A Stratified Sampling Approach for Improved Sampling from a Calibrated Ensemble Forecast Distribution

Before using the Schaake shuffle or empirical copula coupling (ECC) to reconstruct the dependence structure for postprocessed ensemble meteorological forecasts, a necessary step is to sample discrete samples from each postprocessed continuous probability density function (pdf), which is the focus of this paper. In addition to the equidistance quantiles (EQ) and independent random (IR) sampling methods commonly used at present, the stratified sampling (SS) method is proposed. The performance of the three sampling methods is compared using calibrated GFS ensemble precipitation reforecasts over the Xixian basin in China. The ensemble reforecasts are first calibrated using heteroscedastic extended logistic regression (HELR), and then the three sampling methods are used to sample calibrated pdfs with a varying number of discrete samples. Finally, the effect of the sampling method on the reconstruction of ensemble members with preserved space dependence structure is analyzed by using EQ, IR, and SS in ECC for reconstructing postprocessed ensemble members for four stations in the Xixian basin. There are three main results. 1) The HELR model has a significant improvement over the raw ensemble forecast. It clearly improves the mean and dispersion of the predictive distribution. 2) Compared to EQ and IR, SS can better cover the tails of the calibrated pdfs and a better dispersion of calibrated ensemble forecasts is obtained. In terms of probabilistic verification metrics like the ranked probability skill score (RPSS), SS is slightly better than EQ and clearly better than IR, while in terms of the deterministic verification metric, root-mean-square error, EQ is slightly better than SS. 3) ECC-SS, ECC-EQ, and ECC-IR all calibrate the raw ensemble forecast, but ECC-SS shows a better dispersion than ECC-EQ and ECC-IR in this study.