E PA -600 /3 - 7 6-06 5 

August 1976 

C&EEII 

Ecological Research 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 

influences. 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 Information Service, Springfield, Virginia 221 61. 
EPA-600/3-76-065 

August 1976 

MATHEMATICAL MODELING OF PHYTOPLANKTON 

IN LAKE ONTARIO 

Part 2 

Simulations Using Lake 1 Model 

Robert V. Thomann 

Richard P. Winfield 

Dominic M. Di Tor0 

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 Ile, Michigan 48138 

U.S. ENVIRONMENTAL PROTECTION AGENCY 

OFFICE OF RESEARCH AND DEVELOPMENT 

ENVIRONMENTAL RESEARCH LABORATORY 

DULUTH, MINNESOTA 55804 
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. 

ii 
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 simulations 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 nutrient load does not result in an accompanying decrease in 

iii 
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 improvement 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 

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 control for Lake Ontario will, at best, be a "ho1ding"action 

rather than a significant improvement in the status of the 

be 

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 
CONTENTS 

Sections 

I 

I1 

TIT 

IV 

V 

VI 

VI1 

Conclusions 

Recommendations 

Introduction 

Purpose of Research 

Scope of Research 

Lake 1 Model Review 

The Simulation Problem in Large Lakes 

External Nturient Inputs for Simulations 

"Present" Inputs 

Variability of Inputs 

Simulation Inputs 

"Pastoral" Loads 

Historical Loads and the U.S.- 

Canada Agreement 

Results of Simulations 

Continuation of "Present" Inputs 

Response Under Zero Input 

"Pastoral" Responses 

Reduction of Nutrient Inputs 

Vollenweider Reduction 

Water Quality Agreement Loads 

Comparison To Empirical Loading Plots 

Summary of Lake Responses To Nutrient 

Inputs 

Sensitivity of Principal Simulations 

Summary of Simulations Using Reasonable 

Kinetics 

Summary for Range of Nutrient Loads 

Implications for Decision Making 

References 

Page - 

1 

4 

5 

5 

5 

8 

10 

16 

16 

18 

22 

22 

23 

30 

31 

40 

45 

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52 

55 

57 

69 

69 

71 

79 

79 

85 

V 
LIST OF TABLES 

,No. - Page 

1 

2 

3 

9 

10 

11 

Basic physical data of the Lake lmodel 

Estimated 1966-67 nutrient loadings 

Estimated nutrient inputs to Lake Ontario 

Nutrient loadings from Niagara River 

Estimated "pastoral" nutrient loadings 

Approximate historical phosphorus inputs 

Assumed "present" nutrient load distribution 

Computed state of Lake Ontario uiider "pastoral" 

(1966-67 and 1972) 

conditions 

Summary of principal load conditions 

Estimated change in phytoplankton biomass 

Computed distribution of phosphorus and nitrogen 

under different simulation conditions 

components at equilibrium 

9 

16 

17 

21 

24 

26 

32 

51 

73 

75 

76 

vi 
LIST OF FIGURES 

No. Page - 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

Major physical features included in Lake 1 Model 

System diagram - Lake 1 Model 

Time to equilibrium, conservative variable a) reduction in load b) response in concentration 

Illustration of dominant effect of initial condition during a one-year analysis 

The insensitivity of a one-year calculation to 

the overall loss rate 

Frequency distribution mean annual flows of 

Niagara River (18 6 0-19 72 ) 

Approximate historical phosphorus inputs to Lake 

Ontario and the U.S.-Canada Agreement inputs 

Dynamic behavior of phytoplankton biomass in 

epilimnion-continuation of "present" inputs 

Dynamic behavior of phytoplankton, inorganic 

nitrogen and available phosphorus in epilimnioncontinuation of present inputs 

present loads in epilimnion 

inputs 

present inputs 

initial conditions, zero nutrient input 

initial conditions, zero nutrient input 

present initial conditions, zero nutrient input 

nion, rlpastoral" inputs 

nitrogen and available phosphorus in epilimnion, 

"pastoral 'I inputs 

Nutrient limitation effect under continuation of 

Yearly average changes - continuation of present 

Yearly average change (cont.) - continuation of 

Phytoplankton behavior, epilimnion, present 

Maximum and minimum values, epilimnion, present 

Maximum and minimum values- (cont.), epilimnion 

Dynamic behavior of phytoplankton biomass in epilimDynamic behavior of phytoplankton, inorganic 

6 

7 

11 

14 

15 

19 

27 

33 

34 

36 

38 

39 

42 

43 

44 

46 

47 

vii 
18 

19 

20 

21 

22 

23 

24 

25 

26 

27 

28 

29 

30 

31 

32 

Nutrient limitation effect under pastoral inputsepilimnion, 

Yearly average changes - pastoral inputs 

Yearly average change (cont.) - pastoral inputs 

Dynamic behavior of phytoplankton, inorganic 

nitrogen and available phosphorus in epilimnionVollenweider reduction 

Comparison of "immediate" Vollenweider phosphorus 

reduction with a 10 year reduction period 

Dynamic behavior of phytoplankton, inorganic 

nitrogen and available phosphorus in epilimnionWater Quality Agreement reduction 

Yearly average changes - Water Quality Agreement 

Loads 

Yearly average changes (cont.) - Water Quality 

Agreement loads 

Sensitivity of phytoplankton response to kinetic 

assumptions 

Summary of peak phytoplankton response. Reasonable 

kinetics: phytoplankton settling = 0.1 m/day, 

K organic = 0.001/day, K inorganic = 0.0 

Summary of phosphorus components computed at equilibrium, 0-17m, nitrogen loads as in Table 9, 

reasonable kinetics 

Spring and Fall peaks and annual average chlorophyll 

at equilibrium in epilimnion, reasonable kinetics 

Peak phytoplankton chlorophyll, 0-17m, as a function 

of nitrogen and phosphorus input - K organic = 0.0, 

K inorganic = 0.0 

Peak phytoplankton chlorophyll, 0-17m, as a function 

of nitrogen and phosphorus input - K organic = 

0.001/day, K inorganic = 0.0 

Page 

48 

49 

50 

54 

56 

58 

59 

60 

70 

72 

77 

78 

80 

81 

Average annual phytoplankton chlorophyll, 0-17m as a 

function of nitrogen and phosphorus input - Top fig.: 

reasonable kinetics, bottom fig.: pessimistic 

kine tics 82 

viii 
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 

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 concluded 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 variation in the Niagara River loading above is equivalent to a 

population of about 1.6 million or about 25% of the present 

population. I't 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 lead conditions were used as mile posts: 

1) Continuation of present load, phosphorus=75,000 1bs P/day 

2) pastoral loads, phosphorus=20,500 lbs. P/day, 3)Vollenweider 

reduction, phosphorus=46,900 lbs P/day, and 4) U.S.-Canada Water 

Quality Agreement load, phosphorus=54,800 lbs. P/day. Nitrogen 

loading was used at 883,000 lbs N/day for all simulations 

except the pastoral conditions where the loading used 

was 406,000 lbs N/day. 

1 
Under a continuation of present loads and a "reasonable" 

set of system parameters, it is estimated that spring peak 

phytoplankton chlorophyll in +,he 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/l 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 pg/l as compared to 5.8 pg/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 pg/l 

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 implication 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 improvement in water quality. One concludes therefore from this 

one comparison between two models,that empirical loading 

2 
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 phytoplankton 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 hypotheses 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 phytoplankton peak biomass, a total phosphorus loading of 

about 35,000 lbs 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 measurable reductions below present levels of phytoplankton biomass. 

Finally, it should be noted strongly again that the conclusions from these simulations are indicative of open lake 

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 suTgest adjustments 

and corrections. 

and do not reflect near-shore responses which 

3 
SECTION I1 

RECOMMENDATIONS 

Because of the importance of near shore versus open 

lake problems, it is recommended that a detailed verification 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 verification 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. 

4 
SECTION I11 

INTRODUCTION 

PURPOSE OF RESEARCH 

Attention is directed in this report to the utilization 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 loading. The Lake 1 model is therefore viewed as an initial 

framework for estimating whole lake phytoplankton res.ponse 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 geographical 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 chlorophyll a. The emphasis is on the response of the 

open lake total biomass to a range of nutrient loading and the sensitivity of the response to varying 

estimates of model parameters and coefficients. 

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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 swnmary 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 lakewide 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. 

is estimated to be due primarily to zooplankton 

grazing and nitrogen limitation. The broad fall 

peak in phytoplankton is a complex interaction of 

The mid-summer minimum in phytoplankton 

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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Although the model parameters used in the verifications 

are all considered reasonable and within reported literaturn 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 detention 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 detention 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 

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external inputs. This, of course, can be seen from a 

nutrient balance equation for a well-mixed lake. Thus, 

where c=the whole lake nutrient concentration (mg/l), 

W is the external source of nutrients (kg/day), V is 

the lake volume, Q is the flow (m /sec) through the 

lake, to is the hydraulic detention time (=V/Q), 

K(l/day) is the overall decay of the nutrient due 

to settling or chemical reactions, and t is time. 

3 

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 (75,0001bs P/day). If total phosphorus 

were completely conserved (K=O), the total within-lake 

phosphorus concentration, pt, at equilibrium is simply 

from Eq. (11, (for a flow of 6570 m /sec (232,000 ft /see)), 3 3 

12 
or pt = .06 mg/L Now, average observed total phosphorus concentrations in Lake Ontario during the period 1967-70 and 1972- 

73 is about 0.02 mg P/1. For this initial condition, the concentration at the end of the first year would be about8.025 mg/l; 

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 concentrations 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 )r 

a value of K = .OOl/day, gives a value of p at equilibrium of 

about 0.015 mg/l, again close to the present observed concentration. The question then is: "Is a value of K=.OOl/day reasonable?" 

Unfortunately, the verification analysis does not necessarily provide 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. 

t 

Only two courses of action appear open for Lake Ontario. If long 

term data on some aspect of the lake biomass behavior were available, 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 recognition that the long term behavior has only been grossly approximated. 

13 
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15 
SECTION IV 

EXTERNAL NUTRIENT INPUTS FOR SIMULATIONS 

PRESENT " INFUTS 

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 {PHOSPHORUS 

I Metric tons I Metric tons I lbs/Day /Day %I lbs/Day /Day 8 

I I 

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. 

summarized the IFYGL inputs and Table 3 compares 

the two estimates. 

Casey and Salbach3 have 

TABLE 3 

(2r3) ESTIMATED NUTRIENT INPUTS TO LAKE ONTARIO 

(1966-67 and 1972) 

1,000 lbs/day(a) 

Total Phosphorus Total Nitrogen 

SOURCE - 1966-67 1972 1966-67 1972 

Niagara 42.2 45.9 522.2 482.4 

Tributaries 15.6 20.3 191.0 224.9 

Municipal 16.2 20.9 72.6 93.3 

Industrial 1.0 0.4 97.3 20.3 

Sub-Total 75.0 87.5 883.1 820.9 

Atmospheric (b) 9.9 9.9 137.1 137.1 

Groundwater (b) 0.2 0.2 2.0 2.0 

Total 85.1 97.6 1022.2 960.0 

a) 1,000 lbs/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. 

more widely and not in the direction of increasing 

flow. Further, there is a substantial change in the 

The total nitrogen load estimates vary 

I 

17 
estimate of the industrial nitrogen contribution between 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 distribution 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 

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 
5 

0 

I 

v) 

II 

IZ 

I 

IU 

w 

Iw 

U 

c3 

U 

0 

0 

Ia 

a 

a 

-I 

a 

3 

U 

w 

3 

0 

-I 

L 

w 

2 

I0 

IZ 

w 

0 

U 

w 

a, 

- 

LL 

19 
1966-67 estimates, the equivalent total phosphorus 

concentration estimated for the Niagara River was 

about .04 mg P/1 which was the approximate mean 

concentration measured during IFYGL. The standard 

deviation of the concentration is about .006 mg P/1 

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 concentration are uncorrelated) : 

- 

w = 6; 

and 

where 6 is the mean flow, 5 is mean concentration, 

E is mean mass input, s and s are the 

standard deviations of flow, concentration and 

mass input respectively. Applying Eqs. 13) 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 fluctuation 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 215% around the average. 

'Q' c W 

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. 

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 215%. This will, of course, assume 

some considerable importance in any simulations. 
a: 

2 

2 

w 

H 

cl: 

G 

3 

R 

I 

a, I 

tn 

a 

kl3 

a, 

2 

m 

t 

! 

i 

IC 

r 

a 

- IN 

r 

U 

I 

U 

U 

CT 

r 

0 

Ob 

0 

Tr 

Tr 

. 

m 

Om 

0 

b 

I- 4 

I 03 

..I c 

N 1:: 

00 

00 

OM 

om 

m 

m 

om 

0rl 

Tr 

N 

Tr 

. 

om 

04 

N 

. N 

v 

L 

0 

om 

ON 

m 

4 

N 

co 

m 

I I h' h 

.si , 

a 

a 

x 

2 

0 

0 

N 

m 

N 

4 

v 

2 

2- 

2 

a 

0 

0 

4 

rl 

m 

II 

. 

a, 

c, 

-i-i 4 

m 

a, 

c 

a 

-ti 

a 

m 

I=- 

m 

u * 

rl r-i 

a rb 

c, c, 

0 0 

E 5 

21 
SIMULATION INPUTS 

A range of conditions on the external nutrient inputs 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 

6 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 observed conditions in the Lake represent a llseriousrl 

condition or a condition close to "desirable". If 

water quality objectives are set without considering 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 phytoplankton 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 esti22 
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 simulation 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 lbs 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 lbs nitrogen/acre/year and 0.25 lbs 

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 

Water Quality Board .) 

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. 

The organic nitrogen 8 

23 
TABLE 5 

ESTIMATED "PASTORAL" NUTRIENT LOADINGS 

Total Nitrogen 

Organic - N 

Total Inorganic-N 

Ammonia - N 

Organic P 

Inorganic P 

I I 

lbs/day Total 

405,800 

133 700 

273,100 

41 , 800 

231,300 

20 I 500 

19 I 200 

1,300 

7 2 

Lake Ontario Basin: 2.227 x 10 acres(90,132 km 

Niagara Flow: 195,000 efs 

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 procedure to estimate the phosphorus loads was as 

follows: 

+ 

a) The population tributary to Lake Ontario was 

b) Given the 1970 population and load (exclusive 

determined using estimates by O'Connor and Mueller (9) 

of the pastoral input) a per capita loading of 

phosphorus was determined. 

c) A per capita loading of domestic waste water 

d) A time history of the per capita loading was 

was estimated. 

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. 

to provide a basis for comparison to the U.S.-Canada 

Agreement loads. The results of this analysis are 

shown in Table 6. 

f) Atmospheric inputs were not included in order 

TABLE 6 

APPROXIMATE HISTORICAL PHOSPHORUS INPUTS 

(Atmospheric Inputs Not Included) 

Estimated Estimated Load & 

Trib .Popul. Ibs/day/ Load Pastoral Input 

Year (Millions) Capita 1000 lbs/day 1000 lbs/day 

1900 

1910 

1920 

1930 

1940 

1950 

1960 

1970 

2.4 

2.7 

3.1 

3.5 

4.0 

4.6 

5.3 

6.0 

.003 

.003 

.003 

.004 

.004 

.007 

.009 

.011 

7.2 

8.2 

9.3 

14.2 

16.2 

32.2 

47.7 

66.0 

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 

lbs 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 
0 

m 0 

w 

0 

cy) 

0 

cu 0 

P 

\ 

\ 

\ 

I 

I 

I 

I 

0 

0 

F 

0 

00 

0 

co 

0 

e 

0 

(v 

0 

cc 

-rl a, 

E 

ma, 

7aJ 

*eP/d Sql 0001 'lndNl SntlOHdSOHd lVlO1 

27 
the range due to changes in Niagara River input (see 

Table 4) is significant and probably will mask any 

further attempts at detailedrefinementof the estimates 

such as landuse breakdowns. Indeed, for a range of 

+ 14,400 lbs P/day (equal to - one standard deviation), 

and an average per capita loading of 0.009 lbs 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 (6) Several 

points can be noted. The load estimated in 1971 of 

98,600 lbs P/day (44.8 metric tons/day)appears to be an overestimate 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 lbs P/day, simulations were prepared assuming input nutrient loads 

covering this range. 

~t 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 a1 .lo estimated the annual contribution 

of inorganic phosphorus from the sediments to be about 

1.4 x lo6 kg P/year (8,500 lbs 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 lbs P/day, the 

sediment input rises to 16%. Under future load reduction 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 

procedlure 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 111, 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 following 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 rn/day. 

3) Inorpanic 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 verification 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=O and K=O.OOl/day to illustrate the sensitivity 

of the solutions to varying loss rates of organic 

nutrients. The question of the decay or loss of inorganic 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 inorganic 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. 

1 

31 
TABLE 7 

ASSUMED "PRESENT" NUTRIENT LOAD DISTRIBUTION 

System Nutrient Load 

Metric Tons/Day 1000 lbs/Day 

Nitrogen 

Non-living 

Organic N 

250.0 551.4 

Ammonia N 8.5 18.8 

Nitrate N 141.8 

Total 400.3 

Phomhorus 

312.9 

883.1 

Non-living 25.9 

Organic P 

Inorganic P 8.1 

Total 34.0 

57.1 

17.9 

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 

ofO.QOl/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 16vg chlor./l or about 45% 

higher than the present peak. The fall peak also increases to just under 10 vg/l from present values of 

about 8yg/l 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 
I I\ 

0 - 00 0 0 a 

N 

0 - 00 

N N - 

I/~~'ellAHdOt101H3 NOIlNVldOlAHd 

33 
20 

15 

10 

5 

0 

- MICHAELIS LE VEL - -------- 

cn3 

K 

0 

r 

J 

rn 

Q 

> 

a 

a 

A - 

0.20 

0.10 

- MAXIMUM, SPRING 

MA XIMUM, FA L L - 

- 

MINIMUM 

I 1 I I I I I I I I 

2 6 10 14 18 

- 

MAXIMUM 

22 

0.06 

0.04 

0.02 

0.00 

Figure 9. 

MAXIMUM 

MINIMUM 

- 

MICHAEL IS LE VEL 

2 6 10 14 

TIME, years 

18 22 

Dynamic behavior of phytoplankton, inorganic 

nitrogen and available phosphorus in epilimnion-continuation of present inputs 

34 
1 set of system parameters is not in equilibrium with respect 

i 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 Fcg/l, an increase 

of 20% or less than half the increase in the peak spring concentration. Changes then in spring peak concentrations are 

not paralleled by equal changes in the average annual concentrations. 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 f 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 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 below. 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 limitation than does phosphorus. The effect is particularly 

The simulation using 

35 
Io 

w 

LL 

LL 

w 

z 

0 0.8 

I-2 

iz 

z+ 

5: 

0.4 

* 

NO LIMITA TION 

--- ---____ d -------- --- 

- PHOSPHORUS 

- 50% L IMITA TION 

_-____--- ,’ ----- 

- 

MAXIMUM LIMITATION 

- NITROGEN 

/ 

Iz 

w 

cc 

Iz) 

z 

- 

L 

w 

LL 

LL 

w 

z 

t-+ 

oz 0.8 

t 

NO LIMITATION 

---___---~------_---__ 

- PHOSPHO R US 

0.0 I 1 1 1 I/ 1 1 1 1 1 1 

6 10 14 18 22 2 

TIME, years 

k3 

22 

A 0.4 

Iz 

w 

M 

I- 

- 

- 50% LIMITATION 

- 

---_c_- -------- 

NITROGEN 

- MAXIMUM LIMITATION 

Figure 10. Nutrient limitation effect under continuation 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 however, 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. 

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. Nevertheless, the results are interesting and do indicate a 

general direction and sensitivity of the Lake to the 

two primary nutrients. 

The evolution of a nitrogenFigs, 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. 

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 1-19 TIN/1 in segment #1 determines the 

Referring to the chlorophyll concentra37 
6 

4 

2 

0 

-Io a 0.12 

0.00 

v)i 

3 0.06 U 

0 

r 

n 

0.02 d i 

a 

> 

a 0.00 

- 

- SEGMENTNO. 7 

- LAKE A VG 

- SEGMENT NO. 2 

2 6 IO 14 18 22 

SEGMENT NO. 2 - 

LAKE A VG - 

- SEGMENT NO. I I 

2 6 10 14 18 22 

- SEGMENT NO. 2 

7- 

7 

SEGMENTNO. 7 

2 6 10 14 18 22 

TIME, years 

Figure 11. Yearly average changes - continuation of 

present inputs 

3s 
- 0.06 

epa 

a 

oz 

8 

2 0.04 

I€ e 

.-I 

a 

Io 

Iz' 

0 

M 

M 

Q 

0 

0.02 

LAKE A VG 

2 

SEGMENT NQ. 1 

0.00 

0.6 

0.4 

0.2 

0.0 

0.6 

0.4 

0.2 

0.0 

2 6 10 14 18 22 26 

- SEGMENTN0.2 $r LAKEAVG 

SEGMENTNO. 1 

- 

2 6 10 14 18 22 26 

SEGMENTNO. I - 

LAKEAVG - 

- 

SEGMENT NO. 2 

2 6 10 14 1% 

TIME, years 

22 26 

Figure 12. Yearly average change (cont.) - continuation of present inputs 

39 
peak level of phytoplankton of 16.4 pg/l. 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 "biological" 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 projected annual whole lake averages of total phosphorus 

or nitrogen. For example, an annual lake average of 

50 pgP/l is computed which stoichiometrically would 

yield a phytoplankton biomass of 50 1-19 chlorophyll/l 

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 present 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 variables 

with zero external nutrient inputs. The simulation 

therefore is intended to show the behavior of the model 

40 
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 disappear 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 minimum values of both nutrients being at or below Michaelis 

levels. The maximum values of the cheniical 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 

. 0 00 63/day. 

41 
c 

.- 

0 

0 P m 0 0 F- 0 

I 'e 11 A HdOtl 01 H3 N OlX NVl dOlA Hd 

42 
>.f E" 0 

0.0 

0.16 

v,z 

30 0 + 0.12 

a 2, 

?+ 0.08 

zQE 

a 0 0.04 

" 40 

0.00 

& U 0.10 

2- 

Q = 0.00 

z 

2 6 10 14 18 

2 6 10 14 18 

2 6 10 14 18 

2 6 10 14 18 

TIME, years 

Figure 14. Maximum and minimum values, epilimnion, present initial conditions, 

zero nutrient input 

43 
z I 

0.06 t 

5. 0.04 

z 

r 

Q 0.00 

g 0.02 

2 6 10 14 18 

\ 

- 0.4 

z 

2 6 10 14 18 

0.02 

w aA3 

amQO' 

>O Qr a 

1 E 0.01 Qa E 

0.00 

2 6 10 14 18 

0.008 

0.006 

0.004 

0.002 

0.000 

2 6 10 14 18 

TIME, years 

Figure 15. Maximum and minimum values-(cont.) 

epilimnion, present initial conditions, zero nutrient input 

44 
'"PASTORAL 'I RE§ PONSES 

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, (.001/ 

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 pg/l, a decrease of 

about 40% from present peak values. The broad fall 

peak is estimated to decrease to less than 4 pg/l, 

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 nitrogenphosphorus 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/l. 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 
7 1 -2 x 

0 00 0 0 O% .- cv v 

0 

F 

0 

(v 

1/6d 'e 1lAHdOkJ 01 H3 NOlX NWl dOlAHd 

46 
z 

0 

IY 

z 

a 

-I 

n 

0 

I- 

> 

r 

n 

\ 

- 

Z 

F 

2 

a 

w 

c3 

0 

I2 

- 

- 30 \ 

cn 

a - 5 20 

g 10 

-I 

> 

I 

n 

0 

-1 

I 

u 0 

0.30 

MAXIMUM 0.20 

0.10 

0.00 

9 0.030 

E 

1-I 

m 0.010 

Q 

1 

Q 

> 

a 0.000 

- 

2 6 10 14 18 22 

MICHAELIS LEVEL 

- - 

MINIMUM 

2 6 10 14 18 

TIME, years 

Figure 17. Dynamic behavior of phytoplankton, inorganic 

nitrogen and available phosphorus in epilimnion "pastoral" inputs 

47 
!-- 

0 

w 

U 

U 

w 

m 

w 

L1: 

I3 

2 

- 

be, 

w 

LL 

L 

w 

z 

0 -- 

I-Z 

z 

w 

a 

I3 

z 

- 

1 .o 

0.8 

6.6 

0.4 

0.2 

0.0 

1 .o 

0.8 

0.6 

0.4 

0.2 

0.0 

NlTROGEN 

---__------------ 

50% LIMITATION 

PHOSPHORUS 

1 I 1 1 I 1 I I I I 

2 6 10 14 18 22 

TIME, years 

5. FALL BLOOM (day 225-300) 

PHOSPHQRUS 

------- 

50% LIMITATION 

NlTROGE 

MAXIMUM L lMl TA TION 

1 I 1 I 1 I i I 

2 6 10 14 

TIME, years 

18 22 

Figure 18. Nutrient limitation effect under pastoral 

inputs-epilimnion 
SEGMENT NO. 1 

y;I 

QI 

u 1 -> LAKE A VG 

I I I I I I I i I I I 

SEC 

0.30 

0.20 

0.10 

- 

SEGMENT NO. 2 

- LAKE A VG c c 

- SEGMENT NO. 1 

I I I I I I I I I I I I 

I 6 10 14 18 22 2 

I 

SEGMENT NO. 2 

LAKE A VG 

- 

SEGMENT NO. 1 

- 

0;OO J I I I I I I I I I I I I 

vi 

3 

U 

0 

a01 

SQ 

am 

m 

Q 

= a 0.020 

5 E 0.010 

3 0.080 

1 - 

a 

WENT 

Figure 19. Yearly average changes - pastoral inputs 

49 
8.040 

- 1 

Q 

0.030 

vi 

3 

Dz 

0 2 0.020 

2 0.010 

2 

SEGMENT. NO2 

SEGMENT NO. 1 

I 

Q 

I=- 

0.000 

2 6 10 14 18 22 

TIME, years 

SEGMENT NO. 2 

0.4 

ISEGMENT NO. 7 

LAKE A VG 

- 

I I I I I I I I I I I I 

\ 

,z 

0.3 

2 

w 

,c3 

0.2 

I=- a0.1 

0 

I0.0 

‘G 

Figure 20. Yearly average change(cont.)-pastoral 

inputs 

50 
TABLE 8 

COMPUTED STATE OF LAKE ONTARIO 

UNDER I~PASTORAL" CONDITIONS' 

Max. Min . Annual Average 

DuringZ During Whole 

Variable Year Year 0-17m 17-50m Lake 

Chlorophyll ggagr-~g/l 7.0 0.9 2.6 0.4 0.8 

Total Inorganic 

Nit.-mg N/1 0.16 .025 0.10 0.17 0.16 

Available Phosphorus 

mg P/1 0.011 0.001 .007 .012 0.011 

Total Phosphorus 

mg P/1 0.014 0.012 .013 .014 .014 

Total Nitrogen 

mg N/1 0.22 0.19 .21 .22 .22 

bastoral Conditions - 20,500 lbs P/day (9,300 kg P/day) 

-406,000 lbs N/day (184,200 kg N/day) 

- Algal sinking rate - 0.1 m/day 

- Decay of non-living organic nutr5ents- 

. 0 0 l/day 

$laximum 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 ug/l at present to 

about 1.1 pg/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 ug/l. This level 

compares to an estimate of 5.7 vg/l 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 environment. 

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. 

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 6 

referred to as the "Water Quality Agreement" reduction. 

A complete 

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 lbs P/day. 

52 
This would represent a reduction of about 40% from a present input of about 75,000 lbs/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 projected decline in eutrophic state as estimated by Vollenweider. 

Accordingly, a long term dynamic simulation was run 

using 47,008 lbs P/day and present nitrogen loads of 

883,000 lbs 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 phytoplankton biomass. The simulation actually indicates an 

increase in peak biomass to about 15 pg chlorophyll/l. 

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 anticipated 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 equilibrium 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 function drop in load from present loads to 47,000 lbs P/day, 

One would normally expect that load reductions are actually 

53 
2 6 10 14 18 22 

0.30 

It MINIMUM 

MICHAELIS LEVEL 

8.0 

2 6 10 14 18 22 

0.030 1 3 

A 

I 

;3i Q.010 

ef 

t 

MINIMUM 

MICHAELIS LEVEL 

2 0.000 

2 6 18 14 18 22 

TIME, years 

Figure 21. Dynamic behavior of phytoplankton, 

inorganic nitrogen and available 

phosphorus in epilimnion-Vollenweider 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 15vg/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 phytoplankton biomass, on a lake wide average would continue 

to increase and under a 10 year load reduction period 

would reach peak values of 15 ug chlorophyll/l. A 

new equilibrium level of 15 yg/l 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 impEovement 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 phosphorus 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 

6 

55 
I 

LndNl 

I 1 I I I 1 1 1 1 

CD cv 00 * 0 

I/6~’17AbldOUOlH3 NOIYNVldOlAHd YV3d 3NltldS 

P v 0 

cv 

56 
considers an immediate drop in phosphorus load to a 

level of 54,800 lbs 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 m/day and first order loss 

of non-living organic nutrients of .001/day). 

The 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 pg/l 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 phosphorus 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 anticipated 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 municipal and industrial wastes. An appeal of Vollenweider's 

57 
0.30 

0- -1 

zz 

Qm 

0 2- 

E E 0.20 

I-I- a 0.10 

ZW 

-u 

40 

I 

MAXIMUM, SPRING 

MAXIMUM, FALL 

MINIMUM 

MAXIMUM 

MI NIMUM 

MICHA E LIS LEVEL i 

2 6 10 14 18 22 

vi 3 0.06 I 

U 

0 

P 

a. 

a 0.04 

0, 

In MAXIMUM 

4 WE 0.02 L 

MICHAEL IS LEV a 

A 

Q MINIMUM 

- 

z 0.00 

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 
6' 

5 

4 

3 

2 

1 

0 

0.6 

0.0 

wE 

po 0.02 

a 

A 

-I - 

Q 2 0.00 

SEGMENT NO. 1 

LAKEAVG 

~ 

e 

SEGMENT NO. 2 

~ 

2 10 14 18 22 26 

- 

SEGMENT NO. 2 

LAKEAVG 

SEGMENT NO. 1 

SEGMENT NO. 2 

LAKE A VG 

SEGMENT NO. 1 

Figure 24 Yearly average changes - Water Quality 

Agreement loads 

59 
3 QLAKE A VG 

F 

m- 0.03 

2 0.02 

3 

€E 

0 

g -r 

3 QLAKE A VG 

F 

m- 0.03 

2 0.02 

3 

€E 

0 

g -r 

A 

Q 

.-I 

Io 

Iq 6.01 

0.00 

2 6 10 14 18 22 

SEGMENT NO. 2 

~ 

2 6 10 14 18 22 

TIME, years 

Figure 25. Yearly average changes (cont.1- 

Water Quality Agreement loads 

60 
analysis is its simplicity. There was very little available 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 

phosphorus in grams/m2 - year as a function of mean depth 

of the lake with a general division into eutrophic or 0- 

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. 

Others such as Dillon and Rigler l1 and Bachman and Jones 

have also attempted to relate various measures of eutrophication to loading rate or nutrient concentrations. 

Dillon l3 has summarized and critiqued nutrient budget 

models extending from 1963 to 1974. All of the models 

to date, including a detailed analysis by Vollenweider 14 

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 previously, 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 input loading, b) as a corollary, the models and plots 

do not directly relate nutrient loading to the resulting 

plant biomass and, clthe models and plots do not explore 

the interactions between two or more nutrients. 

the models generally assume a completely mixed lake or 

attempt in a minimal way to include stratification. 

12 

Further, 

61 
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 phytoplankton : 

l 

V-=V dP (G -D) P-VKsP-QP 

dt 

QP1 - 52 p1 + w1 v- dP1 'VS1 - dt 

V-=K dP2 p -Qp2-a GP+W2 dt 12 1 PP P 

(5) 

where P = phytoplankton chlorophyll (vg/l), G and D = phytoplankton growth and death rate respectively, (l/day) K = 

phytoplankton sinking rate (l/day) which incorporates the 

sinking velocity, vertical dispersion effects and depth 

of water, Z = zooplankton carbon (mgkl), GZ and D represent 

growth and death rate of zooplankton (lkday), p = dissolved 

and detrital organic phosphorus (mg/l), S1 = overall source 

of organic phosphorus due to plankton respiration and excretion 

(mg/l-day), p2 = inorganic available phosphorus (mg/l), 

K12 = decomposition of organic phosphorus (l/day), 

the phosphorus chlorophyll ratio, W1 and W2 represent 

P P 

S 

Z 

1 

is 

apP 

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 moael . 

3 3 

1 

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 

- - Qpt - VK P 3- Wt dpt 

Vdt- S (9) 

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 Wt 

as a sink of phosphorus, the solution to Eq. (9) is 

simply, 

where (ptlo is the initial concentration of total phosphorus 

and to is the lake detention time (=-I. Eq. (10) shows 

that the time to a new steady state for a constant input 

V 

Q 

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., 

t p=ap 

and then the solution is 

(1 - exp - (aKs - Wt 

Pk - - Q 

+ (ptIo exp (-t/to) 

The exponent is therefore increased 

+ Uto) t> 

by aKs and therefore 

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 pg/l, pt is about 50 vg/l (at 

equilibrium) and K 

is about 0.00013/day, For an eight year detention time, 

l/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. 

is estimated at 0.1 m/day f 90 m and aKs 

S 

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 biomass 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, - vKsP + Wt 

Wt = Qp, + VKsP 

Dividing through by the surface area of the lake and recognizing that Q/A is H/to, where H is the average depth of 

the lake, one obtains 

Wt H 

t, Pt + KsHP 

-= 

A 

The input loading is now an areal rate (gms/m 2 -year). 

65 
Taking logarithms of both sides of (14) gives 

5 

A comparison of Eq. (15) to the plot of Vollenweider 

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 detention time and the phytoplankton biomass and sinking 

rate. 

The inte’rcept, therefore, of a plot of log H versus log 

Wt/A is a variable depending on a complex interaction 

of course, recognized the fact that biomass and the total 

phosphorus are related and provides an excellent qualitative 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 concentration. 

of biomass and total phosphorus concentration. Vollenweider 5 

Only if it is assumed that P=a pt as in Eq. (11) then: 

Wt log a = + log H 

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 l5 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., 

or 

Wt 

- 

H 

= Pt + so 

- 

A 

log Wt/A = log + H log - 

to 

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). However, some insight into the predictive capability of such 

plots can be obtained by rearranging Eq. (14). Therefore, 

or taking logarithms, 

which indicates that the abscissa includes both the 

external loading and within-lake total phosphorus 

concentration. Bachman and Jones l2 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 (- -t Ks) + log Wt/A 

atO 

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 interesting 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 

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. 

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. 

between a dynamic model and the loading plot of Vollenweider 5 

Such plots may be 

65 
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 proposed load reductions. The results of the preceding 

Section indicated the change in peak spring phytoplankton 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, moat pessimistic 

kinetics and the "reasonable" set of kinetics used in the 

last chapter. The results are shown in Fig. 26. 

69 
\ 

h 

z 

4 

Er) 

cu 

Q 

a 

4 

T 

cy 

0 

h 

cr, 

T 

Q 

momom 

rnm-- 

momom 

CJN-- 

(l,’6d) NOINVUllld3 

NI llAHdOklOlH3 NOlXNVldOlAHd XV3d 

m 

m 

fd 

u 

-rl 

c, 

a, 

c 

-4 

x 

0 

a 

m 

a, 

k 

c= 

0 

u 

d 

0 

LI 5-i 

c 

a 

70 
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 

210-20% 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 results of the simulatiops 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 pg chlorophyll/l under the pessimistic 

assumption and a continuation of present loads. The implementation of the WQA loads would reduce this "worst" case 

to about 20 vg/l. 

that include organic decay, the change occasioned by the 

WQA would be about 1 pg/l. 

Under the reasonable kinetics of Fig. 27 

71 
NI llAHdOkjOlH3 NOIXNVldOlAHd XV3d 

72 
Simulation 

Condition 

Continuation 

of Present 

Load 

Water Quality 

Agreement Load 

Vollenweider 

Reduction 

Pastoral 

Loads 

TABLE 9 

SUMMARY OF PRINCIPAL 

LOAD CONDITIONS 

Total 

Phosphorus 

Metric 

tons 

.bs/day day 

75 I 000 34.0 

% 

Of 

present 

100 

i4,800 - 24.8 73 

L6,900 21.3 63 

!O, 500 9.3 27 

Total 

Nitrogen 

Metric 

tons 

Ibs/day day 

883,000 400.4 

% 

of 

present 

100 

883,000 400.4 100 

883,000 400.4 100 

405,900 184.1 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% reduction 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 lbs P/day to about 45,000 lbs 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 phytoplankton 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 

Present Ratio: 

Annual Average (3) 

Lake S imula t ion Spring 

Condition 0-17m 17 - 9 Om Average (2) Peak Cl) 

Continuation of 

Present Loads 1.55 1.25 1.05 1.15 

Water Quality 

Vollenweider 

Reduction 1.35 1.20 0.95 1.05 

Pastoral Loads .65 .55 .5 .5 

Agreement Loads 1.50 1-20 1.00 1-10 

(1) See Table 9 for loads for each condition. K organic = .OOP/day. 

(2) Present peak assumed at 11 pg/l. 

(3) Present annual average assumed at 4.7 pg/l (0-17m); 0.9 pg/l 

(17-90m) and 1.6 pg/1 (lake average) 

75 
bi 

w 

w 

a: 

E 

13 

w 

n 

El 

E 

5 

Q 

u 

9 

4 

\ 

tr 

1. 

.;i OV 

30 

-4 .rl - 

c 

40 

ccl 

a,x ahp 4c 

am34 

cl 

2 

Mw 

rrlrrl 

tnM OM 

44 -4 

LD cc) 

mcc) Nul 

m N 

44 

rmb 

m 

.. .. .. 

76 
I 

\ 

a 

77 
18 

16 

14 

12 

10 

8 

6 

4 

2 

0 

- 

SPRING PEAK 

I 1 I I I I I 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 nutrient 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 simulations 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 maintain present peak phytoplankton chlorophyll at about 11 ug/l, 

the total phosphorus loading must be reduced to about 35,000 

lbs P/day or about a 53% reduction of present inputs. 

since it is estimated that pastoral phosphorus loads were 

about 20,500 lbs P/day, the total load of 35,000 lbs P/day 

represents actually about a 73% reduction of the total nutBut, 

79 
- 

1 N3S3bcd 

80 
M 

c- Q, 

3 

lN3S3Ud 

138 '11OA 

!-- 

z 

W 

m 

w 

1 

a 

0 

Iv) 

a 

I I I a Q a a I 

81 
a 

Q 

0 

ZZ 

J 

u 

a 

0 

I7 

- 

AT EQUILIBRIUM, pg/I 

PHOSPHORUS LOADING, lo4 lbslday 

A VERAGE I~NNUAL 

PHYTOPLANKTON CH L 0 ROPH Y L L a 

AT EQUILIBRIUM, pg/l 

11 

PHOSPHORUS LOADING, lo4 lbslday 

Figure 32 Average annual phytoplankton chlorophyll, 

0-17m as a function of nitrogen and phosphorus 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.(G), 

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 reductions in eutrophication of Lake Ontario may not be 

realized until additional phosphorus reductions significantly 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. Nevertheless,. 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 VI1 

REFERENCES 

1. 

2. 

3. 

4. 

5. 

6. 

7. 

8. 

9. 

10. 

11. 

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. 

Report to the International Joint Commission on the Pollution 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. 

De Cooke, B.G., and D.F. Witherspoon. A Preliminary Lake 

Ontario Water Balance During IFYGL. Proc. 16th Conf. 

Great Lakes Res., IAGLR, 675-683, 1973. 

Casey, D.J., and S.E. Salbach. IFYGL Stream Materials 

Balance Study (LFYGL). Proc. 17th Con€. Great Lakes Res., 

IAGLR, 668-681, 1974. 

Vollenweider, R.A. Scientific Fundamentals of the Eutrophication of Lakes and Flowing Waters, with Particular Reference to Nitrogen and Phosphorus as Factors in Eutrophication. 

Organization for Economic Cooperation and Development, 

Director for Scientific Affairs, Paris, France. 1968. 159 p. 

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. 

Loehr, R.C. Agricultural Runoff - Characteristics and Control. Journal of the Sanitary Engineering Division, ASCE. 

98 (SA 6):909-925, December 1972. 

Great Lakes Water Quality Board. Great Lakes Water Quality 

Annual Report to the International Joint Commission. April 

1973. 

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. 

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. 

Dillon, P.J., and F.H. Rigler. The Phosphorus-Chlorophyll 

Relationship in Lakes. Limnology and Oceanography. 19:767- 

773, 1974. 

85 
2. Bachmanna 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 REPGRT DATA 

(I'k,asr read Iwmrc twtn 011 rhe rcvirsc bepm con 

1, RCPOR7 NO. 2. 

EPA-600/3-76-065 _L____ - 

4. TITLE AND SUBTITLE 

MATHEMATICAL MODELING OF PHYTOPLANKTON IN LAKE 

ONTARIO, PART 2. Simulations Using Lake 1 Model 

1. AUTHORtS) 

Robert V. Thomann, Richard P. Winfield, Dominic M. 

KEY WORDS AND DOCUMENT ANALYSIS ._ 17. 

a. DESCRIPTORS h.lDENTlFlERS/OPEN ENDED TERMS C. COSATI I:icld/Croup 

-- 

-_ - 

06F 

12B 

Water quality, simulation, mathematical Lake Ontario 

models, phytoplankton, nutrients, 

nitrogen, phosphorus 

18. I> IS T R 1 BUT I ON S T A T t ME NT 19. SECURITY CLASS (TitisRcporlf 21. NO. OF PAGES 

D.i Toro, and Donald J. O'Connor . PERFORMING ORG lNlZATlON NAME AN0 ADDRESS 

Manhattan College 

Bronx, New York 10471 

12. SPONSORING AGENCY NAME AND ADDRESS 

U.S. Environmental Protection Agency 

Office of Research and Development 

Environmental Re search Labor at or y 

hluth, Minnesota 55804 

16. SUPPLEMENTARY NOTES 

'ctitq=) 

2. RECIPIENT'S ACCESSIONNO. 

i. REPORT DATE 

August 1976 (Issuing Date) 

i. PERFORMING ORGANIZATION CODE 

3. PERFORMING ORGANIZATION REPORT NO. 

IO. PROGRAM ELEMENT NO. 

1BA608 

11. CONTRACT/GRANT NO. 

Grant R-80Q610 

13. TYPE OF REPORT AND PERIOD COVEEEO 

Final 

14. SPONSORING AGENCY CODE 

EPA-ORD 

See also EPA-66013-75-005, PB-241 046 

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. 

use a simplified dynamic model of phytoplankton - nutrient interactions in a vertically segmented structure. 

cates that the overall loss rates of nutrient are of particular importance. Under 

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. 

tions and the results indicate a tendency for nitrogen limitation to be an increasing 

dominant factor in controlling the spring bloom. 

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. - 

I- 16. ABSTRACT 

The simulations 

The analysis of long term simulations (10-20 years) indiThe interaction of nitrogen and phosphorus is also described by the simulaA estimated "pasroral" load simuRelease to Public 97 ~I 

122. PRICE 

Unlimited I 

EPA Form 2220-1 f9-73) 8 7 A u. 5. GOVERNMENT PRlNTlNG OFFICE: 1976-657-695/5487 Region No. 5- 1 I