Development of a Four-Dimensional Diagnostic Analysis Model for Ensemble Forecast Uncertainty

Evaluating whether an ensemble prediction system (EPS) can accurately represent forecast uncertainty is a key aspect of the model development and ensemble forecast applications. Therefore, a four-dimensional diagnostic analysis model for ensemble forecast uncertainty is proposed in this paper via analyzing the relationship between the ensemble spread and the root-mean-square error (RMSE) of ensemble mean in terms of time evolution (one-dimensional) and spatial distribution (three-dimensional), together with applying the linear variance calibration (LVC) method. Through employing this model and daily operational forecast data of the CMA global EPS (CMA-GEPS) from December 2022 to November 2023, the characteristics of the CMA-GEPS forecast uncertainty are diagnosed and analyzed, and compared against the state-of-the-art operational global EPS from European Centre for Medium-Range Weather Forecasts (ECMWF). Generally, there is a deficiency of underestimation about forecast uncertainty in CMA-GEPS, especially in the tropics; however, this phenomenon of underestimation about uncertainty doesn’t exist everywhere. With respect to certain initialization dates in some seasons and local regions, the spread is shown to be greater than the RMSE, indicating an overestimation of forecast uncertainty. Moreover, the CMA-GEPS performs better in simulating the forecast uncertainty of lower-level variables than upper-level variables, and in comparisons with the mass and thermal fields, the forecast uncertainty of the dynamic field is better captured. Diagnostic analysis using the LVC method reveals that the relevance between the ensemble variance and the ensemble mean error variance of CMA-GEPS is augmented with forecast lead time, and the problem of the underestimation of forecast uncertainty is continuously alleviated. In addition, the ECMWF EPS behaves distinctly better than the CMA-GEPS in representing forecast uncertainty and its growth process, for which the reasons are discussed and illuminated from the perspective of shortcomings in the methods to generate initial and model perturbations, the ensemble size, and the forecast model adopted by CMA-GEPS.