  frameworks  for  waste  load  allocation  studies
employ  simplified representations  of the  horizontal and  vertical
transport processes.  Most  calculation procedures consider  the  lake
as  one   completely   mixed  system.  Even  more   complex  analysis
frameworks   employ   limited   spatial   segmentation  to   represent
important horizontal and vertical transport processes.
2.2.5 Bottom Processes

     Bottom  processes  are  responsible   for  the  sequestering  and
recycling  of  detritus  and  nutrients.  Recycling begins  with  the
consumption  of dissolved  oxygen  in  the  sediment by  heterotrophic
bacteria  utilizing  deposited  organic material.  As  these  bacteria
consume  oxygen,  the sediment  tends  to become  anaerobic.  Transport
of  oxygen into the  sediment occurs  through  diffusion  and  through
the mixing of  the  upper 5 to  20  cm of the sediment because  of the
activities of  benthic organisms,  bottom-feeding fish,  bubbling  of
fermentation,  gases,   and  wind-induced  currents.   The   vertical
migration  rate of  reduced  oxygen-demanding  substances up  through
the sediments  and  into the  overlying waters  is  also  determined  by
these processes.

     Previous  research  indicates  that   in   some   cases   a   thin,
oxidized  micro-layer  at  the  sediment-water  interface  regulates
exchange  between  water  and  sediments.  The  depth  of   the  oxidized
micro-layer  is determined  by the dissolved oxygen  concentration  in
the  water  overlying  the  sediment  and  by  the  rate  of  oxygen
consumption  in the  sediment. When  the oxidized layer is eliminated,
an abrupt release of iron and phosphate has been noted. Release
                                2-25

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of inorganic  phosphorus  to overlying  waters  occurs primarily  as  a
result of the reduction of hydrous ferric oxides.

     Nitrogen  can be  released  from  sediments  under  aerobic  and
anaerobic conditions.  Release  of nitrate could  occur  under  aerobic
conditions,   but  is  unlikely  as  most  of  the  nitrogen  found  in
sediments  is  at  the  oxidation   level  of   ammonia   and  organic
nitrogen.  During  anaerobic  conditions,  interstitial  ammonia  and
dissolved  organic nitrogen  compounds may  reach  overlying  water
through  molecular  diffusion  or  sediment  mixing processes.  Despite
the  ability  of  sediments  to  recycle  nutrients,  sediments  are,  on
the whole,  sinks for  deposited nitrogen, phosphorus, and carbon.
                                2-26

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                             SECTION  3.0

                      MODEL  SELECTION AND  USE
3.1 INITIAL CONSIDERATIONS

3.1.1  Limiting Processes

     As  indicated,  waste load  allocations rely  on the  concept  of
reducing  inputs  of  a  limiting  nutrient  to  control  growth  of
phytoplankton  or  by controlling  a  nutrient  so  that   it  becomes
limiting.  Other  factors  also  limit  the  rate  of  phytoplankton
population growth  and resultant population levels.  Among the other
factors  which may  be  important  are  light  limitations,  hydraulic
retention  times,   settling,  and  grazing  by  zooplankton.  In  most
site-specific   situations,   several   factors   combine   to   limit
phytoplankton growth  and populations.  If  the  limitations on  growth
imposed by factors other  than  nutrient  concentrations  are large,  it
may not be  economically feasible  to  control eutrophication  with
reductions in nutrient  inputs.  The  non-linear modeling procedures
discussed  elsewhere   in  this  document  consider   the  influence  of
certain other factors on  the growth  of  phytoplankton while the less
complex  analysis  procedures   which  are  presented   assume  that
nutrients are the significant factor limiting growth.

     Phosphorus  has   been found  to  be  the  nutrient  which  limits
growth  in  many  lakes.  In addition,  a  lake  that is  not presently
phosphorus limited could become  so  if  a  large  percentage  of  the
phosphorus loading to  the  lake is  removed.  However,  nitrogen  and
silica  have   also  been  identified  as limiting,  nutrients in  some
lakes   and  for  some  periods of time, depending  upon the  seasonal
variations in species  and  phytoplankton  populations.  The  analyst
needs  to consider the following questions on a site-specific basis:
                                 3-1

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          • Is there a limiting nutrient?
          • Which nutrient is limiting?
          • Is one nutrient limiting during all periods of concern?
          • Could control of a nutrient make it limiting?

     There are  several  techniques that  can be employed  to  develop
the  information required  for  answering  the  above  questions.  The
technique  selected  should reflect the  resources  available  for  the
allocation study and  the cost of nutrient  removal  alternatives.  As
anticipated  removal costs  increase,   the   level  of detail  of  the
analysis should  generally increase.  The usual  approach  employed  is
to obtain  data  on  nutrient  concentrations  during early  spring  and
to  assume  complete  or   a  high  conversion  of  nutrients to  phyto-
plankton biomass.   The  determination  of  the  limiting nutrient  is
made on the basis of the relationship  of  the nutrient  concentration
and phytoplankto stoichiometry.

     Another  technique   consists  of   obtaining  data   from  "Algae
Growth Potential" studies  which employ spiking of  algae population
samples by the  various  nutrients of concern.  These  tests  should  be
conducted employing water  and organisms from  portions of  the  lake,
and at the times of year which  are  of  concern. Consideration should
be  given  to  employing  light levels  in the  experiments which  are
consistent with ambient  conditions.

     A  third  technique  employs observed  data  on  lake  nutrient
concentrations and  the  range of available  data on  Michaelis-Menton
half  saturation  constants.  This  technique  may be  helpful  if  only
summer  data   are   available.   Examples   of  this  procedure   and
associated calculations  are  presented in Section  3.4.4.  For  each  of
the possible  limiting nutrients  and  for the periods of  the  year  of
concern,  an approximation of the limitation which
                                 3-2

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might  be  associated  with individual  nutrients can  be obtained  by
application of equations  (3-1),  (3-2),  and  (3-3).

                              RP =   Cp                          (3-1)
                                  Jmp +  p
                              Rn =   Cn                          (3-2'
                                     ca                          (3-3;
                                   Kms + cs
where

Rp,  Rn, Rs/ =        Approximate  reduction  in  ambient  growth  rate
                    associated   with   nutrient   limitations   from
                    phosphorus, nitrogen, and silica respectively.
Cp         =        Observed orthophosphate concentration  (ug/1)
Cn         =        Observed inorganic  nitrogen concentration (NH3  +
                    N03 +  N02)  (ug/1)
Cs         =        Observed      dissolved      inorganic      silica
                    concentration  (ug/1)
Kmp         =        Half  saturation constant  for phosphorus  (ug/1)
                    (reasonable value  = 7 ug/1;  range from 2 to  50
                    ug/1)
Kmp         =        Half  saturation constant  for inorganic  nitrogen
                    (ug/1)  (reasonable  value  =  25  ug/1; range  from
                    10 to 400 ug/1)
Kms         =        Half  saturation constant   for  inorganic  silica
                    (ug/1)  (reasonable value =  30 ug/1)

     The nutrient with the  lowest "R"  value would be  considered the
limiting  nutrient  and  the  approximate  reduction in  ambient  growth
rate associated  with  that  nutrient would be  calculated assuming  a
single nutrient limits  growth
                                 3-3

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(i.e.,  growth   not  controlled  by   the  product   of   Michaelis'
formulations or nutrient limitations).

     The  fourth  technique  is  to provide  the  available  data  to  a
local biologist who is  familiar with the  area and obtain an opinion
on the probable limiting nutrient.

     In projects  where  nutrient control programs  involve important
resources and/or  costs,  consideration  should be  given  to employing
combinations of  the techniques discussed  to identify  the  limiting
nutrient.
3.1.2 Availability of Nutrients

     The nutrient  inputs  to lake  systems  are usually  estimated on
the basis  of the  total  mass of nutrient  which enters  the  system.
Further, two of  the available  eutrophication analysis  techniques
discussed consider only the  total  nutrient  level.  It has been shown
(22)   that   the  various   forms  of   the   nutrients  can  influence
phytoplankton growth rates and populations.  As discussed in Section
2.2.2,  nutrients which  are readily usable  by  phytoplankton include
orthophosphate,  NH3,  N02,   and  N03.  These  are  generally  referred to
to  as  nutrients  in  the   readily  available  form.  Other forms  of
nitrogen and phosphorus  are considered  available  after reactions
such  as hydrolysis or  mineralization of organic  forms.  These forms
of the  nutrient are  considered  in  the  ultimately  available form.
Their impact on phytoplankton  growth  can be substantially less than
the more readily available forms since  competing  processes,  such as
settling,   can  remove   them  from  the  system before  they  impact
phytoplankton growth. Finally,  some forms of nutrients,  such as
                                 3-4

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the phosphorus mineral apatite  and  refractory organic nitrogen,  are
considered  to  be  unavailable  biologically  on the  time scales  of
concern.

     There  are  no laboratory or  experimental techniques which  can
be  employed  in  waste   load  allocation  studies  to  differentiate
readily  available,  ultimately available,  and unavailable  forms  of
any  of  the  nutrients.   Several   (23,  24)   chemical   and  biological
techniques  are  being  developed  in  ongoing  research  efforts  for
differentiating  available  and unavailable  phosphorus.   They  should
not be considered  for use  in most waste  load allocation projects  at
this time.

     Ideally,  the load  allocations  for  nutrients  should  consider
the nutrients which  influence biological  processes.  These nutrients
are  the  sum  of  the  readily  available  and  a  portion  of  the
ultimately  available  nutrients.   The  portion  of  the  ultimately
available nutrients  included in this  idealized situation would vary
on  a   site-specific basis   depending  on   the   nutrient   cycling
processes  (particularly  bottom  processes)  and lake  detention time.
Waste  load allocations  have  not  and cannot  approach  this  ideal.
Rather,  the less  complex  approaches to  eutrophication  analysis,
both  steady-state   (Vollen-weider)   and  time  variable  (residence
calculation),  generally   deal   with  total   nutrient   inputs  and
concentration   levels.   By   contrast,   non-linear   eutrophication
modeling  analysis usually  employs  separate  nutrient  variables  in
the  calculations  for  readily  available  and ultimately  available
nutrients.   The    latter   variable   usually  includes   ultimately
available  and  unavailable nutrients.  The values  of the  settling,
mineralization, and  other  coefficients in  these models  are  probably
altered slightly by inclusion of unavailable
                                 3-5

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nutrients   in   the  nutrient   representations.   This   should   not
represent a  significant problem.  Consideration  should be  given  to
inclusion of all  sources  (readily available,  ultimately available,
and  unavailable)   when  comparisons  of  calculated  total  nutrient
levels  (such  as  total  phosphorus or  total nitrogen)  are made  to
observed levels in a lake.  If  it  is  possible  to  include all sources
of  a nutrient,  then  the   calculated  and  observed  total  nutrient
levels  which  are  compared will  be  consistent  since  the  measured
total nutrient concentrations  will be  influenced  by  all sources and
contain contributions from all nutrient availability categories.

     It  has been  suggested  (25)  that  nutrient  availability  will
vary between types of  sources  (point,  non-point,  agricultural,  bank
erosion, etc.)  and may  even vary with the  location  of  a source.  An
example  of  the latter  situation  is  found  for phosphorus. A point
source  discharge  is  usually  considered to  contain  a very  large
percentage  of  available   phosphorus.   If  this  point  source  is
discharged  directly  to  a  lake,  the  available phosphorus  can enter
biological  processes.  By contrast,  if  the  point source  is located
on a  tributary,  there  are  transformations  of  phosphorus  (26)  which
tend  to  increase  the particulate  forms  (ultimately  available)  and
reduce  the  soluble  forms  (readily available)  of phosphorus.  Thus,
the  location,  as well  as  the type  of source,  can influence  the
forms of phosphorus which enter lakes.

     For  tributaries   to   the  lower   Great   Lakes,   it  has  been
estimated that available phosphorus is approximated by:

     Available P = SRP + aPPt
                                 3-6

-------
where:
          SRP  =    soluble reactive phosphorus
          PPt  =    total particulate phosphorus
          a     =    factor ranging from . 1 to .3
     For municipal discharges,  it  has been estimated  (27)  that  the
available   phosphorus   averages    72    percent    after   chemical
precipitation for phosphorus  removal.  The available P  in effluents
averaged 82  and 55 percent  for soluble  and  particulate phosphorus
respectively.

     Quantitative evaluation  of available  nutrients  in  waste  load
allocations  for  control  of  eutrophication  in  lakes  cannot   be
carried  out  with   the   existing   base  of   data   and  knowledge.
Qualitatively,   it appears  that point source  controls  for discharge
directly   to   lakes  will   be  most   effective   in   control-ling
phytoplankton growth.  Point source  discharges located  upstream  on
tributaries have a lower probable  level  of  effectiveness as do  non-
point  source  controls  which  would  impact  phosphorus   inputs  from
tributaries.  Therefore  from  the   standpoint  of  availability  of
nutrients,   waste  load  reductions  should  initially  be  directed
toward  point   sources  that   directly   discharge   to   a  lake.   If
additional reductions in nutrients are  required,  the point and  non-
point  sources  on tributaries  should be  the  next types  of sources
controlled  with distance  from  the  lake providing  a  qualitative
indication  of  probable relative availability. A more  quantitative
estimate  of tributary  loads  can  be  obtained  from  ambient  water
quality monitoring of lake  inputs  in question. The  overall nutrient
removal required will be determined by the
                                 3-7

-------
quantity  of nutrients  associated  with each  source,  the cost  of
removal and qualitatively by the biological availability.

3.1.3. Estimating Loadings

     Loading estimates  for  nutrient  inputs  to  lakes  are required
for all of  the  analysis frameworks available  to  examine waste load
allocations  in  lakes.   The  tine   scale  over  which  mass  loading
estimates should  be developed  is  determined by  the  retention time
of the  lake. Generally,  annual loading estimates  are required.  For
snail lakes or  lakes  having short detention  times,  the annual load
may have  to be  subdivided  seasonally.  The  loading estimates  should
define mass inputs  of the  limiting nutrient by type and location of
a  source. As  indicated in  Section 2.2.1  and  illustrated  in  Figure
3-1,  the type of sources which must be considered are:
        1. point sources directly  discharging  to  the  lake
        2. atmospheric inputs
        3. intermittent  discharges directly to the  lake from CSO's
           and urban runoff
        4. point  sources,   CSO's,  and  urban  runoff discharges  on
           tributaries
        5. non-point sources which enter the  lake  or  tributaries
        6. erosion  of tributary banks and the  lake  shore line
        7. in-lake  sources   (such as  release  of  nutrients  from
           bottom sediments)
        8. septic tank and  other on-lot disposal  discharges

At  a  minimum,  the measured  nutrient  loads  should include  total
nutrient  levels   (total  P,  total  N,  etc.)  and   readily  available
nutrient  levels  (ortho-phosphate,  NH3,   N02,  N03).  If  possible,
measures  of  particulate   associated  nutrients   should   also   be
obtained.
                                 3-i

-------
                                           Q.P
                                           J"
Settling,
                              tltauspention
                   Nitrogen and Phosphorus
                        Fertilizers
Figure  3-1.  Problem framework  and nutrient sources
                             3-9

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3.1.3.1 Point Source

     Generally,   routine   plant   monitoring   samples   and   flow
measurements will adequately define  the  loads  from point sources if
the  limiting  nutrient  concentration  is  among  the  measurements
obtained. The  length  of  data record analyzed  should  include  a full
year's data, containing any seasonal and weekly variations.
3.1.3.2 Atmospheric Inputs

     Data over  one year  at  several stations  on  the lake  would  be
ideal.  Practically,  several   site-specific   samples   obtained  to
reflect  seasonal  factors  could  be  combined  with  data  in  the
literature  to  develop   estimates   of  atmospheric  inputs.  Spatial
distribution of  atmospheric  input  may be important  in  larger lakes
or those where land use varies significantly around the lake shore.
3.1.3.3 Intermittent Discharges (CSO's and Urban Runoff)

     It  will  usually  be necessary  to  obtain some  representative
samples of CSO  and urban runoff loads for  a  site-specific project.
It may  be necessary  to differentiate the  soluble and  particulate
nutrient  loads  from  these   source  types  if   treatment  feasibility
must ultimately be determined.

     In almost  all cases,  mass loading  estimates on a  seasonal  or
annual basis  will  be made by projections from limited  sampling  in
time and  space. A  model,  such as  SWMM or Storm,  may  be  employed  to
project annual  loads.  Alternatively,  estimates  of the  annual  load
may  be  obtained  by considering  the  nutrient  concentration as  an
independent random variable   (usually log
                                3-10

-------
normally distributed). The  natural  log of the mean and variance can
be estimated from  a  log  normal probability plot. Substituting these
into  equation   (3-4)  provides  an  estimate  of  the  arithmetic mean
(maximum likelihood estimate)  (Ux)   (6)  which, when multiplied by the
runoff flow  for  the  year,  will provide  an  estimate  of the nutrient
load.
                              TI =  e(M + s 2)                      (3-4)
                              Un    <=  n   ~~>n                       \ J ^ I
where
          Un =      maximum  likelihood   estimate  of   the  runoff
                    concentration

          Mn =      natural  log of  the  concentration  at  502   from
                    log probability plot

          Sn2  =      natural log of the  variance  obtained from a log
                    probability plot.

     An estimate of the  annual  runoff can be obtained employing the
volume  runoff coefficient  which is  related to  percent impervious
area as shown in Figure 3-2 and equation  (3-5).
                              Rv = RfCv                         (3-5)


where
               Rv   =    Runoff volume

               Rf   =    Rainfall

               Cv   =    Volume Ratio

     If the  latter  approach is used,  site-specific measurements of
concentration  and runoff  volume  ratio may  be supplemented  by the
data  from  other similar  sites  available  in  the  literature.  If
models are employed to generate
                                 3-11

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STUDY  LOCATION  CODE:


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Figure  3-2.  Relationship  between  impervious  area  and  runoff-to-

                  rainfall  ratio
                                                 3-12

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loads,  site-specific  information  on  wash-off  and  build-up  rates
will  usually  have  to  be   supplemented   by   information  in  the
literature.
3.1.3.4 Non-Point Source Loads

     Non-point source loads will have  to be  estimated based on land
use. The  analyst has a  choice of models  which usually  employ  the
Universal  Soil  Loss  equation with  yield  coefficients  or data  on
areal loadings from various land uses  and  soil  types. The non-point
source   estimates   should  be  checked   against   some   tributary
monitoring data to insure that  the magnitude of estimated non-point
source loads is realistic. This can  be accomplished by sampling  one
tributary with  representative land  use  over a year  and  comparison
of  the  estimated  non-point   source  annual  load with the  measured
tributary  load  less  any  point  sources   or  urban   runoff  loads
entering  the  tributary.  Experience   in  the  Lake  Erie  Basin  has
indicated that,  for  drainage  basins with  high clay  content  soils,
tributary sampling during major runoff events  is required to obtain
an  estimate  of  the  total  annual load.  In  extreme cases,  30 percent
of  the  annual  phosphorus  load  from  a  tributary may  enter  the lake
during a  relatively  few high  tributary flow  events associated with
storms.

     Tributary loads  can vary from  year to year as a result  of  the
type  of  water  year  during   which  measurements are  obtained.  The
intermittent nature  of  the transport  of nutrients associated with
particulates  is usually  responsible  for  much of   the  variation.
Erosion  varies  with  the  water year.  In  addition,  the  particulate
component of the  load alternately settles  and  resuspends  by scour;
thus, this portion of the load has a travel time from
                                3-13

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source to lake which may be  substantially  longer  than the hydraulic
time of travel.

     Estimates  of  nutrients   from  erosion  of  banks   and  lake
shoreline  should be  included  in  the  analysis  particularly  when
total nutrient levels are being considered.

     Malfunctioning or  improperly installed spetic tanks  and other
on-lot  disposal  systems may also  represent significant  non-point
nutrient sources. Estimates  of  this  contribution  should be included
with non-point source estimates
     In  studies  with limited  resources,  the  areal  loading may  be
used to estimate the contribution from small urban areas.
3.1.3.5 In-Lake Sources

     The primary in-lake source of  concern  is  nutrient  release from
bottom  sediments.  This source is  generally associated with  anoxic
hypolimnion conditions  for a part  of the  year.  The first step  in
attempting  to   evaluate   this   potential  source   should  involve
examination of  historical  data  for  low or  zero dissolved  oxygen
levels  in  the hypolimnion  or other  sections  of  the  lake.  If  low
dissolved oxygen concentrations  (below 1 to 2 mg/1)  are  suspected,
consideration should be given to carrying out  a  measurement program
in  the  area  of  concern.  Data should be obtained on  the  seasonal
progression   of   vertical   and    horizontal   structure   measuring
temperature,  dissolved oxygen,   limiting nutrients,  etc.   The  data
collected  can be  analyzed using  mass  balance   formulations  which
include vertical dispersion and settling to determine  if  the  bottom
release of  nutrients  is  significant.  In general,  projects  with  low
bottom dissolved oxygen conditions  should consider employing  one  of
the
                                3-14

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time  variable  analyses  techniques   discussed,   rather   than  the
steady-state  graphical  analysis.  The  reason for  this  is  that  the
time  variable  analysis  can  yield  comparisons  of  calculated  and
observed  nutrient  levels  which  will  provide   information on  the
significance  of bottom  sources of  nutrients.  If bottom  sources  of
nutrients are  significant  for  all portions of the times  when water
quality  problems   are  observed,   nutrient   controls   at  external
sources  may not  be effective  at all  or  may have  a  smaller  than
anticipated  impact. Thus,  the very  objectives  and goals of  the
waste load allocation would be in jeopardy.
3.2 SIMPLIFIED LAKE NUTRIENT MODELS

     Over the  past decade  considerable  effort  has been  devoted to
developing  a  simplified  eutrophication analysis  framework  which
could be used to evaluate  the  trophic  state  of  a lake under present
nutrient discharge conditions  and  predict  a  future  trophic  state
under  modified  future  nutrient  discharges. The  models  developed
involve   two  distinct    steps:   first,  establishing   a   causal
relationship   between   nutrient   loadings    and   lake   nutrient
concentrations,  and  second,  establishing a basis  for  assigning the
lake a trophic state based on lake nutrient concentration.

     Models  of lake  nutrient concentrations  either  involve  the use
of the  conservation  of  mass (mass balance)  principle  or  are direct
empirical correlations  between  pertinent  lake   characteristics  and
observed lake concentrations. The former will be discussed first.
3.2.1 Nutrient Mass Balance Model

     In the simplified analysis  illustrated  in  the  top  of Figure 3-
1, the following assumptions are made:
                                3-15

-------
       the lake is completely mixed
       the lake is at a  steady  state  condition
       total nutrients  (dissolved  and particulate)  are analyzed
       net sedimentation of  nutrients occurs.
The general mass  balance equation for any substance  in a completely
mixed lake  subjected to a net  removal mechanism whose  removal rate
is assumed proportional  to the  lake  concentration is:
                       V  dp  =  SQlPl - Kspv - Qp                  (3-6;
                          dt
where
ZQipi       =    the sum of  all  the  mass  rates of total nutrients
               discharged  to the lake  from all sources (PS & NPS;
                (M/T)  (Qi = flow, L3/T;  p±  = concentration,  M/L3)
p         =    lake nutrient concentration (M/L3)

V         =    lake volume  (L3)

Ks        =    net sedimentation rate  of  (T'1)
               nutrient

Q         =    lake outflow  (L3/T)
Assuming a steady state,  e.g.,  dp/dt  =  0,  and letting W = ZQipi
equation  (3-6) becomes:

                       0  = W  -  (KSV + Q)p                       (3-7;

                       or p  =    W
                                Q  +  KSV
Noting that V = Az  (A = surface area, z  =  mean depth),  Equation (3-
7) can be rearranged  as:
                                 3-16

-------
                       P =     W/A

                            (Q/VU + Ksz~
Letting   W/A  =    w'  where w'  =  areal  loading  rate  (M/L2 - T)
          Q/V  =    p  where p  =  1/r  (T'1)
          r    =    V/Q where r = hydraulic detention time  (T)


Typical units  employed are:  w' (gm/m2 -  yr) ,  z (m) ,   p  and  Ks  (yr"1)
and p(gm/m3 = mg/1).
3.2.2 Use of Phosphorus as the Limiting Nutrient

     Equation  (3-8)  is  recognized as the  form  used by Vollenweider
in relating  phosphorus,  nitrogen  and  other parameters  to  the lake
areal loading  rate  (28,  29,  30,  31). Since  then,  work in the field
has  been  concentrated  on  using  total  phosphorus,  rather  than
nitrogen,  as  the  single  nutrient  to  describe  trophic  state  and
control  eutrophication.   Reckhow  (32)   notes   that  phosphorus  was
selected  since it is  generally considered  the most  manageable  of
the  nutrients  and he  further cites Sawyer's   (33)  reasons  for the
selection:

   1.  existence of  a proven  technology  for removal  of phosphorus
      from wastewaters

   2.  significant  portions  of phosphorus  in domestic wastewaters,
      and all phosphorus in some  industrial  wastes,  are contributed
      by controllable synthetic detergents

   3.  phosphorus  limitation  seems  to  be  the   only  known  means  to
      control the  growth  of nitrogen-fixing blue-green algae.
                                 3-17

-------
Recent  work  reported  by  Rast  and  Lee   (34)  on  33  lakes  and
impoundments in the United  States,  indicated that most of the water
bodies  were phosphorus  limited,  primarily  on  the  basis  of algal
assay  procedures.  Comparisons of  nitrogenrphosphorus ratios  for  a
range  of  algal  species with  the  ratios   of   observed  inorganic
nitrogen:  dissolved  phosphorus  concentrations  in  lakes  led  to
similar conclusions as to the lake  limiting nutrient.

     On  the  basis of   the  above  reasons,   the  remainder   of  the
discussion  will  be focused  on the use  of total phosphorus  in the
eutrophication  analysis.  For  lakes,  determined  to  be  nitrogen
limited, a  preliminary methodology  and example problem is described
in Section 3.2.10.
3.2.3 Total Phosphorus Sedimentation Rate

     Equation   (3-8)   can  be  used   to   predict  lake  phosphorus
concentrations  if  the net  sedimentation  rate  can be  estimated.
Vollenweider  (31)  reported  that  this  loss  rate  (Ks)  could  be
approximated as:

                           LnKs = In 5.5 - 0.85 In "z      (r = 0.79)
 or more approximately by
                                                               (3-9)
          where   Ks = 10/z

                  Ks (yr'1) , ~z (m)
As  noted by  both Thomann  (35)   and  Reckhow  (32),  a  constant  net
sedimentation velocity  (vs)  of 10 m/yr is implied in Equation  (3-9),
where Ks = Vs  / z .
                                 3-18

-------
     Substitution of  this  empirical relationship  into  Equation  (3-
   results in:

                            p =   W'
                                zp +vs
                                                               (3-10;
     Based  on  14  Canadian  lakes,   Chapra  estimated  an  apparent
settling  velocity,  Vs,  of  16  m/yr  (36) .  Using the  same database,
Dillon  &  Kirchner  (39)  estimated  a  value  of  13.2 m/yr,  which was
later refined by  Dillon  to 12.4 m/yr using  a  larger  data base than
used  for   the   preceding  estimate   (35,   36) .   In   a  subsequent
publication,  Vollenweider   (31)   revised   his   empirically  based
estimate of Ks and deduced a value  of:
                            Ks = p°-5
                                                               '3-11
     Vollenweider  (31)  cautions that  vs,  as used  above,  is  not a
real  settling  velocity  but  rather  is  an  integration  of  both
positive and negative settling  velocities  as well as effects due to
demineralization, so  that  using the higher  values  of real settling
velocities   would   be   misleading.   Thomann,   in   a   personal
communication,   suggested  that  real  settling  velocities  might  be
able to be  used for the total  phosphorus  in many  cases  as  long as
the  real  settling  velocities  of  the  particulate  phosphorus  forms
were  adjusted   downward  to  reflect  nonsettling  of the  dissolved
phosphorus .
3.2.4 Alternate Form of Mass Balance Equation

     Dillon &  Rigler  (38)  calculated the  mean annual concentration
of total phosphorus,  using the mass balance  principle  and defining
a lake  retention  coefficient,  R,  as the amount  of total phosphorus
discharged to the lake
                                3-19

-------
which is  retained in the  lake  sediments. Thus,  from the basic mass
balance,  for a steady state,
                             0 = SQlPl _ RZQlPl _ Qp               (3-12;

                 or with  ZQipi = W as previously defined,

                             Qp  =  W  - WR  =  W(l-R)

                             P = W(l-R)  = W-(l-R)

                                 Q       Q/A
                             P = W1(1-R)
                                    qs
     Dillon  used an  empirical relationship  for  R  in  terms  of the
water surface overflow  rate,  qs =  Q/A
      R  =  0.426exp(-0.271qs)  +  0 . 574exp ( 0 . 00949qs) ,  (r = 0.94;
     Larsen  and Mercier  (39),  using a  data base which included  20
lakes, found  that  the following empirical  relationship fit the data
well

                            R =   1                              (3-13)
Substitution of  (3-11)  into  (3-8)  yields

                           p  =   W'                            (3-14
                               z(p+pu'3)

and substitution of  (3-13)  into (3-12)  results in


                            p  = W-(l  -    1     )
                                qs     1  + p(J'b
Rearranging and noting  that  qs = Q/A  =  z Q/V = zp,

                                 3-20

-------
                           p =  W     0.5      =      W         (3-15)
                                zp    i  +  P°-5     z (p+p°-5;
is identical to Equation  (3-14).  Thus,  using the Larsen and Mercier
estimate for the  retention coefficient  and  the latest Vollenveider
loss coefficient reduces the  two  mass  balance models to one and the
same equation.
3.2.5 Comparison of Steady-State Mass Balance Equations

     Two  equations  to estimate  the total  phosphorus concentration
are then  available,  one  using a net loss  coefficient of Ks  = Vs / z
(Equation 3-10)  and the other using Ks  = p0.5  (Equation  3-15).
     A comparison of the predictions  of the two equations was made.
On a unit areal loading basis then, with Vs = 10 m/day,

                          p/W =  (zp  +  V5)'1    from Equation  (3-10)

 will be compared with

                          p/W =  [z(p +P0'5)]"1  from Equation (3-15)

     The comparison  was performed  for  reasonable  bounds  on depths
(z)  for various  hydraulic  detention  times  (r) .  As  indicated in
Table 3-1,  the agreement is  good  for  a  fairly large range in values
of z  and r.  Some differences are  observed for lakes with detention
times at and above ten years.

     Since reasonable  agreement can  exist for  a  reasonable number
of lakes  and  a  physical connotation can be  retained for  the net
sedimentation  rate,  it  is  recommended  that  Equation (3-10)  be  used
as the basic predictive model.
                                 3-21

-------
Table 3-1. VALUES OF  P/W  for Ks  =  Vs/z  and Ks =  p  USING EQUATIONS
           3-10 AND 3-15
z
(m)
1

2

5

10

20

50

100

200

Ks(2)
(a)
(b)
(a)
(b)
(a)
(b)
(a)
(b)
(a)
(b)
(a)
(b)
(a)
(b)
(a)
(b)

.01
0.0091 0
0.0091 0
0.0048 0
0.0045 0
0.0020 0
0.0018 0
0.
0.









.1
.050
.076
.033
.038
.017
.015
0091
0091








r (yr)
1.0




0.067
0.100
0.050
0.050
0.033
0.025







10 100






0.091
0.120
0.083
0.120
0.067 0.095
0.048 0.182
0.091
0.091
0.083
0.045
    p/w =  [z (P_+ KS) r1
    (a) Ks = Vs/z,  (b)  Ks = Vl
                            r
                                 3-22

-------
3.2.6 Other Nutrient Formulations

     In  contrast  to   the   preceding   mass  balance  models  which
estimated  coefficients  using empirical  relationships,  a  number of
investigators  (28,   40,  32)  have  directly  correlated lake  total
phosphorus   concentrations   to  pertinent  lake   characteristics
including  areal   loading,   volumetric   loading   depth,   hydraulic
residence time, and surface overflow rate.

     As  an example,   for  lakes  with z/r <  50  m/yr,  Reckhow  (32)
proposes:
                            p= W'                    , (r2 = 6.876)
                      18z   +  1.05  z  exp(0.012  z)
                     10 +z         T             T
based on  data  from 33 north  temperate lakes. Also,  as  reported in
Reckhow  (32),  Walker based  a relationship  on 105  north temperate
lakes resulting in:

                            p= W'T      1            ,  (r2 = 0.906)
                                 z   1+ 0.824T0'454
     As demonstrated by Reckhow  for  an example lake situation  (Lake
Charlevoix),   the  various  mass  balance  and empirical  models yield
approximately the  same  result,  although only  the  empirical methods
above   were   able   to   generate  uncertainty  ranges   about  the
predictions.
3.2.7 Determination of Allowable Phosphorus Discharges

     The  following  procedures use  trophic  states as  the  basis for
determining  allowable  phosphorus   discharges.   The  procedures  are
equally applicable to  situations where  a  change in trophic state is
not possible  but a significant  water quality  improvement  toward a
specified target condition can still be
                                 3-23

-------
achieved.  In   both   cases,   the  final   selection   of  a  control
alternative will  depend  upon the level of  improvement  and the cost
of the proposed processes.
3.2.7.1 Measures of Trophic State

     As  indicated in  the  introduction,  four  measures  of  trophic
state  were  cited as  guides  often  used  in  classifying lakes  as
oligotrophic,   mesotrophic   and  eutrophic.    These   were   total
phosphorus,  chlorophyll  a,  secchi  depth,  and  hypolimnetic  oxygen.
Primary  emphasis  in  the  last  decade  has  been  given  to  total
phosphorus  and chlorophyll  a. and the  values  cited  in  the  intro-
duction are:

Trophic State       Total Phosphorus (|ig/L)   Chlorophyll a (|ie/l)

Oligotrophic                  <10                      <4
Mesotrophic                   10-20                  A - 10
Eutrophic                     >20                      >10

They  appear to provide  reasonable bounds  in classifying lakes  in
the north  temperate  zone into their appropriate trophic  states.  In
some  southern  and southwestern  lakes,   higher  chlorophyll  a.  and
total   phosphorus   concentrations    are    sometimes    considered
acceptable. As  discussed in Section 2.1, higher concentrations may
also  be   acceptable   in  the  presence   of  certain  site-specific
conditions. In  summary,  judgment  is  required in establishing target
levels of  total phosphorus,  chlorophyll  a or other measures  of lake
water quality.
3.2.7.2 Total Phosphorus

     For  total  phosphorus,   Vollenweider  (30)  compared  the  lake
trophic bounds  of  10 to 20  |ig/l  to  investigator-determined trophic
status for a number of
                                 3-24

-------
European  and North American lakes  and good  agreement  resulted  as
shown in  Figure  3-3.  It  may be  noted that slightly higher values  of
15  and  30  |ig/l  were  also  delineated by  Vollenweider,   implicitly
suggesting  that  those  bounds   may  be  appropriate   also.   Similar
results  are  shown  in the  bottom  of  Figure  3-3  for 33  lakes  and
impoundments  in  the  United  States,   as  reported  by Rast  and  Lee
(34) .
3.2.7.3 chlorophyll a.

     As  reported  in  Thomann  (35),  values of  chlorophyll  a.  from
Bartsch  and Gakstatter   (Figure  3-4)   indicate  that  the  suggested
bounding values of 4 |ig/l and 10 |ig/l are appropriate  for  describing
the  eutrophic   state  of  a  lake.   Using  primarily  north  temperate
lakes,  the  following  relationships  between  total  phosphorus  and
chlorophyll a. concentrations have been  suggested  (41,  34,  42) :
Bartsch and Gakstatter  (41)

                 Log10(chl  a)  =  0 . 8071og10 (p) - 0.194

Rast and Lee  (34)

                 Logio(chl  a)  =  0.761ogi0(p) - 0.259

Dillon and Rigler  (38)

                 Log10(chl  a)  =  1 . 4491og10 (ps)  -  1.136
                                                               (3-16)
                                                               (3-17)
                                                              (3-18)
where  P  and Chi  a.  are  the  total  phosphorus  and  chlorophyll  a.
concentrations,   respectively,  in  |ig/l.   In  Dillon   and   Rigler's
formula,  ps  is  the  spring total phosphorus  value and  chlorophyll  a.
is the summer value.
                                 3-25

-------
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            MEAN DEPTH Z/HYDRAULIC RESIDENCE TIME, TW |m/yr)
Figure 3-3.  Test  of  trophic state indicators
                           3-26

-------
                                          3


                                          O


                                          D,


                                          O '
                                          5  g

                                          O ,"
                                             «>
                                            Jt
                                             »
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3-27

-------
     These three  formulas  are useful  in  estimating the chlorophyll
a concentration resulting  from different  phosphorus concentrations.
This will  further illustrate  the  water  quality  benefits  resulting
from various phosphorus control alternatives.
3.2.7.4 Secchi Depth and Dissolved Oxygen
     Rast  and  Lee  (34)  report a  correlation between  secchi depth
 \z)  and total phosphorus  (p) of:

                  Log10(z) = -0.3591og10(p)  + 0.925            (3-19)
where secchi depth is  in meters  and total phosphorus is in |ig/l for
the  33  lakes,  and impoundments  in  the United  States.  In addition,
using data  from  13  of the above lakes, plus  21 additional U.S. and
Canadian  lakes,  Rast  and  Lee report  a hypolimnetic  oxygen  demand
of:

                           = 0.4671ogio (p)  -  1.07              (3-20)
where Sb is the areal benthic oxygen demand  (gm/m2 day)  and p is the
total phosphorus  in |ig/l. Although  to date  this  predicted benthal
oxygen  demand  has  not  been significantly  used to  classify lakes,
Reckhow  (32) reports that work is underway in this area.
3.2.7.5 Calculation of Allowable Phosphorous Loading

     Allowable loadings may be selected if:

          -  a trophic  state  or acceptable water  quality condition
             is specified
          -  the  bounds   between  trophic   states  are   (or  the
             acceptable condition  is)  specified  in terms  of total
             phosphorus or chlorophyll a.
                                 3-28

-------
It is  presumed the least  eutrophic state  consistent  with resource
constraints  will  be  selected.  The  boundary  concentration  between
oligotrophic, mesotrophic,  and  eutrophic must then  be selected for
either total phosphorus or chlorophyll a.
3.2.7.6 Use of Total Phosphorus to Describe Trophic State
     Values of 10 |ig/l and 20 |ig/l for total phosphorus are commonly
used  to  distinguish  the   three  trophic  states,   although  some
variation  in  these  values  is  clearly  possible  based on  the  data
shown  in Figure  3-3.  It is  to  be noted  that  these values  are
primarily  from  north temperate  lakes and  more tropical  lakes  are
clearly  outside  the data base.   It  is  recommended that  local  data
bases of total phosphorus be  reviewed and correlated with perceived
trophic  states  to  aid  in   the  selection  of  trophic  boundary
concentrations.  For  data poor  systems,  use of  the  10 and 20  |ig/l
modified for  local  conditions can be considered.  In  addition,  some
sensitivity  analysis  could  be  performed  using  slightly  higher
values, and/or 15 and 30 |ig/l total phosphorus.

     Assuming that  10  and 20 |ig/l are selected,  Equation   (3-10)  is
then  rear-ranged  to  yield  a  predictive  equation  for the surface
areal loading rate as follows:

                          W' = pc(zp + vs)
where pc is the critical boundary  total  phosphorus concentration in
gm/m3 or mg/1.
                                3-29

-------
                           W'l  =  0.010 (zp  +  vs)                (3-2i;


                           W'2  =  0. 020 (zp  +  vs)
where W?! and  W'2  are the  areal  surface loading  rates  that divide
oligotro-phic  from   mesotrophic   and  mesotrophic  from  eutrophic
conditions,  respectively. Plots of equations  (3-21)  and  (3-22)  with
an assumed value of 10 m/yr are shown in Figure 3-3.

     Selection of  the  appropriate net  sedimentation  velocity  (v2)
should be  based on  a local  data  base,  with  a  value of 12.4  m/yr
suggested if no data  are available; a possible range of  (vs) from 10
to 16 m/yr has been reported.
3.2.7.7 Use of chlorophyll a to Describe Trophic State
     Chapra  and  Tarapchak  (43)   have   suggested  a  procedure  for
specifying total  phosphorus  areal loadings  in  terms  of chlorophyll
a.  boundary   values   between  trophic   states.   Thomann  (35)   has
summarized the procedure as:

   1)  determine mean  annual concentration of total phosphorus

   2)  estimate the concentration  of  total phosphorus  in the spring
      using the mean  annual concentration

   3)  compute mean summer  chlorophyll a.  concentrations  from spring
      concentrations  of total phosphorus.

   The mean annual concentration  is calculated from Equation (3-10) :
                                   W s
                            p =—	
                                (zp + v=
                                 3-30

-------
The spring  total phosphorus  (ps)  is  calculated  from the mean  value
using a best fit  line  developed by Chapra and Tarapchak:

                             Ps  =0.9p                            (3-23)
The summer  chlorophyll a. concentration  is  estimated from the  Dillon
and Rigler  correlation of  ps  and  chl  a  summer,  Equation  (3-18):
                       Log10(chl a) = 1.4491og10 (ps)  - 1.136
                   Or,  chl  a = 0 . 0731 (ps) 1'449                    (3-24)
where  chl a.  and  P5 are  in  |ig/l.  The  allowable  phosphorus  areal
loadings  are  arrived at by  combining equations  (3-10),   (3-23),  and
(3-24) to give:
                       W' =  0.0055(chl  a)0'69  (zp  +  vs)          (3-25;
where W  is  in gm/m2-yr, chl  a.  is in |ig/l,  z p  and vs are in m/yr.
Chapra and Tarapchak  selected 2.75 |ig/l and 8.7 |ig/l as the boundary
chlorophyll   concentrations   between  the   three   trophic   states,
resulting in:
                       W'l =  0.011 (zp  +  vs)                     (3-26;



                       W'2 =  0.025 (zp  +  vs)                     (3-27;


Use of values of  4  and 10  |ig/l  would result in


                       W'l =  0.014(zp  +  vs)                     (3-28;



                       W'2 =  0.026 (zp  +  vs)                     (3-29;


                                 3-31

-------
where W'i  and W'2 are  the  total  phosphorus  surface  areal  loading
rates  for  the  oligotrophic-mesotrophic  and  mesotrophic-eutrophic
boundaries.

It may  be noted  that  equations  (3-26)  and  (3-21)  yield  an almost
identical value  for  W'i,  whereas  equation  (3-27)  is  somewhat  more
lenient than equation (3-22)  in estimating the value of W2.

     There  are   very  significant differences  in  what  constitute
acceptable  chlorophyll  a.  levels.   Acceptable   levels  will  vary
regionally  and  may  also  vary  among  lakes in  the same  geographic
region due to natural turbidity,  depth,  and historical water usage.
The   generalization   of  the   above   calculation  procedure  with
assignment  of locally  applicable values  of  chlorophyll  a.  and/or
total phosphorus  as  target  objective  should be considered in waste
load allocations.
3.2.8 Calculation Procedure
     Based on  the  foregoing a simplified  calculation  procedure for
nutrient allocations to control lake eutrophication is:
          Step 1. Estimate  the lake volume, surface  area,  and mean
                   depth using  available  bathymetrie  charts  and/or
                   survey data obtained by  state  and local agencies
                   or  academic  institutions.  The  U.S.  Geological
                   Survey's    (USGS)   seven   and   one-half   minute
                   quadrangles may be sufficiently accurate  for the
                   larger lakes to estimate surface  areas.

          Step 2.  Estimate  the  mean  annual outflow  rate.  Ideally,
                   this data would be  obtained from a gaging station
                   at the lake  outlet.  If unavailable, data  from a
                   nearby upstream or downstream  gage  could  be used
                   by  correcting  the  flow  due to  runoff from the
                   drainage   area  between  the  gage  and  the  lake
                   outlet.   Lacking  nearby  gaging   stations,   the
                   drainage  area upstream of the  lake  outlet  may be
                   obtained   from  the  seven  and  one-half  minute
                   quadrangle sheets.  The  product  of  this  area and a
                   flow  per  unit  area   (typical  of  the  type  of
                   drainage  basin)  yields the  lake  outflow.  Values
                   of  annual  and  low   flow  per   unit   area  are
                   available (7).

                   For lakes with detention times  less than the year
                   scale,  mean outflow rates should be obtained from
                   a correspondingly shorter
                                3-32

-------
                   flow data base.  Where urban areas draining to the
                   lake  constitute  a  significant  fraction  of  the
                   total drainage  area, flow  estimates  from  urban
                   runoff  and  combined  sewer  overflows  should  be
                   included  in  the  hydrologie  balance  around  the
                   lake  (6) .  For  lakes with  large surface  areas,
                   surface  precipitation and evaporation should also
                   be included.

          Step 3. Determine  average  annual  total phosphorus  loading
                   due to  all  sources.  These  include  all tributary
                   inflows,  municipal   and   industrial   sources,
                   distributed    urban   and   rural   runoff,    and
                   atmospheric  inputs.  Estimation  of  these  loadings
                   is  discussed   in   Section   3.1.3.   Lacking  an
                   extensive local data base,  the  methodologies and
                   summary  loading tables in  (6,  7,  8)  should prove
                   useful in making a first  estimation.

          Step 4. Assign a net sedimentation  (loss) rate for total
                   phosphorus consistent with a local data base,  (vs
                   = 12.4 m/yr.  if no data  are available)

          Step 5.  Select  trophic  state objectives of  either  total
                   phosphorus or chlorophyll a. consistent with local
                   experience.  Lacking this, total phosphorus limits
                   of  10  ng/1  and   20  ng/1  to  characterize  the
                   "permissible" and  "dangerous"  concentrations can
                   be  considered.  Calculate  values  of W?!  and W2
                   for the  specific lake depth and detention  time.

          Step  6.  Compare  the total  areal  loading determined  in
                   Step 3 to the values of  W'l and W'2  calculated in
                   Step  5.   If  the  lake  loading  places it  in  an
                   undesired trophic  state, determine  the reduction
                   required to  return the  lake to the desired level.

          Step  7.  If  a reduction  is  required,   determine  whether
                   feasible  point  source  controls will  accomplish
                   the  reduction   and  allocate  among  the  various
                   point sources.

          Step 8.  Test  the  results   of  the analysis by:  selecting
                   higher  total phosphorus  concentration  for  the
                   trophic  boundaries;  using  chlorophyll  a.  as  the
                   determinant  of the  trophic boundaries; selecting
                   higher and lower values  of  the  net  sedimentation
                   rate;  etc.

In the foregoing,  a  loading- plot similar  to  Figure 3-3  will prove
useful in the  analysis,  especially when curves  for W'i and  W2 are
drawn on the graph for the various sensitivity analyses of Step 8.
                                3-33

-------
     The  following  example  problem  illustrates   the   calculation
procedure described above:

     Example Problem

     Data:      Lake Geometry

                 Volume            V = 10 x  106m3
                 Surface Area      A = 2 x 106m2

                 Depth             z = 5m
                 Outflow           Q = 0.3 mVsec
        Q = 0.3m3/sec x 3.154 x 107sec/yr = 9.46 x 106m3/yr
               Discharges of Total Phosphorus

                    Point Sources       =    400  kg/yr
                    Non-Point Sources   =    500  kg/yr

Problem:  Determine required  reductions  in the  point  or  non-point
          source  discharge  to  classify   the  lake  as  marginally
          mesotrophic and oligotrophic.

Solution:

     1.   Select a net sedimentation rate  of 12.4 m/yr.

     2.   Assume total phosphorus  trophic boundaries of  10  |ig/l  and
          20
                           W'l = 0.010 (zp + 12.4)              (3-2i;

                           W'2 = 0.020(zp + 12.4)

     3.    with T = V/Q  =  10 x  106m3/9.46 x 106m3/yr =1.06yr
               p =  1/1.06 =  0.943yr"1 =4.7m/yr
                                                               (3-22;
              zp =  5m x 0.943yr"1 = 4.7m/yr,
                                 3-34

-------
               W'l  = 0.010(4.7 + 12.4)  = 0.171 gm/m2-yr

               W'2  = 0.020(4.7 + 12.4)  = 0.342 gm/m2-yr


     4.    The total lake areal loading is:

                W'l = (400  + 500)  kr/yr x IQOOgm/kg
                             2 x 106 m2

                    = 0.451 gm/ m2-yr


     5.    To become marginally mesotrophic, a reduction of

                    0.451 - 0.342 = 0.109 gm/m2-yr


          is required, or

                    0.109 gm/ m2-yr x 2 x 10-  m- = 218 kg/yr
                                      103 gm/kg


          This requires a reduction in the point sources of

                     (218/400)  x 100 = 55%

     6.    To become marginally oligotrophic,  a reduction of

                    0.451 - 0.171 = 0.280 gm/m2-yr

                 or 0.280 x 2 x 106 m2/103 = 560 kg/yr is required

          Since  the point  sources only  amount  to  400  kg/yr,  the
          desired  trophic   status   could  not  be  attained by  only
          point source control.
     7.    A loading  plot  with  the  selected W'i,  and  W'2  curves is
          shown in  Figure 3-5,  together with  the  location  of the
          lake on the plot for three loading conditions: present, 55
          percent point source  load  reduction  and 100 percent point
          source removal.
3.2.9 Comments on Limitations and Applicability

     1.     Reckhow  (32)  advises  caution  in  applying  the  methods
           herein to  shallow  lakes  (depths  less  than approximately
           three meters),  since  he has  often  found unpredictable
           behavior in the total phosphorus con-
                                3-35

-------
            10
         •t
         Cft

         k  i.o
         o
         2
         o
         a
         O

         a.
         i/»
         O
         X
         CL
         o
           0.01

               0,1
     EUTROPHIC

A Present

B 55% Point sooice rccluclion

C 100% Point source reduction
          nr
          I-O
4,7
HI	
 10

(m/yr|
                                                                 OLIGOTROPHIC
100
1000
Figure  3-5.  Effect of  point source  control on trophic  status,  sample problem
                                            3-36

-------
centrations. He  suggests  that  the potential for mixing of
the  sediments  (wind induced)  may be a  factor.  Of over 75
lakes  included  in  the data base  (29,  31,  34,  39,  44),
less  than  ten percent  had  depths less  than  three meters
(see Table 3.2)
Rast and Lee  (34)  note that the Vollenweider approach may
not   be   applicable   to   impoundments   with   hydraulic
detention  times  in order of  a month  or less,  especially
for  those  with marked  stratification  of inflowing waters
during  the growing  season.  In  addition, they observe that
the  critical loading  criteria  may have to be modified for
lakes  with  excessive  macrophytes  and  attached  algae,
because the criteria were developed for planktonic algae.
Chapra  and Tarapchak   (43)  note  that  the  assumption  of
steady  state is  reasonable  when,  on an annual  basis, the
morphometry,  climate and nutrient supply are constant year
to year. In  the  case  of  lakes  undergoing severe cultural
eutrophication,  an  accumulation term must be added to the
mass  balance  equation   to properly   characterize  lake
concentrations.   If   not  accounted    for,   unrealistic
sedimentation  coefficients  might  be selected  which would
lead to unconservative predictions.
Dillon  (October  1971)  discussed lake  restoration projects
and  re-ported  that  for  the  Zellersee  (Switzerland)  and
Lake Washington  (Washington) marked improvements have been
noted after significant phosphorus reductions. However, in
Lakes  Sammamich   (Washington)   and Norrviken  (Sweden),  in
spite of significant phosphorus reductions the areal loads
remained in excess of permissible levels — no improvements
have  been  noted.  Dillon postulates   that  wind-generated
mixing  may  be  regenerating   sediment   phosphorus  in  L.
Norrviken,  a  shallow  lake  (z   =  5.4  m) .  In  Lake Monona
(Wisconsin),   after   removing   a-  point  source,  copper
sulfate  is needed  twenty  years  after  the diversion  to
control algae. However,  "high  loading"  of approximately 2
gm/m2-yr is still present due to agricultural drainage.
Little  Otter Lake  (in  Ontario,  Canada)  (z= 2.7 m, r = 0.1
yr) ,   which had  severe eutrophication  problems  due  to  a
single   industrial   point   source   of   poly-phosphate,
recovered  rapidly upon removal of  the  discharge.  On the
other  hand,  the  Rotsee  (Switzerland),  of  small  size and
with agricultural  drainage,  showed no  improvement when a
wastewater diversion  project was  completed.  Finally,  Den-
mark's  Lyngby-So,  after  a  diversion  of  sewage,  improved
for  four   years  then  incurred  a  significant  macrophytic
growth. Dillon  theorizes that  this may have been due to
increased  light  penetration   occasioned   by  decreased
phytoplankton concentrations.
The  data base  upon which the  analysis  framework has been
tested  is  almost exclusively from  north temperate lakes.
Although the basic mass balance model may still yield good
results for more tropical
                       3-37

-------
Table 3-2. CHARACTERISTICS OF SELECTED  LAKES  IN SIMPLIFIED
           EUTROPHICATION ANALYSIS  DATA BASE
No . Name
Switzerland
1 Agerisee
2 Baldeggersee
3 Dodensee-Obersee
4 Greifensee
5 Hallwilersee
6 Lac Leman
7 Pfaffikersee
8 Turlersee
9 Zellersee
Sweden
10 Hjalmaren
11 Malareo
12 Norrviken
13 Battern
14 Vanern
Italy
15 Maggiore
Canada
16 Beech
17 Bob
18 Cameron
19 Clear
20 Cranberry
21 Eagle-Moose
22 ELA 227
23 Four Mile
24 Green
25 Halls
26 Kamalka
27 Maple
28 Oblong-Haliburton
29 Okanagan
30 Pine
31 Raven
32 Skaha
33 Talbot
34 Twelve Mile-
Bashung
35 Wood
Depth
(m)

48
34
100
19
28
154
18
14
37

6
12.5
5.4
39
25

177

9.8
18.0
7.1
12.5
3.5
12.8
4.4
9.3
6.1
27.2
58.0
11.6
17.7
75.3
7.4
0.73
26.5
0.85

18.1
21.0
TO
(yr)

8.70
4.55
4.88
2.04
3.85
12.00
2.60
2.15
2.70

3.6
2.7
0.571
56.0
8.3

4

0.0441
2.7
0.0529
7.7
0.0159
0.493
4.2
3.8
0.0260
1.0110
0.13
3.1
59
0.054
0.067
1.1
0.20


0.42
110-yr
Areal Loading
(gm/m -yr)
P N

0
1
4
1
0
0
1
0
1

0
0
2.1
0.
0



1
0
2
0.
1
0
0
0
1
0
0
0
0
0
1
0
2
0

0
0

.16
.75
.07
.57
.55
.79
.36
.30
.20

.30
.70
('70)
065
.15

3

.68
.16
.21
040
.28
.23
.34
.11
.77
.22
.32
.86
.12
.39
.06
.22
.20
.10

.35
.50
Tropic
State

0
E
M
E
E
M
E
M
E

E
E
E
0
0- M

M




0- M


E



E


0


M- E



E
Ref .

29,44
29,44
29,44
29,44
29,44
44
29,44
29,44
44

44
44
44
44
44

31

44
44
44
39,44
44
44
39,44
44
44
44
39,44
44
39,44
39,44
44
44
39,44
44

44
39,44
                                 3-38

-------
     Table 3.2. CHARACTERISTICS OF SELECTED LAKES  IN SIMPLIFIED
            EUTROPEICATION ANALYSIS  DATA BASE  (concluded)
No.
Name
Depth
(m)
TO
(yr)
Areal Loading
(gm/m -yr)
P N
Tropic
State
Ref .
United States
36
37
38
39

40
41
42
43
44
45
46
47
48
49
50
51
52
NC
53
Backhawk WI
Brownie MN
Clhoun MN
Camelot-
Sherwood WI
Canadarog NY
Cayuga NY
Cedar MN
Cox Hollow WI
DogFish MN
Dutch Hollow WI
Erie
George NY
Harriet Mn
Huron
Isles MN
Kegonaa WI
Kerr (Roanoke)

Lerr
4.9
6.8
10.6
3

7.7
54
6.1
3.8
4.0
3
18
18
8.8
61
2.7
4.6
10.3

8.2
0.5
2.0
3.6
0.09-0.14

0.6
8.6
3.3
0.5-0.7
3.5
1.8
2.6
8
2.4
21
0.6
0.35
0.2

5.1
2.2
1.18
0.86
2.5

0.8
0.8
0.35
1.8
0.02
1.0
1.06
0.07
0.71
0.13
2.03
6.64
5.2

0.7
23.4


34.6

18.0
14.3

19.1

10.4

1.8




36.2

2.4
E
E
E
E

E
M
E
E
0
E
E
0-M
E
0-M
E
E
E

M
34
34
34
34

34
34
34
34
34
34
44
34
44
31
34
39,34
34

34
(Nutbush) Va
54
55
56
57
58

59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74

75
76
77
Lamb MN
Meander MN
Mendota WI
Menona WI
Michigan- op en
waters
Minnetonka MN
Ontario
Redstone WI
Sallie MN
Sammamish WA
Sebasticook ME
Shagawa MN
Stewart WI
Superior
Tahoe NV
East Twin OH
West Twin OH
Twin Valley WI
Virginia WI
Waldo OR
Washington WA

Wanbesa WI
Weir FL
Wingra WI
4.0
5.0
12
7.8

84
8.3
84
4.3
6.4
18
6.0
5.7
1.9
148
313
5.0
4.34
3.8
1.7
36
33

4.8
6.3
2.4
2.3
2.7
4.5
1.2
30-100

6.3
7.9
0.7-1.0
1.1-1.8
1.8
2.6
0.8
0.08
185
700
0.5-0.9
1.0-1.8
0.4-0.5
0.9-2.8
21
2.4

0.30
4.2
0.4
0.03
0.03
1.2
2.14
0.10

0.1-0.2 ('73)
0.65-0.86
1.5
1.5-4.2
0.7
0.21
0.7
4.8-8.0
0.03
0.05
0.5-0.8
0.2-0.4
1.7-2.0
1.2-1.5
0.017
1.2-2.3
0.47
9.93
0.14
0.9


13

1.3



18
2.8-3.0
13.0

7.8
73.6

0.52
19-31
15-16
17
18.3
0.33
8-19
4.4

2.6
5.1
0
0
E
E
0

E
M
E
E
E
M
E
E
0
0
E
E
E
E
0
E(' 69)
M('74)
E
M
E
34
34
34
44
34

34
31
34
34
34
44
34
34
31
34
34
34
34
34
34
34
34
39,44
34
34
0 = Oligotrophic
M = Meaotropbic
E = Eutrophic
                                 3-39

-------
          lakes, it is possible  that  the  net  sedimentation rate may
          be  different  and  caution  must  be  used.  In  addition,
          acceptable  levels  of  total phosphorus  and  chlorophyll  a.
          may  be  substantially  higher  in  southern  lakes  or  those
          with inputs of high clay content soils.
3.2.10 Preliminary Nitrogen Allocation
     As  indicated previously,  most  recent  investigations  of  the
simplified  eutrophication  method  have   been   restricted  to  the
analysis of  total phosphorus and there  is no equivalent  data base
to  support a  similar  methodology  for  nitrogen.  For  those  cases
where  nitrogen has  been  identified  as  the  limiting  nutrient,  a
tentative  procedure — initially suggested by Vollenweider  (28)  and
discussed  by  Rast and  Lee  (34)  — might  be to  utilize  the  total
phosphorus methodology  for total  nitrogen,  after  suitably adjusting
the trophic boundary loading curves.

     This procedure is  recommended  only  as an interim measure  until
further  investigations  (Rast   and  Lee)   produce  trophic  boundary
concentrations  and   appropriate  removal   coefficients   for  total
nitrogen.  It  should   be  recognized   that   the   use  of  nitrogen
:phosphorus  ratios  is  imprecise,  and  any  interpretation of  data
based  on  these  ratios  should  recognize  the  potential   for  error.
This  type  of  analysis  may be  sufficient  as  a  screening tool  for
nitrogen control  but  may  not  be adequate  to  justify the need  for
expensive nitrogen treatment.

     Assuming  for algae,  a  stoichiometric  nitrogen to  phosphorus
ratio  of  7.2:1   (34),  the  total  nitrogen  loads   at  the  trophic
boundaries  would be  7.2  times   those   for   total   phosphorus.
Vollenweider  (28) found these values  too conservative and suggested
using a  ratio  of  15:1.  Using data  from  the  National Eutrophication
Survey and six Swiss  lakes (34,  44), the 15:1 ratio-
                                3-40

-------
  1000
 «
 &
 >
UN


"s
o
z
z
UJ
O
O
(C
    0.1
                                                     1000
                           2 P {m/yetf I
    Figure  3-6. Total nitrogen loading plot
                        3-41

-------
appears  to  fit  the  data  best,   as   seen   in  Figure  3-6.  Thus,
preliminary trop-hic boundary areal loads are:

                          W'i = 0.15 (z +vs )                    (3-30)
                            N            N

                          W'2 = 0.30 (z +vs )                    (3-31)
                            N            N

where the  subscript  N refers to  nitrogen.  Assuming denitrification
and  nitrogen  fixation  are not  significant,  the  net  sedimentation
rate of total  nitrogen may be similar  to that  for total phosphorus
and values of VsN  could be set equal to 10 to 16 m/yr.  The following
example  problem  illustrates  the  calculation  procedure  described
above:

Example Problem

     Data:

     Lake Geometry: same as in example problem of  Section 3.2.8

                           (z = 4.7 m/yr)

     Outflow rate: sane as in previous example problem

                           (A = 2 x 106 m3)


     Discharges of Total Nitrogen

          Point Sources =  8000 kg/yr
          Non-Point Sources = 4500 kg/yr
     Problem:  Estimate the required reduction  in  the point or non-
               point source load to  classify  the lake as marginally
               mesotrophic.

     Solution:

     1.   Assume a  net sedimentation rate  of total  nitrogen  of 10
          m/yr.

     2.   Assume trophic boundaries for total nitrogen fifteen times
          those of  total  phosphorus,  that is,  150  and 300 |ig/l, so
          that you have:

                          W'i = 0.15(4.7 +10 )   2.21gm/m2-yr
                          W i = 0.30(4.7 +10 )   4.41gm/m2-yr
                            N

                                 3-42

-------
4.  The present areal loading is:
              W' =  (8000 +4500)  kg/yr x  IQOOgm/kg   =  6.25  gm/m2-yr
                             2  x 106m2
   4.    To become marginally mesotrophic,  a reduction of

                  6.25 - 4.41 = 1.84 gm/m2-yr

        is required,  or
                   1.84   gm   x   2  x 106m2
                      	     	 = 3860 kg/yr
                        m-yr     lOOOgm/kg
        This  requires  a  reduction in the point source of

                   3600  x  100  = 46%
                   8000
                              3-43

-------
3.3 TIME VARIABLE MASS BALANCE MODELS

     Models  in  this  category   are   extensions   of  the  approach
developed  by  Vollenweider  (30) .  The  basic  mass  balance  equations
for total phosphorus  in  a  completely  mixed lake,  which Vollenweider
solved for  steady  state,  are employed with provision  for  flows and
loads  which vary  with  time.  The resultant  formulations  calculate
concentrations   that   could   represent   lake-wide  average   total
phosphorus  concentrations  which  are   a   function  of  time.   The
calculated  time history  of  phosphorus  can  then  be  compared  to
observed  phosphorus  concentrations to  provide calibration  for the
analysis  framework.  A  lumped parameter is  employed   to  represent
losses of phosphorus from the system.

     Two  interesting  site  specific   applications  of  time  variable
mass balance models were developed by Chapra  (45) and Larsen  (39) .
The  Chapra application  considered the  Great Lakes  eutrophication
problem  and employed  seven  completely  mixed  segments similar  in
concept  to  the  work of  O'Connor  (46) . The Great  Lakes calculation
included  a  historical simulation extending  from  1800 to  1970,  as
well as  predictive simulation  extending  from  1970  to 2000.  The  time
scale of  this analysis was  decades with  a  yearly  time  step. By  con-
trast, the  work  of Larsen and coworkers on  Shagawa  Lake  considered
an  annual simulation covering the period  1971 to  1976  with  what
appeared  to  be  daily to weekly  time steps.  The  two  site-specific
projects  indicate how the  analysis framework  can be  adjusted to the
time and  space scale  of  the  problem.  The Great Lakes time and space
scales are  large while  Shagawa  Lake  had  a  detention  time ranging
from 0.42 to 1.23 years  for the period investigated.
                                3-44

-------
3.3.1 Formulations

     The phosphorus  residence  time analysis indicated in  Figure  3-7
and Equation  (3-22)  considers  a mass balance for a completely  mixed
lake.
                      dPr  = W  - QPr - S_ + Eg                  (3-32)
                      dt    V    V   V   V
where
     Pr   =    total phosphorus concentration  (M/L3)
     W    =    mass loading rate of total phosphorus  (M/T)
     V    =    lake volume  (L3)
     Q    =    lake outflow  (L3/T)
     S    =    lumped phosphorus removal parameter  (M/T)
     Bs   =    lumped internal source of phosphorus parameter  (M/T)
     There  are  several methods  of  solving  equation  (3-32) .   One
method employs  numerical integration usually  utilizing a  computer.
The  equation is  not  complex,  and  the  input  data  will  usually  be
small;  therefore,  a  mini-computer  could  be  considered.  A  second
method of solving equation  (3-32)  is through integration with Q,  W,
V,  S,  Bs  as  constants. The  resultant  solution  is  presented  in
equation  (3-33)  for boundary  conditions t = 0, Pr =  P0  and  t  = t, Rr
= PT:

     PT = W  - S + Bs (1  - exp  (-t/t0) ) + P0exp(-t/to)            (3-33)
              Q
where
     t0   =    lake detention time V/Q
     P0   =    initial phosphorus concentration  at  t  =  0
     t    =    time interval for which  calculation  is to  be  made,
                                 3-45

-------

                                                 = constant

INFLOW
AND 0
OUTFLOW



LOADING W



RESUSPENS10N ' B

t
_jr=*^_.
2

t,
jj-so/V
«2



Zero
l Time Segment t,
• ^ o-Qj
^ hy€_HQ W = W1
. 	 	 	 ^ e fccry
TIME
Time Segment t2
; i 0 - Q3
Wl L. ~f~~"^ W = Wj
i POS!PT? «
TIME
.... Time Segment l%
....... i - ... o - Q3
; w = w3
i B * 'tro
j Zere po = PT e
                        TIME
     RESPONSE    C
                         TIME
Figure  3-7.  Phosphorus  mass balance  for completely mixed lake
                               3-46

-------
     Equation  (3-33)   can  be   solved  on  a  calculator  or  with  a
computer. The approach  as  shown in Figure 3-6 and the example  is  to
subdivide the time  over which  the  calculation  is  to be carried  out
into time segments,  which may  have  different  lengths ti,  t2,  ...tn,
but with constant  Q,  W, V, S,  and Bs  in  each  of the time  segments.
The  calculation   should  employ   the   first   observed  phosphorus
concentration for  the value of P0 at  t = 0;  PT  is then calculated
using  equation  (3-33)  for  any times  "t"  less than  the first time
segment length ti.  The value of PT is then calculated at t,  and this
value  of PT  is  substituted for P0,  and  the  calculation is  repeated
for any desired times in  the next time segments t2~ti. The  procedure
may  be  repeated  for  as  many   time  segments  as  required.   The
procedure could  even  employ  a  daily  time  step.   Selection of  the
calculation  method   is  really  a  matter  of  preference   for  the
analyst.

     The actual formulation  employed by Larsen et al.  (39)  included
a  lumped first  order  settling  term  v  rather  than  a phosphorus
removal parameter  S.  Equation (3-34)  is  the  differential  equation
and equation  (3-35)  is  the solution for  boundary  conditions t =  0,
Pr = P0 and t = t,  Pr  =  PT.
   dP_r = W + Bs   -  QPr  -  vPr                                   (3-34)
   dt       V      V

   PT =    W  + Bs    (1  -  exp-t (I/to + v) ) + P0exp-t (l/t0 +  v)     (3-35)
        V(l/to + V)
                                 3-47

-------
The  identical  solution  techniques  available  for  equations  (3-32)
and  (3-33)  can be  employed  to  solve equations  (3-34)  and  (3-35) .
The  following-example  illustrates  the   use  of  the  time  variable
model described above.
3.3.2 Example Problem

Data:


V = 107m3
A = 2 x 106m2

"z = 107/2  x 106m2
V'= 0.1 m/day
V = 0.1/5 = 0.02/day =  0.14/wk
Q = 0.3m3/sec = 9.46 x 106m3/yr  =  1.82  x  105m3/wk
t0= 107m3/1.82 x 105m3/wk = 54.95 wks
I/to + v =  1  + 0.14 = 0.1582/wk
          54.95
Problem:  A  lake is  subjected to  a loading  of 17.3  kg/wk  for  46
weeks  and  a bottom  loading of  3  mg/m2/day for  the  last  six weeks
(week  40-46).  Calculate  the phosphorus concentration in  the lake  at
the end of  the following weeks: three, fifteen,  twenty-five,  forty,
and forty-six.  The  initial phosphorus  concentration of  the  lake  is
zero.

Solution:
Period #1  (From 0 to 40 Wks;
W = 17.3 kg/wk
Bs = 0
Pn = 0
     P =   W + Bs    (1 -  exp-t (I/to + v) )  + P0exp-t (l/t0 + v)
         V(l/to  +  V)
                                 3-48

-------
t = 3 wks
     P = 17.3  kg/wk  +  0 (1 - exp-3 x 0.1582)  +  0
          107m3 (0.1582/wk)

       = 1.0936 x  10~5kg (1 - .622) = 0.413  x  10~5kg/m3 =  0.004mg/l
                       m3
t = 15 wks

     P =  .99 x  10"5kg/m3 =  .0099mg/l

t = 25 wks

     P =  1.07 x  10"5kg/m3 =  .0099mg/l

t = 40 wks

     P =  1.0936  x  10"5 (l_e"4° x -1582)= 1.09 x 10"5  kg/m3  =  .0109mg/l

Period #2  (40 to 46  Wks)

     W =  17.3 kg/wk

     Bs =  3mg  x  2 x 106m2 x  7  day =4.2xl07mg= 42kg
        m2/day                wk              wk    wk

     P =  .09 x  10~5 kg/m3  = . 0109mg/l


t = 46-40 wk = wks

     P =  17.3 + 42  (1  -  exp-6(0.1582)) +  1.09  x 10"5 exp-6 x  .1582
          107x 0.1582
                                 3-49

-------
              P = 3.75 x 10"5  (1 - 0.387) + 1.09 x 10"5x  .387
                = 2.3 x 10~5 +  .42 x 10~5

              P = 2.72 x I0~5_kq_ =  .027  mg/1
                             m3
     The above  approach  considered the lake  as  a single completely
mixed  reactor.  The Great  Lakes application,  indicated previously,
considered  seven  completely  mixed  reactors.  Any  type  of  spatial
segmentation  can  be   considered.   In  this   case,  an  equation  is
generated  for  each  spatial  segment,  and  for  segments that  are
connected  by  flow  or  dispersion,  the  resultant  equations  are
coupled.  Figure  3-8   contains   equations  and  representations  for
several spatial  segmentations which may be useful.  The equation set
gets  complicated  rather  rapidly  and generally  requires numerical
solutions using computers.

     The  vertically  segmented   system  with dispersion  has  other
potential  complications  in that the  volumes  Vi  and V2  may change
with time, and  that the  dispersion coefficient  E  may also change as
the density  gradient  changes.  The  analysis  can include a number of
system  features which  could be  important  in  a particular  site-
specific analysis.  Information  in  the  section  on non-linear models
is provided  to  assist  in defining  parameters when segmented systems
are  analyzed.  It   should  be  recognized  that  inclusion of  these
additional features does not  radically change the analysis which is
essentially   a   phosphorus  residence  time   calculation  employing
lumped parameters.
                                3-50

-------
                 Completely Mixed Segments in Series
                  V,df»T
                  — —L.W
                  V,tJPT2
                  - ....... '- ....... •-•
                           - S * B+ Q,
         Completely Mixed Vertical Segments  with Dispersion

                                 w,
                             -ill
7
                                            AsCfos* Sectional Area
                                     B$2
                    W, -*, - Q, PTi * EA (PT2- PTl I
                dt
Figure 3-8. Mass  balance equations  for  horizontally or vertically
            separated completely mixed  segments
                                  3-51

-------
3.3.3 Range of Parameter Values

     The  values  of  out-flow  Q,  loading  W,   and  volume  V can  be
determined  by site-specific  factors  as  a  function of  time.  By
contrast,  the  values  of  removal rate  S  and  source Bs are  really
lumped parameters which represent several  phenomena.  Even  the  first
order term v is a lumped  parameter  which represents  the  settling of
various  types  of particles  and could  include the  resuspension  of
sediment due to winds. Since  the parameters S,  Bs,  and  v are lumped
parameters, their value  is  usually  determined by  analysis  of  site-
specific  data.  The  procedures  can  vary  from  trial  and  error
assignment of parameter values  to calculations which search for the
minimum  of the  square of  the differences  between  calculated  and
observed concentrations (least squares curve fitting techniques).

     The values of  the lumped parameters  should be  either constant
for  the  period of calculation  or the allowed variations  should be
systematic  and associated  with documented  phenomena  such as  the
existence  of   anoxic  conditions,  seasonal variations  in  vertical
structure, etc.  The  usual analysis  considers  single values of  the
removal  parameters  S  and v  over a  yearly period. When the  source
term Bs is  included  in the analysis,  it  is usually varied  such that
Bs equals zero  in  the  spring, winter,  and fall, and has  one non-zero
value  in the   summer.  The maximum  variations  for these  parameters
will be  associated with an annual time  scale  of analysis and should
consider  changes  in  parameter  values  no  more  frequently  than
seasonally.

     As  a  guide to  determining the  value  of  the  lumped parameters,
Bs for Shagawa Lake  ranged  between  6.5  to 11.3 mg/m2 - day during
anoxic periods.
                                3-52

-------
This value should be very  site-specific  depending upon iron content
and other  chemical  aspects of the sediments.  The apparent settling
velocity  v'  ranges  from  .04  and .18  m/day  with  a  good starting
value of 0.1 m/day for site-specific calculations.
The value of S has been defined (39)  by:

                       s = V'ASPT
                                              (3-36)
where
     S
     V
     As
     PT
lumped settling parameter
apparent settling velocity
lake surface area
total phosphorus concentration
The value of v is defined by:
                       v = v-Ag = v—
                            V    z
where
     v
     V
1st order apparent phosphorus removal rate
lake volume
mean lake depth
3.3.4 Model Calibration

     The phosphorus  residence time models  should be  calibrated  by
comparison   of    calculated   and   measured    total   phosphorus
concentration  data.  The  procedure should,  if  possible,  employ  a
part of  the  available data  base  for  defining parameter  values  and
the  remainder  of  the  data  base   should  be employed  to provide  a
somewhat independent check on the calculations.

     If  the  problem  time   scale   is  large  with  the  calculation
employing  annual  average   data   on   flow   and   loads,   the  total
phosphorus levels at turnover or in
                                3-53

-------
the winter  should  be  employed to develop  comparisons  of calculated
and observed data.  For  calculations on the annual  time  scale which
employ daily  or weekly  averages of  loads and  flow,  concentration
data from daily  or weekly sampling could be used.  The data  in this
instance may have  to be  weighted by lake  volume since concentration
gradients are  usually present  during one or  more  seasons   of  the
year.  The calculations could be  compared  to  surface (euphotic zone)
total  phosphorus values as an alternate.

     The general procedure with  this  type  of  calculation framework,
regard-less   of  the  time  scale  used,   is  to  employ  regression
equations to  relate  total phosphorus  to  chlorophyll,  numbers  of
plankton and/or dissolved  oxygen  which are usually  the variables of
concern.  These  curves  should be  lake  specific and curves from  the
literature  can  be employed  if  some  type  of  comparison  is  made
between lake-specific data and  results of  regression  analysis using
data from other  studies.  Section 3.2 on  Simplified Models provides
an  indication  of  some of the  regression  equations that have been
developed which relate water, quality  variables to  total phosphorus
concentration.
3.3.5 Applications and Limitations of Residence Models

The discussion has  centered on residence time  analysis  considering
total  phosphorus.  There  are  no  conceptual  barriers to  employing
similar analysis  for  systems  which  are  limited by  other  nutrients
such as nitrogen or silica.  Analyses  considering  other nutrients do
not  appear  to have  been developed  or  reported.  Use of  residence
time   analysis   for   nutrients  other   than  phosphorus   would  be
subjected  to  additional uncertainties  due  to  the  research  and
developmental  nature   of   initial   applications,   but   could  be
considered for use in
                                3-54

-------
projects where  nutrients  other  than phosphorus  appear  to  control
eutrophication.  It would be prudent to  restrict  these applications
to  sites  where  completed  project  costs   are   large  and  where
extensive  data  on  the  time  and  space  scales  of  concern  are
available,   so  that  testing of  the  calculations and coefficients
could be performed.  Further,  it  will be necessary to  develop site-
specific   information   which   relates   the   limiting   nutrient
concentrations to  water quality variables  of primary concern such
as phytoplankton cell counts, chlorophyll,  and/or dissolved oxygen.

     The residence  time analysis  techniques  have the  advantage  of
providing  a  relatively  simple  framework which  can  be  compared  to
observed site-specific  data  to analyze  eutrophication  in lakes.  The
data  base   required   for analysis  is  not   too   extensive  and  can
include historical information which may be available.

     The disadvantage of this analysis  technique  is  associated with
the  analysis of  an  indirect  indicator of  eutrophication,  e.g.,
total nutrient  concentration rather  than  chlorophyll  or dissolved
oxygen,  and  that lumped parameters  and  coefficients  are employed to
simulate the  collective effects of  a  series of  complex processes,
such as  settling,  resuspension,  bottom  release of nutrients,  etc.,
which can  individually  influence  the  system response  to  nutrient
removal  actions.  Finally,  the   calculations  do  not  include  other
factors such as light  limitations,  hydraulic  limitations on growth,
predation,  etc.
                                3-55

-------
     Phosphorus residence  time analysis  has  been applied  to  small
lakes  with  moderate  environmental   risk and  control  costs.  The
analysis has  also  been employed  for  large lake  systems  with  large
environmental  and  control costs.  In  the  case  of the  Great  Lakes,
other analysis techniques were  also employed  to develop information
for decision making. It is suggested  that consideration be given to
restricting the use  of this  type of  analysis technique  to small or
moderate size projects  (measured  by environmental risk and costs of
solutions)   in  contrast  to   larger   projects.  This  limitation  is
primarily  associated with the  absence  from the  analysis  framework
of primary variables such as dissolved oxygen  and chlorophyll,  and
other potentially important  factors such  as  light limitations, etc.
The use of lumped  parameters also provides a part of  the  basis  for
this suggestion.
                                3-56

-------
3.4 NON-LINEAR EUTROPHICATION_MODELING

3.4.1 General

     Non-linear  eutrophication  modeling  is  an  outgrowth  of  the
pioneering work  of  G.A.  Riley in  the  mid-1940's  (47, 48,  49).  The
advent  of  computers  and  the  focus  of  public  concern  on  water
quality  issues  led  to  expansion  and application  of this  earlier
work  by O'Connor  (46,  50)  et  al.  in  the  late  1960's and  early
1970's. There has been  a  rapid expansion  of the  processes  included
in analysis  techniques  of  this  type  and an  increase in  the  number
of locations  and water  body  types  examined.  The basic  approach  is
very complex, and the level  of experience with use  of this  type  of
calculation  in  decision making  is  small. For  the  most  part,  non-
linear  eutrophication  modeling  has  been  and   probably   should
continue  to  be  considered  an  area   of  active   research   with
applications  concentrated   on complex   problem  settings  where  an
extensive data base either exists or  can be  collected. The  level  of
environmental  risk  and  costs for  control  of  eutrophication  must
usually be large to justify  the  cost  of  application of this  type  of
analysis framework.

     Non-linear  eutrophication   modeling   can   be  divided   into
calculations  which  focus  primarily  on  the base  of the  food  chain
and  those  that  extend the simulation  to include upper  portions  of
the  food web  including  fish.  The present discussion will be  limited
to analysis  techniques  which  concentrate on the base  of the  food
chain,  e.g.,  phytoplankton,   and,  in addition,  will address  water
quality variables such  as  dissolved oxygen.  The broader  food  chain
or web modeling efforts are  appropriate  areas of  research,  but they
are too speculative  for  use in waste load allocation projects.
                                3-57

-------
     Non-linear    eutrophication   modeling    frameworks    employ
relatively   large   numbers  of   coefficients  that   describe   the
chemical,  biochemical,   and biological   reactions  in  addition  to
coefficients which  represent  physical transport  such  as  advection,
dispersion  and  settling.  The   non-linear   equations  are  solved
numerically usually employing  relatively  large  and  complex computer
programs.  The  calculated  system responses are  often  difficult  to
understand  due  to  the   behavior  of   the   non-linear  equations,
feedback of  mass  which control  reaction  velocities,   and  the  sheer
volume  of  numerical output generated by these computations.  These
difficulties, coupled with  the usual  high costs  for data  collection
and  analysis,  suggest  that  it   is   imperative  to  include in  the
project  team  at   least   one    individual  who   has   had  hands-on
experience   with   non-linear  eutrophication  modeling   if   these
techniques are to be used.
3.4.2 Formulations and Ranges of Coefficients

3.4.2.1   Spatial Segmentation and Transport.

A wide  range  of spatial  segmentation  has been employed  to  analyze
eutrophication processes  in  lakes.  Initial efforts on  a  lake often
involve  a  minimum  of  segmentation  such  as  one  or  two  completely
mixed  segments.  For shallow  lakes  where  light penetration  extends
to  the  lake  bottom  and  where  there  is   little  or  no  vertical
variation in  water  quality profiles or temperature,  one  completely
mixed   segment   can  be   considered.   In  deeper  lakes  where   a
thermocline develops  or  light  penetrates only a small  portion  of
the  total  depth, vertical segmentation  can  be  considered  usually
employing a top segment and a bottom segment.
                                3-58

-------
     More  detailed  segmentations   have  also  been  employed  which
separate the littoral zones  and  embayments  from  the  pelagic regions
of  the  lake.  DiToro  (51)   has  employed  still  more  comprehensive
segmentation which included  vertical  segments  which  extend into the
bottom sediments of the  lake. Bottom  sediment  analysis  may prove to
be  a  very  good  verification tool  for lake models.  The  degree  of
segmentation employed for  a site-specific project will  depend upon
the bathymetry  and the   nature  of  the eutrophication problem being
analyzed.  Generally,  vertical  stratification,  bottom  depth,  light
penetration,  and  transport  will  control   segmentation.   As  as
minimum,    care   should   be   exercised   to   provide   sufficient
segmentation so  that depth-averaged  growth rates of  phytoplankton
are  reasonably  representative  of  actual  growth rates,  and  that
vertical structure due to thermoclines can be simulated.

     The  simulations generally consider   anywhere  from  seven  to
twenty state variables which can be defined by measurements such as
nutrient  forms,  carbon,  phytoplankton,  dissolved oxygen,   etc.  The
number of model  coefficients  could be  two  to three  times the number
of  state  variables with reaction rate constants  usually comprising
on  the  order  of  one   half  the   number  of  model  coefficients.
Therefore,  the  addition of  spatial  segments rapidly increases the
complexity  and  size  of  the input  data,  the computer  program,  and
the  computation time.  A  further  problem  can  be  associated  with
assimilation and display of the increased volume of model output.

     Models which employ single, completely mixed segments adjacent
to  points  of  inflow and  outflow   present  no unusual   problems  in
routing  of flows. Time  variable  flow balances  are employed  with
evaporation and rainfall on the lake
                                3-59

-------
surface assumed  to  balance  each other in most  locations.  It may be
necessary to  include variable  lake  volume  in  the  calculations,  if
the system  is subject to flow regulation for  flood control,  water
supply, or navigation purposes.

     For  lakes  where vertical  segments are  adjacent to  points  of
withdrawal and inflow, there  are  several  techniques which have been
employed  to   distribute  flow  vertically  (52) .  They  generally  are
based  on  density   compatibility  which   requires   time  dependent
information on the  temperature  of water  entering the system and the
vertical temperature structure of the segmented  lake system.

     Horizontal  diffusive  transport  coefficients  for  lakes  range
from   104  to  106   cm2/sec.  A   reasonable   value   for   the  first
approximation would be 105 cm2/sec or  could be estimated  from:
                       EH =  0.0056L1'3                          (3-38)

     where

          EH   =    horizontal dispersion coefficient  (cm2/sec.)

          L    =    length scale of the grid segments  (cm)

     The model coefficient EH,  is related to the length scale of the
grid employed  in the computation.  As  this length  scale  exceeds 20
km, the horizontal dispersion coefficient EH,  should reach a maximum
constant value of 106 cm2/sec.

     Vertical transport  usually  is  dominated  by vertical dispersion
Ev.  The  model  parameter can  be estimated from  Figure  3-9  which
presents  data  for  this  coefficient  as  a  function of  the  density
gradient. The vertical
                                 3-60

-------
           o
           8
           2

           U
UJ
O
O


O
           UJ
           a.
           u
                 102J
10'-I
                             o
                                                D _   A A 0
                        Ev" 1-0 cm! /sec
                                                   f Used in Study}
                                                                      _ 1
                                                 V
                10
 -'J
                10
                 - 2
                                                            A A
                   10
                     -7
                                     .........    .   . .      i   1 I  11   I   111
             10'
                               ,-6
                                                            10'
                                                                        -2
10"
                                       OiNSiTY GRADIENT f
                     "  •   '. - :    .-'_:••    ' .    •         ' .           Soyrct  T«tr» tteh (53 >


                LIGENO

                  •  foxworttiy |1968i, Plyme (14|           Q v  Kolesnikov {1961M1 1)


                  *  Foxworthv (1968). Point Source (14)         &  Harremos (196?) (12)
                  Q
    Range of Maximum Density Gradient,        * Jacobsen (Defarst, 19611 S13J
    Aygyst 1974, June 1976, September  1976
                                       0 Foxworthy {1968S,P3tch'(14!
Figure 3-9.  Effect  of  density  gradient  on  vertical dispersion

                coefficient
                                            3-61

-------
dispersion   coefficient   will   vary   seasonally   as   the  density
structure of the  lake  changes.  In addition to the data in Figure  3-
8,  a  number of  empirical formulas are  available  (53)  to estimate
this coefficient.

          1.         Kinetic Structure for  Phytoplankton.
The principle  of  conservation of mass is  employed to structure the
differential   equations   employed   in   non-linear  eutrophication
models.  A  mass   balance  around  segment  J  which  interfaces  with
segments ki,  k2,  ...  kn yields:
dt  = Z QkjPk + Z E'kj (Pk + PJ)  +
      k=l       k=l
                                          (G
                                            pj
                                                '3-39!
where
     Pk
volume of segment j
chlorophyll concentration  in  segment  j
flows between segment k and j
phytoplankton concentration in  segment  k
bulk transport  coefficient due  to dispersion between
segments k and j
growth rate of phytoplankton  in segment j
death rate of phytoplankton in  segment  j
settling coefficient  for   phytoplankton in segment  k
and/or j (Ss  = o for segments  in the horizontal).
     The  first  two  terms  on  the  right  side  of  equation  (3-39)
represent transport,  the third term  incorporates  growth and  death,
and the final terms account for settling.
                                 3-62

-------
     Examination of  this equation  reveals  the factors  included in
the   analysis   and,   therefore,   the  possible   factors   limiting
phytoplankton  population   levels.   In  lakes  or   segments   whose
detention  time  is  small,   transport  can  serve  as  an  effective
limitation  on  growth.  This factor  is indirectly  included  in  the
Vollenweider  type  analysis  and  in  the  residence  time models.  A
second factor  which  can limit  population  levels  is the  growth  and
death terms  in equation  (3-39).  These terms  usually  include, as  a
minimum,  growth  rate formulations which are  temperature,  nutrient,
and  light   dependent;  and  death  rate formulations  which  usually
include  temperature  dependence,   respiration,   and   grazing   by
zooplankton. These factors  are not explicitly included  in  the less
complicated  methods  of  analysis.  They are  indirectly  included in
some  aggregate  form in  the  regressions   employed  to  relate  the
limiting nutrient  concentration to phytoplankton  levels.  The final
limitation  on  phytoplankton  levels  usually  included  in the  non-
linear  eutrophication models   is  the  settling  of  plankton.  This
phenomena  can  be of  importance from  several  standpoints.  Settling
can  result  in  reductions   in  phytoplankton levels  and  removal  of
nutrients  from the lake  and/or from the segments  of the lake where
growth occurs.  Settling  may also  create  a source of  oxygen  demand
in bottom  waters below the  thermocline and in the  lake sediments.
Discussed  in previous  sections,  this  process is  included  in  the
less  complex  formulations  through  the  lumped  nutrient  removal
parameter  and  indirectly in the  regressions  used  for chlorophyll,
dissolved oxygen, and sediment oxygen demands.
                                3-63

-------
     Growth   Rate   Formulation.   The   phytoplankton   growth  rate
formulation can  include  several forms which  are  similar in concept
but differ in the  details  of  the formulations.  The usual conceptual
framework is represented by equation  (3-40):

                        Gp = Kpt(T)r(   Cn  )                     (3-40)
                                    Km +  Cr
where

          Gp   =    growth rate of phytoplankton

          Kpt   =    maximum  specific  growth  rate  at  a  reference
                    temperature usually 20°C

          (T)   =    temperature adjustment term

          r    =    light-induced reduction  in phytoplankton growth
                    rate due to non-optimal incident light

          km  =     Michaelis-Menton or half-saturation constant for
                    the limiting nutrient

          Cn   =    concentration of the limiting nutrient.
     Phytoplankton growth rate GP is usually determined by a maximum
specific  growth   rate   which  is  associated   with  a  particular
temperature,  optimum light,  and adequate  nutrients.  Some  typical
values of this coefficient  are presented in Tables 3-3 and 3-4. The
maximum specific growth  rates used  range between 0.2 and 8 per day.
A starting value for  the model coefficient  in the range of 2 or 2.5
at 20°C could be considered in most studies.

     A  number of  temperature formulations have  been  employed  in
models  and  observed  for  specific  phytoplankton  species.  These
formulations range from
                                 3-64

-------
TABLE  3-3. MAXIMUM  (SATURATED)  GROWTH  RATES AS  A FUNCTION  OF
            TEMPERATURE
         Organism
Temperature
Saturated  Growth
    Rate,  K1
  Base  e,  Day'1
Cholrella ellipsoidea
(green algae)
Nannochloris atomus
(marine flagellate)
Nitzschia clostserium
(marine diatom)


Natural association

Chlorella pyrenoidosa
Scenedesmus quadricauda
Chlorella pyrenoidosa
Chlorella vulgaris
Scenedesmus obliquus
Chlamydomonas reinhardti
Chlorella pyrenoidosa
(synchronized culture)
(high-temperaure strain)
25
15
20
10
27
19
15.5
10
4
2.6
25
25
25
25
25
25
10
15
20
3.14
1.2
2.16
1.54
1.75
1.55
1.19
0.67
0.63
0.51
1.96
2.02
2.15
1.8
1.52
2.64
0.2
1.1
2.4
                                     3-65

-------
TABLE 3-4.  HALF-SATURATION  CONSTANTS  FOR N,  P,  AND  Si UPTAKE   (pM)  REPORTED  FOR MARINE  AND
               FRESHWATER  PLANKTON ALGAE  (After Lehman,   et  al.,   1975)
   Dunaliella
   Tertiolecta
   Honochrysia
     lutheri
   Fragilaria
   tricornutum
    Anabaena
   cylindrical
    polyedra
   Gymnodinium
    splendena
   Coccolithus
                   NO3
                                   Carpenter and Guillard(1971)
                                   Maclsaac and Dugdale (1969)
                                   Caperon and Meyer  (1972)
                                   Eppley,_et al.  (1969)
Caperon and Meyer (1972)

Eppley,_et al.  (1969)

Carpenter and Guillard(1971)


Caperon and Meyer (1972)

Ketchum  (1939)

Hattori  (1962)

Knudsen  (1965)

Eppley,_et al.  (1969)
                                                                             Kitylum
                                                                          brightwellii
  Cyclotella
     nana
Thalassiossire
  fluviatilia
Scenedesinus sp.
  Pediastrum
                                       Thalassiosira
                                                                             Ditylum
                                                                          brightwellii
Blum (1966)

Fuhs,  et al. (1972)
                                                                   3-66

-------
the   classical   formulas    represented   by   equation   (3-41)    to
formulations where  the saturated  growth rate is  a  maximum at  some
temperature and declines at  lower  and  greater  temperatures.
                          KT = K2oe(   '                        (3-41)

where

     KT   =    saturated growth rate  at  the  system temperature

     T    =    system temperature

     K2o   =    saturated growth  rate  at the  reference  temperature
               (20°C in equation [3-41])
     9    =    constant whose value usually  ranges between
               1.01 to 1.18. A typical  starting  value  is  1.06.

     The  light  induced reduction  in  growth rate  has  taken  several
forms  in  the   work  of   various   investigators  (49,   56) .   One
representation,   suggested  by  DiToro   (54)  and  used  fairly  widely,
is:

                          r =  ef  exp (-ai)-exp (-a0)           (3-42)
                               KeH

                          ai = la  exp(-KeH)                    (3-43)
                              Isf

                          a0 =  la                              (3-44)
                              Isf
where
     e    =    2.71828
     f    =    photo period
     H    =    segment depth
     K    =    light extinction coefficient
     Is   =    optimal light intensity
     Ia   =    mean daily light intensity
                                 3-67

-------
     Values of  the light extinction  can be measured  or calculated
depending on  the  complexity of the model  and  availability of data.
The photo period  and mean daily  light intensity vary seasonally and
can  be  estimated from  available records.  Values  of  the  optimal
light  intensity  Is  range   between  70  to  550 Langleys(Ly)/day.  A
starting value  of 300  Ly/day should provide  an adequate  point of
departure for beginning calculations.

     The nutrient limitations are usually  formulated  employing the
Michaelis-Menton  constant  and the Monod  relationship.  Formulations
of  nutrient   limitations have varied  over time  since  the  initial
modeling work in  this  area. There are two  basic  schools of thought
on this  issue.  The first approach assumes that nutrient limitations
are  multiplicative.   The   mathematical   representation   of   this
assumption is shown in equation  (3-45) for three nutrients.

                          Ln =   Cp     Cn       Cs              (3-45)
                                 + Cp  kn + Cn  kg  +Cc
where
Ln =      growth  rate   reduction  factor   due  to   all   nutrient
          limitations
Cp =      concentration of phosphorus
kp =      Michaelis-Menton constant for phosphorus
Cn =      concentration of nitrogen
kn =      Michaelis-Menton constant for nitrogen
Cs =      concentration of silica
Ks =      Michaelis-Menton constant for silica

-------
     The  second  assumption  that  has been  employed  in  developing
formulations  for the  impact  of  limiting  nutrients  has utilized  a
Monod formulation for each nutrient which  could be  limiting  growth.

     The  single  nutrient  limitation  which  results  in  the  lowest
value of  Ln  is  then used in the  calculation of growth  rate  Gp,  for
example, if
                            Cp  <   Cs   <   Cn                (3-46)
       then                kp + Cp   ks + cs    kn +Cn

                          Ln =
     Data  for  the  Michaelis-Menton  constants   are  presented   in
Tables 3-3  to  3-7. Starting values  of 25 |ig N/l,  7  |ig  P/l, and  30
|ig/l can  be  considered for  inorganic  nitrogen,  orthophosphate, and
silica.

     Specific Death Rate.  There are several formulations which have
been  used or  proposed  for representation of  the  specific  death
rate.  They  generally  include   a   respiration   term kz  which   is
temperature  corrected,  and  a   zooplankton  grazing term.  A  typical
formulation is:

                          Dp = kz (T)  + Cq (   kmp  ) Z           (3-47)
                                          Kmp + P
       Specific Death Rate = Respiration + Zooplankton Grazing

where:
Dp   =    specific death  rate
Kz   =    respiration rate  (range  .005  -  .12)
          (consider  first estimate of  .I/day)
(T)  =    temperature correction term
                                 3-69

-------
Table 3-5.
MICHELIS-MENTON HALF-SATURATION  CONSTATNS  (Ks)  FOR  UPTAKE  OF NITRATE  AND AMMONIUM BY
CULTURED MARINE PHYTOPLANKTON AT  18°C Ks UNITS  ARE (jMOLES/LITER  (After Eppley,  et  al.
1969)
                                   NITRATE
  C. Huxley F-5
Neritic diatoms
  Leptocylindrus danicus
  Rhizosolenia stolterfothii
  R. robustad
  Ditylum brightwellii
  Coscinodiscus lineatus
  Asterionella japonica
Neritic or littoral flagellatea
  Gymnodinium splendena
  Monochrusis lutheri
  Isochrysis galbana
  Dunaliella tertiolecta
Natural marine communities (from Maclsaac and Dugdale, 1969)
  Oligotr i hi
  Eutrophi^
                                                         2.0,1.5
                                                         0. 6
                                                         2.6,1.0
                                                         5.4,2.0
aGeometric mean diameter  rounded off  to the nearest micron.
bThis  notation means that 0.2  
-------
TABLE 3-6. MICHAELIS-MENTON  HALF-SATURATION CONSTANTS FOR NITROGEN
           AND  PHOSPHORUS (From DiToro, et al. , 1971)
Organism
Chaetocero gracilis
(maring diatom)
Scenedesmus gracile

Natural Association
Microcystis aeruginosa
(blue-green)
Phaeodactylum tricornutum
Oceanic species
Oceanic species
Neritic diatom
Neritic diatoms
Neritic or littoral
Flagellates
Natural association
01 i go trophic
Natural association
Eutrophic
Nutrient
P04

Total N
Total P
P04
P04

P04
N03
NH3
N03

N03
NH3
N03
NH3
N03
NH3
Michaelis
Constant,
Hg/Liter
as N or P
25

150
10
6a
10a

10
1.4-7.0
1.4-5.6
6.3-28
7.0
8.4-130
7.0-77
2.8
1.4-8.4
14
18
^Estimated.
Source: Tetra Tech  (531
                                 3-71

-------
Table 3-7.  VALUES FOR THE HALF-SATURATION CONSTANT  IN MICHAELIS-MENTON GROWTH FORMULATIONS
Phytoplankton
Description
Total Phytoplankton
Total Phytoplankton
Total Phytoplankton
Total Phytoplankton
Total Phytoplankton
Total Phytoplankton
Total Phytoplankton

Watm Water
Warm Water

Cold Water
Cold Water

Diatoms
Small Diatoms
Large Diatoms
Green
Green
Blue-Green
Blue-Green (N-Fixing)
Blue-Green (non-N-Fixing)
Small Cells Favoring
Low Nutrient
Small Cells Favoring
Low Nutrient
Large Cells Favoring
High Nutrient
Large Cells Favoring
High Nutrient
Readily Graze
Fast Settling
Not Readily Grazed
Not Fast Settling
Maximum
Specific
Growth
Rate (Days-1)
0,
2,
2,
2,
1.
2,
1.

2,
1.

2,
0,

2,
2,
2,
1.
1.
1.6
0,
0,

1.

1.

2,

2,

0,

2,
.2-8.0
.0
.5
.0
.3
.1
.0-2.0

.0
.-2

.5
.-3

.1 (25°C)
.1
.0
.9 (25°C)
.9

.8 (25°C)
.8 (25°C)

.0

.5

.0

.0

.5

.0
HALF-SATURATION CONSTANTS
Nitrogen Phosphorus Silicate Carbon Light References
(mg/1) (mg/1) (mg/1) (mg/1)
(Kcal/m2/sec)
0.025-0.3
0.025
0.025
0.025
0.025
0.025
0.025

0.07
0.05-0.3

0.01
0.1-0.4

-
-
-
-
0.015
0.015
-
-

0.3

0.3

0.4

0.4

0.02

0.4
0,
-
-
0,
0,
0,
0,
0,
0,
0,

0,
0,

-
-
-
-
0,
0,
-
-

0,

0,

0,

0,

0,

0,
.006-0.03
-
-
.005
.010
.002
.006-
.025
.015
.02-0.05

.02
.004-0.08

-
0.03
0.03
-
.0025
.0025
-
-

.03

.03

.05

.05

.02

.05
Baca and Arnett (1976)
0' Conner, et al . (1975)
O'Conner,etal. (1975)
O'Conner,etal. (1975)Conner
O'Conner,etal. (1975)
O'Conner, etal. (1975)
Battelle(1974)

0.03 0.002 Tetra Tech (1976)
0.4-0.6 0.002-0.004 U.S. Army Corps of
Engineers (1974)
0.04 0.003 Tetra Tech (1976)
0.5-0.8 0.004-0.006 U.S. Army Corps of
Engineers (1974)
Bierman (1976)
Canale, et al . (1976)
Canale, et al . (1976)
Bierman (1976)
Canale, et al . (1976)
Canale, et al . (1976)
Bierman (1976)
Bierman (1976)

0.5 0.003 Chen and Orlob (1975)

0.5 0.002 Chen (1970)

0.6 0.006 Chen and Orlob (1975)

0.6 0.004 Chen (1970)
Chen and Wells (1975)
0.05 0.003

0.8 0.006 Chen and Wells (1975)
                                                 3-72

-------
      Table  3-7
VALUES FOR  THE  HALF-SATURATION CONSTANT  IN  MICHAELIS-MENTON GROWTH  FORMULATIONS
Phytoplankton
Description
Saturated
Light
Intensity
(Ft-Candles)
Chemical
Composition
(fraction by weight)
C N P
Temperature
Tolerance
Limits (°C)
Location
of Study
References
Total Phytoplankton
Total Phytoplankton
Total Phytoplankton
Total Phytoplankton
Total Phytoplankton
Total Phytoplankton
Total Phytoplankton

Watm Water
Warm Water

Cold Water
Cold Water

Diatoms
Small Diatoms
Large Diatoms
Green
Green
Blue-Green
Blue-Green (N-Fixing)
Blue-Green (non-N-Fixing)
Small Cells Favoring
Low Nutrient

Small Cells Favoring
Low Nutrient

Large Cells Favoring
High Nutrient

Large Cells Favoring
High Nutrient

Readily Graze
Fast Settling
Not Readily Grazed
Not Fast Settling
      300
      300
      300
      350
      350
                    0.4     0.08    0.015    10-30
                                            10-30

                    0.4     0.08    0.015    5-25
                                            5-25
                    0.5     0.09

                    0.5     0.09
0.015

0.015
                        San Joaguin River
                        San Joaguin Delta Estuary
                        Potomac Estuary
                        Lake Erie
                        Lake Ontaria
                        Grays Harbor/Chehalis
                        River,  Washington
                        N.  Fork Kings River, Calif.
                        N.  Fork Kings River,  Calif.
                                                           Saginaw Bay, Lake Huron
                                                           Lake Michigan
                                                           Lake Michigan
                                                           Saginaw Bay, Lake Huron
                                                           Lake Michigan
                                                           Lake Michigan
                                                           Saginaw Bay, Lake Huron
                                                           Saginaw Bay, Lake Huron

                                                           Lake Washington
San Francisco Bay Estuary


Lake Washington


San Francisco Bay Estuary


Boise River,  Idaho

Boise River,  Idaho
                                                                                              Baca and Arnett  (1976)
0' Conner,
0' Conner,
0' Conner,
0' Conner,
0' Conner,
et al.
et al.
et al.
et al.
et al.
(1975)
(1975)
(1975) Conner
(1975)
(1975)
                                   Battelle (1974)

                                   Tetra Tech (1976)
                                   U.S. Army Corps of
                                   Engineers (1974)
                                   Tetra Tech (1976)
                                   U.S. Army Corps of
                                   Engineers (1974)
Bierman
Canale,
Canale,
Bierman
Canale,
Canale,
Bierman
Bierman
(1976)
et al.
et al.
(1976)
et al.
et al.
(1976)
(1976)
(1976)
(1976)
(1976)
(1976)
Chen and Orlob (1975)


Chen (1970)


Chen and Orlob (1975)


Chen (1970)

Chen and Wells (1975)


Chen and Wells (1975)
                                                                      3-73

-------
                         =  9(1-"U) where 9 = 1.08


Cg =      herbivorous  zooplankton grazing  rate  (range  0.13  to 1.2)
          (consider first  estimate of  .25  1/mg-C-day)

Z  =      zooplankton  carbon

Kmp  =      Michaelis-Menton half-saturation constant  for zooplankton
          grazing  on  phytoplankton  (range  10 -  50)  (consider first
          estimate of  50 jig chlor/1)

P =       phytoplankton  (chlorophyll)  concentration.


     The settling  term Ss  in  equation  (3-39)  can be represented by:
where
                         Ss = W                                  (3-46)
                             H

where

     Ss   =    settling  rate
     H    =    segment depth
     W    =    settling  rate of  phytoplankton  (range
               0 to  .5)  (consider first estimate of 0.1 m/day).

     The non-linear  eutrophication models  continue the computations
by  simultaneously  solving comparable  equations  for   key  nutrient
forms,  detritus  car-bon,  zooplankton,  dissolved  oxygen,  etc. Usual
forms of these equations are:

     Inorganic nutrients  (for each nutrient considered):

     dNi =  TNI - aiGp(I, T,  NZ)P + a2Rp(T)P + a3Rtz(T)Z           (3-49)
     dt
         + a4K0No + SNI

     Organic nutrients (for each nutrient  considered):

     dNo =  TNo - a4K0N0  -  N0Sri + a5RP(T)P + a6Rz(T)Z  +  Sri          (3-50)
     dt

     Zooplankton  (for  each type  considered):

     dZ_ = Tz +  a7K(T)PZ - RZ(T)Z                                 (3-51)
     dt
     Dissolved oxygen:

                                 3-74

-------
     dOz = Toz - Ka(Cs  -  Oz)+ a8Gp(I,  T,  NZ)P  -  a9Rz(T)Z + ai0RP(T)P
     dt  - anK0N0 - B                                           (3-52;
where

P    =    phytoplankton  biomass  (chlorophyll a.)

t    =    time

Gp   =    phytoplankton  growth rate which is defined by
          equation  (3-40)

Rp (T)  =  phytoplankton  respiration adjusted for temperature,
          defined by  equation (3-47)

Tn   =    net transport

K(T)  =    zooplankton grazing,  defined by equation  (3-47)  (grazing)

(Z)  =    zooplankton biomass

NI   =    inorganic nutrient  concentrations

N0   =    organic nutrient  concentrations

Oz   =    dissolved oxygen  concentrations

Rz (T)  =  zooplankton respiration and death rate, temperature
          corrected
                                 3-75

-------
K0   =    decay rate  (hydrolysis, mineralization, biochemical
          degradation) of non-living organic nutrient forms to
          inorganic forms

SNi   =    sources and other sinks of inorganic nutrients

SNo   =    sources and other sinks of organic nutrients

B    =    bottom oxygen demand

Sri   =    settling rate of non-living particulates

Ka   =    reaeration coefficient

Cs   =    oxygen saturation value
ai to  an = appropriate stoichiometric and yield coefficients.


3.4.3 Calibration and Verification

     The   non-linear   eutrophication   models   require   extensive
calibration and verification. Model  output  calculations,  generally,
should be  compared to  data  obtained over  a  full year  and several
years of data  are  required for  proper  verification.  The literature
contains  a  number  of  illustrations  of  model  calibrations  and
verifications  (56,  57,  58, 59,  24) .  All state variables,   including
the species, distributions  of chemicals such  as  orthophosphate and
total phosphorus,  should  be  employed for developing  comparisons of
calculated  and observed water  quality.  Further,  data  from special
studies  such  as   primary productivity and  bottom  release  rates
should be  employed to  test  the  model  calculations. Comparison of
computed steady-state  conditions with  analytical solutions  as well
as internal  program  checks on  conservation of mass  should  also be
considered.

     Particular attention should  be directed  towards   annual  data
which provide  different conditions to test  model adequacy.  Examples
of this type
                                3-76

-------
of  situation  would  be associated  with  data  for  the same  annual
period in  two  years  where water quality  profiles  were different or
with data  for  the same annual  period where the  vertical  structure
was different over two years.

     The  rather  stringent  verification  and calibration  suggested
for non-linear  eutrophication models  is motivated in  part  by their
extreme  complexity,  but they are  primarily driven  by the  lack of
adequate  understanding  of  the   fundamental   processes   governing
eutrophication. This  .  primary driving  force  is  identical  for  all
levels of  eutrophication  analysis,  including  the Vollenweider  and
residence  time calculations.  Therefore,  non-linear  eutrophication
models which are  properly verified and  calibrated will tend  to be
more reliable—or  will  at  least  provide a better  indication of what
is  known versus  what  is  not  known at  a specific  site—than  other
analysis techniques. As a consequence of the lack of  understanding
of  the  fundamental processes  governing eutrophication, waste load
allocations for  control of  eutrophication  in  lakes are  inherently
high risk  exercises when  compared to  other waste  load  allocation
requirements,  as,  for example,  dissolved oxygen in streams.
3.4.4 Supplemental Calculation Procedures
     Calculation  Procedure   for   Aid  in  Defining   the   Relative
Limitations  Placed   on   Phytoplankton  Growth  Rates   by  Various
Processes.  The calculation procedures  presented  below  have not been
employed in past  studies  of  eutrophication. This is pointed out to
emphasize  that  while  some   insights  may  be  obtained  from  the
calculations,   there  are  risks in  employing the procedure  since it
has not been tested and is particularly sensitive to the analytical
                                3-77

-------
accuracy of  the nutrient  measurements and  the  system coefficients
selected.

     Table  3-8  presents  a  summary  of  the  components  employed  in
non-linear  eutrophication  models  together  with  estimates  of the
range and  first starting  values  of some  model  coefficients.  These
data could be employed  to  assess  the relative impact of the  various
processes on the growth of phytoplankton.

     The following example illustrates the calculation procedure:

3.4.5 Example Problem

Data:  Assume measured lake data during August are as  follows:
             H = 10m  (depth)
            Ke = 1.3/m  (extinction coefficient)
            Qi = QP =  lOOOmVday; Pz = lOfig Chi a/1 (incoming
                 Phytoplankton)
        Volume = 106  m3
Orthophosphate = 10(j,g/l
     NH3 +  N03 =  40ng/l
            Si = lmg/1
            P0 = 25|j,g Chi  a./l (outgoing phytoplankton)
   Temperature = 26°C
            la = 475 Lys/day
Problem:  Evaluate the  effect of  the  various  factors  important  in
          non-linear  eutrophication models   (see  Table  3-8,  e.g.,
          advective   transport,    light   limitation,    temperature
          limitation, nutrient
                                 3-78

-------
TABLE 3-8.  SUMMARY OF  FORMULATIONS FOR FACTORS  CONSIDERED IN  NON-
             LINEAR  ECTROPHICATION MODELS AND ESTIMATES FOR RANGE AND
             INITIAL VALUE OF  COEFFICIENTS
FACTOR
Advective Transport
Temperature Adjustment
For Growth
Light Limitation
Nutrient Limitation
Phosphorus
Nitrogen

Silica

Removal
Respiration

Zooplankton Grazing

Settling
                                 FORMULATION
                        r =  ef   [exp(-ai)- exp(-a0)
                             KeH
                          =   Ia  _exp(-KeH)
Cg  kmp
kmp +P
W/H
                                                         COEFFICIENT
                                                            RANGE
                                                       (6)  1.01-1.18
                                                       (Is) 70 to 550

                                                       (Kp) 5 to 550

                                                       (Kn) 10 to 400

                                                       (Ks)  -
                                                       (K2)  .005 -.12
                                                       (6)  1.04-1.1
                                                       Z (Cg)  0.13  -  1.
                                                       (kmp)  10-50
                                                       (W)  0 to  0.5
                                                                         INITIAL VALUE
                                                                         1.06
                                                                         300Lys/Day

                                                                         7|agP/l

                                                                         25(4,gN/l

                                                                         30(4,g/l
                                                                         .I/Day
                                                                         1.08
                                                                         .25P/|ag-C-Day
                                                                         50 |agCh/l
                                                                         0 . 1 m/day
                                       3-79

-------
     limitation,  and removal  process  limitation)  and  determine  if
the potential for  additional phytoplankton growth exists.

Solution:
Entering Lake =  1000  m- x 10pig Chi a x I0_-cm- x   1
                      Day       1           m3     103cm3

              =  107ng Chi a/day

      Leaving =  1000m- x 25|j,g Chi a x 10_- =  2.5  x 107 |j,g Chi a/day
                 day         1         103
Light:

          a0 = 2 (475) = 3.167
                300
          ai = 3.167  exp-1.3 x 10 = 7.16 x 10"6

          ri = 2.718 (0.5)  (exp-7.16 x 10"6 - exp-3.167
                .3(10)
          ri =  .1045 (1.00 - .042)

          ri =  ( .1045) ( .958)  = 0.100
Phosphorus: ri = rp =  10  =  .588     limiting nutrient is phosphorus
                   7  +  10
Nitrogen  :  ri = rn =   40   =  .615
                     25 +  40

Silica:     rs =   1000    = .971
                 30 +  1000
                                 3-80

-------
Temperature  (Growth):
                  (T) =  9'28-20' = 1.068 = 1.594
Temperature  (Respiration):
                  (T)  =  9<28-20> = 1.088 = 1.851
Settling:
                  W  =  0.1  = .01/day
                  H    10
Death:

     Respiration =  0.1  x  1.851  = 0.185/day  (phytoplankton)
     No zooplankton data

Summary:

Transport reduces phytoplankton by:
          1.5 x 107ng Chi/day
Respiration reduces phytoplankton by:

          0.185 x  25|ig  Chi  a/1  x 106m3 x 106 m3 x 10_-cm-_- x   1
                                                   m3     1000cm3
                   4.6       x       109       ng        Chi      a/day
Settling reduces phytoplankton by:

          0.01 x 25  10- x 10- = .25  x 109|_ig Chi  a/day

                        103

Growth increases phytoplankton by:
          = 25 x 1.594  x  .100 x .588 x 25 x 106x  1Q_-
                                                  1000
          = 5.7 x  109 ng Chi a/day
                                 3-81

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Based on the above calculations:

   1.  The  influence of transport at  1000  m3/day  is  small  (e.g.,  1.5
      x  107 «4. 6 x 109 (loss due to respiration)
   2.  Light  limits  growth significantly,  r =  0.100.
   3.  Phosphorus is the limiting nutrient  and  is  less  limiting than
      light,  rp  = .588  >  ri = .100.
   4.  The  calculations indicate very little potential for additional
      phytoplankton growth.

   The basic shortcoming  of these  calculations  is  associated with
the  lack  of  confirmation  for  the  coefficients   employed  in  the
calculation. These computations could be  employed  as a rapid way of
developing  some indication of  the  importance of  various  processes
with respect to system response.
3.4.6 Vertical Dissolved Oxygen Analysis

     One  of  the  most  significant  factors  responsible  for  the
vertical gradients  in water  quality  is the  density  stratification
due  to  temperature.  This  condition is  most pronounced  during  the
summer and generally  produces  a  relatively well-mixed surface layer
and  a poorly-mixed  lower  layer.  Differences  in concentration  of
many  water  quality parameters exist between the two  layers  during
this  period  and are  particularly  evident  in the case  of dissolved
oxygen.   Its   concentration  is  affected not  only by  the  vertical
stratification  and  the  associated dispersion,  but   also  by  the
various  sources  and  sinks  in each zone  photosynthetic  production
and exchange with  the atmosphere  in the upper layer,  and biological
respiration and benthal demand in  the  lower.  The following analysis
includes these reactions with vertical
                                3-82

-------
dispersive  transport  under  a  steady-state  condition  and  has  been
employed in analysis of dissolved oxygen in the New York Bight.

3.4.6.1 Basic Equations and Boundary Conditions

The  basic   differential  equation   which  defines   the   vertical
distribution  of  dissolved oxygen  under steady-state  conditions  is
as follows:

        0 = d_(E(z)  dc) + Zs0 - Zsi                           (3-53)
            dz      dz
in which:

     c    = concentration of dissolved oxygen
     E(z) = vertical dispersion coefficient
      Zs0 = kinetic sources
          = kinetic sinks
     The concentration c may be  expressed  in terns  of the deficit D
=  cs  -  c,  in  which  c  equals  equilibrium saturation  value  of
dissolved  oxygen  for  a  given   surface   temperature.  The  primary
kinetic  source  is  the  photosynthetic  production  of  oxygen  by
phytoplankton  and  the   sink  is  algal  and   bacterial  respiration.
Equation (3-53) may then be expressed as follows:

                  0 = d_(E(z)  dD) + R(z) - P(z)               (3-54)
                      dz      dz
in which  R(z)  and  P(z)  are  the  volumetric oxygen  utilization and
the production  rates,  respectively.  The  former  includes  both the
phytoplankton  and  bacteria  contributions.  Since  production  and
respiration  are  operative  in  the surface  layer,  while  only the
latter  is  effective  in  the  lower  layer,  the  water column  may be
divided into two regions delineated by the thermocline.
                                3-83

-------
Equation  (3-54)   directly  applies  to  the upper  layer,  while  the
lower  layer  is  described  by  this  equation without  the  production
term.

     Since there are  two  second-order  differential  equations,  one
for  each  layer,   four  boundary conditions are  required to  evaluate
the  constants  of integration.  The upper  layer  is  identified by  the
subscript  T  and  the  lower  by  the   subscript  B.   The  boundary
conditions  are   provided   by  flux  balances   at  the   air   water
interface, the  thermocline,  and  the  bed, and  by  the  concentration
equality at the  thermocline:
                          at z = 0: ET dDT = DLD0               (3-55)
                                       dz


                          at z = p: DTp = DBp                   (3-56)


                         ET dDr  = EB dDe                        (3-57)
                            dz      dz

                          at z = H: EB dDe = S                 (3-58)
                                       dz
in which

DO,  Dp     = deficits at the interface and  at  the pycnocline  (M/L3)

KL        = oxygen transfer coefficient  (L/T)

S         = areal oxygen utilization rate  at  the bed  (M/L2T.)


3.4.6.2. Solution of Equations

The first integration of equation  (3-54) for  the upper  layer yields

       ET dDr = p P(z)dz - p  R(z)dz +  Ci                        (3-59)
          dz   * *    * *
                 o
                                 3-84

-------
and the second

                    dz
             DT=*£T(z)  (pP(z)dz - p  R(z)dz + Ci) + C2        (3-60;
Applying the  first  boundary condition  (equation  3-45 to equation 3-
49) yields
                               Cl  =  KLD0
                           and  C?  =  Dn
By  averaging the dispersive  and kinetic  terms in  the  upper layer,
equation  (3-60) becomes  after substituting the values of Ci and C2:

                      DT =  (PT - RT)z2  +  KLD0z  + D0              (3-61)
                              2. ET          ET
In the  lower  layer,  the photosynthetic  contribution is zero and the
first integration of  equation (3-54)  yields

                      EB dDB = -RBz + C3                         (3-62)
                        dz
     Applying  the   fourth   boundary  condition  (equation  3-58  to
equation 3-62) provides  the  evaluation of C3:

                      C3  = S  +  RRH
Substitution of this  into  equation (3-62)  and integration leads to:

                      DB = RBZ- +  z (S +  RBH)+  C4                  (3-63)
                                 3-85

-------
The remaining  constants  D0  and C4 are determined  by the second  and
third boundary conditions  (equations  3-56 and  3-57) .  Equating  (3-
59) and  (3-62)  at z = p and solving  for D0 yields:
                 Do = - (PT-RT) x p + RB[ (H - p) + S]
                          KL                KL
                                                               (3-64)
Equating  (3-61) and  (3-63) at z = p permits evaluation  of  04:

                 C4 = +  (PT-RT) p2 +  p  RB(p-2H) - S            (3-65)
                                       RB(p-2H) - S
                                          2
                    + Do (  1  +  KLP
Thus  equations  (3-61)   with  (3-64)   define  the   concentration  of
dissolved oxygen  deficit in  the  upper layer,  and equations  (3-62)
with  (3-65)   in  the  lower  layer.  Conversion  to  dissolved  oxygen
values  is  made  by  subtracting  the  calculated  deficit  from  the
equilibrium  saturation  values  specific  to  a given  location  for  a
given surface salinity and temperature regime.

     The  various  transfer,  kinetic and density coefficients  can  be
assigned  on  the basis of either direct measurement, values  reported
in  the  literature,  the  previous  calculations,  or any  combination.
The following example illustrates the calculation  procedure.
3.4.7 Example Problem

Data:  The  assumed  lake parameters  needed  in the  calculation  are
listed below. The values may be typical of temperate northern  lakes
during
                                 3-86

-------
the  summer.  Values  for some  of the  parameters listed  immediately
below were derived from the previous  sample  problem results.

Data Derived from Previous Example:
          Depth  (Epilimnion)      =  10m
          Phtoplankton  Cone.      =  25 (j,g  Chi  a./l
          Temperature  (Epilimnion)=  26°C
          ri (light-reduction)    =   0.100
          Settling rate          =   0.10/day
New Data:

Depth  (Hypolimnion)
Temperature(Hypolimnion)
ET [range of 10-25 ftVday (2)]

EB
KL [range of 1-5 ftVday (12)]

S  [range of 0.3-3  (7)]
                                             10m
                                             6°C
                                          =  2.5 X 10"1 cnr/sec
                                          =  23.2 ftVday
                                              0 m2/day
                                              8 ft/day
                                              846 m/day
                                          = 1 gm 02/  m /-day
                                          = 1 mg 02/-m/-day
Problem:  Calculate  the  dissolved  oxygen deficit  at the  air-water
          interface,  the  thermocline,  and  at  the  sediment-water
          interface, assuming steady-state conditions.
Solution:
          Deficit at the air-water  interface
                   D0 = -  (PT-RT)p +  RB[  (H - p) +  S]
                            KL             KL
         Where:
                 PT = Ps(r);  r = 0.100 and ps = 0.25 chl a;  from
                    = 0.625 mg  02/l-day
                 RT =  (0.025)(chl a);  from (7)
                                 3-87

-------
                         =  625 mg 02/l-day

               RB :   No  specific  formulation  exists  for  this  term;
                    however, as  noted in  the  previous example,  the
                    rate of loss of  material  from the  epiliminion
                    into the  hypolimnion  is  one-tenth  the rate  of
                    loss  of   material   due    to   respiration.   In
                    addition,   the  temperature  is   cooler  in  the
                    epilimnion,  so the rate of  02  consumption  should
                    be reduced.
RB = 0.1 (RT)  (T  correction)
   =  (0.1)   (0.625) 1.08(6"20)
   = 0.0213 mg 02/l-day
D0 = ( . 625  - . 625) 10 + (.0213)
                                               (20-10) +  1
         .864
     1.404mg/l
                                              864
Deficit at the sediment-water interface  (z  =  20)
              DB = - (.0213)  (20)- +  20 [1  +  ( .0213)  (20) ]  + 0
              + -
10
1.0
(2)1.0
( (.0213)
2
1
(-30) -1) + 1

.0
.404 (1+
( .846)
2.
(10)
16
                    =   18.09   mg/1,   which  implies  that   a   large
                    potential  exists   in   this   eutrophic   lake  to
                    drive  the  02  at  the sediment-water  interface  to
                    0.

                    Deficit at the pynocline  (z  = 10)
                    DTp  =(.846)  (10)  (1.404) + 1.404
                                2.16
                    =  7.02 mg/1  =>  the  D.O.  concentration at  the
               pynocline is equal  to  1.18 mg/1.
                                 3-f

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3.5 AVAILABLE LAKE EUTROPHICATION MODELS

     This section provides  a partial list and  brief  description of
available lake  eutrophication models and  the  firms,  agencies,  and
individuals  who  have  supported,  developed  and/or  applied  these
models. Not  all  of  the models  listed  are  in the public  domain and
other models  or  modifications exist. The  descriptions  are intended
to provide the reader with  an overall idea of what  is available and
where further information may be obtained.

     The model descriptions,  presented  in  the  form  of  tables,   (one
table per  model),  are  based on a synthesis  of information  from a
brief questionnaire  which  was sent  various  individuals  (identified
in  the  tables   as  respondents)  and published literature.  It  is
hoped,   therefore,   that this  information is  reasonably  current.
However, modifications  of  these models  is a  continuing process and
the  only truly  reliable  sources  of  current  information are  the
individuals involved in this work.

     Lake  eutrophication   models  were  classified   as  simplified
models  (Section  3.2);  time variable mass balance models  (Section
3.3);  and  non-linear  eutrophication  models  (Section  3.4).   The
simplified  models   are  such  that   calculation  can   be  readily
performed on  a  calculator   or  programmed on a  computer if desired.
The  programming  effort  is  minimal  and  therefore packaged programs
are generally not available.

     Computer  programs   for  solving  the   time  variable  phosphorus
residence equations  have been developed by Steven C.  Chapra  at the
Great Lakes  Environ-,  mental  Research  Laboratory (NOAA)  and David
P. Larsen at the Corvallis
                                3-89

-------
Environmental Research Laboratory  (EPA).  Brief  descriptions of each
of  these  models  are  contained  in   Tables  3-9  and  3-10.  Other
computer programs  may also exist,  and  consideration  could be given
to program development on  a  site-specific project since programming
does not necessarily require a major effort.

     Computer  programs  for   solving   the  time-variable  non-linear
eutrophication equations  in  one, two  or  three  dimensions represent
a  major  development  effort;  therefore,  the  potential user should
make use of  available models to the extent possible.  Moreover,  the
application  and  interpretation of  the   output  from  such  models
require  an  experienced   analyst.   Thus,   in  reviewing   available
models, the personnel who  would be  involved in  conducting the study
should be carefully considered.

The non-linear eutrophication models described herein are:

Model                                                       Table
Water Analysis Simulation Program  (WASP)                    3-11
(includes LAKEIA, ERIE01, and LAKE3)

WASP and Advanced Ecosystem Modeling Program  (AESOP)         3-12

CLEAN Program                                               3-13

LAKECO, and ONTARIO                                         3-14

Water Quality for River Reservoir Systems  (WQRRS)            3-15

Grand Traverse Bay Dynamic Model                            3-16


NOTE: WASP and AESOP are related models as are LAKECO and WQRRS.
                                3-90

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  Table  3-9.  DESCRIPTION  OF  CHAPRA'S  TIME VARIABLE  PHOSPHORUS MODEL
Name of Model: Time Variable Total Phosphorus Model
Respondent:

Developer:
Steven C. Chapra

Steven C. Chapra
Great Lakes Environmental Research Laboratory
2300 Washtemaw Ave.
Ann Arbor, Michigan 48104
(313) 668-2250
Year Developed: 1974

Capabilities:   Model  framework  capable  of  computing  deleterious
               effects  of  eutrophication  as  a  function  of  human
               development   of  drainage  basin   for   a  series  of
               individual lakes (developer's note).

               The  model  considers each  lake  or major  segments  of
               each  lake as  completely mixed  segments subject  to
               waste  sources,  inflow  and  outflow,  dispersion,  and
               in-lake  losses of  total  phosphorus.  Waste  sources
               include  domestic   waste,  runoff   from  agricultural,
               urban  and forested  areas,  and  atmospheric  fallout.
               (Separate algorithms  are contained  in the model  to
               estimate  these  loads   based  on   land  use   and
               population     statistics     and    unit     loading
               coefficients.)  In-lake  losses   are  estimated  using
               the  apparent  settling  velocity  approach. The  model
               time step used  in  the  application  to the Great Lakes
               was  one  year  and  the resulting projections  were
               annual average values.

Verification:   See references cited below.

Availability:   Model in public domain

Applicability: The  approach  is general but  the parameters  are  site
               specific for Great Lakes.
Support:
User's Manual
There  is  no  user's  manual  but  several  papers  (see
references)  contain  the  general  information  needed
to run the model.
References:
Technical Assistance
Extent of  technical  assistance would  depend  on user
affiliation and  nature  of application. At  a  minimum
general  guidance  and response to  questions would be
provided.
Chapra (45,60,61)
                                3-91

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 Table 3-10. DESCRIPTION OF LARSEN'S TIME VARIABLE PHOSPHORUS MODEL
Name of Model: Phosphorus Mass Balance Model

Respondent:     David P. Larsen
Developers:
David P. Larsen and John Van Sickle
Corvallis Environmental Research Laboratory  (CERL)
U.S. Environmental Protection Agency
200 S.W. 35th Street
Corvallis, Oregon 97330
 (503) 757-4735
Year Developed: 197!
Capabilities:
Input-output model  for  total  phosphorus  (TP),  time
varying,  to  project   Shagawa  Lake's  response  to
phosphorus   loading   reduction   and   to   project
phosphorus  pattern  in absence  of  phosphorus loading
reduction (developer's note).

The  model  considers  the  lake as  completely mixed,
subject to external sources, inflow and outflows, net
sedimentation,   and  an internal  source  of phosphorus
released  from  sediments.  External sources  of  total
phosphorus  include   domestic   waste,   run-off,   and
precipitation.   Step  functions  are used  to  describe
the   seasonal   variation   of    the   sedimentation
coefficient and  the  sediment  release  rate.  The  time
step used was one week.
Applicability:  The  approach  is  general  but  parameters  are  site
               specific to Shagawa Lake.

Verification:  See references cited, below.
Support:
References:
User's Manual
There is no user's manual

Technical Assistance
Developers  could  act  in  advisory  capacity  given
authority from CERL.

Van Sickle and Larsen  (62) and Larsen et al  (39)
                                3-92

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    Table 3-11. DESCRIPTION OF WATER ANALYSIS SIMULATION PROGRAM

Name  of Model:  Water Analysis  Simulation  Program  (WASP)*-LAKE1A,
ERIE01, and LAKE3
Respondent:     William L. Richardson
               U.S. Environmental Protection Agency
               Large Lakes Research Stations-(LLRS)
               9311 Groh Road,
               Grosse He, Michigan 48138
               (313) 226-7811
Developers:  Robert V. Thomann, Dominic DiToro, Manhattan College, N.Y,
Year Developed:

Capabilities
     1975  (LAKE1)
     1979  (LAKE3)
Model is one  (LAKE1) or three  (LAKE3) dimensional and
computes  concentration  of  state  variable   in  each
completely  mixed   segment  given   input   data  for
nutrient  loadings,  sun-light,  temperature,   boundary
concentration,   and   transport   coefficients.   The
kinetic  structure  includes   linear  and  non-linear
interactions  between  the  following eight variables:
phytoplankton  chlorophyll,  herbivorous  zooplankton,
carnivorous zooplankton,  non-living organic  nitrogen
(particulate   plus   dissolved),   ammonia  nitrogen,
nitrate   nitrogen,   non-living   organic  phosphorus
(particulate    plus   dissolved),    and   available
phosphorus  (usually orthophosphate).  Also,  a refined
biochemical kinetic structure  which incorporates two
groups  of  phytoplankton,   silica  and revised recycle
processes is available.
Verification:   See references cited below.

Availability:   Models  are  in the  public  domain  and  are  available
from Large Lakes Research Stations

Applicability: The model is  general;  however,  coefficients are site
               specific reflecting past studies (see references)
Support:
User's Manual
A  user's  manual  titled  "Water  Analysis  Simulation
Program"   (WASP)   is   available  from   Large  Lake
Research Stations.
References:
Technical Assistance
Technical  assistance  would be  provided if requested
in writing  through  an EPA Program Office or Regional
Office.

Thomann  (63),• DiToro et al  (51,59)
*The Advanced  Ecosystem Model  Program  (AESOP)  described  next  is a
modified version of WASP
                                 3-93

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Table 3-12. DESCRIPTION OF WATER ANALYSIS SIMULATION PROGRAM AND
            ADVANCED ECOSYSTEM MODELING PROGRAM
Name of Model
Respondent:
Developers:
Capabilities:
Verification:
Ava i1ab i1i t y:


Applicability:
Water Analysis  Simulation  Program  (WASP)
Advanced Ecosystem Modeling  Program  (AESOP)
John P. St.  John
HydroQual,  Inc.
1 Lethbridge  Plaza
Mahwah, N.J.  07430
 (201) 529-5151
WASP
Dominic  M.   DiToro,  James J.  Fitzpatrick,   John
L.  Mancini,   Donald  J.   O'Conner,   Robert  V.
Thomann  (Hydroscience,  Inc.)  (1970)

AESOP
Dominic DiToro,  James J.  Fitzpatrick, Robert V.
Thomann  (Hydroscience,  Inc.)  (1975)
The  Water  Quality Analysis  Simulation Program,
WASP,  may be applied to  one-,  two-,  and three-
dimensional  water  bodies,  and models  may be
structured  to  include  linear  and  non-linear
kinetics.  Depending  upon  the modeling framework
the user  formulates, the  user may  choose,  via
input  options,   to  input   constant  or   time
variable  transport  and  kinetic   processes,  as
well as  point  and  non-point  waste   discharges.
The Model Verification Program, MVP,   may be  used
as an indicator of "goodness of fit"  or adequacy
of  the  model  as  a  representation of  the   real
world.

AESOP,  a  modified  version of  WASP,  includes  a
steady  state option and  an  improved transport
component.

To  date  WASP  has been  applied to  over twenty
water   resource   management   problems.   These
applications have  included one-,  two-and three-
dimensional  water   bodies  and   a   number  of
different  physical,   chemical  and  biological
modeling    frameworks,     such    as    BOD-DO,
eutrophication,      and    toxic      substances.
Applications include  several of the Great Lakes,
Potomac Estuary,  Western  Delta-Suisun  Bay  Area
of San Francisco Bay, Upper Mississippi, and New
York Harbor.
WASP is  in public domain  and code is available
from USEPA   (Grosse  Isle   Laboratory  and Athens
Research Laboratory). AESOP is proprietary.
Models  are   general and may  be   applied  to
different types of water bodies and to a variety
of water quality problems.
                                 3-94

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  Table 3-12. DESCRIPTION OF WATER ANALYSIS SIMULATION PROGRAM AND
ADVANCED ECOSYSTEM MODELING PROGRAM  (Concluded)	

Support:        User's Manual
               WASP and MVP documentation is available from USEPA
                (Grosse  Isle   Laboratory)   AISOP  documentation  is
               available from HydroQual.

               Technical Assistance
               Technical assistance  of  general nature from advisory
               to    implementation     (model    set-up,    running,
               calibration/verification, and  analysis)  available on
               contractual basis.
                                 3-95

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              Table  3-13.  DESCRIPTION  OF  CLEAN  PROGRAMS
Name of Model:
Respondent:
                    CLEAN,  CLEANER,  MS.  CLEANER,  MINI.  CLEANER
Developers:
                    Richard A. Park
                    Center for Ecological Modeling
                    Rensselaer Polytechnic Institute
                    MRC-202,  Troy,  N.Y. 12181
                    (518)  270-6494
               Park,   O'Neill,  Bloomfield,   Shugart  et  al  Eastern
               Deciduous  Forest   Biome  International   Biological
               Program (RPI,  ORNL,  and University of Wisconsin)
Supporting Agency:   Thomas 0. Bamwell, Jr.
                    Technology Development and Application Branch
                    Environmental Research Laboratory
                    Environmental Protection Agency
                    Athens,  Georgia 30605
Year Developed:
Capabilities:
                    1973 (CLEAN)
                    1977 (CLEANER)
                    1980 (MS. CLEANER)
                    1981 - estimated completion date for MINI. CLEANER

                    The MINI. CLEANER package  represents  a complete
                    restructuring of the Multi-Segment Comprehensive
                    Lake  Ecosystem  Analyzer   for   Environmental
                    Resources (MS.  CLEANER)  in order  for  it,  to run
                    in  a  memory  space  of  22K  bytes.  The  package
                    includes  a series of simulations  to  represent a
                    variety  of distinct  environments,  such  as  well
                    mixed     hypereutrophic    lakes,     stratified
                    reservoirs,   fish  ponds  and  alpine lakes.  MINI
                    CLEANER   has   been  designed   for  optimal  user
                    application  a turnkey system  that can be used by
                    the most  inexperienced environmental technician,
                    yet can  provide the  full  range  of  interactive
                    editing  and  output  manipulation desired  by the
                    experienced   professional.   Up   to    31   state
                    variables can be  represented in  as  many as  12
                    ecosystem    segments    simultaneously.    State
                    variables include 4  phytoplankton groups,  with
                    or  without  surplus   intracellular nitrogen  and
                    phosphorus;  5 zooplankton groups;  and 2 oxygen,
                    and dissolved carbon  dioxide.  The  model has  a
                    full set  of  readily understood commands and  a
                    machine-independent,   free-format   editor   for
                    efficient usage.  Perturbation  and  sensitivity
                    analysis  can be  performed easily.  The model has
                    been calibrated  and is being validated. Typical
                    output  is provided for a set  of test  data.  File
                    and  overlay  structures  are   described   for
                                3-96

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implementation on virtually any computer with at
least 22K bytes of available memory.
             3-97

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        Table  3-13.  DESCRIPTION OF CLEAN PROGRAMS  (CONCLUDED)
Verification:
Availability:
 The MINI. CLEANER model  is  being verified with data
 from  DeGray  Lake,  Arkansas;  Coralville  Reservoir,
 Iowa;    Slapy   Reservoir,    Czechoslovakia;    Ovre
 Heimdalsvatn,   Norway;   Vorderer   Finstertak   See,
 Austria;  Lake  Balaton,  Hungary;  and  Lago Mergozzo,
 Italy. The phytoplankton/zooplankton  submodels were
 validated for  Vorderer  Finstertaler  See  by Collins
 (Ecology,  vol.  61, 1980,  pp. 639-649).

 Model  are  in  public  domain  and code  is available
 from  Richard A.  Park  (RPI)  and  Thomas  0.  Barnwell
 (EPA/Athens).
Applicability: Model is general.
Support:
User's Manual
A  user's  manual  for  MS.  CLEANER is  available  from
Thomas 0. Barnwell, Jr.
A user's manual for MINI. CLEANER is in preparation.

Technical Assistance
Assistance   may   be   available   from   the   Athens
Laboratory;  code   and  initial  support is  available
for a nominal  service  charge from R.P.I.; additional
assistance is negotiable.

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        Table 3-14. DESCRIPTION OF LAKECO AND ONTARIO MODELS
Name of Model

Respondent:
Developers:
User Developed:

Capabilities:
                                                       Dr.  Chen  was
LAKECO*, ONTARIO

Carl W. Chen
Carl W. Chen
Tetra Tech Inc.
3746 Mount Diablo Blvd. Suite 300
Lafayette, California  94596
 (415) 283-3771
 (original  version developed  when
with Water Resources Engineers)

1970  (original version)
LAKECO
Model   is   one   dimensional  (assumes  lake  is
horizontally    homogeneous)    and    calculates
temperature,  dissolved   oxygen,   and  nutrient
profiles  with   daily  time  step  for  several
years.  Four  algal   species,   four   zooplankton
species,  and  three fish  types  are  represented.
The  model  evaluates  the consequences  of  waste
load    reduction,    sediment    removal,    and
reaeration  as remedial measures.
Verification:



Ava i1ab i1i t y:



Applicability:

Support:
                    ONTARIO
                    Same  as  above  but  in  three
                    application to Great Lakes.
                                 dimensions  for
The  models have  been applied  to more  than 15
lakes by Dr. Chen and to numerous other lakes by
other investigators.

The  model  is  in the  public  domain  and the  code
is   available   from  the  Corps   of  Engineers
(Hydrologie Engineering Center),  EPA, and NOAA.

General
User's Manual
User's  Manuals are  available from
Corps of Engineers, EPA, and NOAA.
                                                         Tetra  Tech,
                    Technical Assistance
                    Technical Assistance  is available  and  would be
                    negotiated on a case-by-case basis.
*A  version  of LAKECO,  contained in  a model  referred to  as  Water
Quality  for  River Reservoir  Systems  (WQRSS)  and supported by the
Corps  of  Engineer  (Hydrologie   Engineering Center)  is  described
separately.

                                 3-99

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 Table  3-15.  DESCRIPTION OF WATER QUALITY FOR RIVER RESERVOIR SYSTEMS
Name of Model: Water Quality for River-Reservoir Systems  (WQRRS)

Respondent:    Mr. R.G. Willey
               Corps of Engineers
               609 Second St.
               Davis, California 95616
               (916) 440-3292

Developers:    Carl W. Chen, G.T. Orlob, W. Norton, D. Smith
               Water Resources Engineers, Inc.

History:       1970  (original version of lake eutrophication model)
               1978  (initial version of WQRRS package)
               1980  (updated version of WQRRS)

Capabilities:   See description  of  LAKECO  in  Table 3-13  (model also
               can consider river flow and water quality).

Verification:  Chattahoochee  River  (Chattahoochee  River Water Quality
               Analysis,   April  1978,   Hydrologie  Engineer  Center
               Project Report)

Availability:   Model is in public domain and code  is available from
               Corps.

Applicability: Model is general.

Support:       User's Manual
               A user's manual is available from Corps.

               Technical Assistance
               Advisory assistance is  available to all users. Actual
               execution assistance  is  available  to Federal agencies
               through an inter-agency funding  agreement.
                                 3-100

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     Table  3-16.  DESCRIPTION  OF  GRAND  TRAVERSE  BAY  DYNAMIC  MODEL
Name of Model: Grand Traverse Bay Dynamic Model-
Respondent:
Developers:
Raymond P. Canale
LTI, Limno-Tech, Inc.
15 Research Drive
Ann Arbor, Michigan 48103
(313) 995-3131

R.P. Canale, S. Nachiappan, D.J. Hineman, and H.E.
Allen
Year Developed: 1973
Capabilities:
The model discretized  the  bay  as  a collection of six
well-mixed  cells  which   were  arranged  such  that
vertically   well-mixed   conditions   were   assumed
throughout  the  bay.   The  water   quality  parameters
considered were dissolved and particulate phosphorus,
particulate  nitrogen,   dissolved  organic  nitrogen,
ammonia,  nitrate,  silica,  total  algae  and  total
zooplankton.   Processes   accounted   for   included
transport   by   water   motion,    growth,    death,
decomposition, biological uptake,  predation, exchange
with  Lake  Michigan,   and  direct  input  from  the
Boardman  River.   The  system  of  dependent  governing
equations are  based on  mass  balances for the various
constituents applied to  each cell. The advective and
dispersive  transport  was  based  on  results  of  a
separate  transient vertically well-mixed  numerical
model.
Verification:
Ava i1ab i1i t y:
Applicability:
Support:
See references, below.
Model is in public domain.
 Models  are  developed  for  specific  applications;
however,  process   formulations  apart   from  fluid
transport are general.

User's Manual
None
               Technical Assistance
               Technical   assistance
               contractual basis.
                         could  be   provided
on
References:
Canale et al  (64, 65), Freedman  (66)
*Limno-Tech  has  developed  and applied  a variety  of models  whose
characteristics depend on the  application.  Some  of  these models are
included in the references.
                                3-101

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3.6 MODEL SELECTION

     The  discussion   on  model   selection   will  be   limited  to
comparisons  among   the  three   classes   of  models   rather   than
individual  models.  We   choose  to  do  this   because  the  major
differences  lie  among  the  classes  of models  and the differences
among models in  the  same class are  relatively  small.  Moreover, the
models  in the non-linear  class  (in which  the  most  variety  among
models    exists)    contain    certain   process    formulations    and
interactions which are  still  in the research phases where  they are
being  modified  and/or   refined.  Thus,  valid  comparison  of  these
models  would  be difficult   (without  actual testing),  subject  to
error, and soon outdated.

     Before  undertaking  the   model  selection   process,   one  may
develop a set  of criteria by asking the following  questions  which
in turn reflect an area of concern:

Technical concerns

     •  Does the model  simulate  the  important processes  in  the
     prototype?

     •  What  are  the  assumptions  in  the  model,   and  are   they
     consistent  with  the available  data and the understanding  of
     the  system?

     • What  are  the  data requirements  of  the model,  and  are  these
     data available or would a  field program be required?

Information transfer and ease of understanding concern

     • Are the principles and internal  operations of  the model easy
     to understand?

     • Are the results  of the model  easily  interpreted and conveyed
     to others who may not have a technical background?
                                3-102

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Resource requirement concerns

     • What  type  of personnel are needed to  operate  the  model,  and
     must  these  personnel have previous  experience with  the  model
     or the class of models?

     • How  expensive is it to  operate  the  model, and what  are  its
     computer requirements?

Availability concern

     • Is  the model available,  and how convenient  is  it  to  obtain?
     Acceptability concern

     • What is  the general  acceptability  of  these  models  in  the
     profession,  and how have they performed in the past?

Technical support concern

     •  Is  the   model   well-documented,  and  is  technical  support
available?

     Detailed  discussion  of  what  is  involved  in  each  of  these
concerns  (or  criteria)  has been  presented in  Chapter II,  Book  1,
dealing  with  conducting  waste  load   allocations  on  streams  and
rivers  where BOD/DO is  the  principal water  quality  issue.  The
reader is referred to that report for this information.

     We will  proceed to apply  these  criteria to the  three  classes
of eutrophication models  and  to compare the models with  respect  to
these  criteria.  We  will  not  discuss   the   technical   criteria
presented  in  previous  sections.  However,  it  is  important  to  note
that   the   steady-state   completely   mixed  assumptions  for   the
simplified  models only  provide  a basis for correlating  field  data.
Therefore,  these models   are  essentially  empirical   and  they  are
therefore  limited by the  range of  conditions for which  they  prove
successful, rather than those assumptions.
                                3-103

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     Table  3-17  shows how  the  models compare  with respect  to  the
non-technical  criteria.  The  table  indicates that  if the  criteria
were  taken  as  a  whole,   then  the  preferred  class  would  be  the
simplified  models,   and  the  least  preferred  class  would  be  the
dynamic non-linear models.  The  key criteria  affecting this  outcome
are   the   simplicity  and  ease  of   application   (low   resource
requirements)  of  the simplified  models.  Indeed,  the   simplified
models have  experienced widespread application  compared  to  the more
complex models. Based on  this comparison,  it would appear  that  the
more complex models  would  be selected only when  technical  criteria
dominated  the  selection  process.   Such  conditions  could  possibly
occur under one or more of the following conditions:

          •  it is essential  to  simulate  the  dynamic response of  the
          receiving water

          •  spatial   non-uniformities   in  the  response   of  the
          receiving water  body  are  clearly the result of  different
          processes or a  mix of processes being important

          •  the   resource  is  highly  significant  with  respect  to
          beneficial  use   and  therefore  the  relative  cost/benefit
          ratio  of   applying   the   dynamic   non-linear  models   is
          reasonable

          •  the  water  body  is complex  and therefore  requires  a
          comprehensive management  plan  keyed  to and evaluated  on
          the basis of controlling specific processes.

This illustration of  conditions under which  the  dynamic non-linear
models may  be  more  appropriate presupposes  a  philosophy that  the
deterministic process of applying a  specific  model  in a  technically
sound  manner  is  a  preferred  basis  for  simulating  teal  world
effects.   In  the  case  of  eutrophication  models  there   is  some
controversy  about their  current  predictive cap-ability  and  much
less controversy that, as our understanding of the processes
                                3-104

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Table 3-17. NON-TECHNICAL CRITERIA APPLIED TO CLASSES OF
            EUTROPHICATION MODELS

                                    Time Varying        Dynamic
                       Simplified   Mass Balance      Non-Linear

Information transfer      easy          easy           difficult
And ease of under-
Standing

Resource requirements     low         moderate           high

Availability              good          good             good

Acceptability             high        moderate         moderate

Technical support         good          good             good
                                3-105

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affecting eutrophication  improves,  these models  will  serve an  ever
more significant analytic function.
                                3-106

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                             SECTION  4.0
                          DATA REQUIREMENTS
4.1 INTRODUCTION

     The  type,   amount  and  quality  of  data  used  in  a  wasteload
allocation  decision  where  the   receiving   water   is   a  lake  or
impoundment  and  where  the  water  quality  concern  is  potential
eutrophication will depend  on  a number of  factors.  Frequently,  the
most important consideration is the  availability  of  funding for the
study.   In  some  cases   the   physical,   chemical,   and  biological
characteristics of the  lake itself are a consideration  of  equal or
greater importance (this  consideration relates  directly to  the type
of model  chosen and  the  model's   subsequent  data needs, i.e.,  for
calibration/verification).  Another consideration  is  the nature  of
the causal  relationship between nutrient  loads  and  lake response.
Some general  comments  about the effects of  these considerations on
data  requirements are presented  below.  Following  these  general
comments  more  specific  guidance  on  the  sampling  and  analysis
programs that may be  required is discussed.
4.2 GENERAL CONSIDERATIONS

     Availability  of  funding  may  limit  the  amount  of  new  data
collected   for   eutrophication  analysis.  Detailed   sampling   and
analytical  programs  require  relatively  large  amounts of  funding,
which  may  not  be  available   for   a   specific  project.   Funding
unavailability may  restrict the  collection of  data  in both  large
and small lakes. A large  lake may be  fed by a number  of tributaries
and may contain areas of restricted circulation, both of which may
                                 4-1

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require  detailed  sampling  to  completely  define the  lake and  its
eutrophication  response.  The  limited  availability  of  financial
resources  may  require  that   the  number  of  stations  and/or  the
frequency of  sampling be restricted.  For  small lakes,  funding  may
be so  restrictive  that site-specific studies might be  limited  to a
site reconnaissance and  the collection  and analysis  of samples  from
a  few  well-conceived  stations  and during  critical  periods.   Of
course,  funding  restrictions  could  limit  site-specific  activities
to only  the site  reconnaissance  data.  In  such  a  case  the  loading
data would have to be developed from literature sources.

     Specific  physical,   chemical,   and  biological  characteristics
may also  determine  the need for additional  sampling  and analytical
services.  On  one  hand, the  ambient  water  quality  of  a  small
completely  mixed  lake probably could  be   characterized  by sampling
and analysis  at  a  single station  near the  center  of  the  lake.  On
the  other  hand,  an  elongated  impoundment stretching many  miles
along  a  submerged  river gorge  could  not  be  characterized  by  a
single  in-lake  sample and might require  several samples  along  the
longitudinal  axis  of  the impoundment.  In  addition,  the  choice  of
available modeling  approaches  and  their different demands  for  data
used  in calibration/verification  is primarily  determined by  lake
characteristics,  although economics  also may play  an  important  role
in model  selection.  Again,  a  small  completely mixed  lake  might  be
best  modeled  by  a  simple mass  balance formulation.  A large  lake
with many tributary,  point  and non-point  source inputs and regions
of restricted  circulation would  be most amenable to  a more complex
application of  the time variable  mass  balance  formulations or  one
of the non-linear
                                 4-2

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eutrophication  models.   Obviously,   the  non-linear   model   would
require  a large  number  of measurements  to  achieve   some  desired
level of reliability.

     As  previously   discussed   in  the  report,   a   good  general
methodology  to   approach  eutrophication  analysis   is   to   begin
analyzing  the  situation  with  literature  information  to obtain  a
preliminary understanding of the  causal  relationships in the  lake
of  interest.  During  this  process,  it may  be  possible   to  reduce
additional  data   collection   and   analysis   activities.  Such   a
reduction  could  result from at  least  two activities.  A  literature
review may uncover baseline  data  for  the  lake which  could  reduce
the  need  for  additional  data  collection  efforts. Furthermore,  a
literature review and  interpretation  may allow  you  to  select  and
ignore  less  important   processes   and/or   factors  affecting  the
eutrophication process.  For instance,   a  calculation  of  the  source
loadings  into   the  lake  using  literature  data  may   show  that  a
certain  tributary source is unlikely to  contribute  much  to  its
nutrient budget.  Consequently,  it  may be possible  to  eliminate  the
sampling of that  tributary and  to  assign it  the  values  calculated
from literature sources.

4.3 SPECIFIC CONSIDERATIONS IN DETERMINING DATA REQUIREMENTS

4.3.1 Problem Identification/Description

     The  initial  step of  any  waste allocation  study  is  to  define
the  nature and the  extent of  the  problem.  Obviously, the  present
and/or potential  eutrophication of  a  specific lake  or impoundment
is  the  dominant  question.  Data  collection and  analysis can  help
define aspects of  the  eutrophication problem  and provide  insight to
the dominant causal relationships.  As
                                 4-3

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mentioned above,  data  can be  gathered  from existing sources  or it
can be collected as part of the project.
     Potential sources of existing data include (67):

          • state lake classification surveys

          • national eutrophication survey

          • U.S. Geological Survey

          • National Oceanic and Atmospheric Administration

          • U.S. Soil Conservation Service

          • U.S. Fish and Wildlife Service

          • U.S. EPA regional offices and STORET data base

          •  state  agencies with  responsibilities corresponding  to
          the federal agencies listed above

          • county health agencies

          • area-wide water quality management agencies

          • water and wastewater treatment plant operators

          • research and educational institutions.

     It may  be possible  to glean  from all  these  sources  all  the
information necessary  to  define the problem.  Information  needed  to
define the problem includes (67):

   1.   summary,  analysis,   and  discussion  of  historical  baseline
       limnological  data

   2.   presentation,  analysis,  and discussion of one  year of current
       baseline  limnological data

   3.   trophic condition  of  lake

   4.   limiting  algal  nutrient
                                 4-4

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   5.   hydraulic  budget  for  lake

   6.   phosphorus budget  (and a  nitrogen budget  when nitrogen  is
       limiting nutrient)  for  lake

     Minimum  requirements  for one  year  of  limnological data  have
been developed by  the U.S.  EPA as part of the  Clean  Lakes  Program.
The requirements are listed in Table 4-1. The  data needs  listed in
Table  4-1  are comprehensive and  should  enable  the analyst  to  gain
some  understanding  of  in-lake  processes  and  to  determine  the
trophic  condition  of   the   lake  and  the  limiting  nutrient  (see
Section  3.1). General  methodologies  for  determining  a  nutrient
budget have been previously described  in this  report  (see  Section
3.1 also) . Lee and Jones  (68)  suggest that water  samples  should be
collected  on  a  weekly  or  no less  than biweekly  basis from  each
tributary  of  the  water  body  which  is  expected  to  contribute  ten
percent  or more  of the  total nitrogen  or  phosphorus input  to  the
water  body.   These  samples  should  be  collected  at   a  point
immediately upstream  of any  backwater  area of  the water body  and
near  a  point suitable  for  tributary  discharge  measurements.  In
addition,  they   note  that  special  measurements  need to  be  taken
during   high-flow   periods,   as   these   flows  often  transport   a
substantial portion of  total  nutrient  input.  They  caution  that
because  most  of  these  nutrients  may be  associated  with  particulate
matter,  the  additional  load of   available   forms   of  nutrients
introduced during high flow may be minimal.

     Reckhow  (69)  has  recently reviewed  the  data on  the  tributary
sampling  frequency required   to  adequately define  the  phosphorus
flux into  a lake.  Ac-cording to his literature evaluation  it would
appear that a  concentration
                                 4-5

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      Table 4-1.  BASELINE LIMNOLOGICAL MONITORING PROGRAM
1.  Sampling Station  Location  - A single  in-lake  site located in
   an  area  that best  represents  the  linnological  properties of
   the lake, preferably the deepest point in the lake. Additional
   samples may be warranted in cases where lake basin morphometry
   creates  distinctly  different  hydrologie  and  limnologie  sub-
   basins; or where  major  lake tributaries  adversely affect  lake
   water quality.

2.  Sampling Depth  - Samples  must be  collected  between one-half
   meter below the  surface  and one-half meter  of the bottom, and
   must  be  collected  at  intervals of every  one  and one-half
   meters, or at six equal depth intervals, whichever number of
   samples is less.

3.  Sampling  Frequency   -  Sample  monthly  during  the  months of
   September  through  April  and  biweekly  during  May  through
   August.  The   sampling  schedule  may be  shifted  according to
   seasonal  differences  at   various   latitudes.   The  biweekly
   samples  must be  scheduled  to  coincide  with  the  period of
   elevated biological  activity.  If possible,  a  set  of samples
   should be  collected immediately following  spring turnover of
   the lake.

4.  Sampling Period  - Samples  must be  collected  between 0800 and
   1600 hours of each  sampling day unless diel  studies are  part
   of the monitoring program.

5.  Chemical Constituents - All samples must be analyzed for  total
   and  soluble   reactive  phosphorus,  nitrite,   nitrate,  ammonia,
   and  organic  nitrogen,  pH,  temperature and  dissolved oxygen.
   Representative alkalinities should be determined.

6.  Biological  Constituents  -  Samples  collected   in   the   upper
   mixing zone must  be  analyzed  for chlorophyll a.. Algal biomass
   in  the  upper mixing zone  should be  determined through  algal
   genera  identification,   and cell  density  counts  (number of
   cells per milliliter),  and converted to  cell  volume based on
   factors  derived  from  total  measurements,   then  reported in
   terms of biomass for each major genera identified.

7.  Physical Measurements - Secchi disk  depth and suspended  solids
   must be measured  at  each sampling period.  The surface area of
   the lake covered by macrophytes between zero and the ten  meter
   depth  contour or twice  the  Secchi disk transparency   depth,
   whichever is  less, must  be reported. In  addition, the surface
   area,  the  maximum  depth,   the average  depth,   the  hydraulic
   residence  time,   the  area  of  the  watershed  (separated  into
   agricultural, urban,  and  forest)  draining  to  the  lake, the
                              4-6

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lake bathymetry  and  a hydraulic  budget  including groundwater
inflow should be determined.
                           4-7

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sampling interval of between 14 and  28  days  is  sufficient  to reduce
the standard error  of  the  annual  phosphorus flux to between 10  and
20 percent of  the  true "flux".  In terms of  confidence  intervals  at
some specified  level of  statistical  significance, we know  that  for
sample sizes greater than  six,  the "t" statistic at the  95 percent
confidence level varies  from 2.5  to 2. Consequently the  predicted
range  of  the  standard error  of   the  mean  from 10 to 20  percent
indicates  a  range  in  confidence  intervals  at  the   95  percent
confidence level  from  25  to 50  percent  for few samples  (i.e.,  6
samples)  to 20  to  40 percent for many  samples.  Reckhow offered  the
following comments  about these conclusions,  though (69):

   1.  More frequent  sampling will still  reduce uncertainty  in  the
      phosphorus concentration,  but at a reduced efficiency.

   2.  Less  frequent   sampling   can   still  be   used   to   estimate
      phosphorus   concentration,   but   at   a    greater   risk   of
      significant error

   3.  Sampling should not be systematic with respect to time (e.g.,
      every two weeks)  . A  better  approach is to establish  sampling
      as systematic with respect  to  flow, with  a random start.  This
      means  that  the  year  should  be  divided  into  n equal  flow
      periods,   for  the purpose  of  taking  n concentration  samples
      per year.

   4.  Consideration  should  be  given   to  a  separate  storm  event
      sampling  program,  particularly  if  it   is  believed  that  a
      significant   fraction   of   the   phosphorus  mass    flux   is
      transported during a few major events.

     If the sampling program is  random,  i.e.,   in choosing  a set  of
n observations, every possible combination of n observations should
have  an  equal  chance  of  being   selected,  then  it  is  possible  to
select  a  statistically  significant   sampling  frequency   with   a
specified confidence level  (70) .  This  estimate   can be  made  if  data
are available  to  characterize the  statistical   distribution  of  the
chosen parameter (typically normal or log normal). If

-------
this data is not  available,  it  is possible to estimate the sampling
frequency if  an  estimate  of the  range  of parameter  values  can be
made.
     Suppose  it  is  desired  to  obtain  an  estimate  of  the  mean
concentration  (of  a normal distribution)  of  the  desired parameter
within some specified  error range  at  a certain level of  statistical
significance.  The specified error range, E, can be calculated:

                            E = + taS                          (4-1)
where ta  denotes the student's t value for a  specified  a  and Sx is
the standard error of the mean as determined by:

                            S_ = VsMl  -  n)                    (4-2)
                                   n      N
where S2 is  the  sample variance,  n  is the number  of units sampled
and N is  the total number  of  units in the population.  An equation
for n can be derived from equations  (4-1)  and  (4-2) as below:

                            n =      1                          (4-3)
                                _E-_+ 1
                                ta2S2
To obtain an estimate  of  n,  an estimate of the population variance,
S2,   must  be  generated.  If  previous  data  is   not  available,  an
estimate  can  be  generated  from  R,   the  estimated  concentration
range:

                            S2 =  (R)2                           (4-4)
                                 4-9

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This  procedure  could  be  used to  predict  the  sampling  frequency
necessary   to   adequately   define   input   as  well   as   in-lake
concentrations.
4.3.2 Model Operation (Including Calibration/Verification)
     The  three  levels  of  models  discussed  in  this  report  have
varying  data   requirements   for  their  operation.   Various   data
requirements for  these  models are  listed  in Table 4-2.  Values  for
some of  the required data,  usually determined  from  field  work  or
literature  reviews,   are   generally held  constant  throughout  the
calibration/verification  stage  of  model operation.  Morphological,
hydrological,  climatological,  and  nutrient   loading  data  would
typically  fall  into this  category.  Values  for  the  kinetic and/or
stoichiometric  coefficients,  on  the other  hand,  may be  adjusted
during calibration  studies in  order that  the  predicted values  of
the state  variables  correspond closely  with the actual  values.  An
example  of  such   a  parameter  is  the   net   sedimentation   rate
coefficient  used in the  simple  mass   balance  approach.  Although
recommended  values   of  that  parameter  can  be  obtained  in  the
literature   (initial  values  for  these  coefficients  are  usually
obtained from  the literature) ,  the output of model runs  using this
value may  not  accurately resemble  the  collected data. In  the case
where  sufficiently   large  differences  exist  between  predicted  and
actual values,  the   value  of the  net  sedimentation  rate  could  be
adjusted so  that  model  output more closely  matches actual  data.  Of
course, if  the  value of the  net  sedimentation rate  is well beyond
the range  of values  generally used  one  should review the  data  and
analysis in an effort to explain and support the selected value(s).
                                4-10

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                                               Table  4-2.  DATA NEEDS  FOR  DIFFERENT  MODEL  TYPES
Model Element
                                                                                 Model  Type

                                                                         Time Variable  Mass  Balance
                      Volume, Average Depth, Surface Area
                      Inflow  (tributaties, groundwater,
                      Precipitation) and Outflow (evaporat-
                      ion and discharge)  (average Annual
                      Values)
Volume, Average Depth,  Surface Area
(possibly some bathymetric information)
                                                                                                            Volume, Average  Depth, Surface Area, Bathymetry
                      Tributaties, Groundwater, Precipitation,
                      Urban Runoff, Wastewater Treatment Plant,
                      Septic Tank Seepage (average annual
                      Vp 1 1 1 r=> a 1
Nutrient Loading
Climatology
Limnology              (No measure of ambient limnological
 (in-lake processes)   parameters reguired, but an estimate
                      of the net sedimentation rate coeffi-
                      cient is reguired)
Same for S.M.B except that averaging
Period may depend on time-step
None Reguired
No measure of ambient limnological
parameters reguired,  but
estimates of a first-order lumped
settling term and a lumped internal
nutrient source coefficient are
reguired)
Same for S.M.B except that averaging
Period may depend on time-step
Ambient Air and Water Temperature,  Insolation,
Average Wind Speed

(Measurements for a large number of limnological
parameters may be reguired.   These  could  include
total and soluble reactive phosphorus;  nitrate,
nitrite, ammonia and organic nitrogen;  silica;
phytoplankton; and zooplankton;  carbon  dioxide
and oxygen concentrations.  Estimates  for a  large
number of stoichiometric and rate coefficients
may be reguired.  Such coefficients may include
light extinction coefficients,  temperature
coefficients, half-saturation coefficients,
nutrient to chlorophyll a ratios,  etc.  In
addition, horizontal and vertical dispersion
coefficients as well as advective flow  terms
nn ' need to be determined.
                                                                               4-11

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4.3.3 Simple Mass Balance Models

The simple mass-balance models  require  the  least data.  Those models
assume that:  1)  the  lake  is completely mixed;  2)  conditions in the
lake are  steady-state;  3)  only total nutrients  (both  dissolved and
particulate)   are  important;  4)   net  sedimentation  of  nutrients
occurs; and  5)  in-lake phosphorus  concentrations which  define the
boundaries between  oligotrophic,  mesotrophic,  and  eutrophic  lakes
can  be determined.  This  approach  results  in  one  equation  which
expresses phosphorus concentra-tion in  terms  of areal  loading rate,
net sedimentation coefficient,  average  depth,  and the  reciprocal of
the hydraulic  residence time.  This  equation  is  then  rearranged to
form  an  expression  for  total  phosphorus  loading  rate  and  then
evaluated  at  the two  phosphorus"  concentrations chosen  to define
trophic state  boundaries.  This results  in  two  equations defining
the  permissible  loading   at  which  the  lake  will  be  eutrophic,
mesotrophic,   or  oligotrophic.   The  analyst   then  compares   the
measured  or  estimated  total nutrient  loading  with the  calculated
permissible loading  derived from the  two equations to  predict the
expected  trophic  state  of the lake. The  data  requirements for  this
process are  restricted to:  1) basic  physical  characterization of
the lake  (average depth,  surface area,  volume,  net outflow rate);
2)  net sedimentation rate;  3)  average  total  nutrient budget; and 4)
allowable  total  nutrient  boundaries  defining  different  trophic
states.

     Methods  for  determining the  physical characteristics of  lakes
have been discussed  in this  report and elsewhere  (67) .  Possible
values  for   the  net   sedimentation  rates  have   been  suggested
previously  in  Sections  3.2  as  discussed  above.  A  check  on  the
accuracy of any choice for this value can be
                                4-12

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made  during  the  calibration  analysis.  A  variety  of  techniques
requiring field  and/or  literature  data  is  available for determining
the nutrient  budget. Even  though these  simple  models may  require
nothing more  than  annual  average nutrient budgets,  it  is important
to obtain accurate nutrient budget data, if possible.

     Allowable  total nutrient  concentration  criteria  defining  the
various  trophic states have  been discussed  previously  in  Section
3.2.  These  criteria may  also  be  defined by  using  the  background
data  collected  in the  problem identification/description phase  to
develop  relationships   between  total   nutrient  concentrations  and
Secchi   disk,   dissolved  oxygen,   phytoplankton   numbers,   and
chlorophyll a measurements.
4.3.4 Time Variable Mass Balance Models

The  data  requirements   for   the   simplest   formulation,   e.g.,   a
completely  mixed  lake,  of  the time  variable  model  can  be  very
similar to the simple mass balance  model  described above.  The major
difference  is  that  the  time  variable  models would  allow and,  of
course,  require   the use  of  the   nutrient  input  data on  a  time
variable basis rather than an  average  annual  basis.  This difference
may be minimal because the nutrient loading data used in the  simple
mass  balance models must  be  representative and must  adequately
incorporate  temporal   variations   in  nutrient   loading.   Another
difference is that  the  time  variable model requires  values  for the
lumped first order  settling term, V,  and  the  lumped internal  source
of nutrient parameter, Bs, while the  simple mass balance models re-
quire only  a net sedimentation term. As  with  the net sedimentation
coefficients initial  values  for V  and  Bs can be  obtained  from the
literature.
                                4-13

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Values of  these  coefficients  that are appropriate  for  a particular
lake  can  then be  obtained during  the  calibration stage  of  model
operation.

     Operationally  the major  benefit  of  the  time  variable  mass
balance model  is that  it  allows the  analyst  to use  time  variable
data  in  the calibration/ verification phase  of his  analysis.  That
is, the analyst  can use the solutions of the  model as  well  as the
appropriate   parameters    to    calculate   the    total   nutrient
concentration  on   a   daily,   weekly,  monthly,   and/or  any  other
appropriate  temporal  basis.  The  analyst  will  presumably  collect
data at least as frequently as the time  steps of  his  model.  Larger
differences  in   the  size  of  the data base required  for  the  time
variable or  simple  mass balance models can arise  when  the  physical
characteristics  of  the lake require  it  to be  segmented vertically
or  horizontally. For  example,  analysis   of a very deep lake  may.
require the  segmentation  of the lake into  several  distinct layers,
requiring    separate    physical,    chemical,    and    biological
characterization.   While   the   differences  in   data   requirements
between the  simple  and  the  time  variable  mass  balance  models  may be
small, the  likelihood  is  that  more data would be  collected for the
time-variable model because it  allows more  explicit use of  a larger
data set in  the  calibration/verification  phases.  On the other hand,
all  the  lake  data for  any  one  year   and/or  source  are  lumped
together in the  simple mass-balance formulations.

     Because of  the  need  to correlate  total nutrient concentrations
with  other  parameters  of  interest  including  dissolved  oxygen,
Secchi disk, chlorophyll  a., and phytoplankton  numbers,  measurements
of the parameters detailed in Table 4-1 need to be implemented.
                                4-14

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4.3.5 Non-Linear Eutrophication Models

As  previously discussed  in  Sec-tion  3.5  a  wide  variety of  non-
linear  models have  been  developed and  applied  to  a  variety  of
situations. Most of  the  models deal explicitly with  only  the lower
members of the food  chain  (e.g.,  up to zooplankton),  although other
models  deal   with  members  of  the  aquatic  food  chain up   to  and
including  fish.  Most models  have the capacity  for one-,   two-,  or
three-dimensional  analysis.  Because of the  wide variety  of  models
available  and  the  diversity  of  options  within  each  individual
model,   it  is  not   possible   to   explicitly   detail   the  data
requirements  of  non-linear  eutrophication  models  in general.  For
specific discussions  of  the data  requirements for  selected models,
the  reader is  encouraged  to  examine  the  calibration/verification
efforts listed in  (56, 57, 58, 59, 24).
                                4-15

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Development  Group WSDG Technical Paper - 00001.
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                                                           3 RiClfiENT'S ACCiSSiQM
4. TITLE ANOSUSTlTiE
  Technical Guidance Manual for Performing Waste  Load
  Allocations,  Book IV, Lakes and Impoundments, Chapter
  2, EutrophicafIon
                                                                   OATi
                               6.
                                           ORGANIZATION COO£
J. AUTMORlS!
  John L. Jtancini
  Cary_Kaufman
Peter A. Mangarella
Eugene P. Driscoll
8 PERFORMING ORGANIZATION fl£PQRT

  60495A/2000
;9. f*£B£OHM»NG ORGANIZATION NAME AND
  Woodward-Clyde  Consultants
  S3 Embarcadero  Center,  Suite 700
  San Francisco,  CA 94111
                                ID, ?«oa*AM ELEMENT NO.
                                 853B2F
                                               NO
                                                           I  68-01-5918
 12. SPONSORING AGENCY NAME AND AOO^ESS
  Monitoring  and  Data  Support Division
  Office of Water Regulations and Standards
  U.S. Environmental Protection Agency
 _V as hi ng ton  D. C. 20460	
                                1*. SPONSORING ACENCV COOi
                                 EPA/700/01
15. SUPPLEMiNTARY NOT1S
16, ABSTRACT"   _           "  :    :                            ~	"	~~~	~

  Waste Load Allocation studies are conducted  by  state agencies under the  guidance
  of the EPA region to  determine NPDES effluent Hesitations and therefore  the  level
  of treatment  required by Publicly Ovned Treatment  Works to protect the beneficial
  uses of  the receiving waters.  The report provides guidance on  conducting studies on
  lakes and iopoundments when the water quality issue is eutrophicatlon and resulting
  decreases in  water quality occur.  (Other manuals  have and will cover different
  problems, e.g., BOD/DO relationships and toxics  in streams.)  This manual discusses ,'
  problea  identification, basic principles of  eutrophication analysis in lakes,  data
  requlrenents, model types and availability,  selection of a model and key inpyt
  parameters, model calibration and verification,  assessing uncertainty in model
  projections,  and  allocating waste loads.           •  •
                                KEY KVOBOS AND OOCUMiMT ANALYSIS
                                                    f tiSS-QPf N IMOSO TE WMS |c  COSATl I ICld CtOup
  Limnology
  Sewage Treatment
  Waste Water
  Mathematical Modeling
  Water Pollution  .
  Regulations
                    Waste  Load Allocation
                    Publicly Owned Treatmen
                      Works
                           Effluent
                      Limitations
                08/D
                08/H
                06/r
11, 01STRi'SufiOw'STATCMENT
  Release to the Public
                  ta. SECURITY" C'LASS iT'ut"Report>
                  _ Unclassified __
              11. NO. Of PACTS"
                  28 SECURITY" CWASS t
                     Unclassified
                                                                         32.
 IP* Cwi* J238-I (R»», <»77)
                              CDITION ti
                                            R-7

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                                   DISCLAIMER
We have made efforts to ensure that this electronic document is an accurate reproduction
of the original paper document. However, this document does not substitute for EPA
regulations; nor is it a regulation itself. Thus, it does not and cannot impose legally binding
requirements on EPA, the states, tribes or the regulated community, and may not apply to
a particular situation based on the circumstances. If there are any differences between this
web document and the statute or regulations related to this document, or the original
(paper) document, the statute, regulations, and original document govern. We may change
this guidance in the future.

Supplemental material such as this disclaimer, a document abstract and glossary entries
may have been added to the electronic document.
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                                    GLOSSARY

Advection - Bulk transport of the mass of discrete chemical or biological constituents by
fluid flow  within a receiving  water. Advection describes the  mass  transport due to the
velocity, or flow, of the waterbody.
Aerobic - Environmental conditions characterized by the presence  of dissolved oxygen;
used to describe biological or chemical processes that occur in the presence of oxygen.
Algae  - Any organisms of a group  of chiefly aquatic microscopic nonvascular plants; most
algae have chlorophyll as the primary pigment for carbon fixation. As primary producers,
algae serve as the base  of the  aquatic food web,  providing food for zooplankton and fish
resources. An overabundance of algae in natural waters is known as eutrophication.
Algal bloom - Rapidly occurring growth and accumulation of algae within a body of water. It
usually results from excessive nutrient loading and/or sluggish circulation regime with a long
residence  time. Persistent and frequent bloom can result in low oxygen conditions.
Ambient water quality - Natural concentration of water quality constituents prior to mixing
of either point or nonpoint source load of contaminants. Reference ambient concentration is
used to indicate the concentration of a chemical that will  not  cause adverse impact to
human health.
Ammonia - Inorganic form  of nitrogen; product  of hydrolysis of organic nitrogen  and
denitrification.  Ammonia is  preferentially used by phytoplankton over nitrate for uptake of
inorganic nitrogen.
Anaerobic -  Environmental  condition  characterized  by zero oxygen  levels.  Describes
biological and chemical processes that occur in the absence of oxygen.
Anoxic - Aquatic environmental conditions containing zero or  little dissolved  oxygen.  See
also anaerobic.
Aquatic ecosystem - Complex of biotic and abiotic components of natural waters.  The
aquatic ecosystem is an  ecological unit that includes the physical characteristics (such as
flow or velocity and depth), the biological community of the water column and benthos,  and
the chemical characteristics such as dissolved solids, dissolved oxygen, and nutrients. Both
living  and  nonliving  components of the aquatic  ecosystem  interact and  influence the
properties and status of each component.
Attached  algae  -  Photosynthetic organisms that  remain in  a  stationary location  by
attachment to hard rocky substrate. Attached algae, usually present in shallow hard bottom
environments,  can significantly influence nutrient uptake and diurnal oxygen variability.
Bacteria - Microscopic, single-celled or noncellular plants, usually saprophytic or parasitic.
Benthal Demand - The demand on dissolved oxygen of water overlying benthal deposits
that results from the upward diffusion of decomposition products of the deposits.
Benthic -  Refers to material, especially sediment, at the bottom of an aquatic ecosystem. It
can be used to describe the organisms that live on, or in, the bottom of a waterbody.
Benthic organisms - Organisms living in, or on, bottom substrates in aquatic ecosystems.
Biomass - The amount, or weight,  of a species, or group of biological organisms, within a
specific volume or area of an ecosystem.
Boundary conditions - Values or functions representing  the state of a system at its
boundary limits.

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Calibration  -  Testing  and tuning of a model to a set of field data not used  in  the
development of the model; also includes minimization of deviations between measured field
conditions and output of a model by selecting appropriate model coefficients.
Chlorophyll - Green  photosynthetic pigment present in many plant  and some bacterial
cells. There are seven known types of chlorophyll; their presence and abundance vary from
one group of photosynthetic organisms to another.
Coastal Waters  - Those waters surrounding the continent which exert  a measurable
influence on uses of the land and on its ecology. The Great Lakes and the waters to the
edge of the continental shelf.
Coliform bacteria - A group of bacteria that normally live within the intestines of mammals,
including humans. Coliform bacteria are used as an indicator of the presence of sewage in
natural waters.
Combined sewer overflows (CSOs) -  A combined  sewer carries both wastewater and
stormwater  runoff.  CSOs  discharged  to  receiving  water  can  result  in  contamination
problems that may prevent the attainment of water quality standards.
Concentration - Amount  of a substance or material in  a given  unit volume  of solution.
Usually measured in milligrams per liter (mg/l) or parts per million (ppm).
Decay - Gradual decrease in the amount of a given  substance in a given  system due to
various sink processes including chemical and biological transformation, dissipation to other
environmental  media, or deposition into storage areas.
Decomposition - Metabolic breakdown of organic materials; the by products formation
releases energy and simple organics and inorganic compounds, (see also respiration)
Denitrification - Describes the decomposition of ammonia compounds, nitrites, and nitrates
(by bacteria) that results in the eventual release of nitrogen gas into the atmosphere.
Detritus  - Any loose material produced directly from disintegration  processes. Organic
detritus consists of material resulting from the decomposition of dead organic remains.
Dispersion - The spreading of chemical or biological constituents, including pollutants, in
various directions from a point source,  at varying velocities depending on  the differential
instream flow characteristics.
Dissolved oxygen (DO) - The amount of oxygen that  is dissolved  in water. It also refers to
a measure of the amount of oxygen available for biochemical activity in water body, and as
indicator of the quality of that water.
Diurnal - (1) Occurring during a 24-hr period;  diurnal variation. (2) Occurring during the day
time  (as opposed to  night time). (3)  In  tidal hydraulics,  having  a period or cycle of
approximately one tidal day.
Domestic  wastewater  -  Also  called  sanitary wastewater,  consists  of wastewater
discharged from residences and from commercial,  institutional, and  similar facilities.
Drainage basin - A part of the land area enclosed by a topographic divide from which direct
surface runoff from  precipitation normally  drains by  gravity into  a receiving water. Also
referred to as watershed, river basin, or hydrologic unit.
Dynamic model - A mathematical formulation describing the physical behavior of a system
or a process and its temporal variability.
Ecosystem  - An interactive system that includes the organisms  of a natural community
association together with their abiotic physical, chemical, and  geochemical environment.

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Epilimnion - The water mass extending from the surface to the thermocline in a stratified
body of water; the epilimnion is less dense that the lower waters and is wind-circulated and
essentially homothermous.
Estuary - That portion  of a coastal stream influenced by the tide of the body of water into
which it flows; a bay, at the mouth of a river, where the tide meets the river current; an area
where fresh and marine water mix.
Euphotic Zone - The lighted region of a body of water that extends vertically from the water
surface to the  depth at which photosynthesis fails to occur because  of insufficient light
penetration.
Eutrophication - Enrichment of an aquatic ecosystem with nutrients (nitrates, phosphates)
that accelerate biological  productivity (growth of algae  and  weeds) and an undesirable
accumulation of algal biomass.
Eutrophication model - Mathematical formulation that describes the advection, dispersion,
and  biological, chemical,  and  geochemical reactions  that  influence  the  growth and
accumulation of algae in aquatic ecosystems. Models of eutrophication typically include one
or more species groups of algae,  inorganic and organic nutrients (N,P), organic carbon, and
dissolved oxygen.
Extinction  coefficient - Measure for the reduction (absorption) of light  intensity within a
water column.
Flux - Movement and transport of mass of any water quality constituent over a given period
of time. Units of mass flux are mass per unit time.
Food Chain  -  Dependence of a series  of organisms, one upon the other,  for food. The
chain begins with plants and ends with the largest carnivores.
Gradient -  The rate of decrease (or increase) of one quantity with respect to another;  for
example, the  rate of decrease of temperature with depth in a lake.
Groundwater - Phreatic water or subsurface water in the zone of saturation. Groundwater
inflow describes the rate and amount of movement of water from a saturated formation.
Half saturation constant - Nutrient concentration at which  the growth rate is  half the
maximum rate. Half saturation  constants  define the nutrient  uptake  characteristics  of
different phytoplankton species. Low half saturation constants indicate the ability of the algal
group to thrive under nutrient depleted conditions.
Heterotrophic - Pertaining to organisms that are  dependent on organic material for food.
Hydrolysis - Reactions that occur between chemicals and water molecules resulting in the
cleaving of a  molecular bond and the formation of new bonds with components of the water
molecule.
Kinetic processes - Description of the rate and mode of change in the transformation or
degradation of a substance in an ecosystem.
Limiting  Factor -  A factor whose  absence, or excessive  concentration,  exerts  some
restraining influence upon  a population through incompatibility with species requirements or
tolerance.
Load allocation (LA) - The portion of a receiving water's total maximum daily  load that is
attributed either to one of its existing or future nonpoint  sources of pollution or to natural
background sources.
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Loading,  Load, Loading rate  - The total amount of  material  (pollutants) entering the
system from one or multiple sources; measured as a rate  in weight per unit time.
Low flow (7Q10) -  Low flow (7Q10)  is the 7 day average  low flow occurring once in 10
years; this probability based statistic is used in  determining stream design flow conditions
and for evaluating the water quality impact of effluent discharge limits.
Macrophyte - Large vascular rooted aquatic plants.
Mass balance - An equation that accounts for  the flux of mass going  into a defined area
and the flux of mass leaving the defined area. The flux in must equal the flux out.
Mathematical model - A system of mathematical expressions that describe the spatial and
temporal distribution of water quality constituents resulting from  fluid transport and the one,
or more, individual processes and interactions within some prototype aquatic ecosystem. A
mathematical water quality model is used as the  basis for waste  load allocation evaluations.
Mineralization - The process by which elements combined in organic form in living or dead
organisms are eventually reconverted  into inorganic forms to be made available for a fresh
cycle of plant growth. The mineralization of  organic compounds  occurs through combustion
and  through metabolism  by living  animals.   Microorganisms are ubiquitous,  possess
extremely  high growth rates and have the ability to degrade all naturally occurring organic
compounds.
Modeling  - The  simulation of some physical  or abstract  phenomenon  or system with
another system  believed to obey the same  physical  laws or  abstract  rules of logic, in order
to predict the behavior of the former (main system) by experimenting with latter (analogous
system).
Monitoring  -  Routine  observation,  sampling   and testing of  designated  locations or
parameters  to  determine  efficiency  of treatment or  compliance with  standards  or
requirements.
Nitrate (NO3) and Nitrite (NO2) - Oxidized  nitrogen species. Nitrate  is the form of nitrogen
preferred by aquatic plants.
Numerical model - Models that approximate  a solution of governing partial  differential
equations  which  describe a  natural  process.  The approximation  uses  a  numerical
discretization of the space and time components of the system or process.
Nutrient - A primary element necessary for the growth of living  organisms. Carbon dioxide,
nitrogen, and phosphorus, for example, are required nutrients for phytoplankton growth.
Nutrient limitation - Deficit of nutrient  (e.g., nitrogen  and phosphorus) required  by
microorganisms in order to metabolize organic substrates.
Organic -  Refers  to  volatile, combustible,   and  sometimes  biodegradable  chemical
compounds  containing  carbon atoms (carbonaceous)  bonded together  and  with other
elements.  The principal  groups  of organic  substances found in wastewater are proteins,
carbohydrates, and fats and oils.
Organic matter - The organic fraction that includes plant  and animal residue at various
stages of decomposition, cells and tissues of soil organisms, and substance synthesized by
the soil population. Commonly determined as the amount of  organic material  contained in a
soil or water sample.
Organic nitrogen - Form of nitrogen bound  to an organic compound.
Orthophosphate  (O_PO4_P) - Form of phosphate available for  biological metabolism
without further breakdown.

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Oxidation - The chemical union of oxygen with metals or organic compounds accompanied
by a removal of hydrogen or another atom. It is an important factor for soil formation and
permits the release of energy from cellular fuels.
Oxygen Deficit - The difference between observed oxygen concentration and the amount
that would theoretically be present at 100% saturation for existing conditions of temperature
and pressure.
Oxygen demand - Measure of the dissolved oxygen used by a system (microorganisms) in
the oxidation of organic matter.  See also biochemical oxygen demand.
Oxygen saturation - Natural or artificial reaeration or oxygenation of a water system (water
sample) to bring the level of dissolved oxygen to saturation.  Oxygen saturation is greatly
influence by temperature and other water characteristics.
Partition coefficients - Chemicals  in solution are partitioned into dissolved and particulate
adsorbed phase based on their corresponding sediment to water partitioning coefficient.
Photosynthesis - The biochemical synthesis of carbohydrate based organic compounds
from  water and  carbon  dioxide  using light  energy  in  the  presence  of chlorophyll.
Photosynthesis occurs in  all  plants,  including  aquatic organisms  such as  algae and
macrophyte. Photosynthesis also occurs in primitive bacteria such as blue green algae.
Phytoplankton - A group of  generally unicellular  microscopic plants characterized by
passive drifting within the water column. See Algae.
Plankton - Group of generally microscopic plants and animals passively floating, drifting or
swimming weakly. Plankton include  the phytoplankton (plants) and zooplankton (animals).
Point source  - Pollutant loads discharged at a specific location from pipes, outfalls, and
conveyance channels from either municipal wastewater treatment plants or industrial waste
treatment facilities. Point sources can also include pollutant loads contributed by tributaries
to the main receiving water stream or river.
Primary productivity - A measure of the rate at which new organic  matter is formed and
accumulated through photosynthesis and chemosynthesis activity  of producer organisms
(chiefly, green  plants). The rate of primary production is estimated by measuring the amount
of oxygen  released (oxygen method) or the amount of carbon assimilated by the plant
(carbon method)
Quality - A term to describe the composite chemical, physical, and biological characteristics
of a water with respect to it's suitability for a particular use.
Reaeration - The absorption of oxygen into water under conditions of oxygen deficiency.
Residence time - Length of time that a pollutant remains within a section of a stream or
river. The residence time is  determined by the streamflow and the volume of the river reach
or the average stream velocity and the length of the river reach.
Respiration -  Biochemical  process by means of which  cellular fuels  are oxidized  with the
aid of oxygen to permit the  release  of the energy required to sustain life; during respiration
oxygen is consumed and carbon dioxide is released.
Scour - To abrade  and wear away. Used to  describe the weathering away of a terrace or
diversion channel or streambed. The clearing  and digging action of flowing water, especially
the downward  erosion by stream water in sweeping away mud and silt on the outside of a
meander or during flood events.
Secchi depth  - A measure of the light penetration into the water column. Light penetration
is influenced by turbidity.

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Sediment  -  Participate  organic  and  inorganic matter  that  accumulates in a  loose,
unconsolidated form on the bottom of natural waters.
Sediment oxygen demand (SOD) - The solids discharged to a receiving water are partly
organics,  and upon  settling to the bottom, they decompose  anaerobically as well as
aerobically, depending on conditions.  The  oxygen consumed  in  aerobic decomposition
represents another dissolved oxygen sink for the waterbody.
Sedimentation - Process of deposition of waterborne or windborne  sediment or other
material; also refers  to the infilling  of bottom substrate in a waterbody  by sediment
(siltation).
Simulation - Refers  to the use  of mathematical models to approximate the observed
behavior of a natural water system in response to a specific known  set of input and forcing
conditions. Models that have  been validated,  or  verified, are  then used  to predict the
response of a natural water system to changes in the input or forcing conditions.
Spatial  segmentation - A numerical discretization of the spatial component of a system
into one or more dimensions; forms the basis for application of numerical simulation models.
STORET - U.S. Environmental  Protection Agency (EPA) national water quality database for
STORage and  RETrieval (STORET).  Mainframe water  quality database that includes
physical, chemical,  and biological data measured in waterbodies  throughout  the  United
States.
Storm runoff - Rainfall that  does not evaporate  or  infiltrate the ground  because  of
impervious land surfaces or a  soil infiltration rate lower than rainfall  intensity, but instead
flows onto adjacent land or waterbodies or is routed into a drain or sewer system.
Stratification (of water body) -  Formation of water layers each  with specific physical,
chemical,  and biological characteristics. As the  density of  water decreases due  to surface
heating, a stable situation develops with lighter water overlaying heavier and denser water.
Substrate - Refers to bottom sediment material in a natural water system.
Surface waters - Water that is  present above the substrate or soil surface.  Usually refers to
natural waterbodies such as rivers, lakes and impoundments, and estuaries.
Suspended solids or load - Organic and inorganic particles (sediment) suspended in and
carried by a  fluid  (water). The suspension  is  governed  by the upward  components  of
turbulence, currents, or colloidal suspension.
Toxic substances -  Those chemical  substances,  such as pesticides,   plastics,  heavy
metals,  detergent, solvent, or any other material  that are poisonous, carcinogenic,  or
otherwise directly harmful to human health and the environment.
Travel time - Time period required by a  particle to cross a transport route  such as a
watershed, river system, or stream reach.
Tributary - A  lower  order stream  compared  to a  receiving  waterbody. "Tributary to"
indicates the largest stream into which the reported stream or tributary flows.
Turbidity - Measure of the amount of suspended material in water.
Turbulence - A type of flow in which any particle may move in any direction with respect to
any other particle and  in a regular or fixed path. Turbulent water is agitated by cross current
and eddies. Turbulent velocity  is that velocity above which turbulent flow will always exist
and below which the flow may be either turbulent or laminar.
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Verification (of a model) - Subsequent testing of a precalibrated model to additional field
data usually under different external conditions to further examine model validity (also called
validation).
Waste load allocation (WLA) - The portion of a receiving water's total maximum daily load
that is allocated to one of its existing or future point sources of pollution.
Wastewater - Usually refers to effluent from a sewage treatment plant. See also domestic
wastewater.
Wastewater treatment - Chemical, biological, and  mechanical  procedures applied to an
industrial or municipal discharge or to any other sources of contaminated water in order to
remove, reduce, or neutralize contaminants.
Water Pollution - Alteration of the aquatic environment in such a way as to interfere with a
designated beneficial use.
Water quality criteria  (WQC)  - Water quality  criteria comprised numeric and narrative
criteria. Numeric criteria are scientifically derived ambient concentrations developed by EPA
or States for  various  pollutants of concern to  protect human health and  aquatic  life.
Narrative criteria are statements that describe the desired water quality goal.
Zooplankton - Very  small animals (protozoans, crustaceans,  fish embryos, insect larvae)
that live in a waterbody and are moved passively by water currents and wave action.
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