-alopment
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RESEARCH REPORTING SERIES
Research reports of the Office of Research and Development. U.S. Environmental
Protection Agency, have been grouped into nine series. These nine broad cate-
gories were established to facilitate further development and application of en-
vironmental technology. Elimination of traditional grouping was consciously
planned to foster technology transfer and a maximum interface in related fields.
The nine series are:
1. Environmental Health Effects Research
2. Environmental Protection Technology
3. Ecological Research
4. Environmental Monitoring
5. Socioeconomic Environmental Studies
6, Scientific and Technical Assessment Reports (STAR)
7. Interagency Energy-Environment Research and Development
8. "Special" Reports
9. Miscellaneous Reports
This report has been assigned to the ECOLOGICAL RESEARCH series. This series
describes research on the effects of pollution on humans, plant and animal spe-
cies, and materials. Problems are assessed for their long- and short-term influ-
ences. Investigations include formation, transport, and pathway studies to deter-
mine the fate of pollutants and their effects. This work provides the technical basis
for setting standards to minimize undesirable changes in living organisms in the
aquatic, terrestrial, and atmospheric environments.
This document is available to the public through the National Technical Informa-
tion Service, Springfield, Virginia 22161.
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EPA-600/3-79-091*
August 1979
VERIFICATION ANALYSIS OF LAKE ONTARIO
AND ROCHESTER EMBAYMENT THREE DIMENSIONAL
EUTROPHICATION MODELS
Robert V. Thomann
Richard P. Winfield
John J. Segna
Manhattan College
Bronx, Nev York 101*71
Grant No. R803680030
Project Officer
William L. Richardson
Large Lakes Research Station
Environmental Research Laboratory - Duluth
Grosse lie, Michigan 1*8138
ENVIRONMENTAL RESEARCH LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
DULUTH, MINNESOTA
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DISCLAIMER
This report has been reviewed by the Environmental Research Laboratory,
Large Lakes Research Station, Grosse lie, Michigan, U.S. Environmental Pro-
tection 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 commer-
cial products constitute endorsement or recommendation for use.
ii
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FOREWORD
The Great Lakes comprise oO% of the surface freshwater in North America
and provide ^5 million people living in the basin with almost -unlimited
drinking water and industrial process water. Five thousand miles of shore-
line provides access for much of the tourist and recreation activity in the
surrounding basin. Lucrative sport and commercial fisheries rely on these
waters as do the transport of tremendous quantities of raw and refined
commercial products and the disposal of residual, industrial and municipal
materials.
This resource represents a complex system of competing water uses as
well as a delicate, interacting ecosystem. Such a situation requires a
balance between the economic well being of the region with the health
related well being of the ecosystem. To arrive at this balance a rational
and quantitative understanding of the interacting and competing components
is required. In this way complex questions can be addressed and optimal
decisions made.
Research sponsored by the U.S. EPA, ERL-D, Large Lakes Research Station
has in large part been directed toward this end. .Primarily the modeling
research has been conducted to synthesize surveillance and research data
and to develop predictive capabilities of the transport and fate of pollu-
tants in the Great Lakes.
This particular report contains the results of a three year research
project to develop water quality models for Lake Ontario and to refine pre-
vious models to address questions of various space and time scales. The
work has been built upon a eutrophication model (LAKE-l) described in the
EPA Ecological Research Series Report (EPA-660/3-75-005) entitled, "Mathe-
matical Modeling of Phytoplankton in Lake Ontario, 1. Model Development and
Verification." The present work expands the LAKE-l model from two vertical
to 67 horizontal and vertical segments. In addition, a further refined seg-
mentation was done in the vicinity of Rochester embayment. Also, a refined
biochemical kinetic structure was tested which incorporates two groups of
phytoplankton, silica, and revised recycle processes. Finally, a statisti-
cal methodology for model verification was developed and applied to test
the "goodness-of-fit" of the various models.
In summary, the report documents the details of the models, data
analysis, and verification procedures. It is our desire to provide suffi-
cient detail that would not be normally available in a journal publication
so that the reader may be able to apply much of this methodology to other
water bodies throughout the world. It is also our intent to document the
iii
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results in detail for those Great Lakes managers and researchers who have
and will develop, recommend, and judge pollution control strategies based
on this research.
Appreciation is extended to scientific reviewers at the University of
Michigan and the NOAA, Great Lakes Environmental Research Laboratory. Also,
this report has been reviewed by several Canadian and State agencies.
William L. Richardson, P.E.
Environmental Scientist
ERL-D, Large Lakes Research Station
Grosse lie, Michigan U8138
iv
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ABSTRACT
A three dimensional time variable model of the phytoplankton and nutri-
ents of Lake Ontario and the Rochester Embayment is examined in detail. The
data from the International Field Year on the Great Lakes (IFIGL) are used as
the primary data base. The data are summarized and statistically analyzed
on a three dimensional grid and segment averages using a 67 segment repre-
sentation of the lake and a 72 segment representation of Rochester Embayment,
are calculated. In addition, averages for eight regions of the lake and
lakewide averages for two depth layers are computed. Average phytoplankton
levels during the period May, 1972 and June, 1973 in the near shore region
are approximately 3 yg/1 higher than open lake values. Similarly, near shore
open lake total phosphorus gradients of about 5 yg P/l appear to persist for
a substantial part of the year. The data base collected during IFYGL ex-
hibited significant spatial and temporal variations at scales of 10 x UO km.
The two data bases available, Canadian Centre for Inland Waters (CCI¥) and
Environmental Protection Agency (EPA),'only agree within certain limits.
The verification analysis of the models indicates that the median rela-
tive error for the results of calculated versus observed chlorophyll on the
segment to segment level is about 30$. The inclusion of diatoms and non-
diatoms and silica limitation in the kinetic structure, only marginally im-
proved the three dimenstional credibility of the model. The Rochester
Embayment model indicated that about 90$ of the total phosphorus input to
the embayment is transport of nutrients from the west of the embayment and
about 10$ is from direct input from the Genesee River and municipal input
from the City of Rochester.
The question of model credibility is examined in detail and it .is con-
cluded that as one progresses to smaller spatial scales, especially to the
scale of the Rochester Embayment, hydrodynamic transport and local disper-
sion become increasingly significant. On the larger spatial scales, system
kinetics dominate and the importance of the hydrodynamic structure is de-
creased. Chlorophyll verification status of the model ranges from an average
of 1.0% relative error on the whole lake scale to 50$ error at the local
embayment scale. In general, the results indicated that the ability of com-
plex three dimensional models to capture the temporal and spatial vari-
ability of phytoplankton dynamics is relatively marginal given the existing
data base and present kinetic structures. Only as the spatial scale of the
problem is increased, do the models appear to accurately reflect the ob-
served variations.
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CONTENTS
Foreword ±±±
Abstract v
Figures ix
Tables xiii
Acknowledgement xiv
I Summary 1
II Conclusions 8
General 8
Specific 8
III Recommendations 10
IV Introduction 11
Purpose 11
Scope of Research 11
The Verification Questions 13
V Data Analysis and Verification Procedure lh
The Lake Ontario Models ill
Verification Analysis Framevork 16
Reduction of the IFYGL Data Base l6
Observation Statistics 21
Verification Statistics 26
Regression Analysis 31
Relative Error 33
VI Analysis of Observed IFYGL Water Quality Data 31*
General IFYGL Conditions 3U
Meteorology-Hydrology 31*
Nutrient Inputs 3*t
Statistical Analysis of Water Quality Data 37
Water Temperature 37
Transparency and Turbidity ^5
Chlorophyll "a" 1*5
Zooplankton 59
Phosphorus 63
Nitrogen 72
Silica 73
Discussion 76
VII . Verification Analysis of Lake 3 Model 79
Introduction • 79
Preliminary - Phase I 80
Sensitivity of Lake 3 Model - Lake Circulation . 80
Initial Comparison Runs 82
vii
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Phase II - IFYGL Conditions 89
Determination of IFYGL Dispersion 90
Results 90
Phase III - Updated Kinetics 93
Lake 1A Kinetics 96
VIII The Rochester Embayment Analysis 105
Purpose 105
Data Base 108
Calibration - Lake 1 Kinetics 112
Transport and Dispersion 112
Phytoplankton and Nutrients 113
Sensitivity 121
Nutrient Loads. 121
Transport 121
Discussion 122
IX Discussion and Summary of Results 129
Chlorophyll '. 129
All Variables 130
References 133
viii
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FIGURES
No.
Page
SI a) Computed chlorophyll contours, Run #5 ........... 3
"b) Chlorophyll regression analysis: calculated vs. observed
EPA data, Run #5, a) June 1972, 1>) eight regions ..... 1*
S2 Median relative error across all variables, a) Lake 3 scale,
67 segments, b) eight regions, c) whole lake scale, two
layers ............................ 7
1 Lake Ontario ......................... 12
2 Lake 3 Model grid ...................... 15
3 Spatial scales used in Lake Ontario analyses ......... 17
k Flow diagram for model verification analysis ......... 18
5 Typical graphical output of EPA, IFYGL data summary for
segment no. 21. (Day 0-Jan. 1, 1972) ............ 20
6 Approximate times of cruises during IFYGL by CCI¥ and EPA . . 20
7 a) Principal EPA-IFYGL stations and the Lake 3 grid ..... 21
b) CCIW-OOPS cruise stations, IFYGL in STORET data base:
1972-1973 ......................... 22
8 Segments for which statistical comparisons for chlorophyll
could be made ........................ 23
9 The eight averaging regions of Lake 3 segments ........ 2U
10 Typical merge of model output (solid line) and data ..... 27
11 Determination of verification score , V ............ 29
12 Possible cases in regression between calculated and observed
values ............................ 32
13 Heat storage; IFYGL data after Elder et al. (1971*) ..... . 35
ik Flow of Niagara and Genesee Rivers during IFYGL ....... 36
15 Some straight line temperature functions derived from
NOAA-BT files ........................ 38
16 Volume-monthly averaged water temperature (NOAA-BT data)
during IFYGL ...................... ... 39
17 Vertical distribution, volume-monthly averaged water temper-
ature (NOAA-BT data) during IFYGL, May-October, 1972 ..... Uo
ix
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No. Page
18 Vertical distribution, volume-monthly averaged water temper-
ature (NOM-BT data) during IFYGL, November, 1972 - June,
1973 ............................. Ul
19 Comparison of CCIW and NOAA (partial) water temperature
data ............................. U3
20 Variation of (a) extinction coefficient (EPA-CCIW data)
and (b) turbidity (CCIW data) for selected months, 0-k m . . . 1*6
21 Comparison of EPA and CCIW chlorophyll "a" (yg/l) contours,
June 1972 .......................... U7
22 Chlorophyll "a" (yg/l) contours, EPA data, August 1972,
June 1973 .......................... U8
23 Comparison of EPA and CCIW volume averaged chlorophyll data . 50
2k Volume-monthly averaged chlorophyll "a" - EPA data ...... 51
25 Vertical distribution, volume-monthly averaged chlorophyll
"a". EPA data, May-October, 1972 .............. 52
26 Vertical distribution, volume-monthly averaged chlorophyll
"a". EPA data, November, 1972 - June, 1973 ......... 53
27 Volume-monthly averaged chlorophyll "a" - CCIW data. (OOPS
and temperature cruises) ................... 5^
28 EPA and CCIW chlorophyll variations 0-17 m, near shore;
(a) Mean, (vol. averaged) (b) wi thin-segment std. error
(vol. averaged) ....................... 56
29 Comparison of within-segment and segment-segment variability
in chlorophyll, EPA data ................... 57
30 Summary of statistical comparison between EPA and CCIW
chlorophyll data ....................... 58
31 Zooplankton carbon, 0-U m and U-17 m, open lake volume
averaged (Data from McNaught, et al., 1975) ......... 6l
32 Herbivorous zooplankton group, mgC/1, Lake 3 averages,
August 1972 (Data from McNaught, et al., 1975) ........ 62
33 Mean and standard errors, herbivorous and carnivorous zoo-
plankton groups, 0-17 m open lake averages (Data from
McNaught, et al., 1975) ................... 63
3k Comparison of EPA (left) and CCIW (right) total phosphorus
(yg P/l), June, 1972 ..................... 6U
35 Variation in volume weighted total dissolved phosphorus
(yg P/l) and total phosphorus (yg P/l), 0-17m, EPA data ... 65
36 Variation in volume weighted total dissolved phosphorus,
orthophosphorus and total phosphorus (yg P/l), 0-17 m,
CCIW data .......................... 66
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No.
Page
37 Vertical variation of total dissolved phosphorus (ug P/l)-
EPA data 69
.38 Total phosphorus variability, 0-17, open lake, EPA and CCIW
(a) within-segment std. error of mean, (b) std. deviation
of segment means 70
39 Comparison of EPA and CCIW whole lake mean, total phosphorus . . 71
hO Variation in nitrogen components, EPA data, 0-17 m. volume-
monthly average 72
1+1 Variation in nitrogen components, CCIW data, 0-17 m volume-
monthly average 73
1+2 Vertical distribution, nitrate nitrogen, EPA data May-October,
1972 75
1+3 Volume-monthly averaged dissolved silica, CCIW data 76
1+U Overall statistical comparison of EPA and CCIW data sets .... 77
1*5 Best estimate circulation regime, Lake 3 model segmentation . . 83
1+6 Sensitivity of phytoplankton chlorophyll to changes in lake
circulation , 8U
!+7 Typical comparison, chlorophyll, segment #l6, Run #1 86
1+8 Distribution of phytoplankton verification score, June 1972,
Run #1 86
1+9 Chlorophyll comparison, Preliminary Phase I Runs l-r3 87
50 a) Segment-segment phytoplankton verification, Preliminary
Phase I, Runs 1-3; (~b) Regional phytoplankton verification,
Preliminary Phase I, Runs 1-3 88
51 Segment-variable verification, Preliminary Phase I, Runs 1-3 . . 89
52 Comparison of Lake 3 model to observed temperature data .... 91
53 Chlorophyll comparison. Run #U, "Full" IFYGL conditions
data, Run #1+ a) June 1972 b) eight regions 92
55 Chlorophyll comparison, Run #5, sinking velocity =0.5 m/day . . 95
56 . Computed chlorophyll contours, Run #5 97
57 Chlorophyll regression analysis: calculated vs. observed EPA
data, Run #1+, a) June 1972 b) eight regions 98
58 Systems diagram, updated Lake 1A kinetics 99
59 Lake 1A kinetic calibration, 1972, all 0-17 m, Segment 1 .... 101
60 Lake 1A kinetic calibration, 1972 (continued) 102
6l Chlorophyll comparisons, Run #6, updated kinetics 101+
62 Location of Rochester embayment 106
xi
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No. Page
63 Rochester embayment segmentation 107
6k U.S. EPA vater quality and coastal chain stations in
Rochester embayment - IFYGL 108
65 Temperature input functions for Region 1, segments 1,2 & 3 . . . 109
66 Assumed Genesee river input concentration to the phytoplankton
model Ill
67 Assumed upper layer (Q—h m) transport regime in Rochester
embayment, flow in cfs 113
68 Typical calibration of advective and dispersive regime,
chloride and temperature, segment 21 Ilk
69 Calibration results, Segment 21 115
70 Calibration results, Segment 21 116
71 Calibration results, Segment 60 117
72 Calibration results, Segment 60 118
73 Comparison between data and model, regional value weighted
averages 0-17 m a) near shore, far shore b) middle region . . . 120
7!* Effect of zero Genesee input and increased boundary consti-
tuents - Segment 21 123
75 Effect of zero Genesee input and increased boundary consti-
tuents - Segment 21 12U
76 Effect of zero Genesee input, increased boundary concentra-
tion and municipal inputs, Segment 27 125
77 Effect of zero Genesee input, increased boundary concentra-
tion and municipal inputs, Segment 27 126
78 Comparison of calculated peak phytoplankton embayment con-
centrations under different conditions on nutrient inputs
and transport 127
79 Summary of chlorophyll verification statistics a) verifi-
cation score test, b) residual standard error of estimate
statistic, c) median relative error 131
80 Median relative error across all variables, a) Lake 3 scale,
67 segments, b) eight regions, c) whole lake scale, two
layers "... 132
xii
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TABLES
No. Page
1 Nutrient loads (IFYGL) "by Lake 3 model segment ........ 37
2 Variation of temperature segment means and differences
"between temperature data sets ................ 1*3
3 Secchi depth analysis - near shore, open lake
h Difference between chlorophyll mean values of EPA and CCIW
data ............................. 55
5 Assignment of zooplanton species to zooplankton groups .... 59
6 Depth intervals, segments and efficiency corrections for
zooplankton data ....................... 60
7 Difference between total phosphorus mean values of EPA
and CCIW data ........................ 68
8 Difference between nitrate nitrogen mean values of EPA
and CCIW data ........................ lk
9 Summary of principal Lake 3 model runs ............ 8l
10 Principal parameter values - Lake 1A kinetics ........ 100
11 Rochester embayment segment grouping for temperature
analysis .... ....................... 110
12 Nutrient input from municipal discharges to Rochester
embayment .......................... 112
13 Comparison of nutrient flux from the Genesee River,
municipal discharges and lake boundary ............ 128
xiii
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ACKNOWLEDGMENTS
Special thanks are due to our colleagues Dr. Dominic M. DiToro and
Dr. Donald J. O'Connor for their continual discussions and insights during
the course of this research. The support and review of our research by the
EPA staff at the Large Lakes Research Station is acknowledged, particularly
that of Mr. William L. Richardson and Mr. Nelson A. Thomas. Mr. Jan-Tai
Kuo carried out the computations on the Rochester Embayment chapter as part
of his work for a Master's Degree in Environmental Engineering and Science.
Special thanks are also due to Ms. Cindy O'Donnell and Mrs. Eileen Lutomski
for their patient typing and correction of the manuscript.
xiv
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SECTION I
SUMMARY
INTRODUCTION
The eutrophication of Lake Ontario due to inputs of nutrients from a
variety of sources is a matter of continuing international concern "by the
United States and Canada. Far reaching programs of nutrient reduction by
the International Agreement on water quality, surveillance programs involv-
ing field work, and continuing "basin-wide planning efforts are part of the
on-going review of the Lake Ontario eutrophication problem. Various empir-
ical and modeling analyses have been used to assist this effort, each with
the expressed intention of relating the present state of the lake to exter-
nal loading of nutrients. Special interest centers on the eutrophication
status of the near shore (out to 10 km) region and the relationships of
this more publicly relevant region of the lake to the state of the open
lake.
The purpose of this work therefore is to further the understanding of
the three-dimensional variation of the phytoplankton and nutrients of Lake
Ontario using several mathematical modeling frameworks of the basic pheno-
mena of phytoplankton growth. During the International Field Year on the
Great Lakes (IFYGL), an extensive field program was launched which provided
data on the near-shore, open-lake, surface and deep water levels of phyto-
plankton and nutrients. These data and earlier work on modeling phyto-
plankton behavior, were used to accomplish the following:
l) summarize and statistically analyze the IFYGL data on a three-
dimensional grid
2) implement and conduct verification analyses of a three-dimen-
sional model of phytoplankton dynamics, called Lake 3 and
develop quantitative bases for determining the degree of model
credibility
3) develop and calibrate a three-dimensional model of the phyto-
plankton for the Rochester embayment of Lake Ontario
U) determine the statistical verification properties of the
models at different levels of spatial averaging.
DATA ANALYSIS
The data from IFYGL collected by both the EPA and CCIW were compiled by
month and on several spatial levels: a) segment averages using a 67 segment
representation of the lake and a 72 segment representation of the Rochester
embayment, b) averages for eight regions of the lake and, c) lake-wide aver-
ages for two depth layers. The temperature analyses indicated near-shore
open lake differences of about 3°C during May-June, 1973. The temperature
- 1 -
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difference in 1972 was one of the causes for higher phytoplankton levels in
these near-shore regions (up to 10 km from shore) were approximately 3 yg/&
higher than the open lake values; this represents an increase of about 50-
100/6 of near-shore values over open-lake values. A general increase is
noted in the spring to open-lake levels of 5-10 yg/& and values in Rochester
embayment of greater than 30 ug/Jl. This is followed by a mid-summer decline
in August and then a broad fall peak through the end of October.
For the nutrients, phosphorus appears to be limiting growth especially
of the non-diatom group of phytoplankton. In open-lake regions, available
silica may also limit diatom growth. Near shore-open lake total phosphorus
gradients of about 5 yg P/£ appear to persist for a substantial part of the
year.
The underlying data base collected during IFYGL therefore exhibited
significant spatial and temporal variation at scales of 10 x Uo km. Only
as the data are aggregated into larger regions (e.g. near-shore, open-lake)
and longer time scales of months does any regularity or deterministic struc-
ture emerge from the data set. Also, the two data bases available (CCIW and
EPA) only agree within certain limits. For example, for chlorophyll on the
segment-segment scale (10 x Uo km), only 60% of the segments exhibited no
statistical difference and the average relative error between the two sets
was 30%.
VERIFICATION ANALYSIS
The three-dimensional models of phytoplankton in Lake Ontario were con-
structed to provide a basis for understanding the basic mechanisms giving
rise to the observed data and to examine the relative effect on such features
as the hydrodynamic transport, nutrient iimit.Rt.1ons and near-shore, open-
lake interactions. The verification status of the models was examined using
three measures: a) a statistical comparison of data monthly means and model
monthly means b) regression analyses of observed and computed values, and
c) relative error of observed and computed output.
The effect on phytoplankton from the horizontal flow transport for
scales of 10 x 40 km does not appear significant and, at those scales, the
behavior of the phytoplankton is governed by system kinetics and vertical
fluxes of temperature and nutrients. However, as one proceeds to more local
scales, e.g. Rochester embayment, the effect of horizontal transport becomes
significantly greater and in some instances, can dominate phytoplankton
behavior.
Several versions of the model were prepared using different values for
key parameters such as the phytoplankton settling rate and incorporating
different kinetic schemes involving nutrient recycling. One version also
included dividing the phytoplankton into two groups: diatoms and non-diatoms
and incorporating silica limitation in the diatom group. Figure S-la shows
the computed values of phytoplankton chlorophyll using the scheme that per-
formed the best in comparisons to the observed data. The near-shore, open-
lake gradients are evident as is the indication that the region along the
south shore and east of Rochester is generally at higher plankton levels
- 2 -
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AUGUST. 1972
0-4 METERS
44<
4-17 METERS
4-17 METERS
17-50 METERS
17-60 METERS
•
Figure Sl(a) Computed Chlorophyll Contours, Run
- 3 -
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LAKE 1 KINETICS, Run 26A
05
to
IE
Q_
O
I
o
Q
LLJ
DC
LLI
CO
CO
O
12
10
en
4
2
0
June 1972
o 1-26 (0-4 m)
m 27-52 (4-17m)
A 53-67 (> 17mj
r-r2 = 0.54
b = 0.78
0 2 4 6 8 10 12 14
CALCULATED CHLOROPHYLLa,
MO/I
Eight regions, 1972
= 0.84
b = 0.92
a = 0.25
= 0.84
Figure
CALCULATED CHLOROPHYLLa,
MO/1
Sl(b) Chlorophyll Regression Analysis: calculated vs.
observed EPA data, Run #5-a) June 1972 b) eight regions
-------
reflecting the inputs along that region. Shown in Figure Sl(b) is the
regression analyses of observed versus calculated chlorophyll values on the
segment-segment level and regional level and illustrates the relative in-
crease in model credibility as the spatial averaging increases. Overall,
the median relative error for the results of Figure Sl(b) is about 30%.
The Rochester embayment model, a small grid (l x 10 km) was used to des-
cribe the behavior of phytoplankton concentration in that area. The model
is identical to the Lake 3 model and is embedded in one segment of that
model. The results from the first calibration run are consistent with the
observed data but do not completely explain local pulses of chlorophyll.
Median relative errors for the chlorophyll were about 50$. The model indi-
cated that about 90% of the total phosphorus input in pounds/day is from
transport of nutrients from the west into the embayment and about 10$ is
from direct input from the Genesee River and municipal input from Rochester.
Under the assumed transport regime, the effect of phosphorus reduction into
the Rochester embayment would be realized most significantly to the east of
the embayment and only under reduced long shore velocity is the effect of
local inputs significant.
MODEL CREDIBILITY '
The questions of model credibility were examined in some detail in order
to provide a basis for questions of the following type. How good is this
model? At what scale is the model better or worse? Do more complicated
kinetic structures improve the performance of the model?
The modeling framework, in general, duplicated the major features of
chlorophyll and nutrient behavior in the Lake, i.e. near-shore-open-lake dif-
ferences and spatial occurrence of the spring bloom. The original Lake 1
kinetics (calibrated on earlier years) when placed into the IFYGL conditions
and a three-dimensional framework, generally overestimated the chlorophyll
levels with median relative errors ranging from 30-Uo$ for different scales
of Lake Ontario and 50% for the "fine scale" Rochester embayment. It is at
the segment-segment level where major differences can occur, i.e. relative
errors of greater than 100$ and entire months where very few segments were
verified by the model under any of the three statistical tests.
It is concluded from the verification statistical analysis of chloro-
phyll that as one progresses to smaller spatial scales, especially to the
scale of the Rochester embayment, hydrodynamic transport and local phenomena
become more and more significant. Often however data are not available to
specifically quantify these phenomena. At the larger spatial scales, system
kinetics dominate and the importance of the hydrodynamic structure is de-
creased. Increased kinetic complexity did not appear to materially affect
model status over the simpler kinetic structure. A calibration effort to a
given year, at the whole lake scale, can reduce median relative errors in
chlorophyll to about 10$ but the 3-dimensional version of the same model at
horizontal scales of 200-1000 km2 results in an increase in the error by more
than three to about 35$-
With the available data base therefore, for a large lake such as Lake
Ontario, the chlorophyll verification status of the model ranges from an
- 5 -
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average 105? error at the whole lake scale to 50$ at the local embayment scale.
The status of the model vas also described in terms of the relative
error across all availables, i.e. the pooling of the relative error of all
segments, months and variables. The resulting distribution of error repre-
sents a single measure of all of the variables simultaneously and provides a
simple and direct answer to the question of model credibility across all
state variables, locations and months.
Figure S-2 summarizes the "behavior of the relative error for all vari-
ables for the run that performed most adequately. This figure shows the
variation of the median relative error month by month during 1972 for the
three spatial scales. At the Lake. 3 scale, the average relative error (med-
ian) for the year is hk% with a peak of 60% in August. Generally, the peak
error increased to over 30035 for some segments in November. For the eight
regions, the 1972 all-variable error decreased slightly to 35?. Finally,
for the whole lake scale, the average relative error is 1.1% indicating again
the improved performance at the larger space scales.
As a general summary then, the complex 3-dimensional model of the phyto-
plankton of Lake Ontario does duplicate the principal features and does con-
tribute to an increased understanding of the mechanisms dominating phyto-
plankton behavior. At the three dimensional scale however, the comparison to
observed data indicates somewhat large relative errors with an overall aver-
age of about h$%. As one directs attention to larger regions of the lake,
the model performance, improves in quantitatively reproducing observed average
conditions. For decision making purposes therefore overall model credibility
ranges from 20% error on the whole lake scale to k$% error on the more local,
near-shore scale.
- 6 -
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IUU
80
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>/6?S = 17%
77
^
A S 0
Fl
i
N
1
1
N
N
Figure S2 Median relative error across all variables,
a) Lake 3 scale, 6? segments, b) eight regions,
c) whole lake scale, two layers.
- 7 -
-------
SECTION II
CONCLUSIONS
GENERAL
In a most general sense, it is.concluded from this vork that the appli-
cation of quantitative measures of eutrophication model performance can be
of value in describing model credibility and in diagnosing model behavior.
The use of measures of model verification depends to a considerable extent
on the available data base, which for this work, was the result of a major
effort during the International Field Year on the Great Lakes. Questions
such as "How good is the model?" may be answered therefore in a quantitative
way,if data are available and within the time and space constraints of that
data. As with all simply stated questions, the complexity of the answer to
model status includes the measures one uses to test model validity, the
scales of the model and its kinetic structure and the uses of the model out-
put. It is important then to quantify, wherever possible, the performance
and credibility status of phytoplankton models under as many temporal and
spatial conditions as possible.
More quantitatively, in terms of median relative error, model chloro-
phyll performance ranges from 1.0% error in chlorophyll at the whole scale
lake to 505t error in chlorophyll at the ^cale of 10-100 km2 in the Rochester
embayment. Similarly, for all variables average relative error ranged from
17/6 to kh% for the best run. It is concluded therefore that the present
deterministic models for Lake Ontario appear to be more applicable at larger
space scales of regional to whole lake scope. Hydrodynamic transport and
non-deterministic, stochastic phenomena appear to be the more dominant in-
fluences at the 1000 km2 scale and less. The three dimensional behavior of
the lake models is qualitatively credible but quantitatively, individual
errors in chlorophyll at the 1000 km2 level may often exceed 100$. The work
also indicates that there is a point of diminishing return in trying to im-
prove model status although this is not to say that an independent review
and analysis of the problem by other researchers could not result in a
"better" model.
SPECIFIC
Extensive statistical comparisons between the two data sets used in
this study indicate that on a 1000 km2 3 dimensional scale over the IFYGL on
the average only about half of the places at which five water quality vari-
ables could be compared displayed no difference between CCIW and EPA. On a
regional basis, the comparisons indicate that about 8h% of the regional
averages for the five variables showed no statistical difference. The two
data sets themselves therefore display considerable variability at 1000 km2
- 8 -
-------
scale. During spring bloom conditions, near shore surface (0-1* chlorophyll
levels were approximately 3 JJg/& higher than open lake levels reflecting the
effect of the spring thermal bar and higher productivity in the more shallow
near shore areas.
Sensitivity analyses at the Lake 3 scale indicate that the horizontal
transport does not significantly affect the calculated distribution of
chlorophyll. Flow reversal and velocity reduction resulted in only minor
changes in chlorophyll indicating that at the scale used in the analysis,
the kinetic structure tends to dominate the calculation. Vertical disper-
sion and horizontal dispersion at the near-shore, open-lake boundary are
however important phenomena in calculating chlorophyll behavior.
For the best run in terms of chlorophyll verification, a "no statisti-
cal difference" (using a "t" test and regression analysis) between observed
data and computed output corresponds to a median relative error of 22% and a
residual standard error of 0.8 ug chlorophyll/^ at the regional scale.
Therefore, it is concluded that at the regional scale 1000-10,000 km2, the
best one could do at the present time is a relative error between observed
and computed of 20% - this error corresponds approximately to "no difference"
between observed and computed values.
For the Rochester embayment, the phosphorus input from the Genessee
River and municipal inputs represents only about 8% of the total input to
the embayment from the external lake boundaries. The major input is from
advective-dispersive transport entering the embayment from the west. Reduc-
tion of phosphorus loadings from the Genessee as municipal sources will
therefore have a limited effect in peak phytoplankton chlorophyll within the
embayment itself; the effect will be felt at some distance to the east. Re-
ductions of phytoplankton chlorophyll in the embayment depends to a greater
extent on reduction of nutrient and biomass fluxes from the westerly trans-
port due principally to the Niagara input.
- 9 -
-------
SECTION III
RECOMMENDATIONS
It is recommended that discussions and investigation continue into the
area of useful measures to determine model credibility and verification
status. This is particularly important for phytoplankton-nutrient models in
the Great Lakes because of the high visibility and potential utilization of
such analysis frameworks. Further such measures should also be applied to
the vhole array of analyses that are used in management of the phytoplankton-
nutrient status of the Lakes including empirical analyses and analyses based
on single nutrients such as total phosphorus.
Continued investigation should be carried out to determine if improve-
ments in model status can be obtained at the more local level (10-100 km2)
scale such as Rochester embayment. This investigation would include the
determination of the relative effects of specifying a more realistic hydro-
dynamic transport regime on model performance.
Within the now quantified ability of the model to reflect the observed
data, analyses of various reductions in external nutrient loading on local
areas such as Rochester embayment should be carried out over time.
Results from future extensions to the existing model either in spatial
or kinetic detail, or results from other models of different construction
could be compared to the verification statistics of the present model to de-
termine whether a quantifiable improvement in performance has been attained.
- 10 -
-------
SECTION IV
INTRODUCTION
PURPOSE OF RESEARCH
A considerable effort was directed towards the observation and under-
standing of the behavior of Lake Ontario (Figure l) during the International
Field Year on the Great Lakes (IFYGL). Part of that effort included the
development and preliminary application of a simplified model of phytoplank-
ton chlorophyll for Lake Ontario, called Lake 1 (Thomann, et al., 1975;
Thomann, et al., 1976). The research reported on herein builds on that
earlier work in several stages:
a) reduction and statistical analysis of IFYGL data using both EPA and
CCIW data,
b) the implementation and detailed verification analysis of a three-
dimensional model of phytoplankton dynamics, called Lake 3, including the
development of more rigorous quantitative bases for determining the degree
of verification,
c) development and calibration of a three dimensional model of phyto-
plankton dynamics for the Rochester embayment of Lake Ontario,
d) determination of the statistical verification properties of the
present phytoplankton models at different spatial scales.
The thrust of these efforts is to provide additional input into the
planning process for eutrophication in Lake Ontario. Specifically, efforts
(a) and (b) provide insight into mechanisms and processes for both the near-
shore and open lake regions. The introduction of more rigorous measures of
verification provides the decision maker with at least a partial answer to
the question of what constitutes a "good" model. The purpose of the
research into the Rochester embayment is to examine the behavior of a more
local scale problem where the region may be influenced by sources of nutri-
ents elsewhere in the lake system as well as discharges directly to the
region itself. The Rochester work therefore is an example of a model of a
local region embedded in the larger Lake 3 model.
SCOPE OF RESEARCH
Geographically, this report is centered on Lake Ontario and Rochester
embayment although the development of the criteria for determining verifica-
tion has application to other problem settings. The problem context is con-
cerned with explaining the temporal and spatial variability and interactions
between phytoplankton chlorophyll, nitrogen and phosphorus forms and other
internal and external factors. The measure of eutrophication is taken as
the chlorophyll level and no further species breakdown or grouping of phyto-
plankton types is attempted in this work. The spatial scale varies from an
- 11 -
-------
i
-N-
t
O N T A
R|0
44C
TORONTO
43°
10 0 10 20 30 40 50
Lake Erie
79<
IT
Figure 1 Lake Ontario
-------
approximate 10 X kO km grid for the Lake 3 model to an approximate 2 X h km
grid for the Rochester embayment. Temporally, the analysis draws on the
IFYGL data collected from May, 1972 through June, 1973.
THE VERIFICATION QUESTIONS
One of the purposes of the research is to highlight the growing need
for detailed and quantitative verification of water quality models that goes
well beyond model computation and determines measures of model adequacy for
the decision maker. Specifically, this research is aimed at the verification
of phytoplankton-nutrient models, the number of which has increased signifi-
cantly in recent years. These models all make use of a similar underlying
deterministic framework of coupled interactive non-linear differential equa-
tions which are solved numerically in discrete space and time.
Indeed, the state of the computing art of such frameworks is advancing
rapidly and today it is no longer of great moment if hundreds of sets of
non-linear equations are successfully solved on a large computer. What is of
significance however, is whether the numerical computations are "reasonable"
representations of the real world. It is at this point that considerable
confusion results both in the realm of the model builder and in the mind of
the decision maker. What is adequate and reasonable? Is it sufficient to
generate computed values that "look" like what is being observed? For
example, is it sufficient that a phytoplankton model simply generate a spring
pulse which has been observed or is there a certain quantitative measure that
must be introduced to determine not only that a spring pulse is calculated
but that its magnitude is correct in some sense? One of the principal ques-
tions addressed in this research is: "What criteria might one use to deter-
mine the adequacy of the model?" It appears that unless a detailed examina-
tion of the comparison of the model to observed data is carried out, there
is no rigorous way of judging the adequacy of the computation. This, of
course, assumes that a data base exists with which to carry out a verifica-
tion analysis. There may be situations where this is not possible; as for
example in projecting phytoplankton conditions in a reservoir that is not
yet in existence. Such a problem context is not considered here. This
research is aimed at detailed verification, where possible, so that the
credibility and utility of a modeling framework are established under sev-
eral statistical tests.
Further, such statistical tests, as will be seen, provide a means for
determining the scale over which a model may be applicable. That is, do the
present deterministic kinetic structures apply equally well over all spatial
scales from local near-shore scales up to open-lake scales?
The research reported on herein is complementary to work also being
completed on similar questions of verification related to the long term
(10 year) behavior of phytoplankton models of Lake Ontario. The results of
both of these efforts will therefore provide information on model credibility
over a range of temporal and spatial scales.
- 13 -
-------
SECTION V
DATA ANALYSIS AND VERIFICATION PROCEDURE
THE LAKE ONTARIO MODELS
The "basic model used in this research is a three-dimensional version of
an earlier model of two vertical segments (Lake 1). The three-dimensional
model, called Lake 3, is constructed to provide additional spatial detail on
the behavior of the phytoplankton-nutrient interactions. The basis of the
Lake 3 model and additional information on its background is given in
Thomann, et al., (1975). The spatial configuration of the computational
grid used for Lake 3 is shown in Figure 2; 67 segments are used. As noted,
five vertical layers are used and an attempt has been made to capture near-
shore phenomena by a ring of segments around the periphery of the lake ex-
tending some 10 km from shore. These near-shore segments have horizontal
spatial dimensions of about 10 km X ho km.
The kinetic structure of the model has been reviewed and discussed pre-
viously (Thomann, et al., 1975) and includes linear and non-linear inter-
actions between eight variables:
l) phytoplankton chlorophyll
2) herbivorous zooplankton
3) carnivorous zooplankton
k) non-living organic nitrogen (particulate plus dissolved)
5) ammonia nitrogen
6) nitrate nitrogen
7) non-living organic phosphorus (jparticulate plus dissolved)
8) "available" phosphorus (usually orthophosphate).
Parameter specification for the model was originally determined on two bases:
(.a) values from the literature on such factors as saturated phytoplankton
growth rate, zooplankton grazing rates etc. and (b) calibration of Lake 1
model to a k year (1967-1970) composite of open-lake data. As discussed
below, this parameter set formed the first basis for the verification of the
Lake 3 model using the IFYGL data base. Extension of the original Lake 1
kinetics have also been incorporated to represent additional phytoplankton-
nutrient interactions such as silica limitation by diatoms.
Data analyses and summaries and comparisons to calculated values from
the Lake 3 model were also conducted using segment aggregations into "near-
shore" and "open-lake" regions and by various aggregations with depth (e.g.
0-17 m, 17-50 m). These results provided an intermediate spatial scale of
comparison.
-------
ll
I
>150 Meters
Figure 2 La,ke 3 Model grid
-------
Finally, as mentioned previously, a preliminary model of the Rochester
embayment was constructed to examine interactions betveen the lake and a more
local area. The various spatial scales that result from Lake 1, Lake 3,
aggregated Lake 3 output and the Rochester embayment model are displayed in
Figure 3. As indicated, the overall analysis discussed in the research
extends from some 10-100 km2 to 13,000 km2 or some three orders of magnitude
in spatial scale.
VERIFICATION ANALYSIS FRAMEWORK
For the 67 segments of Lake 3 and eight dependent variables, 536 non-
linear equations are integrated in time for a maximum period of lU months. A
time step of .08 days is used throughout and solution is accomplished on a
CDC 6600 and requires some 63K of storage and about 1 hour of equivalent main
frame computing time. The model is relatively large and for any one run gen-
erates some 100,000 numbers. The analyst attempting to absorb the behavior
of such a model faces a formidable, indeed almost impossible task since atten-
tion can only be directed towards certain portions of the model (either in
variable or physical space). Furthermore, since the various portions of the
model are so interactive, adjustments to improve the model in one region may
result in an undesirable change in another region. Therefore, a strategy for
determining the behavior of the model and its verification status must be
developed. Figure U shows the flow diagram adopted for the analysis of the
Lake 3 model. The procedure begins by a processing, editing and statistical
analysis of the IFYGL data base including segment and regional summaries and
plots of all data. Similarly, for a given model run, the model output is
processed, edited; summary statistics and summary plots are generated. The
data and model are then merged, overplots produced and various statistical
tests are applied to the data and model information set. Finally, verifica-
tion scores and overall summaries of the "goodness" of the model run are pre-
pared.
Reduction of the IFYGL Data Base
The principal source of data for this work is that collected by the U.S.
and Canada during the IFYGL. Water quality data were obtained by EPA for the
U.S. and the Canada Centre for Inland Waters (CCIW) for Canada. Other agen-
cies such as National Oceanic and Atmospheric Administration (NOAA) obtained
data on physical properties and behavior of the lake such as water tempera-
ture and hydrodynamic circulation.
The IFYGL water quality data base is resident in the storage and re-
trieval system (STORET) of the EPA and contains approximately 200,000 obser-
vas, encompassing 75 water quality parameters and includes the U.S. and
Canadian data. The latter data set is from the OOPS cruises and does not
necessarily include all Canadian data collected during IFYGL. For chloro-
phyll, the Canadian data were augmented using other so-called "temperature"
cruises of CCIW. This data base is the most complete set of observations
obtained to date on Lake Ontario and contains a wealth of information on the
dynamics of the lake. Data statistics are generated for volumes of the Lake
corresponding to the segmentation of the Lake 3 model. Given the approximate
monthly sampling interval of the IFYGL cruises, mean and variance statistics
over a segment and over a month are used. Each cruise station is assigned to
- 16 -
-------
MODEL
DESIGN A TION
HORIZONTAL
NUMBER OF SCALE (km2!
SEGMENTS EPI LIMN ION
SEGMENTS
LAKE 1
LAKE 3
OPEN LAKE
NEA RSHORE
LAKE 3
(AGG REG ATE D) Z^&££$^
67
E
13,000
200-1000
6000- 13,000
X / / 7 / /
ROCHESTER
EMBAYMENT
// / / / / /
n
10-100
Figure 3 Spatial scales used in Lake Ontario analyses
- IT -
-------
Piiocess .
n«t« Rau ~™ ™^^^^ IFYGL Data
IAKE3 A EDIT SUMMARY STATISTICS ^
Model Output Model Output
SUMMARY
PLOTS
fl T
tili
SUMMARY
PLOTS
t\ y
_
^
DATA-MODEL
MERGE
lii?
lRr*.
DIFFERENCE OF
MEANS TESTS
Observed vs.
Computed
RELATIVE
ERROR
«•••
VERIFICATION
i^ cnnpccff,
SUMMARY
c»
I
Figure
die,gjrw for model verification analysis
-------
a model segment so that within a month a given segment may have been spatially
sampled up to h times. After the segment statistics are generated for the
various water quality parameters of interest, a display package is accessed
to generate microfilm or paper plots of the parameter statistics versus time.
The STORET data base is accessible to the user, through program packages
for standard retrievals and manipulations of the data set is large (2 x 105
observations) an approach had to be formulated that would facilitate the
sizable reduction task. Recognizing that the reduced statistical data set
would be used on a different computer system (CDC 6600) and the need to accom-
plish the data reduction in the shortest time possible, such an approach is
a necessity.
The scheme was carried out for each of the 67 segments and a total of
over 200 data reduction runs were made. Each segment required three reduction
runs since a maximum of eight parameters per run could be made and twenty
variables were reduced per segment.
The first step was to prepare decks which described the segment volumes.
Each volume was defined using a latitude/longitude polygon with depth con-
straints. The STORET program Mean was used to generate the segment statis-
tics; monthly mean, standard deviation, number of observations, and the maxi-
mum and minimum values. Since the output from Mean is fixed and the results
were to be transported to the CDC 6600 via data cards, manipulation of the
output file was necessitated. The EPA operating system contains an online
interactive text editor named Wylbur. Using Wylbur and its limited macro
capability, text editing module programs were developed that reduced the
output from lUO to 80 characters per line ajid eliminated all extraneous lines
of information. This compressed data set was then punched and therefore, was
in a form processable by the CDC 6600. A Fortran program was written to
manipulate this data into the format required by the verification analysis
and graphic display programs. The result of this effort was an IFYGL data
set of monthly statistics for twenty variables collected by the EPA for 67
segments for the period May, 1972 through June, 1973. A similar procedure
was followed for the CCIW OOPS cruise data set in STORET. Both data sets
were kept separated to permit statistical comparisons.
A graphical display program was also written in Fortran to display the
temporal variation of the parameters. Monthly means plus or minus one stan-
dard deviation are displayed. The graphical output of this program can be
routed either to paper or microfilm. The use of microfilm for both graphical
and printed output has proven to be of Immense utility when dealing with
large scale problems such as Lake Ontario and is to be recommended. Figure 5
shows a typical output for EPA data and segment No. 21. Data coverage varied
spatially and temporally for different variables and for the EPA and CCIW
data. Figure 6 indicates the temporal coverage of the cruises during IFYGL
and Figure 7 shows the spatial coverage of the sampling stations for both
data sets. Figure 8 compares the two sets for chlorophyll in terms of the
percent of the total 67 segments at which statistical comparisons could be
made. Most other water quality variables had similar coverage. As these
figures indicate, during May-November, 1972, temporal and spatial coverage
was generally good for EPA data and averaged about 80$ of the segments.
- 19 -
-------
SEGMENT 21
^20
%
^
-10
u
0
E0.02
Q °-01
=S0.03
c
a.-a°2
§0.01
0
? 13/Z- • • IS73 •
MEAN *. \ STANDARD
T DEVIATION
T 1 NI
i | xfi5oa o$ , ,
(0
0 0°
" 1? 1 1 1
" I B $ '
«BB«I«PB i i B i
243 487
TIME, days
=&°-8
go.4
" JT
I E o.l
f 0.4
0.2
728
08
•!
, I8 , • . "
?no«i^n i 9 n n i
e o
243 487
TIME, days
728
Figure 5 Typical graphical output of EPA, IFYGL data summary
for segment No. 21. (Day 0-Jan. 1, 1972)
caw H H H H H H H H
EPA
HHHHHHHHIHIHH
H
H H HHHH
J'F'M'A'M'J'J'A'S'O'N'DI j ' F'M'A'M'j
1972 ' 1973
Figure 6 Approximate times of cruises during IFYGL
"by CCIW and EPA
- 20 -
-------
Figure 7 (a) Principal EPA-IFYGL stations and the Lake 3 grid
The CCIW data has less spatial coverage principally because of a lack of
samples at lower depths and because of the reduced horizontal coverage as
shown in Figure 7b. Also, CCIW data were not collected during August, 1972.
After November, 1972 however, both data sets are significantly reduced in
coverage with the exception of the April and June, 1973 surveys.
Observation Statistics
In addition to data reduction by individual Lake 3 segment, reduction
was also accomplished using aggregrated segments as delineated in Figure 9.
As shown, eight averaging regions were used where the horizontal dimension
is divided into "near-shore and open-lake". The data for each segment with-
in each region were volume averaged to obtain a regional average. Therefore,
= observed mean for variable i, segment J and month k, then
ijk
Z V
(1)
where I is the volume averaged concentration for region m and N is the
• ik m
total number of segments contained in region m.
The volume averaging of concentrations over a number of segments also
introduces several additional statistics, e.g. the average variance between
segments within a region. Therefore, there are various statistics that can
be computed from the observed data in addition to mean value statistics.
- 21 -
-------
i
*
O N T A
ROCHESTER $™(
10 0 10 20 30 40 50
10 0 10 20 30
43°-
79° 77°
Figure 7 (t>) CCIW-OQPS cruise stations, IFYGL in STORET data tase: 1972-1973
-------
100% = 67 Segments
CHLOROPHYLL DATA
0
J F
F' M ' A1 M ' J
1973
Figure 8 Segments for which statistical comparisons for chlorophyll
could be made
a) The within-segment variance for variable i, segment j and month k
is given by
n.
J
E , -.2
r=l (xr - x)
n.-l
0
SSi1k
(2)
where n. = the number of points for segment_ j. This is the first variance
computed in the data reduction phase and (x +_ s).., represent the output
shown in Figure 5-
b) The standard deviation of the observed segment mean (used for ver-
ification purposes as discussed below) is given by
s— = s/v/rT7
x j
(3)
This standard deviation is also called the standard error of the mean.
c) In some instances, this latter variance is volume averaged to pro-
vide an estimate of the average within segment standard error for a region.
Therefore,
- 23 -
-------
THE EIGHT AVERAGING REGIONS OF LAKE 3 SEGMENTS
• i
I
E3 REGION 1
Region Designation Depth
> 150 Meters
Near shore
Open lake
Near shore
Open lake
Near shore
Open lake
Open lake
Open lake
0-4 m
0-4
4-17
4-17
17-50
17-50
50-150
>150
Figure 9 The eight averaging regions of Lake 3 segments
-------
EV s-2
2
s- = ZV
x
is used as a measure of regional average intrasegment variance.
The question of the volume averaging of the standard errors of segment
means for regional statistics is a complex one. Issues of spatial and tem-
poral correlations between samples within segments and from segment to seg-
ment preclude a ready assumption of independence. Therefore, an equation
such as:
O T O O
x (*)' - <5)
while easily obtained from variance considerations requires the assumption
of uncorrelated standard errors. It can also be seen that this equation
results in a reduced regional standard error approximately proportional' to
the inverse of the number of volumes used in the region. Thus, if
s = s = ... = c
Xl X2
and all segment volumes are equal, then Equation (5) yields
-2 c2
s- =iT
X
for N volumes in the region. This result does not appear physically realis-
tic since it indicates that the regional mean of the standard errors can
decrease rapidly if the number of aggregated volumes increases. It is for
this reason, that in the absence of a more detailed correlational analysis
in space and time of the data, Eq. (U) is used. It is recognized that Eq.
(4) may not be statistically rigorous and, as such, it is considered solely
as an estimate of the unknown appropriate standard error.
Indeed, a more basic issue might also be addressed; namely, is the
regional average within-segment standard error (no matter how it is esti-
mated), the proper variance to use in a regional testing of means? One
might argue that perhaps the variance of segment means from the overall vol-
ume weighted mean should be used. This results in an estimate of the seg-
ment-segment variance.
d) The variance between segments means within a region is estimated
for variable i and month k from
(6)
2
x
m
N
E (x - x )2
N-l
-------
This estimate therefore represents the variability of each segment mean from
the overall regional volume averaged mean.
e) The total variance of the individual samples could also "be estimated
from the volume weighted sums of squares of deviations, SS , i.e.
J
SST = N SSaver
-------
is the difference of the calculated and observed means where the triple sub-
script has been dropped. This difference is assumed to be distributed as a
student's "t" probability density function. The differences of means is
therefore assumed to be normally distributed. A check of this assumption
for .the total phosphorus on the regional level indicates that the differences
are approximately normal. For phytoplankton chlorophyll, the distribution of
differences is approximately normal dovn to differences of about 0.12 yg/£
where the distribution skews. This would indicate that for chlorophyll a log
or other transformation of differences might be more appropriate. However,
in this work, such a transformation was not made although the behavior of the
statistics under transformed differences should be further explored.
SEGMENT 21
243 487
TIME, days
243 487 728
TIME, days
Figure 10 Typical merge of model output (solid line) and data
The test statistic is given by (Wine, 196U, p. 263).
(10)
where s-r is the estimated standard deviation of the difference of the means
and 6 is the true difference of means. The quantity s-? is
2 2 ,1 _,_ 1 x
- = s ( — + — )
v '
p n n
(11)
for s =
P
„ Z(x - x)2 + Z(c - c)2
2 r T*
n
, a "pooled" variance.
In this latter equation, c represents the computed output at a scale finer
than the actual grid and therefore represents one portion of model variance.
-------
That is, the determination of the model variance would include a computation
at a smaller grid to attempt to model spatial variance. The use of larger
grids as in Lake Ontario obviously permits only a single computation for
each segment. Estimating the variance at a finer spatial scale therefore
would require a computation of significantly greater size than used in this
work.
An additional component of the computed variance would include uncer-
tainties in model input (temperature, transport, dispersion) as well as sys-
tem parameters (growth rates, grazing dynamics, etc.). The determination of
the total model variance would therefore require a number of sensitivity runs
at several time and space scales. Such a computation was not considered
feasible for this work. However, if it is assumed that the computed variance
(essentially unknown) is at least equal to the observed variance, then
(12)
Note that s-r represents the standard deviation of the differences of means
and at maximum for n =2 is equal to s, the sample standard deviation for a
J
segment. For all values of n >2, s-
-------
LU
o
z
LU
DC
CC
D
O
d = MODEL MEAN - OBSERVED MEAN
-V
UNDER-
ESTIMA TION
•«- REGION OF NO STA- H
TISTICALLY SIGNIFICANT
DIFFERENCE BETWEEN
MODEL AND OBSERVED
MEANS (90% CONFIDENCE
LIMITS)
"VERIFIED"
"V" SCORE = 0
+ V
•
OVER-
ESTIMATION
Figure 11 Determination of verification score, V
-------
range of uncertainty on model variance. Thus if this variance were assumed
zero, then the lower "bound on the critical difference is
_ ±2s
dc = —
/n
The distribution of d and the critical regions are shown in Figure 11. As
indicated, if -d
-------
chlorophyll. Therefore, a series of weights, w. , where Zw. = 1, can be
assigned to each variable i representing the relative importance of each var-
iable. The aggregated score for month k is then given by
r n
S = Z Z w.K. ../(nSw.) (19)
k i ^ i ijk i
where r is the number of variables that passed a "t" test of V=0 for month k.
It should be noted that not all segments and variables can be tested at each
month, so that r and n are functions of the data availability for month k.
Regression Analyses
An alternate perspective on the adequacy of a model can be obtained by
regressing the calculated values with the observed values. Therefore, let
the testing equation be
x = a + $c" + e '(20)
where a and (3 are the true intercept and slope respectively between the cal-
culated and observed values and e is the error in x. The model equation (20)
assumes, of course, that c, the calculated value from the phytoplankton model
is known with certainty which is not the actual case. With Equation (20),
standard linear regression statistics can be computed, including
a) The square of the correlation coefficient, r2, (the % variance
accounted for) between calculated and observed and the associated
F statistic to test the significance of the computed r2
b) Standard error of estimate, representing the residual error
between model and data
c) slope estimate, b of 8 and intercept estimate, a of a
d) Tests of significance on the slope and intercept. In this work,
the null hypothesis on the slope and intercept is given by
3=1 and a = 0.
Therefore, the test statistics
—— and a/s
sb
are distributed as student's t with n-2 degrees of freedom. The variance of
the slope and intercept, s2 and s2 are computed according to standard formu-
b a
lae. A two-tailed "t" test is conducted on b and a, separately, with a 5$
probability in .each tail, i.e. a critical value of t of about 2 provides the
rejection limit of the null hypothesis.
Regressing the calculated and observed values can result in several
situations. Figure 12 (b) and (.c) shows that very good correlation may be
obtained but a constant fractional bias may exist (bl); also Figure
12 (a) indicates that poor correlation may be obtained with slope = 1 and
intercept = 0. Finally, Figure 12 (d) indicates the case of good correla-
- 31 -
-------
10
Q
_J
< .
O 4
2
0
CALCULATED {a\
• OBSERVED
0 • /
- o v^"*^*— £ • ft/
° * -. «^
TIME, days ^ •
t ^/Jl
/ 1
" x r* ; ?
" / a = 0
X i I i i
10
8
6
4
2
0
r2= 1 (b)
A6<1
»=o /
/
X
r - • XJ1
/ — i
TIME, days v 1
/
/
~ / .^ *"
^-r* i i i i
2468 10 2468 10
OBSERVED OBSERVED
10
Q
LU n
«- °
<
§ 6
2 4
2
0
6> 1
- a=0 / .^
/^^r
XI1
/ '
: /Xi ^
IS TIME, days
r \ i i i i
10
8
6
4
2
c.
0
r2= 1 (d)
- a>0 / X
X/^1
* X
X / 1 A.
_ / ° •/ v
X TIME, days
1 1 1 1 1
2468 10 2468 10
OBSERVED OBSERVED
Figure 12 Possible cases in regression "between calculated
and observed values
- 32 -
-------
tion may be obtained vith slope = 1 and intercept = 0. Finally, Figure 12
(d) indicates the case of good correlation but for a > 0 a constant bias may
exist. Evaluation of r2, b and a together with the residual standard error
of estimate can provide an additional level of insight into the comparison
between model and data.
Relative Error
An additional simple statistical comparison is given by the relative
error defined as
e = I* - «l (21)
x
for each variable, segment or month. Various aggregations of this error
across regions were also calculated and the cumulative frequency of error
over months or segments is also computed. The difficulties with this sta-
tistic are its relatively poor behavior at low values of x and the fact that
it does not recognize_the variability in the data. In addition, the statis-
tic is poor when x > c since under that condition the maximum relative error
is 100$. As a result, the distribution of this error statistic is most
poorly behaved at the upper tail. Nevertheless, if the median error is con-
sidered, this statistic is the most easily understood comparison and provides
a gross measure of model adequacy. It can also be especially useful in com-
parisons between models.
- 33 -
-------
SECTION VI
ANALYSIS OF OBSERVED IFYGL WATER QUALITY DATA
GENERAL IFYGL CONDITIONS
Met eorology-Hydrology
Philips (197*0 has described the weather during the data-gathering per-
iod of IFYGL as "cold, stormy and dull". Precipitation was generally heavy
and above normal (every month had an above normal number of days of precipi-
tation). Hurricane Agnes arrived on the scene early in the Field Year during
June 20-25, 1972 and caused extensive flooding. Solar radiation during the
period April, 1972-March, 1973 was slightly above normal for only two months
(April-May, 1972). For all other months, solar radiation was below normal,
sometimes averaging a 25% decrease. Philips (197*0 gives a complete review
of all these conditions and a detailed energy budget is presented by Elder
et al. (197*0. Figure 13 compares the weekly heat storage measured by Elder
et al. to the five year average monthly flux. The runoff during IFYGL is
illustrated by the flow from the Niagara and Genesee rivers (Figure 1*0.
The Niagara flow was generally at the highest levels for the period of
record; 5% of time, average annual flows for 1860-1972 were greater than
235,000 cfs. The transient inflows in the smaller tributaries during Hurri-
cane Agnes and the rapid decline in flow during August and September are
indicated by the flow of the Genesee River shown in Figure 1*4-. Much of the
"high frequency", day to day and week to week fluctuations in inflow will,
of course, have only localized effects and will not significantly affect lake
wide water quality.
Nutrient Inputs
A review of the tributary sampling program conducted during IFYGL is
given by Casey and Salbach (197*0 and Hydroscience (1976) has prepared esti-
mates of nutrient inputs for the years 1967-7**- These results indicate total
phosphorus loadings at about 87,100 Ibs/day (39-5 mt/day) for 1972 and
83,200 Ibs/day (37.8 mt/day) for 1973. The principal difference between
years appears to be the uncontrolled runoff from tributaries. As Casey and
Salbach (197*0 have pointed out (along with many others), the estimate of the
tributary load depends significantly on the frequency of water quality samp-
ling. The estimates do not include atmospheric inputs.
The nutrient inputs assumed for each shore-baSed segment of the Lake 3
model are summarized in Table 1.
-------
I
>
CD
-o
CM
I
O
o
LU
DC
O
LU
I
800
600 -
400 -
200 -
0
-200 -
-400 -
-600 -
IFYGL
o 5- YEA R MONTHL Y A VERAGE
30 90 150 210 270 330
TIME, days
Figure 13 Heat storage; IFYGL data after Elder et al. (197*0
- 35 -
-------
36
v>
t>
o 28
8
o*
uj20
DC
10
i*
NIAGARA RIVER AT BUFFALO. NY
*-*~Y^
J'F'M'A'M'J1J1A'S'O'N'D! J1 F'M'A'M'j
1972 1973
26
22
18
*". 14
uT
o
tc
SlO
u
CO
GENESEE RIVER AT ROCHESTER. NY
(6.1 MILES UPSTREAM FROM MOUTH)
J'F'M'A'M'J 'J'A'S'O'N'DI j' F ' M' A'
1972 1973
Figure Ik Flow of Niagara and Genesee Rivers during IFYGL
- 36 -
-------
TABLE 1
Assumed Nutrient Inputs (IFYGL) "by
Lake 3 Segment
Phosphorus(ibs/day)
Nitrogen(ibs/day)
Segment No.
(see Fig. 2)
1
2
1*
5
6
9
10
13
17
21
23
26
31
TOTAL
Less Available
U35
751
1*323
9652
73
2199
8
25
5287
35
320
201
33962
57271
Available
(Diss-ortho P)
803
171*9
9312
2179
10
291
1
1*
1*190
5
1*1*
1029
1*1*99
2l*ll6
Less Available
1550
2567
16151*
50l*ll*
131*
19981*
1*8
161*
221*15
33
1516
13610
16381*7
292U66
NH -N
3751*
25556
1*8303
11279
30
1086
11
37
121*1*2
7
3Ul
l*28o
36533
i^
NO -N
717
1672
1*575
631*08
171
8051*
61
209
22171
1*2
1932
1781*3
206195
327050
STATISTICAL ANALYSIS OF WATER QUALITY DATA
Water Temperature
The temperature regime of the Lake during IFYGL forms an important var-
iable for two reasons: a) the use of temperature as a "tracer" variable
indicating lateral and vertical mixing and b) as a key exogenous driving
variable for the behavior of lake phytoplankton and zooplankton and for tem-
perature mediated bacterial decomposition and recycling kinetics.
The temperature data base used herein utilizes two principal sources.
The first source was built up from the NOAA BT data file which was randomly
read at different times of the year and for each of the segments of the Lake.
A series of straight line approximations over time of year were then applied
to the data and a straight line temperature function constructed for each
segment of the Lake. Figure 15 shows several of these functions. Data from
the transects as given in Stadelmann and Fraser (197!*) were also incorporated
where possible. Initially, data as given by Webb (1971*) were also included;
- 37 -
-------
O
g> 20
TD
LU~ 16
DC
? 12
DC
LU
Q_
S
LU
QC
LU
Q.
LU
I-
oc
LU
0.
LU
8
4
0
<-> 20
O)
16
T3
uj T2
QC
Z)
8
0
SEGMENT 15 (OPEN LAKE, 0-4 m)
150
210
270
330
l F I MI A I Ml J
390 450 510
SEGMENTS?
M I J I J I A • S'O'N'D'JlF'M'A'lVHj
150 210 270 330 390 450 510
SEGMENT 64
M ' J
150
210
S'O'N'D'J'F'M'A'M'J
270 330 390 450 510
Figure 15 Some straight line temperature functions derived from
NOAA-BT files
- 38 -
-------
however, it was found that such data tended to overestimate surface tempera-
tures, in some instances, by several degrees and were not representative of
the 0-k m layer as used in the Lake 3 model.
.The second source of data is the CCIW OOPS data contained in the STORET
system. These data were retrieved, assigned to Lake segments, and segment
statistics were computed as described previously (see Section IV, Observa-
tion Statistics). For this data source, both monthly means as well as stan-
dard errors could be computed in contrast to the first data source where
only monthly means were computed.
The results of volume weighted averages of the NOAA water temperature
data set, using various aggregation schemes are shown in Figures 16-18.
Figure 16 shows the temporal variation for several vertical layers and for
the 0-17 m layer, the near-shore and open-lake averages are also displayed.
It appears from these data that the thermal bar effect was more pronounced
during May-June, 1972 than during the comparable period for 1973. As shown
in Figure 16, the difference between near-shore averages and main lake aver-
ages for 0-17 m. in May-June, 1972 was about 3°C as opposed to an average
difference of about 1°C during May-June, 1973- The near-shore surface layer
cooling in the fall of 1972 is also evident. Further, the Lake apparently
was completely mixed by about December, 1972.
o
o>
-8
of
DC
DC
UJ
0.
S
UJ
I-
cc
20
15
10
5
0
+ 2
0
-2
10
5
0-17 METERS
•—• NEAR SHORE
0—0 OPEN LAKE
0-17 METERS
(Near shore)—
(Open lake)
_ o—017-50 METERS
50-150 METERS
^ o
M'J'J'A'S'O'N'DIJ'F'M'AM'J
1972
1973
Figure 16 Volume-monthly averaged water temperature (NOAA-BT data)
during IFYGL
- 39 -
-------
0
WATER TEMPERATURE, deg C
12 15 18 03
9 12 15 18
0-4
4-17
17-50
50-150
-
_
—
>150 I-
0 «
I /
o»
1
1
0
1
O
/• 1 1 1
• NEAR SHORE
o OPEN LAKE*
MA Y '72
0-4
4-17
17-50
50-150
—
—
>150[-
, ^»\f , ,
j/
i
£ JUN 72
12 15 18
9 12 15 18
17-50 -
50-150 ~
>15o
12 15 18
0
9 12 15 18
17-50 -
50-150 -
>150
OCT '72
Figure 17 Vertical distribution, volume-monthly averaged water temperature
(NOAA-BT data) during IFYGL, May-October, 1972
- UO -
-------
WATER TEMPERATURE, deg C
12 15 18
U— 1
4-17
17-50
50-150
" 1 1
i
•'
/
i
•^ I
>150J- 0
•pi I \
&
7f • NEAR SHORE
r o OPEN LAKE
NOV'72
U— q.
4-17
17-50
50-150
>15o1
- 1 JV' 1 1 1
1!
«A
i
1 150h '/3 0
0-4 pfOT 1
4-17 -J6
17-50 -*0
I
50-150 - 0
t
^ \
>150 |- 0
0-4
4-17
17-50
50-150
>150S
<-> v> u u o o
1! /t/^/?
-llw
i
i
^ i
4-17 - &i
M
17-50 - f»
1 APR
50-150 - 150[- 6
0 3 6 9 12 15 18 0 3 6 9 12 1£
4-17
17-50
50-150
1 /*>•
fir
0*
i
o
•« 1
>150 |- 0 MAY '73
U— 4
4-17
17-50
50-150
^ 1 1 1 ^39 I
- 0^^
/
o
^ i
>1505p i MN'73
Figure 18 Vertical distribution, volume-monthly averaged water temperature
(NOAA-BT data) during IFYGL, November, 1972-June, 1973
-------
These points are further illustrated in Figures IT and 18 which show
the three dimensional temporal behavior of the water temperature. Note, for
example, the differences between the near-shore - open-lake lateral tempera-
ture gradient in May-June, 1972 and for a similar period in 1973. The May,
1972 data clearly show thermocline development in the near-shore region with
the open-lake at near homogeneous vertical temperatures. Also, a persistent
lateral gradient exists at the 17-50 m layer between the near-shore regions
and those of the open lake. A vertical gradient of several degrees continues
to exist in November 1972 but by the following month, the lake is essentially
vertically well-mixed. This condition is modified during winter conditions
to reflect the classical inverse temperature gradient until April 1973 when
near-shore heating begins to develop a thermal bar difference of about 0.7°C.
Surface temperatures in June, 1973 were several degrees higher than the year
earlier and as noted, the degree of lateral temperature stratification is
somewhat less.
Pickett (1976 a, 1976 b) has also provided an extensive review of the
buoy and tower network temperature data and in general, his review provides
similar results. However, the spatial coverage of the network makes it dif-
ficult to resolve near-shore and open-lake gradients over segment monthly
means.
The CCIW set was also volume averaged using the 67 segments of the Lake
3 grid and comparisons were made between both sets. The raw CCIW data per-
mitted calculation of the volume mean standard error for each month and for
the aggregated data set. This variation is shown in Table 2 which indicates
that for the 0-17 m layer, the average standard error of the segment mean
temperature is about 1.0°C for both near-shore and open-lake segments. For
-the 50-150 m layer, the standard error is about an order less or 0.1°C. The
time variability of this standard error shows the greatest spatial fluctua-
tions during July and September. The standard error therefore indicates that
the segment means would be expected to lie between the observed mean +_ 2°C,
95J6 of the time on average. The segment means may vary then over about a
U°C range although it should be recognized that during the winter months, the
standard error is considerably less and averages less than 0.2°C.
Table 2 also compares the absolute value of the difference between vol-
ume weighted mean of the NOAA-BT data set and that of the CCIW data set. In
general, for 0-17 m layer, this mean difference is about 2°C and for the 50-
150 m layer, about 0.3°C. The general trends in the data are, of course,
similar but the CCIW data tended to be higher than the BT data especially
for the surface layers.
Figure 19 shows a statistical comparison of these two data sets of water
temperature using the verification statistics discussed as part of Eqs. (13)-
(16) and assuming the CCIW standard errors to be applicable to both sets. It
is quite surprising to note that segment to segment comparisons indicated
that only 335? of the segments on average showed no difference between the two
data sets. This appears to indicate that there is a sufficient degree of
temporal variability (within a month) and spatial variability (within a seg-
ment) to prevent a more accurate assessment of mean segment temperatures.
- U2 -
-------
TABLE 2
VARIATION OF TEMPERATURE SEGMENT MEANS AND DIFFERENCES
BETWEEN TEMPERATURE DATA SETS
Average1 Std.
Error of CCIW
Segment Means2
Absolute value
of Difference
Between NOAA-BT
Means and CCIW
Means
0-17 m
Near Shore
1.0
Temperature (°C)
0-17 m
Open Lake
1.0
50-150
0.1
1 3
2.1
1.9
0.3
1. Averages over months of May, June, July, September,
October, November, 1972.
2. From Eq. (3)
3. Volume average
UJ
O
z
UJ
oc
UJ>
LL >
100
80
" NEAR-SHORE,
-------
TABLE 3
SECCHI DEPTH & 1% LIGHT DEPTH ANALYSIS
NEAR SHORE, OPEN LAKE
(CCIW DATA)
April, 1972
May, 1972
June, 1972
July, 1972
September, 1972
October, 1972
November, 1972
Average(U-ll/72)
January, 1973
February, 1973
March, 1973
Average
Near Shore
Secchi Depth (mr1^
6.5 (1.2)
k.6 (2.0)
3.2 (0.8)
2.U (1.1)
2.2 (0.5)
3.7 (1.0)
1*.8 (0.3)
3.9
3-6 (1.3)
1».5 (1.2)
U.7 (1.1)
1% Light
Depth(m)
15.7
11.1
7-7
5.8
5-3
9-0
11.6
9*
8.7
10.9
11. U
Average
Open Lake
Secchi Depth (m)
8.2 (1.3)
9-1 (1.2)
7-0 (2.3)
3.8 (1.0)
2.2 (0.5)
5.1 (1.0)
6.2 (0.9)
5-9
6.6 (0.8)
5.6 (1.7)
5-7 (1.5)
1% Light
Depth(m)
1U.8
22.0
16.9
9.2
5-3
12.3
15-0
1U.3
16.0
13.6
13.8
'
No. in ( ) = std. dev. (volume weighted)
1% light depth = 2.U2 (Secchi Depth)
-------
Figure 19 also indicates that the comparison is significantly improved on a
near-shore open-lake average "basis. This improvement is due principally to
the averaging procedure which smooths out segment variability.
One concludes from this analysis that even a variable such as water tem-
perature, fundamental to the phytoplankton model, can only "be specified on a
segment to segment "basis within limits. Overall, these limits are about
1-2°C for segment-monthly means in the epilimnion.
Transparency and Turbidity
Analyses of the data bases for Secchi disk depth (m) extinction coeffi-
cient (nT1) and turbidity (FTU) are shown in Figure 20 and Table 3. The
near-shore - open-lake gradient in extinction coefficient during May, 1972
are clearly indicated in Figure 20Ca) and is also reflected in the turbidity
contours for the same month. The data for October, 1972 turbidity show
marked lateral variations probably from near-shore river discharges. Table 3
further indicates these near-shore - open-lake variations where during the
period April-November, 1972, the difference in Secchi depth averaged about '
2 m. This difference in water transparency undoubtedly is a result of near-
shore phytoplankton growth and discharges of organic and inorganic particu-
lates.
Chlorophyll "a"
An important measure of the eutrophication status of Lake Ontario is
assumed to be the chlorophyll "a" (corrected) concentration in the water col-
umn. Accordingly, a considerable effort is expended to analyze the behavior
of this variable; first, as observed during IFYGL and then through use of the
Lake 3 model. The EPA STORET data base which includes both EPA ,and CCIW OOPS
cruise data is used as the primary data source. The CCIW data were augmented
to include chlorophyll data collected during the so-called "Temperature"
cruises.
In general, on a segment to segment spatial level, the data are highly
variable as measured by the standard error of the mean and only under various
averaging schemes does any definitive structure emerge. Figures 21, 22 & 23
illustrate this point.
Figure 21 shows the June, 1972 EPA and CCIW data plotted for three
layers where the contours have been drawn using the monthly segment averages.
Directing attention first to the EPA contours, it is seen that there is a
rich structure in the chlorophyll surface especially in the upper two layers.
The effect of near-shore preferential growth is noticeable along the south
shore. However, if one contrasts the EPA contours with the CCIW data, a
somewhat different picture emerges, (it should be recognized however, that
the density of southern near-shore stations in the EPA data is considerably
greater than that of CCIW). The comparison provides a first indication of
the spatial "patchiness" that may occur in the chlorophyll data.
Figure 22 shows the August, 1972 and June, 1973 chlorophyll contours
based on EPA data. The August data show a general reduction of chlorophyll
levels from June with still a near-shore - open-lake gradient and maximum
-------
XTINCTION COEFFICIENT, MAY 1972 (rrri)
(a)
TURBIDITY, MAY 1972 (FTU)
ONTA*'°
44°
TORONTO
43°
LAttrlt
TURBIDITY, JUNE 1972 (FTU)
43°
TURBIDITY, OCTOBER 1972 (FTU)
LAtCrlt
-"•
Figure 20 Variation of (a) extinction coefficient (EPA-CCIW data)and
Cbl turbidity (CCIW data) for selected months, 0-h m.
-------
CHLOROPHYLLa, /jg/l
EPA DATA, JUNE 1972
CCIW DATA, JUNE 1972
A 0—4 m .io
-*- O N T A *
43°
Q /VO D>1 TA
•>-
Figure 21 Comparison of EPA and CCIW chlorophyll "a" (Pg/« contours,
June 1972
- 1*7 -
-------
CHLOROPHYLL a, pg/l
EPA DATA. AUGUST 1972 EPA DATA, JUNE 1973
ff
Tl*
ONTA«'°
79*
77*
17-50m
17-50m
NO DA TA
TT
IV
FiKure 22 Chlorophyll "a" (pg/A) contours, EPA data, August, 1972,
June, 1973.
- .-. -
-------
levels at Q-k meters. The June, 1973 data are of interest as a contrast to
the data of a year earlier shown in Fig. 21. Such a comparison reveals a
distinctly different pattern in June, 1973 from that of June, 1972. Pro-
nounced lateral and vertical gradients (for 0-17 m) are not evidenced in
1973. The chlorophyll levels of the lake do not appear therefore to "be
"repeating" from year to year vhen viewed on the segment-segment level of
resolution.
If however, the data are averaged using segment volume weights, a more
consistent picture results as shown in Fig. 23. This figure shows the aver-
age chlorophyll for June, 1972 and 1973 for CCIW and EPA and for a 0-17 meter
depth average and a near-shore, open-lake average. The means plus and minus
one standard error (Eq. U) are given. The EPA, CCIW comparison in June, 1972
is now very good. The near-shore mean difference is only 0.5 ug/£ within a
standard error of about +^1 ug/£. A similar situation prevails for the open
lake data although here the CCIW mean exceeds EPA mean "by about 0.5 ug/£.
The averaging therefore appears to indicate that the two sets are comparable
only when viewed on an aggregated level, but differ significantly when com-
pared on a segment level.
Fig. 23 also shows an open-lake difference between June, 1972 and June,
1973 means of 0.3 ug/fc, a relatively small difference. The near-shore dif-
ference of means between June, 1972 and June 1973 of almost 2 yg/£ indicates
the diversity in the two months as noted above. (The standard errors in
either case however, indicate no statistical difference between the two
months). The averaging therefore leads one to conclude that for the open-
lake, June, 1972 and 1973 are similar but that June, 1973 near-shore chloro-
phyll levels are somewhat less than those of 1972. The reason for this is
apparently due, in part, to the lack of any significant development of a
thermal bar in June, 1973 (See Fig. 17).
Figs. 21-23 illustrate the hazards of drawing detailed inferences from
contoured data of the phytoplankton chlorophyll data. Also, the two data
sets for June, 1972 while different on a segment scale, appear similar on a
scale of near-shore vs. open-lake. Other months however behave quite differ-
ently as discussed more fully below. Further synthesis of the observed
chlorophyll data is achieved then by averaging the data over different ver-
tical and horizontal spatial scales.
Figures 2U-26 show the temporal variation of the 0-U m layer average
and the 0-17 m average and the vertical structure of the chlorophyll. The
EPA data shown in Fig.2U indicates a broad spring peak of greater than 6 ug/&
for the near-shore and about U-5 ygA for the open lake. Peak values tend
to occur during June-July. The data tend to show an August decline followed
by a subsequent second peak in September. A general decline during the fall
then occurs. The difference between near-shore and open-lake is 1-3 ug/& on
average and tends to persist through most of the growing season until about
October. For 0-U m the open-lake spring levels are somewhat lower than the
September-October levels. The effect of averaging over 0-17 m can also be
seen in the decreased August values and increased September values over the
0-U m levels. This is a result
- 1*9 -
-------
LU
(D
T + 1 STAN DA RD ERROR
MEAN
-/ STANDARD ERROR
JUNE JUNE
1972 1973
NEAR SHORE
JUNE JUNE
1972 1973
OPEN LAKE
Figure 23 Comparison of EPA and CCIW volume averaged
chlorophyll data.
- 50 -
-------
I 4
DC
O
£ o
Z
O
i 8
a.
O
Q_
0-4 METER AVERAGE
NEAR SHORE
OBSERVED± 1 SE
0-17 METER AVERAGE
NEAR SHORE
OPEN LAKE
\
0
j ' F ' M ' A M'J'J'A' S'O'N'D! j' F'M'A'M'J
1972 1973
Figure 2k Volume-monthly averaged chlorophyll "a" - EPA data.
of the vertical gradients in chlorophyll over the 0-17 m depth.
Figs. 25 and 26 show the vertical structure of the phytoplankton chlor-
ophyll data of the EPA. (Standard error bars are eliminated in this figure).
The surface inhibition is evident in May-July, 1972 and again in September
and October where maximum chlorophyll levels of up to 8 yg/£ are observed in
the U-17 m layer. The near-shore - open-lake gradient also appears to per-
sist into the 17-50 m layer which may reflect the temperature gradient in
that layer (see Figs. 17 and 18). The unusually high values of chlorophyll
in February and March, 1973 are quite different than the March CCIW data. A
qualitative comparison of Figs. 25 and 26 with the temperature structure
shown in Figs. 17 and 18 indicates the significant effect of the temperature
regime and the associated horizontal and vertical dispersion.
The general pattern of a spring peak, midsummer decline and fall peak
follows that of earlier years. However, the open-lake spring peak during
IFYGL of 5 yg/& in June is lower than previous years , when average peaks gen-
erally ranged from 7 to 9 ug/& (Thomann, et al. , 1975). Further, the spring
peak tends to occur at different times apparently depending on environmental
conditions in any one year.
- 51 -
-------
CHLOROPHYLL a,
6 8 10
8
U-4
4-17
17-50
50-150
~~ 1 l*x. 1 1 I —
— o >»
i X
I /
§ >^
- 0 S • NEAR SHORE
1 o OPEN LAKE
— 0
•
>150!fo/ MAY'72
(
E 0-4
_j 4-17
>
£ 17-50
H*
2:
x 50-150
H-
3 2 4 6 8 10
1 ' °SJ% ' '
jSsr
- vT
1
1
-0
, 1
2i ^•nrn"f ' ^^ '*?
Q > 150 ho
C
0-4
4-17
17-50
50-150
0-4
4-17
17-50
50-150
= — I p—
S *
s S
- /./
/
- p
>150[-0
(
0-4
4-17
17-50
50-150
3 2 4
1 ' &'*
J^
-o
i
-0
1
>150|-0
)246810 024
1 1 R 1 *xj" |
s'^^
•
-o
^^1
>K£ SEP '72
0-4
4-17
17-50
50-150
^
- 150|£
— ^» « ^^
'/ ' '
/
JUN '72
6 8 10
I 1 1
AUG '72
6 8 10
1 1 1
OCT '72
Figure 25 Vertical distribution, volume-monthly averaged chlorophyll "a".
EPA data, May-October, 1972.
-------
0
CHLOROPHYLLS,
8 10 0
8 10
4-17
17-50
50-150
>150"
C
0-4
£ 4-17
c 1-7-50
HI
t-
z
~ 50-150
g >15o1
- 'V*1 ' '
-/
-o
I
*i NOV'72
*
) 24 6 8 1(
" 1* "j ' '
- o •
i
i
i
- o
* / MAR '7 3
-O
U-4
4-17
17-50
50-150
*
3 C
0-4
4-17
17-50
50-150
>15o1
'#"
/
^ ,' FEB'73
) 2 4 6 8 1(
: • js 'i1 '
1
1
1
_ o
1
^ 1
^ ; xl/3/? '73
— o
8 10
u— ^
4-17
17-50
50-150
1 | V*J
— AC
y
_ o •
1
1
1
- 0
1
^t 9
>150 H>
»
JUN '73
Figure 26 Vertical distribution, volume-monthly averaged chlorophyll "a1
EPA data, November 1972-June 1973.
- 53 -
-------
The winter data shown in Figs. 2U-26 indicate significantly higher val-
ues than recorded previously. The mean values of 2-h ug/£ are twice as high
as in earlier years and significantly different than CCIW data collected
during the same period (see Fig. 27). It is unfortunate that only limited
data were obtained in May, 1973- The absence of lakewide data during that
month preclude statements about spring chlorophyll conditions during 1973.
Figure 27 shows similar averages for the CCIW data. Here the absence of
r- 10
OPHYLL,jug/
•^ O> 00
DC
3 2
I
o 0
^^ \*
I10
< 8
> 4
i
Q_ _
2
n
" 0-4-METER A VERAGE
: %
NEAR SHORE f ,^X
_ /
k| J OBSERVED DATA±1 SE
ff
i 5"\
B'' \\ ^i
0 OPEN LAKE t~l*^ «^5l
B*~ ~°***^5*— "kr"
_ 0- r 7-METER A VERAGE
—
NEAR SHORE jpTj1
t
5-' J
ii ii
^&
>
OPEN LAKE \ *?££-**
\f"
1972 1973
Figure 27 Volume-monthly averaged chlorophyll "a" - CCIW data.
(OOPS and temperature cruises).
August, 1972 data is significant since one cannot tell whether a bi-modal
pattern occurred in the CCIW data. A casual inspection of Figs. 27 and 2k
indicates a tendency for higher values in the CCIW data. For example, in
July, 1972, CCIW near-shore, 0-U m mean is about 8 yg/& in contrast to an
EPA mean of about 6 yg/&. Table U and Fig. 28 provide some further compari-
sons between the two data sets.
Table U indicates that for 0-h m and from May-September, 1972, CCIW data
is generally higher than EPA data. However, for U-17 m, near-shore, CCIW
data is always less than EPA data in some instances by significant amounts of
greater than 2 ug/&. For the open-lake, CCIW data is consistently higher
-------
TABLE 1*
DIFFERENCE BETWEEN CHLOROPHYLL MEAN VALUES
OF CCIW AND EPA
DIFFERENCE
(CCIW MEAN) - (EPA MEAN)
1
vn
MONTH
May, 19T2
June
July
Sept
Oct
Nov
March, 1973
0-U
NS
1.6
.h
1.9
U.3
3.8
-1.2
.1
M
OL
• 9
l.H
1.1
1.9
2.7
-1.0
.1
U-1T
NS
1.9
.3
-l.l*
2.7
.5
-.H
-1.0
M
OL
.8
.2
2.9
l.U
-1.2
-.8
-.6
0-17
NS
1.8
.3
-.7
3.1
1.5
-.6
-.6
M
OL
.85
.5
2.5
1.5
.1
-.8
-.U
17-50
NS
2.6
.1
-.8
.9
1.1
-.U
-2.1
M
OL
.6
0
.7
-.5
.1
-.6
0
• _>
NS = near shore
OL = open lake
-------
than EPA until September and in July reached a maximum difference of means of
almost 3 yg/&. This is almost a 50% difference in the two means. The March,
1973 data indicates a substantial difference of about 100$ between the two
data sets, with EPA means of 2.-k ug/Jl and CCIW means of less than 2 pg/£.
Because CCIW data did not extend to depths greater than 50 m, the whole lake
CCIW mean during the growing season is biased by the lack of data at the
deeper depths.
A regression analysis comparing the two data sets averaged over the var-
ious regions of the lake gave the following:
CCIW Chlor. (yg/£) = 0.37 + 0.9MEPA Chlor. , pg/fc)
o
with an r =0.65 and a residual standard error of estimate of 1.7 Vg/£. The
two sets therefore correlated well with each other (both hypothesis of slope
= 1 and intercept = 0 are accepted) although the residual error is quite
large and amounts to almost 50$ of the mean.
Figure 28 shows the variation in the within-segment standard error of
the mean (volume weighted, Eq. k) for the 0-17 m, near-shore data. The
seasonal variation in this statistic is evident with average values during
the growing seasons of 1.5-2.0 Vg/&. Winter values of yg/£ are indicated.
10
8
6
4
2
0
£ 2.0
z
5 1.5
Q_
O 1.0
x 0.5
Q_
cn
nT
Q_
O
CC
O
X
o
JalMEAN
• EPA
(b) WITHIN-SEGMENT STANDARD ERROR
p
j
Q
0/°
Figure
J'F'M'A'M'J'J'A'S' o ' N ID I j ' FMVM A" M Tj
1972 1973
28 EPA and CCIW chlorophyll variations 0-17 m, near shore;
(a) Mean, (vol. averaged) (b) within-segment std. error
(vol. averaged).
- 56 -
-------
The standard error of the mean of 1.5 yg/& indicates that for average segment
values of 6 Ug/&, the "true" mean may be expected to lie in the range from 3
to 9 yg/fc with 95% confidence. With standard errors of 1.5-2.0 yg/fc during
May-September, on a statistical basis, many of the differences in Table h are
not significant. The July, October, November and March conditions do appear
significantly different however with the most significant difference in
March, 1973.
Figure 29 shows a comparison between the variation within a segment and
the variation from segment to segment for 0-h m and near-shore and open-lake
regions (Eq.. U and 5). As seen, the gradients around the near-shore "ring"
are significant and average about 2-3 ug/£ or about U0-50$ of the overall
regional mean. For the open lake, the segment-segment variation of the means
averages about 1-2 ug/& or some 30-50$ of the open-lake mean. These compari-
sons of variability indicate in a general way, that the variance within a
10 x ko km grid is somewhat less than the variance on a scale of about 100 x
1*00 km.
3 4
O _j
z£ 2
2£
o
a. 2
>
°" 0
NEAR SHORE, 0-14 METERS
BETWEEN SEGMENTS
WITHIN SEGMENTS
I
WITHIN SEGMENTS
OPEN LAKE, 0-4 METERS
BETWEEN SEGMENTS
WITHIN SEGMENTS
j FM AM j j
\
WITHIN SEGMENTS
Z
A'S'O'N'DIJ'F'M'A ' M
1972 1973
Figure 29 Comparison of within-segment and segment-segment variability
in chlorophyll, EPA data.
Figure 30 summarizes the comparisons between the two data sets and indi-
cates that on a segment-segment comparison, approximately 60% of the segments
agreed with each other. Note that, for example, for June, 1972, less than
- 57 -
-------
v/i
03
UJ
0
So 100
LL OC
II
20 80
h- a-
UJ
> Q
60
40
20
0
1
REGIONAL AVERAGE
SEGMENT-SEGMENT COMPARISON
100% = NO DIFFERENCE
REGIONAL
AVG=93%
SEG-SEG
AVG =
60.0%
S|O|N|D|J|F|M|AIM|J
j I F I M
1972
Figure 30 Summary of statistical comparison between EPA and CCIW chlorophyll data.
-------
50$ of the segments showed no statistical difference between the two data
sources. This is a quantitative expression of the obvious qualitative dif-
ference shown in Fig. 21. On a regional basis, however, the comparisons are
favorable and average 93$. As indicated previously, similar results were
obtained through regression analyses between the two data sets.
The comparisons lead one to conclude that for the chlorophyll data dur-
ing IFYGL, some significant differences do exist on the segment spatial scale.
The general behavior of the data is however similar, as for example, in the
sustained gradient between near-shore and open-lake biomass levels and peak
values in June-July and September. The differences in mean values of several
Ug/£ chlorophyll must however be recognized especially in the verification
analyses discussed later.
Zooplankton
The data base for the zooplankton compartments in Lake 3 is that of
McNaught et al. (1975) and is reviewed in some detail in that report. For
fixed stations on each cruise (June-October, 1972) zooplankton species and
density (number/m3). for various depth intervals were available. A total of
27 species were identified by McNaught et al. (1975) and were assigned, in
this work, to either herbivorous (Zooplankton #l) or a carnivorous (Zooplank-
ton #2) group. Table 5 shows this assignment. Dry weights and carbon con-
centrations for each specie were estimated. Log means and log statistics of
TABLE 5
ASSIGNMENT OF ZOOPLANKTON SPECIES TO
ZOOPLANKTON GROUPS
Species
Zooplankton
Group (l)
1. Eubosmina coregoni H
2. Bosmina longirostris H
3. Bosmina (unknown) H
k. Daphnia galeata H
5. Daphnia retrocurva H
6. Daphnia longiremis H
8. Ceriodaphnia H
9. Chydorus spaericus H
10. Holopedium gibberum H
11. Cyclopoid Copepodites C
12. Cyclops bicuspidatus C
13. Cyclops vernalis C
(l) H = herbivorous group, #1
C = carnivorous group, #2
Species
Zooplankton
Group (l)
15- Tropocyclops prasinus C
18. Calanoid copepodites H
19. Diaptomus minutus C
20. Diaptomus oregonensis C
21. Diaptomus sicilis C
22. Limnocalanus macrurus C
23. Eurytemora affinis H
2U. Polyphemus pediculus H
25. Alona H
26. Diaphanosoma C
27. Diaptomus siciloides C
-------
the numbers of organisms was then performed and converted to mg/£ for each
segment and month. Since the depth interval reported by McNaught et al.
(1975) was slightly different than the segment layering of the Lake 3 grid,
the assignments in Table 6 were used. Any sums of numbers across species
groups that were zero were taken as .0001 in computing the log means. All
numbers were corrected for net efficiency as suggested by McNaught (1975)
shown in Table 6.
TABLE 6
DEPTH INTERVALS, SEGMENTS AND EFFICIENCY
CORRECTIONS FOR ZOOPLANKTON DATA
Depth
Interval (m)
0-5
Assigned
Lake 3
Segments
1-26
Depth
Interval (m)
0-5
Net
Efficiency
Correction
1.67
5-10
10-15 27-52
15-20
20-25
25-30 53-62
30-1*0
UO-50
50-100
100-150 63-65
150-200 66-67
0-10
0-15
0-20
0-25
0-30
0-1*0
0-50
0-100
0-150
0-200
1.67
1.88
1.88
2.13
2.13
2.13
2.21
2.21
2.21
2.21
- 60 -
-------
Figs. 31-33 summarize the results of this data reduction to the Lake 3
grid. As noted by McNaught et al. (1975) peak zooplankton production
occurred in August, 1972 and the population declined rapidly thereafter.
This is shown in Fig. 31 vhich represents the open-lake volume averaged
data. The substantial vertical gradient in both zooplankton can be noted
where for the herbivorous group, a vertical gradient of about 0.1 mg C/H can
be noticed during the peak month. The total zooplankton carbon in the sur-
face layer reaches a maximum value of about 0.2 mg C/& and about 0.05 mg C/A
for the U-17 m layer. Figure 32 shows the spatial distribution of the her-
bivorous zooplankton group during August, 1972. The horizontal "patchiness"
is clear and the rapid decrease of zooplankton with depth is seen. During
this month, it is interesting to note that there is no clear near-shore -
open-lake gradients except in the Toronto region.
The variability in within-segment and segment-segment data for the
0-17 m average is shown in Fig. 33. During August, 1972, segment-segment
standard deviations ranged upwards of 0.1 yg C/H. This can also be seen
from the contour plots of Fig. 32 which indicates almost a one order of mag-
nitude range in zooplankton carbon over the 0-17 m open-lake region. This,
of course, then reflects the averaging over the 0-17 m depth interval.
O
o>
E
•z.
O
o.
O
O
N
0.10
0.05
0.2
0.1
HERBIVOROUS
ZOOPLANKTON
NO. 1
0-4 m
CARNIVOROUS ZOOPLANKTON NO. 2
AMJJASO
4-17m
TOTAL ZOOPLANKTON
0-4 m
A'M'J'J'A'S'O
1972
1972
Figure 31 Zooplankton carbon, 0-U m and U-17 m, open lake volume
averaged (Data from McNaught, et al., 1975).
- 61 -
-------
Figure 32
43°
LAiErie
79"
r
M
43°
4-17 m
ON T A
RlO
TORONTO
L*JEr»
79° 78" 77°
Herbivorous zooplankton group, mgC/£, Lake 3 averages
August 1972 (Data from McNaught et al., 1975).
- 62 -
-------
0.10
o
en 0.05
0
O 0.10
O
N
0.05
0
HERBIVOROUS
ZOOPLANKTON
NO. 1
CARNIVOROUS ZOOPLANKTON NO. 2
T MEAN ± 1 STANDARD ERROR,
i SEGMENT-SEGMENT
T MEAN ± 1 STANDARD
ERRORf WITHIN-SEGMENT
I
J ' F ' M ' A ' M ' J *J ] A ' S ' O N
1972
Figure 33 Mean and standard errors, herbivorous and carnivorous
groups, 0-17 m open-lake averages (Data from McNaught,
et al., 1975).
The data given in the Appendix and summarized in the figures therefore
indicates a peak of some 0.2 mg C/£ total zooplankton carbon for 0-h m in
August and a standard error between segments of about 0.07 mg C/5, or hO% of
the regional mean.
Phosphorus
The Lake 3 model as described in Section IV incorporates tvo forms of
phosphorus: available phosphorus for phytoplankton growth and unavailable
phosphorus; the latter form including both detrital phosphorus and intermedi-
ate dissolved forms. Total phosphorus in the water column can be computed
- 63 -
-------
TOTAL PHOSPHORUS, fig/I
EPA DATA. JUNE 1972 CCIW-OOPS DATA, JUNE 1972
17-50m
iNT A"'0
-
17-50m
,NTA«"°
7T-
Figure 3h Comparison of EPA (left) and CCIW (right) total phosphorus
(yg P/fc), June 1972.
-------
\n
o
CO
c20
15
CO
D
or
o
x
Q_
CO
O
X
Q_
_l
<
O
5
0
35
30
25
20
15
10
5
0
OBSERVED DATA+1 SE
$ OPEN LAKE
T
-L
Figure 35
J'F'M'A'M'J 'J'A'S'O'N'DIJ'F'M'A'M'J
1972 1973
Variation in volume weighted total dissolved phosphorus (yg P/£) and total
phosphorus Cyg P/£), 0-17 m, EPA data.
-------
Q §20
LLI CO
^w. ^•M.
Si 15
O o
«£10
Q ^0
05
X
Q- «
0
O)
^
CC
O
X
§520
0
X
Q.
< 10
h-
o
H
n
\j
— ot o»
a, ror^i
^-^>rf \P^ T T OBSERVED DATA±1 SE
\ J^^jp ± I NEARSHORE
ORTHO-P i^J^^ ^/ 0-P ^sfr' _ OBSERVED DATA ± 1 SE
^i~**i W * * OP£N LAKE
$ I
T Z
^ I D °
I j[| iv"^s*Sx'o
r*'» T x*
^H
- I OBSERVED DATA±1 SE
1 NEARSHORE
y
2 OBSERVED DATA±1 SE OPEN LAKE
J'F'M'A'M'J'J'A'S'O'N'D J'F'M'A'M'J
1972 1973
Figure 36 Variation in volume weighted total dissolved phosphorus, orthophosphorus and
total phosphorus (yg P/&K O-iT m, CCIW data.
-------
from these forms and the phosphorus equivalent of the phytoplankton and zoo-
plankton. The question of the degree to which various phosphorus forms in
the input can ultimately contribute to phytoplankton growth is a difficult
one and the subject of continuing research. This review of the observed
phosphorus IFYGL data is therefore directed as much to an elucidation of each
of the key phosphorus forms as it is to presenting the data for comparison
to the Lake 3 model.
As will be seen, the phosphorus data as collected by the EPA is, in
some instances, at considerable variance with that of the CCIW. Within the
EPA data set itself, difficulties were encountered, specifically the erratic
behavior of the dissolved orthophosphate phosphorus (DOP). For example,
throughout 1972, the DOP is often simply reported as .001 mg/£ and average
values never exceeded 3.5 yg/&. Boyd and Eadie (1977) in their review of
the two data sets have expressed similar concerns over the dissolved ortho-
phosphate data. Figure 3^ illustrates one of the difficulties with the phos-
phorus data in this case, the total phosphorus (TP). The EPA contour plot
for June shows considerably higher near-shore total phosphorus levels than
CCIW but lower open-lake concentrations. It should be recalled (Fig. 7) that
the spatial coverage of the OOPS cruises was somewhat limited and consider-
ably more data from the U.S. near-shore region is represented in the EPA data
set.
Figures 35 and 36 show the TP and TUP for 0-17 meters near-shore vs.
open-lake and for the two data sets. The comparison between mean values for
all layers is shown in Table 7. The EPA near-shore TP data is generally
higher than that of the CCIW but both tend to indicate a lateral gradient
throughout the sampling period. The EPA gradient between near-shore and the
open-lake ranges from 5-10 yg P/& for total phosphorus. Since a similar
sustained gradient does not exist for the TDP (except for May, 1972) the high
near-shore values are almost exclusively due to particulate P forms. The
CCIW TP data shows some seasonal variation with winter increases of some
5 yg P/&. A substantial difference occurs between EPA and CCIW in the TDP
data during October-December, 1972 where the latter data set rises to 15
in November as opposed to the EPA values of about 7-5 yg/&- Figure 37 shows
the vertical structure in the DOP, CCIW data and indicates some near-shore -
open-lake variability but principally indicates the surface layer decreases
due to phytoplankton growth. The DOP therefore shows the general uptake by
the phytoplankton during the spring and summer months. Minimum values for
this data set occur in September, 1972 and the lake returns to vertical homo-
geneity by January, 1973.
Figure 38 is a further comparison of the variability of the two data
sets. The top figure shows the within-segment standard error of the mean for
the 0-17 m open-lake region calculated from Eq. 00. The lower figure shows
the standard deviation of the segment means CEq. 5). In general, EPA data
are more variable both on the within-segment scale as well as the segment-
segment scale. The EPA standard deviations exceed CCIW by about 2 yg P/&
during 1972 and by as much as 10 yg P/£ in the spring of 1973. The lower
figure is particularly interesting since it indicates a degree of in-homo-
geneity in the open-lake region and therefore reflects the presence of open-
lake gradients of about k-6 yg P/& of total phosphorus. The comparison of
- 67 -
-------
TABLE 7
DIFFERENCE BETWEEN TOTAL PHOSPHORUS MEAN VALUES OF EPA AND CCIW DATA
CCCIW) - (EPA MEAN)
(ug
ox
oo
May, 1972
June
July
September
October
November
March, 1973
0-U
NS
1.
-7.
*
-29
-12
-2
-6
m
OL
10
5
0
0
-3
-2
7
U-17
NS
5
2
2
-12
-12
-3
-2
m
OL
10
8
2
2
-1
0
5
0-17
NS
U
0
*
-17
-12
-3
-3
m
OL
10
7
1
1
-2
0
5
17-50
NS
8
6
0
2
6
2
1
m
OL
9
9
0
0
-U
1
6
Whole
Lake
9
1
2
*
-5
2
6
Note;
indicates difference not computed due to erratic data
-------
ORTHO-PHOSPHOROUS, pg P/l (CCIW DATA)
10 15 20
10 15 20
ERVAL, m
h-
X
j—
Q_
UJ
Q
U— 4
4-17
17-50
50-150
— »l I p I I
— • o
-\ \
1
1
™" ^5
^ \
>150 p MAY '72 b
0-4
4-17
17-50
50-150
^^P rt I 1
™ 9 O
- \X
\
\
>150[- JUN'72 b
0 5 10 15 20 0 5 10 15
U— 4
4-17
17-50
50-150
~£L ' ' ' '
X
*o
1
>150^. JUL'72 I
U-4
4-17
17-50
50-150
V
- V
\
so
1
>150*P SEP '72 6
(NO DA TA FOR AUG '72)
0 5 10 15 20 0 5 10 15
—4
4-17
17-50
50-150
*
" 2
|| • NEAR SHORE
\\ O OPEN LAKE
^^
t X
>150 p OCT'72 \>
U— *f
4-17
17-50
50-150
25
- ' S1 S1
il i
*? i
\ U
NOV'72 \?
> V
>150 p
Figure 37 Vertical variation of total dissolved phosphorus
(yg P/l), 0-17 m, CCIW data.
- 69 -
-------
o
i
10
8
6
CO
i 2
O
£ 0
CO
_j
<
O
10
8
2
0
OPEN LAKE DA TA, 0-17m
O EPA
D CCIW
I M I A I M I Tl
WITHIN-SEGMENT STANDARD
ERROR OF MEAN
"^8
0
(b) STANDARD DEVIATION
OF SEGMENT MEANS
O— O
a
FMAM
J ' J
1972
A so N DJ
M ' A
1973
M J
Figure 38 Total phosphorus variability, 0-17 m, open lake, EPA & CCIW
Ca) within-segnent std. error of mean, (b) std. deviation of segment means.
-------
vhole lake averages is shown in Table 7 and Fig. 39 and. with the exception
of May, 19T2, the mean of both data sets is within +_ 6 yg P/&. For an
overall annual mean of about 20 yg P/& this represents a +_ 25% difference,
a not inconsequential difference. Table 7 displays the differences across
several averaging levels and shows a maximum difference of 29 Ug P/& in the
O'-k m near-shore layer. In most cases, the near-shore EPA data exceeds that
of CCIW and again reflects the more extensive data in that region. It is,
of course, impossible, at this stage, to distinguish real sampling differ-
ences from biases due to individual laboratory techniques. As shown by
Robertson, et al. (197*0, the CCIW and EPA labs differed in their measure-
ment of a replicate Lake Ontario sample by as much as 20 yg P/& (EPA>CCIW)
in September, 1972 and for a four month test differed by an average 3 yg P/&
(CCIW>EPA).
Given these differences, some general conclusions can however be drawn
from the observed phosphorus data. First, near-shore - open-lake total
phosphorus gradients of at least 5 yg P/& appear to persist for a substan-
tial part of the year and is principally of the particulate form. Whole
lake averages range from 17 to 2k yg P/& and near-shore values for the 0-17
m depth interval exceed 30 yg/& during September-October, 1972. Standard
errors of the mean near-shore total phosphorus data range from 2 to 9 yg
P/SL.
-^.
a.
c/T
—5
^^
tc.
i
Q.
05
O ~
I
Q.
H
O
1-
LU
1
«J
in
i
o
Figure
10
5
-5
1 n
-1U
30
25
20
15
10
5
• CCIW MEAN-EPA MEAN
1 _ - • 1
•
^H
— ™
^~
-, OL n "^ Q
"D""8^D o CK^x^D / 0
/ °^°
O
—
0 EPA DATA
— D CC/WO>4r>4
J'F'M'A'M'J'J'A'S'O'N'D J'F'M'A'M'J
1972 1973
39 Comparison of EPA and CCIW whole lake mean, total phosphorus
- 71 -
-------
go
2oc
; 0.3
)^> 0.2
I 0.1
0
0.06
ro 0.04
0.02
0
i 0.6
^_ 0.2
0
OBSERVED DATA±1 SE
\ NEAR SHORE
§ OPEN LAKE
J ' F ' M ' A'M1 J ' J
1972
A1 STOrNlDlJlFlMlAlMlJ
1973
Figure ^0 Variation in nitrogen components, EPA data, 0-17 m volxune-
monthly average.
Nitrogen
Figures kO-k2 show the behavior of several components of nitrogen during
IFYGL over different averaging regions; Fig. ho for the EPA data set and Fig.
Ill for the CCIW data set. As noted in the former figure, the uptake of
nitrate nitrogen results in minimum values during August with an increase in
nitrate to 0.2 mg/A during the full overturn. This is in general agreement
with Fig. hi although the CCIW data shown in that figure indicate substan-
tially lower nitrate levels during May, June, July and September. A compar-
ison between the two data sets is shown in Table 8. Both data sets show
maximum values of ammonia nitrogen of 0.02 mg/Jl which differs significantly
from earlier 1967 data (Thomann, et al. 1975) which showed maximum values of
greater than .05 mg N/£ of ammonia.
- 72 -
-------
The vertical distribution of the nitrate nitrogen data are shown in Fig.
k2. Some evidence of early uptake of nitrogen in the near-shore region dur-
ing May is evident. (However, the differences between the CCIW and EPA data
sets should be recalled). It is interesting to note the substantial vertical
gradient during the summer months where for example, in July, 0-U m NOj-N
open-lake levels are about 0.07 mg/£ but are at a level of 0.2 mg/Jl in the
U-17 m depth interval. The comparable CCIW data show 0-k m concentration of
.01 mg/£ ana k-17 m concentration of 0.03 mg/2.. These latter values and
similar values in September would indicate some limitation on phytoplankton
growth due to low nitrogen levels. Nitrate nitrogen concentrations of about
0.25 mg/£ in the waters from 50 m to the bottom provide a long-term nutrient
pool.
Silica
Silica is an important nutrient for diatoms and represents a means of
examining the behavior of this phytoplankton group. The first version of
Lake 1 did not include this variable, but later extensions (see Section VIII)
incorporate the kinetic uptake of silica and its effect on growth of the
phytoplankton. Figure ^3 summarizes the dissolved silica data from the CCIW
data set and indicates that this variable may influence phytoplankton growth
especially during June-July. During this time, values reach levels of 0.1
mg Si/5, and less which is at levels reported as half saturation constants.
en
< E
§ g 0.06
5 O
< a: 0.04
z. 0.02
0
O)
UJ £
I ••
-------
TABLE 8
DIFFERENCE BETWEEN NITRATE NITROGEN VALUES OF
CCIW AND EPA DATA
(CCIW-EPA) (pg/fc)
Month
May, 1972
June
July
September
October
November
March, 1973
NS
-18
-137
-78
+13
+ 92
+ 65
+93
0-U m
OL
-79
-211
-56
-92
+ 53
+33
+ 99
lt-17
NS
-13
-132
-177
+38
+ ltO
+11
103
m
OL
-132
-113
-157
-2lt
+ 25
+ 2lt
-38
0-17
NS
-lit
-133
-153
+ 31
+ 52
+ 23
+101
m
OL
-120
-136
-133
-ItO
+ 31
+ 26
-6
17
NS
-U8
-lit
-it It
+176
+lt8
+ 8
+ ltlt
-50 m
OL
-157
-133
-236
-Itl
-118
+6
+89
Whole
Lake
-128
-101
-135
-62
-66
+31
+13
-------
NITRATE NITROGEN, mg/l
0 0.1 0.2 0.3 0.4 0.5
0 0.1 0.2 0.3 0.4 0.5
VJTERVAL, m
DEPTH II
0-4
4-17
17-50
50-150
>-,
»^
0-4
4-17
17-50
50-150
*-
-**
(
0-4
4-17
17-50
50-150
i i»x io% i
- n
• NEAR SHORE I
- o OPEN LAKE <^
" MAY '72 XV
— O
) 0.1 0.2 0.3 0.4 0.
• "Np
" JUL '72 %xv
D 0.1 0.2 0.3 0.4 0.
*" CL \
^k
• so
/
"f SEP '72 %£
O-4
4-17
17-50
50-150
--*.
•**.
>150 I
5 (
0 4
4-17
17-50
50-150
«-».
*-*.
>150
5 (
0-4
4-17
17-50
50-150
- A
j
?
" JUN '72 1
^ O
) 0.1 0.2 0.3 0.4 0.
~°kP ' ' '
: V->
o
> AUG '72 \
r ®
3 0.1 0.2 0.3 0.4 0.
" ' ^\^^
l\
\
\
9
,crt"f OCT'72 I
>150 h 0
Figure \2. Vertical distribution, nitrate nitrogen, EPA data
May-October, 1972.
- T5 -
-------
The differences between the near shore and open lake regions are interesting:
in the spring, near-shore silica values are about 0.2 mg/Jl less than the open
lake, whereas in the fall, near-shore values are about 0.1 mg/fc greater than
the open lake. This dynamic difference is probably a reflection of near-
shore diatom flowering in the spring and overspreading the entire lake by
July. The fall difference appears to reflect a sustained diatom gradient
between the open lake and near-shore. The data shown in Fig. 1*3 are used in
the extended kinetic framework of the Lake 3 as discussed in the latter part
of the next section.
CO
<
o
CO
Q
LU
0
CO
CO
0.5
0.4
0.3
0.2
0.1
0.5
0.4
0.3
0.2
0.1
0
0-4 METERS
OBSERVED DATA±1 SE
J NEAR SHORE
J OPEN LAKE T
0-17 METERS
J'F'M'A'M'J' J'A'S'O'N'DIJ'F'MTA'M1j
1972 1973
Figure 1*3 Volume-monthly averaged dissolved silica, CCIW data.
DISCUSSION
An overall measure of the comparison between the two data sets is given
by Figure hk which displays the total number of segment-variables by month
for which there was no difference between the two sets. The Figure follows
Eq.. (18) for equal weights of the variables: chlorophyll, total phosphorus,
total dissolved phosphorus, NHs and NOa. As shown, on a segment-segment
basis, 53/6 of the segment-variables showed no statistical difference, i.e.
on the average about half of the places at which the five variables could be
compared displayed no difference between CCIW and EPA. On a regional basis,
the comparisons indicate that on the average about 8h% of the regional aver-
ages showed no statistical differences.
- 76-
-------
LU
O
2
HI
ce
LU
100
Q LU
80
60
I- Z
Z LU
LU LU
S §
O P-
LU LU
CO OQ
40
LU
O
DC
LU
Q.
20
E
REGIONAL AVERAGE VARIABLE CHLOROPHYLL
SEGMENT-SEGMENT COMPARISON TP TOP NH3 NO3
700% = NO DIFFERENCE FOR ALL SEGMENTS-VARIABLES
REGIONAL A VERAGE = 84%
SEG-SEG
AVG = 53%
J * F I M' A I M I J
1972
M " A I M J
1973
Figure
Overall statistical comparison of EPA and CCIW data sets.
One concludes from this compilation of data that the "basic seasonal
trends in the principal Lake Ontario variables are as previously described
(Thomann, et al. 1975), i.e. a bi-modal variation in phytoplankton chloro-
phyll, a simple seasonal peak in zooplankton and decreases to near-limiting
levels of phosphorus and nitrogen. However, these trends become apparent
only after aggregations and averaging over regions of the lake. Any one seg-
ment of the lake appears considerably more erratic. Furthermore, the degree
of agreement between the EPA and CCIW data sets is somewhat marginal at best
as illustrated by the fact that on a segment-segment comparison level for
chlorophyll, only 60% of the segments agreed statistically. During one month
(October, 1972), only kO% of the segments showed no statistical difference in
their mean values between the two data sets. On the other hand, in regional
comparisons (e.g. near-shore - open-lake), agreement improved to 95% between
the two data bases for chlorophyll.
The results also tend to indicate a relatively high degree of variabil-
ity in all data both within a segment and from segment to segment within a
region. Values of standard errors of the mean for most of the key variables
averaged some 25-50$ of the mean. This kind of statistical variability is
undoubtedly a reflection of the cruise schedules and station density both of
which result in "gaps" in the data over both time and space. In sampling
water bodies of the size of Lake Ontario, little can be done to substantially
- 77 -
-------
reduce these gaps. What can be done however is to recognize the kind of var-
iability that this data analysis indicates and to interpret single cruise
data, cruise transect data, single station data and similar types of analyses
vith caution.
From a verification analysis point of view, the analyses of the observed
data as summarized in this section introduces some real problems. Since the
two data bases agree only within about 50% on a segment scale, it indicates
that at that scale, the data may not be of sufficient density in time and
space to provide a good basis for comparison to calculated output. On a
regional scale however, the data sets generally do agree and aggregated Lake
3 output can then be statistically compared to the observed regionally aver-
aged data. The analyses of the observed data also indicate that the more
prudent course of action is not to merge the two data sets but to compare
model output to each of the'data sets separately. The next section then
explores the verification of the Lake 3 model given the observed data analy-
sis with associated variability.
- 78 -
-------
SECTION VII
VERIFICATION ANALYSIS OF LAKE 3
INTRODUCTION
The purpose of this Section is to present in some detail, the results of
comparisons of the observed IFYGL data to the Lake 3 model. Within this gen-
eral purpose, there are several other objectives:
1. To provide a quantitative verification of Lake 3 using as a starting
basis, the kinetics of the earlier whole lake model.
2. To show the sensitivity and behavior of Lake 3 as compared to the
observed data variability during IFYGL.
3. To highlight the need for quantitative verification of three-dimen-
sional eutrophication models.
The degree of credibility of the analysis framework will obviously
depend on how well the model represents' the real world. The preceding sec-
tion has reviewed the IFYGL data base and has shown that the variability of
the data on a segment-segment level is quite high and that only when suitable
spatial averages are computed does the observed data show any consistent
structure. Further, it was shown in the last section that the two primary
data sources, the EPA and CCIW data often do not agree and in a number of
instances, disagree markedly. The analysis of the credibility of the Lake 3
model must therefore recognize the inherent difficulty in even specifying
observed conditions. The tests given in Section IV incorporates the varia-
bility of the observed data in testing the validity of the model.
The basic philosophy underlying the use of the term "verification" for
the analyses presented here proceeds from the earlier work of Thomann, et al.
(1975). That work was a "second level" calibration of a whole lake model to
a set of data representing an average of four years of observations. (The
basic model had previously been applied in other water bodies, but not large
lakes). Using that work as a starting point, the verification analysis is
conducted using an independent data set (the IFYGL data) and expanding into
three dimensions. The procedure then is to utilize an earlier calibration in
a different setting and determine how well the Lake 3 model "holds up." Fur-
ther explorations beyond this point are then carried out to explore different
kinetic variations to further improve, if possible, the verification status
of the Lake 3 model.
Simons (1976) has reported on a similar analysis of the basic kinetics
in a 3-dimensional model using CCIW data. That analysis, however, was re-
stricted to a single set of kinetics. This work as indicated earlier ex-
plores model credibility at various spatial averaging schemes and quantita-
tively analyzes the resulting model comparisons to observed data. Additional
- 79 -
-------
analyses have also been carried out for the Rochester embayment.
Average temperature, incoming solar radiation, nutrient inputs and river
inflows were used in the earlier work. A kinetic structure was postulated
(based on applications in estuarine systems) and Lake 1 model output was com-
pared to the observed (1967-70) data. The same kinetic structure was initi-
ally employed in this work under both IFYGL conditions and average conditions
using the Lake 3 model segmentation. A number of runs were computed and the
results of the verification analysis have therefore been compiled into three
phases representing the approximate chronological order of the investigation.
Phase I: Preliminary phase - a) Sensitivity analysis of Lake 3 to gen-
eral Lake circulation, b) comparisons of Lake 3 to the IFYGL data using both
average (non IFYGL) input and gradual inclusion of some IFYGL conditions.
Phase II: Complete incorporation of IFYGL conditions, specifically
solar radiation, water temperature, nutrient inputs and vertical and hori-
zontal dispersion - Lake 1 kinetics and parameter values are used throughout.
Phase III: IFYGL conditions, but with variations in the parameter val-
ues and changes in the kinetic structure.
Table 9 is a summary of the principal Lake 3 runs and does not include
all of the various runs that were made under a variety of problem situations.
The difference between Phase I and Phase II runs provide indications of
the degree to which average environmental conditions impact the model results.
The sensitivity of the Lake 3 model to the temperature and dispersion struc-
tures and other inputs peculiar to IFYGL can therefore be explored given the
Phase I results.
Within Phase I, a series of runs were made, each of which incorporated
more of the actual IFYGL environmental conditions. For example, Run #3
incorporated IFYGL initial conditions as measured in May, 1972 by the EPA
together with IFYGL solar radiation and temperature data. Phase II, given
by Run #U represents inclusion of as much of the IFYGL conditions as could
be incorporated with the exception of an IFYGL advective transport regime.
Therefore, for the given kinetic structure of Lake 1, Run #U represents the
"best" test of the verification of the Lake 3 model, since it includes IFYGL
environmental conditions as input without any change in the Lake 1 model
kinetics and parameter values.
The runs of Phase III are intended to show some logical extensions in
the development of the Lake 3 model and incorporate various changes in the
kinetic structure and parameter values.
The following sub-sections review the results of the verification ana-
lysis of the Lake 3 model.
PRELIMINARY PHASE I
Sensitivity of Lake 3 Model - Lake Circulation
The Phase I effort is aimed at further understanding of the behavior of
the model under several different conditions on key model components. One
of the components that is often considered critical to a large lake model is
- 80 -
-------
TABLE 9. SUMMARY OF PRINCIPAL LAKE 3 MODEL RUNS
00
H
Run
Phase No.
Kinetic Initial Solar Radiation
Structure Conditions Input
Transport
Dispersion
Structure
Water Temp. Nutrient
Structure Inputs
System
Parameters
I. Pre- 1
liminary
2
3
II. U
IFYGL
Cond.
III. 5
Revised
Kinetics
and Par-
ameters 6
Lake 1 Lake 1, Aver. Cond.
Jan. 1
TP = 21
Jan. 1 "
Revised
TP=l6 ug/Jl
11 May '72 I.C. IFYGL Cond.
n ti it
ii n ti
-
Lake 1-A " "
Aver . Cond .
(Prelim Lk.
3)
M
n
IFYGL Dis-
persion -
Average
Transport
n
n
Aver. Cond. 196? Cond.
(Prelim Lk. (Tempo-
3) rally
Constant
n n
IFYGL Cond. "
" IFYGL
Input s
ti n
n M
Lake 1 -
Constant
in Time &
Space
n
n
ii
Sinking
velocity =
0.5 m/day
As per
Lake 1-A
Listing
-------
the specification of the general lake circulation, i.e. the net advective
transport. As noted previously, for the Lake 3 model the general circulation
is externally inputted from observed data and one might ask, "How sensitive
are the water quality computations to changes in the Lake circulation"? Some
effort was therefore devoted at this stage to testing the behavior of the
model, specifically the phytoplankton biomass (although all variables were
considered) to changes in the flow regime. Several runs were made using
average temperature and solar radiation conditions and Lake 1 kinetics to
provide some insight into this question. In the initial run, the "best esti-
mate" of the flow regime was inputted. Fig. 1*5 shows the interfacial veloci-
ties used in this circulation regime and represents a synthesis of observed
currents and other information prior to IFYGL. The sensitivity of the phyto-
plankton calculations was estimated by running the model under: a) a rever-
sal of velocity direction by l80°, b) all velocity magnitudes set to zero and
c) all velocity magnitudes set to 0.1 of velocities shown in Fig. 1*5. The
vertical and horizontal dispersion regimes remained the same during each run.
The results of the sensitivity of phytoplankton in the 0-1* m layer and
for the spring bloom are shown in Fig. 1*6. These results are expressed as
the difference between a sensitivity run and the base condition or "correct"
flow run. Figure U6 (a) .shows that the effect of flow reversal for the Lake
as a whole is relatively small (the effect at the exit end to the St. Lawrence
is a boundary effect and not entirely representative of the actual sensitiv-
ity). At most, the difference is about 0-2 ug/& during the spring bloom.
The effect of the zero flow case (Fig. 1*6 (b)) is however considerably more
significant especially for Segment #5, the entrance of the Niagara River.
The substantial buildup in that segment is due to a lack of advection out of
the segment. Only dispersion is acting to decrease concentrations at the
location. Elsewhere throughout the lake however, the effect is less although
still significant. It should be recognized however that this zero flow case
represents a most severe sensitivity test since it assumes that the Lake is
motionless throughout the entire year.
Fig. 1*6 (c) indicates that at velocities equal to 1/10 of the base case
velocities, the chlorophyll values do not differ significantly between the
two cases. Note that even a small amount of advection considerably modifies
the results in Segment #5, the Niagara River segment. The results of these
sensitivity runs to lake circulation indicate that for the lake as a whole,
on scales of about 10 x kO km, errors in horizontal circulation magnitude and
direction do not appear to significantly influence chlorophyll levels and
indicate that system kinetics and time variable vertical dispersion effects
are of generally greater importance.
Initial Comparison Runs
As shown in Table 9» the first two runs of the Preliminary Phase I,
simply used average (non-IFYGL) conditions for the Lake, and provide a basis
for determining the degree to which the Lake 3 model depends on the actual
IFYGL conditions. Run #1 uses January initial conditions as given in the
earlier work. Run #2 uses January initial conditions where the total phos-
phorus was reduced 5 Vg/&- Run #3 is intended to indicate the change in
results if observed May, 1972 conditions (as observed by EPA) together with
- 82 -
-------
WINTER CIRCULATION
SUMMER CIRCULATION
;
TOP LA Yin VELOCITIES Icm/ucl
0-4 meteri
$ DOWNWfLLINC
* UfnfLLINC
280 ell ft
SECOND LAYER V£LOCIT
-------
LfttErit
'•
79°
Figure 1*6 Sensitivity of phytoplankton chlorophyll to changes
in lake circulation.
-------
the 1972 solar radiation and 1972-73 temperature are included. Run #3 presum-
ably then represents a better run in the sense that the initial conditions
are chosen from the observed data. But, these runs do not yet represent the
"full" inclusion of IFYGL conditions.
Not all segments had equal amounts of data and in some cases, significant
data gaps existed for various months. Figure 1*7 shows a typical comparison
for phytoplankton for Segment #16, Run #1. EPA data are used in the Figure.
The gaps in the record can be seen as well as the region of no statistically
significant difference between model and observed mean (Eq. (lM) and the
monthly differences between model mean and the observed mean. "Insufficient
data" indicates that the variance of the sample mean could not be computed due
to only one sample in the segment. The range of the no difference region is
significant and as shown is as much as +_ h ug chlorophyll/A. The application
of Eqs. (15) to (17) would therefore lead to V scores of zero for months such
as July to a maximum overestimation of 3.7 yg/& in June.
Computations such as represented in Fig. 1*7 are carried out for each seg-
ment so that the comparison can also be examined spatially. A typical result
for Run #1 and June, 1972 conditions is shown in Fig. h8 which indicates the
region of the Lake where the run verified observed data and those regions
where the model overestimated the segment mean.
Figures k$ show comparisons between the three runs of the Preliminary
Phase I and the EPA phytoplankton data using spatial averaging on to eight
sub-regions of the Lake 3 model. As shown, for Run #1, the phytoplankton
chlorophyll is overestimated in both the 0-h m and 0-17 layers. Run #2 with
reduced phosphorus initial conditions appears to do considerably better. Run
#3» does poorly again in the 0-U m layer but does well in the 0-17 m layer.
However, one of the purposes of this report is to quantitatively describe the
behavior of Lake 3 compared to observed data. Therefore, using the simple
statistical comparisons given in Section V, a more quantitative comparison
can be made. Figure 50 shows the % of segments that were verified by the
phytoplankton output from the model under two averaging schemes. Thus, for
Run #1, June, 1972, ^6% of the 63 segments at which a comparison could be
made between observed and computed monthly phytoplankton were verified by the
model using an approximate 5% chance of a Type I error. For the phytoplankton
chlorophyll in Fig. 50, the segment-segment comparison indicates an average
level in 1972 of about 50-60/J verification with a noticeable downward trend
toward the fall of 1972. Verification is poor in winter of 1973 and reflects
the high values of chlorophyll reported by the EPA for that period in contrast
to the CCIW data. It can also be noted that the inclusion of observed May,
1972 initial conditions did not substantively improve the verification level.
When the verification is compared on the basis of the eight averaging
regions of the Lake, Fig. UO (b), the verification improves considerably in
1972 but not in the winter of 1973. On this spatial averaging level, the in-
clusion of May, 1972 conditions did improve the verification and for 1972,
Run #3 using the eight regions averaged Qk% verification, i.e. about only one
region out of the eight did not verify in 1972. The winter 1973 picture is
quite poor and reflects model inability to capture a winter "bloom".
- 85 -
-------
NO SIGNIFICANT DIFFERENCE
BETWEEN MEANS
\
M
- MODEL MEAN - OBSERVED MEAN
195% CONFIDENCE LIMITS!
N 0| J F
TIME OF YEAR
Figure 1+7 Typical comparison, chlorophyll, segment #l6, Run #1.
44°
43°
JUNE 1972 CONDITIONS
Contours: PhytoplsnMon Chlorophyll Verification Score (jig/I)
RlO
UttErfe
•-1
79°
77°
Figure 1*8 Distribution of phytoplankton verification score,
June 1972, Run #1.
- 86 -
-------
10
8
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P RUN No. 1
0-4-METER AVERAGE
0-17-METER AVERAGE
T I T T i
T
J FMAMJ JASOND'J FMAMJ
1972 1973
„ RUN No. 2
0-4-METER
AVERAGE
0-17-METER AVERAGE
i/j
'
I I I I
J FMAMJ J ASOND'J FMAMJ
1972 1973
. RUN No. 3
0-4-METER
AVERAGE
0-17-METER AVERAGE
I I I
Uj
*"
OQ
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Figure
J FMAMJ J ASOND'J FMAMJ
1972 1973
Chlorophyll comparison, Preliminary Phase I Runs
'
1-3.
- 87 -
-------
X
Q_
O
or
O
100
80
60
x
o
P 40
20
0
Q_
O
X
Q_
oc
O
UL
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LU
E100
LU
H 80
LU
2 60
V)
£ 40
LU
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I 20
"PERFECT" VERIFICATION
(a)
67-SEGMENT COMPARISON
PRELIMINARY PHASE 1
j' F'M'A'M'J'J'A'S'O'N'DJJ'F'M' A' M' j
1972 1973
"PERFECT" VERIFICATION
RUN NO. 3~"\ /\ /'
: HVy
RUNNo.2 ' \ ^
\
_ 1
- 8-REGION COMPARISON \ /
_ PRELIMINA R Y PHASE 1
I'C'M'A'M' i' i ' A ' o ' n ' M ' n ' i
ft ~
ft
I P I M I A I M I 1
1972
1973
Figure 50 a) Segment-segment phytoplankton verification,
Preliminary Phase I, Runs 1-3.
' b) Regional phytoplankton verification, Pre-
liminary Phase I, Runs 1-3.
-------
Fig. 51 shows that when six variables are included in the verification
scheme and a segment-segment comparison is drawn, that again hO-6o% verifica-
tion is achieved in 1972 and less than that in 1973. The downward trend is
not as obvious in contrast to the phytoplankton verification.
These runs in the Prelininary Phase indicate that the segment-segment
verification average about 50$ while the averaging over eight regions in-
creases the verification level by an additional 30-Uc$. These runs are com-
pared to the EPA data. This is the first indication that the Lake 3 model
verification is poorer as the spatial definition is refined and performs well
only at a larger spatial averaging than the 10 x Ud km grid. The question at
this point then is, "Can improvement be obtained by including more of the
actual IFYGL conditions?" The Phase II run was therefore constructed to pro-
vide an in-depth verification analysis of the Lake 3 model using the Lake 1
kinetics and IFYGL conditions. The results of that analysis follow.
PHASE II - "FULL" IFYGL VERIFICATION ANALYSIS
The basic input data representing IFYGL conditions of solar radiation,
riverflow, nutrient inputs and water temperature have been discussed pre-
viously in Section VI. As noted there, straight line approximations to each
of these variables were used and input was prepared for each model segment,
where appropriate.
100
80
to
ai
m
E
z i
LU UJ
O 40
I-
z
LU
O
01 20
LU
Q.
"PERFECT' VERIFICA TION
RUN NO. 1
1 1 1 1 1
MJJASOND|JFMAMJ
1972 TIME OF YEAR 1973
Figure 51 Segment-variable verification, Preliminary Phase I
Runs 1-3.
- 89 -
-------
Determination of IFYGL Dispersion
The next step in the analysis was to obtain an estimate of the horizontal
and vertical dispersion regime during IFYGL. Accordingly, water temperature
as observed during IFYGL was used as a tracer variable to determine an esti-
mate of the appropriate dispersion regime. As noted previously the sensiti-
vity of the model solutions to the advective transport regime is relatively
small on the scale of the Lake 3 model segmentation.
Kullenberg, et al. (1973, 197*0 have reviewed the horizontal and verti-
cal dispersion in Lake Ontario during IFYGL and have correlated dye disper-
sion tests to several external driving forces such as wind, speed, vertical
shear in the horizontal current and the vertical density structure. During
stratification, a range of 1-10 cm2/sec in the vertical dispersion was esti-
mated - about a factor of four lower than for the open ocean. Based on the
formulation of Kullenberg et al. and recognizing that the mean monthly wind
speed and current structure are relatively constant (within the spatial and
temporal averaging in this analysis), the principal effect on the vertical
dispersion arises from the vertical temperature structure. Figures 15
through 18 of Section VI have detailed the observed temperature structure
during IFYGL. Using Kullenberg et al. (1973, 1971*) as a starting point, a
horizontal and vertical'dispersion regime was postulated and a verification
analysis using the IFYGL data was performed.
The associated comparisons of the calculated mean values to the observed
data is shown in Figure 52. As shown, the verification on the near-shore,
open-lake spatial scale is excellent. It should also be recalled (See
Section VI, Water Temperature) that the statistical comparison between the
two temperature data sets of CCIW and NOAA indicated a poor comparison on a
segment to segment level, but an excellent comparison on the near-shore open-
lake spatial scale. The dispersion regime that resulted in the output of
Fig. 52 was then used in subsequent runs together with actual temperature
data (not computed) for various segments throughout the lake as described in
Section VI.
Results
Figure 53 shows the near-shore, open-lake comparison of the computed
chlorophyll levels to observed data from Run A, (Table 9). Calculated val-
ues were generally higher than observed for the 0-U m depth average were
closer to the observed data for a 0-17 m average. The spring peak is too
high although comparisons appear more favorable, when compared with the CCIW
data. The 1973 winter conditions are not verified due to the use of kinetics
that reflect growth of plankton at more elevated temperatures. The spring
bloom in 1973 is also overestimated by Run #k. A rigorous statistical com-
parison indicates that this run is not substantially different from the first
three preliminary runs indicating that on the whole the inclusion of more
representative IFYGL conditions did not materially affect the results. For
example, the segment-segment average score was 5555 (.for 1972 data only) and
the eight segment average was about Jk%t both scores of which are similar to
the earlier runs. Results for the various nutrients were also similar to the
earlier three runs. A series of regression analyses were also conducted on
Run #1* between calculated and observed values following Equation 19 and some
- 90 -
-------
4-17
17-50
50-150
>1503
//
- 7*
: T
'- 1
MAY 1972
i i i i
12
18
0 4 0—4
4-17
17-50
50-150
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r ,' JUN 1972
>150lf «,,,,,
4-17
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>150
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AUG 1972
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DEPTH INTERVAL,
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>150:
(
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SEP
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1972
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ft*
: "?' OCT 1972
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17-50
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• • NOV 1972
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DEC 1972
i i i i i
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I i^JAN
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t
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1 i i
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8 •
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~ °\ MAY 1973
~ 1° i i i i i
12 " 18 06
WATER TEMPERATURE, °C
12 18
0-4
4-17
17-50
50-150
>150:
: X"
- >r
r ° JUN 1973
o
1 1 1 1 1 1
12
18
NEAR-SHORE
NOAA
OPEN LAKE
NOAA
NEAR-SHORE
CCIW
^H OPEN LAKE
CC/W
Figure 52 Comparison of Lake 3 model to observed temperature data.
-------
VO
ro
10
8
6
^ 4
Z -J
3>
5? Q.
go
^3
QLr
a
EPA-IFGL DATA
0-4-METER AVERAGE NEAR-SHORE £ OBSERVED ±1 SE
-— CALCULATED
0-17-METER AVERAGE OPEN LAKE
OBSERVED ±1 SE
- CALCULATED
j 'F'M'A'M'J'J'A'S'O'N'DIJ'F'M'A'M'J
1972
1973
Figure 53 Chlorophyll comparison. Run #U, "Full" IFYGL conditions
-------
results for chlorophyll are shown in Fig. 5U. The regression for the June
data is over all. epilimnion segments and shows that the model did not predict
the spatial variations. This is true even though only a"bout 6 weeks of pro-
totype time had elapsed since the assignment of initial conditions directly
from observed data. Approximately only 20% of the spatial variability in the
data were accounted for by the model. There is an obvious greater range and
variability in the observed data from segment to segment than is forecast by
the model. The residual standard error is about 2 yg/£. The calculated
slope of 0.5 indicates the model consistently overestimated the data. Median
relative error for the chlorophyll was about Uo$ for 1972. Figure 5^b shows
the regression analysis for the eight averaging regions, for 1972 data only
and for both 1972 and 1973. For the first case, almost 80$ of the variabil-
ity was captured by the model but the slope of about 0.6 indicates that the
model overestimated the data from month to month. Median relative error was
about 30$. The inclusion of the 1973 data significantly worsened the situa-
tion due to the winter data of 2-6 yg/& which was not generated by the model.
These results therefore indicate that at best, with the available data,
Lake 1 kinetics and IFYGL conditions that 50-60$ of segment-segment chloro-
phyll could be verified and 75-85$ of regional averages could be verified.
Further improvement in the verification statistics was therefore sought by
changes first in the model parameters and then in the basic model kinetic
structure.
PHASE III - REVISED KINETICS AND PARAMETERS
The preceding analysis indicated that in general calculated values were
higher than observed especially in the upper layers and are generally lower
than observed winter values. Two options are open: first, adjustment of sys-
tem parameters of given Lake 1 kinetic structure and second, revision and
update of the kinetic interactions and parameter values based on data and
understanding developed since the original conception of the Lake 1 kinetics.
For the first option, several runs were prepared with varying parameter val-
ues such as variable extinction coefficient, nutrient decomposition rates and
settling rates.
Each run was again approximately similar to earlier runs with the excep-
tion of an overall settling rate of 0.5 m/day. This run, designated Run #5
in Table 9, resulted in a segment-segment chlorophyll score of 67$ and a
eight region chlorophyll score of 91$, for the 1972 data only which is an
important improvement over Run #U. For all data, including the winter of
1973, the respective scores drop to 50$ and 65$ respectively. Figure 55 shows
the comparison of Run #5 to the averaged data and qualitatively indicates the
improvement resulting from the increased settling rate. Figure 56 shows the
computed contours for June and August 1972, Run #5. These results can be com-
pared to the observed data contours of Figs. 21 and 22. The point of course
of the entire verification analysis is to make the qualitative comparisons of
contour plots more quantitative. The median segment-segment relative error
for chlorophyll in 1972 was 27$ and the regional error was 22$, both of which
represent a significant reduction from earlier runs.
- 93 -
-------
c- 12
* 10
_J
>
1 R
Q. O
o
cc
O
i 6
o
Q
LU 4
QC
LU
m 2
O
0
JUNE 1972
o No. 1-26 (0-4 m)
a No. 27-52 (4-17m)
_L
0 246 8 10 12
CALCULATED CHLOROPHYLLa,
Figure 5U
_ 12
CO
* 10
I
Q.
O
oc
O
O
o
LU
CD
O
8
6
4
2
1972 0.76 0.58 0.9 1.0
1972+1973 0.39 0.43 1.9 1.6
EIGHT REGIONS:
a 1972
• 1973
0 2 4 6 8 10 12
CALCULATED CHLOROPHYLLa, M9/I
Chlorophyll regression analysis: calculated vs. observed EPA data,
Run #k a) June 1972 b) eight regions
-------
QL
O
DC
O
X
O
2
O
Q_
O
I-
x
0.
10
s
6
4
2
0
10
8
6
4
2
0
0- TO 4-METER
AVERAGE
EPA-/FGL DATA
X OBSERVED ±1SE
NEAR-SHORE
CALCULATED
0- TO 17-METER
AVERAGE
T OBSERVED ±1SE
OPEN-LAKE I.
CALCULATED
J F M A M J J ASONDIJFMAM\J
1972 1973
Figure 55 Chlorophyll comparison, Run #5, sinking velocity - 0.5 m/day.
The most significant improvement vas in the regression analysis as shown
in Fig. 57. These results can be contrasted to those in Fig. 5^- For Run
#5, and the eight regions, intercept and slope were not significantly differ-
ent from zero and unity, respectively, indicating essentially a "perfect"
verification. The residual standard error is about 0.8 ug/&. Therefore, for
this run at the regional level, a "no statistical difference" between observed
and computed values corresponded to a median relative error of 22% and a resi-
dual standard error of 0.8 ug chlorophyll/ 5-.
A single change therefore of the settling velocity significantly improved
the verification status. Segment-segment chlorophyll performance was gener-
ally improved as was the regional average performance. The five fold increase
in sinking velocity to 0.5 m/day, is to some extent a result of the finer ver-
tical grid used in the Lake 3 model as opposed to the Lake 1 model. Although
a sinking velocity of 0.5 m/day is justified in the literature, a run using
an updated kinetic system was incorporated to provide a basis for comparison
between the simple kinetic structure of Lake 1 with a more complicated kine-
tic structure discussed below.
-------
Lake 1A Kinetics
The Lake 1A kinetics have "been developed as part of eutrophication models
constructed for the Lake Huron and Saginaw Bay system and for Lake Erie
(Di Toro and Matystik, 1978; Di Toro and Connolly, 1978). A systems diagram
for the updated kinetics is shown in Fig. 58. The additional state variables
include a division of total phytoplankton chlorophyll into diatom and "others"
chlorophyll compartments and unavailable and available silica.
The principal kinetic changes are as follows:
1) Use of threshold nutrient limitation in contrast to product expres-
sions. Therefore the growth rate is limited by
PI v J.FWI v a. r c i'
'sp ' -~1TFJ KsN UJ sSi L ij
where K , K , K , are the half saturation constants for phosphorus [PO,-P]
Sp Sii StDl *4-
nitrogen [N] and silica [S.], respectively.
2) Mineralization of unavailable to available forms through a Michaelis-
Menton recycle expression with chlorophyll. Therefore, the general expression
for conversion of unavailable forms is
R
[Unavail] •+ [Avail]
f or R = K 6T~2° [chl-a] [Unavail]
[chl-a] + K
sp
where K = mineralization rate & 20°C, K = half-saturationconstant for
chlorophyll [chl-a] limitation. sp
3) Several adjustments to parameters of the basic kinetics. Table 10
lists the parameter values of principal interest. In addition, some vertical
mixing was introduced across the boundary between segments 1 and 2, using the
values of vertical dispersion estimated from the Lake 3 temperature calibra-
tion. The updated kinetics were then used with the Lake 1 model geometry
(see Fig. 3) to calibrate the IFYGL data set for open lake epilimnion and
hypolimnion. The results of this calibration using the parameter values of
Table 10 are shown in Figs. 59 and 60. The principal features of the inter-
active system are properly obtained by the model. The relative distribution
of diatoms and "others" (non-diatoms) is however only marginally calculated
by the model. All chemical variable results are quite good. The verifica-
tion statistics for this calibration of the two segment model are reviewed in
Section VIII.
For Lake 3» the updated kinetics were then inputted using the IFYGL con-
ditions and the results subjected to verification statistical analysis. The
objective of this final run was to determine whether the segment-segment ver-
ification status could be significantly improved by kinetics that presumably
represent a more complete understanding of the phytoplankton-nutrient system.
- 96 -
-------
JUNE. 1972
0-4 METERS
AUGUST. 1972
0-4 METERS
44°
79° 77°
4-17 METERS
4-17 METERS
M
e
L*(E
17-50 METERS
17-50 METERS
'
'•'
Figure 56 Computed chlorophyll contours, Hun #5-
- 9T -
-------
CD
=1
X
Q.
O
o:
O
_j
x
o
Q
LU
CO
00
o
Q_
O
oc
O
_i
I
O
Q
UJ
>
cc
UJ
CO
CD
O
14
12
10
8
4
2
0
1972
o 1-26 (0-4 m)
m 27-52 (4-17m)
A 53-67 (>17m)
• r2 = 0.54
b = 0.78
0 2 4 6 8 10 12 14
CALCULATED CHLOROPHYLL a,
en
14
12
10
8
6
4
2
0
Eight regions, 1972
-2 =
a =
0.84
0.92
0.25
= 0.84
I
I
I
Figure 57
0 24 6 8 10 12 14
CALCULATED CHLOROPHYLLa,
Wl/l
Chlorophyll regression analysis: calculated vs. observed
EPA data, Run #5, a) June 1972 b) eight regions
- 98 -
-------
PHOSPHORUS SPECIES
SILICA SPECIES
*
UNAVAILABLE
PHOSPHORUS
*
AVAILABLE
PHOSPHORUS
Sedimentation
Sedimentation
Sedimentation
NITROGEN SPECIES
Figure 58 Systems diagram, updated Lake 1A kinetics.
- 99 -
-------
TABLE 10. PRINCIPAL PARAMETER VALUES - LAKE 1A KINETICS
Description
Phytoplankton Growth
Saturated Growth Rate g 20°C
Temperature Coef .
Saturating Light Intensity
Half Saturation Const-Phos.
Half Saturation Const-Nit.
Half Saturation Const-Silica
Carbon to chlorophyll ratio
Phosphorus to chlorophyll ratio
Nitrogen to chlorophyll ratio
Silica to chlorophyll ratio
Settling rate for chlorophyll
Phytoplankton Respiration
Endogeneous Respir. Rate @ 20°C
Temperature coef.
Avail, fraction of respired phyto.
Herbivorous Zooplankton
Grazing Rate
Half Sat. Const, for grazing limit
Value
Diatoms Others
2.1
1.09
225-0
2.0
25.0
100.0
100.0
1.0
15.0
1+0.0
.OU
1.08
0.5
•
Half Sat. Const, for assimilation limit.
Mftylnnpti assim. eff .
Respiration rate @ 20°C
Respiration Temperature Coef.
Carnivorous Zooplankton
Grazing Rate
Respiration Rate 6 20°C
Nutrients
Unavail. Nit & Phos Mineral. Rate
Temp Coef for Nit & Phos Rates
Unavail. Silica Mineral. Rate 6 20
@ 20°C
°C
Half Sat. Const for chlor. Limitation
Settling rate of particulate forms
1.6
1.08
350
2.0
25.0
—
100.0
1.0
15.0
—
.07
1.08
0.5
.07
10
5
0.6
0.03
1.0U5
.195
0.007
.03
1.08
.0175
10
Units
day"
None
langleys/day
yg P/S,
yg N/&
yg si/*,
yg C/yg chl-a
yg P/yg chl-a
yg N/yg chl-a
yg Si/yg chl-a
0.2 m/day
day"
None
None
fc/mg C/day-°C
yg chl-a/A
yg chl-a/ Si
None,
day
None
fc/mg C/day-°C
day"1
day"
None,
day
yg chla/fc
0.2 m/day
- 100 -
-------
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V T T T
X | m . >L
1 1 c ' ft/I ' A 1 KM 1 i 1 i 1 A 1 c 1 /"\ 1 M 1 rv
Figure 59 Lake 1A kinetic calibration, 1972, all 0-17m, Segment 1.
-------
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^
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DISSOLVED
- ORTHOPHOSPHATE TOTAL PHOSPHORUS
PHOSPHORUS \
. .-- .. <>E ,T T i L r- -11 n
fflM!s^-__^ e a
1 ^st_^rri
j 'F'M'A'M' j ' J'A'S'O'N'D
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DISSOLVED TOTAL PHOSPHORUS T
ORTHOPHOSPHATE 1
PHOSPHORUS
T ,,_LT T i 9
- iu J J ? 5 4
T ,..|. 1^ ,
1 i i i j $ i
j 'F'M'A'M' j ' J'A'S'O'N'D
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Figure 60 Lake 1A kinetic calibration, 1972 (continued)
-------
Figure 6l shows the comparison of the regional average output to regional
average data as before. As indicated, the computed "behavior of the phyto-
plankton is somewhat different than earlier runs due principally to the inter-
actions between the diatom and non-diatom groups. The run does not capture
the midsummer decline as well as earlier runs but does reproduce the fall
conditions. In contrast to all previous runs, Run #6 does somewhat better in
1973. However, one generally would conclude that the inclusion of the more
complicated kinetics did not markedly improve the qualitative comparison.
Verification scores and regression analyses were similar to Run #U. Median
relative error showed some improvement on the regional basis and averaged
Overall, the results of all of these runs and verification analyses indi-
cate that the model as presently conceived performs markedly better at larger
space scales. Best performance was with the original Lake 1 kinetics but
with a settling velocity of 0.5 m/day. The updated and more complicated
kinetic structure resulted in only a marginal improvement in model verifica-
tion status. Median relative error in chlorophyll ranged from 22-32% on a
regional basis and 30-^0% on a segment-segment basis. A more detailed dis-
cussion of these results, together with the analysis of the Rochester Embay-
ment is given in Section VIII.
- 103 -
-------
OS
=1
I
Q.
O
CC
O
X
O
z
O
Q_
O
I
Q.
12
10
8
6
4
2
0
0- TO 4-METER
A VERAGE
NEAR-SHORE
OPEN-LAKE
OBSERVED ± 1 SE
CALCULATED
OBSERVED ± 1 SE
CALCULATED
M" J
J "A rS ' O ' N ' D I J ' F ' M ' A
1972
T AT
1973
12
10
8
6
4
2
0
0-TO 17-METER
'AVERAGE
NEAR-SHORE <£ OBSERVED ± 1 SE
- CALCULATED
OPEN-LAKE OBSER VED ± 1 SE
--- CALCULATED
M ' j ' J^A'S'O'N'DIJ'F'M'A'M'J
1972 1973
Figure 6l Chlorophyll comparisons, Run #6,
updated kinetics.
-------
SECTION VIII
THE ROCHESTER EMBAYMENT ANALYSIS
PURPOSE AND SCOPE
The Rochester embayment is located along the south shore of Lake Ontario
and serves as a water supply for the city of Rochester, New York (Fig. 62).
The Genesee River with an average flow of 3,000 ft /sec., discharges into the
embayment. Phytoplankton biomass in the embayment, as indicated by chloro-
phyll a concentration, reaches a spring peak on the order of 25 ug/1 as com-
pared to a mean peak of 6-10 yg/1 in the open lake water of Lake Ontario. A
marked phytoplankton chlorophyll a concentration gradient is also observed in
this embayment. The special characteristics of geomorphology and phyto-
plankton concentration in the embayment is one of the motivations for this
research work.
This work is parallel to the analysis of the Lake 3 phytoplankton model
of Lake Ontario. An identical three-dimensional, time variable model is used
to carry out this investigation of'Rochester embayment. This model is class-
ified as a "small grid" model with spatial scale on the order of 1 x 3 km
defining the Rochester embayment. The Lake 3 model utilizes larger grids
with a scale on the order of 10 x Uo km defining Lake Ontario. Temporally,
the model is constructed to provide analysis of the seasonal changes of
plankton and nutrients.
The purposes of this analysis are: to estimate model credibility on a
smaller scale than the Lakes scale and to test the sensitivity of phyto-
plankton in the embayment to different nutrient inputs, hydrodynamic trans-
port regimes and open lake boundary conditions. The effort is therefore
directed to the problem of constructing near-shore eutrophication models
where a sizeable fraction of the model boundary is given by open-lake
conditions.
The embayment area is defined by segment 17 and the lower segments of
the larger Lake 3 model. Figs. 2 and 62 show the location of segment 17 in
Lake Ontario. The embayment is about 50 km long, 10 km wide and the depth
reaches a maximum of 90 meters. The vertical segmentation as shown in Fig.
63 in the embayment is identical to that of the Lake 3 model. The embayment
is divided into a grid of 72 segments in four layers; 0-U m, U-17 m, 17-50 m
and below 50 m. The thermocline is set at 17 meters during the vertical
stratification period. The upper two layers, 0-h meters and U-17 meters are
considered to represent the epilimnion. The distribution of available data
together with the desire to be consistent with the Lake 3 grid influenced the
selection of these depths. The boundaries between horizontal sections follow
the 17 meter and 50 meter contour lines. Segment 21 is the segment which
- 105 -
-------
i
i
ROCHESTER EMBAYMENT
Model Boundaries
10 0 10 20 30 40 50
79°
Figure 62 Location of Rochester embayment.
-------
ROCHESTER EMBAYMENT SEGMENTATION
17-50 METERS
Embayment Model Location
: — '
BELOW 50 METERS
Milne 1 1
0 5
VtA U . - I
0 10
10
Figure 63 Rochester enfbayment segmentation.
- 107 -
-------
receives the discharge of the Genesee River. Since marked phytoplankton
concentration gradients are observed in the nearshore region, smaller seg-
ments were used in that region.
DATA BASE AND MODEL INPUT
The data sources for this investigation were obtained from the following:
1. Environmental Protection Agency's Water Quality Storage and
Retrieval System, STORET
2. Report to the International Joint Commission on the Pollu-
tion of Lake Ontario and the International Section of the
St. Lawrence River (1969)
3. Limnological Data Reports, Lake Ontario, 1966-1969, Canada
Centre for Inland Waters, CCIW
U. U.S. IFYGL Coastal Chain Program. (1973).
The U.S. IFYGL stations in the embayment are the major data which were
retrieved from STORET. Figure 6U shows the spatial distribution of these
stations. Spatial density of sampling stations is such that some segments
contain no sampling stations which can result in difficulties during valida-
tion of the small-grid model.
77°50'
77°40'
: .
77°30'
77°20'
77° 10'
43° 2O"
43° 15'
COASTAL CHAIN-
CURRENT BUOYS
^igure 6U U.S. EPA water quality and coastal chain stations in
Rochester embayment - IFYGL
Segment statistics for each variable such as monthly mean, standard
deviation, etc. are compiled by each segment for model comparison using
latitude/longitude polygon method. Details are given in Section V. The
temporal distribution of the STORET IFYGL data is from May, 1972 to June,
1973.
For transport and dispersion calibration, an annual time variable heat
flux function is inputted to the top layer of the embayment and is advected
- 108 -
-------
and dispersed throughout the entire body. The output is then compared to the
measured data to determine the validity of assumed transport regime. The
heat flux forcing function was taken as similar to that of the Lake 3 model
(See Fig. 13).
Water temperature data, as with the Lake 3 model, were employed in two
ways: as a tracer variable, for the calibration of the dispersion regime and
as input into the phytoplankton model.
A marked temperature gradient is observed in the embayment. The Genesee
River's discharge has an obvious effect on themal distribution in near-shore
embayment. For example, the temperature in near-shore segments (e.g. seg-
ment 21, h2 and further downstream near-shore segments) are lower than that
of more open-water sections during November because the Genesee River has
cooled while the open lake temperature is still elevated at the beginning of
winter. .The temperature data were obtained from STORET, CCIW and U.S. IFYGL
coastal chain program. Groups of segments were defined as regions and each
region had its own time variable temperature function inputted. Table 11
shows the grouping of segments into regions and Fig. 65 shows a typical tem-
perature function for region 1 composed of the three outer surface segments.
25
20
o
o
15
QC
£ 10
LU
0
J I F I M I A I M I J J A S O I N D
Figure 65 Temperature input functions for Region 1,
segments 1, 2 & 3.
- 109 -
-------
Table 11. Rochester Embayment segment groupings for temperature
analysis
DEPTH
SEGMENTS OF ROCHESTER EMBAYMENT
TEMPERATURE
REGION
Q-h meter
1, 2, 3
U, 5, 6, 7
8, 9, 10, 11, 12
13, 1U, 15
16, IT, 18
19, 20
21
22, 23
24, 25, 26, 27
1
2
3
U
5
6
7
8
9
1*-17 meter
28, 29, 30
31, 32, 33, 3U
35, 36, 37, 38, 39
Uo, Ui, 1*2
U3, Ul*
1*5, U6, U7
U8
U9, 50
51, 52, 53, 5U
10
11
12
13
1U
15
16
17
18
17-50 meter
55, 56, 57
58, 59, 60, 61
62, 63, 61*, 65, 66
67, 68, 69
19
20
21
22
Below 50 meter 70, 71, 72
23
Initial conditions were chosen from STORET data. Due to the lack of
data in the beginning of 1972 during IFYGL, the first day for this modeling
work is taken as May 1, 1972. This allows the choice of initial concentra-
tion for the model from measured data. In contrast to the Lake 3 work, no
sensitivity runs were made with variable initial conditions. Since the
hydraulic detention time of the embayment is about 10 days, the initial con-
ditions generally do not dominate the solution.
Time variable boundary concentration inputs are taken from Lake 3 seg-
ment average values which were compiled from the STORET IFYGL data base.
The major tributary into the embayment is the Genesee River, the inputs
of which were taken from STORET data. Assignment of straight line input
functions to each of the model variables is based on these data.
- 110 -
-------
gs^(
A_/
J ' F ' M ' A
o
BLE PHOSPH
3
<
<
1973
1.6
_ 1.2
o>
E 08
04
.^^^,.
- ./x ,-S
(tm^~
0
M'J'J'A'S'O'N'D'J'F'M'A
1972 1973
1.0
0.8
_ 0.6
lo.4
0.2
mm.
~- A A
/ \ / \
k / V- ^-/ V .
>i ' -»0— •«»»,, ^" " W^— ™««
0
.M'J'J'A'S'O'N'DIJ'FIMIA
1972 1973
.Z(J
E ' .
0.05
sA^A
• — ^ (
M'J'J'A'S'O'N'D'J'F'M'A
1972 1973
Figure 66 Assumed Genesee river input concentration to the phytoplankton model.
-------
The Rochester area is the second largest source of municipal waste dis-
charging directly to Lake Ontario. Waste discharges from Rochester enter
Lake Ontario either directly or via the Genesee River. The waste inputs of
the metropolitan Rochester area, including all municipal, industrial inputs
and the Genesee River is about 9% of phosphorus, 5.*+$ of nitrogen and l.U$
of chloride, load from all sources discharged to Lake Ontario (IJC, 1969).
The near-shore muncipal discharges are based on the IJC Report (1969) and the
work of Casey and Salbach (197*0.
Figure 66 show assumed Genesee time variable concentrations to the
phytoplankton model. Table 12 is the waste loading data from the muncipal
discharges which are assumed constant in time.
TABLE 12. Nutrient input from municipal discharges
to Rochester embayment
System
11
Input Segment
22 23
Loads in Ibs/day
Total
Nitrogen
Non-living
Organic N
Ammonia N
Nitrate N
Total N
Phosphorus
Non-living
Organic P
Inorganic P
Total P
1,085
3,285
270
1*,6UO
565
1,260
1,825
1,199
3,630
299
5,128
619
1,381
2,000
22
66
6
9U
17
38
55
2,306
6,981
575
9,862
1,201
2,679
3,880
CALIBRATION
Transport and Dispersion
The advective and dispersive regime for the model geometry must be
established so that it can be used as input into the phytoplankton model.
The same approach as used in Lake 3 was applied in the Rochester analysis.
It is assumed that the advective component is known (e.g. from coastal chain
data and other modeling work). The vertical and horizontal dispersion is
estimated from water temperature data with an external heat flux in the top
layer. In addition, for the Rochester embayment, some chloride gradients
do exist, so chloride concentration was used as a further trace for the ad-
vective-dispersive regime.
- 112 -
-------
U.S. IFYGL Coastal Chain Program (1973) provided near-shore current vel-
ocity measurements at the western end of the embayment (see Fig. 6U). Velo-
city is measured by the along-shore component (u) and component normal to
shore (v). Temporal distribution of data is from May to October, 1972.
Due to the relatively small magnitude of the current velocity normal to
the shore, it was neglected as an advective component and assumed to be in-
corporated in the lateral dispersion. The general direction of flow is
towards the east. The flow was then estimated by taking the average along-
shore current velocity for each section between U, 17 and 50 meter contour
lines. The discharge of the Genesee River (3,000 cfs) is added to segment
21 and flows were balanced. Figure 67 shows the estimated transport regime
of the top layer which was then used as input into the phytoplankton model.
43°25'
77°50'
7 7° 30'
77° 20'
77° 10'
43° 20-
43° 15'-
6^ -"
ROCHESTER) (iRONDEQUOlT BAY
5 MILE
Figure 67 Assumed upper layer (0-U m) transport regime in Rochester embayment,
flow in cfs.
The dispersion regime is taken as similar to that of the Lake 3 model.
The vertical exchange between the segments of second layer and third layer
is varied throughout the year to simulate thermocline formation during the
vertical stratification period from mid-May to mid-September. The vertical
exchange within the epilimnion and hypolimnion is held constant (20 cm /sec)
throughout the year. The horizontal exchange is used to simulate the thermal
bar effect from April to June between the embayment boundary and the open
lake water body. That is, during the thermal bar period, the embayment does
not exchange with the open lake although advective inputs continue to enter
from the western end of the embayment.
Figure 68 shows a typical comparison of model output to chloride and
temperature data for segment 21. Similar results were obtained at other
segments. The calibration is considered sufficient for this first phase of
investigation and is especially interesting since it was obtained with the
first run of the model. The transport regime as indicated above together
- 113 -
-------
with the assumed dispersion regime from Lake 3 proved sufficient. No de-
tailed statistical comparisons (as in Lake 3) were conducted at this stage
of the analysis.
CD
E
O
Z
Ld
O
z
O
O
LU
o
QC
O
I
O
o
LU
tr
QC
Ul
Q.
5
Ul
40
30
20
10
I
MEAN ± 1 STANDARD DEVIATION
M ' j ' J 'A'S'O'N'D'J'F'M'A'M
1972 1973
40
30
10
0
M'J TJ 'A1 S'O'N'D'j1 F'M'A'M
1972 1973
Figure 68 Topical calibration of advective and dispersive regime,
chloride and temperature, segment 21.
- llU -
-------
30
ROCH/EMBAY SEGMENT 21
BASE RUN
en
*
id
o
M ' J ' J I A ' S ' 0 ' N ' D ' J • F ' M ' A
1972 1973
1 0.4
0.1
0
60
120
1972
180 240
300
1973
360
0.6
0.4
M ' J ' J ' A ' S • 0 ' N ' D
1972
J ' F ' M ' A
1973
Figure 69 Calibration results, Segment 21.
- 115 -
-------
ROCH/EMBAY SEGMENT 21
BASE RUN
o. 10
CD
o
^0.05
i
M ' J I J • A ' S
1972
'O'N'D'J'
F ' M ' A '
1973
£- 0.4
|t
I^S 0.2
•
t i
1 1 1 1 1
60
120
1972
180 240
300 360
1973
o
zc.
Q_
0.01
I
p
Mlj'J'A'S'O'N'D'J1 F'N
1972 1973
Figure JO Calibration results, Segment 21.
- 116 -
-------
ROCH/EMBAY SEGMENT 60
BASE RUN
en
5.20
Q_
§ 10
0
M ' J ' J ' A ' S ' 0 '
1972
N ' D ' J ' F ' M ' A
1973
2 0.4
<_j
I E 0.2
fe 0.1
o
M
0
i i i i
III!
0 60
120
1972
180
240 300
1973
360
0.8
'0.6
0.2
0
M' J'J'A'S'O'N'D'J'F'M'A'
1972 1973
Figure 71 Calibration resxilts, Segment 60.
- 117 -
-------
ROCH/EMBAY SEGMENT 60
BASE RUN
g 0.10
8
oc
g 0.05
o
M • J ' J
A ' S ' 0 ' N ' D
1972
J ' F ' M
1973
£-0.4
O
•y? ««^^
£
-------
Phytoplankton and Nutrients
The kinetic structure, number of variables and parameters used in the
calibration of the Rochester embayment phytoplankton model are the same as
those used in. Lake 1 (Thomann, et al., 1975). Boundary and initial condi-
tions were specified as described previously.
Figures 69 to 72 show the calibration of model output to data for seg-
ment 21 and segment 60; two segments representative of results obtained
throughout the model. Two points may be noted: a) the general trends are
duplicated although for segment 21, the peak value of 15-25 yg/1 chlorophyll
was not reached by the model, b) there is a considerable degree of noise in
the data reflecting the variable inputs from the Genesee and the lakewide
input transport.
It should be indicated that the results shown in Figs. 69 to 72 repre-
sent a single run of the phytoplankton model using a constant transport
regime, variable dispersion, variable Genesee River input, constant munici-
pal input and variable boundary conditions. Lake 1 kinetics are used through-
out with constant parameters.
The spring peak of phytoplankton chlorophyll a for segment 21 is calcu-
lated at about 15 yg/1. A maximum peak of about 18 yg/1 is calculated for
segment 27, which is located at the eastern boundary of the embayment. The
reasons for this are discussed below in the section on sensitivity analysis.
Analysis of model output indicates that both nitrogen and phosphorus
nutrient limitation occurs although the limitation is not severe at any time
in the year. This can also be seen from inspection of the nitrogen and
available phosphorus data in Figs. 69 to 72. Levels are generally high rela-
tive to half-saturation constants. Nitrogen has its most pronounced effect
throughout the entire embayment in the July and August period. Analyses of
comparisons between observed and computed values and regional averaging have
also been carried out analogously to the preceding section on Lake 3. The
embayment was divided into near-shore, middle and far-shore regions where
near-shore is approximately a 1 km distance perpendicular to the shoreline.
The middle region is from about 1 km to 5 km and the far shore region is 5 km
to 10 km from shore. Figure 73 shows the comparison for these regions and
for 0-17 m. The substantial near-shore peak of 33 yg chlorophyll/K, was not
reproduced by the model. This may result from the constant transport used
throughout the computation. The model calculates a spatial gradient of about
5 yg/& (for 1-10 km2) in contrast to the approximate 2 ug/£ gradient in the
Lake 3 scale (10-100 km2).
Statistical comparison indicated 53$ of segment chlorophyll verified
and about kk% of regional average chlorophyll verified. Average residual
standard error of estimates for June-October 1972 on a segment-segment basis
averaged about 2.1+ yg chlorophyll/A. These results indicate that the model
only marginally captures the high frequency small spatial scale phenomena.
As noted, this may be due in part to the simplified hydrodynamic transport
used at this stage; further work should explore the possibility that a more
realistic transport regime would improve the verification status of the
Rochester embayment model.
- 119 -
-------
Q)
40
30
20
10
0
_ J-
NEA R-SHORE: J DA TA
MODEL
FAR-SHORE: J DATA
MODEL
M'J'J'A'S'O'N'DIJ'F'M'A
IE
Q>
O
oc
O
o
1972
1973
30
20
10
0
MIDDLE REGION: MEASURED
CALCULATED
M'J'J'A'S'O'N'D
1972
1973
Figure 73 Comparison betveen data and model, regional value weighted averages
0-17 m a) near-shore, far-shore b) middle region.
- 120 -
-------
SENSITIVITY ANALYSIS
Nutrient Loads
In order to understand the behavior of the Rochester embayment dynamics,
a series of sensitivity analyses have been carried out using different
nutrient loadings and transport regimes. The purpose is simply to explore
the nutrient load and transport effect on the phytoplankton concentrations
in the embayment.
Analysis of different levels of the Genesee River input and boundary
concentration which is transported to the model boundary from near shore
and open lake water permits estimates of the relative contribution of each
phytoplankton growth in the embayment. This would be the first inidcation
of the expected effect of nutrient reduction programs of sources directly
discharging to the embayment. Some typical results which are compared to
the base run (the calibration run discussed previously) are shown in Figs.
7U to 77 and are summarized in Fig. 78. These sensitivity runs, one with
zero Genesee River load and the other with boundary concentrations increased
by 1.5 (but keeping the same Genesee River load) as in base run are par-
ticularly informative. First, it can be seen that the removal of the
Genesee load has no effect on phytoplankton in segment 21 and only a slight
effect on segment 27. Nutrient concentrations are however reduced every-
where. This provides an interesting example of a response in nutrients due
to a load reduction but without an accompanying reduction in biomass. This
is principally due to the transport into and through the model boundaries
which influence the growth kinetics of the phytoplankton.
The concentrations of each variable however do respond directly where•
boundary concentrations were increased by 50$. The phytoplankton chloro-
phyll a increases about 5 ug/& at spring peak in both segments 21 and 27-
This indicates the relative importance and dominance of the transport
through the model. In order to demonstrate this importance, Table 13 has
been prepared. The comparison was prepared by calculating the advective-
dispersive flux across the model boundaries and comparing it to the direct-
discharge inputs. As indicated, the relative mass contribution during
June-August of the Genesee and municipal inputs is small. The dominant in-
put is from the long-shore transport. Relatively little flux occurs across
the lateral boundaries of the model with the open lake. Therefore, the
near-shore loading rate from the western boundary plays an'important role
on the concentration of nutrients in the embayment and because this trans-
port also advects biomass into the embayment, the western boundary provides
a significant effect on the phytoplankton. Recognizing the 10 day detention
time in the embayment, observed phytoplankton in the embayment during aver-
age long shore eastward drift is dominated by inputs from the rest of the
lake rather than from within Rochester embayment. Since the Niagara River
influences the boundary concentration transported into the embayment (from
the Lake 3 work) these results indicate the indirect influence of the
Niagara input on the quality of the Rochester embayment.
Transport
Two sensitivity runs were also prepared by changing the magnitude of
the transport regime through the embayment. The first run is with a
- 121 -
-------
flow at 0.5 that of the base run and the second with zero transport, although
lateral and vertical dispersion is maintained. The concentration of each
variable increases somewhat at the 50JJ decrease in flow reflecting the shift
to the more dominant influence of the Genesee River. However, the calculated
concentration is significantly increased if the flow is assumed to be zero,
especially in segment 21 and 28 which are the segments which receive the
Genesee River. The only transport is by dispersion and therefore the residence
time is greatly increased giving the phytoplankton more time to grow; thus, in
segment 21 at zero net transport, calculated chlorophyll levels reached 26 yg/£
under the base run. It is also interesting to note that the spring peak and
fall peak of phytoplankton happen earlier than those of the base run. The fall
bloom is also higher than the spring peak in segments 21 and U8. Under zero
flow conditions, phytoplankton growth is more limited by phosphorus than
nitrogen.
DISCUSSIOM
A small, grid, three dimensional, time variable phytoplankton model is used
to describe the behavior of phytoplankton concentration in the Rochester embay-
ment. This model is identical to and embedded in one region of the Lake 3
model of Lake Ontario. The parameters used herein are the same as those used
in the Lake 1 model. Transport calibration is done using temperature and
chloride as conservative tracers. The agreement between calculated and
measured data achieved indicates that the Rochester Embayment transport regime
is consistent with observation. EPA IFYGL data were used for phytoplankton
calibration between May 1, 1972 and April 30, 1973. The results from the
first calibration run are favorable but do not completely explain local pulses
of chlorophyll. The results indicate the importance of the boundary concen-
trations on the internal dynamics of the Rochester embayment.
Sensitivity runs indicate that the peak phytoplankton concentration
reached in the embayment is strongly influenced by the advective component of
the hydrodynamic regime. The boundary concentration of nutrients and plankton
at the western boundary which is transported into the embayment strongly
influences the phytoplankton concentration in the embayment. The Genesee River
load and Rochester municipal discharge has a minor effect on phytoplankton
concentration in area of discharge. The effect of these loads is magnified
further downstream (in the eastern segments of the embayment).
- 122 -
-------
ROCH/EMBAY SEGMENT 21
*
10
.
.BASE RUN
•WITHOUT GENESEE RIVER LOADING
• BOUNDARY CONCENTRATION
INCREASED BY 15
M'J'J'A'S'O'N'D'J
1972
m
F M
1973
A S 0 N 0 J F M A
1972
1973
Figure
of zero Genesee input and increased boundary
constituents - Segment 21.
- 123 -
-------
ROCH/EMBAY SEGMENT 21
If 0.10
| 0.05
.
'
0
•BASE RUN
WITHOUT GENESEE RIVER LOADING
•BOUNDARY CONCENTRATION
INCREASED BY 1.5
M J J A ' S O1 N D J F I M A1
1972 1973
- 0.4
0.2
.•I-" I I I 1 I I
61
120
1972
180
240
300
1973
360
Ol M i j i J i A'S'O'N'D' J1 F ' M i A
1972 1973
Figure 75 Effect of zero Genesee input and increased boundary
constituents - Segment 21.
- 12U -
-------
30
ROCH/EMBAY SEGMENT 27
en
*
Q
§ 10
> BASE RUN
• WITHOUT GENESEE RIVER LOADING
• BOUNDARY CONCENTRATION
INCREASED BY 1.5
• FORCING FUNCTION ADDED
MJ JASONDJFM'A
1972 1973
LlJ
22
0.6
0.2
J A S'O'N'D'J F M ' A
1972 1973
Figure 76 Effect of zero Genesee input, increased boundary concentration
and municipal inputs, Segment 21.
- 125 -
-------
ROCH/EMBAY SEGMENT 27
E0.10
s
I
0.05
0
• BASE RUN
•WITHOUT GENESEE RIVER LOADING
- —BOUNDARY CONCENTRATION
INCREASED BY 1.5
— •FORCING FUNCTION ADDED
M J'J'A'S'O'N'D'J'F'M'A'
1972 1973
,0.03
0.02
on
o
Q-
0.01
J A]S O'N D J F "
1972 1973
A
Figure 77 Effect of zero Genesee input, increased boundary
concentration and municipal inputs, Segment 27-
- 126 -
-------
^ 30
3.
EL r1 20
O C
0
SEGMENT 21
BASE
RUN
B.C.X.
1.5
ZERO
GENESEE
RIVER
MUNICIPAL
LOADING
ZERO
FLOW
<
LU
Q_
CHLOROPHYLL a, jug/I
-* M GJ
O O 0 O
SEGMENT 27
—
BASE B.C.X. ZERO ZERO
RUN 1.5 GENESEE FLOW
Figure 78
RIVER
MUNICIPAL
LOADING
Comparison of calculated peak phytoplarxkton embayment concentrations
under different conditions on nutrient inputs and transport.
- 127 -
-------
TABLE 13. Comparison of nutrient flux from the Genesee River,
municipal discharges and lake boundary
Ave. June, July and August Nutrient Flux
Total P Total N
#/day % #/day %
Genesee River
Loading Rate 5,^69 17,51*!
Municipal Discharge
from Rochester Area
Advective-Dispersive
Flux-Transport along
shore
0-k meter
U-17 meter
17-50 meter
Below 50 meter
Dispersive Flux
from Main Lake
0-U meter
1*-17 meter
17-50 meter
Below 50 meter
3,880
9,3U9 8*
25,701
53,379
26,1*91
6,338
111,909 92%
32
-15
178
113
308 0%
9,862
27.U03 1.65?
297,325
807,620
506, Uoi
120,710
1,732,056 99.0?
227
-2,917
-3.75U
-U,032
-10,Vf6 -0.6%
- 128 -
-------
SECTION IX
DISCUSSION AND SUMMARY OF RESULTS
In this Section, the questions initially posed at the beginning of the
Report are examined in the light of the preceding results. How good is this
model? At what scale is the model better or worse? What is the level of
credibility of the modeling framework? Do more complicated kinetic struc-
tures improve the performance of the model?
Several general points seem to emerge. The underlying data base col-
lected during IFYGL exhibits significant spatial and temporal variation at
scales of 10 X ^0 km. Only as the data are aggregated into larger regions
(e.g. nearshore, open-lake) and longer time scales of months does any regu-
larity or deterministic structure emerge from the data set. Also, the two
data bases available (CCIW and EPA) only agree within certain limits. For
example, for chlorophyll on the segment-segment scale (10 X Uo km), only 60%
of the segments exhibited no statistical difference and the average relative
error was 30%. On a regional basis however, 93% of the segments passed a
"t" test.
The modeling framework, in general, duplicates the major features of
chlorophyll and nutrient behavior in the Lake, i.e. near shore-open lake dif-
ferences and spatial occurrence of the spring bloom (e.g. see Fig. 56). The
original Lake 1 kinetics (calibrated on earlier years) when placed into the
IFYGL conditions and a three-dimensional framework generally overestimated
the chlorophyll levels with median relative errors ranging from 30-^0$ for
different scales of Lake Ontario and 50% for the "fine scale" Rochester
embayment. It is at the segment-segment level where major differences can
occur, i.e. relative errors of greater than 100% and entire months where very
few segments were verified by the model under any of the three statistical
tests. The purpose of the additional analyses of the Lake 3 kinetic struc-
ture was to determine whether it was possible to improve the level of veri-
fication in a significant way at the different spatial scales.
CHLOROPHYLL
Figure 79 is a complete summary of the chlorophyll verification statis-
tics plotted relative to the scale of the model. The most notable feature is
the general decrease in the performance of the modeling framework at smaller
spatial scales, i.e. the model performance improves as the level of aggrega-
tion increases to the eight regions and the whole lake (see Fig. 3). At
these latter scales, for Run #U which represent no change in the original
kinetic structure, the percent of segment that verified was about 75$, resi-
dual errors were about 0.5 ug chlorophyll/5, and median relative error was
about 30%. Run #5 which represented a change of sinking velocity from the
original kinetics to 0.5 m/day indicates a general level of improvement in
- 129 -
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model performance. Run #6, which includes an extensive updated kinetic
structure did not result in a significant improvement at the 200-10,000 km2
level but did at the whole lake level only because that kinetic set was first
"tuned" to the data using the two segment model.
It is concluded from the results of Figure 79 that as one progresses to
smaller spatial scales, especially to the scale of Rochester embayment,
hydrodynamic transport and local phenomena become more and more significant.
Often however data are not available to specifically quantify these phenomena.
At the larger spatial scales, system kinetics dominates and the scale of the
hydrodynamic structure is decreased. Increased kinetic complexity did not
appear to materially affect model status over the simpler kinetic structure.
A calibration effort to a given year at the whole lake scale can reduce
median relative errors in chlorophyll to about 10% (Run #6) but the 3-dimen-
sional version of the same model at horizontal scales of 200-1000 km2 results
in an increase in the error by more than three to about 35/5.
With the available data base therefore for a large lake such as Lake
Ontario, the chlorophyll verification status of the model ranges from an
average 10% error at the whole lake scale to 50/6 at the local embayment scale.
ALL VARIABLES
The status of the model can also be described in terms of the relative
error across all variables, i.e. the pooling of the relative error of all
segments, months and variables. The resulting distribution of error repre-
sents a single measure of all of the variables simultaneously and provides a
simple and direct answer to the question of model credibility across all
state variables locations and months.
Since Run #5 generally performed more adequately than the other runs,
Fig. 80 has been selected to represent the behavior of the relative error
for all variables. This figure shows the variation of the median relative
error month by month during 1972 for the three spatial scales. At the Lake 3
scale, the average relative error (median) for the year is hh% with a peak of
60% in August. Generally, the peak error increased to over 300/6 for some
segments in November. For the eight regions, the 1972 all-variable error
decreased slightly to 35? which closely parallels the change in relative
error for chlorophyll (Fig. 79(b)). Finally for the whole lake scale, the
average relative error is Yl% indicating again the improved performance at
the larger space scales.
- 130 -
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RUN NO. 5
D RUN NO. 6
HORIZ. SCALE {km2): 10-100100-500 200-1,000 1.000-10,000 13,000
NO. OF SEGMENTS:
MODEL:
9RE-
72 GIONS 67
l i 1
ROCHESTER
EMBAYMENT
8 REGIONS
LAKE 3
LAKE 1, 1A
Figure 79
Summary of chlorophyll verification statistics
a) verification score test, t>) residual standard
error of estimate statistic, c) median relative error.
- 131 -
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IUU
80
60
40
20
'
(a) LAKE 3 SCALE,
1972 Average
: i
§ M J
o
QJ
-Q TOO
CC 0
0^80
£ 8 60
— -Q
5-° 20
UJ § 0
DC
a 100
UJ
S 80
60
40
20
0
I
J
575
? for,
I
'EGM
a// va
!E/\
rial
l
ITS
j/es = 44%
1
A S 0
(b) E/GHT FfEG/ONS SCALE
1972 A verage for a// v
/ f^5
M J
(c)TWOLAYi
1972 A
u /
M J
\
1
J
E7?SC
verage
/
-14 —
PS
J
1
aric
i
ibles = 35%
1
A S 0
'ALE
• for all vat
23
~m~
riaL
41
1
)/es= 17%
n
A S 0
I
N
1
1
N
14
M
\
N
Figure 80 Median relative error across all variables,
a) Lake 3 scale, 6? segments, t>) eight regions,
c) whole lake scale, two layers.
- 132 -
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REFERENCES
Boyd, J.D. and B.J. Eadie, 1977. Evaluation of U.S. IFYGL
chemical data at the Master Stations, in IFYGL Bull. No. 21
NOAA, Rockville, Md., pp. U9-6l.
Canada Centre for Inland Waters, Limnological Data Report s^,
Lake Ontario. 1966-1969. Canadian Oceanographic Data Centre,
Burlington, Ontario.
Casey, D.J. and S.E. Salbach, 1971*. IFYGL stream materials
balance study (IFYGL). Proc. 17th Conf. Great Lakes Research
International Association Great Lakes Research, pp. 668-681.
DiToro, D.M. and W.F. Matystik, Jr., 1978. Mathematical models
of vater quality in large lakes. 1. Lake Huron and Saginaw
Bay - Model Development, Verification and Limitations. U.S.
EPA, ERL, Duluth, Minn. In preparation.
DiToro, D.M. and J.C. Connolly, 1978. Mathematical models of
water quality in large lakes. 2. Lake Erie. U.S. EPA, ERL,
Duluth, Minn. In preparation.
Elder, F.C. , F.M. Boyce, J.A. Davies, 197^. Preliminary energy
budget of Lake Ontario for the period May through November,
1972 (IFYGL). Proc. 17th Conf. Great Lakes Research, Inter-
national Association Great Lakes Research, pp. 713-72U.
Hydroscience, Inc. 1976. Assessment of the effects of nutrients
loadings on Lake Ontario using a mathematical model of the
phytoplankton. Report prepared for International Joint
Commission, Windsor, Ontario by Hydroscience, Westvood, New
Jersey, 116 pp.
International Lake Erie and International Lake Ontario - St.
Lawrence River Water Pollution Control Boards, 1969. Report
to the International Joint Commission on the Pollution of
Lake Ontario and the International Section of the St. Lawrence
River, Vol. 3.
Kullenberg, F. et al., 1973. An experimental study of diffusion
characteristics in the thermocline and hypolimnion regions of
Lake Ontario. Proc. l6th Conf. Grt. Lks. Res. IAGLR, Ann
Arbor, Mich., pp. 77U-790.
- 133 -
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Kullenberg, G. et al., 197^. Vertical mixing characteristics
in the thermocline and hypolimnion regions of Lake Ontario
(IFYGL). Proc. 17th Conf. Grt. Lks. Res. IAGLR, Ann Arbor,
Mich., pp. U25-U3U.
McNaught, D.C., M. Buzzard and S. Levine, 1975. Zooplankton
production in Lake Ontario as influenced by environmental
perturbations. U.S. EPA, ORD, Corvallis, Oregon. EPA -
660/3-75-021, 155 pp.
Phillips, D.W. IFYGL Weather highlights (IFYGL). Proc. 17th
Conf. Great Lakes Research, International Association Great
Lakes Research, pp. 296-320.
Pickett, R.L. 1976 a, Distribution and Variability of Physical
Lake Properties, in IFYGL Bulletin No. 17, NOAA, Rockville,
Maryland, pp. 78-9*1.
Pickett, R.L. 1976 b, Lake Ontario Temperature and Current
Profiles in IFYGL Bulletin No. 18, NOAA, Rockville, Maryland,
PP. 53-55.
Robertson, A., F.C. Elder and T.T. Davies, 19lh. IFYGL Chem-
ical Intercomparisons (IFYGL). Proc. 17th Conf. Great Lakes
Research, International Association Great Lakes Research,
pp. 682-696.
Simons, T.J. 1976. Analysis and simulation of spatial variations
of physical and biochemical process in Lake Ontario. J. Grt. Lks.
Res. Vol. 2 (2) pp. 215-233.
Stadelmann, P. and A. Fraser, 197^. Phosphorus and nitrogen
cycle on a transect in Lake Ontario during the International
Field Year 1972-1973 (IFYGL). Proc. 17th Conf. Great Lakes
Research, International Association Great Lakes Research,
pp. 92-108.
State University of New York at Albany, 1973. U.S. IFYGL
Coastal Chain Program, Report l6; Basic Data for the Rochester
Coastal Chain, Atmospheric Sciences Research Center, April.
Thomann, R.V., D.M. Di Toro, R.P. Winfield and D.J. O'Connor,
1975. Mathematical Modeling of Phytoplankton in Lake
Ontario. 1. Model Development and Verification, EPA-
660/3-75-005, ORD, Corvallis, Oregon, 177 PP-
Thomann, R.V., R.P. Winfield, D.M. Di Toro and D.J. O'Connor,
1976. Mathematical Modeling of Phytoplankton in Lake
Ontario, 2._ Similations Using Lake 1_ Model. EPA-660/3-76-
065, U.S. EPA, ORD, Environmental Research Laboratory,
Duluth, Minn., 87 pp.
-------
We"b~b, M. S. 197^- Mean Surface Temperatures of Lake Ontario
During the IFYGL. Proc. 17th Conf. Great Lakes Research,
International Association Great Lakes Research, pp. 471-
Wine, R.L. 196k. Statistics for Scientists and Engineers.
' Prentice-Hall, Inc., Englewood Cliffs, H.J. , 671 pp.
- 135 -
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TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
. REPORT NO.
EPA-600/3-79-094
3. RECIPIENT'S ACCESSION NO.
». TITLE AND SUBTITLE
Verification Analysis of Lake Ontario and Rochester
Embayment Three Dimensional Eutrophication Models
5. REPORT DATE
August 1979 issuing date
6. PERFORMING ORGANIZATION CODE
. AUTHOR(S)
Robert V. Thomann, Richard P. Winfield, and John
J. Segna
8. PERFORMING ORGANIZATION REPORT NO.
I. PERFORMING ORGANIZATION NAME AND ADDRESS
Manhattan College
Environmental Engineering and Science Program
Bronx, New York 10471
1O. PROGRAM ELEMENT NO.
1BA769
11. CONTRACT/GRANT NO.
R803680030
12. SPONSORING AGENCY NAME AND ADDRESS
Environmental Research Laboratory - Duluth, Minn.
Office of Research and Development
U.S. Environmental Protection Agency
Duluth, Minnesota 5580U
13. TYPE OF REPORT AND PERIOD COVERED
Final
14. SPONSORING AGENCY CODE
EPA-600/03
15. SUPPLEMENTARY NOTES
Supplements previous reports EPA-660/3-75-005 and EPA-600/3-76-065
16. ABSTRACT
A three dimensional time variable model of the phytoplankton and nutrients of
Lake Ontario and the Rochester Embayment is examined in detail. The data from the
International Field Year on the Great Lakes (IFYGL) are used as the primary data
base. The data are summarized and statistically analyzed on a three dimensional
grid and segment averages using a 67 segment representation of the lake and a 72
segment representation of Rochester Embayment, are calculated. In addition,
averages for eight regions of the lake and lakewide averages for two depth layers
are computed. Average phytoplankton levels during the period May, 1972 and June,
1973 in the near shore region are approximately 3 yg/£ higher than open lake values.
Similarly, near shore open lake total phosphorus gradients of about 5 yg P/£ appear
to persist for a substantial part of the year. The data base collected during
IFYGL exhibited significant spatial and temporal variations at scales of 10 x 40 km.
The two data bases available, Canadian Centre for Inland Waters (CCIW) and
Environmental Protection Agency (EPA), only agree within certain limits.
17.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b.lDENTIFIERS/OPEN ENDED TERMS C. COSATI Field/Group
Mathematical Models
Water Quality
Statistical Analysis
Great Lakes
Lake Ontario
Rochester Embayment
Ecological Modeling
U8G
18. DISTRIBUTION STATEMENT
Release Unlimited
19. SECURITY CLASS (This Report)
Unclassified
21. NO. OF PAGES
150
20. SECURITY CLASS (Thispage)
Unclassified
22. PRICE
EPA Farm 2220-1 (R»v. 4-77) PREVIOUS EDITION is OBSOLETE
136
US GOVERMKIIT PBKIING OFFICt: 1979 -657-060/5413
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