Extending a joint probability modelling approach for post-processing ensemble precipitation forecasts from numerical weather prediction models

Statistical post-processing has been widely employed to correct bias and dispersion errors in raw ensemble precipitation forecasts from numerical weather prediction models. One prominent post-processing scheme is to establish a joint probability model by fitting a bivariate distribution of raw forecasts and corresponding observations. However, current joint probability models only incorporate ensemble mean as the predictor, and ensemble spread is not considered. This is a major disadvantage of joint probability models as ensemble spread can be informative for forecast uncertainty. In this paper, we propose a two-step calibration approach to combine the strengths of joint probability models and the useful information included in the ensemble spread. In the first step, we take the seasonally coherent calibration (SCC) model as an example of joint probability models to calibrate the ensemble mean. As SCC for precipitation forecasts involves transformations for data normalization and special treatments of zero values, we explore three different ways to estimate ensemble mean values when establishing the SCC model. In the second step, we re-calibrate the ensemble forecasts produced in the first step to incorporate ensemble spread information from the raw forecasts. The performance of this two-step calibration is evaluated using ensemble precipitation forecasts from the Australian Bureau of Meteorology. We find that forecasts calibrated using the two-step calibration have better skills than SCC calibrated forecasts, especially for heavy precipitation events. Strengths of joint probability models and raw ensemble spread information are well utilized in the proposed two-step calibration approach.