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Scientific Investigations Report 2008–5104

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### Prepared in cooperation with the South Dakota Department of Transportation

## Peak-Flow Frequency Estimates Based on Data through Water Year 2001 for Selected Streamflow-Gaging Stations in South Dakota

| Contents | Citation | More InformationAbstract
Numerous users, including the South Dakota Department of Transportation, have continuing needs for peak-flow information for the design of highway infrastructure and many other purposes. This report documents results from a cooperative study between the South Dakota Department of Transportation and the U.S. Geological Survey to provide an update of peak-flow frequency estimates for South Dakota.

Estimates of peak-flow magnitudes for 2-, 5-, 10-, 25-, 50-, 100-, 200-, and 500-year recurrence intervals are reported for 272 streamflow-gaging stations, which include most gaging stations in South Dakota with 10 or more years of systematic peak-flow records through water year 2001. Recommended procedures described in Bulletin 17B were used as primary guidelines for developing peak-flow frequency estimates. The computer program PEAKFQ developed by the U.S. Geological Survey was used to run the frequency analyses. Flood frequencies for all stations were initially analyzed by using standard Bulletin 17B default procedures for fitting the log-Pearson III distribution. The resulting preliminary frequency curves were then plotted on a log-probability scale, and fits of the curves with systematic data were evaluated. In many cases, results of the default Bulletin 17B analyses were determined to be satisfactory. In other cases, however, the results could be improved by using various alternative procedures for frequency analysis.

Alternative procedures for some stations included adjustments to skew coefficients or use of user-defined low-outlier criteria. Peak-flow records for many gaging stations are strongly influenced by low- or zero-flow values. This situation often results in a frequency curve that plots substantially above the systematic record data points at the upper end of the frequency curve. Adjustments to low-outlier criteria reduced the influence of very small peak flows and generally focused the analyses on the upper parts of the frequency curves (10- to 500-year recurrence intervals).

The most common alternative procedures involved several different methods to extend systematic records, which was done primarily to address biases resulting from nonrepresentative climatic conditions during several specific periods of record and to reduce inconsistencies among multiple gaging stations along common stream channels with different periods of record. In some cases, records for proximal stations could be combined directly. In other cases, the two-station comparison procedure recommended in Bulletin 17B was used to adjust the mean and standard deviation of the logs of the systematic data for a target station on the basis of correlation with concurrent records from a nearby long-term index station. In some other cases, a “mixed-station procedure” was used to adjust the log-distributional parameters for a target station, on the basis of correlation with one or more index stations, for the purpose of fitting the log-Pearson III distribution.

Historical adjustment procedures were applied to peak-flow frequency analyses for 17 South Dakota gaging stations. A historical adjustment period extending back to 1881 (121 years) was used for 12 gaging stations in the James and Big Sioux River Basins, and various other adjustment periods were used for additional stations. Large peak flows that occurred in 1969 and 1997 accounted for 13 of the 17 historical adjustments. Other years for which historical peak flows were used include 1957, 1962, 1992, and 2001.

A regional mixed-population analysis was developed to address complications associated with many high outliers for the Black Hills region. This analysis included definition of two populations of flood events. The population of flood events that composes the main body of peak flows for a given station is considered the “ordinary-peaks population,” and the population of unusually large peak flows that plot substantially above the main body of peak flows on log-probability scale is considered the “high-outlier population.” All peak flows assigned to the high-outlier population were identified as high outliers by the Grubbs-Beck outlier test. For each gaging station, the final frequency curve was determined by using joint-probability theory to combine the ordinary-peaks probability distribution for the gaging station with the regional high-outlier probability distribution. This nonstandard application of the mixed-population procedure in Bulletin 17B was able to accommodate the different populations of flood events that have occurred in the Black Hills region.             |  |  |  | **Version 1.3**First posted August 2008Version History**Download report** (5.7 MB pdf)
**Appendix 1****Data** (896 KB PDF)

**Appendix 2****Graphs** (8.1 MB PDF)

**Table 8****Excel spreadsheet**(505 KB) |
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### Contents

Abstract

Introduction

Peak-Flow Frequency Estimates

Hydrogeologic Considerations Regarding Peak-Flow Frequency Estimates

Procedures for Frequency Analyses

General Procedures for Fitting the Log-Pearson Type III Probability Distribution

Procedures for Skew Coefficient and Low Outliers

Procedures for Gaging Stations Affected by Regulation

Record-Extension Procedures

Historical Adjustment Procedures

Procedures for Gaging Stations in the Black Hills Region

Characteristics of Gaging Stations and Frequency Analyses by Major River Basin

Red River of the North and Minnesota River Basins

Minor Tributaries to Missouri River

Grand River

Moreau River

Cheyenne River

Cheyenne River and Belle Fourche River Main Stems

Cheyenne and Belle Fourche River Tributaries in the Black Hills Region

Cheyenne River Tributaries Downstream from the Black Hills Region

Bad River

White River

James River

Vermillion River

Big Sioux River

Summary

References

Appendix 1. Additional data

Appendix 2. Graphs

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### Suggested Citation

Sando, S.K., Driscoll, D.G., and Parrett, Charles, 2008, Peak-flow frequency estimates based on data through water year 2001 for selected streamflow-gaging stations in South Dakota: U.S. Geological Survey Scientific Investigations Report 2008–5104, 367 p.

### More Information

**http://sd.water.usgs.gov/**

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