### Techniques for Estimating the Magnitude and Frequency of Peak Flows on Small Streams in the Binational U.S. and Canadian Lake of the Woods–Rainy River Basin Upstream from Kenora, Ontario, Canada, Based on Data through Water Year 2013

By: Christopher A. Sanocki**Tara J. Williams-Sether**Peter A. Steeves**Victoria G. Christensen**

                            https://doi.org/10.3133/sir20195012

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- Table:  **Table 1**                            (39.7 kB xlsx)                          Hydrologic, basin, and climatic characteristics and peak-flow frequency discharges for streamgages used in the regional regression analysis for the Lake of the Woods–Rainy River Basin
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#### Abstract

First posted April 22, 2019

**For additional information, contact:**
Director, Upper Midwest Water Science Center U.S. Geological Survey2280 Woodale DriveMounds View, MN 55112

A binational study was initiated to update statistical equations that are used to estimate the magnitude and frequency of peak flows on streams in Manitoba and Ontario, Canada, and Minnesota that are contained within the binational Lake of the Woods–Rainy River Basin upstream from Kenora, Ontario, Canada. Hydraulic engineers use peak streamflow data to inform designs of bridges, culverts, and dams, and water managers use peak streamflow data to inform regulation and planning activities. However, long-term streamflow measurements are available at few locations along the more than 20,000 miles of stream/ditch networks within the binational Lake of the Woods–Rainy River Basin upstream from Kenora, Ontario, Canada.

Estimates of peak-flow magnitudes for 66.7-, 50-, 20-, 10-, 4-, 2-, 1-, and 0.2-percent annual exceedance probabilities equivalent to annual flood-frequency recurrence intervals of 1.5-, 2-, 5-, 10-, 25-, 50-, 100-, and 500-year recurrence intervals, respectively, are presented for 49 streamgages in Minnesota and adjacent areas in the Province of Ontario, Canada, based on data collected through water year 2013. Peak-flow frequency information was subsequently used in regression analyses to develop equations relating peak flows for selected recurrence intervals to various basin and climatic characteristics.

The study area includes 49 streamgages located in the binational Lake of the Woods–Rainy River Basin upstream from Kenora, Ontario, Canada, and is represented by southern portions of the Canadian Provinces of Manitoba (2 percent) and Ontario (56 percent) and the northern portion of the U.S. State of Minnesota (42 percent). The study area was represented by three regions that were defined in previous studies in the U.S. State of Minnesota and another in the Canadian Province of Ontario. The two Minnesota regions A and B were developed using a multiple regression method and hydrologic landscape units were used to validate regions in Minnesota. The Ontario region A was developed using a multiple regression method and standardized residuals from the 100-year recurrence intervals.

Canadian maximum instantaneous peak-flow data were converted from a calendar year to a water year (October 1 to September 30) and where the annual maximum instantaneous peak-flow value was not available in HYDAT, the Sangal method was applied to known average daily flow values to estimate an annual maximum instantaneous peak-flow value. Geographic information system software was used to calculate eight characteristics investigated as potential explanatory variables in the regression analyses.

The procedure for estimating peak-flow frequency for selected exceedance probabilities for a specific ungaged site depends on whether the site is near a streamgage on the same stream or is on an ungaged stream. For an ungaged site near a streamgage on the same stream, the drainage-area ratio method can be used. For an ungaged site on an ungaged stream, the regional regression equations developed for this study should be used.

All equations presented in this study will be incorporated into StreamStats, a web-based geographic information system tool developed by the U.S. Geological Survey. StreamStats allows users to obtain streamflow statistics, basin characteristics, and other information for user-selected locations on streams through an interactive map.

#### Suggested Citation

Sanocki, C.A., Williams-Sether, T., Steeves, P.A., and Christensen, V.G., 2019, Techniques for estimating the magnitude and frequency of peak flows on small streams in the binational U.S. and Canadian Lake of the Woods–Rainy River Basin upstream from Kenora, Ontario, Canada, based on data through water year 2013: U.S. Geological Survey Scientific Investigations Report 2019–5012, 17 p., https://doi.org/10.3133/sir20195012.

ISSN: 2328-0328 (online)

#### Study Area

#### Table of Contents

- Acknowledgments
- Abstract
- Introduction
- Methods
- Development of Regional Regression Equations
- Application of Regional Regression Equations
- Summary
- References

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