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

Before using the Schaake Shuffle or Empirical Copula Coupling to reconstruct the dependence structure for post-processed ensemble meteorological forecasts, a necessary step is to sample discrete samples from each post-processed 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, we propose to use the Stratified Sampling (SS). 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 analysed by using EQ, IR, and SS sampling in Empirical Copula Coupling (ECC) for reconstructing post-processed ensemble members for 4 stations in the Xixian basin. The results show that: (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 sampling 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.