Refinement of a regression-based method for prediction of flow-duration curves of daily streamflow in the conterminous United States

Scientific Investigations Report 2018-5072

Water Availability and Use Science Program



Regional regression is a common tool used to estimate daily flow-duration curves (FDCs) at ungaged locations. In this report, several refinements to a particular implementation of the regional regression method for estimating FDCs are evaluated by consideration of different methodological options through a leave-one-out cross-validation procedure in the 19 major river basins of the conterminous United States. Regression analyses in this report are based on streamflow data from water years 1981–2013 (October 1, 1980 to September 30, 2013) from 1,378 mostly undisturbed watersheds. Linear regression using selected basin characteristics at 27 quantiles with nonexceedance probabilities ranging from 0.02 to 99.98 percent was applied. The regression computations were primarily by weighted least squares, with left-censored Gaussian regression solved by maximum likelihood in the presence of zero-valued quantiles.

The regional regression method as applied to the FDC estimation problem includes several methodological options that require determination of the better of two or more choices. The options considered in this report include (1) the setting of the maximum number of basin characteristics considered in the regression models for each region, (2) the method of placing the quantiles into groups (“flow regimes”) having the same basin characteristics used as independent variables, (3) the maximum number of candidate models retained from regressions at the single-quantile level that are retained for testing of the best model at the flow-regime scale, and (4) whether drainage area should be forced into the models. In all, 5 binary options were considered for most regions, resulting in 32 methodological combinations. Leave-one-out cross-validation predictions of FDC quantiles at each streamgage used in the study were used to evaluate compared options. Various performance measures were computed based on the predicted quantiles; these were combined by region and the methods were ranked for each measure.

Based on examination of the ranked methods compared across the measures, the following treatments produced the more accurate results: (1) using fewer basin characteristics (of the two options considered), (2) utilizing a variance of the unit FDC-based method of determining the flow regimes rather than fixed regimes, (3) retaining more models from the quantile-level regressions regime-wide consideration, and (4) forcing drainage area into the regression models. Results of analyses also indicate that performance varies more by region than by methodological option, with FDCs in arid regions and those with a large value of a measure of intraregional FDC heterogeneity being harder to predict, particularly with respect to the low-flow quantiles.

Suggested Citation

Over, T.M., Farmer, W.H., and Russell, A.M., 2018, Refinement of a regression-based method for prediction of flow-duration curves of daily streamflow in the conterminous United States: U.S. Geological Survey Scientific Investigations Report 2018–5072, 34 p.,

ISSN: 2328-0328 (online)

Study Area

Table of Contents

  • Abstract
  • Introduction
  • Methods of Study
  • Refinement of a Regression-Based Method for Prediction of Flow-Duration Curves
  • Summary
  • Acknowledgments
  • References Cited
  • Appendix 1
  • Appendix 2
  • Appendix 3

Additional publication details

Publication type:
Publication Subtype:
USGS Numbered Series
Refinement of a regression-based method for prediction of flow-duration curves of daily streamflow in the conterminous United States
Series title:
Scientific Investigations Report
Series number:
Year Published:
U.S. Geological Survey
Publisher location:
Reston, VA
Contributing office(s):
Illinois Water Science Center
Report: vi, 34 p.; Appendixes 1–3; Data Release
United States
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