U.S. Department of the Interior 

U.S. Geological Survey 

A Two-Dimensional Hydrodynamic


Model of the St. Clair–Detroit 


River Waterway in the Great 


Lakes Basin


By DAVID J. HOLTSCHLAG, and 


JOHN A. KOSCHIK, Detroit District, U.S. Army Corps of Engineers


Water-Resources Investigations Report 01-4236 

Prepared in cooperation with the 


MICHIGAN DEPARTMENT OF ENVIRONMENTAL QUALITY, 


SOURCE WATER ASSESSMENT PROGRAM AND 


DETROIT WATER AND SEWERAGE DEPARTMENT


Lansing, Michigan


2002

U.S. DEPARTMENT OF THE INTERIOR 

GALE A. NORTON, Secretary 

U.S. GEOLOGICAL SURVEY 

Charles G. Groat, Director 

The use of trade or product names in this report is for identification 

purposes only and does not constitute endorsement by the 

U.S. Government. 

For additional information write: Copies of this report can be purchased 

District Chief U.S. Geological Survey


U.S. Geological Survey Branch of Information Services


6520 Mercantile Way, Suite 5 Box 25286


Lansing, MI 48911-5991 Denver, CO 80225-0286

CONTENTS 

Abstract .............................................................................................................................................................................

Introduction .......................................................................................................................................................................

Location of Study Area ...........................................................................................................................................

Purpose and Scope ..................................................................................................................................................

Previous Studies ......................................................................................................................................................

Acknowledgments ...................................................................................................................................................

Implementation of the Hydrodynamic Model...................................................................................................................

RMA2 Code ............................................................................................................................................................

Applications and Capabilities........................................................................................................................

Equations Governing Two-Dimensional Surface-Water Flow ......................................................................

Form of the Equations .........................................................................................................................

Discretization and Solution of the Equations......................................................................................

Surface-Water Modeling System...................................................................................................................

Conceptual Model as a Feature Map.......................................................................................................................

Geographic Data............................................................................................................................................

Boundary Conditions.....................................................................................................................................

Geometry, Continuity-Check Lines...............................................................................................................

Material Zones...............................................................................................................................................

Numerical Model as Finite-Element Mesh.............................................................................................................

Bathymetry Data ...........................................................................................................................................

Editing the Finite-Element Mesh ..................................................................................................................

Curving Element Edges.................................................................................................................................

Renumbering the Mesh .................................................................................................................................

Model Parameters..........................................................................................................................................

Calibration of the Hydrodynamic Model ..........................................................................................................................

Parameter Estimation Code .....................................................................................................................................

Calibration Scenarios ..............................................................................................................................................

Boundary Conditions...............................................................................................................................................

Expected Flows and Water-Levels used in Calibration ...........................................................................................

Parameter Estimation Results..................................................................................................................................

Parameters Estimates and Uncertainties........................................................................................................

Parameter Sensitivities ..................................................................................................................................

Simulated and Expected Flows and Water Levels.............................................................................................................

Model Development Needs and Limitations.....................................................................................................................

Summary and Conclusions................................................................................................................................................

References Cited ...............................................................................................................................................................

Appendix A. UNI file used in UCODE parameter estimation analysis of the 


St. Clair–Detroit River model..............................................................................................................................

Appendix B. PREPARE input file used in UCODE parameter estimation analysis 


of the St. Clair–Detroit River model ...................................................................................................................

Appendix C. Example of TEMPLATE files used to generate control files in the


UCODE parameter estimation analysis of the St. Clair–Detroit River model....................................................

Appendix D. Excerpt from EXTRACT file used to process output files from UCODE


parameter estimation analysis of the St. Clair–Detroit River model...................................................................

Con
FIGURES 

1. Map showing St. Clair–Detroit River study area...............................................................................................

2. Schematic of boundary conditions for the St. Clair–Detroit River Waterway...................................................

3,4. Maps showing:


3. Locations of flow-measurement cross sections and water-level gaging stations on St. Clair River .........

4. Locations of flow-measurement cross sections and water-level gaging stations on Detroit River ...........

5–16. Graphs showing:


5. Water levels during flow-measurement events on St. Clair River and selected calibration scenarios ......

6.	 Estimated Manning’s n values and 95-percent confidence intervals for 25 material zones in the


St. Clair–Detroit River Waterway..............................................................................................................

7. Composite scaled sensitivities for Manning’s n parameters in corresponding material zones .................

8.	 Composite scaled sensitivities of flows at measurement cross sections on St. Clair and


Detroit Rivers ............................................................................................................................................

9.	 Composite scaled sensitivities of water levels at selected gaging stations on the St. Clair–Detroit


River Waterway .........................................................................................................................................

10. Relation between expected and simulated flows on St. Clair River for seven calibration scenarios ........

11.	 Relation between expected and simulated water levels on St. Clair River and Lake St. Clair for 


seven calibration scenarios........................................................................................................................

12. Relation between expected and simulated flows on Detroit River for seven calibration scenarios ..........

13.	 Relation between expected and simulated water levels on Detroit River for seven calibration 


scenarios ....................................................................................................................................................

14. Distribution of flow residuals by calibration scenario...............................................................................

15. Distribution of water-level residuals by calibration scenario....................................................................

16, 17. Box plots showing:


16. Distribution of flow residuals by flow-measurement cross section...........................................................

17. Distribution of water-level residuals by gaging station, St. Clair–Detroit Waterway ...............................

TABLES 

1. Water-level gaging stations on the St. Clair–Detroit River Waterway................................................................

2.	 Boundary specifications for calibration scenarios near the headwaters of St. Clair River and near the


mouth of Detroit River........................................................................................................................................

3. Selected local inflows to the St. Clair–Detroit River Waterway .........................................................................

4. Expected flows and standard errors for scenarios used in model calibration .....................................................

5. Expected water levels and standard errors for scenarios used in model calibration...........................................

IV Contents 
CONVERSION FACTORS, ABBREVIATIONS, AND VERTICAL DATUM 

CONVERSION FACTORS 

Multiply By To obtain 

acre (ac) 0.4047 hectare 

cubic foot per second (ft3/s) 0.02832 cubic meter per second 

gallon (gal) 3.785 liter 

inches (in.) 25.4 millimeters 

International foot (ft) 0.3048 (exactly) meters 

mile (mi) 1.609 kilometer 

square mile (mi2) 2.590 square kilometer 

Temperature in degrees Celsius ( ̊C) can be converted to degrees Fahrenheit ( ̊F)


by the following equation:


 ̊C = ( ̊F-32)/1.8


VERTICAL DATUM 

The vertical datum currently used throughout the Great Lakes is the International Great Lakes Datum 

of 1985 (IGLD 1985), although references to the earlier datum of 1955 are still common. This datum 

is a dynamic height system for measuring elevation, which varies with the local gravitational force, 

rather than an orthometric system, which provides an absolute distance above a fixed point. The primary reason for adopting a dynamic height system within the Great Lakes is to provide an accurate 

measurement of potential hydraulic head. The reference zero for IGLD (1985) is a tide gage at 

Rimouski, Quebec, which is located near the outlet of the Great Lakes–St. Lawrence River system. 

The mean water level at the Rimouski, Quebec, gage approximates mean sea level. 

Con
A Two-Dimensional Hydrodynamic


Model of the St. Clair–Detroit River 


Waterway in the Great Lakes Basin


By David J. Holtschlag, and John A. Koschik, 

Detroit District, U.S. Army Corps of Engineers 

Abstract 

The St. Clair–Detroit River Waterway connects Lake Huron with Lake Erie in the Great 

Lakes basin to form part of the international 

boundary between the United States and Canada. 

A two-dimensional hydrodynamic model is developed to compute flow velocities and water levels 

as part of a source-water assessment of public 

water intakes. The model, which uses the generalized finite-element code RMA2, discretizes the 

waterway into a mesh formed by 13,783 quadratic 

elements defined by 42,936 nodes. Seven steadystate scenarios are used to calibrate the model by 

adjusting parameters associated with channel 

roughness in 25 material zones in sub-areas of the 

waterway. An inverse modeling code is used to 

systematically adjust model parameters and to 

determine their associated uncertainty by use of 

nonlinear regression. Calibration results show 

close agreement between simulated and expected 

flows in major channels and water levels at gaging 

stations. Sensitivity analyses describe the amount 

of information available to estimate individual 

model parameters, and quantify the utility of flow 

measurements at selected cross sections and 

water-level measurements at gaging stations. Further data collection, model calibration analysis, 

and grid refinements are planned to assess and 

enhance two-dimensional flow simulation capabilities describing the horizontal flow distributions 

in St. Clair and Detroit Rivers and circulation 

patterns in Lake St. Clair. 

INTRODUCTION 

The Michigan Department of Environme

Quality (MDEQ) Source Water Assessment Pro

(SWAP), with the cooperation of the Detroit Wa

and Sewerage Department (DWSD) is assessing 

vulnerability of public water intakes to contami

on the St. Clair–Detroit River Waterway. Publi

intakes on the waterway provide water to about 

4.5 million people in the Detroit, Michigan area

as well as about 2 million others in Michigan an

Canada. As part of this assessment, the U.S. G

cal Survey (USGS) and the Detroit District of th

Army Corps of Engineers (USACE) are develop

a two-dimensional hydrodynamic model of the 

waterway. 

This report facilitates the implementation 

SWAP by documenting the initial implementati

calibration of a hydrodynamic model, which pro

generalized description of advective movement 

waterway. Model hydrodynamics will be comb

with field characterizations of stochastic disper

characteristics, which are to be determined from 

ing buoy studies (Holtschlag and Aichele, 2001

implement a particle-tracking analysis. Particle

tracking analysis is a computer simulation techn

that represents the movement of hypothetical pa

in the water. Particle-tracking simulations runn

ward in time will be used to identify areas likel

impacted by downstream movement of constitu

from point sources; simulations running backw

in time will be used to identify areas likely to b

tributing to public water intakes or other areas o

concern. 

Introd
Location of Study Area 

St. Clair River, Lake St. Clair, and Detroit River 

form a waterway that is part of the international boundary between the United States and Canada (fig. 1). The 

waterway, which connects Lake Huron with Lake Erie, 

is a major navigational and recreational resource of the 

Great Lakes basin. St. Clair River (the upper connecting channel) extends about 39 mi from its headwaters 

at the outlet of Lake Huron near Port Huron, Michigan, 

to an extensive delta area. Throughout its length, water 

levels (water-surface elevations) decrease about 5 ft as 

the river discharges an average of 183,000 ft3/s from a 

drainage area of about 222,400 mi2. Local tributaries 

to St. Clair River include Black River at Port Huron, 

Michigan, Pine River at St. Clair, Michigan, and Belle 

River at Marine City, Michigan. Lake St. Clair 

receives water from St. Clair River, and lesser amounts 

from Clinton River in Michigan and the Thames and 

Sydenham Rivers in Ontario, Canada. Along the 25-ft 

deep navigational channel, the lake has a length of 

35 mi. The lake’s round shape, with a surface area of 

430 mi2, and shallow depths that average about 11 ft, 

make it equally susceptible to winds from all directions. Detroit River (the lower connecting channel) 

receives water from Lake St. Clair and lesser amounts 

from River Rouge in Michigan, where it flows 32 mi 

to Lake Erie. Water levels fall about 3 ft within 

Detroit River, which has an average flow of about 

187,000 ft3/s. 

Purpose and Scope 

As part of the Source Water Assessment Program 

(SWAP) of the Michigan Department of Environmental 

Quality (MDEQ), this report documents the initial 

implementation and calibration of a two-dimensional 

hydrodynamic model of the St. Clair–Detroit River 

Waterway. The model extends from a National Oceanic and Atmospheric Administration (NOAA) gaging 

station at Fort Gratiot near Port Huron, Michigan, at 

the headwaters of St. Clair River on Lake Huron, to a 

Canadian Hydrographic Service (CHS) gage at Bar 

Point, Ontario, at the mouth of Detroit River on Lake 

Erie. 

In this report, model implementation and calibration efforts have focused on reproducing flows (total 

discharges) in major branches formed by numerous 

islands and dikes in the waterway and by matching 

water levels near gaging stations. Additional fie

collection, analysis, and model calibration are r

to assess and enhance the model’s ability to rep

horizontal velocity distributions within channel

St. Clair and Detroit Rivers and circulation patt

Lake St. Clair. 

The model developed in this report is bas

a two-dimensional approximation to a flow syst

that may exhibit three-dimensional flow charact

particularly near abrupt changes in flow directio

or depth. Further, the model is intended for app

tions involving the far field problem in which v

accelerations are negligible and velocity vector

ally point in the same direction over the entire d

of the water column at any instant of time. The 

model assumes a homogeneous fluid with a free 

face. Thus, simulations during periods of temp

stratification or ice cover would be of uncertain 

ability. The Coriolis force, an inertial force cau

by the earth’s rotation, was not included in mod

computations at this stage in model implementa

Previous Studies 

The U.S. Army Corps of Engineers (USA

Waterway Experiment Station (WES) in Vicksb

Mississippi, developed a prototype two-dimens

model of the St. Clair–Detroit River Waterway 

Detroit District USACE (Ron Heath, USACE-W

written commun., 1999). The resulting model w

modified and adapted for use in a joint study by 

Environment Canada and the Detroit District U

to assess the effects of encroachments on water 

in St. Clair and Detroit Rivers (Aaron Thompso

Environment Canada, written commun., July 20

Tsanis, Shen, and Venkatesh (1996) implement

RMA2 on St. Clair and Detroit Rivers; results in

that simulated currents closely matched field m

ments of drifting buoys. Williamson, Scott, and 

(1997) developed a two-dimensional finite-elem

model of the St. Clair–Detroit River system for 

Canadian Coast Guard for water-level predictio

assessment of structures in the river systems. S

and others (1989) compared currents measured 

Lake St. Clair with particle tracking results com

based on two-dimensional hydrodynamic mode

simulations. 

2 A Two-Dimensional Hydrodynamic Model of the St. Clair–Detroit River Waterway in the Great Lakes Basin 
83o 82o45’ 

43o 

42o 

International 

boundary 

0 5 10 MILES 

0 5 0 15 KILOMETERS 

LAKE HURON 

MONROE 

Windsor 

Detroit 

LAKE ERIE 

St. Clair 

River 

Detroit 

River 

Lake St. Clair 

WAYNE 

ONTARIO 

ST. CLAIR LAPEER 

OAKLAND MACOMB 

Mt. Clemens 

Pontiac 

Lapeer 

Sarnia Port Huron 

Bar Point 

CANADA 

UNITED STATES 

��� ���

��� ���

��� ���

Thames River 

Sydenham 

Clinton River

River 

St. Clair Shores 

gaging station 

1

Base from U.S. Geological Survey 1:500,000 map, 1970. 

EXPLANATION 

INTERNATIONAL BOUNDARY 

U.S. COUNTY BOUNDARY 

CITY CENTER 

GAGING STATION 

Figure 1. St. Clair–Detroit River study area. 

LAKE MICHIGAN 

LAKE

HURON 

LAKE SUPERIOR 

MICHIGAN MICHIGAN 

CANADA 

Lake 

St. Clair 

STUDY AREA 

LAKE 

ERIE USA 

90o 

83o 47o 

42o 

Introd
Acknowledgments 

A binational technical workgroup provided suggestions, recommendations, and data that facilitated 

model implementation. Workgroup members and 

associates included Bradley Brogren, Michigan 

Department of Environmental Quality, Source Water 

Assessment Program; Gang Song, Detroit Water and 

Sewerage Department; Syed Moin, Aaron Thompson, 

and Ralph Moulton of Environment Canada, Canada 

Centre for Inland Waters; Jeffrey Oyler, National 

Oceanic and Atmospheric Administration, National 

Ocean Service; Ronald Solvason, Canadian 

Hydrographic Service; Saad Jasim, Windsor Utilities 

Commission; and Stanley Reitsma, Great Lakes 

Institute for Environmental Research, University of 

Windsor. Eileen Poeter, Colorado School of Mines, 

Department of Geology and Geological Engineering, 

provided generous technical assistance with the implementation of UCODE (Poeter and Hill, 1998). Brian 

Link and Lisa Taylor of NOAA provided bathymetry 

data for the model. 

IMPLEMENTATION OF THE 

HYDRODYNAMIC MODEL 

In this report, implementation of the hydrodynamic model refers to the process of creating input files 

that describe the geometry, bathymetry, hydraulic characteristic, and boundary conditions of the St. Clair– 

Detroit River Waterway for simulation by use of the 

generalized hydrodynamic model RMA2. This process 

includes: (1) delineation of the St. Clair–Detroit River 

Waterway and discretization into finite elements, 

(2) specification of type and location of boundary conditions needed to simulate flow, (3) initial grouping of 

elements into material zones thought likely to have 

similar hydraulic properties, (4) estimation of channel 

and lake bottom elevations from scattered bathymetry 

data, and (5) editing and manipulation of the mesh to 

ensure an efficient and accurate simulation. 

RMA2 Code 

RMA2 (Donnell and others, 2000) is a ge

ized computer code for two-dimensional hydrod

namic simulation. It computes depth-averaged 

horizontal velocity components and water level

subcritical, free-surface flow. RMA2 implemen

finite-element solution of the Reynolds form of 

Navier-Stokes equation for turbulent flows. Fri

calculated with the Manning’s equation, and ed

cosity parameters are used to control numerical 

ity and describe energy losses associated with v

and turbulence. U.S. Army Corps of Engineers 

(USACE) Waterway Experiment Station (WES

tains RMA2 in the public domain. A compiled 

of RMA2 version 4.35 (Donnell and others, 199

was dimensioned for a maximum of 165,000 no

55,000 elements was used in the implementatio

model to accommodate 84 continuity check line

to sum simulated flow at selected locations. 

Applications and 

Capabilities 

RMA2 is a general-purpose code designe

solve the far-field problem in which vertical acc

tions are negligible and velocity vectors have si

magnitude and direction throughout the depth o

water column at any instant of time. RMA2 is 

used (Soong and Bhowmik, 1993; Hauck, 1992

Deering, 1990) for two-dimensional steady stat

transient simulations of flows and water levels a

islands in rivers, reservoirs, and estuaries. The 

assumes a vertically homogeneous fluid and no 

stratification. 

Equations Governing 

Two-Dimensional 

Surface-Water Flow 

Form of the Equations 

RMA2 solves the depth-integrated equati

fluid mass and momentum conservation in two 

zontal directions (Donnell and others, 2000, p. 3

continuous forms of these equations are: 

4 A Two-Dimensional Hydrodynamic Model of the St. Clair–Detroit River Waterway in the Great Lakes Basin 
(1) 

(2) 

(3) 

where 

h = depth, 

u,v = velocities in the Cartesian directions, 

x,y,t = Cartesian coordinates and time,

ρ = density of fluid, 

E.. = eddy viscosity parameter, 

for xx = normal direction on x axis surface, 

for yy = normal direction on y axis surface, 

for xy and yx = shear direction on each 

surface, 

g = acceleration due to gravity, 

a = elevation of channel or lakebed bottom, 

n = Manning’s n parameter quantifying 

roughness characteristics, 

1.486 = conversion from SI (metric) to English units, ζ = empirical wind shear coefficient, 

Va = wind speed, 

Ψ = wind direction, 

= rate of earth’s angular rotation, and 

= local latitude. 

ω 

φ 

Discretization and 

Solution of the Equations 

In this report, the St. Clair–Detroit River 

Waterway is discretized into a set of piecewise continuous functions described by finite elements. This 

discretization is used to approximate the contin

variation of flow velocities and water levels des

by the governing equations. The two-dimensio

ments used exclusively in the model are either t

lar or quadrilateral elements defined by three or 

corner nodes, respectively. In addition to corner 

all elements contain midside nodes to improve t

ity to model curved boundaries. With the addit

midside nodes, quadratic interpolation of flow v

ties throughout the element also is possible. 

Equations (1), (2), and (3) are solved by th

element method using the Galerkin method of 

weighted residuals (Donnell and others, 2000, p

Shape functions, used for interpolation of flow 

ties and water depths computed at the nodes to 

areas in the element, are quadratic for velocity 

linear for depth. Integration in space is perform

Gaussian integration. Derivatives in time are ap

mated by nonlinear finite differences. Flows an

levels are assumed to vary over each time interv

the form: 

which is differentiated with respect to time, and 

finite difference form. Letters A, B, and C are c

stants. 

The solution is fully implicit and the set o

simultaneous equations is solved by Newton-Ra

nonlinear iteration (Donnell and others, 2000, p

Generally, less than eight iterations are required 

obtain a valid solution, depending upon the diff

between the initial conditions and the final solu

and the specified convergence criteria. The com

code executes the solution by means of a front-

solver, which assembles a portion of the matrix 

solves it before assembling the next portion of t

matrix. 

Surface-Water Modeling 

System 

The Surface-Water Modeling System (SM

computer program for pre- and post-processing 

selected surface-water models, including RMA

(Environmental Modeling Research Laboratory, 

Implementation of the Hydrodynamic 
SMS has three primary modules needed to develop a 

hydrodynamic model for simulation with RMA2. 

These include the Map Module, the Mesh Module, and 

the Scatter Point Module. The modules were used in 

turn to develop a geometry file describing the location 

of nodes that define the size and shape of finite elements and the hydraulic properties of elements needed 

for flow computations. 

Conceptual Model as a 

Feature Map 

The conceptual model of flow in the waterway 

synthesizes available geographic and hydraulic data 

into a form that is suitable to model building. Principally, the conceptual model describes the geometry of 

the waterway and the boundaries of the flow-system. 

The conceptual model was developed within the Map 

Module of the SMS by use of feature objects. The feature map describing the conceptual model was used to 

generate the finite element mesh of the numerical 

model needed for flow computations. 

Geographic Data 

The geometry of the waterway was delineated 

based on the channel configurations shown on recreational charts of Detroit River, Lake St. Clair, and St. 

Clair River (National Oceanic and Atmospheric 

Administration, 1999). Shoreline information on the 

charts was integrated into the conceptual model by 

scanning portions of the charts to create electronic 

image files. These images files, in Tagged Image File 

Format (TIFF), were geographically referenced to the 

southern zone (2113) of the Michigan State Plane 

Coordinate System, North American Datum of 1983 

(MSPCS 83) by use of latitude and longitude tick 

marks shown on the charts. The TIFF files provided a 

background upon which feature objects were digitized 

to represent the channel and shoreline within the Map 

Module. 

Feature objects include nodes, vertices, arcs, and 

polygons. A feature arc is a line segment formed by 

end points referred to as feature nodes and intermediate 

points called feature vertices. Generally, two longitudinal arcs of approximately equal lengths were used to 

describe opposite sides of the shoreline. After initial 

positioning needed to delineate the shoreline meanders, 

the features vertices were automatically redistributed to 

improve the uniformity of spacing and to provid

nearly equal number of vertices on either side o

reach. Upper and lower limits of the reach wer

nated by defining transverse arcs that connected 

upstream and downstream nodes of the longitud

arcs. Feature vertices were automatically distri

across the transverse arcs. Generally, the distan

between vertices in the transverse arcs were spa

about one half the distances of vertices along th

tudinal arcs to provide detail in describing the v

ity of cross channel velocities. For uniform rea

the number of vertices at either end of the reach 

the same unless changes were needed to accom

an island or tributary. The arcs describing the r

were joined to form feature polygons, defined a

the perimeter by the locations of feature nodes 

vertices. 

Polygons were assigned a mesh generatio

method and hydraulic properties. Together with 

distribution of feature nodes and vertices, the m

generation method controls the initial placemen

nodes that delineate finite elements inside the p

gons. Different meshing methods produce diffe

types of elements and different arrangements of 

In this report, the two mesh generation methods 

were the coons patch and adaptive tessellation. 

A coons patch requires that the surroundi

polygon contain either three or four arcs, and w

method commonly applied to triangular and qu

eral polygons defining the connecting channels

coons patch produces a highly regular mesh pat

that initially contains either triangular or quadri

elements. In contrast, adaptive tessellation is ap

ble to a polygon that contains any number of arc

thus adaptable to irregularly shaped polygons, l

those defining Lake St. Clair. Tessellation initia

forms a dense mesh of triangular elements. Ma

the triangular elements are automatically combi

form quadrilateral elements, which provide a m

concise mesh, and provides for faster solutions 

greater numerically stability. The mesh resultin

adaptive tessellation contains a mixture of trian

and quadratic elements that has a less regular ap

ance than elements in a coons patch. 

All polygons were assigned an initial valu

for Manning’s n, a hydraulic parameter that des

channel roughness in equations (1) and (2). Th

value was selected because it was thought to be 

the plausible range of likely Manning’s n value

Higher n values indicate greater friction losses 

6 A Two-Dimensional Hydrodynamic Model of the St. Clair–Detroit River Waterway in the Great Lakes Basin 
u d --------------------

result in reduced flow or higher water levels within a 

particular channel of the waterway. This value was 

modified during the calibration phase to improve the 

match between expected and simulated flows and water 

levels. 

In addition to channel roughness, each polygon 

was initially assigned a starting value for eddy viscosity, E in equations (1) and (2). Eddy viscosity controls 

both the stability of the numerical solution and the distribution of velocities across the channel. In particular, 

the Galerkin method of weighted residuals used by 

RMA2 uses the eddy viscosity terms to stabilize the 

numerical solution (Donnell and others, 2000, p. 46). 

Values of eddy viscosity that are too small allow 

changes in the direction of velocity vectors that are too 

great for the numerical solution to converge. Thus, a 

minimum value of eddy viscosity is required to achieve 

numerical stability. Lower values of eddy viscosity 

allow greater variability in the velocity distribution 

within the waterway. 

In this report, eddy viscosity is assumed to be 

isotropic, that is Exx = Exy = Eyx = Eyy in equations (1) and (2). Further, simulations were started 

with eddy viscosities that were initially assigned based 

on polygon (material type). After these simulations 

had converged, eddy viscosities were reassigned based 

on the assigned Peclet number, P. The Peclet number 

dynamically adjusts the value of E after each model 

iteration based on the computed velocity, size, and fluid 

density of each element. In particular, 

ρ ⋅⋅ x E = P - (5) 

where 

ρ = fluid density, 

u = average elemental velocity, 

dx = length of element in streamwise direction, 

and 

E = eddy viscosity. 

Boundary Conditions 

Boundary conditions (BC) describe hydraulic 

conditions, such as flows and water levels, at the limits 

of the model area, which are constant for steady-state 

simulations and vary with time for transient simulations. Boundary conditions are needed to eliminate the 

constants of integration that arise when numerically 

integrating the governing equations to solve for u, v, 

and h (Equation 1–3) in the interior of the solution 

domain (Donnell and others, 2000, p. 38). In th

report, flow boundaries were used to describe c

tions at the headwaters of St. Clair River near th

gaging station at Fort Gratiot (NOAA station nu

9014098), at selected intervening tributaries, in

Black River, Pine River, Belle River, Clinton R

Sydenham River, Thames River, and River Rou

for the net inflow over Lake St. Clair (fig. 2). A 

level boundary was used to describe the hydrau

dition at the mouth of Detroit River near Bar Po

Ontario, where the Canadian Hydrographic Ser

operates a gaging station. Boundary condition 

tions were defined as an attribute of a feature ar

flow boundaries conditions specified that the flo

direction at the boundary was perpendicular to 

corresponding feature arc. 

Geometry, Continuity-Check 

Lines 

According to Donnell and others (2000, p

RMA2 globally maintains mass (flow) conserva

a weighted residual manner. Locally, Geometry

nuity-Check Lines (GCLs) can be used to check 

apparent mass changes by a different method u

direct integration. Large discrepancies, greater 

percent, between the results of these two metho

cate probable oscillations in the numerical solut

a need to correct large boundary break angles, a

a need to improve model resolution. Large mas

servation discrepancies can lead to difficulty wh

hydrodynamics are used for transport models. 

GCLs were used to integrate simulated ve

in order to compute flow at selected cross sectio

These simulated flows were compared with exp

flows to aid model calibration. To minimize the 

crepancy between inflows specified at the boun

and flows simulated at the GCLs, the GCLs we

ented as nearly perpendicular to flow as possibl

utility SLOPEFIX was applied to curve the land 

water interface, GCLs were extended across the 

way from land to land, and the water-level conve

criterion was set to low value (0.0001 ft). 

Material Zones 

Material zones define sub-areas of the wa

with constant Manning’s n values and Peclet nu

Material zones were formed by grouping contig

polygons within a branch or reach of the waterw

some reaches, for example, two material zones 

Implementation of the Hydrodynamic 
Flow at the headwaters 

of St. Clair River near 

the Fort Gratiot gage, 

Port Huron, Michigan 

Water level at Bar Point, 

Ontario, Canada 

Flow at the mouth of 

Black River near Port 

Huron, Michigan 

Flow at the mouth of 

Pine River near 

St. Clair, Michigan 

Flow at the mouth of 

Belle River near 

Marine City, Michigan 

Flow at the mouth of 

Clinton River near Mount 

Clemens, Michigan 

Net atmospheric and 

ground-water inflow to 

Lake St. Clair 

Flow at the mouth 

of Thames River, 

Ontario, Canada 

Flow 

mouth of 

Sydenham River, 

Chenal Ecarte Ontario, Canada

Johnston 

Channel 

Chenal Ecarte 

Belle River 

Pine River 

Black River 

Lake St. Clair Lake St. Clair 

Thames River 

Sydenham River Sydenham River

Flow at the mouth of 

River Rouge near 

Dearborn, Michigan 

River Rouge 

Clinton River 

Detroit River Detroit River 

St. Clair River St. Clair River 

at the 

Figure 2. Boundary conditions for the St. Clair–Detroit River Waterway. 

8 A Two-Dimensional Hydrodynamic Model of the St. Clair–Detroit River Waterway in the Great Lakes Basin 
designated for the two branches formed on either side 

of an island. This configuration allowed the estimation 

of parameters describing the effective Manning’s n 

values on both branches, based on available flow information for each branch. In reaches without islands, 

material zones joined polygons between gaging stations, so that water-level data could be used to determine the effective Manning’s n values. In all cases, the 

effective Manning’s n values estimated for a material 

zone reflected both the hydraulic roughness of the 

channel, and small discrepancies between model and 

waterway geometry and bathymetry. 

Numerical Model as 

Finite-Element Mesh 

Once all the polygons in the model area were 

delineated, meshing techniques specified, boundary 

conditions described, and material zone assignments 

made, the feature map was converted to a finite element 

mesh. Conversion of the conceptual model created a 

finite element mesh with 42,936 nodes forming 1,773 

triangular elements and 12,010 quadrilateral elements. 

The average size of an element was 0.035 mi2 

(22.4 ac); elements ranged in size from 0.000728 mi2 

(0.466 ac) to 0.241 mi2 (154 ac). Bathymetry data 

were used to estimate channel and lakebed elevations at 

nodes. Finally, the mesh was edited to enhance numerical stability and efficiency, in preparation for model 

calibration. 

Bathymetry Data 

Bathymetry data were obtained from three 

sources. Bathymetry data for St. Clair and Detroit 

Rivers were obtained primarily from a bathymetry 

survey by NOAA in 2000 (Brian Link, NOAA, Great 

Lakes Environmental Research Laboratory, written 

commun., 2000). In this survey, data were generally 

obtained as transects separated by about 328 ft 

(100 m). The data included about 20,900 soundings of 

St. Clair River and 22,700 soundings of Detroit River. 

NOAA provided a preliminary conversion of depths to 

elevations (referenced to IGLD 1985) by analyzing 

water levels at gaging stations during the time of the 

survey. Horizontal coordinates of the soundings were 

converted from UTM (Universal Transverse Mercator) 

Zone 17 meters to MSCPS 83 (Zone 2113) Inte

tional feet by use of the computer program Cor

(U.S. Army Corps of Engineers, 2000). 

Bathymetry data for Lake St. Clair were o

from a compilation of bathymetry surveys cond

by the USACE, NOAA National Ocean Service 

and the Canadian Hydrographic Service (CHS) 

Taylor, NOAA, written commun., 1999). Data 

these surveys include about 119,000 soundings 

St. Clair and distributaries in the St. Clair Delta

from the NOAA 2000 survey were used in area

St. Clair Delta where data from the NOAA 2000 

and earlier surveys of Lake St. Clair overlapped

Finally, about 200 supplementary bathymetry d

points were obtained by use of depth informatio

shown on NOAA recreational charts for localize

where other survey information was sparse. 

In all, about 134,000 bathymetry soundin

used to describe the bathymetry of the St. Clair–

River Waterway. Linear interpolation was used 

pute channel elevations at nodes based on the sc

bathymetry soundings. In linear interpolation, 

soundings are first triangulated to form a tempo

triangular network. Then, nodes are located in 

angular network and elevations at nodes are int

lated from soundings forming the vertices of th

surrounding triangle (Environmental Modeling 

Research Laboratory, 1999, p. 13-6). 

Editing the Finite-Element 

Mesh 

The geometry of the finite-element mesh 

mines the accuracy and stability of RMA2 simul

Elements that were automatically generated fro

feature map did not always have geometric prop

that satisfied critical mesh-quality criteria. The

ria include: (1) a minimum interior angle greate

20 degrees, (2) concave quadrilaterals, (3) chan

adjacent element areas that are less than 50 perc

(4) eight or fewer connecting elements, and a m

mum interior angle 130 degrees. Tools provide

SMS environment were used to identify and co

these deficiencies. 

In some model areas, modifications to the 

map were used to regenerate a mesh that met th

cal mesh-quality criteria. In other areas, mesh-

Implementation of the Hydrodynamic 
tools within the Mesh Module of SMS were used to 

manually correct deficiencies. Mesh editing tools 

include moving nodes, splitting quadrangles, swapping 

diagonal components of split quadrangles, and merging 

triangular elements. When editing was completed, all 

mesh quality criteria were satisfied, except those relating to bathymetry. To conform to the data from the 

bathymetry surveys, node elevations did not always 

produce elements that satisfied the mesh-quality criteria of ambiguous gradient and maximum slope. 

Because of the flow depths generally involved and the 

boundary conditions specified, these deficiencies are 

not expected to degrade the accuracy or stability of 

RMA2 simulations. 

Curving Element Edges 

Prior to release 4.2 of RMA2, mass (flow) losses 

could occur at irregular boundaries of the finite element 

mesh. Although curving (isoperimetric) external 

boundaries are no longer needed to prevent this loss, 

they may be used to improve mesh aesthetics, to add 

length without additional resolution, and to aid in flow 

conservation when RMA2 results are used for transport 

applications (Donnell and others, 2000, p. 11). In this 

report, external boundaries were curved in an attempt 

to improve the apparent flow continuity at GCLs by use 

of the utility program SLOPEFIX (Donnell and others, 

2000, p. 232). SLOPEFIX curves a boundary by 

moving the midside nodes. The utility program was 

used to read an RMA2 geometry file, curve the boundaries, and rewrite the geometry file. The program does 

not curve edges involved with boundary-condition 

assignments tagged as GCLs. The output geometry file 

generated by SLOPEFIX was re-edited to ensure that 

mesh-quality criteria were still satisfied. 

Renumbering the Mesh 

The finite-element mesh represents thousands 

of equations, which if solved simultaneously, could 

cause a computer to run out of memory. Thus, RMA2 

uses an iterative numerical technique to solve the governing partial differential equations. The front width, 

the number of equations in the numerical model’s solution matrix that are assembled simultaneously, determine the size of the matrix that is used by the finite 

element solvers. A smaller front width leads to a 

smaller matrix and more efficient solution. To minimize the front width of the finite-element mesh, the 

mesh was renumbered starting from a node strin

downstream stage boundary on the mouth of De

River. The front width of the model after renum

was 488. 

Model Parameters 

Model parameters are hydraulic characte

of the waterway that are represented in the equa

motion, equations (1) and (2), but that cannot b

sured directly in the field. Instead, values of mo

parameters are inferred from flow and water-lev

In this report Manning’s n values, which nomin

quantify channel roughness or resistance to flow

were the primary model parameters. The effect

Manning’s n values inferred from flow and wat

information were used to describe both the effe

channel roughness and the effects of small disc

cies between the actual and model characterizat

waterway geometry and bathymetry. 

Manning’s n values were assigned to 25 m

zones within the waterway. The material zones 

spond to reaches within the waterway where wa

level or flow data is available to support estimat

the effective Manning’s n values. Thus, flow m

ments were used to infer possibly different effe

Manning’s n values on individual branches arou

major islands because of discrepancies between 

and waterway bathymetries, rather than actual d

ences in channel roughness characteristics. Iden

whether differences in effective Manning’s n va

between material zones are caused by differenc

channel roughness characteristics or small discr

cies between actual and model characterization 

waterway geometry and bathymetry is problem

because both factors affect channel conveyance

determines water-level and flow characteristics. 

Values of channel roughness vary continu

over the model area both spatially and temporal

(Sellinger and Quinn, 2001, and Williamson, Sc

and Lord, 1997). In this report, however, it was 

sary to limit the number of model parameters to 

effective estimation with available data. Eleme

that were thought to have similar roughness cha

istics were grouped together into material zone

where measurements could be used to estimate 

magnitudes and uncertainties. Material zone de

tions and element geometry can be accessed on 

Internet at the URL (Universal Resource Locato

http://mi.water.usgs.gov. 

10 A Two-Dimensional Hydrodynamic Model of the St. Clair–Detroit River Waterway in the Great Lakes Basin 
Eddy viscosity is a second model parameter 

that controls the numerical stability of the solution 

and the variation of velocities through a cross section. 

Eddy viscosity values were dynamically assigned on 

the basis of a uniform Peclet number equal to 15, 

which is within the recommended range of 15 through 

40 (Donnell and others, 2000, p. 48). Peclet numbers 

greater than 20 were found to cause numerical 

instability in some simulations. 

CALIBRATION OF THE 

HYDRODYNAMIC MODEL 

Model calibration is a process of adjusting model 

parameters to improve the match between simulated 

and expected values. Traditionally, this is a manual 

process. In this report, however, a universal inverse 

modeling code (UCODE, version 3.02, Poeter and Hill, 

1998) was used to make these adjustments systematically. Specifically, 25 values of effective Manning’s n, 

were estimated for identified material zones in the St. 

Clair–Detroit River Waterway by the use of UCODE, a 

procedure that applies a nonlinear regression technique 

to minimize the sum of squared weighted residuals 

(differences between simulated and expected values of 

flows and water levels). In addition to parameter estimates, UCODE provides information on the uncertainty of individual parameters, correlations among 

parameters, and the sensitivity of parameters to 

individual measurements. 

Parameter Estimation 

Code 

UCODE is a universal code for parameter estimation that is written in the programming language 

PERL (Practical Extraction and Report Language). 

UCODE was used to help (1) manipulate RMA2 input 

and output files, (2) execute RMA2 with different 

parameter sets, (3) compare simulated with expected 

values, (4) apply a nonlinear regression code (Hill, 

1998) to adjust parameter values in response to the 

comparison, (5) generate statistics for use in evaluating 

the uncertainty and correlation structure of estimated 

parameters, and (6), identify the contribution of individual observations or observation sets on parameter 

estimates. 

Parameter estimation with UCODE proce

through a set of iterations until the user-specifie

ria for convergence is attained or the specified m

mum number of iterations is completed. In this 

convergence criteria specified that either the ma

parameter change be less than 2 percent or that 

ferences in the sum of squared weighted residu

change by less than 2 percent over three iteratio

Within an iteration, each parameter is, in 

changed (perturbed) by one percent, while the r

ing parameters are held constant at their initial 

or the values estimated at the end of the previou

tion. RMA2 is executed for each unique param

set to complete the iteration. When an iteration 

completed, parameter sensitivities are calculate

each observation as the ratio of change in simul

values to the change in parameter values. Thes

tivities together with the model residuals are us

nonlinear regression to update all parameter est

simultaneously for the next iteration. 

To initiate the parameter estimation proce

UCODE reads a universal (UNI) input file, such 

SCD.SS.UNI (Appendix A). This file contains s

control variables, the name of the inversion mo

(MRDRIVE.EXE, which computes the nonline

regression), commands needed to execute RMA

narios, variables governing the output, and a lis

observations including their expected values an

uncertainties. 

Next, UCODE reads a prepare (PRE) file

as SCD.SS.PRE (Appendix B). The PRE file in

whether function files are used in the analysis (

were not); the name of template (TPL) files and 

sponding RMA2 input control files; and the nam

parameters being estimated. Reasonable minim

maximum values for estimated parameters are s

fied in the PRE file. These limits, however, do n

strain the final estimated parameter values, but 

provide a range for comparison. All parameters 

estimated in log space, so that the only effective 

straint was that parameters in arithmetic space w

greater than zero. This constraint is consistent w

physically-plausible range for Manning’s n valu

The PRE file also specifies parameter starting v

perturbations (the fractional amount that param

are perturbed to calculate sensitivities), format 

reading and writing the parameter values, and w

or not a particular parameter is to be estimated 

particular run. 

Calibration of the Hydrodynamic M
Next, UCODE reads the template (TPL) files, 

such as SCD.SS1.TPL (Appendix C). TPL files are 

identical to the corresponding input control files for 

RMA2, except that parameters values are replaced with 

parameter names enclosed by special delimiters. 

Finally, UCODE reads an extract (EXT) file, such as 

SCD.SS.EXT (Appendix D). Information in the EXT 

file is used to find simulated values in RMA2 output 

files that match measurements described in the UNI 

file. 

Calibration Scenarios 

Calibration scenarios are idealized hydraulic 

conditions associated with selected flow measurement 

events that were developed to efficiently calibrate 

the model throughout a wide range of flow and waterlevel conditions. The scenarios use steady-state simulations to approximate transient flow and water-level 

conditions during flow-measurements events. This 

approach reduces computational requirements to a feasible level with available computer resources. Criteria 

used to develop the scenarios are described in the 

following paragraphs. 

In this report, a flow-measurement event refers to 

a period of about 3 days when sets of 20 or more flow 

measurements were obtained at various cross sections 

on St. Clair or Detroit Rivers. In 1996, the Detroit 

District USACE, the primary agency measuring flows 

on the Great Lakes, began using ADCP (Acoustic 

Doppler Current Profilers) equipment to measure flow. 

Flow measurement events are scheduled at about 6-

week intervals during the ice-free season; measurement 

events on the two connecting channels (St. Clair and 

Detroit Rivers) generally occur within 14 days of one 

another. Selected cross sections used in the calibration 

are shown on figures 3 and 4. From 1996 to 2000, 

about 18 flow measurements sets have been obtained 

on both St. Clair and Detroit Rivers. 

Water levels are monitored continually at gaging 

stations along the waterway (table 1). Thus, water 

level data are available from most stations for all flow 

measurement events. Average water levels, computed 

from hourly water-level values during flow measurement events, are shown (fig. 5) for selected gaging stations on St. Clair River. Of the 18 flow measurement 

events on St. Clair River from 1996 to 2000, seven 

events were selected as calibration scenarios because 

they were considered sufficient to span the rang

flows and water levels during the period in whic

ADCP measurements were available. 

Boundary Conditions 

Calibration scenarios were simulated by 

ing event-specific flows at the headwaters of St

River (table 2); average inflows of selected inter

tributaries and direct inflow to Lake St. Clair (ta

and event-specific water levels at the mouth of D

River (table 2). Flows at the headwaters of St. 

River were based on the average flow measured 

vidual cross sections during the corresponding 

surement event. Inflows from all intervening 

tributaries on the St. Clair–Detroit River Waterw

direct inflow to Lake St. Clair contribute only a 

component of the total flow in the waterway. T

vide flexibility for future applications, however

age inflows for selected intervening tributaries w

estimated and included in the model calibration 

sis. Inflow estimates at the mouth of these tribu

were based on flow records at upstream or near

gaging stations and adjusted for differences bet

the gaged drainage area and the drainage area a

mouth of the tributary. Water levels at the mou

Detroit River were based on average water leve

during the measurement event at the Bar Point g

(table 1, CHS gage number 12 005). No wind d

were included in the boundary specifications. 

Expected Flows and 

Water-Levels Used in 

Calibration 

Both flow and water-level information wa

to calibrate the model. Flow information descr

the expected flow through the major channels in 

waterway formed by islands and dikes. Belle I

example, causes flow in Detroit River to branch 

Fleming Channel and a channel near Scott Mid

Ground (fig. 4). ADCP flow measurements nea

branches were used to develop regression equat

quantify the relation between flow proportions 

vidual channels and flow magnitude in the main 

nel (Holtschlag and Koschik, 2001). These equ

were used to compute the expected flows and co

sponding standard errors in the individual chan

around islands as a function of flows specified f

scenario at the headwaters of St. Clair River (ta

12 A Two-Dimensional Hydrodynamic Model of the St. Clair–Detroit River Waterway in the Great Lakes Basin 
13,550,000 13,670,000 

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Figure 3. Locations of flow-measurement cross sections and water-level gaging stations on St. Clair River. 

Calibration of the Hydrodynamic M
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EXPLANATION 

FLOW-MEASUREMENT 

CROSS SECTION 

GAGING STATION 

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Figure 4. Locations of flow-measurement cross sections and water-level gaging stations on Detroit River. 

14 A Two-Dimensional Hydrodynamic Model of the St. Clair–Detroit River Waterway in the Great Lakes Basin 
Table 1. Water-level gaging stations on the St. Clair–Detroit River Waterway 

[MSPCS 83 is the Michigan State Plane Coordinate System of 1983. No. number] 

Gage location, in MSPCS 83 N

Water body Operating Gaging Brief gaging International Feet (zone 2113) m

agency station No. station name 

Easting Northing no

St. Clair River .............. 

Lake St. Clair............... 

Detroit River ................ 

NOAA1 9014098 Fort Gratiot 13,643,354 555,153 

CHS2 11 940 Point Edward 13,643,720 549,313 

NOAA 9014096 Dunn Paper 13,643,352 553,801 

NOAA 9014090 Mouth of Black River 13,644,341 543,047 

NOAA 9014087 Dry Dock 13,638,138 532,639 

NOAA 9014084 Marysville 13,632,429 518,293 

NOAA 9014080 St. Clair State Police 13,627,991 483,990 

USACE3 CE 214 2CC Roberts Landing 13,622,120 427,154 

CHS 11 950 Port Lambton 13,623,527 427,226 

NOAA 9014070 Algonac 13,617,678 413,229 

USACE CE 213 45C North Channel 13,600,268 415,000 

USACE CE 212 72A Middle Channel 13,583,967 396,640 

USACE CE 734 37A South Channel 13,605,954 397,300 

NOAA 9034052 St. Clair Shores 13,524,546 358,232 

NOAA 9044049 Windmill Point 13,511,750 315,966 

USACE CE 737 832 Belle Isle 13,503,340 309,393 

NOAA 9044036 Fort Wayne 13,467,999 293,618 

NOAA 9044030 Wyandotte 13,453,697 258,449 

CHS 11 995 Amherstburg 13,463,040 237,404 

NOAA 9044020 Gibraltar 13,443,806 217,802 

CHS 12 005 Bar Point 13,463,182 207,175 

1NOAA is the National Oceanic and Atmospheric Administration.
 2CHS is the Canadian Hydrographic Service.


3USACE is the U.S. Army Corps of Engineers.


Water levels measured at gaging stations 

upstream of Bar Point, Ontario, also were used in 

model calibration. The expected values of water level 

for each scenario were computed as the average of 

hourly water levels recorded during the corresponding 

measurement event (table 5). The standard errors 

of the water-level data included both static and 

dynamic components. The static component accounted 

for possible small errors in the absolute datum of the 

gaging station and differences between the location of 

the station and the nearest model node used for comparison. The static component was 0.02 ft for all 

stations. The dynamic component accounted for the 

variability of water levels during the correspond

measurement event; it was computed as the stan

deviation of hourly water-level values. The stan

errors of the water-level data were computed as 

square root of the sum of the variances of the st

and dynamic components, although a minimum 

dard error of 0.05 was applied to all water-level 

The standard errors of the flow data, measured i

feet per second, and water-level data, measured 

were used to weight the two types of data prope

so that they could be used together in the calibr

analysis. 

Calibration of the Hydrodynamic M
--

--

--

--

--

--

--

--

--

--

--

M a y 13-1 4 , 1 996 

J u ne 1 0 -12 , 1 996 

J u ly 8 -1 0 , 1 9 9 6 

M a y 5 -7, 1 997 

J u ne 9 -1 1, 1 997 

A u g. 4 -6 , 1997 

S e p t. 8 -1 0 , 1 9 9 7 

O c t. 6 -8, 1 997 

J u ly 2 1 -2 3 , 19 98 

A u g. 1 0 -1 3 , 19 98 

S e p t. 2 1 -2 4 , 1 9 9 8 

O c t. 2 6 -2 9 , 1 9 9 8 

J u ne 1 4 -17 , 1 999 

J u ly 2 0 -2 2 , 19 99 

A u g. 2 5 -2 7 , 19 99 

S e p t. 2 3 -2 4 , 1 9 9 9 

N o v. 3 -5 , 1 9 9 9 

J u ne 2 7 -29 , 2 000 

Calibration 

scenario 

Date of flow 

measurement event 

(-- indicates not applicable) 

1 

2 

3 

4 

5 

6 

7 

Note: Lines connect water-level symbols for 

calibration scenarios to facilitate identification, 

not to indicate the slope of the water surface. 

Water levels not available at all gaging stations 

for all measurement events. 

wo-Dimensional Hydrodynamic Model of the St. Clair–Detroit River Waterway in the Great Lakes Basin 

581


580


579


WATER LEVEL, IN FEET ABOVE IGLD 1985


578


577


576


575


574


573


572


571


570


569


568


Fort 

Gratiot 

Dunn 

Paper 

Point 

Edward 

Mouth 

Dry 

Dock 

Marine 

City 

Port 

Lambton 

North 

Channel 

Middle 

Channel 

Windmill 

Point 

Belle 

Fort 

Wayne 

Amhertsburg 

Gibraltar 

Bar 

Point 

St. Clair 

State 

Police 

Roberts 

Landing 

Algonac South 

Channel 

St. Clair 

Shores 

Wyandotte 

of Black 

River 

Isle 

GAGING STATION 

Figure 5. Water levels during flow-measurement events on St. Clair River and selected calibration scenarios. 
1

2

3

4

5

6

7

Parameter Estimation 

Results 

In addition to parameter estimates and uncertainties, parameter estimation results include parameter 

sensitivity information that describes the ability to estimate model parameters given the network of flow and 

water-level information available, and the implications 

of the parameter estimates on the accuracy of model 

estimates of flows and water levels. Parameter estimation, however, is constrained by the availability of 

computer resources needed to simulate the model iteratively with alternative sets of parameter values and to 

evaluate alternative material zone configurations. 

Parameter estimation by use of UCODE is an 

efficient, but computer-intensive process. Seven 

steady-state calibration scenarios were used to estimate 

25 model parameters associated with channel roughness in designated material zones. Each steady-state 

simulation required about 0.25 hours on a dual Intel 

Pentium III 550 MHz (megahertz) Xeon TM processor 

running under the Microsoft Windows NT operating 

system. Each simulation started with initial conditions 

(flow velocities and water levels at individual nodes) 

computed from the previous iteration from the corresponding scenario. Thus, 10 iterations of a 25-

parameter estimation with seven steady-state scenarios 

required about 438 hours of computer time. This estimation process was repeated several times either to 

achieve convergence of the estimation process, or to 

evaluate alternative parameterizations using different 

material zone configurations. The parameter estimation results that follow converged under the criterion 

that changes in the weighted sum of square residuals 

from three consecutive parameter estimation runs 

differed by less than 2 percent. 

Parameters Estimates and Uncertainties 

Parameter estimates and corresponding w

of 95-percent confidence intervals (fig. 6) range

widely among the 25 designated material zones

Parameter estimates associated with Manning’s 

ranged from 0.0084 for the material zone River 

on Detroit River (DETRRouge) to 0.0660 for th

rial zone Bois Blanc Island on lower Detroit Ri

(DETBobloIs). Parameter values are thought to 

account both for discrepancies in flow areas bet

actual conditions and the model representations

well as for actual differences in channel roughn

characteristics. To limit parameter estimates to 

cally plausible values, parameter estimation occ

in log space; corresponding estimates were exp

ated prior to substitution into the hydrodynamic 

Table 2. Boundary specifications for calibration scen

the headwaters of St. Clair River and near the mouth 

River 

E

Expected w

flow near the n

headwaters Dates of flow- m

of St. Clair Scenario measurement De

River at event Fort Gratiot at 

(in cubic feet (in 

per second) IG

November 3–5, 1999 173,201 

October 26–29, 1998 194,065 

July 8–10, 1996 217,259 

August 4–6, 1997 222,539 

September 23–24, 1999 174,993 

May 5–7, 1997 213,719 

September 21–24, 1998 197,907 

Table 3. Selected local inflows to the St. Clair–Detroit River Waterway 

Water body 

Waterway component Approximate drainage area Approximate averag

receiving inflow (square miles) (cubic feet per sec

Black River ................................................ St. Clair River 746 489 

Pine River .................................................. St. Clair River 194 119 

Belle River ................................................. St. Clair River 777 478 

Sydenham River......................................... Lake St. Clair 2,043 1,861 

Clinton River ............................................. Lake St. Clair 1,206 928 

Thames River............................................. Lake St. Clair 4,330 4,857 

Net lake inflow (Atmospheric, and 

surface- and ground-water sources)....... Lake St. Clair 670 626 

River Rouge ............................................... Detroit River 467 312 

Calibration of the Hydrodynamic M
Flow- 

(pp) 

wo-Dimensional Hydrodynamic Model of the St. Clair–Detroit River Waterway in the Great Lakes Basin 

measure- Scenario 1 Scenario 2 Scenario 3 Scenario 4 Scenario 5 Scenario 6 Scenario 7 ment 

cross 

section Expected Standard Expected Standard Expected Standard Expected Standard Expected Standard Expected Standard Expected Standard 

error error error error error error error 

St. Clair River 

CS208 55,557 1,236 63,820 1,282 73,406 1,449 75,647 1,511 56,253 1,238 71,916 1,413 65,379 1,299 

CS210 118,133 1,236 130,733 1,282 144,342 1,449 147,380 1,511 119,228 1,238 142,292 1,413 133,017 1,299 

CS216 144,166 889 160,258 946 177,855 1,083 181,818 1,127 145,557 892 175,189 1,056 163,195 963 

CS218 30,121 889 34,893 946 40,490 1,083 41,807 1,127 30,521 892 39,616 1,056 35,799 963 

CS222 6,399 625 8,023 654 10,043 741 10,535 773 6,531 627 9,720 722 8,342 663 

CS230 167,888 625 187,128 654 208,302 741 213,090 773 169,547 627 205,085 722 190,652 663 

CS232 78,880 2,225 86,231 2,310 93,919 2,663 95,599 2,783 79,527 2,225 92,778 2,590 87,539 2,348 

CS240 57,495 1,673 66,226 1,744 76,344 2,015 78,706 2,113 58,231 1,675 74,772 1,957 67,873 1,772 

CS242 31,513 1,833 34,671 1,944 38,040 2,218 38,786 2,304 31,789 1,838 37,535 2,165 35,240 1,977 

CS234 6,356 832 6,948 907 7,568 991 7,703 1,010 6,408 838 7,476 978 7,054 921 

CS236 42,615 2,217 46,586 2,388 50,740 2,646 51,647 2,715 42,965 2,229 50,123 2,602 47,293 2,425 

CS238 29,909 2,414 32,696 2,624 35,611 2,877 36,248 2,938 30,154 2,432 35,179 2,837 33,192 2,664 

Detroit River 

CS003 134,187 1,770 149,522 1,973 166,571 2,197 170,452 2,248 135,504 1,788 163,969 2,163 152,347 2,010 

CS008 48,373 1,770 53,901 1,973 60,047 2,197 61,446 2,248 48,848 1,788 59,109 2,163 54,919 2,010 

CS015 55,684 1,460 64,196 1,503 74,176 1,675 76,523 1,740 56,397 1,462 72,617 1,637 65,811 1,520 

CS029 126,876 1,460 139,228 1,503 152,442 1,675 155,374 1,740 127,954 1,462 150,461 1,637 141,455 1,520 

CS100 47,784 1,179 53,236 1,313 59,296 1,463 60,676 1,497 48,252 1,190 58,371 1,440 54,240 1,338 

CS101 95,824 1,110 105,960 1,185 117,038 1,331 119,531 1,375 96,700 1,115 115,360 1,304 107,809 1,204 

CS102 39,264 929 44,540 987 50,596 1,109 52,003 1,148 39,711 933 49,658 1,086 45,529 1,002 

CS120 40,517 1,776 45,140 1,979 50,278 2,204 51,448 2,255 40,914 1,794 49,494 2,170 45,991 2,016 

CS121 9,572 2,050 14,495 2,283 20,889 2,543 22,480 2,602 9,964 2,070 19,850 2,504 15,487 2,327 

CS122 48,136 1,764 51,722 1,870 55,251 2,113 55,987 2,185 48,459 1,769 54,743 2,068 55,340 1,902 

CS123 84,647 2,197 92,379 2,277 100,512 2,594 102,295 2,703 85,327 2,197 99,302 2,529 93,760 2,312 

CS141 21,484 2,431 23,157 2,623 24,831 2,829 25,185 2,874 21,634 2,448 24,588 2,798 23,448 2,658 

CS142 12,201 2,146 13,316 2,342 14,488 2,548 14,745 2,593 12,299 2,163 14,313 2,517 13,515 2,377 

CS143 20,396 1,701 22,259 1,858 24,218 2,027 24,648 2,065 20,559 1,714 23,927 2,002 22,591 1,886 

CS161 21,531 2,017 26,574 2,216 32,964 2,500 34,541 2,581 21,939 2,034 31,933 2,450 27,574 2,257 

CS162 9,524 1,027 11,078 1,105 12,756 1,225 13,123 1,257 9,658 1,033 12,506 1,204 11,362 1,123 

CS163 38,854 2,886 41,880 3,116 44,907 3,386 45,547 3,448 39,125 2,905 44,468 3,344 42,407 3,160 

CS164 8,195 2,009 8,943 2,192 9,730 2,385 9,903 2,427 8,260 2,025 9,613 2,356 9,077 2,225 

CS165 64,252 2,269 70,120 2,502 76,294 2,750 77,647 2,805 64,767 2,289 75,375 2,713 71,169 2,543 
(p) 

Scenario 1 Scenario 2 Scenario 3 Scenario 4 Scenario 5 Scenario 6 Scenario 7 Station 

name 

Expected 

Standard 

error 

Expected 

Standard 

error 

Expected 

Standard 

error 

Expected 

Standard 

error 

Expected 

Standard 

error 

Expected 

Standard 

error 

Expected 

Standard 

error 

Fort Gratiot............. 577.724 0.396 578.902 0.207 580.003 0.156 581.230 0.135 577.992 0.191 580.580 0.274 579.495 0.191 

Dunn Paper............. 577.335 .325 578.470 .189 579.554 .134 580.705 .110 577.615 .161 580.131 .220 579.052 .168 

Port Edward............ 1NA NA 578.196 .159 NA NA 580.363 .120 NA NA 579.860 .214 578.800 .148 

Mouth of Black 

River ................... 577.277 .233 578.102 .163 579.187 .131 580.320 .099 577.423 .144 579.788 .202 578.718 .153 

Dry Dock................ 576.727 .330 577.742 .147 578.819 .122 579.961 .093 576.967 .107 579.423 .172 578.370 .135 

St. Clair State 

Police.................. 575.550 .183 576.537 .096 577.647 .100 578.682 .064 575.843 .075 578.182 .099 577.176 .086 

Marine City ............ 574.747 .100 NA NA 576.854 .071 577.867 .052 574.980 .068 577.420 .089 576.405 .065 

Roberts Landing..... 574.415 .093 NA NA 576.422 .021 577.505 .040 574.730 .064 577.115 .102 NA NA 

Port Lambton.......... NA NA NA NA NA NA NA NA NA NA NA NA 575.927 .049 

Algonac .................. 574.276 .063 575.083 .025 576.203 .071 577.241 .025 574.538 .059 576.903 .070 575.753 .046 

North Channel ........ 574.169 .051 576.229 .051 577.138 .038 574.496 .067 576.759 .104 

South Channel ........ 573.842 .060 574.812 .031 576.044 .069 577.010 .036 574.227 .115 576.672 .089 575.502 .055 

Middle Channel...... 573.793 .046 574.650 .022 575.873 .044 576.827 .030 574.128 .065 576.508 .076 575.335 .048 

St. Clair Shores ...... 573.335 .119 574.533 .036 575.731 .053 576.770 .033 573.878 .060 576.339 .087 575.198 .050 

Windmill Point ....... 573.039 .119 574.297 .050 575.459 .059 576.485 .054 573.591 .102 576.111 .124 574.983 .096 

Belle Isle ............... 572.970 .149 NA NA NA NA NA NA 573.516 .105 NA NA NA NA 

Fort Wayne ............. 572.247 .238 573.553 .064 574.708 .111 575.709 .051 572.881 .130 575.314 .140 574.246 .111 

Wyandotte .............. 571.797 .304 573.129 .085 574.297 .148 575.275 .060 572.562 .120 574.882 .176 573.830 .142 

Amherstburg........... 571.507 .334 572.848 .097 574.257 .170 574.988 .069 572.161 .194 574.624 .198 573.551 .160 

Gibraltar ................. 570.381 .641 571.900 .161 573.107 .293 574.138 .117 571.314 .304 573.710 .351 572.742 .224 

Calibration of the Hydrodynamic Model 

1NA indicates that data were not available or that data from a nearby gaging station were used in its place. 

19 
0.11


0.1 

0.09 

0.08 

0.07 

0.06 

0.05 

0.04 

0.03 

0.02 

0.01 

0 

Expected value 

Lower 95-percent limit 

Upper 95-percent limit 

EXPLANATION 

MANNIN

G’S n VALUE 

SCRUpper 

SCRDryDock 

SCRInterIs 

SCRFawnIsE 

SCRAlgonac 

ChenalEcar 

SCRNorth 

SCRMiddle 

SCRFlats 

SCRCutoff 

BassettCh 

LakStClair 

DETUpper 

DETBelleIN 

DETRRouge 

DETFightIs 

DETTrenton 

DETStonyIs 

DETLivChUp 

DETAmhChUp 

DETSugarE DETBobloIs 

DETLivChLo 

DETAmhChLo 

DETSugarW

PARAMETER REACH IDENTIFIER 

Figure 6. Estimated Manning’s n values and 95-percent confidence intervals for 25 material zones in the St. Cla

Detroit River Waterway. 

20 A Two-Dimensional Hydrodynamic Model of the St. Clair–Detroit River Waterway in the Great Lakes Basin 
-------

--------

-------

High parameter correlation (0.97) was detected 

between the parameter associated with channel roughness 

of upper Livingstone Channel on lower Detroit River 

(DETLivChUp) and upper Amherstburg Channel on lower 

Detroit River. In addition, moderate correlation (0.95) 

was detected between upper Detroit River (DETUpper) and 

the channel north of Belle Isle on upper Detroit River 

(DETBelleIN), near Scott Middle Ground. Correlation 

among parameters implies ambiguity in the true parameter 

values. That is, simultaneous changes in two highly correlated parameters may produce the same value of the weighted 

sum of squares of residuals. Additional calibration data or a 

reconfiguration of material zones is needed if either estimated parameter is physically implausible. Other than the 

two parameter pairs identified, no other parameter 

correlations greater than 0.85 were detected. 

Parameter Sensitivities 

Parameter sensitivity measures the extent to which 

model estimates of flow or water level change in response to 

changes in parameter values. Thus, a sensitivity value is 

calculated for each observation of flow and water level with 

respect to each parameter. UCODE applies the centraldifference estimator as the final estimator of sensitivity as 

(6) 

where 

sij is the sensitivity of the i

th observation to the jth 

parameter, which is defined using, 

∂yi 

∂b -

j 

the partial derivative of the change in i

th simulated 

value with respect to the j

th parameter. 

∆2 yˆ


∆2b - indicate the central difference estimate of the change


in the simulated value caused by the parameter value 

change ∆b 

b	 a vector of the values of the estim

parameters, in this report, corresp

to channel roughness values, 

∆b	 a vector in which all values are ze

except for the parameter for which 

sensitivities are being calculated, 

yˆ [b + ∆b] and yˆ [b – ∆b] indicates the flo

water-level simulated by use of th

parameter values represented by 

(b + ∆b) or (b – ∆b) , respective

(Poeter and Hill, 1998, p. 8). 

In this report, sensitivities were calculated 

perturbing parameters by one percent. 

Scaling the parameter sensitivity va

the magnitudes of the corresponding para

and the uncertainties of the observations f

tates the evaluation of the importance of d

observations to the estimation of a single 

ter or the importance of different paramet

the calculation of a simulated value (Hill, 

p. 15). In both cases, greater absolute val

associated with greater importance. Scale

parameter sensitivities are calculated as 

where 

∂ yˆ i 

∂b -

j 

is estimated by the central differen

estimator Equation 6, 

bj is the estimated parameter, and 

wii is the variance associated with the 

measurement. 

Parameter composite scaled sensitivities 

(ParmCSS) are calculated for each param

summing the scaled sensitivities over all m

surements. ParmCSS indicate the total am

Calibration of the Hydrodynamic M
information provided by the measurements for the estimation of the corresponding parameters. In particular, 

ParmCSS values were computed as: 

where ND is the number of measurements in the 

regression analysis. In this report, the number of measurements is 338. Results of the sensitivity analysis 

indicate a wide variation in composite scaled se

ties for the 25 model parameters (fig. 7). The e

Manning’s n for Detroit River near Fighting Isl

(DETFightIs) has the greatest sensitivity and D

River at Sugar Island East (DETSugarE) has th

composite scaled sensitivity. 

Measurement composite scaled sensitivit

(MeasCSS) are calculated in a manner similar t

ParmCSS. Here, however, the summations also 

occurred over the scenarios and the parameters 

25


C

O

M

P

O

SITE SCALED 

SEN

SITIVI

TY 

SCRUpper 

20


15


10


5


0


SCRInterIs


SCRDryDock


SCRFawnIsE


ChenalEcar


SCRAlgonac


SCRNorth


SCRMiddle


SCRFlats


SCRCut

off


B

assettCh


LakStClair


DETUpper


DETBelleIN


DETRRouge


D

ETFightIs


DETStonyIs


DETTrenton


DETLivChUp


DETAmhChUp


DETLivChLo


DETAmhChLo


DETBobloIs


DETSugarW


DETSugarE


EFFECTIVE MANNING’S n VALUE 

Figure 7. Composite scaled sensitivities for Manning’s n parameters in corresponding material zones. 

22 A Two-Dimensional Hydrodynamic Model of the St. Clair–Detroit River Waterway in the Great Lakes Basin 
identify the total amount of information provided by differ- water-level measurements. Standard devia

ent types of measurements at various locations. Values of MeasCSS were more near equal with value 

MeasCSS were computed as: and 4.83 for water level and flow measurem

respectively. Water-level measurements on 

Clair River at Roberts Landing and Port Hu

(each scenario contained only one of these 

surements) were most informative; water le

The information provided, as described by the Detroit River at Gibraltar were least inform

MeasCSS values, varied widely between measurement Flow measurements near Belle Isle at cross 

types and among measurement locations (figs. 8 and 9). tions CS-015 and CS-029 were most inform

The average MeasCSS value for water-level measurements flow measurements on Detroit River west o

was 13.6 and the average MeasCSS for flow measurements American Grassy Island were least informa

was 7.31, which reflects generally greater weights for about model parameters. 

22 

20 

18 

16 

14 

12 

10 

8 

6 

4 

2 

0 

CROSS SECTION IDENTIFIER 

C

O

M

P

O

SITE SCALED 

SENSI

TIVI

TY 

C

S-208 

C

S-216 

CS-210 

C

S-218 

C

S-222 

CS-2

30 

C

S-232 

C

S-234 

C

S-236 

CS-2

38 

C

S-240 

C

S-242 

C

S-003 

CS-0

08 

CS-015 

C

S-029 

C

S-100 

C

S-101 

C

S-102 

C

S-120 

CS-1

21 

C

S-122 

C

S-123 

C

S-141 

CS-1

42 

C

S-143 

C

S-161 

C

S-162 

CS-1

63 

C

S-164 

C

S-165 

Figure 8. Composite scaled sensitivities of flows at measurement cross sections on St. Clair and Detroit 

Rivers. 

Calibration of the Hydrodynamic M
24 A Two-Dimensional Hydrodynamic Model of the St. Clair–Detroit River Waterway in the Great Lakes Basin 

River Waterway. 

Figure 9. Composite scaled sensitivities of water levels at selected gaging stations on the St. Clair–Detroit 

C

O

M

P

O

SITE SCALED 

SENSI

TIVI

TY


0 

GAGING STATION IDENTIFIER 

4 

8 

12 

Fort Gratiot


Dunn Paper


Point Edward


Mouth of Black River


Dry Dock


St. Clair State Police


Marine City


Roberts Landing


Port Lambton


North Channel


Middle Channel


South Channel


Algonac


St. Clair Shores


Windmill Point


Belle Isle


Fort Wayne


Wyandotte


Amherstburg


Gibraltar

SIMULATED AND EXPECTED 

FLOWS AND WATER LEVELS 

Overall, simulated and expected values of 

flows and water levels on St. Clair–Detroit River 

Waterway are in close agreement (figs. 10–13). Inspection of the distribution of residuals, formed by the 

differences between expected and simulated flows 

and water levels, however, provides additional detail 

on the model fit. In particular, expected flows are 

consistently greater than simulated flows for all scenarios (fig. 14). This apparent bias may be due to an under 

accounting of simulated flows at GCLs, rather than 

an actual flow loss in the model. According to B.P. 

Donnell (USACE, written commun., 2001), a 3-5 percent under accounting of flows at GCLs is normal, 

although sometimes this discrepancy can be reduced 

by lowering the convergence parameter in RMA2 to 

0.0001 ft or less, increasing the local mesh density, 

and applying the SLOPEFIX utility. In addition, some 

scenarios show consistent discrepancies between 

expected and simulated water levels. In particular, 

expected water levels are consistently lower than simulated water levels for scenarios 2 and 3, and expected 

water levels are consistently higher than simulated 

water levels for scenario 5 (fig. 15). The steady-state 

approximation to transient conditions during the 

measurement events may explain some of the 

discrepancies in the calibration scenarios. 

Expected flows are consistently higher th

simulated flows at some flow-measurement cro

sections. On St. Clair River, expected flows are 

consistently higher than simulated flows at on t

east side of Stag Island (CS-208), and consisten

lower on the west side (CS-210) (fig. 16). Simi

for Detroit River, expected flows are consistentl

higher on the south side of Peche Island (CS-00

than on the north side (CS-003). This discrepan

might be resolved by introducing additional ma

zones, although the low sensitivities in these are

(fig. 8) may make improvements problematic. 

tivities could change, however, with changes in 

rial configurations. Expected water levels at the 

Dock gaging station on St. Clair River are gene

higher than simulated values (fig. 17). Given, t

generally high sensitivities to water levels at bo

the Mouth of Black River and Dry Dock gaging 

tions (fig. 9) and high composite scaled sensitiv

for parameters SCRDryDock and SCRInterIs (fi

some subdivision or reconfiguration of the boun

defining the nearby material zones may improv

the model fit. Simulated water levels at Belle I

(fig. 17) appear higher than expected values, ho

this discrepancy is based on data from only two 

calibration scenarios. 

Simulated and Expected Flows and Water L
225,000


200,000 

175,000 

150,000 

125,000 

100,000 

75,000 

50,000 

25,000 

0 

0 25,000 50,000 75,000 100,000 125,000 150,000 175,000 200,000 

Cross Symbol Section 

CS-208 

CS-210 

CS-216 

CS-218 

CS-222 

CS-230 

CS-232 

CS-234 

CS-236 

CS-238 

CS-240 

CS-242 

Line of agreement 

EXPECTED FLOW, IN CUBIC FEET PER SECOND 

Figure 10. Relation between expected and simulated flows on St. Clair River for seven calibration scenarios. SIMULATED FLOW, IN CUBIC FEET PER SECOND


26 A Two-Dimensional Hydrodynamic Model of the St. Clair–Detroit River Waterway in the Great Lakes Basin 
582


581


580


579


578


577


576


575


574


573


573 574 575 576 577 578 579 580 581 

Symbol Gaging Station 

Fort Gratiot 

Point Edward 

Dunn Paper 

Mouth of Black River 

Dry Dock 

Marine City 

Roberts Landing 

Port Lambton 

Algonac 

North Channel 

Middle Channel 

South Channel 

St. Clair Shores 

Line of agreement 

EXPECTED WATER LEVEL, IN FEET ABOVE IGLD 1985


Figure 11. Relation between expected and simulated water levels on St. Clair River and Lake St. Clair for seven 

calibration scenarios. SIMULATED WATER LEVEL, IN FEET ABOVE IGLD 1985


Simulated and Expected Flows and Water L
180,000


160,000 

140,000 

120,000 

100,000 

80,000 

60,000 

40,000 

20,000 

0 

0 20,000 40,000 60,000 80,000 100,000 120,000 140,000 160,000 1

Symbol Cross Section 

CS-003 

CS-008 

CS-015 

CS-029 

CS-100 

CS-101 

CS-102 

CS-120 

CS-121 

CS-122 

CS-123 

CS-141 

CS-142 

CS-143 

CS-161 

CS-162 

CS-163 

CS-164 

CS-165 

Line of agreement 

EXPECTED FLOW, IN CUBIC FEET PER SECOND 

Figure 12. Relation between expected and simulated flows on Detroit River for seven calibration scenarios. SIMULATED FLOW, IN CUBIC FEET PER SECOND


28 A Two-Dimensional Hydrodynamic Model of the St. Clair–Detroit River Waterway in the Great Lakes Basin 
577


576


575


574


573


572


571


570


570 571 572 573 574 575 576 

Symbol Gaging Station 

Windmill Point 

Belle Isle 

Fort Wayne 

Wyandotte 

Amherstburg 

Gibraltar 

Line of agreement 

EXPECTED WATER LEVEL, IN FEET ABOVE IGLD 1985


Figure 13. Relation between expected and simulated water levels on Detroit River for seven calibration scenarios. 

SIMULATED WATER LEVEL, IN FEET ABOVE IGLD 1985


Simulated and Expected Flows and Water L
8,000 

DIFFERENCE BETWEEN EXPECTED AND 

6,000 

SIMULATED FLOW, IN CUBIC FEET PER SECOND 

4,000 

2,000 

0 

-2,000 

-4,000 

-6,000 

1 2 3 4 5 6 7 

CALIBRATION SCENARIO 

EXPLANATION 

Upper whisker 

Upper quartile 

Median 

Lower quartile 

Lower whisker 

Outlier data extreme 

Figure 14. Distribution of flow residuals by calibration scenario. 

30 A Two-Dimensional Hydrodynamic Model of the St. Clair–Detroit River Waterway in the Great Lakes Basin 
0.6


0.4 

0.2 

0 

-0.2 

-0.4 

-0.6 

-0.8 

1 2 3 4 5 6 7 

CALIBRATION SCENARIO 

EXPLANATION 

Upper whisker 

Upper quartile 

Median 

Lower quartile 

Lower whisker 

Outlier data extreme 

Figure 15. Distribution of water-level residuals by calibration scenario. AND SIMULATED WATER LEVEL, IN FEET
 DIFFERENCE BETWEEN EXPECTED 


Simulated and Expected Flows and Water L
8,000


6,000 

4,000 

2,000 

0 

-2,000 

-4,000 

-6,000 

FLOW-MEASUREMENT CROSS SECTION 

EXPLANATION 

Upper whisker	

Lower whisker 

Outlier data extreme 

Upper quartile 

Median 

Lower quartile 

Figure 16. Distribution of flow residuals by flow-measurement cross section. DIFFERENCE BETWEEN EXPECTED AND 
 SIMULATED FLOW, IN CUBIC FEET PER SECOND
 CS-208
 CS-210
 CS-216
 CS-218
 CS-222
 CS-230
 CS-232
 CS-234
 CS-236
 CS-238
 CS-240
 CS-242
 CS-003
 CS-008
 CS-015
 CS-029
 CS-100


CS-101
CS-102
CS-120
CS-121
CS-122
CS-123
CS-141
CS-142
CS-143
CS-161
CS-162
CS-163

32 A Two-Dimensional Hydrodynamic Model of the St. Clair–Detroit River Waterway in the Great Lakes Basin 
0.6 

DIFFERENCE BETWEEN EXPECTED 

AND SIMULATED WATER LEVEL, IN FEET 

0.4 

0.2 

Point Edward 

Mouth of Black River 

0 

Dry Dock 

St. Clair State Police

-0.2 

Marine City 

Roberts Landing

-0.4 

-0.6 

North Channel 

-0.8 

South Channel 

Middle Channel 

St. Clair Shores 

Fort Wayne

EXPLANATION 

Wyandotte

Upper whisker 

Outlier data extreme 

Upper quartile 

Median 

Lower whisker Lower quartile 

Figure 17. Distribution of water-level residuals by gaging station, St. Clair–Detroit River Waterway. 

Amhertsburg 

Port Lambton 

Algonac 

Windmill Point 

Belle Isle 

Fort Gratiot 

Dunn Paper 

Simulated and Expected Flows and Water L
MODEL DEVELOPMENT 

NEEDS AND LIMITATIONS 

The implementation and calibration of the 

hydrodynamic model of the St. Clair–Detroit River 

Waterway described in this report focuses on correctly 

distributing flows throughout the many branches of the 

waterway formed by islands, and on matching water 

levels near gaging stations. Although quantifying the 

accuracy of this type of simulation is a necessary component of calibration, additional model development is 

needed to conduct source-water assessments and to 

enhance emergency preparedness. In particular, more 

information is needed on velocity distributions, particularly near public water intakes, and on wind effects. 

Velocity distributions, indicated by point velocity data, 

can affect the time of constituent travel through the 

waterway, and the mixing characteristics of the flow. 

In addition, restrictions imposed by the model formulation, constraints on data acquisition, and limitations of 

computing resources need to be recognized in order to 

properly interpret simulation results and document the 

status of model development. 

The model documented in this report simulates 

horizontal (two-dimensional, vertically averaged) 

velocity components and water levels at 42,936 nodes 

throughout the waterway. Quadratic interpolation can 

be used to compute velocities and water levels anywhere within the 13,783 elements formed by these 

nodes. Simulated flows were computed by integrating 

simulated (point) velocities and water levels at geometry, continuity-check lines (GCLs). The simulated 

flows and water levels were compared to corresponding 

measured values in an iterative calibration procedure 

that determined appropriate values of Manning’s n (the 

effective channel roughness) in 25 designated material 

zones within the waterway. The calibrated model provides a basis for simulating flows and water levels over 

the range of data measured between 1996 and 2000. 

Faster computer processors will help determine 

whether changes in material zones designations can be 

used to reduce the number of parameters or increase 

the accuracy of the simulations. 

The calibration procedure did not compare simulated point velocities with measured point velocities 

obtained during ADCP measurements. Thus, the accuracy of simulated point velocities has not been 

assessed. Point velocity data were not included in initial calibration efforts because the persistence and 

uncertainty of measured point velocity values has not 

been evaluated. Statistical analyses of point ve

fields are needed to determine their spatial struc

and to identify possible covariates, such as flow

water levels, that may influence their characteri

Further calibration using point velocity data is p

Several model parameters can be adjusted 

improve the match between simulated and mea

point velocity data. Eddy viscosity and Mannin

control the horizontal variability of simulated v

ties. In particular, lower eddy viscosity values 

greater variability in simulated velocities within 

channel cross section. Lower eddy viscosity va

however, also can decrease the numerical stabil

the simulations. Because eddy viscosities vary 

element size and flow velocities, eddy viscosity 

ments for individual elements are commonly ba

either the Peclet number or Smagorinski coeffic

(Donnell and others, 2000, p. 48). Future calib

efforts are planned to determine the preferred m

for assigning eddy viscosities based on accurac

stability criteria, and their appropriate paramete

tions, which may vary spatially. 

Horizontal velocity distributions also may 

affected by local variability in channel roughne

characteristics described by Manning’s n. Ligh

tration in shallow areas may enhance vegetative 

growth and effectively increase Manning’s n, th

decreasing local velocities. Thus, future calibra

efforts will attempt to determine parameters des

the depth, and perhaps seasonal, dependence of 

Manning’s n. 

According to Donnell and others (2000, p

conventional RMA2 depth-averaged calculation

flow around a bend tends to over predict stream

velocities on the inside bank of a river. When w

flows around bend, a radial acceleration is deve

that forces the surface water to the outside of th

and the water near the bed to the inside of the c

a phenomena that is commonly referred to as a 

secondary or helical flow pattern. RMA2 canno

quately predict the effect of this behavior on the 

averaged velocities. To improve predictions of 

averaged velocities around curves, a secondary 

corrector, referred to as the bendway correction

added to RMA2 in version 4.5 (Donnell and oth

2000, p. 93). The computational effectiveness o

option for improving the match between simula

measured point velocities will be assessed as par

future calibration efforts. 

34 A Two-Dimensional Hydrodynamic Model of the St. Clair–Detroit River Waterway in the Great Lakes Basin 
The governing equations in RMA2 (equations 1 

and 2) include an empirical wind shear coefficient, ζ , 

and eight alternative wind shear stress formulations 

that provide considerable flexibility for simulating the 

effect of wind on flow. Wind effects are extremely 

difficult to implement in a two-dimensional model, 

however, because wind-driven currents are threedimensional in nature (Donnell and others, 2000, 

p. 111). Signell, List, and Farris (2000) report that 

bottom wind-driven currents flow downwind along the 

shallow margins of the basin, but flow against the wind 

in the deeper regions. In this report, no assessments of 

wind effects on flow or water levels in the connecting 

channels or Lake St. Clair were made because of limited data on winds and associated current over Lake St. 

Clair. A planned installation of a wind station on Lake 

St. Clair in 2001, anticipated drifting buoy deployments in 2002, and existing water-level monitoring 

stations will provide a basis for selecting an appropriate wind-shear stress formulation, estimating associated parameters, and assessing the adequacy of the 

simulations. 

In addition to calibration improvements, mesh 

refinements will be applied near selected public water 

intakes and perhaps GCLs to increase the density of 

nodes and improve the local accuracy of flow simulations. In addition, boundary elements will be created at 

selected intakes to facilitate simulation of pumping 

withdrawals. These refinements will provide additional detail on local two-dimensional velocity characteristics to more effectively quantify the susceptibility 

of public water intakes by use of particle-tracking analysis. Similarly, refinements in the model mesh at possible points of contaminant release may provide 

additional information to aid preparation of emergency 

responses. 

In addition to model limitations discussed in the 

“Applications and Capabilities” section of this report, 

other constraints on model applications are likely to 

persist. In particular, ice commonly forms on the connecting channels and Lake St. Clair during prolonged 

periods of cold weather. Ice formation in the connecting channels restricts the flow area and reduces flow 

velocities. Although this effect might be approximated 

by increasing Manning’s n values describing flow resistance, the uncertainty of simulated flows and waterlevels during ice-affected periods is likely to remain 

high for the foreseeable future. Furthermore, there 

are no plans to routinely obtain flow information 

during ice-affected periods to provide a basis for 

improvements. Such flow information is neede

describe the nonlinear, highly time-dependent n

ice-affected flow (Holtschlag and Grewal, 1998

addition, application of flow simulation results 

restricted to constituents that move with the dep

averaged water velocity; a situation that is unlik

with immiscible fluids or those having a density 

different from water. 

SUMMARY AND 

CONCLUSIONS 

St. Clair–Detroit River Waterway connec

Huron with Lake Erie in the Great Lakes basin 

forms part of the international boundary betwee

United States and Canada. Public intakes withi

waterway provide a water supply for about 6.2 

people. Michigan Department of Environmenta

ity and Detroit Water and Sewerage Departmen

the cooperation of U.S. Geological Survey and 

District of the U.S. Army Corps of Engineers, a

developing a two-dimensional hydrodynamic m

the waterway to help assess the vulnerability of 

water supply to contamination. 

The waterway model is based on RMA2, 

eralized finite-element hydrodynamic numerica

model for two-dimensional (depth averaged) sim

tion. RMA2 is designed for far-field problems 

which vertical accelerations are negligible and v

vectors generally point in the same direction ov

entire depth of the water column at any instant o

RMA2 computations are based on a free surfac

ice conditions) and a vertically homogeneous fl

(no temperature stratification). The Surface Wa

Modeling System (SMS) was used to facilitate 

implementation of data input files needed to de

the geometry, bathymetry, and hydraulic charact

of the waterway for simulation with RMA2. 

The model discretizes the waterway into 

element mesh containing 13,783 quadratic elem

defined by 42,936 nodes. Flow and water-level 

ary conditions are defined at the limits of the wa

to allow simulation of steady-state and transien

dynamic conditions. The primary flow boundar

fication is at the headwaters of St. Clair River n

Fort Gratiot gaging station operated by NOAA. 

tional flow boundaries are located on selected tr

ies and on Lake St. Clair. A stage boundary is l

at the mouth of Detroit River at the CHS gaging 

Summary and Conclus
near Bar Point, Ontario. Adjoining finite elements are 

grouped into 25 material zones. Each zone was 

assigned an initial value of Manning’s n, a parameter 

associated with channel roughness, and eddy viscosity, 

a parameter that controls the numerical stability of the 

solution and the simulated velocity distribution. 

Bathymetry data defining channel and lakebed elevations were obtained from various field surveys, including a survey of the connecting channels by NOAA in 

2000, and data shown on NOAA charts. The mesh was 

edited to meet mesh-quality criteria needed for efficient 

and accurate simulations. 

The model was calibrated by systematically 

adjusting values of Manning’s n in 25 material zones to 

improve the match between simulated and expected 

flows in major channels and water levels at gaging stations. Seven steady-state calibration scenarios were 

developed from among 18 flow-measurement events on 

St. Clair River from 1996 to 2000. The scenarios effectively spanned the available flow and water-level data. 

Expected flows in major channels were determined on 

the basis of average measured flow on St. Clair River 

during the calibration scenario, and on regression equations developed using data from all flow-measurement 

events. Expected water levels were based on the average of hourly water-level measurements during the scenario corresponding to a flow-measurement event. The 

universal parameter estimation code, UCODE, was 

used to systematically adjust model parameters, and to 

describe their associated uncertainty and correlation. 

Sensitivity analysis was used to describe the amount of 

information available to estimate individual parameters 

and to quantify the utility of information available on 

flows at individual cross sections and water levels at 

selected gaging station. 

Overall, there is close agreement between 

lated and expected flows and water levels. Exp

flows were somewhat higher, however, than sim

flows in all scenarios because of an apparent un

accounting of flows at GCLs, where simulated 

is accumulated. Other minor discrepancies betw

simulated and expected flows and water levels m

be reduced by future changes in the material zo

configurations. 

Additional data collection, model calibra

analysis, and grid refinements are needed to ass

enhance two-dimensional flow simulation capab

describing the horizontal flow distributions in S

and Detroit Rivers and circulation patterns in L

Clair. Two-dimensional flow simulations result

be used with particle tracking analysis to assess 

susceptibility of public water intakes to contam

REFERENCES CITED 

Deering, M.K., 1990, Practical Applications of 

Hydrodynamic Modeling—Proceedings of 

1990 National Conference: New York, Hyd

Engineering, American Society of Civil Eng

p 755–760. 

Donnell B.P., Finnie, J.I., Letter, J.V., Jr., McAn

W.H., Roig, L.C., and Thomas, W.A., 1997

guide to RMA2 WES Version 4.3: U.S. Arm

Corps of Engineers Waterway Experiment 

227 p. 

Donnell B.P., Letter, J.V., Jr., McAnally, W.H., 

Thomas, W.A., 2000, Users guide to RMA

Version 4.5: U.S. Army Corps of Engineer

Waterway Experiment Station, 264 p. 

36 A Two-Dimensional Hydrodynamic Model of the St. Clair–Detroit River Waterway in the Great Lakes Basin 
Environmental Modeling Research Laboratory, 1999, 

SMS Surface-water modeling system reference 

manual (version 7): Provo, Utah, Environmental 

Modeling Systems, Inc., 342 p. 

Hauck, L.M., 1992, Hydrodynamics at mouth of 

Colorado River, Texas: U.S. Army Corps of 

Engineers Waterway Experiment Station Technical 

Report WES/TR/HL-92-11, 103 p. 

Hill, M.C., 1998, Methods and guidelines for effective 

model calibration: U.S. Geological Survey WaterResources Investigations Report 98-4005, 90 p. 

Holtschlag, D.J., and Aichele, S.A., 2001, Visualization 

of drifting buoy deployments on St. Clair River 

near Public Water Intakes—October 3–5, 2000, 

U.S. Geological Survey Open-File Report 01-17, 

http://mi.water.usgs.gov/splan2/sp08903/ 

SCRIndex.html. 

Holtschlag, D.J., and Grewal, M.S., 1998, Estimating 

ice-affected streamflow by extended Kalman 

filtering: Journal of Hydrologic Engineering, July, 

p. 174–181. 

Holtschlag, D.J., and Koschik, J.A., 2001, Steady-state 

flow distribution and monthly flow duration in 

selected branches of St. Clair and Detroit Rivers, 

two connecting channels of the Great Lakes: U.S. 

Geological Survey Water-Resources Investigations 

Report 01-4135, 58 p. 

National Oceanic and Atmospheric Administration, 

1999, Recreational chart 14853—Detroit River, 

Lake St. Clair, and St. Clair River: U.S. 

Department of Commerce, National Ocean 

Service, 1:15000 scale. 

Poeter, E.P., and Hill, M.C., 1998, Documentation of 

UCODE, A computer code for universal inverse 

modeling: U.S. Geological Survey WaterResources Investigations Report 98-4080, 116 p. 

Schwab, D.J., Clites, A.H., Murthy, C.R., Sanda

Meadows, L.A., and Meadows, G.A., 1989

effect of wind on transport and circulation 

St. Clair: Journal of Geophysical Research

no. C4, April, p. 4947–4958. 

Sellinger, C.E., and Quinn, F.H., 2001, Assessm

impacts of increased weed growth on Detro

flows: National Oceanic and Atmospheric 

Administration Technical Memorandum G

119, 12 p. 

Signell, R.P., List, J.H., and Farris, A.S., 2000, 

currents and sediment transport in Long Isl

Sound—A Modeling Study: Journal of Co

Research, v. 16, no. 3, p. 551–566. 

Soong, T.W., and Bhowmik, N.G., 1993, Twodimensional hydrodynamic modeling of a r

the Mississippi River in Pool 19: Champaig

Illinois State Water Survey Division Repor

EMTC93R003, 14 p. 

Tsanis, I.K., Shen, Huihua, and Venkatesh, S., 1

Water currents in the St. Clair and Detroit R

Journal of Great Lakes Research, v. 22, no

p. 213–223. 

U.S. Army Corps of Engineers, 2000, Corpscon 

Windows (v. 5.11.08): U.S. Army Corps of 

Engineers Topographic Engineering Center

Alexandria, Va. 

Williamson, D.C., Scott R.D., and Lord, Stephe

1997, Numerical modeling of the St. Clair/

River system and seasonal variations in hea

in Proceedings of the 1997 Canadian Coas

Conference, Guelph, Ontario, May 21–24, 

Canadian Coastal Science and Engineering 

Association, p. 176–184. 

References 
Appendix A.


UNI File used in UCODE Parameter Estimation


Analysis of the St. Clair–Detroit River Model

UCODE Files 

# UNI file for SCD8.


3 # Phase 1 provides parameter substitution and forward modeling 


# using the starting parameter values specified in the prepare file


### Sensitivity and regression control


1 # Differencing for sensitivity calculations: (1-> forward; 2-> central)


0.02 # Tolerance, convergence criterion based on changes in estimated parameter values


0.02 # SOSR, convergence criterion based on changes in model fit


0 # Do not apply quasi-Newton updating


5 # Maximum number of iterations


0.5 # Maximum fractional parameter changes


d:\usgs\wrdapp\ucode3.02\bin\mrdrive # Path and name of inverse code


#


21 # Number of application models (one for each steady-state simulation)


d:\usgs\sms\models\rma2v435.exe < SCD8.SS1.bat


del SCD8.SS1.ihot


ren SCD8.SS1.ohot SCD8.SS1.ihot


d:\usgs\sms\models\rma2v435.exe < SCD8.SS2.bat


del SCD8.SS2.ihot


ren SCD8.SS2.ohot SCD8.SS2.ihot


d:\usgs\sms\models\rma2v435.exe < SCD8.SS3.bat


del SCD8.SS3.ihot


ren SCD8.SS3.ohot SCD8.SS3.ihot


d:\usgs\sms\models\rma2v435.exe < SCD8.SS4.bat


del SCD8.SS4.ihot


ren SCD8.SS4.ohot SCD8.SS4.ihot


d:\usgs\sms\models\rma2v435.exe < SCD8.SS5.bat


del SCD8.SS5.ihot


ren SCD8.SS5.ohot SCD8.SS5.ihot


d:\usgs\sms\models\rma2v435.exe < SCD8.SS6.bat


del SCD8.SS6.ihot


ren SCD8.SS6.ohot SCD8.SS6.ihot


d:\usgs\sms\models\rma2v435.exe < SCD8.SS7.bat


del SCD8.SS7.ihot


ren SCD8.SS7.ohot SCD8.SS7.ihot


# 


# Printing options


1 # Scale sensitivity: (0, none; 1, dimensionless; 1% scaled; 3, 1 and 2);


0 # Print-intermediate (0, no print; 1, print);


1 # Print graphing files (0, no; 1, yes);


3 # Number of sets of normally distributed random numbers to generate


#


# OBSERVATIONS 


# Obsname value statistic stat-flag plot-sym 


# Scenario 1: Steady-state flow simulation for Nov. 3-5, 1999


# St. Clair River Flow


SS1QCS208 55557 1236 1 1 # CG 04


SS1QCS210 118133 1236 1 1 # CG 05


SS1QCS216 144166 889 1 1 # CG 08


SS1QCS218 30121 889 1 1 # CG 09


SS1QCS222 6399 625 1 1 # CG 11


SS1QCS230 167888 625 1 1 # CG 12


SS1QCS232 78880 2225 1 1 # CG 13


SS1QCS240 57495 1673 1 1 # CG 17


SS1QCS242 31513 1833 1 1 # CG 18


SS1QCS234 6356 832 1 1 # CG 14


SS1QCS236 42615 2217 1 1 # CG 15


SS1QCS238 29909 2414 1 1 # CG 16


Appen
# Detroit River Flows


SS1QCS003 134187 


SS1QCS008 48373 


SS1QCS015 55684 


SS1QCS029 126876 


SS1QCS100 47784 


SS1QCS101 95824 


SS1QCS102 39264 


SS1QCS120 40517 


SS1QCS121 9572 


SS1QCS122 48136 


SS1QCS123 84647 


SS1QCS143 20396 


SS1QCS165 64252 


SS1QCS142 12201 


SS1QCS164 8195 


SS1QCS141 21484 


SS1QCS163 38854 


SS1QCS161 21531 


SS1QCS162 9524 


# Stages 


SS1SFG 577.724 


SS1SDP 577.335 


SS1SMBR 577.277 


SS1SDD 576.727 


SS1SSCT 575.550 


SS1SMC 574.747 


SS1SRL 574.415 


SS1SALG 574.276 


SS1SNorC 574.169 


29956


SS1SSouC 573.842 


SS1SMidC 573.793 


SS1SSCS 573.335 


SS1SWP 573.039 


SS1SBelle 572.970 


SS1SFW 572.247 


SS1SWYN 571.797 


SS1SAmher 571.507 


SS1SGIB 570.381 


#


1770 1 1 

1770 1 1 

1460 1 1 

1460 1 1 

1179 1 1 

1110 1 1 

929 1 1 

1776 1 1 

2050 1 1 

1764 1 1 

2197 1 1 

1701 1 1 

2269 1 1 

2146 1 1 

2009 1 1 

2431 1 1 

2886 1 1 

2017 1 1 

1027 1 1 

0.396 1 1 

0.325 1 1 

0.233 1 1 

0.330 1 1 

0.183 1 1 

0.100 1 1 

0.093 1 1 

0.063 1 1 

0.051 1 1 

0.060 1 1 

0.046 1 1 

0.119 1 1 

0.119 1 1 

0.149 1 1 

0.238 1 1 

0.304 1 1 

0.334 1 1 

0.641 1 1 

# CG 21


# CG 22


# CG 24


# CG 25


# CG 29


# CG 30


# CG 31


# CG 32


# CG 33


# CG 34


# CG 35


# CG 37


# CG 42


# CG 36


# CG 41


# CG 54


# CG 40


# CG 38


# CG 39


Gage Node


# NOAA 9014098 


# NOAA 9014096 


# NOAA 9014090 


# NOAA 9014087 


# NOAA 9014080 


42935


42839 


41658 


40852


37154


# USACE SCR at Marine City; Node 35169


# USACE SCR at Roberts Landing; Node 329

# NOAA 9014070 31568


# USACE North Channel of St. Clair River

# USACE South Channel of St. Clair River

# USACE Middle Channel of St. Clair River

# NOAA 9034052 18594


# NOAA 9044049 16127


# USACE Detroit River at Belle Isle; 153

# NOAA 9044036 12815


# NOAA 9044030 8923


# CHS on Detroit River at Amherstburg; Nod

# NOAA 9044020 2803


# Scenario 2: Steady-state flow simulation for Oct. 26-29, 1998


# St. Clair River Flow


SS2QCS208 63820 


SS2QCS210 130733 


SS2QCS216 160258 


SS2QCS218 34893 


SS2QCS222 8023 


SS2QCS230 187128 


SS2QCS232 86231 


SS2QCS240 66226 


SS2QCS242 34671 


SS2QCS234 6948 


SS2QCS236 46586 


SS2QCS238 32696 


# Detroit River Flows


SS2QCS003 149522 


SS2QCS008 53901 


SS2QCS015 64196 


1282 1 1 # CG 04 

1282 1 1 # CG 05 

946 1 1 # CG 08 

946 1 1 # CG 09 

654 1 1 # CG 11 

654 1 1 # CG 12 

2310 1 1 # CG 13 

1744 1 1 # CG 17 

1944 1 1 # CG 18 

907 1 1 # CG 14 

2388 1 1 # CG 15 

2624 1 1 # CG 16 

1973 1 1 # CG 21 

1973 1 1 # CG 22 

1503 1 1 # CG 24 

42 A Two-Dimensional Hydrodynamic Model of the St. Clair–Detroit River Waterway in the Great Lakes Basin 
SS2QCS029 139228 1503 1 1 # CG 25 

SS2QCS100 53236 1313 1 1 # CG 29 

SS2QCS101 105960 1185 1 1 # CG 30 

SS2QCS102 44540 987 1 1 # CG 31 

SS2QCS120 45140 1979 1 1 # CG 32 

SS2QCS121 14495 2283 1 1 # CG 33 

SS2QCS122 51722 1870 1 1 # CG 34 

SS2QCS123 92379 2277 1 1 # CG 35 

SS2QCS143 22259 1858 1 1 # CG 37 

SS2QCS165 70120 2502 1 1 # CG 42 

SS2QCS142 13316 2342 1 1 # CG 36 

SS2QCS164 8943 2192 1 1 # CG 41 

SS2QCS141 23157 2623 1 1 # CG 54 

SS2QCS163 41880 3116 1 1 # CG 40 

SS2QCS161 26574 2216 1 1 # CG 38 

SS2QCS162 11078 1105 1 1 # CG 39 

# Stages 

SS2SFG 578.902 0.207 1 1 # 9014098 

SS2SDP 578.470 0.189 1 1 # 9014096 

SS2SPE 578.196 0.159 1 1 # CHS Point Edward 

SS2SMBR 578.102 0.163 1 1 # 9014090 

SS2SDD 577.742 0.147 1 1 # 9014087 

SS2SSCT 576.537 0.096 1 1 # 9014080 

SS2SALG 575.083 0.025 1 1 # 9014070 

SS2SSouC 574.812 0.031 1 1 # USACE South Channel of St. Clair River

SS2SMidC 574.650 0.022 1 1 # USACE Middle Channel of St. Clair River

SS2SSCS 574.533 0.036 1 1 # 9034052 

SS2SWP 574.297 0.050 1 1 # 9044049 

SS2SFW 573.553 0.064 1 1 # 9044036 

SS2SWYN 573.129 0.085 1 1 # 9044030 

SS2SAmher 572.848 0.097 1 1 # CHS on Detroit River at Amherstburg; Nod

SS2SGIB 571.900 0.161 1 1 # 9044020 

# 

# Scenario 3: Steady-state flow simulation for July 8-10, 1996


# St. Clair River Flow


SS3QCS208 73406 


SS3QCS210 144342 


SS3QCS216 177855 


SS3QCS218 40490 


SS3QCS222 10043 


SS3QCS230 208302 


SS3QCS232 93919 


SS3QCS240 76344 


SS3QCS242 38040 


SS3QCS234 7568 


SS3QCS236 50740 


SS3QCS238 35611 


# Detroit River Flows


SS3QCS003 166571 


SS3QCS008 60047 


SS3QCS015 74176 


SS3QCS029 152442 


SS3QCS100 59296 


SS3QCS101 117038 


SS3QCS102 50596 


SS3QCS120 50278 


SS3QCS121 20889 


SS3QCS122 55251 


1449 1 1 # CG 04 

1449 1 1 # CG 05 

1083 1 1 # CG 08 

1083 1 1 # CG 09 

741 1 1 # CG 11 

741 1 1 # CG 12 

2663 1 1 # CG 13 

2015 1 1 # CG 17 

2218 1 1 # CG 18 

991 1 1 # CG 14 

2646 1 1 # CG 15 

2877 1 1 # CG 16 

2197 1 1 # CG 21 

2197 1 1 # CG 22 

1675 1 1 # CG 24 

1675 1 1 # CG 25 

1463 1 1 # CG 29 

1331 1 1 # CG 30 

1109 1 1 # CG 31 

2204 1 1 # CG 32 

2543 1 1 # CG 33 

2113 1 1 # CG 34 

Appen
SS3QCS123 100512 


SS3QCS143 24218 


SS3QCS165 76294 


SS3QCS142 14488 


SS3QCS164 9730 


SS3QCS141 24831 


SS3QCS163 44907 


SS3QCS161 32964 


SS3QCS162 12756 


# Stages


SS3SFG 580.003 


SS3SDP 579.554 


SS3SMBR 579.187 


SS3SDD 578.819 


SS3SSCT 577.647 


SS3SMC 576.854 


SS3SRL 576.422 


SS3SALG 576.203 


SS3SNorC 576.229 


29956


SS3SSouC 576.044 


SS3SMidC 575.873 


SS3SSCS 575.731 


SS3SWP 575.459 


SS3SFW 574.708 


SS3SWYN 574.297 


SS3SAmher 574.257 


SS3SGIB 573.107 


#


2594 1 1 # CG 35 

2027 1 1 # CG 37 

2750 1 1 # CG 42 

2548 1 1 # CG 36 

2385 1 1 # CG 41 

2829 1 1 # CG 54 

3386 1 1 # CG 40 

2500 1 1 # CG 38 

1225 1 1 # CG 39 

0.156 1 1 # 9014098 

0.134 1 1 # 9014096 

0.131 1 1 # 9014090 

0.122 1 1 # 9014087 

0.100 1 1 # 9014080 

0.071 1 1 # USACE at Marine City 

0.021 1 1 # USACE at Roberts Landing 

0.071 1 1 # 9014070 

0.051 1 1 # USACE North Channel of St. Clair River

0.069 1 1 # USACE South Channel of St. Clair River

0.044 1 1 # USACE Middle Channel of St. Clair River

0.053 1 1 # 9034052 

0.059 1 1 # 9044049 

0.111 1 1 # 9044036 

0.148 1 1 # 9044030 

0.170 1 1 # CHS on Detroit River at Amherstburg; Nod

0.293 1 1 # 9044020 

# Scenario 4: Steady-state flow simulation for August 4-6, 1997


# St. Clair River Flow


SS4QCS208 75647 


SS4QCS210 147380 


SS4QCS216 181818 


SS4QCS218 41807 


SS4QCS222 10535 


SS4QCS230 213090 


SS4QCS232 95599 


SS4QCS240 78706 


SS4QCS242 38786 


SS4QCS234 7703 


SS4QCS236 51647 


SS4QCS238 36248 


# Detroit River Flows


SS4QCS003 170452 


SS4QCS008 61446 


SS4QCS015 76523 


SS4QCS029 155374 


SS4QCS100 60676 


SS4QCS101 119531 


SS4QCS102 52003 


SS4QCS120 51448 


SS4QCS121 22480 


SS4QCS122 55987 


SS4QCS123 102295 


SS4QCS143 24648 


SS4QCS165 77647 


SS4QCS142 14745 


SS4QCS164 9903 


1511 1 1 # CG 04 

1511 1 1 # CG 05 

1127 1 1 # CG 08 

1127 1 1 # CG 09 

773 1 1 # CG 11 

773 1 1 # CG 12 

2783 1 1 # CG 13 

2113 1 1 # CG 17 

2304 1 1 # CG 18 

1010 1 1 # CG 14 

2715 1 1 # CG 15 

2938 1 1 # CG 16 

2248 1 1 # CG 21 

2248 1 1 # CG 22 

1740 1 1 # CG 24 

1740 1 1 # CG 25 

1497 1 1 # CG 29 

1375 1 1 # CG 30 

1148 1 1 # CG 31 

2255 1 1 # CG 32 

2602 1 1 # CG 33 

2185 1 1 # CG 34 

2703 1 1 # CG 35 

2065 1 1 # CG 37 

2805 1 1 # CG 42 

2593 1 1 # CG 36 

2427 1 1 # CG 41 

44 A Two-Dimensional Hydrodynamic Model of the St. Clair–Detroit River Waterway in the Great Lakes Basin 
SS4QCS141 25185 2874 1 1 # CG 54 

SS4QCS163 45547 3448 1 1 # CG 40 

SS4QCS161 34541 2581 1 1 # CG 38 

SS4QCS162 13123 1257 1 1 # CG 39 

# Stages 

SS4SFG 581.230 0.135 1 1 # 9014098 

SS4SDP 580.705 0.110 1 1 # 9014096 

SS4SPE 580.363 0.120 1 1 # CHS Point Edward 

SS4SMBR 580.320 0.099 1 1 # 9014090 

SS4SDD 579.961 0.093 1 1 # 9014087 

SS4SSCT 578.682 0.064 1 1 # 9014080 

SS4SMC 577.867 0.052 1 1 # USACE at Marine City 

SS4SRL 577.505 0.040 1 1 # USACE at Roberts Landing 

SS4SALG 577.241 0.025 1 1 # 9014070 

SS4SNorC 577.138 0.038 1 1 # USACE North Channel of St. Clair River

29956 

SS4SSouC 577.010 0.036 1 1 # USACE South Channel of St. Clair River

SS4SMidC 576.827 0.030 1 1 # USACE Middle Channel of St. Clair River

SS4SSCS 576.770 0.033 1 1 # 9034052 

SS4SWP 576.485 0.054 1 1 # 9044049 

SS4SFW 575.709 0.051 1 1 # 9044036 

SS4SWYN 575.275 0.060 1 1 # 9044030 

SS4SAmher 574.988 0.069 1 1 # CHS on Detroit River at Amherstburg; Nod

SS4SGIB 574.138 0.117 1 1 # 9044020 

# 

# Scenario 5: Steady-state flow simulation for Sep. 23-24, 1999


# St. Clair River Flow


SS5QCS208 56253 


SS5QCS210 119228 


SS5QCS216 145557 


SS5QCS218 30521 


SS5QCS222 6531 


SS5QCS230 169547 


SS5QCS232 79527 


SS5QCS240 58231 


SS5QCS242 31789 


SS5QCS234 6408 


SS5QCS236 42965 


SS5QCS238 30154 


# Detroit River Flows


SS5QCS003 135504 


SS5QCS008 48848 


SS5QCS015 56397 


SS5QCS029 127954 


SS5QCS100 48252 


SS5QCS101 96700 


SS5QCS102 39711 


SS5QCS120 40914 


SS5QCS121 9964 


SS5QCS122 48459 


SS5QCS123 85327 


SS5QCS143 20559 


SS5QCS165 64767 


SS5QCS142 12299 


SS5QCS164 8260 


SS5QCS141 21634 


SS5QCS163 39125 


SS5QCS161 21939 


SS5QCS162 9658 


1238 1 1 # CG 04 

1238 1 1 # CG 05 

892 1 1 # CG 08 

892 1 1 # CG 09 

627 1 1 # CG 11 

627 1 1 # CG 12 

2225 1 1 # CG 13 

1675 1 1 # CG 17 

1838 1 1 # CG 18 

838 1 1 # CG 14 

2229 1 1 # CG 15 

2432 1 1 # CG 16 

1788 1 1 # CG 21 

1788 1 1 # CG 22 

1462 1 1 # CG 24 

1462 1 1 # CG 25 

1190 1 1 # CG 29 

1115 1 1 # CG 30 

933 1 1 # CG 31 

1794 1 1 # CG 32 

2070 1 1 # CG 33 

1769 1 1 # CG 34 

2197 1 1 # CG 35 

1714 1 1 # CG 37 

2289 1 1 # CG 42 

2163 1 1 # CG 36 

2025 1 1 # CG 41 

2448 1 1 # CG 54 

2905 1 1 # CG 40 

2034 1 1 # CG 38 

1033 1 1 # CG 39 

Appen
# Stages Gage Node 

SS5SFG 577.992 0.191 1 1 # NOAA 9014098 42935 

SS5SDP 577.615 0.161 1 1 # NOAA 9014096 42839 

SS5SMBR 577.423 0.144 1 1 # NOAA 9014090 41658 

SS5SDD 576.967 0.107 1 1 # NOAA 9014087 40852 

SS5SSCT 575.843 0.075 1 1 # NOAA 9014080 37154 

SS5SMC 574.980 0.068 1 1 # USACE SCR at Marine City; Node 35169 

SS5SRL 574.730 0.064 1 1 # USACE SCR at Roberts Landing; Node 329

SS5SALG 574.538 0.059 1 1 # NOAA 9014070 31568 

SS5SNorC 574.496 0.067 1 1 # USACE North Channel of St. Clair River

29956 

SS5SSouC 574.227 0.115 1 1 # USACE South Channel of St. Clair River

SS5SMidC 574.128 0.065 1 1 # USACE Middle Channel of St. Clair River

SS5SSCS 573.878 0.060 1 1 # NOAA 9034052 18594 

SS5SWP 573.591 0.102 1 1 # NOAA 9044049 16127 

SS5SBelle 573.516 0.105 1 1 # USACE Detroit River at Belle Isle; 153

SS5SFW 572.881 0.130 1 1 # NOAA 9044036 12815 

SS5SWYN 572.562 0.120 1 1 # NOAA 9044030 8923 

SS5SAmher 572.161 0.194 1 1 # CHS on Detroit River at Amherstburg; Nod

SS5SGIB 571.314 0.304 1 1 # NOAA 9044020 


#


#


# Scenario 6: Steady-state flow simulation for May 5-7, 1997


# St. Clair River Flow


SS6QCS208 71916 1413 1 1 # CG 04 

SS6QCS210 142292 1413 1 1 # CG 05 

SS6QCS216 175189 1056 1 1 # CG 08 

SS6QCS218 39616 1056 1 1 # CG 09 

SS6QCS222 9720 722 1 1 # CG 11 

SS6QCS230 205085 722 1 1 # CG 12 

SS6QCS232 92778 2590 1 1 # CG 13 

SS6QCS240 74772 1957 1 1 # CG 17 

SS6QCS242 37535 2165 1 1 # CG 18 

SS6QCS234 7476 978 1 1 # CG 14 

SS6QCS236 50123 2602 1 1 # CG 15 

SS6QCS238 35179 2837 1 1 # CG 16 

# Detroit River Flows 

SS6QCS003 163969 2163 1 1 # CG 21 

SS6QCS008 59109 2163 1 1 # CG 22 

SS6QCS015 72617 1637 1 1 # CG 24 

SS6QCS029 150461 1637 1 1 # CG 25 

SS6QCS100 58371 1440 1 1 # CG 29 

SS6QCS101 115360 1304 1 1 # CG 30 

SS6QCS102 49658 1086 1 1 # CG 31 

SS6QCS120 49494 2170 1 1 # CG 32 

SS6QCS121 19850 2504 1 1 # CG 33 

SS6QCS122 54743 2068 1 1 # CG 34 

SS6QCS123 99302 2529 1 1 # CG 35 

SS6QCS143 23927 2002 1 1 # CG 37 

SS6QCS165 75375 2713 1 1 # CG 42 

SS6QCS142 14313 2517 1 1 # CG 36 

SS6QCS164 9613 2356 1 1 # CG 41 

SS6QCS141 24588 2798 1 1 # CG 54 

SS6QCS163 44468 3344 1 1 # CG 40 

SS6QCS161 31933 2450 1 1 # CG 38 

SS6QCS162 12506 1204 1 1 # CG 39 

# Stages Gage Node 

SS6SFG 580.580 0.274 1 1 # NOAA 9014098 

SS6SDP 580.131 0.220 1 1 # NOAA 9014096 

2803


42935


42839 


46 A Two-Dimensional Hydrodynamic Model of the St. Clair–Detroit River Waterway in the Great Lakes Basin 
SS6SPE 579.860 0.214 1 1 # CHS Point Edward 42476 

SS6SMBR 579.788 0.202 1 1 # NOAA 9014090 41658 

SS6SDD 579.423 0.172 1 1 # NOAA 9014087 40852 

SS6SSCT 578.182 0.099 1 1 # NOAA 9014080 37154 

SS6SMC 577.420 0.089 1 1 # USACE SCR at Marine City; Node 35169 

SS6SRL 577.115 0.102 1 1 # USACE SCR at Roberts Landing; Node 329

SS6SALG 576.903 0.070 1 1 # NOAA 9014070 31568 

SS6SNorC 576.759 0.104 1 1 # USACE North Channel of St. Clair River

29956 

SS6SSouC 576.672 0.089 1 1 # USACE South Channel of St. Clair River

SS6SMidC 576.508 0.076 1 1 # USACE Middle Channel of St. Clair River

SS6SSCS 576.339 0.087 1 1 # NOAA 9034052 18594 

SS6SWP 576.111 0.124 1 1 # NOAA 9044049 16127 

SS6SFW 575.314 0.140 1 1 # NOAA 9044036 12815 

SS6SWYN 574.882 0.176 1 1 # NOAA 9044030 8923 

SS6SAmher 574.624 0.198 1 1 # CHS on Detroit River at Amherstburg; Nod

SS6SGIB 573.710 0.351 1 1 # NOAA 9044020 2803 

#


#


# Scenario 7: Steady-state flow simulation for Sep. 21-24, 1998


# St. Clair River Flow


SS7QCS208 65379 1299 1 1 # CG 04 

SS7QCS210 133017 1299 1 1 # CG 05 

SS7QCS216 163195 963 1 1 # CG 08 

SS7QCS218 35799 963 1 1 # CG 09 

SS7QCS222 8342 663 1 1 # CG 11 

SS7QCS230 190652 663 1 1 # CG 12 

SS7QCS232 87539 2348 1 1 # CG 13 

SS7QCS240 67873 1772 1 1 # CG 17 

SS7QCS242 35240 1977 1 1 # CG 18 

SS7QCS234 7054 921 1 1 # CG 14 

SS7QCS236 47293 2425 1 1 # CG 15 

SS7QCS238 33192 2664 1 1 # CG 16 

# Detroit River Flows 

SS7QCS003 152347 2010 1 1 # CG 21 

SS7QCS008 54919 2010 1 1 # CG 22 

SS7QCS015 65811 1520 1 1 # CG 24 

SS7QCS029 141455 1520 1 1 # CG 25 

SS7QCS100 54240 1338 1 1 # CG 29 

SS7QCS101 107809 1204 1 1 # CG 30 

SS7QCS102 45529 1002 1 1 # CG 31 

SS7QCS120 45991 2016 1 1 # CG 32 

SS7QCS121 15487 2327 1 1 # CG 33 

SS7QCS122 55340 1902 1 1 # CG 34 

SS7QCS123 93760 2312 1 1 # CG 35 

SS7QCS143 22591 1886 1 1 # CG 37 

SS7QCS165 71169 2543 1 1 # CG 42 

SS7QCS142 13515 2377 1 1 # CG 36 

SS7QCS164 9077 2225 1 1 # CG 41 

SS7QCS141 23448 2658 1 1 # CG 54 

SS7QCS163 42407 3160 1 1 # CG 40 

SS7QCS161 27574 2257 1 1 # CG 38 

SS7QCS162 11362 1123 1 1 # CG 39 

# Stages Gage Node 

SS7SFG 579.495 0.191 1 1 # NOAA 9014098 42935 

SS7SDP 579.052 0.168 1 1 # NOAA 9014096 42839 

SS7SPE 578.800 0.148 1 1 # CHS Point Edward 42476 

SS7SMBR 578.718 0.153 1 1 # NOAA 9014090 41658 

SS7SDD 578.370 0.135 1 1 # NOAA 9014087 40852 

Appen
SS7SSCT 577.176 0.086 1 1 # NOAA 9014080 37154 

SS7SMC 576.405 0.065 1 1 # USACE SCR at Marine City; Node 35169 

SS7SPL 575.927 0.049 1 1 # CHS at Port Lambton 

SS7SALG 575.753 0.046 1 1 # NOAA 9014070 31568 

SS7SSouC 575.502 0.055 1 1 # USACE South Channel of St. Clair River

SS7SMidC 575.335 0.048 1 1 # USACE Middle Channel of St. Clair River

SS7SSCS 575.198 0.050 1 1 # NOAA 9034052 18594 

SS7SWP 574.983 0.096 1 1 # NOAA 9044049 16127 

SS7SFW 574.246 0.111 1 1 # NOAA 9044036 12815 

SS7SWYN 573.830 0.142 1 1 # NOAA 9044030 8923 

SS7SAmher 573.551 0.160 1 1 # CHS on Detroit River at Amherstburg; Nod

SS7SGIB 572.742 0.224 1 1 # NOAA 9044020 2803 

# 

END 

48 A Two-Dimensional Hydrodynamic Model of the St. Clair–Detroit River Waterway in the Great Lakes Basin 
Appendix B.


PREPARE Input File used in UCODE


Parameter Estimation Analysis of the


St. Clair–Detroit River Model

# Prepare Input File for the St. Clair - Detroit River System


#


# No function file


F no


#


# List of template files and associated model input files


<SCD8.SS1.tpl


>SCD8.SS1.bc


<SCD8.SS2.tpl


>SCD8.SS2.bc


<SCD8.SS3.tpl


>SCD8.SS3.bc


<SCD8.SS4.tpl


>SCD8.SS4.bc


<SCD8.SS5.tpl


>SCD8.SS5.bc


<SCD8.SS6.tpl


>SCD8.SS6.bc


<SCD8.SS7.tpl


>SCD8.SS7.bc


#


# Parameter 


/!SCRUpper,,! 


/!SCRDryDock! 


/!SCRInterIs! 


/!SCRAlgonac! 


/!SCRFlats,,! 


/!SCRFawnIsE! 


/!ChenalEcar! 


/!SCRNorth,,! 


/!SCRMiddle,! 


/!SCRCutoff,! 


/!BassettCh,! 


/!LakStClair! 


/!DETUpper,,! 


/!DETBelleIN! 


/!DETRRouge,! 


/!DETFightIs! 


/!DETStonyIs! 


/!DETTrenton! 


/!DETSugarW,! 


/!DETBobloIs! 


/!DETLivChLo! 


/!DETLivChUp! 


/!DETAmhChUp! 


/!DETAmhChLo! 


/!DETSugarE,! 


#


END


0.0286721 0.01 


0.0253656 0.01 


0.0233593 0.01 


0.0216357 0.01 


0.0390826 0.01 


0.0211818 0.01 


0.0153055 0.01 


0.0252233 0.01 


0.0199496 0.01 


0.0293515 0.01 


0.0227179 0.01 


0.0238171 0.01 


0.0198704 0.01 


0.0214061 0.01 


0.0184265 0.01 


0.0312344 0.01 


0.0490775 0.01 


0.0365092 0.01 


0.0472579 0.01 


0.0677871 0.01 


0.0315868 0.01 


0.0172790 0.01 


0.0250071 0.01 


0.0339551 0.01 


0.0318956 0.01 


0.05 0.01 %12.9f 1 1


0.05 0.01 %12.9f 1 1


0.05 0.01 %12.9f 1 1


0.05 0.01 %12.9f 1 1


0.05 0.01 %12.9f 1 1


0.05 0.01 %12.9f 1 1


0.05 0.01 %12.9f 1 1


0.05 0.01 %12.9f 1 1


0.05 0.01 %12.9f 1 1


0.05 0.01 %12.9f 1 1


0.05 0.01 %12.9f 1 1


0.05 0.01 %12.9f 1 1


0.05 0.01 %12.9f 1 1


0.05 0.01 %12.9f 1 1


0.05 0.01 %12.9f 1 1


0.05 0.01 %12.9f 1 1


0.05 0.01 %12.9f 1 1


0.05 0.01 %12.9f 1 1


0.05 0.01 %12.9f 1 1


0.10 0.01 %12.9f 1 1


0.05 0.01 %12.9f 1 1


0.05 0.01 %12.9f 1 1


0.05 0.01 %12.9f 1 1


0.05 0.01 %12.9f 1 1


0.05 0.01 %12.9f 1 1


Appen
Appendix C.


Example of TEMPLATE Files used to Generate


Control Files in the UCODE Parameter Estimation


Analysis of the St. Clair–Detroit River Model

T1 St. Clair–Detroit River Waterway


T2 SCD8 - SCD7 after applying fixslope


T3 Steady State Low-Flow Run for Nov. 3-5, 1999


SI 0


$L 63 62 60 0 0 3 0


$M 1


TR 0 -1 1 0


GCL 1 


GCL 


GCL 


GCL 


GCL 


GCL 


GCL 


GCL 2 


GCL 


GCL 3 


GCL 


GCL 


GCL 4 


GCL 5 


GCL 


GCL 6 


GCL 


GCL 7 


GCL 


GCL 8 


GCL 


GCL 9 


GCL 10 


GCL 


GCL 11 


GCL 12 


GCL 


GCL 


GCL 13 


GCL 


GCL 14 


GCL 15 


GCL 16 


GCL 17 


GCL 18 


GCL 19 


GCL 20 


GCL 21 


GCL 


GCL 22 


GCL 23 


GCL 


GCL 


GCL 24 


GCL 25 


GCL 


GCL 26 


GCL 


GCL 


GCL 27 


GCL 


1 3 5 7 9 11


13 15 17 19 21 23


25 27 29 31 33 35


37 39 41 43 45 47


49 51 53 55 57 59


61 63 65 67 69 71


73 75 -1


41588 41585 41582 41579 41576 41573


41567 41561 41559 41564 41570 -1


39811 39808 39805 39799 39757 39748


39742 39739 39733 39731 39736 39745


39751 -1


39224 39222 39227 39230 39233 39236 -1


39265 39262 39259 39256 39253 39250


39247 39244 39241 39239 -1


37154 37151 37148 37145 37142 37139


37133 37127 37125 37130 37136 -1


34754 34751 34748 34745 34742 34739


34733 34727 34725 34730 34736 -1


34241 34238 34235 34232 34229 34226


34223 34220 34218 -1


34166 34164 34169 34172 34180 -1


33077 33074 33071 33068 33065 33062


33056 33050 33048 33053 33059 -1


32176 32178 32181 -1


31582 31471 31372 31281 31204 31189


31186 31183 31177 31171 31169 31174


31180 -1


29065 29062 29056 29050 29048 29053


29059 -1


27674 27676 -1


24097 24094 24091 24089 -1


25491 25177 24886 24888 -1


29903 29901 29906 29909 29912 -1


30101 30098 30095 30093 -1


25945 25942 25939 25937 -1


27780 27778 27783 -1


16080 16078 16043 16041 16046 16049


16052 16055 16058 16061 -1


16066 16064 16069 16072 16075 -1


15824 15821 15790 15766 15702 15646


15649 15652 15661 15664 15667 15670


15673 15676 15679 15682 -1


15593 15590 15587 15584 15581 15579 -1


14971 14969 14974 14977 14980 14983


14986 14989 14992 14995 -1


14097 14091 14084 14082 14076 14070


14068 14073 14079 14088 14094 14100


14103 14106 14109 14112 -1


12813 12807 12801 12795 12789 12787


12792 12798 12804 12810 12816 12819


Appen
GCL 12822 -1


GCL 28 11864 11858 11852 11846 11837 11835


GCL 11842 11902 11911 11917 11923 11929


GCL 11980 -1


GCL 29 9785 9779 9773 9767 9765 -1


GCL 30 10113 10111 10116 10119 10123 10126


GCL 10129 -1


GCL 31 10957 10955 10960 10963 10966 -1


GCL 32 8199 8196 8193 8190 8188 -1


GCL 33 4833 4827 4821 4819 4824 -1


GCL 34 4260 4258 4263 4266 4269 -1


GCL 35 5394 5391 5388 5382 5376 5374


GCL 5379 5385 -1


GCL 36 4057 4051 4046 4044 3955 -1


GCL 37 4057 4168 4275 4376 4396 -1


GCL 38 2331 2334 2338 2342 2345 2464 -1


GCL 39 2225 2228 -1


GCL 40 3929 3931 3934 3937 3944 -1


GCL 41 3453 3447 3445 3450 3456 3459 -1


GCL 42 2556 2554 2559 2562 2565 2568


GCL 2571 -1


GCL 43 3033 3030 2899 2766 2733 2730


GCL 2727 2724 2721 2719 -1


GCL 44 2139 2137 1989 1987 1992 1995 -1


GCL 45 1880 1878 1883 2018 2021 -1


GCL 46 42932 42926 42920 42914 42908 42906


GCL 42911 42917 42923 42929 42935 -1


GCL 47 41694 41692 -1


GCL 48 37385 37383 -1


GCL 49 34594 34592 -1


GCL 50 32251 32254 -1


GCL 51 25520 25518 -1


GCL 52 28471 28469 -1


GCL 53 12277 12275 -1


GCL 54 3903 3775 3656 3546 -1


TZ 0 0 0 0 0


DE 0 0 4


TI 10 4 0.00010 0.00000


FT 15


IC 575. 0 0.25


CO RD 1 1 0.030683920 3.0305200 0.030971330 0.05552626


HNT 1 !SCRUpper,,! 


HNT 38 !SCRUpper,,! 


HNT 2 !SCRUpper,,! 


HNT 39 !SCRDryDock! 


HNT 3 !SCRDryDock! 


HNT 4 !SCRDryDock! 


HNT 5 !SCRInterIs! 


HNT 6 !SCRInterIs! 


HNT 8 !SCRAlgonac! 


HNT 11 !SCRAlgonac! 


HNT 14 !SCRFlats,,! 


HNT 7 !SCRFawnIsE! 


HNT 40 !ChenalEcar! 


HNT 12 !SCRNorth,,! 


HNT 13 !SCRMiddle,! 


HNT 15 !SCRCutoff,! 


HNT 16 !BassettCh,! 


56 A Two-Dimensional Hydrodynamic Model of the St. Clair–Detroit River Waterway in the Great Lakes Basin 
HNT 17 !LakStClair! 

HNT 18 !LakStClair! 

HNT 19 !LakStClair! 

HNT 20 !DETUpper,,! 

HNT 41 !DETUpper,,! 

HNT 22 !DETBelleIN! 

HNT 42 !DETRRouge,! 

HNT 25 !DETRRouge,! 

HNT 26 !DETFightIs! 

HNT 29 !DETFightIs! 

HNT 27 !DETFightIs! 

HNT 28 !DETFightIs! 

HNT 43 !DETStonyIs! 

HNT 35 !DETTrenton! 

HNT 36 !DETSugarW,! 

HNT 37 !DETSugarW,! 

HNT 46 !DETBobloIs! 

HNT 48 !DETBobloIs! 

HNT 32 !DETLivChLo! 

HNT 44 !DETLivChUp! 

HNT 33 !DETAmhChUp! 

HNT 45 !DETAmhChLo! 

HNT 47 !DETSugarE,! 

PE 1 15 1.000 1.000 1.000 1.000 1.000 

BHL 1 570.052 

BQL 46 173201 4.29014 0.5 

BQL 47 489 5.43537 0.5 

BQL 48 119 6.18352 0.5 

BQL 49 478 4.45179 0.5 

BQL 50 1861 4.22988 0.5 

BQL 51 928 6.18352 0.5 

BQL 52 4857 3.19418 0.5 

BQL 53 312 5.47077 0.5 

RAT 17 0.001448 

RAT 18 0.001448 

RAT 19 0.001448 

END Simulation at time = 0.00 

STOP 

Appen
Appendix D.


Excerpt from EXTRACT File used to Process


Output Files from UCODE Parameters Estimation


Analysis of the St. Clair–Detroit River Model

# Extract file for St. Clair - Detroit Simulation Model


#


# Scenario 1: Nov. 3-5, 1999


<SCD8.SS1.OUT


o SS1SSouC


+300


/NODAL VELOCITY, DEPTH AND ELEVATION..../


/ 29239 /


c114_120


o SS1SBelle


/ 15300 /


c74_80


o SS1SNorC 


/ 29958 /


c114_120


o SS1SWP


/ 16127 /


c74_80


o SS1SGIB


/ 2803 /


c34_40


o SS1SALG


/ 31568 /


c114_120


o SS1SSCS


/ 18594 /


c74_80


o SS1SRL


/ 32920 /


c114_120


o SS1SAmher


/ 6141 /


c34_40


o SS1SMC


/ 35169 /


c114_120


o SS1SSCT


/ 37154 /


c114_120


o SS1SWYN


/ 8923 /


c34_40


o SS1SMidC


/ 25939 /


c74_80


o SS1SDD


/ 40852 /


c114_120


o SS1SFW


/ 12815 /


c34_40


o SS1SMBR


/ 41658 /


c114_120


o SS1SDP


/ 42839 /


c114_120


o SS1SFG


Appen
/ 42935 /


c114_120


#


# St. Clair River Flows


o SS1QCS208 # 55004 
 1234 1 1 CG 04


/ CONTINUITY CHECKS ... TIME STEP =/


# / 4 /


+6


c20_30


o SS1QCS210 # 


/ 5 /


c20_30


o SS1QCS216 # 


/ 8 /


c20_30


o SS1QCS218 # 


/ 9 /


c20_30


o SS1QCS222 # 


/ 11 /


c20_30


o SS1QCS230 # 


/ 12 /


c20_30


o SS1QCS232 # 


/ 13 /


c20_30


o SS1QCS234 # 


/ 14 /


c20_30


o SS1QCS236 # 


/ 15/


c20_30


o SS1QCS238 # 


/ 16 /


c20_30


o SS1QCS240 # 


/ 17 /


c20_30


o SS1QCS242 # 


/ 18 /


117258 1234 1 1 CG 05


143055 887 1 1 CG 08


29804 887 1 1 CG 09


6295 624 1 1 CG 11


166564 624 1 1 CG 12


78361 2225 1 1 CG 13


6314 827 1 1 CG 14


42335 2207 1 1 CG 15


29712 2400 1 1 CG 16


56911 1671 1 1 CG 17


31292 1829 1 1 CG 18


# Detroit River Flows


c20_30


o SS1QCS003 # 


/ 21 /


c20_30


o SS1QCS008 # 


/ 22 /


c20_30


o SS1QCS015 # 


/ 24 /


c20_30


o SS1QCS029 # 


/ 25 /


c20_30


o SS1QCS100 # 


/ 29 /


c20_30


133137 1756 1 1 CG 21


47994 1756 1 1 CG 22


55117 1459 1 1 CG 24


126014 1459 1 1 CG 25


47411 1170 1 1 CG 29


62 A Two-Dimensional Hydrodynamic Model of the St. Clair–Detroit River Waterway in the Great Lakes Basin 
o SS1QCS101 # 95124 1106 1 1 CG 30


/ 30 /


c20_30


o SS1QCS102 # 38909 926 1 1 CG 31


/ 31 /


c20_30


o SS1QCS120 # 40201 1762 1 1 CG 32


/ 32 /


c20_30


o SS1QCS121 # 9263 2034 1 1 CG 33


/ 33 /


c20_30


o SS1QCS122 # 47876 1760 1 1 CG 34


/ 34 /


c20_30


o SS1QCS123 # 84103 2197 1 1 CG 35


/ 35 /


c20_30


o SS1QCS142 # 12123 2132 1 1 CG 36


/ 36 /


c20_30


o SS1QCS143 # 20265 1690 1 1 CG 37


/ 37 /


c20_30


o SS1QCS161 # 21209 2004 1 1 CG 38


/ 38 /


c20_30


o SS1QCS162 # 9418 1023 1 1 CG 39


/ 39 /


c20_30


o SS1QCS163 # 38636 2871 1 1 CG 40


/ 40 /


c20_30


o SS1QCS164 # 8142 1996 1 1 CG 41


/ 41 /


c20_30


o SS1QCS165 # 63839 2253 1 1 CG 42


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o SS1QCS141 # 21363 2418 1 1 CG 54


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