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Prepared in cooperation with the MICHIGAN DEPARTMENT OF ENVIRONMENTAL QUALITY, SOURCE WATER ASSESSMENT PROGRAM, and the DETROIT WATER AND SEWERAGE DEPARTMENT

Flow distribution and monthly flow duration in selected branches of St. Clair and Detroit Rivers

U.S. Geological Survey Water-Resources Investigations 01-4135

By D. J. Holtschlag and J. A. Koschik1


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Abstract

St. Clair and Detroit Rivers are connecting channels between Lake Huron and Lake Erie in the Great Lakes waterway, and form part of the boundary between the United States and Canada. St. Clair River, the upper connecting channel, drains 222,400 square miles and has an average flow of about 182,000 cubic feet per second. Water from St. Clair River combines with local inflows and discharges into Lake St. Clair before flowing into Detroit River. In some reaches of St. Clair and Detroit Rivers, islands and dikes split the flow into two to four branches. Even when the flow in a reach is known, proportions of flows within individual branches of a reach are uncertain. Simple linear regression equations, subject to a flow continuity constraint, are developed to provide estimators of these proportions and flows. The equations are based on 533 paired measurements of flow in 13 reaches forming 31 branches. The equations provide a means for computing the expected values and uncertainties of steady-state flows on the basis of flow conditions specified at the upstream boundaries of the waterway. In 7 upstream reaches, flow is considered fixed because it can be determined on the basis of flows specified at waterway boundaries and flow continuity. In these reaches, the uncertainties of flow proportions indicated by the regression equations can be used directly to determine the uncertainties of the corresponding flows. In the remaining 6 downstream reaches, flow is considered uncertain because these reaches do not receive flow from all the branches of an upstream reach, or they receive flow from some branches of more than one upstream reach. Monte Carlo simulation analysis is used to quantify this increase in uncertainty associated with the propagation of uncertainties from upstream reaches to downstream reaches. To eliminate the need for Monte Carlo simulations for routine calculations, polynomial regression equations are developed to approximate the variation in uncertainties as a function of flow at the headwaters of St. Clair River. Finally, monthly flowduration data on the main channels of St. Clair and Detroit Rivers are used with the equations developed in this report to estimate the steady-state flow-duration characteristics of selected branches.

 

Computation

The following spreadsheets implement the equations developed in the referenced report to compute the magnitudes and uncertainties of flows on selected branches of St. Clair and Detroit Rivers. Users may download the spreadsheets and respecify inflows at boundaries to meet their interests. When downloading, a warning will be displayed indicating that the spreadsheets contain macros, which need to be enabled for use.

 

Flow Distribution in Branches of St. Clair and Detroit Rivers Microsoft® Excel® Spreadsheet:

Spreadsheet for specifying and computing proportions and flows in English units (SCDFlowDist.English.xls 963KB).
Spreadsheet for specifying and computing proportions and flows in metric units (SCDFlowDist.Metric.xls 965KB).

 

If you do not have Microsoft® Excel®, you can download a viewer for free at:
Microsoft® Excel® Viewer
Use of this software product does not imply endorsement by U.S. Government.

 

1Mr.Koschik is with the US Army Corps of Engineers in Detroit.


Citation:

Holtschlag, D.J., and Koschik, J.A., 2001, Flow distribution and monthly flow duration in selected branches of St. Clair and Detroit Rivers within the Great Lakes Waterway: Date Posted: May 9, 2006: U.S. Geological Survey Water Resources Investigations Report 01-4135, 66 p.
[http://pubs.water.usgs.gov/wrir01-4135/]

Contents

Abstract
Introduction
Purpose and Scope
Study Area
Flow-Measurement Data
Flow-Distribution Analysis
Estimation of Flow Proportions in Branches
Two-Branch Reaches
Three- and Four-Branch Reaches
Branch Flow in Reaches with Fixed Total Flows
Branch Flow in Reaches with Uncertain Total Flows
Monte Carlo Analysis of Flow Uncertainties
Regression Estimators of Variance Ratios
Flow-Duration Analysis
Summary and Conclusions
References Cited
Appendix A. Selected Flow Measurements
Appendix B. Example of MATLAB Function Developed to Simultaneously Estimate Reach Parameters
Appendix C. Listing of Matlab Code Used in the Monte Carlo Analysis of Flow Magnitudes and Uncertainties

 

Figures

1. Study area showing the St. Clair and Detroit Rivers within the Great Lakes Waterway

2. Locations of selected flow-measurement cross sections on St. Clair River within the Great Lakes Waterway

3. Locations of selected flow-measurement cross sections on Detroit River within the Great Lakes Waterway

4. Schematic describing terminology for reaches with fixed or uncertain flows

5. Relation between flow in the Stag Island reach and flow proportions in branches near cross-sections CS-208 and CS-210 on St. Clair River within the Great Lakes Waterway

6. Relation between flow in the Dickinson-Harsens Island reach and estimated and measured flow proportions in branches near cross-sections CS-232, CS-240, and CS-242 on St. Clair River within the Great Lakes Waterway

7. Relation between flow in the Fighting-Grassy Island reach and flow proportions in branches near cross-sections CS-100, CS-101, CS-102 on Detroit River within the Great Lakes Waterway

8. Relation between estimated proportions and residuals at cross-sections CS-232, CS-240, and CS-242 near Dickinson-Harsens Island reach on St. Clair River within the Great Lakes Waterway

9. Relation between estimated proportions and residuals at cross-sections CS-100, CS-101, CS-102 near Fighting-Grassy Island reach on Detroit River within the Great Lakes Waterway

10. Time-series plot of monthly average flows for St. Clair and Detroit Rivers within the Great Lakes Waterway

11. Monthly flow-duration characteristics for St. Clair and Detroit Rivers within the Great Lakes Waterway

12. Estimated monthly flow-duration characteristics for selected branches of St. Clair River within the Great Lakes Waterway

13. Estimated monthly flow-duration characteristics for selected branches of upper Detroit River within the Great Lakes Waterway

14. Estimated monthly flow-duration characteristics for selected branches of lower Detroit River within the Great Lakes Waterway

 

References

1. Equations for computing flow proportions in St. Clair and Detroit Rivers within the Great Lakes Waterway

2. Average local inflows at selected boundaries to the St. Clair-Detroit River Waterway

3. Summary of proportions and flows on selected branches of St. Clair and Detroit Rivers within the Great Lakes Waterway from Monte Carlo simulation

4. Monte Carlo estimates of the ratios of variances of uncertain flows to fixed flows for specified flows at the headwaters of St. Clair River within the Great Lakes Waterway

5. Regression coefficients for estimation of variance ratios in reaches with uncertain flows for St. Clair and Detroit Rivers within the Great Lakes Waterway

6. Parametric estimates of flows and proportions of selected branches of St. Clair and Detroit Rivers within the Great Lakes Waterway computed by use of estimated variance ratios

A1. Selected flow measurements on St. Clair River near Stag Island, Ontario, Canada

A2. Selected flow measurements on St. Clair River near Fawn Island, Ontario, Canada

A3. Selected flow measurements on St. Clair River near Walpole Island, Ontario, Canada

A4. Selected flow measurements on St. Clair River near Dickinson-Harsens Islands, Michigan

A5. Selected flow measurements on St. Clair River at Bassett-Seaway Island, Ontario, Canada

A6. Selected flow measurements on Detroit River near Peche Island, Ontario, Canada

A7. Selected flow measurements on Detroit River near Belle Isle, Michigan

A8. Selected flow measurements on Detroit River near Fighting Island and Grassy Island, Ontario, Canada, and Grassy Island, Michigan

A9. Selected flow measurements on Detroit River near Grosse Ile and Stony Island, Michigan

A10. Selected flow measurements on Detroit River near Bois Blanc Island, Ontario, Canada

A11. Selected flow measurements on Detroit River near Bois Blanc Island and Livingstone Channel, Ontario, Canada

A12. Selected flow measurements on Detroit River near the gap in Livingstone Channel, Ontario, Canada

A13. Selected flow measurements on Detroit River near Sugar Island, Michigan


For additional information, contact:

U.S. Geological Survey
Michigan Water Science Center
6520 Mercantile Way, Suite 5
Lansing, MI 48911-5991
GS-W-MIlns_DC@usgs.gov
or visit our Web site at:
http://mi.water.usgs.gov

 


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Last modified: Tuesday, May 09 2006, 03:44:00 PM
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