Evaluation of a nonparametric post-processor for bias correction and uncertainty estimation of hydrologic predictions


James D. Brown, NOAA/National Weather Service, Office of Hydrologic Development, 1325 East–west Highway, Silver Spring, MD 20910, USA.

E-mail: James.D.Brown@noaa.gov


This paper evaluates a nonparametric technique for estimating the conditional probability distribution of a predictand given a vector of predictors. In the current application, the predictors are formed from a multimodel ensemble of simulated streamflows, such that the hydrologic uncertainties are modelled independently of any forcing uncertainties. The technique is based on Bayesian optimal linear estimation of indicator variables and is analogous to indicator cokriging (ICK) in geostatistics. By developing linear estimators for the conditional probability that the observed variable does not exceed several thresholds, ICK provides a discrete approximation of the full conditional probability distribution. The weights of the predictors can be chosen to minimize the expected error variance at each threshold (the Brier score) or, without loss of analytical tractability, a combination of the error variance and the expected square bias conditional upon the observation, i.e. the Type-II conditional bias (CB). The latter is referred to as CB-penalized ICK (CBP-ICK) and is an important enhancement to ICK. Indeed, the biases in atmospheric and hydrologic predictions generally increase towards the tails of their probability distributions. The performance of CBP-ICK is evaluated for selected basins in the eastern USA using a range of probabilistic verification metrics and associated confidence intervals for the sampling uncertainties. Overall, CBP-ICK produces unbiased and skillful estimates of the hydrologic uncertainties, with some sensitivity to the calibration data period at high flow thresholds. More generally, we argue that the common aim in statistical post-processing of ‘maximizing sharpness subject to reliability (Type-I CB)’ should be recast to accommodate both the Type-I and Type-II CBs, as both are important for practical applications of hydrologic predictions. Copyright © 2012 John Wiley & Sons, Ltd.