Traditional hydrometeorological forecasts are generated in a deterministic manner, i.e., the forecast of a certain hydrometeorological event is provided in the form of a single space-time series, which is inherently incapable of accounting for forecast uncertainty. To assess forecast uncertainty, ensemble forecasting has gained popularity in recent years. Rather than providing only one deterministic forecast, ensemble forecasts provide several possible scenarios for each event and thus allow uncertainty assessment of the forecasts. Ensemble forecasts not only improves the forecast accuracy, but also extend the forecast lead times over deterministic forecasts.
However, all raw forecasts from meteorological or hydrological models suffer from various kind of errors and biases and they need to be corrected before being used in applications. For example, raw forecasts may suffer from overestimation or underestimation problems, i.e., the mean of raw precipitation forecasts during a long time may be higher or lower than that of observations. Another common kind of errors in ensemble forecasts is under-dispersion, which means the ensemble spread of raw forecasts is too narrow, and leads to over-confident forecasts such that the observations may often fall out of the prediction interval of raw ensemble forecasts.
Statistical post-processing is a useful tool to correct the biases and dispersion errors in raw forecasts while preserving the predictive skill of the raw forecasts. Statistical post-processors are statistical models that relate observations with the forecasts obtained directly from a meteorological or a hydrological model. Figure 1 illustrates how a typical statistical post-processor works. First, the raw forecasts of a specific event and the corresponding observations in the training period (e.g., a 60-day window around Jun. 15th in 20 years) are fed into a statistical model to derive the joint probability distribution between the raw forecasts and the observations. Then given new forecasts in the future, the fitted statistical models are applied to generate new calibrated probability forecasts. Finally, to apply meteorological forecasts as inputs of hydrological models, ensemble forecasts need to be generated, which should preserve the spatio-temporal and inter-variable statistical dependency structure.
An review article by Qingyun Duan and his team members provides a systematic review of commonly used statistical post-processing methods in hydrometeorological forecasting, with focus on newly developed methods in recent years. The article mainly reviews post-processing methods from three aspects: (1) post-processing methods for hydrological or meteorological forecasts from single models; (2) multi-model post-processing methods to combine forecasts from different models; (3) post-processing methods for generating ensemble members that preserve spatio-temporal and inter-variable dependency of forecasts. Some perspectives on further development of statistical post-processing methods are also presented in the review.
Text kindly contributed by Qingyun Duan and Wentao Li.