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Scientific Investigations Report 2009–5133

Prepared in cooperation with the Michigan Department of Environmental Quality, Michigan Department of Transportation, U.S. Army Corps of Engineers, and
U.S. Fish and Wildlife Service

Estimated Bankfull Discharge for Selected Michigan Rivers and Regional Hydraulic Geometry Curves for Estimating Bankfull Characteristics in Southern Michigan Rivers

By Cynthia M. Rachol and Kristine Boley-Morse


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Regional hydraulic geometry curves are power-function equations that relate riffle dimensions and bankfull discharge to drainage-basin size. They are defined by data collected through surveys conducted at stable stream reaches and can be used to aid watershed managers, design engineers, and others involved in determination of the best course of action for an unstable stream. Hydraulic geometry curves provide a mechanism through which comparisons can be made between riffle dimensions collected at an unstable stream to those collected at stable streams within the same region. In 2005, a study was initiated to delineate regional hydraulic geometry curves for Michigan. After
in-office review of 343 U.S. Geological Survey streamgaging stations and an extensive field reconnaissance effort, 44 stable reaches were selected for this study. Detailed surveys that included cross-sectional and longitudinal profiles and pebble counts were conducted at selected streamgages, which were distributed throughout Michigan. By use of survey data from riffle cross sections and water-surface slope, bankfull discharge was estimated and compared to flood-recurrence intervals using regional flood equations. This comparison shows that bankfull discharges in Michigan recur more frequently than every 2 years.

Regional hydraulic geometry curves were developed rather than statewide curves owing to large differences in factors that control channel geometry across the State. However, after the data were subdivided according to ecoregions, it was determined that there were enough data to delineate regional hydraulic geometry curves only for the Southern Lower Michigan Ecoregion. For this ecoregion, geometry curve equations and their coefficients of determination are:

     Width = 8.19 x DA0.44; R2 = 0.69,
     Depth = 0.67 x DA0.27; R2 = 0.28,
       Area = 4.38 x DA0.74; R2 = 0.59,


     DA is the drainage area and
     R2 is the coefficient of determination.

By use of discharge estimates for the Southern Lower Michigan Ecoregion, a bankfull discharge curve was delineated. The corresponding equation and its coefficient of determination are:

     Discharge = 4.05 x DA0.95; R2 = 0.60.

Posted October 16, 2009

For additional information contact:
Director, Michigan Water
   Science Center
U.S. Geological Survey
6520 Mercantile Way, Suite 5
Lansing, MI 48911–5991

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Suggested citation:

Rachol, C.M., and Boley-Morse, Kristine, 2009, Estimated bankfull discharge for selected Michigan rivers and regional hydraulic geometry curves for estimating bankfull characteristics in southern Michigan rivers: U.S. Geological Survey Scientific Investigations Report 2009–5133, 300 p.






Bankfull Discharge Comparison to Flood-Frequency Statistics

Regional Hydraulic Geometry Curves

Summary and Conclusions

References Cited

Appendix    1.  Longitudinal-profile survey data

Appendix 2–1.  Riffle cross-section survey data used for regional curve development and bankfull discharge estimation

Appendix 2–2.  Ancillary riffle cross-section survey data

Appendix 3–1.  Riffle pebble-count data

Appendix 3–2.  Reach average pebble-count data

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