Water Resources of Michigan
Flow distribution and monthly flow duration in selected branches of St. Clair and Detroit Rivers
US Geological Survey Water-Resources Investigation 01-4135
Lansing, Michigan 2001
By: D. J. Holtschlag and J. A. Koschik
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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 mi2 and has an average flow of about 182,000 ft3/s. 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 flow-duration 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.
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).
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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: U.S. Geological Survey Water Resources Investigations Report 01-4135, 66 p.
(Mr.Koschik is with the US Army Corps of Engineers in Detroit.)
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