Methods for estimating flow-duration curve and low-flow frequency statistics for ungaged locations on small streams in Minnesota

Scientific Investigations Report 2015-5170
Prepared in cooperation with the Minnesota Pollution Control Agency
By: , and 



Knowledge of the magnitude and frequency of low flows in streams, which are flows in a stream during prolonged dry weather, is fundamental for water-supply planning and design; waste-load allocation; reservoir storage design; and maintenance of water quality and quantity for irrigation, recreation, and wildlife conservation. This report presents the results of a statewide study for which regional regression equations were developed for estimating 13 flow-duration curve statistics and 10 low-flow frequency statistics at ungaged stream locations in Minnesota. The 13 flow-duration curve statistics estimated by regression equations include the 0.0001, 0.001, 0.02, 0.05, 0.1, 0.25, 0.50, 0.75, 0.9, 0.95, 0.99, 0.999, and 0.9999 exceedance-probability quantiles. The low-flow frequency statistics include annual and seasonal (spring, summer, fall, winter) 7-day mean low flows, seasonal 30-day mean low flows, and summer 122-day mean low flows for a recurrence interval of 10 years. Estimates of the 13 flow-duration curve statistics and the 10 low-flow frequency statistics are provided for 196 U.S. Geological Survey continuous-record streamgages using streamflow data collected through September 30, 2012.

The study area includes 196 streamgages located within Minnesota and 50 miles beyond the State’s borders in North Dakota, South Dakota, Iowa, and Wisconsin. The study area was divided into five regions that were developed in a previous study using the concept of hydrologic landscape units. Geographic information system software was used to calculate 18 characteristics investigated as potential explanatory variables in regression analyses for each streamgage drainage basin. Trend analyses indicated statistically significant trends in summer 7-day low flows that were not related to precipitation patterns for 19 streamgages. For 16 of these streamgages, the streamflow record was subset using structural change analysis to identify the most recent period of record without a significant trend. The three remaining streamgages with significant trends were excluded from the final analysis because the effective period of record without a significant trend was less than 10 years.

Because several streams in this study have zero flow as their minimum reported flow, weighted left-censored regression was used to analyze the flow data in an unbiased manner, with weights based on the number of years of record. A total of 115 regression equations were developed in this study to calculate flow-duration curve and low-flow frequency statistics for ungaged locations in the study area. In addition, data from 25 pairs of streamgages were used to develop drainage-area ratio equations that can be used to estimate streamflow statistics at ungaged locations on streams that have a streamgage in another location. Streamflow statistics estimated using regional regression and drainage-area ratio equations were compared among regions. For regions A, D, and E, drainagearea ratio equations were more accurate than regional regression equations for flows, but regional regression equations were more accurate for high flows. For region F, regional regression equations were consistently more accurate than drainage-area ratio equations. For region BC, the pattern in accuracies of regional regression and drainage-area ratio equations between low flows and high flows was not consistent.

Equations developed in this study apply only to stream locations where flows are not substantially affected by regulation, diversion, or urbanization. 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

Ziegeweid, J.R., Lorenz, D.L., Sanocki, C.A., and Czuba, C.R., 2015, Methods for estimating flow-duration curve and low-flow frequency statistics for ungaged locations on small streams in Minnesota: U.S. Geological Survey Scientific Investigations Report 2015–5170, 23 p.,

ISSN: 2328-0328 (online)

Study Area

Table of Contents

  • Abstract
  • Introduction
  • Methods for Data Development
  • Regional Regression Analysis
  • Drainage-Area Ratio Calculations
  • Limitations of Regression Equations
  • Constructing Consistent Flow-Duration Curves
  • StreamStats
  • Summary
  • Acknowledgments
  • References Cited
  • Appendix 1. Detailed Streamgage Information Used to Conduct Analyses
Publication type Report
Publication Subtype USGS Numbered Series
Title Methods for estimating flow-duration curve and low-flow frequency statistics for ungaged locations on small streams in Minnesota
Series title Scientific Investigations Report
Series number 2015-5170
DOI 10.3133/sir20155170
Year Published 2015
Language English
Publisher U.S. Geological Survey
Publisher location Reston, VA
Contributing office(s) Minnesota Water Science Center
Description Report: vi, 23 p.; Appendix
Country United States
State Iowa, Minnesota, North Dakota, South Dakota, Wisconsin
Online Only (Y/N) Y
Additional Online Files (Y/N) Y
Google Analytic Metrics Metrics page
Additional publication details