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A Nonparametric Postprocessor for Bias Correction of Hydrometeorological and Hydrologic Ensemble Forecasts

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  • 1 NOAA/National Weather Service, Office of Hydrologic Development, Silver Spring, Maryland, and University Corporation for Atmospheric Research, Boulder, Colorado
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Abstract

This paper describes a technique for quantifying and removing biases from ensemble forecasts of hydrometeorological and hydrologic variables. The technique makes no a priori assumptions about the distributional form of the variables, which is often unknown or difficult to model parametrically. The aim is to estimate the conditional cumulative distribution function (ccdf) of the observed variable given a (possibly biased) real-time ensemble forecast. This ccdf represents the “true” probability distribution of the forecast variable, subject to sampling uncertainties. In the absence of a known distributional form, the ccdf should be estimated nonparametrically. It is noted that the probability of exceeding a threshold of the observed variable, such as flood stage, is equivalent to the expectation of an indicator variable defined for that threshold. The ccdf is then modeled through a linear combination of the indicator variables of the forecast ensemble members. 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 expectation of the observed variable at many thresholds, ICK provides a discrete approximation of the full ccdf. Since ICK minimizes the conditional error variance of the indicator variable at each threshold, it effectively minimizes the continuous ranked probability score (CRPS) when infinitely many thresholds are employed. The technique is used to bias-correct precipitation ensemble forecasts from the NCEP Global Ensemble Forecast System (GEFS) and streamflow ensemble forecasts from the National Weather Service (NWS) River Forecast Centers (RFCs). Split-sample validation results are presented for several attributes of ensemble forecast quality, including reliability and discrimination. In general, the forecast biases were substantially reduced following ICK. Overall, the technique shows significant potential for bias-correcting ensemble forecasts whose distributional form is unknown or nonparametric.

Corresponding author address: James Brown, NOAA/NWS/OHD, 1325 East-West Highway, Silver Spring, MD 20910. Email: james.d.brown@noaa.gov

Abstract

This paper describes a technique for quantifying and removing biases from ensemble forecasts of hydrometeorological and hydrologic variables. The technique makes no a priori assumptions about the distributional form of the variables, which is often unknown or difficult to model parametrically. The aim is to estimate the conditional cumulative distribution function (ccdf) of the observed variable given a (possibly biased) real-time ensemble forecast. This ccdf represents the “true” probability distribution of the forecast variable, subject to sampling uncertainties. In the absence of a known distributional form, the ccdf should be estimated nonparametrically. It is noted that the probability of exceeding a threshold of the observed variable, such as flood stage, is equivalent to the expectation of an indicator variable defined for that threshold. The ccdf is then modeled through a linear combination of the indicator variables of the forecast ensemble members. 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 expectation of the observed variable at many thresholds, ICK provides a discrete approximation of the full ccdf. Since ICK minimizes the conditional error variance of the indicator variable at each threshold, it effectively minimizes the continuous ranked probability score (CRPS) when infinitely many thresholds are employed. The technique is used to bias-correct precipitation ensemble forecasts from the NCEP Global Ensemble Forecast System (GEFS) and streamflow ensemble forecasts from the National Weather Service (NWS) River Forecast Centers (RFCs). Split-sample validation results are presented for several attributes of ensemble forecast quality, including reliability and discrimination. In general, the forecast biases were substantially reduced following ICK. Overall, the technique shows significant potential for bias-correcting ensemble forecasts whose distributional form is unknown or nonparametric.

Corresponding author address: James Brown, NOAA/NWS/OHD, 1325 East-West Highway, Silver Spring, MD 20910. Email: james.d.brown@noaa.gov

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