Revealing the Butterfly Effect in Deep Learning Weather Prediction Model via Kinetic Energy Spectra Change

The butterfly effect—where tiny uncertainties in initial conditions rapidly amplify into drastically different outcomes—is a main reason for using ensembles in probabilistic weather forecasting. While this sensitivity is clearly seen in numerical weather prediction (NWP) models, early deep learning weather prediction (DLWP) models failed to capture it. Recent advances including GenCast, however, have shown the ability to generate ensembles and rival the performance of traditional probabilistic NWPs. In this study, we investigate whether GenCast exhibits the butterfly effect by analyzing the evolution of kinetic energy spectrum over forecast lead time, in comparison two traditional NWPs: IFS-HRES and IFS-ENS. The research is based on 52 forecasts initialized every Monday during 2021, and all spectral metrics are averaged over initial times to obtain robust ensemble statistics. NWP spectra reveal a distinct upscale error cascade. In contrast, GenCast’s spectrum remains unsaturated and fluctuates regardless of lead time, except at the mesoscale, where it stabilizes very early in the forecast. This suggests that GenCast’s ensemble diverges primarily at the synoptic-scale, skipping the mesoscale. Furthermore, Fourier analysis of the jet stream revealed that small-scale topographic forcing does not effectively dissipate jet stream kinetic energy, further supporting the observed spectral behavior of GenCast. Analyzing the gradient of kinetic energy could provide a complementary perspective on jet stream realism, especially in ensemble generated by DLWPs. These results highlight a critical limitation of current DLWP ensemble systems: while they can mimic ensemble spread at larger scales, they fail to emulate the physical mechanisms through which small-scale uncertainties amplify and cascade in the atmosphere. Addressing this gap is essential for advancing DLWP toward truly physics-consistent ensemble forecasting.