Anisotropic Spectral Error Dressing for Calibrated Ensemble Weather Forecasts

Abstract

Data-driven weather models achieve remarkable deterministic skill but lack native uncertainty quantification. Existing post-processing methods that convert deterministic forecasts into probabilistic ensembles typically assume isotropic error structure, ignoring directional patterns in forecast errors. We show that GraphCast forecast errors exhibit significant quasi-zonal anisotropy, with zonal modes containing $4.26\times$ more power than meridional modes. To exploit this structure, we propose Anisotropic Spectral Error Dressing (ASED), a training-free method that models within-degree anisotropy via the normalized order ratio $\mu = |m|/l$, partitioning modes into 3 $\mu$-bins across 4 degree bands. On WeatherBench2 Z500 at 5-day lead time, ASED achieves 2.92% global CRPS improvement over standard spectral error dressing, with 82.4% of gridpoints showing improvement. Our results demonstrate that exploiting directional error structure can meaningfully improve probabilistic calibration without model retraining.