oEPA
United States
Environmental Protection
Agency
Environmental Research
Laboratory
Duluth MN 55804
EPA-600 3 79-015
February 1979
Research and Development
Results of a Joint
U.S.A./U.S.S.R.
Hydrodynamic and
Transport
Modeling Project
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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-600/3-79-015
February 1979
RESULTS OF A JOINT U.S.A./U.S.S.R. HYDRODYNAMIC
AND TRANSPORT MODELING PROJECT
by
John F. Paul and William L. Richardson
Large Lakes Research Station
Environmental Research Laboratory-Duluth
Grosse He, Michigan 48138
U.S.A.
Alexandr B. Gorstko
Institute of Mechanics and Applied Mathematics
Rostov State University
Rostov-on-Don
U.S.S.R.
and
Anton A. Matveyev
Hydrochemical Institute
Hydrometeorological Services
Novocherkassk
U.S.S.R.
ENVIRONMENTAL RESEARCH LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
DULUTH, MINNESOTA 55804
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DISCLAIMER
This report has been reviewed by the Large Lakes Research Station,
Environmental Research Laboratory-Duluth, Grosse lie, Michigan, U.S.
Environmental Protection Agency, and approved for publication. Mention of
trade names or commercial products does not constitute endorsement or recom-
mendation for use.
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FOREWORD
The Environmental Research Laboratory - Duluth is concerned with the
effects of pollutants on freshwater ecosystems, particularly the Laurentian
Great Lakes. The development and verification of mathematical models
describing the transport and fate of pollutants in freshwater ecosystems
are carried out at the Large Lakes Research Station at Grosse He, Michigan.
This report describes a modeling effort accomplished under the Lakes
and Estuaries Project of the U.S.A./U.S.S.R. Agreement on Cooperation in
the Field of Environmental Protection. Models developed by scientists in
one country were applied to aquatic systems in the other country and com-
pared to existing data. The accomplishments of these researchers demon-
strate the utility of joint scientific collaborations between countries.
Donald I. Mount, Ph.D.
Director
Environmental Research Laboratory
Duluth, Minnesota
111
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PREFACE
The U.S.A./U.S.S.R. Agreement on Cooperation in the Field of Environ-
mental Protection was first signed in 1972 and has just recently been re-
negotjiated. Eleven areas of cooperation were enumerated, ranging from air
and water pollution to legal aspects. As a result of this agreement,
hundreds of scientists and engineers from the two participating countries
have made exchange visits.
This present work was accomplished under the auspices of Project
02.02-12, Protection and Management of Water Quality in Lakes and Estuaries,
of the Environmental Agreement. The intent of the authors in undertaking
this particular work was to provide a contact between researchers in the
two countries who were involved in describing and modeling various aspects
of the processes in large bodies of water. It was also our desire to do a
modeling project whereby scientists from both countries could work together,
each providing some part of their expertise for the benefit of the project.
We think that we have accomplished this and hope that others will think so
also. We would like readers of this report to keep in mind that this work
was initiated and completed in a relatively short period of time compared
to the normal frame of time for a scientific project. This work did not
encompass all that we had originally intended. We realize that it was more
important for us to show how scientists from our two countries could work
together on a definite project rather than to make sure we completed every-
thing. Since this was just an initial modeling effort, many areas could
not be covered in as much detail as one would have liked. Hopefully, the
modeling efforts between the scientists of our two countries will be con-
tinued in the near future and the fruits of these joint undertakings will
be an increase in the credibility of the use of modeling in the aquatic
environment.
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ABSTRACT
A joint modeling project with scientists from the U.S.A. and U.S.S.R.
has been accomplished. The three geographical areas investigated include
Lake Baikal and the Sea of Azov in the U.S.S.R. and Saginaw Bay, Lake Huron
in the U.S.A. The modeling approaches ranged from those employing material
and mass conservation to describe water movement to those involving
solution of the complete three-dimensional hydrodynamic equations. The
model calculations were compared to available data and, in all cases, rea-
sonable agreement was obtained.
This report covers a period from May 1977 to December 1977, and work
was completed as of April 1978.
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CONTENTS
Foreword 1-11
Preface iv
Abstract v
Figures ix
Tables xi
Acknowledgements xii
1. Introduction 1
2. Conclusions and Recommendations 3
3. Lake Baikal 4
Background of Lake Baikal and Selenga River Region ... 4
Experimental Data and Methods 6
Whole Lake Circulation 6
Circulation in the Selenga River Shallows 7
Problems to be Addressed 9
4. Saginaw Bay 12
Background of Saginaw Bay 12
Experimental Data and Methods 13
Problems to be Addressed 13
5. Sea of Azov 19
Background of Sea of Azov 19
Experimental Data and Methods 19
Problems to be Addressed 26
6. Mathematical Models 27
Hydrodynamic Model 27
Summary of hydrodynamic component 27
Summary of dispersion component 30
Transport Models 31
Type 1 transport model 31
Type 2 transport model 34
Comparison of transport models 36
7. Results 37
Lake Baikal 37
Hydrodynamic and dispersion calculations 37
Type 1 transport calculation 58
Saginaw Bay 58
Type 1 transport calculation 58
Type 2 transport calculation 58
Sea of Azov 58
Hydrodynamic and dispersion calculation 58
Type 1 transport calculation 78
VII
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References 83
Appendices
A. Text of U.S.A./U.S.S.R. Agreement on Cooperation in the
Field of Environmental- Protection 86
B. Background on the Sea of Azov and Lake Baikal ecosystems ... *
C. Results of hydrodynamic and dispersion calculations for
Lake Baikal and Sea of Azov *
D. Meteorological, hydrological and chemical data for Selenga
Shadows in May-June 1976 *
*These appendices appear in a separate volume.
V1.lt
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FIGURES
Number Page
1 Lake Baikal 5
2 Selenga River Region of Lake Baikal 8
3 Observed surface currents in the Selenga River Region
of Lake Baikal 10
4 Saginaw Bay, including 1974 sampling network 13
5 Inner Saginaw Bay, Segment 2, water quality for
1974-1976 17
6 Sea of Azov 20
7 Observed currents in Sea of Azov during Summer of 1957 ... 22
8 Type 2 transport model calibration process for
Saginaw Bay 35
9 Hydrodynamic model grid for Lake Baikal calculation .... 38
10 Frequency of winds over Lake Baikal in the Summer and
Autumn 40
11 Hydrodynamic model calculation for Lake Baikal with
southwest wind 41
12 Hydrodynamic model calculation for Lake Baikal with
northwest wind 43
13 Hydrodynamic model calculation for Lake Baikal with
southwest wind and northern basin ice covered 46
14 Lake Baikal whole lake dominant currents 48
15 Dispersion model calculation for Lake Baikal with
southwest wind 50
16 Sample results from Hydromet cruise in Selenga Shallows
on 28-29 May 1976 54
IX
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Number Page
17 Landsat satellite images of Lake Baikal 56
18 Fourteen-segment Type 1 transport model for Lake Baikal . . 59
19 Sixteen-segment Type 1 transport model for Saginaw Bay ... 61
20 Type 2 transport model calibration with 1965 Saginaw Bay
chloride concentrations 62
21 Type 2 transport model verification with 1974 Saginaw Bay
chloride concentrations 63
22 Type 2 transport model water exchanges for Saginaw Bay ... 64
23 Hydrodynamic model grid for Sea of Azov calculation .... 67
24 Hydrodynamic model calculations for Sea of Azov 70
25 Surface salinity in Sea of Azov after six months with
and without increased Don River flow 73
26 Dispersion model calculation for Sea of Azov 74
27 Type 1 transport model calculation for Sea of Azov 79
x
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TABLES
Number Page
1 Annual. Average Water Balance for Lake Baikal During the
Period 1901-1970 4
2 Saginaw Bay Cruise Schedule for 1974-1975 15
3 Analytical Methodology for Saginaw Bay Water Quality
Parameters 16
4 Parameters of Inflow/Outflow for Sea of Azov During Summer
of 1957 25
5 Long Term Water Balance for Sea of Azov 21
6 Hydrodynamic and Dispersion Model Parameters for
Lake Baikal 39
7 Characteristics of Fourteen-Segment Type 1 Transport
Model for Lake Baikal 60
8 Hydrodynamic and Dispersion Model Parameters for Sea of
Azov 65
9 Parameters for Three Wind Cases of Sea of Azov Cal-
culations 68
10 Type 1 Transport Model Salinity for Sea of Azov 82
XI
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ACKNOWLEDGEMENTS
This work could not have been undertaken without the sponsorship of the
coordinators for the Lakes and Estuaries Project, Drs. T.T. Davies and A.A.
Zenin.
We would like to thank Ms. Elaine Fitzback for providing "Uason for our
two groups during the course of this work.
Dr. Michael Sydor, University of Minnesota-Duluth, provided the Landsat
satellite images.
We would like to thank the staff of the Large Lakes Research Station
for providing us with assistance on this report. In particular, we wish to
thank Mr. Nelson A. Thomas, Chief of the Large Lakes Program, for providing
the American authors with the opportunity to participate in this project.
Our special gratitude to Ms. Debra Caudill who typed the manuscript.
XII
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SECTION 1
INTRODUCTION
The United States of America (U.S.A.) and Union of Soviet Socialist
Republic (U.S.S.R.) are confronted with many environmental problems which
can affect the health and welfare of their respective societies. Expanding
populations and industries, and increasing urbanization and farming have re-
sulted in alterations to the hydrosphere and to changes in loads of waste
materials which effect the quality of the environment. The mutual concern
for the environment provided the impetus for the U.S.A./U.S.S.R. Agreement
on Cooperation in the Field of Environmental Protection signed in 1972
(Appendix A).
As part of the Agreement, Project 02.02-12, Protection and Management
of Water Quality in Lakes and Estuaries, was initiated. Although the two
nations share no common boundaries on any lake or estuary, they do share a
common concern for water quality preservation, and the need to understand
the physical, chemical, and biological processes that effect and determine
water quality. To share scientific knowledge on limnological processes, a
joint modeling project was initiated during the exchange visit by Soviet
representatives to the U.S.A. in 1976.
In June 1977, Dr. Tudor T. Davies from U.S. Environmental Protection
Agency (EPA), Environmental Research Laboratory, Gulf Breeze, Florida, and
Dr. John F. Paul and Mr. William L. Richardson from EPA, Large Lakes
Research Station, Grosse lie, Michigan, visited the Institute of Mechanics
and Applied Mathematics, Rostov State University, Rostov-on-Don, U.S.S.R.
They met with Drs. A.A. Zenin, A.A. Matveyev, A.B. Gorstko and F.A. Surkov.
During this visit, the details of the joint modeling project were arranged,
and a project report outline prepared. As a first step, it was agreed to
compare formulations and results of hydrodynamic and transport models
developed by the two groups. The objective was to provide a basis for
further verification of lakewide and nearshore hydrodynamic and transport
models.
It was agreed that three geographical areas and three model formula-
tions would be investigated. The areas are:
1. Lake Baikal (U.S.S.R.) with special emphasis on
the Selenga River plume
2. Saginaw Bay, Lake Huron (U.S.A.)
3. Sea of Azov (U.S.S.R.)
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The three modeling approaches are:
1. Hydrodynamic modeling using conservation equa-
tions for mass, energy, and momentum as developed
by Dr. Paul
2. Transport modeling using mass conservation as
developed by Drs. Gorstko and Surkov, referred
to as type 1
3. Transport modeling using conservation of material
and water mass as applied to Saginaw Bay by Mr.
Richardson, referred to as type 2
Approaches 1 and 2 would be applied to Lake Baikal and to the Sea of
Azov, and approaches ?. and 3 to Saginaw Bay. The model results were to be
compared to availabe data, and if possible, to each other. The result of
this would provide additional verification for the models, and determine
whether or not refinements were necessary.
This report provides a general background summary on each of the 3
water bodies, followed by a synopsis of the mathematical models used. The
applications of these models and comparisons with available data are then
presented. The appendices provide reference materials for those unfamiliar
with the U.S.A./U.S.S.R. Environmental Agreement, additional background on
Lake Baikal and the Sea of Azov, detailed results of the hydrodynamic and
dispersion calculations summarized in the main report, and data for the
Selenga shallows region of Lake Baikal in May-June 1976. Appendices B, C,
and D appear in a separate volume, which is available from National Techni-
cal Information Services (NTIS).
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SECTION 2
CONCLUSIONS AND RECOMMENDATIONS
The results of the model calculations were compared to available data
and, in all cases, reasonable agreement was obtained.
It was shown that the hydrodynamic model calculation for the Sea of
Azov could be useful in assessing the effects of hydrologic modifications.
The results of the work completed under this project, including compari-
sons between U.S.A. and U.S.S.R. models and comparisons to field data, have
permitted the participants to make an initial determination of the degree of
agreement and validity of the existing hydrodynamic and transport models.
This work represents a preliminary step in a possible comprehensive com-
parison of modeling methodology in the two countries among researchers for
both hydrodynamic and biochemical models. It is hoped this project will
lead to further cooperation among modelers of both countries.
A more detailed comparison of models will require a continuing commit-
ment by both nations, as well as by the individual modelers. The time re-
quired for the present study was about one month, with two weeks spent in
each country.
It may be desirable to continue this type of work through the Inter-
national Institute of Applied Systems Analysis (IIASA) in Laxenburg,
Austria. The total time required would be on the order of one to two years,
with periodic exchange visits to IIASA by the persons involved.
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SECTION 3
LAKE BAIKAL
BACKGROUND OF LAKE BAIKAL AND SELENGA RIVER REGION
The basin of Lake Baikal is located almost centrally in Asia, in a very
rugged mountain province in south Siberia, the Baikal Region. The charac-
teristic geomorphological features of the region include medium and high
mountain ranges extending over 1500 km in the southwest to northeast direc-
tion, and an alternation of ridges and trenches, the largest of which is
filled with waters of the lake.
Lake Baikal is the oldest and deepest intracontinental body of water in
the world. The formation of the Baikal trench began about 30 million years
ago. The watershed area of the lake is 0.54 million km2, and the area of
the lake itself is 31.5 thousand km2. The length of the lake is 636 km;
maximum width, 79 km; minimum width, 25 km; maximum depth, 1620 m; and
volume of the water mass, about 23 thousand km3. The topography of the
lake is shown in Figure 1. The trench of Lake Baikal is divided into three
basins, of which the middle one is the deepest. It is separated from the
southern basin by the Selenga shallows, a delta formed by the lake's
largest tributary, the Selenga River. The contribution of the Selenga
amounts to about 50% of the total runoff into the lake. Table 1 provides
an annual average water balance for the lake (Vikulina and Kashinova 1973").
TABLE 1. ANNUAL AVERAGE WATER BALANCE FOR LAKE BAIKAL DURING THE
PERIOD 1901-1970 ^
_ Inflow _ Outflow
Precipitation 9.29 Runoff to Angara River 60.39
Condensation on lake Evaporation 10.77
surface .82
River inflow 58.75
Groundwater inflow 2.30
Total 71.16 Total 71.16
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UPPER ANGARA
NIZHNEANGARSK :^^. RIVER
(Depth contours expressed in meters.)
SLYUDYANKA"' '.^.^^Siyifc^rpr!
Figure 1. Lake Baikal
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Lake Baikal contains approximately 4/5 of the total surface water re-
serves of the U.S.S.R. However, the importance of the lake does not end
there. During the past approximately 1 million years, when this body of
water was formed in its present boundaries, special characteristics were
developed: low solute content, high transparency, low temperature, and
high saturation with dissolved oxygen.
Lake Baikal's ecosystem is distinct and closely balanced. In the
course of its evolution, its organisms have adapted to conditions varying
little with time, and have reacted very sensitively to changes in these
conditions. Indicative of this sensitivity is the fact that organisms of
the open deepwater parts of the lake do not dwell in the shallow regions
near the delta, which are subjected to the action of the river runoff.
EXPERIMENTAL DATA AND METHODS
Limnological measurements in Lake Baikal are made by a number of
agencies and institutes in the U.S.S.R. These include:
1. Hydrochemical Institute of the Main Administration of the
Hydrometeorological Service of the U.S.S.R. (hydrochemistry)
2. State Hydro1logical Institute of the Main Administration of the
Hydrometeorological Service of the U.S.S.R. (hydrology)
3. Irkutsk Administration of the Hydrometeorological Service of the
U.S.S.R. (hydrology and meteorology)
4. Trans-Baika1 Administration of the Hydrometeorological Service of
the U.S.S.R. (hydrochemistry and hydrology of the Selenga River)
5. Limnological Institute of the Siberian Branch of the U.S.S.R.
Academy of Sciences (hydrobiology, hydrology, and chemistry of
sedimentat ion)
6. Irkutsk State University ^hydrobio1ogy)
The relevant data for this report, summarized below, are the
meteorology, current measurements, temperature, transparency, and
concentration of suspended solids. A description of these data for Lake
Baikal and the shallows of the Selenga River is provided in Appendix B.
Whole Lake Circulation
The primary cause of water movement in Lake Baikal is the wind. In
localized areas, like the Selenga River shallows, an appreciable influence
is also exerted by inertial forces formed by large inflows. In the central
and southern regions of the lake, northwesterly winds predominate (31% of
the time on an annual basis). Near the eastern shore of southern Baikal,
strong southeasterly winds are frequent. The wind speed distribution is
approximately the same for all directions on an annual basis. The mean
speeds are 5-10 m/sec, but speeds of 16-20 m./sec occur during the
spring-summer period.
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Several types of circulation patterns are formed by the wind. Six or
seven large scale cyclone-type spirals have been observed in all three
basins. Within these, there are several raesoscale eddies and secondary cir-
culations, particularly in regions with heterogeneous bottom topography and
shoreline morphometry.
The currents throughout the Take have an annual variation. They in-
crease with intensification of winds after the ""ake n's cleared of ice in
May and June, decline during the calmer summer periods, and increase during
the autumn storm period. The observed average speed of the Ta^ge scale
circulation is about 2-3 km per day (2.3-3.5 cm/sec) during the navigation
season, and 1-1.5 km per day (1.1-1.8 cm/sec"* during the ice free period.
Large scale gusts an order of magnitude higher have been observed over
short periods.
In the nearshore region '8-10 km from shore), the currents are almost
uniformly directed over the vertical column. The currents do vary with dis-
tance from shore, e.g., the currents at a distance of 0.4 to 0.6 km from
shore are 1.5 to 2 times lower than those at a distance .of 1.5 to 2 km.
Steady longshore currents begin to appear about 1.5 to 2.5 km (Aybund
1973"). At 2-3 km, the currents are 1.5 to 2 times lower than at 3 to 5 km.
In the deepwater, the maximum observed current speeds appear at 25 to 50 m
depth. The magnitude of the currents then decreases to the 100 m depth, be-
low which the currents become almost homogeneous in both magnitude and di-
rection. According to observations in southern Lake Baikal during the navi-
gation period, average current speeds are in the range of 12-18 cm/sec at
15 m depth, and 4-8 cm/sec at 50 m and below.
The vertical variation of the current structure is determined to a con-
siderable degree by the temperature stratification in the water. During
stratification, the deepwater parts of the lake separate into three zones:
1) the upper (dynamically active), 2) the deep, and 3) the bottom zone. The
upper zone includes 30% of the total depth and is characterized by large
current speeds with highly variable current direction. In the deep zone,
the currents change little with time and in speed. The bottom zone, not in-
cluding the bottom friction layer, is characterized by a slight increase in
current magnitude.
During the cold season, the currents remain but their speed is much
reduced. A major part of the time (60%), the magnitude of the currents
under the ice is less than 2 cm/sec. However, in areas located far from
the shore, speeds of 5-9 cm/sec that persist for 5-1.2 days have been
recorded.
Circulation in the Selenga River Shallows
The Selenga River is the largest tributary of Lake Baikal. The
drainage area composes 83.4% of the lake runoff area, and the river inflow
amounts to 50% of the total runoff into the lake. The topography of
Selenga River Shallows is shown in Figure 2. The distribution of the river
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Depth contours expressed in meters.
Solid lines represent cruise data.
Broken lines represent interpolated values.
Dots (•) represent cruise stations.
SELENGA DELTA
0 10 20
KILOMETERS
Figure 2. Selenga River Region of Lake Baikal.
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water into the lake takes place in a system of numerous delta branches,
numbering up to 30 during high river flow. The distribution of the river
water through these branches is highly variable, but mostly depends on time
of year and river flow. The speed of the entering river water varies from
6 cm/sec to 70 cm/sec, with penetration of the water into the lake varying
from .3-.4 km to 9 km.
The distribution of the Selenga River water, once it enters the lake,
is highly dependent upon the local wind field. During southwesterly winds,
the river water has been detected along the eastern and northeastern shore
of the lake at up to 130 km. In the presence of northeasterly winds, the
river water is transported to the region south of the delta. Examples of
observed surface currents and their short-term variation in the Selenga
River Shallows region are shown in Figure 3. It should be noted that the
current patterns are dependent on the perseverance of the wind from a
particular direction.
PROBLEMS TO BE ADDRESSED
Of particular importance to the existing and future water quality of
the lake as a whole, and to the Selenga River area in particular, is the
Selenga River basin. Anthropogenic factors influence the character of the
Selenga River and its chemical runoff. It is hoped that rational efforts
and sound measures will be undertaken to preserve a healthy ecosystem, and,
at the same time, allow for economic development of the Baikal region. The
planned development in the lake basin from 1971 to 2000 will amount to over
10 billion rubles (13.6 billion dollars), with approximately 6% of this
amount spent on environmental protection. During the next 30 years, a 4 to
5-fold increase in gross industrial production, 3-fold increase in agricul-
tural production, and 1.5-fold increase in timber production are antici-
pated. In addition, the population is expected to increase by a factor of
1.5 during this same period. Most of these increases will be centered in
two regions: 1) the basin along the course of the Selenga River southwest
of the lake, and 2) along the Baikal-Amur railway under construction in the
area north of the lake.
The importance of the Selenga River Region, and of the shallow zone
encircling it, can be related to the growth and development of the Selenga
whitefish young in this area. After the larvae have hatched in April and
May, the whitefish remain in the delta for 35-45 days, and in the shallows
until mid-August. Hence, until the end of June, the whitefish young are
influenced directly by chemical runoff, and during the subsequent period
are exposed to its influence in the diluted shallow waters. If the level
of toxic pollutants in the water of the Selenga River from April to August
is detrimental to these fish, there is no doubt that it can have an even
stronger influence on the remaining trophic links in this region of the
lake.
One objective of this U.S.A./U.S.S.R. joint modeling project is to
attempt to describe the circulation and transport characteristics of Lake
Baikal for the whole lake, and for the Selenga River Shallows area using
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WIND
WIND
(1) Prevailing southwesterly wind (30 Aug 1972).
(2) Prevailing northwesterly wind (31 Aug 1972).
(3) Steady lasting northwesterly wind (8 Sep 1972).
Figure 3. Observed surface currents in the Selenga River Region
of Lake Baikal.
10
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mathematical models. Combined with the existing knowledge of transport and
circulation obtained from a qualitative description of experimental data, a
better understanding of cause and effect reTationships should be obtained.
This could eventually lead to the construction of more detailed biochemical
models for management purposes. In addition, th-'s analysis may provide
experimentalists w:th new insights for data observation.
11
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SECTION 4
SAGINAW BAY
BACKGROUND OF SAGINAW BAY
Saginaw Bay was formed about five thousand years ago following the final
retreat of the Pleistocene Ice and recession of Lake Saginaw. The bay re-
mains as a shallow arm of Lake Huron, having an average depth of 5 m, a
width of 42 km at its mouth, a minimum width of 21 km, and a length of 82 km
from Saginaw River to the mouth (Figure 4).
Although small in size compared to all of Lake Huron, the bay is an im-
portant water resource to the State of Michigan and the Great Lakes Region
of the United States. Its surface area of about 2960 km2, shoreline of 230
km, and volume of 300 million cubic meters serves a variety of water uses.
Saginaw Bay is illustrative of a high water-use requirement from a water
body of degraded quality that resulted from municipal and industrial inputs
and from runoff of agricultural and urban land.
Historically, Saginaw Bay has been one of the more productive commer-
cial fishing areas in the Great Lakes. Even today, the bay has the highest
fish productivity of the entire Lake Huron ecosystem. The fishing industry
was established in the early 1800's and reached a peak in 1902 with
6,432,000 kg production. Since the 1930's, production and types of fishes
have been so severely altered that, in 1966, the production reached an ebb
of 1,160,000 kg.
In addition to water supply, commercial fishing, and waste assimila-
tion, the bay provides for extensive recreational uses including boating,
fishing, and swimming. Also, the bay is an important navigational waterway
for commercial vessels with foreign exports totaling over 7 million metric
tons. This shipping, however, requires a navigation channel to be dredged
through the inner bay and up the Saginaw River. Over 380,000 cubic meters
of spoil are removed annually, some of which are disposed of in the bay.
The bay receives the waste discharges and runoff from a drainage basin
serving over 1.2 million people (1970). Over 50% of the basin is farm
land, 34% forest, 3.5% urbanized, and 1.2% is recreational land. Products
of the basin include sugar beets, beans, corn, wheat, dairy and livestock.
Industrial products include food, automobiles, chemicals, and lumber.
These activities contribute large amounts of waste materials to the bay as
reflected by the material loads measured at the tributary mouths.
12
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SAG IN AW BAY
1974 Sampling Network
o BOAT STATION
A WATER INTAKE
- MODEL SEGMENTS
SAGINAW RIVER
Figure 4. Saginaw Bay, including 1974 sampling network.
13
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EXPERIMENTAL DATA AND METHODS
The U.S. Environmental Protection Agency, Large Lakes Research Station
CLLRS) at Grosse He, Michigan, has sponsored surveys of water quality in
the bay since 1974 ("Smith et al. 1977). The surveys have been conducted
to: 1) establish a water quality baseline, 2^ provide data for modeling
biochemical processes and dynamics, and 3) provide a comprehensive document
for the International Joint Commission (IJC) Upper Lakes Reference Study.
Location of sampling stations are ^'ndicated in Figure 4. During
1974-75, 30 cruises ''Table 2) were conducted by the Cranbrook Institute of
Science in support of and in conjunction with several other organizations.
Each survey was conducted over a 3-day period by two vessels. The
analytical methodology used for each water qua1l'ty parameter is summarized
in Table 3. Quality control procedures were incorporated into the
laboratory program. All data were processed and stored in the EPA STORET
system, a water quality data base system.
The data for 1974 to 1976 were analyzed for the IJC Water Quality Board
using one way analysis of variance to determine the existence of discernible
trends. The bay was divided into 5 segments of unique characteristics and
the data grouped and averaged for each segment. In general, the analysis
revealed increases in the inner bay, Segment 2, for chlorophyll a_, total
phosphorus, and total Kjeldahl nitrogen (see Figure 5). The data indicates
that enrichment of the bay has increased during the period 1974-1976.
PROBLEMS TO BE ADDRESSED
The primary water quality problems determined in Saginaw Bay are en-
rn'chment and the resultant problems associated with overabundance of algae,
particularly taste and odor in municipal water supplies. Historically,
total dissolved solids (chlorides) from solution mining in the basin have
been a primary concern in the bay. In the 1960's, chlorides were recorded
at over 100 mg/1 near the Saginaw River. Control programs implemented in
the 1970's have reduced present values to about 40 ing/I. More recent water
quality problems relate to toxic substances detected in fishes in the bay.
To adequately manage water quality in this complex environment, LLRS
has undertaken a research program to develop an understanding of cause and
effect relationships involved with these water quality problems. Bierman
(1976) has developed a raultispecies eutrophication model for the bay.
DiToro and Matystik (1976^ have calibrated a chlorophyll £ phytoplankton
biomass model, Canale and Squire (1976) have developed a steady state phos-
phorus and chloride transport model, and Richardson (1974 and 1976) has
calibrated and verified a steady-state chloride transport model and cali-
brated a time variable chloride transport model. All of these models de-
pend heavily on a quantification of the net circulation in the bay over a
particular time scale. The steady-state models use a time average of sever-
al weeks to a season, whereas the time variable models require suitable
resolution oVer the entire annual biological growth cycle.
14
-------
TABLE 2. SAGINAW BAY CRUISE SCHEDULE FOR 1974-75
Cruise/survey
Cruise 1
Sampling dates
11/5-7/73
Cruise 2 1 2/3-4/73
Cruise 3
2/18-21/74
Cruise 4 | 3/25/74
Cruise 5
Cruise 6
Cruise 7
Cruise 8
Cruise 9
Cruise 10
Cruise 11
Cruise 12
Cruise 13
Cruise 14
Cruise 15
Cruise 16
Cruise 17
Cruise 18
Cruise 19
Diurnal Survey
(Sta. 56)
Cruise 20
Cruise 21
Diurnal Survey
(Sta. 56)
Cruise 22
Cruise 23
Diurnal Survey
(Sta. 56)
Cruise 24
Cruise 25
Diurnal Survey
(Sta. 56)
Cruise 26
Cruise 27
Diurnal Survey
(Sta. 56)
Cruise 28
4/16-20/74
No. stations
sampled
37
41
16
7
44
4/28-30/74 59
5/13-17/74 51
6/2-5/74
47
6/18-22/74 59
7/8-10/74 59
7/25-27/74 59
8/25-27/74 59
9/18-20/74 59
10/6-8/74 58
11/11-14/74 I 36
12/16-18/74 23
2/17-19/75
3/18/75
4/9-11/75
4/28-29/75
4/30-2/75
5/20-22/75
6/2-3/75
6/5-8/75
6/25-27/75
7/11-12/75
7/13-16/75
7/29-31/75
8/16-17/75
8/18-20/75
9/3-5/75
9/21/75
9/23/75
Cruise 29 j 10/9-11/75
Diurnal Survey
(Sta. 56)
Cruise 30
Cruise 31
Cruise 32
10/25-26/75
10/27-29/75
11/16-18/75
12/16/75
33
15
30
1
37
37
1
32
37
1
37
36
l
37
37
1
19
37
1
29
35
9
Satellite pass dates
10/31-11/1/73
12/5 & 6/73
2/15 & 16/74
3/23 & 24/74
4/10 & 11/74
4/28 & 29/74
5/1.6 & 17/74
6/3 & 4/74
6/21 & 22/74
7/9 & 10/74
7/27 & 28/74
9/1. & 2/74
9/19 & 20/74
10/7 & 8/74
11/12 & 13/74
12/18 & 19/74
2/20 & 21/75
3/27 & 28/75
4/1 & 2/75
5/1 & 2/75
5/19 & 20/75
6/6 & 7/75
6/24 & 25/75
7/12-13/75
7/30-31/75
8/17 & 18/75
9/4 & 5/75
9/22 & 23/75
10/10 & 11/75
10/28 & 29/75
11/15 & 16/75
12/21 & 22/75 :
15
-------
TABLE 3. ANALYTICAL METHODOLOGY FOR SAGINAW BAY
WATER QUALITY PARAMETERS
Parameters
Temperature
Oxygen, dissolved
Specific conductivity
Chloride, filtered
pH
Akalinity, total
Secchi disc depth
Chlorophyll at non-filterable
Carbon, filt. organic
Carbon, unfilt. organic
Solids, unfilt. total
Silicates, filt. reactive
Ammonia, filtered total
Nitrate + Nitrite, filt.
Nitrogen, unfilt. Kjeldahl
Phosphates, filt. reactive
Phosphorus, flit, total
Phosphorus, unfilt. total
Sodium, unfiltered
Potassium, unfiltered
Calcium, unfiltered
Magnesium, unfiltered
Where
measured
in on at
situ ship LLRS
X X
X
X
X
X X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Max. time
to analysis
(in situ)
(in situ)
10 min.
48 hrs.
10 min.
10 min.
(in situ)
4 wks.
2 wks-sealed
7 mos-analyzed
2 wks-sealed
7 mos-analyzed
2 wks.
48 hrs.
48 hrs.
48 hrs.
48 hrs.
48 hrs.
48 hrs.
48 hrs.
6 mos.
6 mos.
6 mos.
6 mos .
Methods
Submerged thermistor
probe; termometry
Submerged KC1 probe
Electric conductance measurement
Ferric
thiocyanate color reaction
Submerged combination pH probe
Sulfuric acid (0.02N)
titration to pH 4.5
Visual estimation
Extraction & spectrophotometry
(SCOR/UNESCO)
Sealed ampuole wet
oxidation & IR analysis
Sealed ampuole wet
oxidation & IR analysis
Gravimetric measurement
"Molybdenum blue" color reaction
Berthelot color reaction
Sulfanilimide (diazo) color reaction
Digestion & autoanalysis for ammonia
"Phospho-molybdenum blue"
color reaction
Digestion & autoanalysis for phosphate
Digestion & autoanalysls for phosphate
Flame Atomic Absorption
Spectrophotometry (undigested)
Flame Atomic Absorption
Spectrophotometry (undigested)
Flame Atomic Absorption
Spectrophotometry (undigested)
Flame Atomic Absorption
Spectrophotometry (undigested)
Equipment/
instrumentation
Martek Mark II Monitor
Martek Mark II Monitor
Beckman RC19 Conductivity Bridge
Technicon AA2 Auto Analyzer
Martek Mark II Monitor
Fisher 520 pH/Ion Meter
Burette & Fisher 520 pH/Ion Meter
9 cm diam. B & W disc
P-E Coleman 124 Double
Beam Spectrophotometer
Oceanography International 052413
& MSA 300 IR analyzer
Oceanography International 052413
(, MSA 300 IR analyzer
Mettler H10 Balance
Technicon AA2 Auto Analyzer
Technicon AA2 Auto Analyzer
Technicon AA2 Auto Analyzer
Heating Block
and Technicon AA2 Auto Analyzer
Technicaon AA2 Auto Analyzer
Heating Block
and Technicon AA2 Auto Analyzer
Heating Block
and Technicon AA2 Auto Analyzer
Instrumentation Laboratory 353
AA Spectrophotometry
Instrumentation Laboratory 353
AA Spectrophotometry
Instrumentation Laboratory 353
AA Spectrophotometry
Instrumentation Laboratory 353
AA Spectrophotometry
-------
0.05
1 I 0.04
g z
co :- 0.03
g <
£ «
-J z 0.02
< uj
s §
H 8 o-01
INCREASING TREND.
SEGMENT 2
74
75
YEAR
76
10 KM
J10MI
BOAT STATION
WATER INTAKE
MODEL SEGMENTS
O
O
oc
z
o
0.5
0.4
0.3
0.2
0.1
0
. INCREASING
•
•
•
TR
END
74. 75 76
YEAR
If
ll
-J (-
I <
u a:
o !r
uj Z
I- ^J
u y
ui Z
a: o
cc o
O
o
20
18
16
14
12
10
INCREASING TREND
74.
75
YEAR
76
Figure 5. Inner Saginaw Bay, Segment 2, water quality
for 1974-1976.
17
-------
The problem to be addressed in this report is that of describing
chloride transport in Saginaw Bay as a method of quantifying circulation
patterns.
18
-------
SECTION 5
SEA OF AZOV
BACKGROUND OF SEA OF AZOV
The Sea of Azov is a comparatively small body of water located between
45° and 47° N latitude, and 35° and 39° E longitude (Figure 6). Its area
is 38,000 km2, and the volume is about 320 km3- The Sea of Azov is shallow.
Its maximum depth is approximately 13 meters, with an average depth of about
8 meters.
The sea is an important source of fish protein and, thus, is an
important resource to the Rostov Region of the U.S.S.R. One hundred and
four species of fish have been identified in the bay, nine of which
comprise 90% of the fish biomass. Also, 332 phytoplankton species, 155
zooplankton species, and 180 benthos species have been identified.
Large quantities of materials from the Sea of Azov drainage basin and
hydrological modifications on the major rivers have had considerable impact
on water quality, and subsequent effects on biological processes. The most
common pollution components are oxygen demanding materials (BOD), wastes
from petroleum production, phenolic compounds, detergents, pesticides, and
nutrients. The content of heavy metal salts in the pelagic zone of the sea
are at the level of the natural geochemical background.
A much more serious impact may result, however, if a barrier is con-
structed between the Black and Azov Seas, as has been proposed. The pur-
pose of a barr?'er would be to reduce the salinity influx from the Black Sea.
However, this may have a deleterious impact on the Sea of Azov. One purpose
of modeling the Sea of Azov is to predict the consequences of such potential
modifications. However, before predictions can be made, it is necessary to
calibrate and verify models for existing conditions. For this report, on]y
the hydrodynamic and transport components of the model formulation will be
considered, and only the hydrological and meteorological data will be dis-
cussed. More details on the Sea of Azov are presented in Appendix B.
EXPERIMENTAL DATA AND METHODS
One of the key processes in the Sea of Azov is the water exchange
between various parts of the sea and the associated redistribution of the
solutes, suspensions, and organisms. The dynamics of the seawater are
19
-------
to
o
35
47
30'
DEPTH:
5m
10m
35° LONGITUDE 36°
37C
38C
47C
30'
46°
30'
45C
39C
Figure 6. Sea of Azov.
-------
essentially determined by the wind, and the horizontal water exchange is
determined by the wind-generated system of currents. Typical of the Sea of
Azov is the short time lag of the process. Because of the shallowness of
the sea and unstable wind conditions, the speed and direction of currents
can change very rapidly.
According to the data in the Hydrometeorological Handbook for the Sea
of Azov (Anonymous 1972^, wind-generated currents of 2-10 cm/sec have the
highest frequency (up to 60%). Currents with speed of 10-20 cm/sec,
corresponding to winds of 5-10 m/sec, have a frequency of about 30%. The
maximum currents do not exceed 60-80 cm/sec. Some observations of currents
during the summer of 1957 are shown in Figure 7. Parameters relevant to
these currents are listed in Table 4.
During the cold half of the year, easterly winds prevail. Their
frequency during this period amounts to 45-50%, and the frequency of
westerly winds, about 30%. The wind speed during the fall and winter
periods reaches an average maximum of 6-7 m/sec. Storms with easterly
winds of over 10-15 m/sec also occur at that time.
In spring and summer, the wind patterns change. The frequency of
westerly winds increases to 38-45% and that of easterly winds decreases to
25-30%. Later (July - August), the wind speed drops to the annual minimum,
which amounts to a long-term average of 4.2 m/sec. During the course of a
year, the frequency of northerly and southerly winds does not usually ex-
ceed 10%, and the frequency of calms is approximately 7%.
In addition to wind, the following factors also contribute to the
dynamics of the sea: runoff, atmospheric precipitation, evaporation, and
water exchange with the Black Sea through the Kerch Straits. Data on a
long-term average water balance are listed in Table 5.
TABLE 5. AVERAGE WATER BALANCE FOR SEA OF AZOV
(km3/year)
Gain
Loss
Inflow from river 41
Precipitation 14
Inflow from Black Sea 32
Evaporation 36
Outflow to Black Sea 51
Total
87
Total
87
The water exchange between the Sea of Azov and Black Sea is the most
variable component of the water balance. During the period of observation,
the maximum annual outflow through the straits was 67.1 km3 (1932) and the
minimum was 38.8 km3 (1950). The extremes of annual inflow from the Black
Sea were 38.1 km^ (1950) and 28.9 km3 (1932), while the extremes of net
water exchange were 38.1 km3 (1932) and 0.7 km3 (1950).
21
-------
CASE 1
WIND (m/sec)
—- [ CUR RENTS (cm/sec)
Figure 7a. Observed currents in Sea of Azov
during Summer of 1957.
22
-------
CASE 2
WIND (m/sec)
CURRENTS (cm/sec)
Figure 7b. Observed currents in Sea of Azov
during Summer of 1957.
23
-------
CASES
WIND (m/sec)
CURRENTS (cm/sec)
Figure 7c. Observed currents in Sea of Azov
during Summer of 1957-
24
-------
TABLE 4. PARAMETERS OF INFLOW/OUTFLOW FOR SEA OF AZOV
DURING SUMMER OF 1957
ho
Parameters specific to
Case 1
Don river flow 530
(m3/sec)
Kuban river flow 500
(m3/sec)
Evaporation 2.4
(mm/day)
Precipitation 0
(mm/day)
current observations
Case 2 Case 3
600 570
520 450
2.0 2.8
0 0.4
Average parameters
(km3
Flow from Sea of
Azov to Black Sea
Flow from Black Sea
to Sea of Azov
Net flow out of
Sea of Azov
for the
/month)
June
2.9
2.0
.9
summer 1957
July August
1.4 1.4
4.6 3.2
-3.2 -1.8
-------
A systematic study of the hydrometeorological regime of the Sea of Azov
began in 1922. Up to that time, only periodic measurements had been made.
In connection with projects to regulate the runoff of the Don and Kuban
Rivers during 1949, a number of scientific and planning institutes carried
out additional studies that made it possible to prepare forecasts of
possible changes in the hydrological regime of the sea. Observations made
up to 1959 were classified and correlated in the Hydrometeorological
Handbook for the Sea of Azov (Anonymous 1972). At the present time, the
Azov Scientific Research Fishery Institute, the chief organization engaging
in comprehensive investigations of the Azov ecosystem, routinely conducts
four cruises per year in April, July, August, and October.
PROBLEMS TO BE ADDRESSED
A considerable portion of the catchment basin of'the Sea of Azov is
located in a zone of insufficient precipitation. For th-'s reason, the
river runoff is very limited, amounting to an average of 41 km3 (Gorstko
1976). The bulk of the runoff is due to two rivers, the Don and the Kuban
(27.9 and 13.9 km3 annual contribution, respectively). The exceptional
variability of the Don River inflow with time (52 km3 in 1942 and 11.8 km3
in 1950) causes large fluctuations in the total water reserves of the
basin. The river runoff of the Azov Basin is used for the needs of indus-
try, agriculture, power engineering, water transport, municipal water sup-
ply and fisheries. The Sea of Azov is the closing link in the utilization
of the water. It follows from genera1 ecological considerations that the
effects of anthropogenic action in the basin should accumulate in the
ecosystem of the Sea of Azov. This is indeed the case (Gorstko and Surkov
1975*).
The principal problem areas for the Sea of Azov created by man are the
following:
1. Irreversible removal of a considerable part of the runoff
2. Seasonal, leveling out of river drainage
3. Reduction in the breeding areas of migratory and semimigratory
fishes resulting from the difficulty of access to spawning grounds
4. Change in biogem'c and mineral runoff
The state of natural equilibrium of the Sea of Azov ecosystem has
already been disturbed by man's activities and is now in an intermediate
state. The direction of future anthropogenic activity within the Sea of
Azov basin is an unresolved issue. Several a^ernative approaches are
possible. A mode ""ing framework for the entire ecosystem is underway at the
Institute of Mechanics and Applied Mathematics, University of Rostov. It
is anticipated that the mode1ing efforts will influence management deci-
sions that will be made for the basin.
One objective of this U. S.A. ./U. S.S.R. joint modeling project is to
describe the hydrodynamic and material transport characteristics of the
sea. It is hoped that this work will provide a basis to be used in
assessing the alternative approaches for future activity within the basin.
26
-------
SECTION 6
MATHEMATICAL MODELS
HYDRODYNAMIC MODEL
This effort is composed of two components: the basic hydrodynamic
calculation and the transport of dissolved and/or suspended material. Each
component will be discussed separately.
Summary of Hydrodynamic Component
The equations for the hydrodynamic component are derived from the
time-dependent, three-dimensional equations for conservation of mass,
momentum, energy, and salinity. The principal assumptions used are:
(a) The pressure is assumed to vary hydrostatically .
(b) The rigid-lid approximation is made, i.e., the
vertical velocity at the undisturbed water surface
is assumed to be a constant value. The assumed con-
stant value is usually zero. This approximation is
used to eliminate surface gravity waves and their
associated small time scales, greatly increasing the
maximum allowable time step in the numerical computations.
For applications where evaporation and/or precipitation
are important, an appropriate non-zero value is used.
(c) Eddy coefficients are used to account for the turbulent
diffusion effects. The horizontal coef f f icients are
assumed to be constant, but the vertical coefficients
are assumed to be some function of the local dependent
variables.
The resulting equations are:
9u 3u2 3uv 3uw __ 1 3P _3
3t 3x 3y 3y o p 3x 3x
3/A3u-./A u..
(AH 3° + fe (AV fc
27
-------
__ 9v
9z
= _ _
3t 8x 37 9z 9z ^DH 9x; 9y
(Bv
as + au§ + 2z§ + 32§ = _a a§ _a •
at 8x 9y 9z 9z H 3x' 9y H 9y
* il (Bv >• -
i g - 8, (6)
P dz
p = f(T,S), (7)
where
x,y = horizontal coordinates,
z = vertical coordinate,
u,v = fluid velocities in x and y directions,
w = fluid velocity in z-direction,
t = time,
p = pressure,
T = temperature,
S = salinity,
p = density,
fQ = Coriolis parameter,
AJJ = horizontal eddy viscosity,
Ay = vertical eddy viscosity,
p = density at reference conditions,
BJJ = horizontal eddy conductivity,
By = vertical eddy conductivity,
Bu = horizontal eddy diffusivity for salinity,
By = vertical eddy diffusivity for salinity,
g = gravitational acceleration, and
f(T,S) = equation-of-state.
28
-------
Before the above equations are put into appropriate finite-difference
form, they are transformed by a stretching of the vertical coordinate.
With such a transformation, the same number of vertical grid points can be
present in the shallow as in the deeper parts of the water body. This en-
sures that in the shallow areas there is no loss of accuracy in the computa-
tions due to lack of vertical resolution. The transformation is:
0-<-> z/h(x,y) .
The boundary conditions used with the equations are the following: the
bottom and sho^e are taken as no-slip, impermeable, no-flux surfaces; in-
flows or outflows along with appropriate fluxes of heat and salinity are
specified at rivers; at the water surface, a wind-dependent stress, a
specified heat flux, and a zero flux for sa1in;ty are specified. The ini-
tial conditions used are either some simple specification for the variables
(e.g., zero^ or specification of all variables from some previous calcula-
t i on .
The equations are put into finite-difference form in both space and
time. The spatial discretizing is accomplished by integration of the dif-
ferential equations about appropriate grn'd cells. The equations are ex-
plicit in time, except with respect to the Coriolis terms and the vertical
diffusion terms x^hich are written implicitly. This is done to eliminate the
small vertical diffusion t''me step restriction and the instability asso-
ciated with explicit form of the CorioHs terms.
The equations as written can not be solved directly if the rigid-lM
condition is to be satisfied. To develop a solution scheme, an additional
equation is derived directly from the other equations and the rigid-lid con-
dition. Th^'s equation is derived by vertically summing the two difference
equations for the horizontal velocities, then taking the difference analog
of the divergence. The rigid-lid condition is used along with the verti-
cally summed continuity and hydrostatic pressure equations. The result is
a Poisson-type difference equation in the surface pressure. The surface
pressure is the "integration constant" resulting from the vertical summa-
tion of the hydrostatic pressure equation. The surface pressure is a func-
tion of the horizontal coordinates. This procedure for deriving the
Poisson-type equation for the surface pressure, a modification of the SMAC
procedure by Amsden and Harlow (1970), is different than previous models
which first derived the pressure equation from the differential equation,
then discretized it (Paul and Lick 1974, Paul 1976). The distinction be-
tween these two procedures is that with the use of the latter, the finite-
difference equation that results for the pressure will not necessarily be
directly deriveable from the finite-difference forms of the horizontal
momentum equations. This is strictly a numerical error associated with
approximating the differential equations; however, ttv's error reflects in
the inability of the numerical solution to satisfy the rigid-lid condition
to an acceptable degree. Even if direct methods are used to solve the
finite-difference pressure equation or if an iterative procedure is used
29
-------
with stringent convergence criteria, errors are man;fested in the vertical
velocity at the r-'gld lid. These errors are not always small, especially in
problems where there is significant differences in depths between the shal-
low and deep areas of the water body. These errors might not appear to be
of much significance in some calculations, but they do create appreciable
errors when the resultant velocities are used to calculate dispersion of
substances in the body of wate^. A1 so, i-f advantage is taken of the time
implicit nature of the vertical diffusion terms 'i.e., t^'me steps are large
with respect to the explicit vei-tica"! diffusion time limit"1, these errors
become large and ultimately make the solutions meaningless. Complete de-
tails of this numerical procedure appear ;n the report by Paul and L;ck
'1978^.
Summary of Dispersion Component
The transport and dispersion of material in the turbulent flow will be
described in a manner similar to that used for the transport and turbulent
dispersion of heat and momentum. Refer to Sheng ^1975^ for a summary of
this procedure. The concentrations of the mater1'a1 to be dispersed are
treated as continuous on the length sca^s considered. The concentrations
are sufficiently small so that they do not significantly alter the density
of the water (the momentum equations can be solved independently), and they
function as complete1y conservative substances in the water column convected
w'th the loca1 fluid velocities. The on1;/ exception to the "latter condition
will be when gravitational settling is important for the material con-
sidered. In this situation, the vert^ca1 convection of the materia1 is en-
hanced by a settling velocity. The bas^c equation used to predict the dis-
persion of the material is:
9(Cv)
9y
+ _9 f-n ^") + -2 Cn ££} (8)
r\ ^ J^TT «\ ' r\ ^ U1J r. ' J V U '
8y H 3y 9z V 9z
where
C = concentration of material per unit volume,
x,y = horizontal coordinates,
z = vertical coordinate,
t = time,
u,v = particle (or fluid) velocities in the x and y d-frections,
w = particle velocity (the sum of the fluid velocity and the
settling velocity, wg, of the substance relative to the fluid)
in the z direction,
Drr = horizontal eddy diffusivity, and
D = vertical eddy diffusivity.
30
-------
The boundary conditions used are that all surfaces have zero net flux
of the material through them except at rivers. In this latter situation,
the net flux is either into or out of the water, depending on the flow of
the river. The magnitude of the flux depends on the local concentration of
the material. The same transformation of the vertical coordinate that is
used for the hydrodynamic component is used here. The finite-difference
analysis of the equation is similar to that used for the hydrodynamic
component. Paul and Patterson (1977) have used this basic dispersion
component to calculate the transport of larval fishes in the western basin
of Lake Erie.
TRANSPORT MODELS
Type 1 Transport Model
In this section, a model of water exchange between different regions of
a water body will be presented. It is important because water exchange
determines, to a considerable degree, the changes in the concentration of
solutes, phytoplankton, zooplankton, etc., in the water mass. These
changes are very substantial for the ecosystem as a whole.
A universal means of solving such problems involves the use of
hydrodynamic equations for calculating the currents in a body of water, and
the subsequent calculation of the dynamics of concentrations of the
material, by means of a turbulent diffusion equation, on the basis of the
flow pattern obtained. This turbulent diffusion equation is:
3- = - div (C • u) + div (E, grad C) + y (9)
where
C = concentration of the material,
t = t ime,
u = velocity vector,
E = turbulent diffusivity, and
y = source or sink term.
In practical calculations, the differential relations are replaced by their
finite-difference analogs. The computations (usually done with a computer)
are performed for discrete instants of time on a discrete grid which
approximates the body of water.
Let us now consider a description of the calculations for the concen-
tration dynamics of the material. Let the body of water be divided into n
regions, each of which is assumed to be homogeneous in concentration. The
following notation is introduced:
31
-------
C.. - concentrations of material at time t In region i.
V,j - volume of region i at time t,
Yic - external loading of material into region i between times t
and t+1,
Q.. . - volume of flow from region i to region j at time t, and
K. - first order decay coefficient of the material.
The equation for the concentration dynamics of the substance is:
C.t+1 = [C.'fV.* - ZQf^ + SQ^* C.' + y.* - K V.fc C.'l./V t*1, i-l,2,...,n (10)
.1 j "
The terms on the right hand side of Equation '10") have the following
meanings:
C. V. - amount of material in region i at time t,
C . *• EQ - . fc - amount of material transported out of region i to all
1 j J
neighboring regions,
ZQj^ x. - amount of material transported into region i from all
neighboring regions,
y. - external loading into region i,
K.: V.*" C^ - chemical decomposition in region i.
In conformity with the two terms on the right hand side of the turbu-
lent diffusion equation (9), the quantities Q^. are assumed to consist of
two terms :
The first term corresponds to the transport between regions i and j due to
the mean currents, and the second term describes the mixing due to fluctu-
ating disturbances relative to the mean currents.
The equation of concentration dynamics (10) makes it possible to compute
the concentrations xt+l only if values for all the variables on the right
hand side of the equation a*"e known. The values of concentration x1- for
the previous time step are assumed to have been computed or specified as
initial conditions. The values yt of loadings of the material, have to be
specified. The decay constants, K.^, of the material may be different for
separate regions of the body of water because of possible differences in
physicochemical conditions of the region, and must also be specified. The
32
-------
remaining values of the volumes, V^ , V^ , of each of the regions and
flows, Q-JJ , depend on the hydrological regime. They may be either speci-
fied or computed separately.
Thus, equation (10) can be used for different purposes. If the condi-
tions in the body of water are sufficiently stable, one can calculate the
steady state of the concentrations by equating quantities at times t and
t+1. This results in:
C. = C. (1 - ~ Z Q..) + J- E Q.. C. + y. - K. C.,
11 V. . 11 V. . ji J i 11
i J i J
i = l,2,...,n (11)
Simple rearrangement results in the equation
AC = y,
where A is a square matrix of order n with coefficients
A. . =
K. + - Z Q. ., for i = j
i V. . xii' J
- ~- Q.., for i i i
V. . V
and C and y are column vectors with components C . and y ., respectively.
The steady state results are obtained as the solution of the linear
system
C = A"1 y.
Hence, if the values of flow, Q-H, between the regions are specified or esti-
mated in some manner, and if the concentrations of the material may be con-
sidered to be in a steady state, then from a given loading y, one can compute
the concentration distribution.
The second method of using Equation (11) consists of computing the tran-
sient concentrations C. The transient values of volumes, V £*-, and flows be-
tween regions, Q-j^ , can be computed with a suitable hydrological model. For
a shallow body of water characterized by wind-driven flow, this can be done
by means of a model analogous to the one used for simulating the hydrologic
regime of the Sea of Azov.
In this model, a time step of 5 days was chosen. It was assumed that for
a 5-day average wind velocity vector there exists a corresponding slope of
the water surface, which to a first approximation was assumed to be an ideal
plane. These assumptions were based on data from natural observations and
level fluctuations of the Sea of Azov.
33
-------
The sequence of the calculations in the model is as follows: first, the
average surface elevations of each of the regions are calculated from the
average wind velocity vector. From the surface elevation of the region, the
volume V-^t+l is calculated. Comparison of V±l and Vi1-"1"-*- indicates that an in-
crease (or decrease) of water is required by region i. From the arrangement
of the regions, one determines from which adjacent region this water is trans-
ported. Also considered are inflows of water with river runoffs, and the
balance of evaporation and precipation at the sea surface.
Type 2 Transport Model
An economical approach to quantifying circulation in segmented water
bodies has been developed by Thomann (1972). This approach utilizes one of
the basic conservation principles, mass balance, to trace a material through
segmented systems. Any material for which the reactions are known may be used
as the tracer. For Lake Ontario and Lake Huron, Thomann, et al., (1975), and
DiToro and Matystik (1976) have used temperature as a transport tracer. For
Saginaw Bay, chloride is an appropriate tracer because of the large source in
the Saginaw River and the relatively sharp gradients in the bay.
Richardson ( 1974 and 1976) has calibrated and verified a quasi-steady-
state chloride transport model for Saginaw Bay. The approach used is de-
picted in Figure 8. Given a chloride river loading and chloride concentra-
tions in the bay, the circulation parameters become the unknowns. These para-
meters are determined through an iterative process using a computer solution
of the mass balance formulations given below:
dck
V, T-^ = 0 = Z [-Q, . (a, .c. + 6, .c.) + E,1 . (c. - c. )] - V.K, c. + W. ,
k dt . l xkj kj k kj ] kj j k k k k k'
where
o
c^ = concentration per unit volume (M/L ),
_ 3
= bulk dispersion coefficient = EkjAkj/Lj(L /T) ,
KV = decay coefficient (1/T),
E^ = dispersion coefficient (L
o
V, = volume of segment k (LJ),
K
E^.. = bulk dispersion coefficie
L-; = average length of adjacent sections (L) ,
f\
A]H = cross-sectional area between segments k and j (L ),
a, . = dimensionless coefficient to account for unequal
segment dimensions,
6« = l~\i' 3
Q . = advcective transport parameter (L /T) , and
kj
W = source of c in mass units per time (M/T) .
k
34
-------
MODEL CALIBRATION PROCESS
NFLUENCE FROM
LAKE HURON
SEGMENTATION
Depth D
Area A
Volume V
Length L
Wt
BAY CIRCULATION
Advection Q
Dispersion E
BAY CHLORIDE CONCEN-
TRATIONS CM
CHLORIDE LOADINGS Wk
INPUT
V
D
COMPUTE CHLORIDE
CONCENTRATION
RESET
Figure 8. Type 2 transport model calibration process
for Saginaw Bay.
35
-------
The units are:
L = length,
T = time, and
M = mass.
The parameters a and B, . are determined by:
KJ fcj
L.
OL = J
\j L. + L '
J J K
where positive solutions to the equations are guaranteed by the criterion
0. . >1 -
kj kj
Initial estimates of the transport parameters for dispersion, E, and ad-
vection, Q, are made, and concentration of chloride is computed. The computed
concentrations are compared to the measured average concentrations in each seg-
ment. The process of selecting new values of E and Q, directed by the magni-
tude and direction of the previous error, is repeated until the computed con-
centrations are approximately equal to that measured.
Comparison of Transport Models
The two transport models are similar in that they try to predict water move-
ments with basic conservation equations. They differ by which conservation
equation is used.
The type 1 model (Gorstko and Surkov) calculates the changes in water move-
ment with time by using surface elevation changes. For the application to the
Sea of Azov, the water surface slope is related to a time-averaged wind. By
neglecting diffusion, a unique set of water transports from one time step to
the next is calculated. A difficulty with this model is that a non-zero
steady-state solution for water transport cannot be calculated because it only
calculates transports resulting from the changes in surface elevation.
The type 2 model (Richardson) calculates water movement and diffusive trans-
port through an iterative process of comparing computed and observed material
concentration values. A set of time-dependent transports is developed with this
model that gives reasonable agreement with observed data, i.e., the transports
are adjusted until the agreement is satisfactory. Since water movement and dif-
fusion are both solved for, a unique solution is not obtainable because the
equations are underdetermined. This model does require a reasonable data base
of observed concentrations if the time-dependent transports are to be charac-
terized with some degree of resolution. The iterative procedure has not been
automated so it does require extensive user interaction.
The choice of transport model which is better for a particular application
depends on the data available and the physical characteristics of the water
body.
36
-------
SECTION 7
RESULTS
LAKE BAIKAL
Hydrodynamic and Dispersion Calculations
The parameters used for the application of the hydrodynamic model to
Lake Baikal are listed in Table 6. The vertical diffusion is dependent on
the local depth, resulting in larger mixing in the deeper sections of the
lake. Figure 9 indicates the horizonta1 gri-d scheme used for the discreti-
zation process. Constant-density calculations were performed for the four
main wind directions on the lake; these are listed as Cases 1 through 4 in
Table 6. These main wind directions are the same as indicated in the
Baikal Atlas (Anonymous 1969). Figure 10, taken from the Baikal Atlas, in-
dicates the relative frequency of the four wind directions during the summer
and autumn periods. The water current data with which the calculations are
compared is only of a general nature since lakewide currents for specific
episodes in time were not obtainable during the course of this study.
Since an insufficient amount of data was available on the thermal regime
for the entire lake, the calculations were performed assuming this aspect
to be negligible. The wind direction for Case 1, from the southwest, was
also used in a calculation with the northern basin of the lake ice covered.
This type of calculation is of interest to assess the significance of the
ice cover on the central and southern basins. The northern basin is
generally ice covered through the middle of May, and occasionally until the
beginning of June (Anonymous 1969).
Detailed results of the hydrodynamic calculations are presented in
Appendix C. All of the calculations were performed for 12 days of real
time, after which essentially steady-state conditions were obtained. Fi-
gures 11 and 1.2 show the surface velocities and vertically integrated
velocities for the southwest wind (Case 1) arid the northwest wind (Case 3).
For all of the calculations, the results are typical of what might be ex-
pected from the simple theory of motion which balances Coriolis force,
vertical friction, and horizontal pressure gradients. The deep areas of
the lake are generally characterized by geostrophic motion, while the
shallower areas are markedly influenced by vertical friction. The magni-
tude and directions of the surface currents indicate the different balances
in the motion as one goes from shallow to deep waters. The general circula-
tion of the lake is composed of the basic circulation in the three basins.
Because the northern and southern basins are relatively flat in their long
dimension compared with the central basin, the magnitude of the vertically
integrated velocities for the southwest wind are smaller in these basins
37
-------
ANGARA
RIVER
A/
SCALE:
0 100 200
KILOMETERS
CO
SELENGA
RIVER
UPPER
•ANGARA
RIVER
BARGUZIN
RIVER
Figure 9. Hydrodynamic model grid for Lake Baikal calculation.
-------
TABLE 6. PARAMETERS FOR LAKE BAIKAL HYDRODYNAMIC MODEL
Grid spacings
Horizontal extents
Number of grid points
Minimum depth
Maximum depth
Coriolis parameter (53°N)
Horizontal eddy viscosity
Vertical eddy viscosity
Surface wind stress
Wind directions:
Case 1
Case 2
Case 3
Case 4
River flows:
Selenga
Barguzin
Upper Angara
Angara
Horizontal eddy diffusivity
Vertical eddy diffusivity
Particle settling velocity
where:
h = local depth
ho = reference depth
15 km y-direction
7.8 km x-direction
600 km y-direction
150 km x-direction
41 y-direction
21 x-direction
8 z-direction
10 m
1620 m
1.16xlO~4/sec
10 cm /sec
3.85 (1 + 258.7 £-)cm2/sec
ho
1 dyne/cm
Southwest
Northeast
Northwest
Southeast
9.64x108 cm3/sec
4.10xl08 cm3/sec
5.78xl08 cm3/sec
19.52xl03 cm3/sec
106 cm2/sec
.385 (1 + 258.7 £-) cm3/sec
ho
10 m/day
39
-------
FREQUENCY OF FALL WINDS (PERCENT):
FROM LEFTSIDE INW) FROM RIGHT UP LAKE (SW) DOWN LAKE (IMEI FREQUENCY
SIDE (SEI OF CALM
FREQUENCY OF SUMMER WINDS /PERCENT!:
FROM LEFTSIDE (NW) FROM RIGHT UP LAKE (SW) DOWN LAKE (NE) FREQUENCY
SIDE (SE; OF CALM
Figure 10. Frequency of winds over Lake Baikal
in the summer and autumn.
40
-------
N
0
SCALE:
100 200 15 CM/SEC
KILOMETERS
WIND
H^-:T
SURFACE VELOCITIES
Figure lla. Hydrodynamic model calculation for Lake Baikal
with southwest wind.
-------
N
WIND
SCALE:
100 200
KILOMETERS
0
h* '-i/ • fsH*i
£-.
.~*~*'*\ \*- »; -_J I
^1-K^-,- :"P
VERTICALLY INTEGRATED VELOCITIES
**^\'%*-f*
—3 f ^ t ••:»»
rr- ^ >;.,»:*,
Figure lib. Hydrodynamic model calculation for Lake Baikal
with southwest wind.
-------
N
WIND
SCALE:
0 100 200 15 CM/SEC
KILOMETERS
SURFACE VELOCITIES
Figure 12a. Hydrodynamic model calculation for Lake Baikal
with northwest wind.
-------
N
V
WIND
0
SCALE:
1 1
100 200
KILOMETERS
VERTICALLY INTEGRATED VELOCITIES
Figure 12b. Hydrodynamic model calculation for Lake Baikal
with northwest wind.
-------
compared to the central basin. Th's is in agreement with the steady-state
solutions obtained for simple basins by Gedney (1971"*. He solved the equa-
tions which balance Cor^olis force, pressure gradients, and vert:ca1 fric-
tion. For constant depth basins, the steady-state vertically integrated
velocities are everywhere equal to zero, while for parabolic shaped basins,
the vertically integrated velocities form two rotating gyres, with the
magnitudes dependent on the degree of the bottom slopes. Thus, the gyres
in the calculations for the vertically integrated veloc't'es are functions
of the local topography. Differences are apparent for the different wind
direction calculations, but this is because the basins are e1ongated and
the topography is highly variable.
The surface velocities and vertically integrated ve1ocities for a south-
west wind with the northern bas'-'n covered with ice are shown in Figure ""3.
It can be seen that the currents in the central and southern basins are re-
latively unaffected by the ice cover. The currents in the northern bas?'n
are almost non-existent, because the lake currents are mainly wind-driven.
The minimal current that does exist i-n this basin is primarily due to the
inflow of the Upper Angara River.
Data on surface currents in the Selenga region were presented earlier
in Figure 3. Three cases were shown: prevailing southwesterly winds,
prevailing northwester1y winds, and steady lasting northwester1y winds.
The first two are separated by only a day, and it is apparent that the
currents on the second day show the effects of the previous day's winds.
This can be seen by comparing the second and thn'rd plot. The currents in
the third plot compare quite well with the surface current calculation for
the northwesterly wind (Figure T2). The f^rst plot compares reasonable
we11 with the calculation for the southwestern w'nd ''Figure 11), but dis-
crepancies do exist, apparently a function of the transitory behavior of
the currents. The second plot appears to be some combination of the two
calculations, as would be expected.
The on1y data for lake-wide currents is a plot which appears in the
Baikal Atlas (Figure 14). This is depicted as representative of the typi-
cal currents that exist in the lake. With reference to the wind frequency
plot for the lake (Figure 10\ it can be seen that for the most part, the
winds from the southwest are the most typical. A comparison of the data
plot (Figure 14) with the vertical!y integrated velocities calcinated for a
southwest wind (Figure 11) indicates a very good agreement. The observed
gyres are replicated quite well in the calculation. The data plot does not
indicate magnitudes of the currents so no comparisons can be made on this
aspect.
Using the steady-state currents that were calculated, the transport and
dispersion of material in the lake were calculated. A series of 8 calcula-
tions were performed: for each of the four main wind directions, for
material which is neutrally buoyant and for material which has a gravita-
tional settling velocity of 10 meters per day. Th'-'s settling velocity
corresponds with the mean Stokes settling velocity for the predominant
particle sizes observed in the suspended material in the Selenga River
runoff (see Appendix B). The two calculations for each current pattern in-
45
-------
N
SCALE:
+
0
100
KILOMETERS
200 15 CM/SEC
ON
WIND
r"n ;> i—LJ
» * . • • • • »->
-------
N
SCALE:
\ 1
0 100
KILOMETERS
200
WIND
T-n-S'a*
CO \/E/?
VERTICALLY INTEGRATED VELOCITIES
Figure 13b. Hydrodynamic model calculation for Lake Baikal with southwest wind
and northern basin ice covered.
-------
NIZHNEANGARSK
SLYUDYANKA
UST' BARGUZIN
Figure 14. Lake Baikal whole lake dominant currents.
48
-------
dicate the difference in distributions that can be achieved when one con-
siders dissolved material (neutrally buoyant) and suspended material (posi-
tive settling velocity). The parameters used for the calculations are
listed in Table 6. The calculations were performed for 28 days of real time
for each circumstance. Material was entered continuously during the cal-
culation through the Selenga, Barguzin and Upper Angara Rivers. The mate-
rial concentration in each river was set equal to 1.0. Since the transport
equations are linear in the material concentration, the actual concentra-
tion level is not important in the calculation. The results for all the
calculations are presented in Appendix C. Figure 15 indicates surface and
bottom concentrations with a southwest wind for both neutrally buoyant and
suspended material. The effect of the settling velocity on the concentra-
tion distributions is important. The main reason for this is that the cur-
rents over the water column are, in general, going in different directions.
If the material remains essentially uniform over the water column (i.e., for
the neutrally buoyant material), then the material is primarily transported
by the currents over the upper portion of the water column. These are the
currents which have the larger magnitude. When gravitational settling is
introduced, the material tends to concentrate near the bottom, and thus, is
transported horizontally by the currents that are near the bottom. Since
these currents are in generally in a different direction than the near sur-
face currents, the concentration distribution appears different.
The data that is available for comparison with the calculations are
shown in Figure 16. These data are taken from the Hydromet cruise in the
Selenga River Region of the lake on May 28-29, 1976 (refer to Appendix D
for the data that was available for this study). The plots are for P0^~^
(a dissolved substance) and total suspended solids. The winds over the
region were highly variable during the cruise, ranging from southwest to
southeast during the first part of the cruise, and to northeast during the
final part of the cruise. A reasonable comparison can be made with the
calculations for the southwest wind (Figure 15). The currents in the
vicinity of the Selenga delta are easterly near the surface and over most
of the vertical column near the river area of the lake. As one goes away
from the river area, the subsurface currents are generally southwesterly.
The suspended solids settle out as they enter the lake and are transported
by the near-bottom currents. The dissolved material remains nearly uniform
vertically, and is transported out into the lake by the subsurface
currents. The data generally agree with the calculated distributions.
Additional data available for the Selenga region are the Landsat satel-
lite images shown in Figure 17- These images record observations of June
21, 1975, and July 9, 1975. Unfortunately, no wind information was avail-
able for these dates. The images do indicate the same sort of suspended
solids pattern as was observed during the May 28-29, 1976, Hydromet cruise
(Figure 16).
Type 1 Transport Calculation
The steady-state transport model developed by Gorstko and Surkov (type
1) was applied to a 14 segment model of Lake Baikal. The segmentation
49
-------
Ul
o
SCALE:
CONCENTRATION
(PER VOLUME)
A 1.0000
B 0.1000
C 0.0100
D 0.0010
E 0.0001
0
100
KILOMETERS
SURFACE CONCENTRATIONS (NO SETTLING VELOCITY)
200
Figure 15a. Dispersion model calculation for Lake Baikal with southwest wind.
-------
SCALE:
CONCENTRATION
(PER VOLUME)
A 1.0000
B 0.1000
C 0.0100
D 0.0010
E 0.0001
0
100
KILOMETERS
BOTTOM CONCENTRA TIONS (NO SETTLING VELOCITY)
200
Figure 15b. Dispersion model calculation for Lake Baikal with southwest wind.
-------
SCALE:
CONCENTRATION
(PER VOLUME)
A 1.0000
B 0.1000
C 0.0100
D 0.0010
E 0.0001
0
100
KILOMETERS
200
SURFACE CONCENTRATIONS (SETTLING VELOCITY, 10m/day)
Figure 15c. Dispersion model calculation for Lake Baikal with southwest wind.
-------
Ln
U)
SCALE:
CONCENTRATION
(PER VOLUME)
A 1.0000
B 0.1000
C 0.0100
D 0.0010
E 0.0001
0
100
KILOMETERS
200
BOTTOM CONCENTRATIONS (SETTLING VELOCITY, Wm/day)
Figure 15d. Dispersion model calculation for Lake Baikal with southwest wind.
-------
Ol
NEAR SURFACE CONTOURS OF
P0~3, mg/l
IMPLIED FLOW OF MATERIAL
Figure 16a. Sample results from Hydromet cruise in Selenga Shallows
on 28-29 May 1976.
-------
NEAR SURFACE CONTOURS OF
SUSPENDED SOLIDS, mg/l
IMPLIED FLOW OF MATERIAL
Figure 16b. Sample results from Hydromet cruise in Selenga Shallows on 28-29 May 1976,
-------
Figure 17a. Landsat satellite images of Lake Baikal
•
-------
Figure 17b. Landsat satellite images of Lake Baikal.
-------
scheme is indicated in Figure 18, and the segment characteristics are indi-
cated in Table 7- The water exchanges between segments that were determined
for typical winds over the lake are indicated in Figure 18. These water
exchanges agree with the general lakewide circulation observed in the lake,
shown in Figure 14 (Anonymous 1969).
SAGINAW BAY
Type 1 Transport Calculation
The type 1 steady-state model developed by Gorstko and Surkov (1975)
was applied to a 16-segment model for Saginaw Bay. The segmentation scheme
was identical to that used by Richardson (1976^, and was applied to the
1965 data for chloride concentrations in the bay. The calculated and ob-
served concentrations are shown in Figure 19 along with the water exchanges
between segments that were determined. The calculated chloride concentra-
tions agree with the observations, and the calculated water exchanges are
similar to that determined by Richardson (1976), who applied the type 2
transport model under the same conditions. Refer to the next section for
his analysis and results.
Type 2 Transport Calculation
Through an iterative process, a type 2 transport model for chloride in
Saginaw Bay was calibrated and verified by Richardson (1976). Average
chloride loads to the bay of 2.8 million kg/day and 1.2 million kg/day were
measured in 1965 and 1974, respectively. The calibration with June-
November 1965 data that was obtained is shown in Figure 20. Verification
with June-November 1974 data is shown in Figure 21. Figure 22 shows the
advective transport scheme used for both of these computations. Disper-
sion from segment to segment varies from about 3.9 km2/day near the Sagi-
naw River and along the southeast shore of the bay, to 14.6 km2/day along
the northwest shore.
SEA OF AZOV
Hydrodynamic and Dispersion Calculation
The parameters used for the application of the hydrodynamic model to
the Sea of Azov are listed in Table 8. The equation-of-state is based upon
the form used by Crowley (1968) for oceanic calculations. It is:
p - P0 = 10~3 (28.14 - .0735T - .00469T2 + (.802 - .002T) (S-35)) (11)
where
p = density of water (gin/cm^),
PO = 1 gm/cm,
58
-------
UPPER ANGARA
. .'.RIVER
ANGARA RIVER
{.. BARGUZIN
'' RIVER
iSELENGA RIVER
MASS TRANSPORT
SEGMENT BOUNDARIES
Figure 18. Fourteen-segment type 1 transport model for Lake Baikal.
59
-------
TABLE 7. CHARACTERISTICS OF FOURTEEN-SEGMENT TYPE 1
TRANSPORT MODEL FOR LAKE BAIKAL
ON
o
Segment
Number
Surface
Area
Volume
N
S(km2)
V(km3)
1
1150
230
2
2950
590
3
2325
465
4
3150
630
5
2550
510
6
2050
410
7
2850
770
8
1175
235
9
1625
325
10
1725
345
11
1575
315
12
2200
440
13
1950
390
14
1850
370
Inflow: Selenga 2.5 knr/yr
Barguzin 1.063 km^/yr
Upper Angara 1.5 km-Vyr
Outflow: Angara 5.063 km /yr
-------
1965 RESULTS
CHLORIDE CONCEN
TRATION, mg/l
CALCULATED
'• OBSERVED
WATER EXCHANGES
BETWEEN SEGMENTS
Figure 19. Sixteen-segment type 1 transport model for Saginaw Bay.
-------
CHLORIDE CONCENTRATION, mg/l
MEASURED
CALCULATED
Figure 20. Type 2 transport model calibration with 1965 Saginaw Bay
chloride concentrations.
62
-------
(a) March through June, 1974
-N-
40
50
CHLORIDE CONCEN-
TRA TION, mg/l
-00—CALCULATED
"DO--- MEASURED
(b) July through November, 1974
Figure 21. Type 2 transport model verification with 1974 Saginaw Bay
chloride concentrations.
63
-------
000
•• NETADVECTIVE
FLOW (m3/sec)
@ MODEL SEGMENT
NUMBER
LAKE HURON
0| |10KM
—MOMI
C5>
Figure 22. Type 2 transport model water exchanges
for Saginaw Bay.
64
-------
TABLE 8. PARAMETERS FOR SEA OF AZOV HYDRODYNAMIC MODEL
Gr-'d spacings
Horizontal extents
Number of grid points
Minimum depth
Maximum depth
Corlolis parameter ^46°flO
Horizontal eddy viscosity
Vertical eddy v*scos;ty
Horizontal eddy diffusiv'ty
Vertical eddy diffusivity
Partite settling
6.84 km y-d i rec t i on
9.46 km x-direcf-on
362.5 km y-direction
2T7.5 km x-d-irection
54
24
8
1 m
13 m
y-direction
x-dlrection
z -direct1" on
1.046x10 4/sec
3xl06 cra2/sec
25 cm2/sec
3x10 cm /sec
10 cm2/sec
10 m/day
65
-------
T = temperature (°C), and
S = salinity
The Sea of Azov is generally mixed vertically because it is so shallow,
and it is generally of uniform temperature during the summer (around 20°C).
Th^s value for the temperature was used in the equati on-of-state. Figure 23
indicates the horizontal grid scheme used for the discretization process.
Variable-density, uniform temperature calculations were performed to make
comparisons with currents that were observed during the summer of 1957.
These currents and winds were presented earlier in Figure 7. The data d^'d
not suggest what currents these were: surface currents, near-surface cur-
rents, vertically averaged currents, or vertically integrated currents. One
additiona1 calculation was performed usi-ng the bas^'c wind from the second
observed case for an increased Don River flow of 5 km3 /year. This corre-
sponds to the amount of water that is considered for rediversion back into
the river in an effort to reverse the trend of increasing salinity in the
sea. It was hoped that the two calculations would indicate if the trend
could be changed. Table 9 indicates the conditions specific to each of the
calculations that were made. The basic data for inflows, outflows, evapora-
tion, etc., are from Table 4. The flows in each direction through the
straits between the Sea of Azov and the Black Sea were based on historical
records (Semenov 1972 ">. Typical flows for the summer were used, with flow
from the Sea of Azov into the Black Sea in the surface portion of the
straits and flow intrusion into the Sea of Azov through the deeper portion
of the straits. The salinity of water flowing from the Black Sea was set
at 17 gm/kg. One diffic^ty that did. develop when applying the conditions
to the model was in the detail of the wind field (e.g., Case 3 is con-
sidered essentially a constant westerly wind situation). However, it was
found that a completely constant wind could not be used to calculate the
current pattern suggested for this wind. Since existing data indicated
that the wind ;s constant to within 7-10 m/sec, a wind pattern with varia-
tion over th^'s range was tried in the calculation. Part of the calculation
procedure with the model thus consisted of experimenting with different
wind patterns, within the limits specified by the data, to determine what
would best approximate the observed results.
Complete results of the calculations are presented in Appendix C. All
of the calculations were performed for 2 days of real time with the wind
and river flows constant over this time period. The initial conditions for
the salinity distribution were obtained from the initial salinity values
used in the transport model of Gorstko and Surkov for the sea (see next sec-
tion'*. After 2 days, the currents achieved quasi-steady-state. The salin-
ity distribution was still slowly varying in time, and thus affecting the
current calculations, but these changes were small and had a negligible
affect on the comparison with the observed data. The results for Case 3 of
the observed data were obtained for both a spatially uniform wind, and for
a slightly varying wind. It was observed that the calculated currents below
the surface and the vertically integrated currents were significantly af-
fected by the spatial variation of the wind. Sample results for the cur-
rents at 2 meters below the water surface are shown in Figure 24. These
currents agree best with the observed data. The major discrepancies appear
66
-------
DON
'RIVER
N
\
SCALE:
0 25 50
I i i
KILOMETERS
BLACK SEA KUBAN
STRAITS RIVER
Figure 23. Hydrodynamic model grid for Sea of Azov calculation.
-------
TABLE 9. PARAMETERS FOR THREE WIND CASES
OF SEA OF AZOV CALCULATIONS
Q^ ''Don)
Q2 (Kuban)
Evaporation
Precipitation
Net flow out
Flow from Sea
Black Sea
o
m-Ysec
cm-Vsec
2
m /sec
o
cm /sec
mm/day
cm , /sec
mm/day
cm /sec
straits
cm /sec
of Azov to
cm^/sec
Flow from Black Sea to
Sea of Azov
cm^/sec
Case 1
530
5 . 3xl08
500
5.0xl08
2.4
10.4xl08
0
0
-.IxlO8
7.7xl08
7.8xl08
Case 2
600
6.0x10
520
5.2xl08
2.0
8.7xl08
0
0
2.5xT08
8.4xl08
5.9xl08
Case 2a
760
7.6x10°
520
5.2x10
2.0
8.7xl08
0
0
4.1xl08
9.6xl08
5.5xl08
Case 3
570 8
5.7x10
450
4.5xl08
2.8
12.2xlOB
0.4
l.SxlO8
-.2xl08
7 . 7xl08
7.9xl08
68
-------
in replicating the center of the gyre for all of the cases. Problems also
appear in duplicating the currents for Case 1 south of the Tagonrog Bay
area and along the southern shore of the sea. These probTerns may be due to
the variations rn the wind that probably occurred during the observations,
but for which no information is available.
The results of the calculations to determine the effect of an increased
flow in the Don River are shown in Figure 25 for the surface sa^in^'ty dis-
tributions. These calculations are identical to the previous except that
they represent 6 months of real time. A comparison does indicate that the
increased river flow can change the salinity in the sea. The results indi-
cate an average drop of .1 gm/kg in saninity for the sea over the time
period of increased river flow. It should be remembered that these cal-
culations are for a somewhat arbitrary flow through the straits. The re-
sults are sensitive to the conditions specified at the straits, and a dif-
ferent change in average salinity could be obtained for different condi-
tions. The f1ow conditions used were typical of the summer when the Black
Sea flow into the Sea of Azov was maxima1.
The transport and dispersion of material in the sea were made using the
currents calculated for Cases 1 and 3. For each case, two different calcul-
ations were performed: one for neutrally buoyant particles, and one for
particles with gravitationa1 settling velocities of 10 m/day. The first
corresponds to dissolved materials, and the second to suspended so1ids.
The calculations were performed for 28 days with material continually added
through the Kuban and Don Rivers. The material concentration in the rivers
was arbitrarily set to 1.0. Since the equations to be solved are linear,
the actual concentration va1ues are not important. The results of the cal-
culations are presented in Append;x C. Figure 26 shows the surface and
bottom concentrations with the Case 1 calculated currents for both dis-
solved and suspended material. The calculation for the suspended material
is not significantly different than the dissolved material calculation.
This may seem odd since the same settling velocity was used in the Lake
Baikal transport calculation and the results there were decidedly different.
This is explained when the relative importance of verti.ca1 mixing and gravi-
tational settling for these two applications is examined. This is indi-
cated by a vertical Reynolds number based upon the settling velocity, i.e.,
Wgh/Dy, where wg is the settling velocity, h is the depth and DV is the
vertical turbulent diffusn'vity. For the Sea of Azov calculation, this num-
ber is approximately 1, while for the Lake Baikal calculation, this number
ranges from 10 to 100. So, the gravitatinal settling is significantly more
important than vertical mixing for the Lake Baikal calculation, while for
the Sea of Azov calculation, both are of equal importance. This behavior
is typical of shallow seas and lakes, that is, suspended so1ids remain in
the water column for long periods of time. The flux out of the water column
is determined by the bottom boundary condition. This detail has not been
addressed in this study. Another observation of the results for the dis-
persion calculation is that materials added from the Kuban River disperse
throughout the sea much more rapidly than materials added from the Don
River. This is mainly due to the reduced flow occurring in Tagonrog Bay.
Material input from the Don River has to be transported through this bay
69
-------
CASE1
VELOCITIES 2 METERS
BELOW SURFACE
N
tttttffftttt,
15 CM/SEC
Figure 24a. Hydrodynamic model calculation for Sea of Azov.
-------
CASE 2
VELOCITIES 2 METERS
BELOW SURFACE
N
4
_l. . .».,,»»^
*»• • «•«•«•«•*'«-«-
SCALE:
0 25 50
I 1 1
KILOMETERS
15 CM/SEC
Figure 24b. Hydrodynamic model calculation for Sea of Azov.
-------
N
CASES
VELOCITIES 2 METERS
BELOW SURFACE
JT:...
-•*
=^
>*>$
15 CM/SEC
Figure 24c. Hydrodynamic model calculation for Sea of Azov.
-------
DON RIVER FLOW:
760 m3/sec
600m3/sec
KILOMETERS
SURFACE SALINITY CONCENTRATIONS
Figure 25. Surface salinity in Sea of Azov after six months with and
without increased Don River flow.
-------
N
CASE1
NO SETT LING
SCALE:
0 25 50
CONCENTRATION
(PER VOLUME)
A
B
C
D
E
F
G
H
I
J
K
1.00000
0.30000
0.10000
0.03000
0.01000
0.00300
0.00100
0.00030
0.00010
0.00003
0.00001
SURFACE CONCENTRATIONS
Figure 26a. Dispersion model calculation for Sea of Azov.
-------
CASE 1
NO SETT LING
SCALE:
N
r
CONCENTRATION
(PER VOLUME)
A
B
C
D
E
F
G
H
I
J
K
1.00000
0.30000
0.10000
0.03000
0.01000
0.00300
0.00100
0.00030
0.00010
0.00003
0.00001
BOTTOM CON CENTRA TIONS
Figure 26b. Dispersion model calculation for Sea of Azov.
-------
CASE 1
SETTLING, 10m/day
SCALE:
N
CONCENTBA TION
(PER VOLUME)
SURFACE CON CENTRA TIONS
A
B
C
O
E
F
G
H
I
J
K
1.00000
0.30000
0.10000
0.03000
0.01000
0.00300
0.00100
0.00030
0.00010
0.00003
0.00001
Figure 26c. Dispersion model calculation for Sea of Azov.
-------
CASE 1
SETTLING, 10m/day
SCALE:
0 25 50
I 1
N
CONCENTRATION
(PER VOLUME)
A 1.00000
B 0.30000
0.10000
0.03000
0.01000
0.00300
0.00100
0.00030
0.00010
0.00003
0.00001
BOTTOM CONCENTRA TIONS
Figure 26d. Dispersion model calculation for Sea of Azov.
-------
before it enters the main portion of the sea, while the Kuban River empti.es
almost directly into the main porf'on of the sea. No data were available
for tVs study to compare with the dispersion calculations.
Type 1 Transport Calculation
The type 1 steady-state transport mode1 developed by Gorstko and Surkov
C1975") was applied to a 7-segment model for the Sea of Azov. The model was
applied to the 3 cases observed during the summer of 1957 ''Figure 7 and
Table 4">. The water exchanges determined for the 3 cases are shown in Fi-
gure 27. These agree with the observed currents (Figure 7). The transient
transport model was applied to salinity dynamics using the water exchanges
determined for Case 2. Table 10 indicates the initial saTinity values, and
the values calculated 5 davs later. The calculated results agree within
one percent with the observed
78
-------
CASE 1
2 SEGMENT NUMBER
DIRECTION OF TRANSPORT
SEGMENT BOUNDARY
Figure 21 a. Type 1 transport model calculation for Sea of Azov.
79
-------
CASE 2
2 SEGMENT NUMBER
DIRECTION OF TRANSPORT
SEGMENT BOUNDARY
Figure 27b. Type 1 transport model calculation for Sea of Azov.
80
-------
CASES
2 SEGMENT NUMBER
DIRECTION OF TRANSPORT
----- SEGMENT BOUNDARY
Figure 27c. Type 1 transport model calculation for Sea of Azov.
81
-------
TABLE 10. TYPE 1 TRANSPORT MODEL SALINITY
FOR SEA OF AZOV
Initial salinity
Segment (gm/kg)
t 10.761
2 10.641
3 9 . 884
4 10.686
5 6.915
6 3.940
7 1.451
Calculated salinity
after 5 days
(gm/kg)
10.736
10.620
9.846
10.667
6.796
3.787
1.382
82
-------
REFERENCES
Amsden, A.A. and F.H. Harlow. 1970. The SMAC method: A numerical tech-
nique for calculating incompressible fluid flows. Los Alamos
Scientific Laboratory, Report No. LA-4370, Los Alamos, New Mexico.
Anonymous. 1969. Atlas of Baikal. Govt. Dept. Geodosy and Cartography,
Irkutsk and Moscow.
Anonymous. 1972. Hydrometeorologjcal handbook for the Sea of Azov.
Gidrometeoizdat, Leningrad.
Aybund, M.M. 1973. Results of full-scale studies of currents in southern
Baikal. Trudy GGI, Issue 203. Gidrometeoizdat, Leningrad.
Bierman, V.J. 1976. Mathematical model of the selective enhancement of
blue-green algae by nutrient enhancement. In: Modeling biochemical
processes in aquatic ecosystems (R.P. Canale, ed.) Ann Arbor Science
Publishers, Ann Arbor, Michigan, pp. 1-31.
Canale, R.P. and J. Squire. 1976. A model for total phosphorus in Saginaw
Bay. J. Great Lakes Res., I.A.G.L.R., Vol. 2, No. 2, pp. 364-373.
Crowley, W.P. 1968. A global numerical ocean model: Part 1. J. Computa-
tional Physics, Vol. 3, pp. 111-147.
DiToro, D.M. and W.F. Matystik. 1976. Phytoplankton biomass model of Lake
Huron and Saginaw Bay. Proc. of the EPA Conf. on Environmental
Modeling and Simulation (W.R. Ott, ed.), EPA-600/9-76-016, pp. 614-618.
Gedney, R.T. 1971. Numerical calculations of the wind-driven currents in
Lake Erie. NASA TM X-52985.
Gorstko, A.B. and F.A. Surkov. 1975. Mathematics and problems of conser-
vation. Moscow.
83
-------
Gorstko, A.B. 1976. Mathematical mode^ng and problems of utilization of
water resources. RGU.
Paul, J.F. and W.J. Lick. 1974. A numerical model for thermal plumes and
river discharges. Proc. 17th Conf. Great Lakes Res., I.A.G.L.R., pp.
445-455.
Paul, J.F. 1976. Modeling the hydrodynamic effects of large man-made modi-
fications to lakes. Proc. of the EPA Conf. on Environmental Modeling
and Simulation <"W.R. Ott, ed.), EPA-600/9-76-016, pp. 171-175.
Paul, J.F. and R.L. Patterson. 1977. Hydrodynamic simulation of movement
of larval fishes in western Lake Erie and their vulnerability to power
plant entrainment. Proceedings of the 1977 Winter Simulation
Conference fR.J. Highland, R.G. Sargent and J.W. Schmidt, ed.), WSC
Executive Committee, pp. .305-316.
Paul, J.F. and W.J. Lick. 1978. Numerical model for three-dimensional
variable-density, rigid-lid hydrodynamic flows: Vol. 1, details of the
numerical model. Report in preparation.
Richardson, W.L. 1974. Modeling chloride distribution in Saginaw Bay.
Proc. 17th Conf. Great Lakes Res., I.A.G.L.R., pp. 462-470.
Richardson, W.L. 1976. An evaluation of the transport characteristics of
Saginaw Bay using a mathematical model of chloride. In: Modeling
biochemical processes in aquatic ecosystems (R.P- Canale, ed.), Ann
Arbor Science Publishers, Ann Arbor, Michigan, pp. 113-139.
Semenov, A.E., ed. 1972. Hydrometeorological investigations of the
southern seas and Atlanta Ocean. Collected Works of the Laboratory of
the Southern Seas, Volume 11. Moscow.
Sheng, Y.-Y. P. 1975. The wind-driven currents and contaminant dispersion
in the near-shore of large lakes. Lake Erie International Jetport
Model Feasibility Investigation Report 17-5, Contract Report H-75-1,
U.S. Army Engineer Waterways Experiment Station, Vicksburg, Miss.
Smith, V.E., K.W. Lee, J.C. Filkins, K.W. Hartwell, K.R. Rygwelski, and
J.M. Townsend. 1977. Survey of chemical factors in Saginaw Bay (Lake
Huron). EPA-600/3-77-125.
84
-------
Thomann, R.V. 1972. Systems Analysis and Water Quality Management.
Environmental Science Services Division, New York.
Thomann, R.V., D.M. DiToro, R.P. Winfield and D.J. O'Connor. 1975. Mathe-
matical modeling of phytoplankton in Lake Ontario. Part 1, model
development and verification. EPA-660/3-75-005.
Vikulina, Z.A. and T.D. Kashinova. 1973. Water balance of Lake Baikal.
Trudy GGI, Issue 203, pg. 268. Gidrometeoizdat, Leningrad.
85
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APPENDIX A
AGREEMENT ON COOPERATION IN THE FIELD OF ENVIRONMENTAL PROTECTION
BETWEEN THE UNITED STATES OF AMERICA AND THE UNION OF SOVIET
SOCIALIST REPUBLICS
The Government of the United States of America and the Government of
the Union of Soviet Socialist Republics:
Attaching great importance to the problems of environmental
protection;
Proceeding on the assumption that the proper utilization of contempo-
rary scientific, technical and manageable achievements can, with appro-
priate control of their undesirable consequences, make possible the
improvement of the interrelationship between man and nature;
Considering that the development of mutual cooperation in the field of
environmental protection, taking into account the experience of countries
with different social and economic systems, will be beneficial to the
United States of America and the Union of Soviet Socialist Republics, as
well as to other countries;
Considering that economic and social development for the benefit of
future generations requires the protection and enhancement of the human
environment today;
Desiring to facilitate the establishment of closer and long-term co-
operation between interested organizations of the two countries in this
field;
In accordance with the Agreement between the United States of America
and the Union of Soviet Socialist Republics on Exchanges and Cooperation
in Scientific, Technical, Educational, Cultural, and Other Fields in 1972-
1973, signed April 11, 1972, and developing further the principles of mu-
tually beneficial cooperation between the two countries;
Have agreed as follows:
86
-------
Article 1
The Parties will develop cooperation in the field of environmental
protection on the basis of equality, reciprocity, and mutual benefit.
Article 2
This cooperation will be aimed at achieving the most important aspects
of the problems of the environment and will be devoted to working out mea-
sures to prevent pollution, to study pollution and its effect on the
environment, and to develop the basis for controlling the impact of human
activities on nature.
It will be implemented, in particular, in the followinr reas:
Air pollution;
Water pollution;
Environmental pollution associated with agricultural
product!on;
Enhancement of the urban environment;
Preservation of nature and the organization of preserves;
Marine pollution;
Biological and genetic consequences of environmenta1
pollution:
Influence of environmental changes on climate;
Earthquake prediction;
Arctic and subarctic ecological systems;
Legal and administrative measure for protecting environ-
mental quality.
In the course of this cooperation the Parties will devote special at-
tention to joint efforts improving existing technologies and developing
new technologies which do not pollute the environment, to the introduction
of these new technologies into everyday use, and to the study of their
economic aspects.
The Parties declare that, upon mutual agreement, they will share the
results of such cooperation with other countries.
Article 3
The Parties will conduct cooperative activities in the field of envi-
ronment protection by the following means:
Exchange of scientists, experts and research scholars;
Organization of bilateral conferences, symposia and
meetings of experts;
Exchange of scientific and technical information and docu-
mentation, and the results of research on environment;
87
-------
Joint development and implementation of programs and pro-
jects in the field of basic and applied sciences;
Other forms of cooperation which may be agreed upon in the
course of the imp1ementation of this Agreement.
Article 4
Proceeding from the aims of this Agreement the Parties will encourage
and facilitate, as appropriate, the establishment and development of
direct contacts and cooperation between institutions and organizations,
governmental, public and private, of the two countries, and the conclu-
sion, where appropriate, of separate agreements and contracts.
Article 5
For the implementation of this Agreement a US-USSR Joint Committee on
Cooperation in the Field of Environmental Protection shall be established.
As a rule this Joint Committee shall meet once a year in Washington and
Moscow, alternately. The Joint Committee shall approve concrete measures
and programs of cooperation, designate the participating organizations re-
sponsible for the realization of these programs and make recommendations,
as appropriate, to the two Governments.
Each Party shall designate a coordinator. These coordinators,
between sessions of the Joint Committee, shall maintain contact between
the United States and Soviet parts, supervise the implementation of the
pertinent cooperative programs, specify the individual sections of these
programs and coordinate the activities of organizations participating in
environmental cooperation in accordance with this Agreement.
Article 6
Nothing in this Agreement shall be construed to prejudice other agree-
ments concluded between the two Parties.
Article 7
This agreement shall enter into force upon signature and shall remain
in force for five years after which it will be extended for successive
five year periods unless one Party notifies the other of the termination
thereof not less than six months prior to its expiration.
The termination of this Agreement shall not affect the validity of
agreement and contracts between interested institution and organizations
of the two countries concluded on the basis of this Agreement.
88
-------
DONE on May 23, 1972 at Moscow in duplicate, in the English and
Russian languages, both texts being equally authentic.
FOR THE UNITED STATES
OF AMERICA:
Richard Nixon
President of the United States
of America
FOR THE UNION OF SOVIET
SOCIALIST REPUBLICS:
N. V. N.V. Podgorny
Chairman of the Presidium of the
Supreme Soviet of the U.S.S.R.
89
-------
TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
1. REPORT NO.
EPA-600/3-79-015
2.
4. TITLE AND SUBTITLE
RESULTS OF A JOINT U.S.A./U.S.S.R. HYDRODYNAMIC
AND TRANSPORT MODELING PROJECT
3. RECIPIENT'S ACCESSION" NO.
5. REPORT DATE
February 1979
6. PERFORMING ORGANIZATION CODE
7.AUTHORS) John F> Paulj William L. Richardson,
Alexandr B. Gorstko (Rostov State University), Anton
A. Matveyev (Hydrochemical Institute, Hydromet)
8. PERFORMING ORGANIZATION REPORT NO.
9. PERFORMING ORGANIZATION NAME AND ADDRESS
Large Lakes Research Station
Environmental Research Laboratory-Duluth
Grosse lie, Michigan 48138
10. PROGRAM ELEMENT NO.
1BA769
11. CONTRACT/GRANT NO.
12. SPONSORING AGENCY NAME AND ADDRESS
Environmental Research Laboratory - Duluth, MN
Office of Research and Development
U.S. Environmental Protection Agency
Duluth, Minnesota 55804
13. TYPE OF REPORT AND PERIOD COVERED
Final
14. SPONSORING AGENCY CODE
EPA/600/03
15.SUPPLEMENTARY NOTES Performed as part of project 02.02-12 (Water Quality in Lakes
and Estuaries) of U.S.A./U.S.S.R. Environmental Agreement. Appendices B, C, and D
are bound separately and available from NTIS.
16. ABSTRACT
A joint modeling project with scientists from the U.S.A. and U.S.S.R. has been
accomplished. The three geographical areas investigated include Lake Baikal and
the Sea of Azov in the U.S.S.R. and Saginaw Bay, Lake Huron in the U.S.A. The
modeling approaches ranged from those employing material and mass conservation
to describe water movement to those involving solution of the complete three-
dimensional hydrodynamic equations. The model calculations were compared to
available data and, in all cases, reasonable agreement was obtained.
This report covers a period from May 1977 to December 1977, and work was completed
as of April 1978.
17.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b.lDENTIFIERS/OPEN ENDED TERMS C. COSATI Field/Group
Hydrodynamics
Mathematical models
Circulation
Lakes
Lake Baikal
Sea of Azov
Saginaw Bay
Wind Driven Circulation
U.S.A./U.S.S.R. Environ-
mental Agreement
08/H
20/D
13. DISTRIBUTION STATEMENT
RELEASE TO PUBLIC
19. SECURITY CLASS (ThisReport)
UNCLASSIFIED
21. NO. OF PAGES
102
20. SECURITY CLASS (Thispage)
UNCLASSIFIED
22. PRICE
EPA Form 2220-1 (9-73)
90
i U.S. GOVERNMENT PRINTING OFFICE: 1979-657-060/1601
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