A spectral test of the butterfly effect and physical consistency in the diffusion-based GenCast's ensembles

Abstract

With the rapid development of deep learning weather prediction (DLWP) models like GenCast, rigorous evaluation of their physical consistency is essential. This study investigates the dynamical fidelity of GenCast against ECMWF IFS-HRES and IFS-ENS using comprehensive kinetic energy (KE) and difference kinetic energy (DKE) spectra over 2021. Unlike the physically consistent error growth in IFS-ENS, GenCast exhibits weak planetary-scale growth and a persistent, flattened KE tail at high wavenumbers starting from the first forecast step. These mesoscale artifacts persist across multiple GenCast variants and AIFS-ENS, indicating a broader challenge for noise-conditioned generation. Helmholtz decomposition further reveals white-noise-like variance rather than balanced dynamics. Spatially, weak interactions between large-scale and mesoscale wind fields suggest a misrepresentation of topography-flow interactions. Furthermore, analyses of KE gradient (divided by del KE divided by) revealed that GenCast fails to reproduce the sharp, filamentary structures, instead generating broad, isotropic, and noisy patterns. These findings suggest that current noise injection mechanisms in DLWPs produce noisy artifacts mimicking variance without reproducing realistic error growth physics. Improving these mechanisms is vital for developing physically consistent DLWPs.