EP A/600/A-96/002
TWO-DIMENSIONAL MODELING OF CURRENT CIRCULATION AND
CONTAMINANT TRANSPORT IN SURFACE WATERS
Mohamed A. Abdelrhman and Edward H. Dettmann, U.S. Environmental Protection Agency,
National Health and Environmental Effects Research Laboratory, Atlantic Ecology Division. 27
Tarzwell Drive, Narragansett, RI 02882.
The main objectives of this paper are to briefly describe and evaluate three different applications
of two-dimensional, depth-averaged, finite-element models for hydrodynamics (RMA2) and
transport (RMA4) ([1] and [2], respectively), which were run using the FastTABS user interface
[3]. Model evaluations are based on the ease and success of performing simulations, calibration,
reproduction of prediction runs, and CPU time. A 190-MHz DEC Alpha 2100 Server was used
to run these applications. The models are used to simulate dynamic flow circulation and transport
in the New Bedford Harbor and Slocum River estuaries, side embayments of Buzzards Bay, MA,
as well as steady-state circulation in Lake Havasu, an in-line impoundment on the Colorado River
in Arizona (Figure 1). The applications included different physical conditions and were used to
address environmental issues in surface waters such as flushing behavior, residence time, salinity
distribution, and origins of different water masses, which may be responsible for observed
contamination. The three applications are briefly presented in the order of their complexity.
Lake Havasu showed signs of contamination by coliform bacteria in the London Bridge Channel
and Thompson Bay (Figure la). The modeling effort focused on defining current circulation
patterns and the origins of water masses entering the channel for selected meteorological
conditions, as a guide to future field sampling. The results will serve to guide future studies to
identify possible areas of coliform loading and transport pathways for these bacteria. Steady-state
conditions were assumed in the Colorado River and Lake Havasu. The finite-element grid
consisted of 1515 quadratic triangular elements with a total of 3300 nodes. Hydrodynamic
simulations identified circulation patterns in the lake for a wet summer season with 15,000 cfs
flow and a dry winter season with flow of 6,000 cfs during calm winds. Wind effects on
circulation were simulated for prevailing southerly summer winds of 10 mph and northwesterly
winter winds of 17.3 mph. Figure la shows summer circulation during prevailing southerly
winds. Water masses along the northern shore of The Island and from the middle region of the
lake entered the London Bridge Channel during windy periods, while during calm periods only
water flowing along the eastern boundary entered the channel. These steady-state simulations of
the hydrodynamic model were easy to perform and converged to the solutions in 27 seconds of
CPU time [4].
The New Bedford Harbor (NBH) estuary displays stressed ecological conditions due to a heavily
populated and industrialized watershed. The region north of Rt. 1-195 (Figure lb) has elevated
levels of PCBs and has been designated as a Superfund site. Tidal flushing, salinity distribution
and velocity field were simulated [5] as part of an in-progress multidisciplinary study of the
effect of multiple stressors on estuarine ecosystems. A finite-element grid was constructed with
a total number of 1076 quadratic triangular and quadrilateral elements including 3194 nodes.
Tidal flushing was calculated for 9 tidal cycles during extreme spring and neap tidal conditions.
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The NBH was treated as a vertically well-mixed estuary during the simulation period.
Hydrodynamic results were calibrated using field observations of water surface elevation and
flow velocity. The model grid was refined a few times to avoid model instabilities and obtain
successful calibration results. Transport simulations were calibrated using observations from a
dye study. For the median freshwater inflow rate of 0.54 m3/s, freshwater residence time varied
from 2.5 days for spring tide to 3.5 days for neap tide during calm wind conditions. Figure lb
shows the simulated dye distribution 9 spring tidal cycles (112 hr.) after tagging the estuary north
of the hurricane barrier with 100 ppb of a conservative tracer. The area north of Rt. 1-195 had
the poorest flushing behavior, as indicated by maintainance of the highest concentrations during
the flushing simulation. These results are being used with observed ecological data to evaluate
effects of anthropogenic stressors. The CPU times for the hydrodynamic and transport simulations
for 9 tidal cycles were 58.4 and 5.3 minutes, respectively, with a time step of 30 minutes.
The Slocum River estuary was selected as a less-stressed reference system for NBH during the
ecological study mentioned above. Tidal flushing, salinity distribution and current velocities were
simulated [6] to aid evaluation of ecosystem health under natural stresses (e.g., salinity, flushing
behavior, etc.). This estuary has extended tidal flats, and model boundaries change location as
a result of wetting and drying during tidal flooding and ebbing. Moreover, a complex sand bar
system is exposed at the mouth of the estuary during low tidal stages. This restricts flow out of
the estuary, causing a delay of approximately two hours in the time of low tide inside the system.
A finite-element grid of 1632 quadratic triangular and quadrilateral elements with a total of 4775
nodes was used for model simulations. The models treated the moving boundary problem by
excluding or adding elements to the solution domain according to water surface elevation. This
process triggered instabilities in the hydrodynamic model and mass loss in the transport model
which were hard to control. The time step was reduced from 30 minutes to 15 minutes and
extensive grid refinements were tried, but did not always control model instabilities. This problem
was addressed by allowing gradual wetting and drying of elements by assuming a linear
relationship between water surface elevation and water coverage of an element at low water
levels (referred to as "element porosity"). This technique reduced abrupt changes in the solution
domain, and improved mass conservation. The model became stable for many run conditions, and
calibration of the hydrodynamic model was performed using field measurements of water surface
elevation for a full tidal cycle. Calibration of the transport model was performed using field
measurements of salinity along the length of the estuary at slack high tide. The hydrodynamic
and transport models simulated a period of 9 tidal cycles prior to the field survey of salinity,
using field measurements of freshwater inflow and predicted tide elevations from NOAA tide
tables. Freshwater residence time was 4.07 days and 5.31 days for spring and neap tidal
conditions, respectively, with a median freshwater inflow of 0.7 m3/s. Figure lc presents the
distribution of salinity during slack ebb of a spring tide. CPU times for 112 hr. of simulation
(time step = 15 min.) were 262 and 16 minutes for the hydrodynamic and transport simulations,
respectively.
The RMA2 and RMA4 models are suitable for use by scientists and engineers with some
modeling background. Application of the depth-averaged finite element models for steady-state
conditions in Lake Havasu was direct, easy, and satisfactory. After a few trials and minor grid
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refinements, the application to the dynamic conditions in NBH, which had fixed boundaries, was
successful and calibration was satisfactory with a model time step of 30 minutes. The application
to the Slocum River estuary was much more difficult because of model instability triggered by
and mass loss arising during wetting and drying of elements. This proved to be a particularly
difficult problem in regions with a steep water surface slope. Grid refinement and reduction of
simulation time step did not always eliminate model instability, which was generally alleviated
by use of an algorithm simulating gradual wetting and drying of individual elements. Such
stability problems are commonly encountered with moving boundary problems, and indicate the
need for further development of algorithms for smooth handling of such applications.
The user interface available for RMA2 [3] permits screen-based grid generation and specification
of input data, screen-based editing of the grid and input data, as well as graphical viewing of
simulation results, and is quite convenient. The user interface for RMA4 does not allow for
screen-based input or editing of input data, but does permit graphical viewing of model output.
For applications with the number of grid nodes used in these applications, run times on 486-based
personal computers were quite slow, making early phases of the work described here tedious, but
run times on the DEC Alpha 2100 and comparable work stations are fast enough for convenient
model use. Brief theoretical basis with general mass and momentum conservation equations are
included in model documentation [3], users must refer to other documents (e.g., [1] and [2]) to
ascertain that physical processes relevant to their application are included in the models. The
limitations of two-dimensional models in describing vertical variations due to wind forcing and
buoyancy (density variation) effects should not be underestimated. Three-dimensional models are
better suited to such cases. The transport model implements the advection-diffusion equation with
sink-source and first-order decay terms. More sophisticated water quality and contaminant
processes are not treated by the model. Robustness of these models will be tested in future
applications, which may include coupling to water quality and ecological models for use on
advanced computers.
References:
1.	King, I.P., 1988. RMA2 - A Two Dimensional Finite Element Model for Flow in
Estuaries and Streams, Version 4.2, Resource Management Associates, Lafayette, CA.
2.	King, I.P., and R.R. Rachiele, 1989. RMA4 - A Two Dimensional Finite Element Water
Quality Model, Version 3.0, Resource Management Associates, Lafayette, CA
3.	BOSS International, 1993. BOSS FastTABS, Hydrodynamic Modeling Reference
Manual, BOSS Corporation, Madison, WI.
4.	Abdelrhman, M.A., 1994. "Preliminary Modeling of Current Circulation in Lake Havasu,
Colorado River, Arizona-California," Draft Report Submitted to USEPA Region DC,
Science Applications International Corporation, Narragansett, RI.
5.	Abdelrhman, M.A., and E.H. Dettmann, In preparation a. "Modeling of Current
Circulation, Residence Time, and Salinity Distribution in New Bedford Harbor,
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Massachusetts," Draft U.S. Environmental Protection Agency Report, Environmental
Research Laboratory, Narraganssett, RI.
6. Abdelrhman, M.A., and E.H. Dettmann, In preparation b. "Modeling of Current
Circulation, Residence Time, and Salinity Distribution in Slocum River, Massachusetts,"
Draft U.S. Environmental Protection Agency Report, Environmental Research
Laboratory, Narraganssett, RI.
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1 km
1 km
1 km
0^02
7.5?
01 0*6,
London Br.
, Channel
MyjL Thompson
Bay
6.0*
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Hurricane Barrier
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Figure I: Sample simulation results: (a) current vectors and velocity contours (fps) in Lake Havasu during prevailing summertime
winds, (b) dye distribution (ppb) in New Bedford Harbor at high tide 9 tidal cycles after tagging with a uniform concentration of 100
ppb, and (c) salinity distribution (parts per thousand) in the Slocum River at low tide.
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TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
1 REPORT NO.
EPA/600/A-96/002
2.
3. RECI
4, TITLE AND SUBTITLE
TWO-DIMENSIONAL MODELING OF CURRENT CIRCULATION AND
CONTAMINANT TRANSPORT IN SURFACE WATERS
5. REPORT DATE
6. PERFORMING ORGANIZATION CODE
7. AUTHORIS)
Mohamed A. Abdelrhman arid Edward H. Dettmann
8, PERFORMING ORGANIZATION REPORT NO,
NHEERL-NAR-1741
9. PERFORMING ORGANIZATION NAME AND ADDRESS
US EPA National Health and Environmental Effects
Research Laboratory-Atlantic Ecology Division
27 Tarzwell Drive
Narragansett, RI 02882
10. PROGRAM ELEMENT NO.
11. CONTRACT/GRANT NO.
12. SPONSORING AGENCY NAME AND ADDRESS
13. TYPE OF REPORT AND PERIOD COVERED
Peer Prnrpprli rinc;
14. SPONSORING AGENCY CODE
15. SUPPLEMENTARY NOTES
Proceedings of EPA Workshop on Next Generation of Environmental Models Computation
Methods. Bay City, MI 8/7-9/95
16. ABSTRACT
The main objectives of this paper are to briefly describe and evaluate three different applications
of two-dimensional, depth-averaged, finite-element models for hydrodynamics (RMA2) and
transport (RMA4) ([1] and [2], respectively), which were run using the FastTABS user interface
[3]. Model evaluations are based on the ease and success of performing simulations, calibration,
reproduction of prediction runs, and CPU time. A 190-MHz DEC Alpha 2ICO Server was used
to run these applications. The models are used to simulate dynamic flow circulation and transport
in the New Bedford Harbor and Slocum River estuaries, side embayments of Buzzards Bay, MA,
as well as steady-state circulation in Lake Havasu, an in-line impoundment on the Colorado River
in Arizona (Figure 1). The applications included different physical conditions and were used to
address environmental issues in surface waters such as flushing behavior, residence time, salinity
distribution, and origins of different water masses, which may be responsible for observed
contamination. The three applications are briefly presented in the order of their complexity.
17.
KEY WORDS AND DOCUMENT ANALYSIS
a. DESCRIPTORS
b. IDENTIF IE RS/OPEN ENDED TERMS
c. COSATI Field/Group
Models
two-dimensional
current circulation
contaminant transport
surface waters
hydrodynamics
New Bedford Harbor, MA


18. DISTRIBUTION STATEMENT
RELEASE TO PUBLIC
19. SECURITY CLASS (This Report)
UNCIARRTFTED
21. NO. OF PAGES
5
20. SECURITY CLASS (This page)
IIMPI ARRTFTFn
22. PRICE
EPA Form 2220-1 (R#v. 4-77) previous edition is obsolete

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