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 model development and ensemble forecast applications. Therefore, a four-dimensional diagnostic analysis model for ensemble forecast uncertainty is proposed in this paper. It works by analyzing the relationship between the ensemble spread and the root-mean-square error (RMSE) of the ensemble mean in terms of the temporal 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 China Meteorological Administration (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 of the European Centre for Medium-Range Weather Forecasts (ECMWF). Generally, there is a deficiency shown by CMA-GEPS in that it underestimates the forecast uncertainty, especially in the tropics. However, this problem does not exist everywhere. At certain initialization times in some seasons and over local regions, the spread is found to be greater than the RMSE, indicating an overestimation of forecast uncertainty. Moreover, CMA-GEPS performs better in simulating the forecast uncertainty of lower-level variables than upper-level variables; and in comparison 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 underestimated forecast uncertainty is continuously alleviated. In addition, the ECMWF EPS behaves distinctly better than CMA-GEPS in representing the forecast uncertainty and its growth process, the reasons for which are discussed and elucidated from the perspective of shortcomings in the methods to generate the initial and model perturbations, the ensemble size, and the forecast model adopted by CMA-GEPS.