Articles | Volume 21, issue 6
Hydrol. Earth Syst. Sci., 21, 3093–3103, 2017
Hydrol. Earth Syst. Sci., 21, 3093–3103, 2017

Cutting-edge case studies 28 Jun 2017

Cutting-edge case studies | 28 Jun 2017

On the probability distribution of daily streamflow in the United States

Annalise G. Blum1,2, Stacey A. Archfield2, and Richard M. Vogel1 Annalise G. Blum et al.
  • 1Civil and Environmental Engineering, Tufts University, Medford, MA 02155, USA
  • 2U.S. Geological Survey, Reston, VA 20192, USA

Abstract. Daily streamflows are often represented by flow duration curves (FDCs), which illustrate the frequency with which flows are equaled or exceeded. FDCs have had broad applications across both operational and research hydrology for decades; however, modeling FDCs has proven elusive. Daily streamflow is a complex time series with flow values ranging over many orders of magnitude. The identification of a probability distribution that can approximate daily streamflow would improve understanding of the behavior of daily flows and the ability to estimate FDCs at ungaged river locations. Comparisons of modeled and empirical FDCs at nearly 400 unregulated, perennial streams illustrate that the four-parameter kappa distribution provides a very good representation of daily streamflow across the majority of physiographic regions in the conterminous United States (US). Further, for some regions of the US, the three-parameter generalized Pareto and lognormal distributions also provide a good approximation to FDCs. Similar results are found for the period of record FDCs, representing the long-term hydrologic regime at a site, and median annual FDCs, representing the behavior of flows in a typical year.

Short summary
Flow duration curves are ubiquitous in surface water hydrology for applications including water allocation and protection of ecosystem health. We identify three probability distributions that can provide a reasonable fit to daily streamflows across much of United States. These results help us understand of the behavior of daily streamflows and enhance our ability to predict streamflows at ungaged river locations.