EPA-600/3-76-065
August 1976
Ecological Research Series
MATHEMATICAL MODELING OF
PHYTOPLANKTON IN LAKE ONTARIO
Part 2
Simulations Using Lake 1 Model
Environmental Research Laboratory
Office of Research and Development
U.S. Environmental Protection Agency
Duluth, Minnesota 55804
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RESEARCH REPORTING SERIES
Research reports of the Office of Research and Development, U.S. Environmental
Protection Agency, have been grouped into five series. These five broad
categories were established to facilitate further development and application of
environmental technology. Elimination of traditional grouping was consciously
planned to foster technology transfer and a maximum interface in related fields.
The five series are:
1. Environmental Health Effects Research
2. Environmental Protection Technology
3. Ecological Research
4. Environmental Monitoring
5. Socioeconomic Environmental Studies
This report has been assigned to the ECOLOGICAL RESEARCH series. This series
describes research on the effects of pollution on humans, plant and animal
species, and materials. Problems are assessed for their long- and short-term
wifluences. Investigations include formation, transport, and pathway studies to
determine the fate of pollutants and their effects. This work provides the technical
basis for setting standards to minimize undesirable changes in living organisms
in the aquatic, terrestrial, and atmospheric environments.
This document is available to the public through the National Technical Informa-
tion Service, Springfield, Virginia 22161.
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EPA-600/3-76-065
August 1976
MATHEMATICAL MODELING OF PHYTOPLANKTON
IN LAKE ONTARIO
Part 2
Simulations Using Lake 1 Model
by
Robert V. Thomann
Richard P. Winfield
Dominic M. Di Toro
Donald J. O'Connor
Manhattan College
Bronx, New York 10471
Grant No. R-800610
Project Officer
William .Richardson
Large Lakes Research Station
Environmental Research Laboratory-Duluth
Grosse lie, Michigan 48138
U.S. ENVIRONMENTAL PROTECTION AGENCY
OFFICE OF RESEARCH AND DEVELOPMENT
ENVIRONMENTAL RESEARCH LABORATORY
DULUTH, MINNESOTA 55804
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DISCLAIMER
This report has been reviewed by the Environmental Research
Laboratory-Duluth, U.S. Environmental Protection Agency, and
approved for publication. Approval does not signify that the
contents necessarily reflect the views and policies of the U.S,
Environmental Protection Agency, nor does mention of trade
names or commercial products constitute endorsement or
recommendation for use.
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ABSTRACT
The results of a series of simulations of the response of
the open lake region of Lake Ontario to various levels of
nutrient input are described in this report. The simula-
tions use a simplified dynamic model of phytoplankton -
nutrient interactions in a vertically segmented structure.
The lake is assumed to be well-mixed in the horizontal
direction.
The problem of long term simulations (10-20 years) that
draw on short term observation and verification periods
(5 years) is discussed and it is indicated that the overall
loss rates of nutrient are of particular importance. Under
a hypothesized, but reasonable, set of model parameters,
the simulations indicate that the present observed open
lake phytoplankton biomass of Lake Ontario does not appear
to be in equilibrium with the present input nutrient load.
Therefore, if the present load is continued,it is estimated
that spring peak phytoplankton chlorophyll in the epilimnion
will continue to increase to a new level about 45% higher
than present levels. The interaction of nitrogen and
phosphorus is also described by the simulations and the
results indicate a tendency for nitrogen limitation to be
an increasing dominant factor in controlling the spring
bloom.
A " pastoral" simulation using load estimates, indicative
of conditions prior to man's intensive activity provides
an approximation of an early state of the lake. This
"hindcast" indicates that spring phytoplankton levels were
some 40% less than present levels and average
annual epilimnion biomass under equilibrium with present
loads is about twice that under pastoral conditions.
A series of analyses is also conducted comparing simulations
from the dynamic model to estimates made from simplified
plots of loading versus lake geometry. The results from
the dynamic model indicate that a reduction in external nut-
rient load does not result in an accompanying decrease in
111
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phytoplankton biomass, due to the hypothesized non-equilibrium
condition of Lake Ontario. The dynamic model results are
therefore in contrast to the results one would obtain from
using "admissable" loading concept which indicates an im-
provement in lake trophic status.
Analysis of lake response to the U.S.-Canada Water Quality
Agreement (WQA) loads using the hypothesized parameters
indicates about a 6% reduction in peak phytoplankton at
equilibrium.
The implications of the results appear to be of some
importance since the analyses indicate that it may be
difficult to achieve measurable reductions below present
levels of phytoplankton biomass in the open lake. From a
decision and policy making viewpoint then, the simulations
tend to indicate that maximum point source nutrient con-
trol for Lake Ontario will, at best, be a "holding"action
rather than a significant improvement in the status of the
open lake.
This report was submitted in partial fulfillment of
Grant Number R 800610 to the Environmental Engineering
and Science Program, Manhattan College, Bronx, New York
by the U.S. Environmental Protection Agency. Work was
completed as of April, 1975.
IV
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CONTENTS
Sections Page
I Conclusions 1
II Recommendations 4
III Introduction 5
Purpose of Research 5
Scope of Research 5
Lake 1 Model Review 8
The Simulation Problem in Large Lakes 10
IV External Nturient Inputs for Simulations 16
"Present" Inputs 16
Variability of Inputs 18
Simulation Inputs 22
"Pastoral" Loads 22
Historical Loads and the U.S.-
Canada Agreement 23
V Results of Simulations 30
Continuation of "Present" Inputs 31
Response Under Zero Input 40
"Pastoral" Responses 45
Reduction of Nutrient Inputs 52
Vollenweider Reduction 52
Water Quality Agreement Loads 55
Comparison To Empirical Loading Plots 57
VI Summary of Lake Responses To Nutrient
Inputs 69
Sensitivity of Principal Simulations 69
Summary of Simulations Using Reasonable
Kinetics 71
Summary for Range of Nutrient Loads 79
Implications for Decision Making 79
VII References 85
v
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LIST OF TABLES
No. Page
1 Basic physical data of the Lake 1 model 9
2 Estimated 1966-67 nutrient loadings 16
3 Estimated nutrient inputs to Lake Ontario
(1966-67 and 1972) 17
4 Nutrient loadings from Niagara River 21
5 Estimated "pastoral" nutrient loadings 24
6 Approximate historical phosphorus inputs 26
7 Assumed "present" nutrient load distribution 32
8 Computed state of Lake Ontario under "pastoral"
conditions 51
9 Summary of principal load conditions 73
10 Estimated change in phytoplankton biomass
under different simulation conditions 75
11 Computed distribution of phosphorus and nitrogen
components at equilibrium 76
VI
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LIST OF FIGURES
No. Page
1 Major physical features included in Lake 1 Model 6
2 System diagram - Lake 1 Model 7
3 Time to equilibrium, conservative variable a) re-
duction in load b) response in concentration 11
4 Illustration of dominant effect of initial condi-
tion during a one-year analysis 14
5 The insensitivity of a one-year calculation to
the overall loss rate 15
6 Frequency distribution mean annual flows of
Niagara River (1860-1972) 19
7 Approximate historical phosphorus inputs to Lake
Ontario and the U.S.-Canada Agreement inputs 27
8 Dynamic behavior of phytoplankton biomass in
epilimnion-continuation of "present" inputs 33
9 Dynamic behavior of phytoplankton, inorganic
nitrogen and available phosphorus in epilimnion-
continuation of present inputs 34
10 Nutrient limitation effect under continuation of
present loads in epilimnion 36
11 Yearly average changes - continuation of present
inputs 38
12 Yearly average change (cont.) - continuation of
present inputs 39
13 Phytoplankton behavior, epilimnion, present
initial conditions, zero nutrient input 42
14 Maximum and minimum values, epilimnion, present
initial conditions, zero nutrient input 43
15 Maximum and minimum values- (cont.), epilimnion
present initial conditions, zero nutrient input 44
16 Dynamic behavior of phytoplankton biomass in epilim-
nion, "pastoral" inputs 46
17 Dynamic behavior of phytoplankton, inorganic
nitrogen and available phosphorus in epilimnion,
"pastoral" inputs 47
VII
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Page
18 Nutrient limitation effect under pastoral inputs-
epilimnion 48
19 Yearly average changes - pastoral inputs 49
20 Yearly average change (cont.) - pastoral inputs 50
21 Dynamic behavior of phytoplankton, inorganic
nitrogen and available phosphorus in epilimnion-
Vollenweider reduction 54
22 Comparison of "immediate" Vollenweider phosphorus
reduction with a 10 year reduction period 56
23 Dynamic behavior of phytoplankton, inorganic
nitrogen and available phosphorus in epilimnion-
Water Quality Agreement reduction 58
24 Yearly average changes - Water Quality Agreement
Loads 59
25 Yearly average changes (cont.) - Water Quality
Agreement loads 60
26 Sensitivity of phytoplankton response to kinetic
assumptions 70
27 Summary of peak phytoplankton response. Reasonable
kinetics: phytoplankton settling = 0.1 m/day,
K organic = 0.001/day, K inorganic =0.0 72
28 Summary of phosphorus components computed at equil-
ibrium, 0-17m, nitrogen loads as in Table 9,
reasonable kinetics 77
29 Spring and Fall peaks and annual average chlorophyll
at equilibrium in epilimnion, reasonable kinetics 78
30 Peak phytoplankton chlorophyll, 0-17m, as a function
of nitrogen and phosphorus input - K organic = 0.0,
K inorganic =0.0 80
31 Peak phytoplankton chlorophyll, 0-17m, as a function
of nitrogen and phosphorus input - K organic =
0.001/day, K inorganic =0.0 81
32 Average annual phytoplankton chlorophyll, 0-17m as a
function of nitrogen and phosphorus input - Top fig.:
reasonable kinetics, bottom fig.: pessimistic
kinetics 82
Vlll
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ACKNOWLEDGEMENTS
Grateful thanks are due to EPA personnel at the Great Lakes
Research Station including Messrs. William Richardson,
Nelson Thomas and Dr. Tudor Davies. Their cooperation and
enthusiasm helped to make the conduct of this research most
enjoyable. Special thanks are also due to Mr. Jan Tai Kuo
of Manhattan College, for his assistance and to Miss Cindy
O'Donnell for her patience in typing the report manuscript.
IX
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SECTION I
CONCLUSIONS
For large lakes such as Lake Ontario, it is difficult to
estimate the effects of various nutrient input levels due
to the short observation period of the lake relative to
its size. Verification analyses would of necessity have to
be conducted over a number of years up to at least a decade
in order to estimate overall loss rates of nutrients from
the lake system. The long term simulations are particularly
sensitive to these decay rates. Nevertheless, it is con-
cluded that a reasonable set of kinetic parameters can be
hypothesized and simulations can be carried out under
different input nutrient conditions.
Estimates of present nutrient loading to Lake Ontario can
vary widely (+ 15%) partly due to difficulty in accurately
estimating Niagara River input. For phosphorus, the varia-
tion in the Niagara River loading above is equivalent to a
population of about 1.6 million or about 25% of the present
population. It will be difficult then to estimate future
changes in input load because of this inherent variability.
Simulations using the simplified Lake 1 Model were carried
out over a range of nutrient conditions. It should be
stressed that the conclusions to follow represent open lake
responses under hypothesized (albeit reasonable) system
kinetics. Near shore responses and resulting conclusions
may be considerably different than indicated below.
Four principal load conditions were used as mile posts:
1) Continuation of present load, phosphorus=75,000 Ibs P/day
2) pastoral loads, phosphorus=20,500 Ibs. P/day, 3)Vollenweider
reduction, phosphorus=46,900 Ibs P/day, and 4) U.S.-Canada Water
Quality Agreement load, phosphorus=54,800 Ibs. P/day. Nitrogen
loading was used at 883,000 Ibs N/day for all simulations
except the pastoral conditions where the loading used
was 406,000 Ibs N/day.
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Under a continuation of present loads and a "reasonable"
set of system parameters, it is estimated that spring peak
phytoplankton chlorophyll in the epilimnion will continue
to increase to a new level about 45% higher than present
peaks. About 8-10 years would elapse to reach this new
equilibrium. Average annual biomass in the epilimnion
is computed to increase by about 20%. The simulation also
indicates an increasing tendency for the spring bloom to
be controlled more by nitrogen than phosphorus.
Simulations made under "pastoral" conditions representing
estimated background loading prior to man's 20th Century
activities indicates spring peak chlorophyll values
about 7 pg/1 or some 40% less than present levels. This
simulation therefore provides a first approximation to
the state of Lake Ontario prior to the turn of the century.
The results indicate average annual phytoplankton chlorophyll
in the epilimnion to be about 2.6 yg/1 as compared to 5.8 yg/1
annual average in equilibrium with the present load. It is
estimated therefore that the average annual phytoplankton
in the epilimnion at equilibrium with present loads is about
twice the level that existed under some previously unstressed
environment. The load however has increased by about 3.7
times over the same period.
A simulation conducted using the "admissable" loading from
empirical plots of Vollenweider (a 40% phosphorus reduction)
indicate an increase in spring peak biomass to about 15 yg/1
chlorophyll. The results indicate an exception to the general
axiom that a reduction in external loads will result in an
improvement in water quality. This is in contrast to the impli-
cation inherent in the use of loading plots which indicate
that a reduction in external load will of necessity improve
lake quality. If the hypothesis that Lake Ontario is
not yet in equilibrium with the present loads is correct,
then the "admissable" loading does not result in an improve-
ment in water quality. One concludes therefore from this
one comparison between two models,that empirical loading
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plots may not be appropriate for large lakes such as the
Great Lakes.
The Water Quality Agreement (WQA) load simulation (a 27%
phosphorus reduction) indicated that the open lake phyto-
plankton of Lake Ontario may continue to increase for a
period of about 15 years or until the late 1980's. The
WQA phosphorus load is calculated to result in only about
a 6% reduction in peak phytoplankton at equilibrium. Given
the variability in load estimates and observed fluctuations
in open lake biomass such a change would be difficult to
detect. This is not meant to imply that the WQA program
is not a good one, but simply that under the stated hypo-
theses the computations indicate that the hopes for an
expected response of Lake Ontario may not be as high as
anticipated under the Agreement.
It is estimated that to maintain present open-lake phyto-
plankton peak biomass, a total phosphorus loading of
about 35,000 Ibs P/day would be necessary. This loading
represents conditions of approximately the 1940's and
also represents about a 73% reduction in present loading
above the pastoral background load. Since only about 60%
of the total load discharged is from point sources, the
results indicate that it may be difficult to achieve measur-
able reductions below present levels of phytoplankton biomass,
Finally, it should be noted strongly again that the con-
clusions from these simulations are indicative of open lake
conditions and do not reflect near-shore responses which
may be quite different and further that the simulations
are based on an hypothesized, but apparently reasonable
set of kinetics. Also, research into predicting the
future dynamic behavior of phytoplankton in large lakes
is still very much in its infancy which would indicate
that additional research may lead to varying conclusions.
Nevertheless, policies and decisions will still have to
be made even though future research may suggest adjustments
and .corrections,
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SECTION II
RECOMMENDATIONS
Because of the importance of near shore versus open
lake problems, it is recommended that a detailed veri-
fication and analysis of the Lake 3 model be conducted.
Some simulations should be carried out with the Lake 3
model to delineate the time for the near shore to reach
a new dynamic equilibrium.
Since the simulations using the Lake 1 model were
particularly sensitive to the overall loss rates of
the nutrients, it is recommended that: 1) a modeling
framework of phosphorus chemistry be developed and
verified to attempt to define these critical parameters
2) investigations begin into the development and verifi-
cation of a sediment model to utilize the only available
historical trace of the state of Lake Ontario.
Finally, and most importantly, it is strongly recommended
that additional analyses be conducted of Lake 1 model
responses. Continuing up-dating and verification together
with simulations under a variety of conditions, should be
carried out preferably by one of the operating agencies
in the Great Lakes.
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SECTION III
INTRODUCTION
PURPOSE OF RESEARCH
Attention is directed in this report to the utiliza-
tion of a simplified model of phytoplankton dynamics
of Lake Ontario (the Lake 1 model) to estimate the
lake-wide response to various levels of nutrient load-
ing. The Lake 1 model is therefore viewed as an initial
framework for estimating whole lake phytoplankton re-
sponse and to provide some input into the ongoing
decision making process on Lake Ontario.
A range of external nitrogen and phosphorus loading
is examined and the sensitivity of the results to
various model parameters is examined. All of the
work is aimed at providing estimates of phytoplankton
biomass to a first approximation. It should be
stressed that the results presented herein are to
serve only as general indicators of the direction
to be expected under remedial nutrient control programs.
SCOPE OF RESEARCH
This report follows Part 1, Model Development and
Verification and builds on that work. As such,
the details of the model are not presented and only
the general structure and a summary of the results
of the verification analysis are given. The geo-
graphical scope is lake-wide and the simulations
are,therefore, for the whole lake only. Near shore
problems are not considered herein. The measure of
eutrophication is taken as the phytoplankton chloro-
phyll a. The emphasis is on the response of the
open lake total biomass to a range of nutrient load-
ing and the sensitivity of the response to varying
estimates of model parameters and coefficients.
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NUTRIENT INPUTS
ENVIRONMENTAL INPUTS
NIAGARA RIVER
TRIBUTARIES MUNICIPAL
INDUSTRIAL WASTES
SOLAR RADIATION
WATER TEMPERATURE
LIGHT EXTINCTION SYSTEM PARAMETERS
EPI LIMN ION
VERTICAL EXCHANGE " TRANSPORT
J I \
Figure 1 Major physical features included in Lake 1 model
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UPPER TROPHIC
LEVEL NO. 2
CARBON
UPPER TROPHIC
LEVEL NO. 1
CARBON
CARNIVOROUS
ZOOPLANKTON
CARBON
HERBIVOROUS
ZOOPLANKTON
CARBON
PHYTOPLANKTON
CHLOROPHYLL
BIOLOGICAL SUB-MODEL
ORGANIC
NITROGEN
NITROGEN CYCLE
AMMONIA
NITROGEN
PHOSPHORUS CYCLE
ORGANIC
PHOSPHORUS
NITRATE
NITROGEN
AVAILABLE
PHOSPHORUS
CHEMICAL-BIOCHEMICAL SUB-MODEL
Figure 2 System diagram - Lake 1 model
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LAKE 1 MODEL REVIEW
Fig. 1 shows the geometry of the Lake 1 model. The
principal features included in the model are:
a) a two layer system with a sediment layer,
the mixing and stratification being accomplished
by vertical exchange
b) phytoplankton settling
c) external environmental inputs of nutrients
d) external environmental inputs of solar
radiation, water temperature and other
system parameters.
The system diagram showing the interaction of the
key variables is given in Fig. 2. Ten dependent
variables are included and incorporate the major
features of the interactions of phytoplankton,
zooplankton and nutrients. Table 1 gives the
basic physical data used and complete details are
given in (1).
Extensive analyses and summary data from 1967-1970
formed the basis for verification of the model. The
results of the verification indicated that the model
provides a reasonable comparison to observed lake-
wide average values of chlorophyll, zooplankton
carbon, and various forms of nitrogen and phosphorus.
The analyses indicate that the spring growth phase
and peak phytoplankton biomass are primarily controlled
by increasing light and temperature and phosphorus
limitation. The mid-summer minimum in phytoplankton
is estimated to be due primarily to zooplankton
grazing and nitrogen limitation. The broad fall
peak in phytoplankton is a complex interaction of
nutrient regeneration (up to five times the external
nutrient inputs), subsequent nutrient limitation and
then the fall overturn. Both nitrogen and phosphorus
are important nutrients in this dynamic succession.
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TABLE 1
BASIC PHYSICAL DATA OF THE LAKE 1 MODEL
Surface
o j. Volume T-. j_u Area Flow
Segment volume Depth 2 3
Segment No. Interface (m xlO ) % (Meters) (meters } cfs m /sec %
1 297,000 19 17 43,500 1232 19
1-2 1.64.1010
2 1,373,000 81 73.3 188,500 5323 81
2-3 0.89.1010
3 (sediment) - 0.15*
Note: Vertical dispersion coefficient between segments No. 1 and 2
2 2
varied from 0-> 6.7 cm /sec (0->-0.78 m /day)
* Segment #3 depth is arbitrary
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Although the model parameters used in the verifications
are all considered reasonable and within reported litera-
turn ranges, no claim is made as to the uniqueness of
the particular parameter set that was finally derived.
Nevertheless, the conclusion of the model development
and verification stage of the work indicated that a
sufficient base had been established to use the model
for preliminary simulations of various levels of nutrient
reduction. The simulations using the Lake 1 model are
therefore the primary topic of this report.
THE SIMULATION PROBLEM IN LARGE LAKES
The estimation of future levels of water quality on
large lake systems is complicated by the long deten-
tion time of the lake and the usual relatively short
period of observed data on the state of the lake.
Changes in lake water quality are therefore difficult
to perceive on a year to year basis. For example,
for Lake Ontario, with an eight year hydraulic deten-
tion time, the relevant time scale of interest is
on the order of tens of years; i.e. it may take
10-20 years for the lake to respond to changes in
external inputs. Fig. 3 shows this effect. The
observation time for Lake Ontario of about 5 years
is short compared to the response time. A difficult
problem in prediction is therefore presented: namely,
the estimation of long term system response based on
a short observational period. The problem is somewhat
analogous to attempting to estimate the frequency
of occurrence of a one in ten year drought flow based
on one or two years of record.
In the verification analyses reported on in Part I of
this work, the time variable responses computed
for a period of one year were responsive primarily to
the specified initial conditions rather than the
10
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03
T3
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§ 60
40
20
CO
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11
1
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: i
: i
0
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!
(a)
1 1 1 1 1 1 1 1 1 1 1 1
10 20 30 40 50 60
TIME, years
_ 0.10
CT>
E 0.08
z
0.06
£E 0.04
z
o 0.02
z
8 o.oo
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EQUIVALENT
1 i I I ll I I I I I I I I
10
20 30
TIME, years
40
50
60
Figure 3. Time to equilibrium, conservative variable a) reduction
in load, b) response in concentration
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external inputs. This, of course, can be seen from a
nutrient balance equation for a well-mixed lake. Thus,
c = -g-
where c=the whole lake nutrient concentration (mg/1) ,
W is the external source of nutrients (kg/day) , V is
the lake volume, Q is the flow (m /sec) through the
lake, tQ is the hydraulic detention time (=V/Q) ,
K( I/day) is the overall decay of the nutrient due
to settling or chemical reactions, and t is time.
If one is now approaching a year of data or even
several years of data, two estimates must be made.
First, the external load, W must be estimated and
then the overall loss rate of the nutrient given by
K must be determined. The external nutrient load
is estimated from a variety of data sources (see
next section) but usually for a given year or group
of years close to the sampling for the nutrients.
The overall decay rate is either estimated as part
of the settling of the phytoplankton as in the dynamic
phytoplankton model or is estimated from the nutrient
data itself. But, the latter course of action assumes
the lake to be in equilibrium with the present load,
an assumption that cannot be checked until the lake
has actually been observed for a period of at least
one-two detention times (8-16 years for Lake Ontario) .
The dilemma is made clear by an example from Lake
Ontario .
"Present" total phosphorus load to the Lake is about
34,000 kgP/day (75,000lbs P/day) . If total phosphorus
were completely conserved (K=0) , the total within- lake
phosphorus concentration, pfc, at equilibrium is simply
from Eq. (1) , (for a flow of 6570 m3/sec (232,000 f t3/sec) ) ,
Pt - £
12
-------
or p = .06 mg/1. Now, average observed total phosphorus con-
centrations in Lake Ontario during the period 1967-70 and 1972-
73 is about 0.02 mg P/l. For this initial condition, the con-
centration at the end of the first year would be aboutQ.025 mg/1 ;
close to the observed value. Fig. 4 indicates these results
and shows the dominant effect of the initial condition during the
first year. Three choices are open now to the analyst: a) assume
the present load is not in equilibrium with the present concen-
trations and that the system is conservative, b) assume the lake
is not in equilibrium with the present concentrations but that
there is some loss in the system, or c) assume that the lake is
in equilibrium with the present load and estimate the decay rate
from the data.
12 3
For a lake with a large volume such as Lake Ontario, (1.67-10 m ),
a value of K = .001/day, gives a value of p at equilibrium of
about 0.015 mg/1, again close to the present observed concentra-
tion. The question then is: "Is a value of K=.001/day reasonable?"
Unfortunately, the verification analysis does not necessarily pro-
vide the needed information. Fig. 5 shows that for Lake Ontario
the difference at the end of one year of analysis with or without
a value of K is too slight to determine a reasonable estimate.
Only two courses of action appear open for Lake Ontario. If long
term data on some aspect of the lake biomass behavior were avail-
able, a long term simulation would provide information on the
decay rate. Only the sediments seem to contain some hope for
constructing a long term record of the state of the lake. The
difficulty at the present time of course, is that it is not yet
possible to deal in a reasonable way with the available sediment
data on pore water chemistry or on the chemistry of the solid
phase. The second course of action therefore appears to be the
most fruitful. Reasonable hypotheses on the phosphorus and
nitrogen components (e.g. phytoplankton and detrital settling)
can be formulated and tested on the dynamic model. Simulations
based on those results can then be prepared but with full recog-
nition that the long term behavior has only been grossly approx-
imated .
13
-------
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Q.
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0.06
TOTAL
0.04
INCREASE DUE TO
EXTERNAL SOURCE
0.02
0.00
EQUILIBRIUM
CONCENT R A TION
INITIAL CONDITION
DECREASE
0
Figure 4.
10
TIME, years
15
Illustration of dominant effect of initial condition
during a one-year analysis
-------
0.06
0.04
*
z
O
DC
I-
z
UJ
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oc
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85 0.02
O
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AT EQUILIBRIUM
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AT END OF 1 YEAR
0.0
APPROXIMATE
RANGE OF
, "PRESENT"AVERAGE
'/////////A
0.5 1.0
OVERALL LOSS RATE-K, 0.001/day
Figure 5 The insensitivity of a one-year calculation to the overall
loss rate
-------
SECTION IV
EXTERNAL NUTRIENT INPUTS FOR SIMULATIONS
"PRESENT" INPUTS
The principal sources of nutrients to the whole
lake are: 1) the Niagara River, including input
from Lake Erie and waste discharges on the
Niagara River itself, 2) other tributary inputs
in the Lake Ontario basin, 3) direct discharges
of municipal and industrial wastes, 4) local
drainage to the Lake and, 5) atmospheric inputs.
The major contributions are from the first three
categories although atmospheric inputs may prove
to also be significant.
The estimated 1966-67 loading to the Lake is shown
in Table 2 as estimated by the IJC.
TABLE 2
ESTIMATED 1966-67
NUTRIENT LOADINGS
SOURCE NITROGEN
Niagara
Tributaries
Municipal
Industrial
Total
Ibs/Day
522,200
191,000
72,600
97,300
883,100
Metric tons
/Day %
236.9 59
86.6 22
32.9 8
44.1 11
400r5
PHOSPHORUS
Ibs/Day
42,200
15,600
16,200
1,000
75,000
Metric tons
/Day
19.1
7.1
7.3
.5
34.0
%
56
21
22
1
As shown, the major input is the Niagara River which
includes discharges on the Niagara River itself as
well as the output from Lake Erie. Direct municipal
16
-------
and industrial discharges to the Lake account for
about 20%, the remainder of the load enters from
tributaries to the Lake.
Additional sampling was conducted during IFYGL by
both the U.S. and Canada. Casey and Salbach have
summarized the IFYGL inputs and Table 3 compares
the two estimates.
TABLE 3
ESTIMATED NUTRIENT INPUTS TO LAKE ONTARIO
(1966-67 and 1972)
(a)
(2,3)
SOURCE
1,000 Ibs/day
Total Phosphorus
1966-67 1972
Total Nitrogen
1966-67 1972
Niagara
Tributaries
Municipal
Industrial
Sub-Total
Atmospheric '
Groundwater '
Total
42.2
15.6
16.2
1.0
75.0
9.9
0.2
85.1
45.9
20.3
20.9
0.4
87.5
9.9
0.2
97.6
522.2
191.0
72.6
97.3
883.1
137.1
2.0
1022.2
482.4
224.9
93.3
20.3
820.9
137.1
2.0
960.0
a) 1,000 Ibs/day = 0.454 metric tons/day
b) Atmospheric and groundwater inputs for 1966-67
assumed equal to 1972 input.
For total phosphorus, the load estimates (excluding
precipitation and groundwater) are reasonably close and
the difference in Niagara River and tributary loads
can be partially accounted for by the higher flows
during IFYGL. The total nitrogen load estimates vary
more widely and not in the direction of increasing
flow. Further, there is a substantial change in the
17
-------
estimate of the industrial nitrogen contribution be-
tween 1966-67 and 1972. The relative magnitude of
the atmospheric input can also be noted.
One of the difficulties in the simulation analyses
was the specification of expected future loading or
the loads that were discharged to the Lake in prior
years. The difficulty results primarily from varying
load estimates at different times such as indicated
in Table 3 and from different sampling procedures.
The importance of the Niagara River input indicates
a need to estimate the range in load to be expected
from the Niagara River even if point source load
reduction were accomplished.
VARIABILITY OF THE INPUTS
As shown in Tables 2 and 3/ one of the primary inputs
of nutrients to the Lake is from the Niagara River
which has an average annual flow of about 202,000 cfs
with a mean annual standard deviation of about 19,000 cfs,
Therefore, about 70% of the time, the average annual
flow is between about 180,000 to 220,000 cfs, or a
range of 40,000 cfs. Fig. 6 shows the frequency dis-
tribution of annual flows for the Niagara River for
the period 1860-1972. Flow during the first 9 months
of IFYGL averaged about 228,000 cfs for the
months of April-December, 1972. Niagara River flow
during the 1966-67 nutrient loads estimated by the
2
International Joint Commission (IJC) was about
190,000 cfs. The two periods for which nutrient
load estimates were made differed in Niagara flow
by about 40,000 cfs.
The nutrient concentrations of the Niagara River vary
over a fairly wide range. For example, during the
18
-------
v>
M
u
o
O
O
LJJ
g 210
<
I
o
CO
X
_i
<
D
2.
Z
<
Z
<
LJJ
_»
§
»
3
150
0.1 1 10 50 90 99 99.9
PERCENT OF TIME FLOW EQUAL TO OR GREATER THAN THAT SHOWN
Figure 6. Frequency distribution mean annual flows of Niagara
River (1860-1972)
-------
1966-67 estimates, the equivalent total phosphorus
concentration estimated for the Niagara River was
about .04 mg P/l which was the approximate mean
concentration measured during IFYGL. The standard
deviation of the concentration is about .006 mg P/l
or about 15% of the mean. One can then calculate
the mean and standard deviation of the nutrient
mass input as follows (assuming that flow and con-
centration are uncorrelated):
W = Qc (3)
and
sw =V (Q)2(sc)2 + (c")2(sQ)2 + s^ s* (4)
where Q is the mean flow, c is mean concentration,
W is mean mass input, sn, s and s are the
y c \v
standard deviations of flow, concentration and
mass input respectively. Applying Eqs. <3) and (4)
to nitrogen and phosphorus for the 1966-67 and the
1972 IFYGL estimates gives the results shown in
Table 4. Particular attention is drawn to the
last column, i.e. the range of the expected fluctua-
tion in the nutrient loads. This range is taken as
two standard deviations and as shown is about 30%
of the average load or the load from the Niagara
River may vary +15% around the average.
It can be assumed as a lower bound that tributary
inputs together with the municipal, industrial and
other inputs vary by approximately the same percentage.
A
Casey and Salbach estimate a range of 14-21% for
total phosphorus for the Genesse, Oswego and Block
River. Overall then, one may expect the load estimates
to vary by about +15%. This will, of course, assume
some considerable importance in any simulations.
20
-------
TABLE 4
NUTRIENT LOADINGS FROM NIAGARA RIVER
Flow (cfs)
(m /sec)
Total Phosphorus (Ibs/day)
(as P) (metric
tons/day)
Total Nitrogen (Ibs/day)
(as N) (metric
tons/day)
1966-672
190,000
5,300
42,200
19.1
522,200
236.9
1972 IFYGL 3
228,000
6,400
45,900*
20.8
482,400
218.8
Average
X
202,000
5,700
42,400
19.3
470,400
214.
Estimated
Std. Dev.
s
19,000
540
7,700
3.5
62,300
28.0
Range of Expected
Fluctuation
=2s
38,000
1,100
14,400
7.0
124,500
56.
*Canadian estimate = 51,100 Ibs/day (23,200 kg/day)
-------
SIMULATION INPUTS
A range of conditions on the external nutrient in-
puts has been examined. However, in order to place
the "present" loads into an historical perspective,
a preliminary analysis was made of the nutrient inputs
that might have existed at some distant time in the
past. These loads were termed the Pastoral Loads.
In addition, a review was made of nutrient reductions
as suggested by Vollenweider and the Great Lakes
Water Quality Agreement . The simulations were
therefore prepared using a wide range of input nutrient
loads with the Pastoral Loads as a baseline condition.
Pastoral Loads
It is difficult to evaluate whether presently ob-
served conditions in the Lake represent a "serious"
condition or a condition close to "desirable". If
water quality objectives are set without consider-
ing what the state of the water body would be if man
had not happened on the stage, unrealistically high
expectations might occur. It must always be remembered
that even before the coming of man, there was phyto-
plankton biomass in Lake Ontario. The question is,
"What is a reasonable level of biomass for Lake
Ontario at some time in the past?" An estimate
must therefore be made of the loads that existed
before any substantial effect by man's activities.
The settlement of the Great Lakes Basin caused the
nutrient loads being placed on the lakes to increase
greatly. Lake Ontario's nutrient loads are heavily
influenced by man, both within its basin and by
man's influence on the upper lakes. Keeping in
mind that point sources are the most readily controlled
sources of pollution, the problem posed was to esti-
22
-------
mate what Lake Ontario water quality would be if only
background, non-point sources of nutrients were allowed
to enter the lake. This setting was viewed as a
"pastoral" condition, similar to the time when the
basins were principally rural areas, with no major
population centers, and hence no significant human
waste water affecting the lake.
The conditions which determined the pastoral simula-
tion were as follows. The entire basin was considered
to be a rural area with no significant human waste
water entering the lake directly. The nutrient load
from the Niagara River was assumed to reflect a
"pastoral" condition in the upper lakes. It was
assumed that the present conditions on Lake Huron
could be used as an approximation to what the
pastoral conditions would be in Lake Erie.
Loehr summarizes characteristics of rural runoff
and reports 0.20 to 0.28 Ibs of total phosphorus
per acre per year and total nitrogen loading of
1.3 to 2.9 pounds per acre per year in runoff
from rural areas containing no significant human
wastewater contributions to the streams. Loading
rates of 2.0 Ibs nitrogen/acre/year and 0.25 Ibs
phosphorus/acre/year were therefore used for the
basin contribution to the nutrient loads. The
Niagara River load was calculated using southern
Lake Huron mean concentration data (Great Lakes
Q
Water Quality Board .) The organic nitrogen
load was assumed to be ten times the organic
phosphorus load. Table 5 shows the estimates of the
pastoral loads used in the simulations.
Historical Loads and the U.S.-Canada Agreement
The estimates of the pastoral loads provide a lower
bound on the external nutrient inputs to the Lake.
23
-------
TABLE 5
ESTIMATED "PASTORAL" NUTRIENT LOADINGS
Total Nitrogen
Organic - N
Total Inorganic-N
Ammonia - N
Nitrate - N
Total Phosphorus
Organic P
Inorganic P
Lake Ontario Basin
Compon
Ibs/acre/yr
2.0
1.4
0.6
0.1
0.5
0.25
0.238
0.012
ent
Ibs/day
122,000
86,400
36,600
6,100
30,500
L53,000
14,500
800
Niagara River
Compc
mg/1
0.270
0.0450
0.225
0.034
0.191
.005
.0045
.0005
nent
Ibs/day
283,800
47,300
236,500
35,700
200,800
5,200
4,700
500
Total
Ibs/day
405,800
133,700
273,100
41,800
231,300
20,500
19,200
1,300
7 2
Lake Ontario Basin: 2.227 x 10 acres (90,132 km )
Niagara Flow: 195,000 cfs
24
-------
The estimates of the present loads (1967-72) provide
a measure that indicates the increase in load that
has occured over the past 50-100 years. Two additional
input patterns are important: a) the historical load
pattern between the present and say, the turn of the
century and, b) the expected future load pattern.
Any attempt at estimating the past nutrient inputs
over the preceding five decades is paved with many
difficulties. The effects of input from Lake Erie,
population growth, the introduction of phosphorus
detergents and varying land use practices are several
examples of important phenomena that contribute to
the nutrient input. In addition, as noted previously,
normal flow and concentration variations in the Niagara
River input alone can vary by as much as - 15%. A
detailed study would be necessary to delineate each
of these components. Such a study is clearly outside
the scope of this work. However, in order to provide
at least some basis for placing the loads used in
the simulation in an historical context, the simplest
and most crude analysis was performed to estimate
the historical load pattern since 1900. Because of
the importance of phosphorus and the U.S.-Canada
Agreement on phosphorus (see below), the historical
analysis was restricted to that nutrient. The pro-
cedure to estimate the phosphorus loads was as
follows:
a) The population tributary to Lake Ontario was
(9)
determined using estimates by O'Connor and Mueller
b) Given the 1970 population and load (exclusive
of the pastoral input) a per capita loading of
phosphorus was determined.
c) A per capita loading of domestic waste water
was estimated.
d) A time history of the per capita loading was
graphically estimated considering the introduction
25
-------
of detergent phosphorus beginning in 1950.
e) The resulting intermediate loads were then
calculated, to which was added the pastoral input.
f) Atmospheric inputs were not included in order
to provide a basis for comparison to the U.S.-Canada
Agreement loads. The results of this analysis are
shown in Table 6.
TABLE 6
APPROXIMATE HISTORICAL PHOSPHORUS INPUTS
(Atmospheric Inputs Not Included)
Estimated Estimated Load &
Pastoral Input
1000 Ibs/day
27.2
28.2
29.3
34.2
36.2
52.2
67.7
86.0
Fig. 7 is a plot of the approximate total phosphorus load
and for the latter two decades the range due to variations
in Niagara River flow and concentration is also plotted.
This range represents - 77001bsP/day as shown in Table 4
and is reasonable since the range in Niagara River annual
flows from 1950-1972 was from 161,000 cfs to 231,000 cfs.
This flow range covers the expected range in Niagara
River mean annual flow.
As shown in Table 6 and Fig. 7, total phosphorus loads to
the whole of Lake Ontario have increased by about 15,000
Ibs P/day for each 10 years since about 1950. The total
load is now about three times the load at the turn of
the century and about 2.4 times the 1940 load, prior
to the introduction of detergents. As shown in Fig. 7,
26
Trib.Popul
Year (Millions)
1900
1910
1920
1930
1940
1950
1960
1970
2.4
2.7
3.1
3.5
4.0
4.6
5.3
6.0
. Ibs/day/
Capita
.003
.003
.003
.004
.004
.007
.009
.011
Load
1000 Ibs/day
7.2
8.2
9.3
14.2
16.2
32.2
47.7
66.0
-------
IV)
100
co
T3
V)
I
O
o
=>
Q_
CO
D
DC
O
I
Q_
CO
O
I
Q.
O
60
40
20
50
NOTE: ATMOSPHERICS SEDIMENT
INPUTS NOT INCLUDED
co
CL
40 £
o
o
30
U.S.-CANADA
AGREEMENT
20
0
1900
10
1910
1920
1930
1940
1950
1960
1970
0
CD
E
h-"
D
Q.
CO
D
DC
Q.
CO
O
Q_
Figure 7. Approximate historical phosphorus inputs to Lake
Ontario and the U.S.-Canada Agreement inputs
-------
the range due to changes in Niagara River input (see
Table 4) is significant and probably will mask any
further attempts at detailed refinement of the estimates
such as land use breakdowns. Indeed, for a range of
14,400 Ibs P/day (equal to - one standard deviation),
and an average per capita loading of 0.009 Ibs P/day,
the variation in Niagara River input is equivalent to
a basin population of 1.6 million or about 25% of the
present population. It should be stressed again that
the loads shown are illustrative only and represent
only the crudest of estimates.
The simulation question discussed earlier assumes
particular importance in the light of these estimates.
The phosphorus input to the Lake has been increasing
significantly over the past two decades and there
have been significant year to year changes due to changes
in Niagara River flow. As such, the state of the Lake
in 1967-70 and again in 1972 the years of intensive
sampling, represents some integrated average response
of the past loads.
Fig. 7 also shows the loads promulgated under the U.S.-
Canada Agreement on phosphorus control Several
points can be noted. The load estimated in 1971 of
98,600 Ibs P/day (44.8 metric tons/day)appears to be an over-
estimate of the input so that future estimates of
input may show an apparent reduction. The range of
input load from the Niagara River will increase the
difficulty of estimating the changes in load as part
of the Agreement. For all practical purposes, in
terms of simulation, the Agreement loads represent an
approximate step function decrease (or instantaneous
decrease) in load to conditions of the early 1950's.
In the light of the range of loads shown in Fig.7,
extending from a pastoral level of some 20,000 Ibs P/day
28
-------
to maximum levels of about 100,000 Ibs P/day.- simula-
tions were prepared assuming input nutrient loads
covering this range.
It should also be noted that this range of external
inputs includes any uncertainty in the possible release
of phosphorus from the sediments to the hypolimnion.
Bannerman et al. estimated the annual contribution
of inorganic phosphorus from the sediments to be about
1.4 x 106 kg P/year (8,500 Ibs P/day) or 10% of the total
phosphorus input (see Table 3). As indicated previously,
the range of the external load input is about - 18% so
that the contribution from the sediments would tend to
be masked and in any event is covered by the external
loading range.
Nevertheless, the importance of the sediments as a
phosphorus source cannot be completely ignored especially
as external sources are reduced. For example, at the
U.S.-Canada Agreement load of 54,800 Ibs P/day, the
sediment input rises to 16%. Under future load re-
duction therefore, further attention should be directed
towards the role of the sediments.
29
-------
SECTION V
RESULTS OF SIMULATIONS
A variety of simulations have been carried out using
the Lake 1 model and the range of loads indicated in
Section IV. Except for one illustrative case, the
procedure followed in each simulation was similar.
The Lake 1 model kinetic structure was used including
the initial conditions of the 1967-70 period. A new
external load was then imposed, representing a step
function decrease or increase in the load. The model
was then run until a new dynamic equilibrium was obtained.
No attempt was made to estimate an actual future load
time history; rather, a range of external conditions
was imposed to illustrate the nature of the Lake response.
As discussed in Section III, the verification analysis
is most responsive to the initial conditions as opposed
to the external inputs. Yet, one of the key parameters,
the overall loss rate of a nutrient is critical to the-
response of the lake over the long term. This is shown
in Fig. 5. The verification analysis provides only
an estimate of the loss of phytoplankton nitrogen and
phosphorus to the sediments. It is not possible to
estimate from the short observation period available
the decay of detrital and other forms of organic nutrients
or the decay of dissolved inorganic forms. The follow-
ing range of conditions was therefore used in the
simulations:
1) Non-living organic nitrogen and phosphorus
assumed at two levels (a) conservative or (b) A
loss from the system at a rate of .001/day (equivalent
to an approximate settling rate of .1 m/day)
2) Phytoplankton phosphorus and nitrogen settling
rate of .1 m/day.
3) Inorganic forms of nitrogen and phosphorus are
assumed to be conservative.
30
-------
This range of conditions on the decay or loss of nutrient
from the system is believed to be reasonable. However,
it should be stressed that the only real check to date
is on the second condition. The results of the veri-
fication analyses indicated that the dynamic behavior
of the phytoplankton can be verified with a settling
velocity of about 0.1 m/day for the Lake 1 model. It
appears plausible to assign a similar settling velocity
to the other organic forms although some fraction of
that form is undoubtedly dissolved. Consequently,
this form of nutrient was assumed at the two levels
of K=0 and K=0.001/day to illustrate the sensitivity
of the solutions to varying loss rates of organic
nutrients. The question of the decay or loss of inorgan-
ic forms is considerably more difficult. Chemical mechanisms
of co-precipitation and minerialization may be the cause
of a loss of inorganic forms, however the degree to
which this loss may occur in Lake Ontario is not
known. It appears however, that such a loss is probably
not significant and as such, it is assumed that the in-
organic nutrient forms are conserved. The importance
of this assumption is discussed below.
"Reasonable" kinetics for the simulations presented in
this chapter therefore include loss rates of .001/day
for the organic forms, a zero loss for the inorganic
forms and a phytoplankton settling rate of 0.1 m/day.
CONTINUATION OF "PRESENT" INPUTS
The first series of runs examined the model response
due to a continuation of present inputs where "present"
was used as the nitrogen and phosphorus input distribution
shown in Table 7. This distribution is identical to
that used in the verification analysis . Atmospheric
and sediment inputs are not included explicitly but
are incorporated in the range of results discussed
below.
31
-------
TABLE 7
ASSUMED "PRESENT" NUTRIENT LOAD DISTRIBUTION
System Nutrient Load
Metric Tons/Day 1000 Ibs/Day
Nitrogen
Non-living 250.0 551.4
Organic N
Ammonia N 8.5 18.8
Nitrate N 141.8 312.9
Total 400.3 883.1
Phosphorus
Non-living 25.9 57.1
Organic P
Inorganic P 8.1 17.9
Total 34.0 75.0
Figure 8 shows the dynamic behavior of the phytoplankton
biomass in the epilimnion for a continuation of the loads
indicated in Table 7 and for a decay of organic nutrients
of 0.001/day. This represents a "reasonable" condition
on the system decay coefficients. As can be seen, the
spring peak of phytoplankton reaches a new dynamic
equilibrium after about 8-10 years or about equal to
the detention time of the Lake.
The spring peak under this "reasonable" condition reaches
a maximum value of over 16yg chlor./l or about 45%
higher than the present peak. The fall peak also in-
creases to just under 10 yg/1 from present values of
about 8 jag/1 or about 25% increase. The dynamic behavior
of the phytoplankton under these conditions can be
understood further from Fig. 9 which also shows the
behavior of the inorganic nitrogen and available
phosphorus. All variables are for the epilimnion.
As shown, the lake as described by a "reasonable"
32
-------
OJ
U)
O)
a.
O
a:
O
I
O
z
O
I-
Q.
O
H
X
Q_
20
10
0
20
10
0
20
10
0
(11.4)
(15.9)
(16.4)
y
17
(13.2)
(16.0)
10
(16.4)
(14.1)
(14.9)
(15.3) (15.7)
(15.8)
(15.8)
8
(16.1)
(16.2)
11
12
13
14
15
16
(16.4)
(16.4)
A/0 TE: VA L UES IN PA R EN THESES ARE
COMPUTED PEA K SPRING VA L UES
18
19
20 '
TIME, years
Figure 8. Dynamic behavior of phytoplankton biomass in epilimnion-
continuation of "present" inputs
-------
^ >""
2 ^ 20
H
x
o 10
DC
o
^_ 0.30
s
DC
O)
E
K
co
DC
O
X
Q_
CO
O_
Q_ O)
uj E
CO
_J
0.20
0.10
0.0
0.06
0.04
0.02
0.00
MAXIMUM, SPRING
MAXIMUM, FALL
MINIMUM
10
14
18
22
MAXIMUM
MICHAELIS LEVEL
10
14
18
^MINIMUM
MAXIMUM
MINIMUM
MICHAELIS LEVEL
10 14
TIME, years
Figure 9. Dynamic behavior of phytoplankton, inorganic
nitrogen and available phosphorus in epilim-
nion-continuation of present inputs
34
-------
set of system parameters is not in equilibrium with respect
to the present loads. Peak biomass continues to increase with
the continuation of present loads. In contrast to the change
in the peak spring biomass, the average annual biomass in the
epilimnion is computed to change by about 0.9 yg/1, an increase
of 20% or less than half the increase in the peak spring con-
centration. Changes then in spring peak concentrations are
not paralleled by equal changes in the average annual concen-
trations. This is discussed more fully below. Also, after
some initial time, the increase in biomass is controlled by
the nitrogen and not the phosphorus as indicated by the increase
in the minimum level of phosphorus about the Michaelis level.
"Michaelis level" refers to the concentration of nutrient at
which the growth rate of the phytoplankton is half of the
maximum growth rate. This can also be seen in Fig. 10 in
which N/KM + N represents the nutrient limitation for either
nitrogen or phosphorus and KM is the appropriate Michaelis
level. The nutrient balance in the spring is surprisingly
sensitive to the distribution of the nitrogen and phosphorus
concentrations. This can also be seen from the present data
which indicate that the spring peak is controlled primarily
by phosphorus but that nitrogen levels are approaching levels
in the spring that could control growth. The simulation using
the mix of nitrogen and phosphorus input loads as shown in
Table 7 indicates that nitrogen may be the nutrient that will
affect growth more than the phosphorus. This, of course,
depends on the nitrogen-phosphorus input load distribution.
A full summary across all load distributions is given be-
low. The results as shown in Fig. 10 are however extremely
interesting since they show that the lake may be in a delicate
balance and that what appears to be a limiting nutrient during
one period of years may not continue to affect growth in the
same manner in later years. In both the spring and fall,
nitrogen assumes a relatively greater role in nutrient limita-
tion than does phosphorus. The effect is particularly
35
-------
A. SPRING BLOOM (day 120-165)
LU
LL
U_
LU
2
2^ 0.8
LJJ
E
I-
ID
0.4
0.0
NO LIMITATION
PHOSPHORUS
50% LIMITATION
MAXIMUM LI MIT A TION
NITROGEN
I I I I/ I I
10 14
TIME, years
18
o
O z 0.8
I- +
B. FALL BLOOM (day 225-300)
NO LIMITATION
\-
z.
LJJ
E
I-
0.4
0.0
PHOSPHORUS
50% LIMITATION
MAXIMUM LIMITATION
I I i /I I I
NITROGEN
\ I
10 14
TIME, years
18
22
Figure 10.
Nutrient limitation effect under continua-
tion of present loads in epilimnion
36
-------
noticeable in the spring bloom where after about 3-4 years,
nitrogen becomes more limiting. It whould be stressed how-
ever, that the model does not include any nitrogen fixing
algae which would alter the nutrient limitation effect
especially in the fall when blue green algae would be dominant
Also, the computed shift to nitrogen limitation reflects,
to some degree, the particular model structure that is
used in the simulation. The evolution of a nitrogen-
limited system is a much more complex phenomena of
species adaptation and readjustment of the upper trophic
levels than is indicated by the Lake I model. Neverthe-
less, the results are interesting and do indicate a
general direction and sensitivity of the Lake to the
two primary nutrients.
Figs. 11 and 12 show the behavior of the annual average
values for segment #1 (0-17 meters), segment #2 {17-90
meters) and the lake average concentration, weighted
volumetrically. Referring to the chlorophyll concentra-
tions in Fig. 11, the substantial difference between
annual average epilimnion level and the lake average
can be noted. Also, the relatively small change of
13% in the lake average concentration can be contrasted
to the change in the peak concentration of 45% shown in
Figs. 8 and 9. The total inorganic nitrogen (TIN)
plot shown in Fig. 11 indicates that the lake is in
equilibrium on an annual average basis with that nutrient.
The effect of the nitrogen limitation is quite clear from
a comparison of the TIN and the available phosphorus.
The latter nutrient is continuing to increase although
the biomass in the epilimnion has reached an equilibrium
level governed essentially by the conversion of the TIN
in the upper layer. Note however, that the stoichiometric
conversion does not apply to the annual averages but to
the peak values shown in Figs. 8 and 9. That is, the
approximately 165 yg TIN/1 in segment #1 determines the
37
-------
o
^
« °-
e§
I2
*g
0.36
< 0)
g E 0.24
OZ
0.12
0.00
uS
S 0-06
O
x
§_ 0.04
<
0.02
0.00
SEGMENT NO. 1
LAKEAVG
SEGMENT NO. 2
10
14
18
22
SEGMENT NO. 2
LAKEAVG
SEGMENT NO. /
I I
10
14
18
22
SEGMENT NO. 2
=====
LAKEAVG
.
SEGMENT NO. 1
6 10 14
TIME, years
18
22
Figure 11. Yearly average changes - continuation of
present inputs
-------
CO
D
cc
O
CO C^
O en
<
I-
o
0.06
0.04
0.02
0.00
0.6
en
E
LLJ
CD
O
CC.
5 0.2
_J
<
I-
g 0.0
0.6
O
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cc.
O _
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< E
CJ
a
o
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0.0
SEGMENT NO. 2
10
14
18
SEGMENT NO. 2 & LAKE AVG
SEGMENT NO. 1
j I
10
14
18
SEGMENT NO. 1
LAKE AVG
SEGMENT NO. 2
I I I
10 14 18
TIME, years
LAKE AVG
22
22
22
26
26
26
Figure 12
Yearly average change (cont.) - continua-
tion of present inputs
39
-------
peak level of phytoplankton of 16.4 yg/1. Because of
the nature of the spring and fall blooms, a similar
simple relationship does not exist between the TIN and
the annual average chlorophyll.
Fig. 12 shows the total phosphorus, nitrogen and "bio-
logical" carbon (phytoplankton and zooplankton). Again,
the total phosphorus and nitrogen plots show that the
lake is not in equilibrium with the present phosphorus
load. It is clear from Fig. 12 and the preceding figures
that it would be difficult to make meaningful statements
about phytoplankton biomass just from models that pro-
jected annual whole lake averages of total phosphorus
or nitrogen. For example, an annual lake average of
50 ygP/1 is computed which stoichiometrically would
yield a phytoplankton biomass of 50 yg chlorophyll/1
which is significantly higher than that calculated by
the dynamic kinetic model. A similar argument applies
to the total nitrogen.
One concludes therefore that a continuation of present
loads will result in a continual increase in peak
biomass for about a decade and that nitrogen would
become increasingly important as a limiting nutrient.
Peak biomass is estimated to increase by 45% over pre-
sent levels under a continuation of present nutrient
inputs. Further,- models and analyses that deal only
with annual lake averages and total nutrients may be
severely in error in projections, at least when compared
to the results of the dynamic model.
RESPONSE UNDER ZERO INPUT
In order to further study the behavior of the Lake under
different load conditions, a run was constructed which
utilized the present initial conditions of all v
-------
dynamics as the lake "winds down." The run is not
intended in any way to be a realistic representation
of the behavior of the lake in the past but rather is
simply another insight into the behavior of the model
with no external forcing functions.
Fig. 13 shows the phytoplankton chlorophyll in the
epilimnion over a 16 year computation with zero nutrient
input and present initial conditions. (The first
year computation differs slightly from that in Fig.
8 due to some differences in recycle kinetics.) The
results show that the fall bloom is the first to dis-
appear and is essentially gone by about 5-6 years and
the system is characterized for the remainder of the
computation by a single peak. The peak occurs later
and later in the year so that by the 10th year, the
peak occurs close to the end of June.
Figs. 14 and 15 show the change in the maximum and
minimum values of key variables for the zero nutrient
input case. The rapid decrease in the zooplankton is
interesting and accounts in part for the disappearance
of the fall phytoplankton bloom. The decrease of
the zooplankton reduced the fall recycling of nutrients
leading to the decline of the fall bloom. Fig. 15
shows that both nitrogen and phosphorus interact to
control phytoplankton growth as indicated by the min-
imum values of both nutrients being at or below Michaelis
levels. The maximum values of the chemical variables
and the phytoplankton appear to exhibit a type of first
order decay over time although the zooplankton decline
and the available phosphorus (for the first three
years) are exceptions. The equivalent first order
decay for the maximum phytoplankton chlorophyll is about
,00063/day.
41
-------
10
-------
0.00
6 10
TIME, years
Figure 14. Maximum and minimum values, epilim-
nion, present initial conditions,
zero nutrient input
43
-------
cr 0.08
o> 0.3
£ 0.2
<
£ 0.1
Z 0.0
0.02
0-01
0.00
z^ 0.008
MAXIMUM
MINIMUM
I 1
10
flQ 01 _
E t
MAXIMUM
MINIMUM
10
6 10
TIME, years
14
14
14
18
18
18
Figure 15. Maximum and minimum values-(cont.)
epilimnion, present initial condi-
tions, zero nutrient input
44
-------
"PASTORAL" RESPONSES
As discussed in Section IV, an estimate was made of the
nutrient loads that prevailed at some earlier time, a
so-called pastoral condition. The loads are shown in
Table 5. The results of such a simulation provide an
approximate basis for measuring the degree to which present
biomass exceeds some earlier level. Using "reasonable"
long term kinetics, i.e. sinking of phytoplankton and
decay of the non-living organic nutrient fraction, (.00I/
day), the results are summarized in Figs. 16-20.
As shown in Figs. 16 & 17, the spring peak value is
estimated to decrease to about 7 yg/1, a decrease of
about 40% from present peak values. The broad fall
peak is estimated to decrease to less than 4 yg/1,
a decrease of almost 50% from present fall values.
Fig. 17 can be contrasted to Fig. 9, the continuation
of present loads. As the comparison indicates, the
pastoral load system is primarily phosphorus limited
in the spring. This is further indicated by Fig. 18(a)
which shows phosphorus limitation in the spring at a
constant level of about 0.28 although nitrogen approaches
the 50% limitation in later years. Fig. 18 also
shows the nutrient limitations for the fall bloom
and surprisingly indicates that the growth during that
time is progressively more nitrogen limiting. This
again may be an effect of the particular nitrogen-
phosphorus load distributions used for the pastoral case.
A different mix of nutrients would result in a different
nutrient limitation effect.
The yearly average changes computed for the pastoral
loads are shown in Figs. 19 and 20. Phytoplankton
chlorophyll on the annual average in the epilimnion
decreases by about 40% to an equilibrium value of less
than 3 yg/1. The time to equilibrium for each of the
variables is about 10-15 years. The results of the
computation on the state of the Lake under these
pastoral conditions are summarized in Table 8.
45
-------
20
^ 10
O5
a.
(10.6)
(10.5) (10.0) (9.5)
(9.2) (8.8) (8.5) (8.3)
20
8
Q_
O
DC
O
z 10
o
z
o
-(8'1) <7'9> <7'8> (7.6) (7.5) (7.4) (7.3) (7.3)
9
10 11
12
13 14
15
16
0_
O
I
°- 10
NOTE: VALUES IN PARENTHESES ARE
COMPUTED PEAK SPRING VALUES
(7.2) (7.2) (7.1) (7.1)
17
Figure 16
18 19
20
TIME, years
Dynamic behavior of phytoplankton biomass in epilimnion,
"pastoral" inputs
-------
_ 30
>K
£o
10
O
O
z z
< 05
HI-
0
0.30
0.20
0.10
0.00
% 0.030
QC
O
X
g _ 0.020
to 0.010
< 0.000
SPRING MAX
FALL MAX
I
MINIMUM
10
14
18
MAXIMUM
MICHAELIS LEVEL
J I I
. MINIMUM
I I
10
14
18
22
MAXIMUM
MICHAELIS LEVEL
-.MINIMUM.
10 14
TIME, years
18
Figure 17.
Dynamic behavior of phytoplankton, inorganic
nitrogen and available phosphorus in epilim-
nion "pastoral" inputs
47
-------
A. SPRING BLOOM (day 120-165)
o
LLJ
LJ_
a i-o
2
^^ 0.8
0.4
^ 0.2
DC
=> 0.0
/NO LIMITATION
NITROGEN
50% LIMITATION
I I
PHOSPHORUS
I I I
10 14
TIME, years
18
22
o
LU
1.0
2^0.8
£ +
S 0.6
LLI
E
i-
0.4
0.2
0.0
B. FALL BLOOM (day 225-300}
NO LIMITATION
PHOSPHORUS
NITROGEN
, MAXIMUM LI MIT A TION
I /I I I I I
10 14
TIME, years
18
22
Figure 18. Nutrient limitation effect under pastoral
inputs-epilimnion
48
-------
Q_O_
o '
0
0.30
o
°'20
cc ..
oz
ZUJ
cc
o
0.10
0.00
0.020
co _
O--.
Q- O5
ujE
CO
<
0.010
> 0.000
<
I
SEGMENT NO. 1
LAKEAVG
j SEGMENT
II I I I I III I I I NO 2
10
14
18
22
SEGMENT NO. 2
SEGMENT NO. 1
I I I I I I I I I I I I
10
14
18
22
SEGMENT NO. 2
J I I L
SEGMENT NO. 1
J I I I I L
10 14
TIME, years
18
22
26
26
Figure 19. Yearly average changes - pastoral inputs
49
-------
0.040
a.
0.030
DC
O
CO
O
I
O_
0.020
O
0.010
0.000
SEGMENT. NO 2
'
SEGMENT NO. 7
LAKE AVG
I I I I I I I I I I
10 14
TIME, years
18
22
oc
H
o
0.4
0.3
2
0.1
0.0
SEGMENT NO. 2
5555======
SEGMENT NO. 1
LAKE AVG
i I i I I 1 1 1 1 1 1 L
10 14
TIME, years
18
22
Figure 20. Yearly average change(cont.)-pastoral
inputs
50
-------
TABLE 8
COMPUTED STATE OF LAKE ONTARIO
UNDER "PASTORAL" CONDITIONS1
Max. Min. Annual Average
Variable
Chlorophyll "a"-yg/l
Total Inorganic
Nit.-mg N/l
Available Phosphorus
mg p/1
Total Phosphorus
mg P/1
Total Nitrogen
mg N/l
During-
Year
7.0
0.16
0.011
0.014
0.22
During
Year
0.9
.025
0.001
0.012
0.19
0-17m
2.6
0.10
.007
.013
.21
17-50m
0.4
0.17
.012
.014
.22
Whole
Lake
0.8
0.16
0.011
.014
.22
T>astoral Conditions - 20,500 Ibs P/day (9,300 kg P/day)
-406,000 Ibs N/day (184,200 kg N/day)
- Algal sinking rate - 0.1 m/day
- Decay of non-living organic nutrients-
.001/day
Maximum and minimum occur at different times for different
variables.
51
-------
Chlorophyll for the whole lake average decreases only
slightly from a level of about 1.6 yg/1 at present to
about 1.1 yg/1 under the pastoral conditions. This is
a decrease of 30%,somewhat lower than the epilimnion
annual average.
Overall, the simulation indicates a type of lower
bound that one can use as a measure of the increase in
biomass that has occurred in Lake Ontario due to increased
nutrient inputs. The results indicate that the average
annual phytoplankton chlorophyll in the epilimnion under
the pastoral loading was about 2.6 yg/1. This level
compares to an estimate of 5.7 yg/1 as the annual
average that is in equilibrium with the present load.
It is estimated therefore that the average annual
phytoplankton in the epilimnion is about twice the level
that existed under some previously unstressed environ-
ment.
REDUCTION OF NUTRIENT INPUTS
A variety of simulations were carried out under different
combinations of nitrogen and phosphorus inputs and under
different levels of key system parameters. A complete
summary is given in Section VI. Some details of two
particular levels of nutrient reductions are given here
because of their importance. The first level is that
indicated by Vollenweider , referred to as the
"Vollenweider" reduction and the second level is that
required by the Great Lakes Water Quality Agreement
referred to as the "Water Quality Agreement" reduction.
Vollenweider Reduction
In his pioneering paper on the relationship between
external nutrient input and resulting eutrophic state
of lakes, Vollenweider provided a basis for determining
the allowable nutrient load to bring a lake to a more
desirable eutrophic state. For Lake Ontario, an
"admissable" loading from Vollenweider is about 0.4 gms/
m2-year of total phosphorus or about 47,000 Ibs P/day.
52
-------
This would represent a reduction of about 40% from a pres-
ent input of about 75,000 Ibs/day. Empirical plots similar
to the original plots of Vollenweider appear to be in wide
use. It is therefore of interest to determine whether the
results of the dynamic simulation would agree with a projec-
ted decline in eutrophic state as estimated by Vollenweider.
Accordingly, a long term dynamic simulation was run
using 47,000 Ibs P/day and present nitrogen loads of
883,000 Ibs N/day with the reasonable kinetics of each
of the earlier runs. The results are summarized in
Fig. 21 and as shown, the 40% reduction in phosphorus
does not result in a concomitant reduction in phyto-
plankton biomass. The simulation actually indicates an
increase in peak biomass to about 15 yg chlorophyll/1.
The system remains phosphorus limited in the spring as
shown by the minimum values of phosphorus approaching the
Michaelis level, although nitrogen also has an important
effect on growth. The calculations indicate therefore that
a 40% reduction in phosphorus input actually results in
an increase in biomass over present conditions and, from
these calculations, does not result in an improvement
over present conditions. This, of course, can be anti-
cipated given the kinetics used in the simulations which
indicated the Lake Ontario is not in equilibrium with
the present inputs. These results indicate that the
present observed condition is approximately in equili-
brium with a load that is less than the load Vollenweider
projected as necessary for improvement in the lake. This
is a reflection of one of the hazards of the empirical
plots which assume that the present observed condition
of a lake is in equilibrium with the present observed
input nutrient load. This does not appear to be the
case for Lake Ontario.
The simulation shown in Fig. 21 was for an "immediate"
reduction of 40% of total phosphorus, i.e. a step func-
tion drop in load from present loads to 47,000 Ibs P/day.
One would normally expect that load reductions are actually
53
-------
^ 25
05
15
O.X
o
o
co
o
C
l
OTAL INORGA
ITROGEN, mg
p p
-» ro
o o
0.00
^ 0.030
DC
O
X
c/5 _ 0.020
O--
XQ-
Q. o)
uj E
m 0.010
<
0.000
Figure 21.
MAXIMUM, SPRING
MAXIMUM, FALL
MINIMUM
10
14
18
22
MAXIMUM
MINIMUM
MICHAELIS LEVEL
l < I i ' i I L
10
14
18
22
MAXIMUM
MINIMUM
f MICHAELIS LEVEL
10 14
TIME, years
18
22
Dynamic behavior of phytoplankton,
inorganic nitrogen and available
phosphorus in epilimnion-Vollen-
weider reduction
54
-------
accomplished over a period of time. A run was therefore
prepared assuming that the reduction is accomplished
linearly over a 10 year period. The results comparing
the two patterns of load reduction are shown in Fig.22.
Under a 10 year time interval to accomplish the 40%
reduction, peak biomass would continue to increase to
16yg/l or about 45% higher than present levels and then
gradually decrease to the new equilibrium value of
about 15yg/l. As one would expect the time to reach
a new equilibrium increases to about 25 years.
One concludes therefore from an examination of the
Vollenweider reduction case, that Lake Ontario phyto-
plankton biomass, on a lake wide average would continue
to increase and under a 10 year load reduction period
would reach peak values of 15 yg chlorophyll/1. A
new equilibrium level of 15 yg/1 would be reached in
about 25 years. The results indicate a surprising
exception to the general axiom that a reduction in
external loads will result in an improvement in
water quality- If the hypothesis that Lake Ontario
is not yet in equilibrium with the present loads
is correct, then a reduction in load will not necessarily
result in an improvement in water quality. The results
shown in Figs. 21 and 22 illustrate this exception and
indicate the importance of considering the dynamic
behavior of large lakes in decisions regarding nutrient
reductions.
Water Quality Agreement Loads
Because of the international importance of the phosphorus
loads agreed to by the United States and Canada , a
simulation was prepared using the agreed upon phosphorus
input. Fig. 7 shows the approximate historical phos-
phorus inputs to Lake Ontario and the United States -
Canada Agreement loads. Because the Water Quality
Agreement (WQA) loads are to be accomplished over a 5
year period, the load pattern can be approximated by a
step function decrease. The simulation therefore
55
-------
O)
Ul
CTi
20
X
a.
O
O 16
_j
I
O
12
a.
I8
Q.
*
LU 4
Q_
QC
85 o
REDUCTION OF PHOSPHORUS
OVER 10 YEARS
\-
D
a.
TIME, years
I-
D
o.
'IMMEDIA TE" 40% REDUCTION
OF PHOSPHORUS
TIME, years
I I
1111
15 21
TIME, years
27
33
Figure 22
Comparison of "immediate" Vollenweider phos-
phorus reduction with a 10 year reduction
period
-------
considers an immediate drop in phosphorus load to a
level of 54,800 Ibs P/day or an overall reduction
of less than 30%. Nitrogen loads were retained at
present levels. Kinetics are as before (phytoplankton
sinking velocity of 0.1 in/day and first order loss
of non-living organic nutrients of .001/day).
Th.e results are summarized in Figs. 23-25 and as one
might expect from the preceding discussion, phytoplankton
biomass is computed to continue to increase under the
WQA loads. Fig. 23 indicates that peak values are
estimated to increase to over 16 yg/1 or about 50%
higher than present peak levels. The system tends to
be phosphorus limited. The yearly average changes
shown in Figs. 24 and 25 indicate the relative insensitivity
of whole lake annual averages as a measure of response.
The epilimnion average annual responses indicates a time
to equilibrium of about 10 years, yet peak biomass
reaches equilibrium in about 15 years.
These calculations indicate that under the WQA loads,
the phytoplankton biomass of the open lake may
continue to increase for about a period of 15 years
or until the late 1980's. The 27% reduction in phos-
phorus would result in only about a 6% reduction in
peak phytoplankton at equilibrium. This is not meant
to imply that the WQA program is not a good one. These
computations indicate that the hopes for an expected
response of Lake Ontario may not be as high as antici-
pated under the Agreement.
Comparison to Empirical Loading Plots
As indicated previously, one of the classical works in
lake eutrophication and the effects of nutrient loadings
is that of Vollenweider . His work represented one
of the first synthesis of water quality data related
to accelerated eutrophication of lakes, with external
sources of nutrients, due to such inputs as "natural"
runoff, agricultural runoff and point sources of muni-
cipal and industrial wastes. An appeal of Vollenweider's
57
-------
_, 0) ^0
^ =t
O . or>
H * 20
^_l
"^ 1
|^15
Sfe10
i v~/
l~ oc
>0 5
Q- -r
r^ 0
CJ U
TOTAL INORGANIC
NITROGEN, mgN/l
p p o
'-* fo co
o o o
0/1/1
.uu
CO n f\c
AILABLEPHOSPHORU
mgP/l
ope
b o c
N) -^ C
< 0.00
MAX/MUM, SPRING
_ ^ MAXIMUM, FALL
MINIMUM
i 1 i i i i i i i i
2 6 10 14 18 2:
~ ^.^ ' MAXIMUM
MICHAELIS LEVEL M^IMUM
2 6 10 14 18 2:
MAXIMUM
MICHAELIS LEVEL
MINIMUM \
l i "^""""1""""" iii i
1 1 f
6 10 14
TIME, years
18
22
Figure 23.
Dynamic behavior of phytoplankton,
inorganic nitrogen and available
phosphorus in epilimnion-Water
Quality Agreement reduction
58
-------
o
0*1 5
h- r
£j 4
<>
-i1 3
51 a. *
00
to 2
£i 1
O
o
- ^^^' SEGMENT NO. 1
_
LAKEAVG
SEGMENT NO. 2
2 6 10 14 18 22 2(
Oc
.D
o
2~^
£-
^ CD
OE0.4
2LU
n nn
SEGMENT NO. 2
^ LAKEAVG
^^^^*^ ^
^^ ~~ SEGMENT NO. 1
'^
\
10 14
TIME, years
18
22
26
Figure 24 Yearly average changes - Water Quality
Agreement loads
59
-------
0.04
Q.
O)
DC
o
ol 0.02
CO
O
X
Q_
< 0.01
o
H
0.00
0.5
0.4
E 0.3
ai
O
§ 0.2
£0.1
O
0.0
SEGMENT NO. 2
SEGMENT NO. 1
I I I \ \ \ \ \ \ L
10
14
SEGMENT NO. 2
10 14
TIME, years
18
22
LAKEAVG
I I I I I \ I \ \
18
22
Figure 25. Yearly average changes (cont.)-
Water Quality Agreement loads
60
-------
analysis is its simplicity. There was very little avail-
able to environmental managers of lake water quality
that linked external loadings (which are controllable
in various degrees) to a measure of eutrophication. The
graphical plot of nutrient loading to the lake such as
2
phosphorus in grams/m - year as a function of mean depth
of the lake with a general division into eutrophic or o-
ligotrophic lakes provided a basis for decision making.
For a given depth of the lake, the "admissable" loading
can be read directly from the plot. This in turn can
be translated into treatment requirements. Indeed, for
the Great Lakes system, the analysis of Vollenweider
presumably formed an important input into the Great
Lakes Water Quality Agreement and also for nutrient
controls in other lakes of the world.
11 12
Others such as Dillon and Rigler and Bachman and Jones
have also attempted to relate various measures of eutro-
phication to loading rate or nutrient concentrations.
13
Dillon has summarized and critiqued nutrient budget
models extending from 1963 to 1974. All of the models
14
to date, including a detailed analysis by Vollenweider
deal with a nutrient such as total phosphorus as the
starting point. Inferences are then drawn from the models
as to relative degrees of eutrophication. In addition
to these models, various empirical plots, as noted pre-
viously, have been developed to relate loading to response
or nutrients in the lake to phytoplankton biomass. There
are at least three major shortcomings to these attempts
at exploring observed behavior: a) the empirical plots
are non-dynamic and assume a one to one correlation between
observed nutrient and/or biomass concentrations and in-
put loading, b) as a corollary, the models and plots
do not directly relate nutrient loading to the resulting
plant biomass and, c)the models and plots do not explore
the interactions between two or more nutrients. Further,
the models generally assume a completely mixed lake or
attempt in a minimal way to include stratification.
61
-------
f
The dynamic model of phytoplankton behavior ! which forms
the basis for the simulations reported herein provides a
means for displaying the relationship between loading
and nutrient plots and a dynamic mathematical modeling
framework. The hope is that each of the approaches
can be demonstrated to result from assumptions made
on the more generalized dynamic phytoplankton model.
In this way.- the underlying unity and direction will
be more apparent. While the assumption of a well mixed
lake is quite restrictive and not necessary, it is used
here in order to provide some comparability between
the analyses.
For a completely mixed lake, the following equations
may be used to represent the dynamics of the phyto-
plankton :
V = V (G - D ) P - V K P - QP (5)
v at = v (Gz ~ V z - QZ
V =VSl - Qp1 - K12 PI + W;L (7)
V dlT =Kl2Pl - QP2 - "PPV + W2 (8)
where P = phytoplankton chlorophyll (ug/1) , G and D = phyto-
plankton growth and death rate respectively, (I/day) Kg =
phytoplankton sinking rate (I/day) which incorporates the
sinking velocity, vertical dispersion effects and depth
of water, Z = zooplankton carbon (mg/1) , GZ and DZ represent
growth and death rate of zooplankton (I/day) , PI = dissolved
and detrital organic phosphorus (mg/1) , S-j^ = overall source
of organic phosphorus due to plankton respiration and excretion
(mg/l-day) , p2 = inorganic available phosphorus (mg/1) ,
K, 2 = decomposition of organic phosphorus (I/day), a^ is
the phosphorus chlorophyll ratio, V^ and W2 represent
62
-------
external loadings of organic and inorganic phosphorus
respectively (kg/day) and V, (km ), Q (m /sec) are the
lake volume, and outflow respectively. For simplicity
only one nutrient has been considered here, the lake
is not assumed to stratify and the only loss of nutrient
is through phytoplankton settling, assumptions which can
be quite important. Further, it should be recognized
that all growth, death and predation terms are complicated
non-linear functions of such factors as nutrients, light,
temperature and grazing rates. Details of the full lake
model are given in the earlier report on the Lake
Ontario model
If total phosphorus is used as the relevant nutrient
variable, then it can be shown that summing Equations
(5) and (8) and using phosphorus equivalents of all
plankton gives
V -sr^ = - Qp. - VK P + W. (9)
Qt t S t
where p. is the total phosphorus concentration and W
is the total phosphorus external loading.
Note that one of the forcing functions for the total
phosphorus is the phosphorus equivalent of the sinking
phytoplankton biomass. As such, strictly speaking,
Eq. (9) is not solvable since P is a variable. However,
keeping P constant temporarily, and combining with W
as a sink of phosphorus, the solution to Eq. (9) is
simply-
W. - K VP ,. t
p,. = (1 - exp(~)) + (p.) exp(~) (10)
t Q fco fc ° fco
where (p.) is the initial concentration of total phosphorus
and tQ is the lake detention time (=Q). Eq. (10) shows
that the time to a new steady state for a constant input
63
-------
is reached in about 2-3 times the detention time of the
lake. For Lake Ontario, this would be about 16-24 years.
However, the effect of the sinking biomass and losses
of organic nutrient fraction serves to reduce that time
to perhaps 10-15 years based on the previously discussed
long term simulation runs.
This effect of the sinking biomass can also be seen by
letting the phytoplankton biomass be some fraction of
the total phosphorus, i.e.,
P = <* pt
and then the solution is
Wt
Pt = -§ (1 - exp - (aKs + l/to) t)
+ (pt)Q exp (-t/t0) (12)
The exponent is therefore increased by aK and therefore
s
the time to reach a new steady state is decreased. For
Lake Ontario, and a continuation of present loads (Figs.
11 and 12) , P is about 6 \ig/l, Pt is about 50 ug/1 (at
equilibrium) and K is estimated at 0.1 m/day * 90 m and
is about 0.00013/day. For an eight year detention time,
1/t is .00034/day and the value of the exponent is
therefore about .00047/day or an equivalent response
time of 5.8 years. The loss of phosphorus through the
sinking biomass therefore reduces the response time by
about 2.3 years. The difficulty, of course, in any
practical problem is that the ratio P/Pt is exactly
the variable that must be projected under a different
loading regime and hence is not explicity known.
Therefore, under constant loadings in time, presently
observed total phosphorus would be correlated with waste
loadings some years earlier. But, loadings to Lake
Ontario have, of course, not been constant in time
64
-------
(Fig. 7) so that the presently observed total phosphorus
is correlated with some overall average loading over
approximately the past few decades.
This simple dynamic analysis on a total nutrient such
as phosphorus serves to illustrate the uncertainty
underlying plots of loading rate and nutrient for the
same year. This was also shown in the simulation using
the Vollenweider reduction which indicated that bio-
mass would continue to increase even after the reductions
were accomplished.
Another difficulty is that the relationship between
biomass and the relevant total nutrient is confounded
in the empirical plots. That is, the direct computation
of phytoplankton biomass under different external nutrient
loading is not possible from equations that deal only
with the total nutrient concentration in the lake. This
can be seen by the results summarized in the preceding
discussion (see especially Figs. 11 and 12 and 24 and 25.)
Nevertheless, accepting the notion that one is always
seeking a simple representation of complex phenomena,
the steady state assumption in Eq. (9) can be made,
giving
0 = Qp. - VK P + W.
"C S "C
or W. = Qp. + VK P (13)
U U O
Dividing through by the surface area of the lake and recog-
nizing that Q/A is H/tQ, where H is the average depth of
the lake, one obtains
2
The input loading is now an areal rate (gms/m -year)
65
-------
Taking logarithms of both sides of (14) gives
Wt
log <£-) = log (Pt/tQ + KsP) + log H (15)
A comparison of Eq. (15) to the plot of Vollenweider 5
indicates that the slope of the latter should be unity
(for the model used here) , and that the intercept is a
function of the total phosphorus concentration, the de-
tention time and the phytoplankton biomass and sinking
rate.
The intercept, therefore, of a plot of log H versus log
W. /A is a variable depending on a complex interaction
- 5
of biomass and total phosphorus concentration. Vollenweider
of course, recognized the fact that biomass and the total
phosphorus are related and provides an excellent qualita-
tive discussion of these interactions (5. p. 78ff.).
Eq. (15) shows quantitatively that the more eutrophic
lakes would generally have larger values of the intercept,
thus providing some basis for the division originally
made by Vollenweider . The intercept also indicates
that it is not possible, in general, to predict the biomass
level for a change in Wt/A due to the confounding of the
biomass level with the total in-lake phosphorus concen-
tration.
Only if it is assumed that P=a p as in Eq. (11) then:
Wi- 1
log ^ = log (P( -±- + K )) + log H (16)
A atQ s
which permits a direct relationship between biomass and
external loading for constant a. The difficulty with
Eq. (16) is the necessity to specify the fraction, a
which may vary under different eutrophic states. For
example, Table 11 (page 76) shows that a did indeed vary
significantly for the simulations carried out in this
report .
Recently, Vollenweider and Dillon have reexpressed
the loading versus depth plot to include the detention
66
-------
time and have suggested a plot of loading against depth
divided by the detention time. It can be noted from
Eq. (14) that this plotting is not possible without
again confounding the detention time in the intercept,
i.e. ,
]T = Pt + KsV tf (17)
or log wt/A = log (pt +KstQP) + log |- (18)
o
As shown, the detention time also appears in the intercept
as well as the independent variable which explains the
"bending" of the lines using Eq. (18). However, whether
Eq. (18) or Eq. (15) (or other variations thereof) are
used, the phytoplankton biomass is still incorporated
in the intercept and therefore not directly predictable.
Other formulations have therefore attempted to incorporate
the phytoplankton biomass as a plotting variable. For
example, Dillon and Rigler have explored log of the
summer phytoplankton biomass versus the logarithm of
the spring total phosphorus concentration. Because of
the specified time periods such a plot is a representation
of Eqs.(5)-(.8) in a complex way and is strictly an empirical
relationship not readily derivable from Eqs.(5)-(8). How-
ever, some insight into the predictive capability of such
plots can be obtained by rearranging Eq. (14) . Therefore,
or taking logarithms,
W
log P = - log Ks + log (^ - Pt/tQ) (20)
which indicates that the abscissa includes both the
external loading and within-lake total phosphorus
12
concentration. Bachman and Jones have used Eq. (20)
but plotted log P versus log Wt/V. The dilemma of trying
to predict biomass response is made clear by Eq. (20) .
67
-------
Due to the interaction of biomass, nutrient concentration
in the lake and external mass nutrient loading, it is
not possible to directly estimate the response since a
reduction in loading requires an estimate of the new
lake total phosphorus which in turn requires an estimate
of the new phytoplankton biomass. Only by simultaneous
solution of a set of equations such as Eqs. (5)-(8)
can such predictions be directly made.
Of course, the assumption of Eq. (11) can again be made
to give
log P = - log H (- + K ) + log W./A (21)
ato t
which as before requires an a priori specification of a.
Eq. (21) however would appear to be a useful equation
to use for plotting purposes but may be risky to use for
prediction purposes.
One concludes, therefore, that simplified plots of loading
rate versus lake geometry and flushing rates or plots
of a presumed limiting nutrient and biomass while interest-
ing in describing the general trends in lakes, are too
crude a level of analysis to premit meaningful statements
to be made about the effects of reduction in waste load
on phytoplankton biomass. Indeed, the one comparison
between a dynamic model and the loading plot of Vollenweider
as indicated above produces results in conflict with
the projection from the loading plot. Such plots will
always show an implied improvement in lake status as load
is decreased, yet the dynamic results show that if the
lake is not in equilibrium (such as is hypothesized for
Lake Ontario) then the projections from the empirical
plots may be significantly in error. Such plots may be
of some use for short detention time lakes which reach
equilibrium quickly- However, one would conclude from
the results presented in this Section that empirical
loading plots are not appropriate for large lakes such
as the Great Lakes.
68
-------
SECTION VI
SUMMARY OF LAKE RESPONSES TO NUTRIENT INPUTS
The preceding results indicated a variety of responses
of Lake Ontario to external nutrient inputs. A summary
and comparision of the responses is given in this Section
together with the results of simulations over a complete
range of nutrient loads.
SENSITIVITY OF PRINCIPAL SIMULATIONS
Table 9 shows a summary of the principal load simulations
which highlight key points of departure in various pro-
posed load reductions. The results of the preceding
Section indicated the change in peak spring phytoplank-
ton chlorophyll under a long term kinetic structure
that included a decay of the non-living organic nutrient
forms of 0.001/day. The most pessimistic assumption
with respect to phytoplankton changes would be to assume
that the organic fraction (as well as the inorganic
fraction) of the nutrients is conserved. Under that
kinetic assumption then, the only loss of nutrient from
the system is from sinking phytoplankton which, in this
model, are eliminated from the system when the biomass reaches
the sediment.
The most optimistic assumption would be to assume that
the Lake is presently in equilibrium with respect to the
present nutrient loads, especially the phosphorus load. As
indicated previously, this implies some loss of inorganic
phosphorus through a mechanism of chemical precipitation.
While there is considerable uncertainty over the potential
effect of this mechanism, the possibility of a sink of
inorganic phosphorus does exist. Therefore, a series of
runs were prepared for the load conditions of Table 9 and
incorporating the most optimistic kinetics, most pessimistic
kinetics and the "reasonable" set of kinetics used in the
last chapter. The results are shown in Fig. 26.
69
-------
JE
O
CC =
25
20
15
10
°z
zo
O
I-
>
I
a.
25
20
15
10
5
PRESENT
PESSIMISTIC
REASONABLE
OPTIMISTIC
I I I I I I
8 12 16 20 24
VOLLENWEIDER
PESSIMISTIC
^^v
REASONABLE
OPTIMISTIC
_L
8 12 16 20 24
YEARS
25
20
15
10
25
20
15
10
I I
WQA
PESSIMISTIC
m^^^
REASONABLE
I
I
OPTIMISTIC
I
8 12 16 20 24
PASTORAL
OPTIMISTIC
PESSIMISTIC
REASONABLE
J L
8 12 16 20 24
YEARS
Figure 26 Sensitivity of phytoplankton response to kinetic assumptions
-------
As one would expect, the responses vary widely over the
range of assumed conditions. Under the most optimistic
setting, the response of the Lake is immediate (a direct
consequence of the equilibrium assumption) and positive as
contrasted to the reasonable set of kinetics. However,
while the optimistic setting is possible, the degree to which
the inorganic phosphorus is removed from the Lake is quite
uncertain, at the present time. Therefore, it appears more
reasonable that such removal by chemical precipitation is
not occurring in any substantial amount (to say, within
-10-20% of the incoming load) and that the primary removal
mechanism is by settling of particulate phosphorus forms.
The remainder of this chapter therefore, summarizes the re-
sults of the simulations under the "reasonable" set of kinetics
used earlier.
SUMMARY OF SIMULATIONS USING REASONABLE KINETICS
Fig. 27 is a summary plot of the principal simulation
conditions, each under the reasonable kinetic assumptions.
The most obvious result in Fig. 27 is the relatively small
change between the continuation of present loads and the
WQA loads which indicates that it may be difficult to detect
any substantive change under the WQA. It should be stressed
again however, that all the results shown and discussed
previously are for the Lake 1 model which assumes a
horizontally well-mixed lake. The results in Fig 27 are
therefore for lake wide conditions in the epilimnion.
Near shore responses may be quite different. Further,- as
previously indicated in Fig. 26, peak values may reach
as high as 22 yg chlorophyll/1 under the pessimistic
assumption and a continuation of present loads. The imple-
mentation of the WQA loads would reduce this "worst" case
to about 20 yg/1. Under the reasonable kinetics of Fig. 27
that include organic decay, the change occasioned by the
WQA would be about 1 yg/1.
71
-------
to
I
Q_
O
oc
O
n:
Q_
LLJ
Q_
18
16
14
12
10
8
6
4
2
PRESENT CONDITION
WQA CONDITION
VOLLENWEIDER CONDITION
PASTORAL CONDITION
6 8 10 12 14 16 18 20 22 24
YEARS
Figure 27
Summary of peak phytoplankton response. Reasonable
kinetics: phytoplankton settling = 0.1 m/day,
K organic = 0.001/day, K inorganic = 0.0
-------
TABLE 9
SUMMARY OF PRINCIPAL
LOAD CONDITIONS
Simulation
Condition
Continuation
of Present
Load
Water Quality
Agreement Load
Vollenweider
Reduction
Pastoral
Loads
Total
Phosphorus
Metric
tons
Ibs/day day
75,000 34.0
54,800 24.8
46,900 21.3
20,500 9.3
%
of
present
100
73
63
27
Total
Nitrogen
Metric
tons
Ibs/day day
883,000 400.4
883,000 400.4
883,000 400.4
405,900 184.1
%
of
present
100
100
100
46
73
-------
Table 10 is a further elaboration of the system responses
for the reasonable kinetics. The relatively small impact
of the WQA loads are well as the Vollenweider reduction
case can be seen. In fact, the model computations indicate
that at the very best, one could expect about a 40% reduc-
tion from present phytoplankton levels.
A further breakdown of the nutrient components at equilibrium
in the epilimnion is given in Table 11 and plotted in Fig. 28.
Reasonable kinetics again apply. The most interesting feature
of the response is the relative insensitivity of the average
annual response in phytoplankton over a range of phosphorus
reduction. Furthermore, one of the important ratios in the
empirical annual average plots as discussed in Section V
and given in Eq. (16) is the ratio of phytoplankton biomass
to total nutrient. Table 11 shows this ratio to increase
from .12 to .20 and Fig. 28 shows the continued increase
in total phosphorus but without an accompanying increase in
phytoplankton chlorophyll. A constant assumption on the
ratio, a, as required by Eq. (16) for use in the empirical
plots does not appear to be a viable assumption for Lake
Ontario, at least when compared to the computed results of
Lake 1. The reason the ratio changes, is of course due to
the fact that the Lake is estimated to be progressively more
nitrogen limited as one increases the phosphorus load. This
is further illustrated in Fig- 29 which shows the phytoplankton
biomass under difficult levels of phosphorus loading. As
shown, for a range of phosphorus load from present loads of
about 75,000 Ibs P/day to about 45,000 Ibs P/day, the chlorophyll
level is relatively insensitive. At further reductions, the
slope is approximately linear. These results indicate the hazards,
and uncertainty of simple models of lake nutrients and phytoplank-
ton biomass. In the case of Lake Ontario, two factors seem to
preclude the use of simplified models, a) the relatively long
detention time of the lake and b) the interaction of both nitrogen
and phosphorus as important growth limiting nutrients.
74
-------
TABLE 10
ESTIMATED CHANGE IN PHYTOPLANKTON BIOMASS
UNDER DIFFERENT SIMULATION CONDITIONS
... _ Simulation
Simulation
Condition
Continuation of
Present Loads
Water Quality
Agreement Loads
Vollenweider
Reduction
Pastoral Loads
JA.U. LW . Z.1 .
Present
Spring
Peak(2)
1.55
1.50
1.35
.65
Annual
0-17m
1.25
1.20
1.20
.55
Average
17-90m
1.05
1.00
0.95
.5
(3)
Lake
Average
1.15
1.10
1.05
.5
(1) See Table 9 for loads for each condition. K organic = .001/day.
(2) Present peak assumed at 11 yg/1.
(3) Present annual average assumed at 4.7 ug/1 (0-17m); 0.9 ug/1
(17-90m) and 1.6 yg/1 (lake average)
75
-------
TABLE 11
COMPUTED DISTRIBUTION OF PHOSPHORUS AND NITROGEN COMPONENTS AT EQUILIBRIUM
Annual Average - Segment #1 (0-17 m)
CTi
Simulation
Condition ^
Continuation P
of Present
Loads N
Water Quality
Agreement P
Loads N
Vollenweider P
Reduction N
Pastoral P
Loads N
Total
Nutrient
cone.
yg/i
50
408
35
415
29
421
13
205
Equiv<
Phyto]
yg/i
5.8
58.
5.7
57.
5.6
56.
2.6
26.
alent
plankton
%<2>
12
14
17
14
19
13
20
13
Equiva
Zoopla
ug/l
1.7
17.
1.7
17
1.7
17
1.0
10.
lent
nkton
%
3
4
5
4
6
4
8
5
Non-Li
Organi
Forms
yg/i
5.9
168.
5.4
167.
5.2
165.
2.4
70.
ving
c
%
12
41
15
40
18
39.0
18.0
34.
Inorga
Nutri
yg/i
36.6
165
22
174
16.5
183
6.9
99
nic
ent
%
73
41
63
42
57
44
54
48
(1) See Table 9 for loads for each condition
(2) Percent of total nutrient concentration
-------
<
tu
CD
UJ
60
50
40
30
20
10
ORGANIC&
ZOOPLANKTON
PHOSPHORUS
TOTAL PHOSPHORUS
INORGANIC
PHOSPHORUS
I
I
I
10 30
"PASTORAL"
INPUT
40 50 60
VOLLEN. WQA
RED.
"PRESENT"
O OBSERVED TOTAL
PHOSPHORUS
"PRESENT"
PHYTOPLANKTON
CHLOROPHYLL
70 * 80
"PRESENT"
INPUT
INPUT - TOTAL PHOSPHORUS, 1000 Ibs P/day
Figure 28 Summary of phosphorus components computed
at equilibrium, 0-17m, nitrogen loads as
in Table 9, reasonable kinetics
-------
18
16
O)
14
X
O. 19
O 1Z
DC
O
I
O
10
O 8
6
Q_
O
2 I-
0
SPRING PEAK
AVERAGE ANNUAL
\
\
i
0 10 20 30 40 50 60 70 80 90
INPUT - TOTAL PHOSPHORUS, 1000 Ibs P/day
Figure 29 Spring and Fall peaks and annual average
chlorophyll at equilibrium in epilimnion,
reasonable kinetics
78
-------
SUMMARY FOR RANGE OF NUTRIENT LOADS
In order to explore the full behavior of the Lake 1 model
response, a complete series of simulations was conducted
over a range of nutrient inputs under two kinetic assumptions
on the organic decay coefficient, representing the pessimistic
and reasonable cases. Therefore, inorganic forms of the nut-
rient are assumed conserved under the two assumptions. The
results are shown in Figs. 30-32 and permit a first
estimate to be made of the open Lake response for 0-17 meters
under different combinations of nitrogen and phosphorus loading.
The shape of the functional relationship in Figs. 30 - 32
is particularly interesting and shows the regions where either
phosphorus or nitrogen is limiting. For example, if nitrogen
loadings are kept at present levels, the model will become
more and more phosphorus limited as the phosphorus load is
reduced. On the other hand, if nitrogen levels are at present
levels and phosphorus loads continue to increase, the simula-
tions indicate that nitrogen will become progressively more
limiting and there will be no increase in peak biomass even
though phosphorus loads are increasing.
Plots such as Figs. 30 - 32 are useful for assessing effects
of uncertainty in load estimates as discussed in Section IV.
Effects of sediment releases of nutrient can be estimated by
simply adding the net flux of nutrient to the external load.
Figs. 30 - 32 show, in this regard that if the sediment
input is approximately 10% of the external load , the
phytoplankton response is relatively insensitive to this
source except in the region where either nutrient may be
limiting.
IMPLICATIONS FOR DECISION MAKING
One can also determine from Fig. 31 that in order to main-
tain present peak phytoplankton chlorophyll at about 11 yg/1,
the total phosphorus loading must be reduced to about 35,000
Ibs P/day or about a 53% reduction of present inputs. But,
since it is estimated that pastoral phosphorus loads were
about 20,500 Ibs P/day, the total load of 35,000 Ibs P/day
represents actually about a 73% reduction of the total nut-
79
-------
00
o
T3
O
*O
tI
o"
16
14
12
10
o 8
o
o
cr
PRESENT
PASTORAL
3 4 f 5 f 6 7 + 8 9
PHOSPHORUS LOADING, 104 Ibs/day
PH YTOPLA NKTON
CHLOROPHYLL a AT
EQUILIBRIUM,
10 11 12
Figure 30
Peak phytoplankton chlorophyll, 0-17m, as a function
of nitrogen and phosphorus input - K organic = 0.0,
K inoraanic = 0.0
-------
CO
IT\
o
16
14
12
10
8
6
O
O
PRESENT
PASTORAL
PEAK PHYTOPLANKTON
CHLOROPHYLL a AT
EQUILIBRIUM, \tg/l
23
1 2f 3 4 f 5 f 6 7 f 8 9 10
PHOSPHORUS LOADING, 104 Ibs/day
11 12
Figure 31 peak phytoplankton chlorophyll, 0-17m, as a function
of nitrogen and phosphorus input - K organic = 0.001/day,
K inorganic = 0.0
-------
16
14
12
10
-*
8
6
o
o
0
PRESENT
PASTO -- 1
RAL 3
g
AVERAGE ANNUAL
PHYTOPLANKTON CHLOROPHYLL a
AT EQUILIBRIUM, ng/l
-8
-7
6
5
4
0
t-
I
fr
Ul
ct
«* \
\ \ \ \
13 5 7 9 11
PHOSPHORUS LOADING, 104 Ibs/day
/W£Y?/4 G£ X*/V/V6//4/.
PHYTOPLANKTON CHLOROPHYLL a
AT EQUILIBRIUM,
2h
0
3 '5' 7 ' 9 11
PHOSPHORUS LOADING. 104 Ibs/day
Figure 32 Average annual phytoplankton chlorophyll,
0-17m as a function of nitrogen and phos-
phorus input-Top fig.: reasonable kinetics,
bottom fig.: pessimistic kinetics
82
-------
rient input. This total includes both point municipal and
industrial inputs which are reasonably controllable as well
as agricultural non-point sources for which control procedures
are not yet available. Finally, only about 60% of the
total load discharged to the lake is from point sources.
The results therefore tend to indicate that if present
conditions are to be maintained, nutrient inputs from Lake
Erie together with some form of non-point control as well
as extensive point source control will be required. It
may therefore be difficult to achieve reductions below
present values of biomass.
The results of these simulations indicate that the
language of policy documents such as the Water Quality
Agreement may be somewhat overly optimistic; e.g. "The
Government of the United States of America and the
Government of Canada, determined to restore and enhance
water quality in the Great Lakes System;..." (Ref.(6),
page 2.) This is not to say that the present policy
is not a good one. Quite the contrary, the phosphorus
removal policy presently being implemented is certainly
in the right direction and was formulated based on the
the best available information at the time.
This research has simply indicated that hoped for re-
ductions in eutrophication of Lake Ontario may not be
realized until additional phosphorus reductions signi-
ficantly beyond the WQA are achieved. The primary
reason for this effect is the hypothesis that Lake
Ontario eutrophication is continuing to increase due
to the present input so that the nutrient loads and
lake wide quality are not in equilibrium.
Finally, it should be noted strongly again that these
simulations are indicative of open lake conditions
and do not reflect "near-shore" responses which may
be quite different. Also, research into the dynamic
83
-------
behavior of phytoplankton in large lakes (or for lakes
in general) is still very much in its infancy. Neverthe-
less, policies and decisions will continue to have to be
made even as ongoing research may indicate conflicting
results. It is hoped that this work has provided some
additional insight into the behavior of Lake Ontario to
aid in the development of further policies on nutrient
control for the lake.
84
-------
SECTION VII
REFERENCES
1. Thomann, R.V., D.M. Di Toro, R.P. Winfield and D.J. O'Connor.
Mathematical Modeling of Phytoplankton in Lake Ontario, 1.
Model Development and Verification. Environmental Protection
Agency,- Corvallis, Oregon. EPA 660/3-75-005. March 1975.
177 p.
2. Report to the International Joint Commission on the Pollu-
tion of Lake Erie, Lake Ontario and the International Section
of the St. Lawrence River, Vol. 3. International Lake Erie
and International Lake Ontario - St. Lawrence River Water
Pollution Control Boards, 1969. 329 p.
3. De Cooke, B.C., and D.F. Witherspoon. A Preliminary Lake
Ontario Water Balance During IFYGL. Proc. 16th Conf.
Great Lakes Res., IAGLR, 675-683, 1973.
4. Casey, D.J., and S.E. Salbach. IFYGL Stream Materials
Balance Study (IFYGL). Proc. 17th Conf. Great Lakes Res.,
IAGLR, 668-681, 1974.
5. Vollenweider- R.A. Scientific Fundamentals of the Eutro-
phication of Lakes and Flowing Waters, with Particular Refer-
ence to Nitrogen and Phosphorus as Factors in Eutrophication.
Organization for Economic Cooperation and Development,
Director for Scientific Affairs, Paris, France. 1968. 159 p.
6. Great Lakes Water Quality Agreement with Annexes and Texts
and Terms of Reference Between the United States and Canada.
Signed at Ottawa. April 15, 1972.
7. Loehr, R.C. Agricultural Runoff - Characteristics and Con-
trol. Journal of the Sanitary Engineering Division, ASCE.
98 (SA 6):909-925, December 1972.
8. Great Lakes Water Quality Board. Great Lakes Water Quality
Annual Report to the International Joint Commission. April
1973.
9. O'Connor, D.J., and J.A. Mueller. A Water Quality Model of
Chlorides in Great Lakes. Journal Sanitary Engineering, Div-
Proc. ASCE. 96 (SA 4):955-975, August 1970.
10. Bannerman, R.T., D.E. Armstrong, R.F. Harris, and G.C.
Holdren. Phosphorus Uptake and Release by Lake Ontario
Sediments. Environmental Protection Agency, Corvallis,
Oregon. EPA-660/3-75-006. February 1975. 51 p.
11. Dillon, P.J., and F.H. Rigler. The Phosphorus-Chlorophyll
Relationship in Lakes. Limnology and Oceanography. 19:767-
773, 1974.
85
-------
12. Bachmann, R.W., and J.R. Jones. Phosphorus Inputs and Algal
Blooms in Lakes. Iowa State Journal of Research. 49 (2,pt.2):
155-160, 1974.
13. Dillon, P.J. A Critical Review of Vollenweider's Nutrient
Budget Model and Other Related Models. Water Research Bulletin,
AWRA. 10 (5):969-989, 1974.
14. Vollenweider, R.A. Input-Output Models with Special References
to the Phosphorus Loading Concept in Limnology- Presented at
Conference on Chemical-Ecological Considerations for Defining
the Goal of Water Pollution Control. Kastamenbaum Society,
April, 1972, CCIW, Burlington, Ontario, 1973. 48 p.
15. Vollenweider, R.A., and P.J. Dillon. The Application of the
Phosphorus Loading Concept to Eutrophication Research. Natural
Resources Council of Canada, NRCC, No. 13690, Association
Commission on Scientific Criteria for Environmental Quality,
CCIW, Burlington, Ontario. 1974. 42 p.
86
-------
" TECHNICAL REPORT DATA
(I'li-asc read iNUructioiix on the reverse before completing)
I. ntPOHT NO. 2.
_EPA-600/3-76-065
4. TITLE AND SUBTITLE
MATHEMATICAL MODELING OF PHYTOPLANKTON IN LAKE
ONTARIO, PART 2. Simulations Using Lake 1 Model
3. RECIPIENT'S ACCESSION-NO.
5. REPORT DATE
August 1976 (Issuing Date)
6. PERFORMING ORGANIZATION CODE
7. AUTHOH(S)
Robert V. Thomann, Richard P. Winfield, Dominic M.
Pi Toro, and Donald J. O'Connor
8. PERFORMING ORGANIZATION REPORT NO.
9. PERFORMING ORG "VNIZATION NAME AND ADDRESS
Manhattan College
Bronx, New York 10471
10. PROGRAM ELEMENT NO.
1BA608
11. CONTRACT/GRANT NO.
Grant R-80Q610
12. SPONSORING AGENCY NAME AND ADDRESS
U.S. Environmental Protection Agency
Office of Research and Development
Environmental Research Laboratory
D'uluth, Minnesota 55804
13. TYPE OF REPORT AND PERIOD COVERED
Final
14. SPONSORING AGENCY CODE
EPA-ORD
15. SUPPLEMENTARY NOTES
See also EPA-660/3-75-005, PB-241 046
16. ABSTRACT
The results of a series of simulations of the response of the open lake region of
Lake Ontario to various levels of nutrient input are described. The simulations
use a simplified dynamic model of phytoplankton - nutrient interactions in a verti-
cally segmented structure. The analysis of long term simulations (10-20 years) indi-
cates that the overall loss rates of nutrient are of particular importance. Under
reasonable set of model parameters, the simulations indicate that the present ob-
served open lake phytoplankton biomass of Lake Ontario does not appear to be in
equilibrium with the present input nutrient load. Therefore, if the present load
is continued, it is estimated that spring peak phytoplankton chlorophyll in the
epilimnion will continue to increase to a new level about 45% higher than present
levels. The interaction of nitrogen and phosphorus is also described by the simula-
tions and the results indicate a tendency for nitrogen limitation to be an increasing
dominant factor in controlling the spring bloom. A estimated "pastoral" load simu-
lation, indicative of conditions prior to man's intensive activity, indicates that
spring phytoplankton levels were some 40% less than present levels and average annual
epilimnion biomass under equilibrium with present loads is about twice that under
pastoral conditions.
17.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
Water quality, simulation, mathematical
models, phytoplankton, nutrients,
nitrogen, phosphorus
b.lDENTIFIERS/OPEN ENDED TERMS
Lake Ontario
c. COSATI Field/Group
06F
12B
13. DISTRIBUTION STATl-MENT
Release to Public
19. SECURITY CLASS (Tin's Kcport)
Unlimited
21. NO. OF PAGES
97
20. SECURITY CLA^S (This page J
Unlimited
22. PRICE
EPA Form 2220-1 (9-73)
87
U.S. GOVERNMENT PRINTING OFFICE:
Region No. 5-11
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