Click here for
DISCLAIMER
Document starts on next page
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
-------
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
-------
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.
-------
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
-------
ACKNOWLEDGEMENTS
The contents of this section have been removed to comply with
current EPA practice.
-------
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
-------
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
-------
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
-------
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
-------
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
-------
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
-------
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
-------
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
-------
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
-------
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
-------
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
-------
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
-------
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
-------
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
-------
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
NONACC
NITROGEN
SINKING ^
DHV
SIBLE SINKING
4
ZO
k
TO
^
OP
T RESPIRATION
DT.awKTnw
i
0
H
' C/3
LANKTON O
W
1
NITROG
DETRIT.
i
1
<:
rt
|
J
EN ORG
US ^. NIT
k
i
§
W
Q
RESPIRATION
RESPIRATION
1
MTIC
ROGEN ^. AMMC
i t
NITRATES
SINKING PHYTOPLANKTON RESPIRATION
TOTAL T
NONACCESSIBLE ^ SINKING
NITROGEN
SEDIMENTS
1
ZOOPI
j
PHOSPHORUS ^ ORGANIC ^ INORGANIC
D
i
§
' W
CANTON W
ETRITl
L i
<
D
JS PHOSPHORUS PHOSE
, i
W
Q
RESPIRATION
HORUS
L
\
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)
UJ
I
I-
Z
«
O
o
a.
oc
o
UJ
N
cr
O
z
1,0-
1.0-
(d) P/Ps
0.5-
Chterophyta
Otitoms
Flagellates
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
-------
0,56
Q.4S-
§ 0,42
0.35-
0.28-
a.
e
10
v
Q
O
a,
O
Z 0.21-
I
HI
e
O 0,14
<
0.0? -n
: to oomrtett *it»l
-.-—^ s«niele + NO3 , NHj - N + P04 - f * Trace e(em«n«
>.»«igf Sample + PO4 - P
- _ -41 S«mate, Sampie + NO, — N. 8«mo(e + NH, — N
+ Tr«ee tiwnaou, and
Actual I*kf
S 10 13
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
-------
2.0
1.5
•e
I
Cf>
ec
o
2
{£
O
0,5 •
A Daphnta Magna
X D. Schodleri
+ D, pulex
» 0, saltata
* Acartia elaus
O A. tonsa
Q Centrop*9i
• C. typicys
..-' .P*
^•""
10
15
,.....*
-...+
20
25
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
-------
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
-------
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
-------
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
-------
• 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
-------
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
-------
(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
-------
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
-------
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
-------
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
-------
u
k-
-J
J
<
c
o
Z
3
C
w
o
1.0-
0,9 —
OJ —
0.7-
0.6 —
O.S —
0.4 —
0.3—
0.2—J
0.1 —
0.0-
Lew Dsenettien Storage, Tight Soils,
Sl**P LansJ, Wet ¥«tr», Little
Rywott from Imoervioyi to
P*rvioi»
\-High
iooie Soili, Flat L»nd, Dry
¥e*rt, RyncH from lmp*rvioy|
to Ptrvioui Af«*t
Tit lit II
10 20 30 40 50 60 70 SO
90
100
PERCENT IMPERVIOUS AREA
STUDY LOCATION CODE:
^JT) ypper Whit* Rock, Oallai
(5) tower Whitt Rock, O«H»
Turtle Cr**k, Dallas
Htntjrn Cr»€k, N«w York C««¥
Soring Crmfc Eatt. New Y*fk Citv
\TJ ThurttorrSatin. N*m Vork City
(f) Fourth Craak. Knoiwillf
@ ThireCftefc, Knoxvill*
nffl Pint Cf»*k, Kne«¥ill«
@ Plantation Wills, Knoxville
nS Nor*»«mp»n,
Madison,
Tulw. Oklahoma
Durham, Norm C*fOlin»
Trout RM«. ftoanoke,
LEGEND
""""""" •* """ ' • • "Storm" Equation Ettinwtt IJ2)
»___.___. E««f>iiofl of Miller and ViaBJnsn {1 1)
Suip»et Error, Dirsaion of ProbaM* Corr»«ion
Figure 3-2. Relationship between impervious area and runoff-to-
rainfall ratio
3-12
-------
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
-------
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
-------
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
-------
10 J
•r 1-0 -
>
N
Ol
0.1 -
0.01
10 4
^ 1.0 ;
o
o
o
to
c
o
a.
w>
O
I
a.
0,1 -
0.01
0.1
*as
t
16
32
Eytrophte
• 25
• •
.X
IZ * 30
» «2 « »<§
-W- IjrTrrr-
x
85*
» Excessive
y/
/ / Perfnissible
/
S3 23-8^,
O « Ji«-
36
O'J
Oiisotrophic
O«8
10
1 n ««t 1911 or - i nd ie« «l
Trophic Sntt:
t Eutrophie
Rut and Lee 1341
T T 1 I 1 S'fT
100
T ni
1000
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
»
? -
c o
a.£
c- o
O '£
J2 —
k. D
r>
»>
U.
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
-------
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
-------
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
-------
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
-------
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
-------
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
-------
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
-------
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
-------
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
-------
implementation on virtually any computer with at
least 22K bytes of available memory.
3-97
-------
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.
-------
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
-------
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
-------
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
-------
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
-------
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
-------
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
-------
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
-------
affecting eutrophication improves, these models will serve an ever
more significant analytic function.
3-106
-------
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
-------
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
-------
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
-------
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
-------
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
-------
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
-------
lake bathymetry and a hydraulic budget including groundwater
inflow should be determined.
4-7
-------
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
-------
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
-------
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
-------
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
-------
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
-------
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
-------
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
-------
REFERENCES
1. U.S. EPA. 1974. The Relationships of Phosphorus and Nitrogen to
the Trophic State of Northeast and North-Central Lakes and
Reservoirs. National Eutrophication Survey Working Paper No. 23.
2. National Academy of Science and National Academy of Engineering.
1972. Water Quality Criteria. A Report of the Committee on Water
Quality.
3. Brezonik, P.L. 1976. Trophic classifications and trophic state
indices: rationale, progress, prospects. Report No. ENV-07-76-01.
Department of Engineering Sciences. University of Florida.
4. Dobson, H.F., M. Gilbertson, and P.G. Sly. 1974. A summary and
comparison of nutrients and related water quality in lakes Erie,
Ontario, Huron, and Superior. Journal of Fishery Research Board
Canada, 31:731-738.
5. Wetzel, R.G. 1975. Limnology. W.B. Saunders Company,
Philadelphia,
6. U.S. Environmental Protection Agency. 1979. A Statistical Method
for the Assessment of Urban Stormwater. Prepared by Hydroscience,
Inc. for the U.S. EPA, Non-Point Sources Branch, Washington, B.C.
EPA-440/3-79-023.
7. 1976. Areawide Assessment Procedures Manual. Prepared by
Hydroscience, Inc. for the U.S. EPA, Office of Research and
Development, Municipal Environmental Research Laboratory,
Cincinnati, Ohio. EPA-600/9-76-014.
8. 1977. Water Quality Assessment, A Screening Method for Non-
designated 208 Areas. Prepared by Tetra Tech, Inc. for the U.S. EPA
Environmental Research Laboratory, Athens, GA. EPA-600/9-77-023.
9. Lee, David R. 1977. A Device for Measuring Seepage Flux in Lakes
and Estuaries. Limnology and Oceanography. Vol. 22, 140.
10. Canale, R.P., L.M. DePalma, and A.H. Vogel. 1976. A plankton-
based food web model for Lake Michigan. In Modeling Biochemical
Processes in Aquatic Ecosystems. Edited by R.P. Canale. Ann Arbor
Science Publishers Inc. Ann Arbor, Michigan, pg. 33-74.
11. Rich, L.G. 1973. Environmental Systems Engineering. McGraw-
Hill, Inc. New York.
R-l
-------
12. Manhattan College. 1978. Mathematical Modeling of Natural Water
Systems. Summer Institute Notes.
13. Standard Methods for the Examination of Water and Wastewater,
American Public Health Association. 1975. Washington, B.C.
Fourteenth Edition.
14. Bole, J.B. and J.R. Allan. 1979. Uptake of Phosphorus from
Sediment by Aquatic Plants, Myriophyllum spicatum and Hydrilla
verticullata. Water Research. Vol 12, 353.
15. Kuflikowski, T. 1977. Macrophytes of the Dam Reservoir at
Goczalkowice. Acta Hydrobiology. Vol. 19, 145-155.
16. Carignan, R. and J. Kalf. 1979. Quantification of the Sediment
Phosphorus Available to Aquatic Macrophytes. Journal Fishery
Research Board Canada. Vol. 36,1002.
17. Sheldon, R.B. and C.W. Boylen. 1977. Maximum Depth Inhabited by
Aquatic Vascular Plants. Amer. Midi. Natur. Vol. 97, 248-254.
18. Jupp, B.P. and D.H.N. Spence. 1977. Limitations on Macrophytes
in a Eutrophic Lake, Lock Leven. Journal Ecology. Vol. 65, 175-186.
19. Thornton, K.W. 1977. Approaches for Assessing Eutrophication
Potentials in Reservoirs. U.S. Army Corps of Engineers Waterways
Experiment Station. Information Exchange Bulletin.
20. Conover, A.J. 1966. Assimilation of Organic Matter by
Zooplankton. Limnology and Oceanography. 11, 338-345.
21. Fischer, H.B., J. Imberger, N.H. Brooks, E.J. List, and R.C.Y.
Koh. 1979. Mixing, in Inland and Coastal Waters. Academic Press.
New York.
22. Goering, J.J. 1972. The Role of Nitrogen in Eutrophic
Processes. In Water Pollution Microbiology. Edited by Ralph
Mitchell. Wiley-Interscience. New York.
23. DePinto, J.V. et al. 1980. Phosphorus Removal in Lower Great
Lakes Municipal Treatment Plants. EPA Grant R806817-01
24. Loehr et al. 1980. Phosphorus Management Strategies for Lakes.
Ann Arbor Science Publishers, Inc. Ann Arbor, Michigan.
25. Porcella, D.B. and A.B. Bishop. 1975. Comprehensive Management
of Phosphorus Water Pollution. Ann Arbor Science Publishers, Inc.
Ann Arbor, Michigan.
26. Cowen, W.F. 1974. Nitrogen and Phosphorus Availability in Lake
Ontario Tributary Waters During IFYGL. Paper presented at
University of Waterloo Conference.
R-2
-------
27. Gakstatter, J.H., M.O. Allum, S.E. Dominquez, and H.R. Grouse.
1978. A survey of phosphorus and nitrogen levels in treated
municipal waste-water. Journal Water Pollution Control Federation.
50:718.
28. Vollenweider, R.A. 1968. The Scientific Basis of Lake and
Stream Eutrophication, With Particular Reference to Phosphorus and
Nitrogen as Eutrophication Factors. Tech. Rep. OECD, Paris.
DAS/CSI/68.27.
29. Vollenweider, R.A. 1969. Moglichkeiten und Grenzen elementarer
Modelle der Stoffbilanz von Seen (Possibilities and Limits of
Elementary Models Concerning the Budget of Substances in Lakes).
Arch. Hydrobiol. 66.
30. Vollenweider, R.A. 1975. Input-Output Models with Special
Reference to the Phosphorus Loading Concept in Limnology. Schweiz.
J. Hydrol. 37.
31. Vollenweider, R.A. 1976. Advances in Defining Critical Loading
Levels for Phosphorus in Lake Eutrophication. Mem. Inst. Ital.
Idrobiol. 33.
32. Reckhow, K.H. 1979. Quantitative Techniques for the Assessment
of Lake Quality, USEPA Office of Water Planning & Standards.
Washington, B.C., EPA-440/5-79-015.
33. Sawyer, C.N. 1971. ABC's of Cultural Eutrophication and Its
Control. Water and Sewage Works. 118, No. 9.
34. Rast, W. and G.F. Lee. 1978. Summary Analysis of the North
American (US Portion) OECD Eutrophication Project: Nutrient
Loading-Lake Response Relationship and Trophic State Indices.
USEPA, ERL. Corvallis, Oregon EPA-600/3-78-008.
35. Thomann, R.V. 1980. The Eutrophication Problem. Basic Models of
Natural Water Systems. Summer Institute, Manhattan College.
36. Chapra, S. 1975. Comment on an "Empirical Method of Estimating
the Retention of Phosphorus in Lakes" by Kirchner, W.B., and P.J.
Billion, Water Resources Research. 2 No. 6.
37. Dillon, P.J. and W.B.Kirchner. 1975. "Reply to Chapra's
Comment" Water Resources Research. 2, No. 6.
38. Dillon, P.J. and F.H. Rigler. 1975. A Simple Method for
Predicting the Capacity of a Lake for Development Based on Lake
Trophic Status. Jour. Fish. Res. Bd. Can. 32, 1519.
39. Larsen, D.P., J. Van Sickle, K.W. Malueng, and P.O. Smith.
1979. The Effect of Wastewater Phosphorus Removal on Shagawa Lake,
Minnesota: Phosphorus Supplies, Lake Phosphorus and chlorophyll a..
Water Research. 13 pp. 1259-1272.
R-3
-------
40. Gakstatter, J.H., M.D. Allurn, and J.M. Omernick. 1975. Lake
Eutrophi-cation: Results from the National Eutrophication Survey.
USEPA, ERL. Corvallis, Oregon.
41. Bartsch, A.F. and J.H. Gakstatter. 1975. Management Decisions
for Lake Systems on a Survey of Trophic Status, Limiting Nutrients
and Nutrient Loadings. American-Soviet Symposium on Mathematical
Models to Optimize Water Quality Management. USEPA Gulf Breeze ERL.
EPA-600/9-78-024.
42. Dillon, P.J., and F.H. Rigler. 1974. The' Phosphorus-
Chlorophyll Relationship in Lakes. Limnology and Oceanography. Vol.
19 (5) .
43. Chapra, S.C., and S
and its Relationship to
Resources Research. Vol.
J. Tarapchak. 1976. A chlorophyll a Model
Phosphorus Loading Plots for Lakes. Water
12, No. 6.
44. Dillon, P.J. 1974. The Application of the Phosphorus Loading
Concept to Eutrophication Research. Paper prepared for the National
Research Council of Canada by Canada Centre for Inland Waters.
45. Chapra, S.C. 1977. Total Phosphorus Model for the Great Lakes.
Jour. Environ. Engr. Divi., ASCE.. 103, 147-161.
46. O'Connor, D.J., R.V. Thomann and D.M. DiToro. 1973. Dynamic
Water Quality Forecasting and Management. U.S. EPA Ecological
Research Series. EPA-660/3-73-009.
47. Riley, G.A. 1946. Factors Controlling Phytoplankton Populations
on Georges Bank. J. Marine Res. 6(1), 54-73.
48. Riley, G.A. 1947. Seasonal Fluctuations of the Phytoplankton
Populations in New England Coastal Waters. Journal of Marine
Research. 6(2), 114-25.
49. Riley, G.A., H. Stommel, and D.F. Bumpus. 1949. Quantitative
Ecology of the Western North Atlantic. Bull-Bingham Oceanog. Coll.
12(3), 1-169.
50. O'Connor, P.S. and R.V. Thomann. 1971. Water Quality Models:
Chemical, Physical and Biological Constituents in Estuarine
Modeling: An Assessment. George H. Ward, editor. U.S. EPA Research
Series 16070 DZM.
51. DiToro, D.M. and J.P. Connolly. 1980. Mathematical Models of
Water Quality in Large Lakes Part 2: Lake Erie. U.S. EPA-600/3-80-
065.
52. Markofsky M. and D.R.P. Harleman. 1971. A Predictive Model for
Thermal Stratification and Water Quality in Reservoirs. U.S. EPA
Water Quality Office. Research Grant No. 16130 DJH.
53. Tetra Tech., Inc. 1978. Rates, Constants,
Formulations in Surface Water Quality Modeling U.S.
105.
and Kinetic
EPA-600/3-78-
R-4
-------
54. DiToro, D.M., D.J. O'Connor, and R.V. Thomann. 1971. A Dynamic
Model of Che Phytoplankton Population in the Sacramento-San Joaquin
Delta. Adv. Chem. Series 106. Amer. Chem. Soci. Wash., D.C. pp.
131-180.
55. Steele, J.H. 1965. Notes on Some Theoretical Problems in
Production Energy. In Primary Production in Aquatic Environments.
C.R. Goldman, Ed. Mem. Inst. Hydrobiol. p. 368-98. 18 supp.
University of California Press.
56. Thomann, R.V., R.P. Winfield and D.M. DiToro. 1974. Modeling of
Phytoplankton in Lake Ontario (IFYGL). Proc. 17th Conference Great
Lakes Research. International Association of Great Lakes Research.
pp. 135-149.
57. Thomann, R.V., D.M. DiToro, R.P. Winfield and D.J. O'Connor.
1975. Mathematical Modeling of Phytoplankton in Lake Ontario. I.
Development and Verification. Environmental Research Laboratory.
U.S. EPA, Corvallis, Oregon. EPA-660/3-75-005.
58. Thomann, R.V., R.P. Winfield, D.M. DiToro and D.J. O'Connor.
1976. Mathematical Modeling of Phytoplankton in Lake Ontario 2.
Simulations Using. Lake 1 Model. Environmental Research Laboratory,
U.S. EPA, Duluth, Minnesota. EPA-660/3-76-065.
59. DiToro, D.M. and W.F. Motystik. 1980. Mathematical Models of
Water Quality in Large Lakes. Part 1, Lake Huron and Saginaw Bay.
U.S. EPA Environmental Research Laboratory. Duluth, Minnesota. EPA-
600/3-80-056.
60. Chapra, S.C. and W.C. Somzogni. 1979. Great Lakes Total
Phosphorus Budget for the mid 1970's. Journal Water Pollution
Control Federation. V51 (10):2524-2.533
61. Chapra, S.C. 1980. Simulation of Recent and Projected Total
Phosphorus Trends in Lake Ontario. Journal of International Assoc.
Great Lakes Res. 6 (2):101-112.
62. Van Sickle, J. and D.P. Larsen. 1978. Modeling Phosphorus
Dynamics in Shagawa Lake. U.S. EPA Environmental Research
Laboratory. Corvallis, Oregon. CERL - 049.
63. Thomann, R.V., R.P. Winfield, and J.J. Segna. 1979.
Verification Analysis of Lake Ontario and Rochester Embayment Three
Dimensional Eutro-phication Models. U.S. EPA Environmental Research
Laboratory. Duluth, Minnesota. EPA-600/3-79-094.
64. Canale, R.P., S. Nachiappan, D.J. Hineman, and H.E. Allen.
1973. A Dynamic Model for Phytoplankton Production in Grand
Traverse Bay. Proc. 16th Conf. Great Lakes Res. Int'l Assoc, of
Great Lakes Res. 21-33.
65. Canale, R.P. and J. Squire. 1976. A Model for Total Phosphorus
in Saginaw Bay. J. Great Lakes Res. International Assoc. Great
Lakes Res. (22):364-373.
R-5
-------
66. Freedmn, P.L. et al. 1979. Assessing Storm Overflow Impacts on
Lake Water Quality. Proc. Int. Symp. on Urban Storm Runoff, pp.
115-123.
67. U.S. EPA. 1980. Clear Lakes Program Guidance Manual. U.S. EPA
440/5-81-003.
68. Lee, G. Fred and R. Anne Jones. 1980. Study Program for
Development of Information for Use of OECD Eutrophication Modeling
in Water Quality Management. A report for the AWWA Quality Control
in Reservoirs Committee.
69. Reckhow, K.R. 1978. Lake Phosphorus Budget Sampling Design.
Paper Presented at the 1978 American Geophysical Union Chapman
Conference on the Design of Hydrologie Data Networks.
70. Ponce, S.L. 1980. Statistical Methods Commonly Used in Water
Quality Data Analysis. USDA Forest Service Watershed Systems
Development Group WSDG Technical Paper - 00001.
R-6
-------
TECHNICAL REPORT DATA
(Pittse rail Instructions on iht .'event fat/am catrtptttingl
l. JWQ«T
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
-------
INSTRUCTIONS
1. REPORT NUMBER
Insert the LPA report number as it appears on the cover or the publication.
2. LEAVE BLANK
3. RECIPIENTS ACCESSION NUMBER
Reserved for use by each report recipient.
4. TITLE AND SUBTITLE
Title should indicate clearly and briefly the subject coverage of the report, and be displayed prominently. Set
subtitle, if used, in smaller type or otherwise subordinate it to main title. When a report is prepared in more
than one volume, repeat the primary title add volume number and include subtitle for the specific title.
5. REPORT DATE
Each report shall carry a date indicating at least month and year. Indicate the basis on which if was selected
(e.g date of issue date of approval, date of preparation, etc.).
6. PERFORMING ORGANIZATION CODE
Leave blank.
7. AUTHOR (S)
Give names(s) in conventional order (John R. Doc. J. Robert Doc. etc./. List author's affiliation if it Jaflers from
the performing organization.
8. PERFORMING ORGANIZATION REPORT NUMBER
Insert if performing organization wishes to assign this number.
9. PERFORMING ORGANIZATION NAME AND ADDRESS
Give name, street, city, state, and ZIP code. List no more than two levels of an organizational hierarchy
10. PROGRAM ELEMENT NUMBER
Use the program element number under which the report was prepared. Subordinate numbers may be
included in parentheses.
11. CONTRACT/GRANT NUMBER
Insert contract or pant number under which report was prepared
12. SPONSORING AGENCY NAME AND ADDRESS
Include ZIP code
13. TYPE OF REPORT AND PERIOD COVERED
Indicate interim final, etc., and if applicable, dales covered.
14. SPONSORING AGENCY CODE
Insert appropriate code.
15. SUPPLEMENTARY NOTES
Enter information not included elsewhere but useful, such as Prepared in cooperation with translation of
Presented To be published in Supersedes, Supplements, etc.
16. ABSTRACT
Include a brief (200 words or less) factual summary of the most significant information contained in the report
It the report contains significant bibliography or literature survey, mention it here.
17. KEYWORDS AND DOCUMENT ANALYSIS
(a) DESCRIPTORS • Select from the Thesaurus of Engineering Scientific Terms the proper authorized terms
that identify the major concept of the research and are sufficiently specific and precise to be used as index
entries for catalog ing.
(b) IDENTIFIERS AND OPEN-ENDED TERMS • Use identifiers for project names, code names, equipment
designators, etc Use open-ended terms written in descriptor form for those subjects for which no descriptor
exists.
(c) COSATI FIELD GROUP • Field and group assignments are to be taken from she 1965 COSATI (Subject
Category List. Since the majority of documents are multidisciplinary in nature, the Primary Field Group
assignment(s) will be specific discipline, area of human endeavor, or type of physical object. The application
(s) will be cross-referenced with secondary Field Group assignments that will follow the primary posting(s)
18. DISTRIBUTION STATEMENT
Denote releasability to the public or limitation for reasons other than security for example "Release Unlimited"
any availability of the public, with address and price.
19. & 20. SECURITY CLASSIFICATION
DO NOT submit classified reports to the National Technical Information service.
21. NUMBER OF PAGES
Insert the total number of pages, including this one and unnumbered pages, but exclude distribution list, if any
22. PRICE
Insert the price set by the National Technical Information Service or the Government Printing Office, if known.
-------
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.
R-9
-------
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.
R-10
-------
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.
R-ll
-------
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.
R-12
-------
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.
R-13
-------
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.
R-14
-------
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.
R-15
-------
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.
R-16
------- |