Improving Spatial Uncertainty Representation in Sub-seasonal Wind Speed Forecasts Using Quantile Regression, VAE and Diffusion

The uncertainty quantification in sub-seasonal wind speed forecasting is important for risk assessment and decision-making. One way to improve dynamical forecast skills is to regress information from forecasts of large-scale fields to surface fields by a supervised learning model. For such a statistical downscaling approach, Tian et al. (2024) demonstrated that spatially independent stochastic perturbations based on model residuals can improve the representation of ensemble dispersion. However, this method is limited in fully representing complex spatial correlations and maintaining physical consistency across meteorological fields. Recent advances in probabilistic deep learning models offer promising new approaches for uncertainty quantification, particularly in capturing spatial dependencies.

 

This study investigates how different statistical downscaling methods can better represent dynamic spatial uncertainty in sub-seasonal ensemble forecasts compared to the independent stochastic perturbation approach. We examine three probabilistic deep learning methods with distinct uncertainty quantification mechanisms: the Quantile Regression for direct modeling of distribution quantiles, the Variational Autoencoders (VAE) for latent space sampling, and the Diffusion model for iterative denoising-based distribution modeling. Our two-stage framework first trains these regression models on the ERA5 reanalysis to establish their capacity for spatial uncertainty representation from the 500hPa geopotential height (Z500) to the surface wind speeds (U100), then applies these probabilistic models to the ECMWF Z500 hindcasts to regress U100 ensembles.

 

Comprehensive verification reveals distinct characteristics of each method. First, in terms of grid point-wise metrics (the MSE and the CRPS), all these probabilistic methods achieve comparable forecasting skills to independent stochastic perturbations, despite their different approaches to uncertainty representation. Second, spatial structure analysis through Empirical Orthogonal Functions (EOF) analysis and zonal energy spectra demonstrates notable differences: while all methods effectively capture large- and medium-scale features, they differ significantly in representing small-scale spatial correlations. The grid-independent nature of independent stochastic perturbations leads to over-representation of small-scale variations, whereas the Diffusion model shows superior performance across all spatial scales. The Quantile Regression and the VAE show relatively limited skill in capturing small-scale spatial features. These findings suggest that probabilistic downscaling methods, particularly the Diffusion model, can better reconstruct spatial characteristics while maintaining comparable forecasting skills.

 

Our results indicate that probabilistic downscaling methods can provide more realistic representations of spatial uncertainty compared to the independent stochastic approach, particularly in reconstructing spatial correlations and maintaining physical consistency. This study advances our understanding of how deep learning methods can improve uncertainty quantification in sub-seasonal forecasting.

 

Tian, Ganglin, et al. "Improving sub-seasonal wind-speed forecasts in Europe with a non-linear model." arXiv preprint arXiv:2411.19077 (2024).