Abstract
Abstract. In many simulations of historical daily streamflow distributional bias arising from the distributional properties of residuals has been noted. This bias often presents itself as an underestimation of high streamflow and an overestimation of low streamflow. Here, 1168 streamgages across the conterminous USA, having at least 14 complete water years of daily data between 1 October 1980 and 30 September 2013, are used to explore a method for rescaling simulated streamflow to correct the distributional bias. Based on an existing approach that separates the simulated streamflow into components of temporal structure and magnitude, the temporal structure is converted to simulated nonexceedance probabilities and the magnitudes are rescaled using an independently estimated flow duration curve (FDC) derived from regional regression. In this study, this method is applied to a pooled ordinary kriging simulation of daily streamflow coupled with FDCs estimated by regional regression on basin characteristics. The improvement in the representation of high and low streamflows is correlated with the accuracy and unbiasedness of the estimated FDC. The method is verified by using an idealized case; however, with the introduction of regionally regressed FDCs developed for this study, the method is only useful overall for the upper tails, which are more accurately and unbiasedly estimated than the lower tails. It remains for future work to determine how accurate the estimated FDCs need to be to be useful for bias correction without unduly reducing accuracy. In addition to its potential efficacy for distributional bias correction, this particular instance of the methodology also represents a generalization of nonlinear spatial interpolation of daily streamflow using FDCs. Rather than relying on single index stations, as is commonly done to reflect streamflow timing, this approach to simulation leverages geostatistical tools to allow a region of neighbors to reflect streamflow timing.
Highlights
Simulation of historical daily streamflow at ungauged locations is one of the grand challenges of the hydrological sciences (Sivapalan, 2003; Sivapalan et al, 2003; Hrachowitz et al, 2013; Parajka et al, 2013)
These results are discussed in detail below, beginning with a discussion of the bias and accuracy in the original kriged simulations. This is followed by a consideration of the effectiveness of bias correction with observed flow duration curve (FDC) as emblematic of the theoretical potential of this approach
The distributions of errors in the nonexceedance probabilities closely reflect the distribution of bias in the observation-dependent tails (Fig. 5, box plots C and F). These results show that the inaccuracy in the nonexceedance probabilities will obscure, at least partially, the improvement offered by bias correction when considering the observation-dependent errors, even when an observed FDC is used for bias correction
Summary
Simulation of historical daily streamflow at ungauged locations is one of the grand challenges of the hydrological sciences (Sivapalan, 2003; Sivapalan et al, 2003; Hrachowitz et al, 2013; Parajka et al, 2013). Over the past 20 years, at least, research into simulation of historical streamflow has increased. Regardless of the method used for the simulation, uncertainty will always remain and may result in some distributional bias (Farmer and Vogel, 2016). The objective of this work is to present a technique to correct for bias in the magnitudes of a streamflow simulation. While the mechanics of this technique are not novel, the novelty of this work lies in the generalization of this technique for use in bias correction. The method is intended for use at ungauged sites and an idealized experiment is constructed to demonstrate both the potential utility and one example of realized utility
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