## EPA-600 

## /3

# -76-06 

## 5 August 1976 

# C&EEII

EcologicalResearchSeriesResearchreportsoftheOfficeofResearchandDevelopment, U.S. Environmental ProtectionAgency,have been grouped into fiveseries.Thesefivebroad categorieswereestablishedtofacilitatefurtherdevelopmentandapplicationof environmentaltechnology.Eliminationoftraditionalgroupingwasconsciously plannedtofostertechnologytransferand amaximuminterfaceinrelatedfields. Thefiveseriesare: 1. EnvironmentalHealthEffectsResearch 2. EnvironmentalProtectionTechnology 3. EcologicalResearch 4. EnvironmentalMonitoring 5. SocioeconomicEnvironmentalStudies ThisreporthasbeenassignedtotheECOLOGICALRESEARCHseries.Thisseries describesresearchontheeffectsof pollutiononhumans,plant and animal species,andmaterials.Problemsareassessedfortheirlong-andshort-term influences.Investigationsincludeformation,transport,andpathwaystudiesto determinethefateofpollutantsandtheireffects.Thisworkprovidesthetechnical basisforsettingstandardstominimizeundesirablechangesinlivingorganisms intheaquatic,terrestrial,andatmosphericenvironments.

Thisdocumentisavailabletothepublicthroughthe NationalTechnicalInformationService,Springfield,Virginia22161.EPA-600/3-76-065 August 1976

MATHEMATICAL MODELING OF PHYTOPLANKTON IN LAKE ONTARIO Part 2 SimulationsUsing Lake 1Model

Robert V. Thomann Richard P. Winfield DominicM. Di Tor0 Donald J. O'Connor

Manhattan College Bronx,New York 10471

Grant No. R-800610

ProjectOfficer William Richardson Large Lakes Research Station EnvironmentalResearch Laboratory-Duluth Grosse Ile,Michigan 48138

U.S. ENVIRONMENTAL PROTECTIONAGENCY

OFFICE OF RESEARCH AND DEVELOPMENT

ENVIRONMENTALRESEARCH LABORATORY DULUTH,MINNESOTA 55804DISCLAIMER
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.

iiABSTRACT 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. Theproblem 

### of long term simulations (10-20years) that draw on short term observation and verificationperiods

(5years) 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 equilibriumwith 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" simulationusing load estimates, indicative of conditionsprior to man's intensive activity provides an approximation of an early state of the lake. This "hindcast"indicates that spring phytoplankton levelswere some 40% less than present levels and average annual epilimnion biomass under equilibriumwith present loads is about twice that under pastoral conditions. A series of analyses is also conducted comparing simulations from the dynamic model to estimatesmade from simplified plots of loading versus lake geometry. The results from the dynamic model indicate that a reduction in externalnutrient load does not result in an accompanying decrease in
iiiphytoplankton biomass, due to the hypothesized non-equilibrium condition of Lake Ontario. The dynamic model results are therefore in contrast to the results onewould 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 implicationsof the results appear to be 

### of some importance since the analyses indicate that itmay 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 ProtectionAgency. Work was completed 

### as of April, 1975.

ivCONTENTS
Sections I I1 

### TIT

IV

V

VI

VI1 Conclusions Recommendations Introduction Purpose of Research Scope of Research Lake 

### 1Model 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 Continuationof "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 DecisionMaking References Page 

# -

1 4 5 5 5 8 10 16 16 18 22 22
23 30 31 40 45 52 52 55 57
69 69
71 79 79 85

VLIST 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 

### 1Model System diagram

# - Lake 

### 1Model 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 60-19

### 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

vii18
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 reductionperiod Dynamic behavior of phytoplankton, inorganic

nitrogen and available phosphorus in epilimnionWater Quality Agreement reduction Yearly average changes

# -Water QualityAgreement

Loads Yearly average changes (cont.)

# -Water Quality

Agreement loads Sensitivityof 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 Fallpeaks 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 

### kinetics 82

viiiACKNOWLEDGEMENTS
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 reportmanuscript.

ixSECTION 

### 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 observationperiod 

### 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 kineticparameters 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, thevariation 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 inherentvariability. 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 (albeitreasonable) system kinetics. Near shore responses and resulting conclusions may be considerably different than indicatedbelow. Fourprincipal 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. 1Under a continuation of present loads and a "reasonable" set 

### of system parameters, it is estimated that spring peak phytoplankton chlorophyll in +,heepilimnion 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 increaseby about 20%. The simulation also indicatesan increasing tendency for the spring bloom to be controlledmore by nitrogen than phosphorus. Simulationsmade under "pastoral" conditions representing estimated background loading prior toman's 20th Century activities indicates spring peak chlorophyllvalues about 

### 7 pg/l or some 40% less than present levels. This simulation thereforeprovides 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 equilibriumwith the present load. It is estimated therefore that the average annual phytoplankton in the epilimnion at equilibriumwith present loads is about twice the level that existed under somepreviously unstressed environment. The load however has increasedby about 3.7 times over the sameperiod. 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 loadswill 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 equilibriumwith thepresent loads is correct, then the "admissable" loading does not result in an improvement in water quality. One concludes therefore from this one comparisonbetween two models,that empirical loading

2plots 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 15years 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 thevariability 

### in load estimates and observed fluctuations in open lake biomass such a changewould 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 totalphosphorus 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 phytoplanktonbiomass. 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 intopredicting the future dynamic behavior of phytoplankton in large lakes is stillvery much in its infancy which would indicate that additional researchmay lead to varying conclusions. Nevertheless,policies and decisions will still have to be made even though future researchmay suTgest adjustments and corrections. and do not reflectnear-shore responseswhich

3SECTION I1 RECOMMENDATIONS

Because 

### of the importanceof near shoreversus open lake problems, it is recommended that a detailed verificationand analysis 

### of the Lake 3model be conducted. Some simulations should be carried outwith the Lake 3 model to delineate the time for the near shore to reach a new dynamic equilibrium. Since the simulations using the Lake 1model were particularly sensitive to the overall loss rates of the nutrients, it is recommended that: 

### 1) amodeling 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 

### 1model responses. Continuing up-dating and verification together with simulationsunder a variety of conditions, should be carried out preferably by one of the operating agencies in the Great Lakes.

4SECTION I11 INTRODUCTION
PURPOSE OF RESEARCH Attention is directed in this report to the utilization 

### of a simplifiedmodel of phytoplankton dynamics of Lake Ontario (theLake 1model) to estimate the lake-wide response to various levels of nutrient loading. The Lake 1 model is thereforeviewed as an initial framework for estimating whole lake phytoplankton res.ponseand to provide some input into the ongoing decisionmaking process on Lake Ontario.

A range of external nitrogen and phosphorus loading is examined and the sensitivity 

### of the results to variousmodel 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 resultspresented herein are to serve only as general indicators of the direction to be expected under remedial nutrient controlprograms.
SCOPE OF RESEARCH This report follows Part 1,Model Development and Verification and builds on thatwork. 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.

5v) W a 

## z a 

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7

### LAKE 1MODEL REVIEW Fig. 

### 1 shows the geometry of the Lake 

### 1model. The principal features included in themodel are: a) a two layer systemwith a sediment layer, themixing and stratificationbeing 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 themajor features of the interactionsof 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 themodel. The results of the verification indicated that themodel 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 temperatureand 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.

8Ll 

## w a 

# % rl 

### w k4 

# 2 w x FIE

Ll 

### 4 W H m

U H m rl

N m N rl

0 0 v) m

# .

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9Although 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 particularparameter set thatwas finally derived. Nevertheless, the conclusionof 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 1model 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 thereforepresented: namely, the estimation of long term system responsebased on a short observationalperiod. The problem 

### is somewhat analogous to attempting to estimate the frequency of occurrence of a one in ten year drought flowbased 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 responsiveprimarily to the specified initial conditions rather than the

10n (D 1 0 CD

0 

### Ln

0d0 

### m 

# R

0F11external inputs. This, of course, can be seen from a nutrientbalance equation for a well-mixed lake. Thus,

where c=thewhole 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 severalyears of data, two estimatesmust 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 overalldecay 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 equilibriumwith the present load, an assumption that cannotbe checked until the lake has actually been observed for a period of at least one-two detention times (8-16years 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 (75,0001bsP/day). If total phosphorus were completely conserved (K=O), the total within-lake phosphorus concentration,pt, at equilibrium is simply from Eq. (11, (fora flow of 6570m /sec (232,000 ft /see)), 3 3

12or 

### 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 firstyear. Three choices are open now to the analyst: a) assume the present load is not in equilibriumwith the present concentrations and that the system is conservative,b) assume the lake 

### is not in equilibriumwith 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: "Isa 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 simulationwould 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 reasonableway 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. Reasonablehypotheses on the phosphorus and nitrogen components (e.g. phytoplankton and detrital settling) can be formulated and tested on the dynamicmodel. Simulations based on those results can then be prepared but with full recognition that the long term behavior has only been grossly approximated.

13d

### o 

### d cv 0 0 Q Q 0

14

# 8 0

15SECTION 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 industrialwastes, 4) local drainage to the Lake and, 5) atmospheric inputs. The major contributions are from the first three categories although atmospheric inputsmay 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. Directmunicipal

16and 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 IFYGLby 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 (1966-67and 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 estimatesvary

I
17estimate of the industrialnitrogen 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 thatwere discharged to the Lake in prior years. The difficulty resultsprimarily fromvarying load estimates at different times such as indicated in Table 3 and from different sampling procedures. The importanceof 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 amean 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 InternationalJoint Commission (IJC) was about 190,000 cfs. The two periods forwhich nutrient load estimates were made differed in Niagara flow by about 40,000 cfs.
The nutrient concentrationsof the Niagara River vary over a fairlywide range. For example,during the

18

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191966-67 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 themean 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, s and s are the 

## E is mean mass input, 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 fluctua

### tion in the nutrient loads. This range is taken as two standard deviations and as shown is about 30% of the average load or the load from the Niagara River may vary 215% around the average. 'Q' c W

It can be assumed as a lower bound that tributary inputs together with themunicipal, 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, onemay expect the load estimates to vary by about 215%. This will, of course, assume some considerable importance in any simulations.a:

2

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21SIMULATION 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 analysiswas made of the nutrient inputs that might have existed at some distant time in the past. These loadswere termed the Pastoral Loads. In addition,a reviewwas made of nutrient reductions as suggested by Vollenweider' and the Great Lakes 6 Water Quality Agreement 

### . The simulations were thereforeprepared using a wide range 

### of input nutrient loadswith the PastoralLoads 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 setwithout considering what the state of the water body would be if man had not happened on the stage,unrealistically high expectationsmight occur. Itmust alwaysbe remembered that even before the coming of man, therewas 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 thereforebe made 

### of the loads that existed before any substantial effect by man's activities.
The settlement of the Great Lakes Basin caused the nutrient loadsbeing 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 themost readily controlled sources of pollution, the problem posed was to esti22mate what Lake Ontario water qualitywould 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 areawith 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. Itwas assumed that the present conditions on Lake Huron could be used as an approximation to what the pastoral conditionswould be in Lake Erie.
Loehr' summarizes characteristicsof 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 (GreatLakes 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 theU.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

23TABLE 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

20I500 19I200

1,300



### 7 2 Lake Ontario Basin: 2.227 x 10 acres(90,132 km Niagara Flow: 195,000 efs

24The estimates 

### of the present loads (1967-72)provide 

### ameasure 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 (seebelow), 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

25of detergent phosphorus beginning in 1950. e) The resulting intermediate loads were then calculated, towhich 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 thewhole 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,

260 

### 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

### SntlOHdSOHdlVlO1

27the 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 landusebreakdowns. 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 (44.8metric tons/day)appears to be an overestimate of the input 

### so that future estimates 

### of inputmay 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

28to 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 inorganicphosphorus from the sediments to be about 1.4 

### x lo6 kg P/year (8,500lbs P/day) or 10%

### of the total phosphorus input (seeTable 3). As indicated previously, the range 

### of the external load input is about

# - 18% 

### so that the contribution from the sedimentswould tend to be masked and in any event is covered by the external loading range. 

### +

Nevertheless,the importanceof 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.

29SECTION 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 1model 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 tobe conservative.

30This 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 1model. 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 considerablymore difficult. Chemicalmechanisms of co-precipitationand minerializationmay be the cause of a loss 

### of inorganic forms,however the degree to which this lossmay 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 inputswhere "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 explicitlybut are incorporated in the range of results discussed below. 1

31TABLE 

### 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 

# - N 

# - 0 00 

# - N 

### a N 

### I/~~'ellAHdOt101H3 NOIlNVldOlAHd

33

### 20 15 10

5 0

- 

### MICHAELISLE

### VEL - 

### --------

cn3 K 

### 0 

## r

J 

### rn 

### Q 

## > 

# a

a A 

# - 0.20

0.10 

## - MAXIMUM, SPRING

MAXIMUM,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



## - MICHAELIS

### 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 equilibriumwith 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 concentrationsare 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 indicatedby 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. themix of nitrogen and phosphorus input loads as shown in Table 7 indicates that nitrogen may be the nutrient thatwill 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 lakemay be in a delicate balance and that what appears to be a limiting nutrient during one period of yearsmay not continue to affect growth in the samemanner in lateryears. In both the spring and fall, nitrogen assumes a relatively greater role in nutrient limitation than does phosphorus. The effect isparticularly The simulation using

35I

### o w LL LL 

### w 

## z 

## 0 0.8 I-2 

## iz 

# z+ 5: 0.4 * NOLIMITATION 

# ------____ 

# d--------

# ---

- PHOSPHORUS 

# - 50%LIMITATION 

## ,’ 

# _-____--- 

# ----- - MAXIMUMLIMITATION NITROGEN 

## - /I

## z w 

### ccIz) 

## z 

# -

L w LL LL 

### w 

## z t-+ 

## oz0.8 t NOLIMITATION 

# ---___---~------_---__ PHOSPHORUS 

# - 0.0

# I 1 1 

## 1 

# I/ 1 1 1 1 1 1 6 10 

### 14 18 22 2 

### TIME,years



# k3 22 A 

### 0.4I

## z w M I- 

# - 

# - 50%LIMITATION


# - ---_c_- 

# --------
NITROGEN 

# - MAXIMUMLIMITATION

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. Itwhould be stressed however, that themodel does not include any nitrogen fixing algae which would alter the nutrient limitation effect especially in the fall when blue green algaewould 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 amuch more complexphenomena of species adaptation and readjustment of the upper trophic levels than is indicatedby the Lake Imodel. 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 (0-17meters), segment #2 (17-90 meters) and the lake average concentration,weighted volumetrically. tions in Fig. 11, the substantialdifference between annual average epilimnion level and the lake average can be noted. Also, the relatively small change of 13% in the lake average concentrationcan 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 averagebasis with that nutrient. The effect of the nitrogen limitation is quite clear from a comparison of the TIN and the availablephosphorus. The latter nutrient is continuing to increase although the biomass in the epilimnion has reached an equilibrium level governed essentiallyby the conversion of the TIN in the upper layer. Note however, that the stoichiometric conversion does not apply to the annual averagesbut to the peak values shown in Figs. 8 and 9. That is, the approximately 165 1-19 TIN/1 in segment #1determines 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



## - LAKEAVG

- 

### SEGMENTNO.

### 2


### 2 6 

## IO 14 18 22 SEGMENTNO.2

- 

### LAKEAVG -



## - SEGMENTNO.I

I



### 2 6 10 14 18 

### 22

- 

### SEGMENTNO.2



### SEGMENTNO.7 7



# 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 

## aI

## oI

## z' 0 M M 

### Q 0 

### 0.02 LAKEAVG 

### 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 

## -

- SEGMENTNO.2 

### 2 6 10 

### 14 1% 

### TIME,years 

### 22 26
Figure 12. Yearly average change (cont.)

# - continuation of present inputs

39peak level 

### of phytoplankton of 16.4 pg/l. Because of the nature of the spring and fallblooms, 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 (phytoplanktonand zooplankton). Again, the total phosphorus and nitrogen plots show that the 

### lake is not in equilibriumwith the present phosphorus load. It is clear from Fig. 12 and thepreceding figures that itwould be difficult to make meaningful statements about phytoplankton biomass just frommodels 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 1-19chlorophyll/l which is significantlyhigher than that calculated by the dynamic kineticmodel. A similar argument applies to the total nitrogen. One concludes therefore that a continuation

### of present loadswill 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 increaseby 45% over present levels under a continuation of present nutrient inputs. Further,models and analyses that deal only with annual lake averages and total nutrientsmay be severely in error in projections, at least when compared to the results of the dynamicmodel. 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

40dynamics as the lake "windsdown." 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 computationdiffers slightly from that in Fig. 8 due to some differences in recycle kinetics.) The results show that the fallbloom is the first to disappear and is essentially gone by about 5-6 years and the system is characterized for the remainder of the computationby a single peak. The peak occurs later and later in the year so thatby the 10th year, the peak occurs close to the end of June. Figs. 14 and 15 show the change in themaximum 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 zooplanktonreduced the fall recycling of nutrients leading to the decline of the fallbloom. Fig. 15 shows that both nitrogen and phosphorus interact to control phytoplankton growth as indicatedby theminimum values of both nutrientsbeing 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 zooplanktondecline and the availablephosphorus (for the first three years) are exceptions. The equivalent first order decay for the maximum phytoplankton chlorophyll is about



## . 00063/day.

41

# c

.-
0

0 m 0 P 0 0 F- 

### I 'e

### 11 

### A

### HdOtl01

### H3NOlXNVl

### dOlAHd

42

## >.f 

# E" 0

0.0 

### 0.16 v,z 30 0

### + 

### 0.12 a 2,



# ?+0.08 

## zQE a0 

### 0.04 40 

# " 0.00

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# & 0.10


### 2- Q

# = 0.00 

## z 2 6 10 

### 14 18

10 

### 14 18 

### 2 6

10 14 

### 18 

### 2 6



### 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

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### Qr a 

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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 formeasuring 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 7pg/l, a decrease of about 

### 40% from present peak values. The broad fall peak is estimated to decrease to less than 

### 4pg/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 fallbloom 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 nutrientswould 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 0 00 0 O% .- cv v 0 F 0 (v 1/6d 

### 'e

### 1lAHdOkJ01

### H3NOlXNWldOlAHd

46

## z 0IY 

## z 

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### I- 

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### a



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MAXIMUM 

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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 

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I-Z 

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# ---__------------ 50%LIMITATION
PHOSPHORUS 

## 1 

## I 1 1 

# I 1 

## I I 

# I I 2 

### 6 

### 10 14 18 22 

### TIME,years


### 5. 

### FALLBLOOM (day

### 225-300)

PHOSPHQRUS
50%LIMITATION 

# ------- NlTROGE MAXIMUM

### LlMlTA TION 

## 1 

## I 1 

## I 1 

# I i 

# I 2 

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### 14 

### TIME,years 

### 18 22
Figure 18. Nutrient limitation effect under pastoral inputs-epilimnionSEGMENTNO.1
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### u 1 LAKEAVG 

# -> I I I I I I I 

### i I I I SEC

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0.20

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# - SEGMENTNO.1 

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# 5E 0.010 

# 3 0.080 1 

# - a WENT

Figure 19. Yearly average changes

# - pastoral inputs

498.040 

# - 1 Q 0.030 vi 3 Dz 0 

# 2 0.020 

# 2 0.010 

# 2 SEGMENT.NO2 SEGMENTNO.1 I Q I=-
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Figure 20. Yearly average change(cont.)-pastoral inputs

50TABLE 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 (184,200kg N/day) 

# -Algal sinking rate

# - 0.1 m/day 

# - Decay of non-living organic nutr5ents-



## . 0 0l/day $laximumand minimum occur at different times for different variables.

51Chlorophyll 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 ameasure 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 thepastoral loadingwas about 2.6 ug/l. This level compares to an estimate of 5.7 vg/l as the annual average that is in equilibriumwith the present load. It is estimated therefore that the average annual phytoplankton in the epilimnion is about twice the level that existed under somepreviously 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 systemparameters. 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 Agreement6 referred to as the "WaterQuality 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 amore 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.
52This would represent a reduction of about 40% from a present input of about 75,000 lbs/day. Empirical plots similar to the originalplots 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 kineticsused 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 equilibriumwith the present observed input nutrient load. This does not appear to be the case for Lake Ontario. The simulation shown in Fig. 21was 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



# I

# t MINIMUM MICHAELISLEVEL 

### 8.0 2 

### 6 10 

### 14 18 22 

### 0.030

## 1 3

A

I 

### ;3i Q.010 ef 

# t

MINIMUMMICHAELIS

### LEVEL 

# 2 0.000 

### 6 18 14 18 22 

### 2 

### TIME,years Figure 21. Dynamic behavior of phytoplankton, inorganic nitrogen and available phosphorus in epilimnion-Vollenweider reduction

54accomplished 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 reductionare shown in Fig.22. Under 

### a 10 year time interval to accomplish the 40% reduction,peak biomasswould 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 onewould expect the time to reach 

### a new equilibrium increases to about 25 years. One concludes therefore from an examinationof the Vollenweider reduction case, that Lake Ontario phytoplankton biomass, on a lake wide averagewould continue to increase and under a 10 year load reductionperiod 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 equilibriumwith 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 simulationwas prepared using the agreed upon phosphorus input,

### Fig. 

### 7 shows the approximate historicalphosphorus inputs 

### to Lake Ontario and the United States

# - Canada Agreement loads. Because theWater 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 1 1 

## 1 

## 1 

# I CD 

### cv 00 

# * 0 

## I/6~’17AbldOUOlH3 NOIYNVldOlAHdYV3d3NltldS P v 0 

### cv

56considers an immediate drop in phosphorus load to a level of 54,800 lbs P/day or an overall reduction of less than 30%. Nitrogen loadswere 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 thepreceding 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,yetpeak biomass reaches equilibrium in about 15years. These calculations indicate that under the WQA loads, the phytoplankton biomass of the open lakemay 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 theWQA program is not a good one. These computations indicate that the hopes for an expected response 

### of Lake Ontariomay not be as high as anticipated under theAgreement. Comparison to Empirical Loading Plots As indicated previously, one of the classical works in lake eutrophicationand the effects of nutrient loadings is that of Vollenweider 

## . His work represented one of the first synthesisof 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 industrialwastes. An appeal of Vollenweider's 57

### 0.30 0- -1 

## zz Qm 0

## 2- 

# EE 0.20

I-I- 

### a 

### 0.10 ZW 

## -u 40

I MAXIMUM, SPRING MAXIMUM,FALL

MINIMUM

MAXIMUM



### MINIMUM MICHAELISLEVEL i 

### 2 6 10 

### 14 

### 18 22 

### vi 3 

### 0.06

### I U 0 P a. 

### a 

### 0.04 0, In MAXIMUM

4 

### WE0.02 

# L

MICHAELIS

### 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 SEGMENTNO.1

LAKEAVG

~ SEGMENTNO.2 e

~



### 2 10 

### 14 

### 18 22 26

- SEGMENTNO.2 LAKEAVG
SEGMENTNO.1

SEGMENTNO.2 LAKEAVG

SEGMENTNO.1

Figure 24 Yearly average changes

# -Water Quality Agreement loads

59

# 3Q

### LAKEAVG 

# F m-0.03 

# 2 0.02 3 €E 0 

# g -r 

# 3Q

### LAKEAVG 

# F m-0.03 

# 2 0.02 3 €E 0 

# g -r A Q .-II

## oIq 

### 6.01



### 0.00 2 6 

### 10 14 18 

### 22
SEGMENTNO.2

~



### 2 6 10 14 18 

### 22 

### TIME,years Figure 25. Yearly average changes (cont.1- Water Quality Agreement loads

60analysis is its simplicity. There was very little available to environmental managers of lakewater quality that linked external loadings (which are controllable in various degrees) to 

### ameasure 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 lakesprovided a basis for decisionmaking. For a given depth of the lake, the "admissable"loading canbe 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 theworld. Others such as Dillon and Rigler 

### l1 and Bachman and Jones have also attempted to relatevarious 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 analysisby 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 thesemodels,various empirical plots, 

### as noted previously, have been developed to relate loading to response or nutrients in the lake to phytoplanktonbiomass. There are at least threemajor shortcomings to these attempts at exploring observed behavior: a) the empiricalplots 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 interactionsbetween two or more nutrients. themodels generally assume a completelymixed lake or attempt in a minimal way to include stratification. 12

Further,

61The dynamic model 

### of phytoplankton behavior which forms the basis for the simulationsreported 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 assumptionsmade 

### on the more generalized dynamicphytoplanktonmodel. In thisway, the underlying unity and directionwill be more apparent. While the assumption of a well mixed lake is quite restrictiveand 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
dP2 -Qp2-a GP+W2 V-=K p 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 

## = decompositionof organic phosphorus (l/day), the phosphorus chlorophyllratio,W1 and W2 represent P P S

Z 1

is apP

62external 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

63is 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 yearsbased on the previously discussed long term simulation runs. This effect 

### of the sinkingbiomass can also be seenby letting the phytoplankton biomass be some fractionof the total phosphorus, i.e.,

t p=ap
and then the solution is
(1

# - exp

# - (aKs 

# -Wt Pk

# -- Q

+ (ptIoexp (-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 thatmust be projected under a different loading regime and hence is not explicity known. is estimated at 0.1 m/day f 90m and aKs S

Therefore,under constant loadings in time,presently observed totalphosphorus would be correlatedwith waste loadings someyears 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 fewdecades. 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. Thiswas also shown in the simulationusing theVollenweider reduction which indicated that biomass would continue to increase even after the reductions were accomplished. Another difficulty is that the relationshipbetween biomass and the relevant total nutrient is confounded in the empiricalplots. 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 representationof 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/m2-year).

65Taking 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 themodel 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 lakeswould generally have larger values 

### of the intercept, thus providing some basis for the division originally made by Vollenweider. The interceptalso 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 relationshipbetween 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
66time 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 variablewhich explains the "bending"

### of the lines using Eq. (18). However,whether 

### Eq. (18) or Eq. (15) (orother variations thereof) are used, the phytoplankton biomass is still incorporated in the intercept and thereforenot 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 relationshipnot 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). 67Due to the interactionof biomass,nutrient concentration in the lake and externalmass 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 inwaste load onphytoplankton

### biomass. Indeed, the one comparison

as indicated above produces results in conflictwith 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 isnot in equilibrium (suchas is hypothesized for Lake Ontario) then the projections from the empirical plots may be significantly in error. of some use for short detention time lakeswhich reach equilibrium quickly. However, one would conclude from the resultspresented 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

65SECTIONVI 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. SENSITIVITYOF 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 chlorophyllunder 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 (aswell 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 phytoplanktonwhich, in this model, are eliminated from the systemwhen the biomass reaches the sediment. The most optimistic assumptionwould be to assume that the Lake is presently in equilibriumwith 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 thismechanism, the possibility of a sink of inorganic phosphorus does exist. Therefore,a series of runswere 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 llAHdOklOlH3NOlXNVldOlAHdXV3d 

## 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

70As 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 (adirect 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 (tosay,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 itmay 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 1model which assumes a horizontally well-mixed lake. The results in Fig 27 are therefore for lake wide conditions in the epilimnion. Near shore responsesmay 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 1pg/l. Under the reasonable kinetics of Fig. 27

71

## NI llAHdOkjOlH3NOIXNVldOlAHdXV3d

72Simulation 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 I000 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

73Table 10 is a further elaboration of the system responses for the reasonable kinetics. The relatively small impact of the WQA loads are well as theVollenweider 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 SectionV and given in Eq. (16) is the ratio of phytoplankton biomass to total nutrient. Table 11 shows this ratio to increase from .12 to -20and 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 progressivelymore 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 simplifiedmodels, a) the relatively long detention time of the lake and b) the interaction of both nitrogen and phosphorus as important growth limiting nutrients.

74TABLE 10 ESTIMATED CHANGE IN PHYTOPLANKTON BIOMASS UNDER DIFFERENT SIMULATION CONDITIONS Simulation

Present Ratio:
Annual Average(3) Lake Simula t ion Spring Condition 0-17m 17

# -9Om 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)

75bi 

### 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 

### 4cam34

cl

2 Mw

rrlrrl

tnM OM 44 -4 LD cc) mcc) Nul m N 44rmb m 

# .. .. 

## ..

76I 

# \ 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

# -TOTALPHOSPHORUS,1000IbsP/day Figure 29 Spring and Fall peaks and annual average chlorophyll at equilibrium in epilimnion, reasonable kinetics

78SUMMARY FOR RANGE OF NUTRIENT LOADS In order to explore the full behavior of the Lake 1model response, a complete series of simulationswas 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 combinationsof 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 nitrogenwill become progressively more limiting and therewill be no increase in peak biomass even thoughphosphorus 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 regionwhere either nutrientmay be limiting. IMPLICATIONSFOR 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

80M c- Q,

3 

### lN3S3Ud

138 

### '11OA

!-- 

### z W m w 1 

### a 0Iv) 

## a 

# I I I a Q a a 

# I

81

### a Q 0 

### ZZ J 

### u 

## a 0I7 

# - ATEQUILIBRIUM,pg/I



# PHOSPHORUSLOADING,lo4lbslday

AVERAGE

# I~NNUAL PHYTOPLANKTON CHL0 ROPHYLLa ATEQUILIBRIUM,pg/l 11



# PHOSPHORUSLOADING,

# lo4lbslday
Figure 32Average annual phytoplankton chlorophyll, 0-17m as a function of nitrogen and phosphorus input-Top 

### fig.: reasonable kinetics, bottom fig.: pessimistic kinetics

82rient input. This total includesboth pointmunicipal and industrial inputs which are reasonably controllable as well as agricultural non-point sources forwhich controlprocedures 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 thereforebe 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 Agreementmay 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 removalpolicy presently being implemented is certainly in the right direction and was formulatedbased on the thebest available information at the time. This research has simply indicated that hoped for reductions in eutrophication of Lake Ontariomay not be realized until additional phosphorus reductions significantly beyond the WQA are achieved. Theprimary reason for this effect is the hypothesis that Lake ,Ontarioeutrophication is continuing to increase due to the present input 

### so that the nutrient loads and lakewide 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"responseswhich may be quite different. Also, research into the dynamic

83behavior of phytoplankton in large lakes (or for lakes in general) is stillvery much in its infancy. Nevertheless,. policies and decisions will continue to have to be made even as ongoing researchmay 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.

84SECTIONVI1 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. MathematicalModeling of Phytoplankton in Lake Ontario, 1. Model Development and Verification. Environmental Protection Agency, Corvallis, Oregon. EPA 660/3-75-005. March 1975. 177p. 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 InternationalLake 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 ScientificAffairs, 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 LakesWater 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 ProtectionAgency, 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.

852. BachmannaR.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. 48p. 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.

86TECHNICALREPGRTDATA (I'k,asrreadIwmrctwtn011 rhercvirscbepmcon 1,RCPOR7NO. 2. EPA-600/3-76-065

_L____ 

## - 4.TITLEANDSUBTITLE

MATHEMATICAL MODELING OF PHYTOPLANKTON INLAKE ONTARIO, PART 2. SimulationsUsing Lake 1Model

1.AUTHORtS)

Robert V. Thomann, Richard P. Winfield, DominicM.

KEYWORDSANDDOCUMENTANALYSIS

._ 17. a. DESCRIPTORS h.lDENTlFlERS/OPENENDEDTERMS C. COSATII:icld/Croup 

## -- 

# -_ - 06F 12B Water quality, simulation, mathematical Lake Ontario models, phytoplankton, nutrients, nitrogen, phosphorus

18.I>IST R1BUTIONSTATtMENT 19.SECURITY CLASS(TitisRcporlf 21.NO.OFPAGES D.iToro, and Donald J. O'Connor

.PERFORMINGORGlNlZATlONNAMEAN0ADDRESS Manhattan College Bronx, New York 10471

12.SPONSORINGAGENCYNAMEANDADDRESS U.S. Environmental ProtectionAgency Office of Research and Development Environmental Research Laboratory hluth,Minnesota 55804 16.SUPPLEMENTARY NOTES 'ctitq=) 2. RECIPIENT'SACCESSIONNO.
i. REPORT DATE

August 1976 (Issuing Date) i. PERFORMINGORGANIZATIONCODE

3. PERFORMINGORGANIZATIONREPORTNO.

IO.PROGRAMELEMENTNO. 1BA608 11.CONTRACT/GRANTNO.

Grant R-80Q610 13.TYPEOFREPORTANDPERIODCOVEEEO Final 14.SPONSORINGAGENCYCODE 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 avertically 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 lakephytoplankton biomass of Lake Ontario does not appear to be in equilibriumwith the present input nutrient load. Therefore, if the present load is continued, it is estimated that spring peak phytoplankton chlorophyll in the epilimnionwill continue to increase to a new level about 45%higher thanpresent 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 conditionsprior toman's intensive activity, indicates that springphytoplankton levels were some 40% less than present levels and average annual epilimnion biomass under equilibriumwithpresent 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
EPAForm2220-1f9-73) 87 Au.5.GOVERNMENTPRlNTlNGOFFICE:1976-657-695/5487Region No. 5-1I