Fitting Three- and Four-Parameter Probability Distributions to Daily Streamflow

Abstract:

Daily streamflow information is critical for solving any number of hydrologic problems. One promising approach to estimate a time series of daily streamflow at an ungauged location is to estimate a continuous, daily, period-of-record flow-duration curve (FDC) at the ungauged location and use the timing of observed streamflows from a donor streamgauge to transform the FDC at the ungauged location into a time series of streamflow. Ideally, if one were to find a suitable probability density function (pdf) to represent daily streamflow, only the parameters of the distribution would need to be estimated at the ungauged location. Determining the pdf of daily streamflow could also provide functional linkages between the pdfs of daily precipitation and other catchment processes toward a probabilistic framework which explains how catchments filter the precipitation signal. Three- and four parameter distributions were fit to daily streamflow observations from streamgauges located in the north- and southeastern United States. No suitable three or four-parameter probability distribution were found to adequately represent the distribution of daily streamflow, particularly at streamflow quantiles greater than 0.9 and less than 0.01 exceedence probabilities. Furthermore, the properties of these distributions caused estimated streamflows to be bounded at both the highest and lowest streamflow quantiles, creating a severe bias in the estimation of the FDC. Traditional goodness-of-fit statistics were also unable to revealing this lack of fit; only examination of the individual probability plots showed this inadequacy.