Application of the Spatial Scale Analysis in Verification of Ensemble Precipitation Prediction

With the increasing resolution of ensemble prediction models, existing ensemble forecast verification approaches face challenges in concurrently evaluating forecast accuracy and uncertainty. To address this limitation, this study develops a complementary multi-scale diagnostic framework for ensemble precipitation verification, using Discrete Cosine Transform (DCT) spectral analysis and Haar wavelet decomposition to examine different aspects of forecast uncertainty and precipitation error structure. Applied to a North China rainstorm event in 2024 forecasted by the China Meteorological Administration Regional Ensemble Prediction System (CMA-REPS), the proposed framework identifies a scale-dependent upscale evolution of ensemble-error decorrelation, which is consistent with the three-stage error-growth conceptual model proposed in previous mesoscale predictability studies. The temporal evolution of the decorrelation scale λ₀ quantitatively characterizes the loss of ensemble coherence with increasing forecast lead time. Precipitation energy analysis indicates that the model systematically underestimates fine-scale and mesoscale precipitation energy below 160 km and misrepresents the scale structure of rainstorm precipitation. Furthermore, this study proposes a general dynamically weighted ensemble metric framework, including the ensemble mean squared error (EMSE) and the ensemble intensity-scale skill score (EIS). In principle, the weights can be derived from observation-independent reference spectra, such as climatological or historical precipitation energy spectra, allowing the framework to be extended to real-time evaluation and scale-adaptive post-processing. In the present diagnostic weighting experiment, EMSE is reduced by 5.6%–7.5% at the meso-β scale (~160 km), indicating that member differentiation at this scale has potential value for scale-adaptive ensemble post-processing. This work provides a complementary multi-scale diagnostic workflow for jointly examining ensemble uncertainty evolution and scale-dependent precipitation error sources, offering useful insights for improving ensemble perturbation strategies and post-processing techniques.