Spread/Error relationship and spatial error structure of precipitation ensemble nowcasting: Comparison of STEPS and generative AI

TL;DR

The paper analyzes ensemble properties of a pre-trained latent diffusion model (LDCast) and STEPS for rainfall nowcasting over Belgium to determine whether ensemble content conveys dynamical spatial information. It shows that both models are mildly underdispersive but provide error estimates across scales, with event-type adaptation in the perturbation spectra; however, spatial localization of ensemble error is not improved by either model compared to tailored surrogate ensembles. Through spectral, covariance, and spatial metrics, the study demonstrates that the ensembles primarily encode statistical structure rather than true dynamical spatial information, signaling limits for operational use without retraining or model redesign. The findings motivate retraining LDCast on region-specific data, evaluating additional generative models, and examining spatial anisotropy and ensemble-size effects to enhance spatiotemporal reliability in nowcasting. Overall, the work advances understanding of how modern generative nowcasting ensembles reflect (or fail to reflect) physical spatial dynamics, with practical implications for forecast confidence and decision-making in radar-based rainfall prediction.

Abstract

The predictability of the generative AI-based nowcasting model LDCast (trained on another region) is evaluated over Belgium, together with the pysteps implementation of the nowcasting algorithm STEPS. STEPS and LDCast are slightly underdispersive, but the ensemble spread provides an estimation of the error at almost all scales. Both models adapt the properties of their ensembles to the type of event, either convective or stratiform. The spatial scores of the STEPS and LDCast ensembles are compared with those of surrogate ensembles having some key properties, revealing that both STEPS and LDCast have very little ability to spatially localise the ensemble mean error vector through their ensemble members. This suggests that the content of STEPS and LDCast ensembles is informative in terms of statistics, but not in terms of dynamics.

Figures (8)

• Figure 1: Spectral error and spectral variance, for STEPS and for LDCast, and for convective and for stratiform events (averaged over events). Dashed lines display the spectral variance and dotted lines display the spectral error. The color represents the lead time. The power spectra of observations are represented by thick black lines.
• Figure 2: Ratios of the spectral variance over the de-biased spectral error, for STEPS and LDCast, and for convective and stratiform events (averaged over the events). The color represents the lead time. Horizontal dashed grey lines mark where the ratio is $1$. Ratio $<1$: underdispersion, ratio $>1$: overdispersion.
• Figure 3: Eigenvalues $\lambda_i$ of the covariance matrix. Evolution of the eigenvalues for convective and stratiform events for STEPS (A.) and LDCast (B.). Normalized eigenvalues for convective and stratiform events, for STEPS and LDCast, after 15 minutes (C.) and after 90 minutes (D.) (each line is the eigenvalue spectrum for one event).
• Figure 4: Histograms of the $c_{ij}$ for $j = 1, 5, 10$ and $15$ (for all events) after 15 minutes.
• Figure 5: Evolution of the spectra of the eigenvectors for convective and stratiform events, for LDCast and STEPS ensembles. The spectra are averaged over all events. The color represents the corresponding eigenvalue.