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This research critically evaluates how probabilistic machine learning weather models handle kinetic energy transfer across spatial scales, revealing significant limitations in capturing the butterfly effect and ensemble spread growth compared to physics-based baselines. The findings highlight a fundamental tension where these AI systems can generate skillful forecasts while simultaneously misrepresenting the underlying physical mechanisms of error propagation. For the community, this underscores the necessity of rigorous spectral analysis to ensure ML models align with known dynamical constraints before deployment in high-stakes forecasting.
Butterfly Effect and the Kinetic Energy Cascade in Probabilistic Machine Learning Weather Prediction Models
arXiv:2609.18489v1 Announce Type: cross Abstract: This study analyses kinetic energy (KE) spectra, difference kinetic energy (DKE) spectra, and signatures of KE transfer across spatial scales in four state-of-the-art probabilistic machine learning weather prediction (MLWP) models: NeuralGCM-ENS, FourCastNet 3, AIFS-ENS, and GenCast. Results are compared with those from the physics-based numerical weather prediction model IFS-ENS. While NeuralGCM-ENS successfully reproduces the expected upscale transfer of KE, noise injection at its encoder stage underestimates mesoscale KE. Conversely, AIFS-ENS, GenCast, and FourCastNet 3 produce realistic KE spectral magnitudes but do not capture the expected upscale transfer of KE. In particular, AIFS-ENS and GenCast, which employ spatially uncorrelated stochastic perturbations, exhibit enhanced accumulation of KE at high wavenumbers. All examined models exhibit upscale error growth, reflected by the progressive shift of the DKE spectral peak toward larger wavelengths over time. However, the MLWP models struggle to reproduce the rapid initial growth of ensemble spread at small spatial scales associated with the butterfly effect. The results show that MLWP models can misrepresent the known scale transfer of kinetic energy despite producing skilful weather forecasts.
Abstract:This study analyses kinetic energy (KE) spectra, difference kinetic energy (DKE) spectra, and signatures of KE transfer across spatial scales in four state-of-the-art probabilistic machine learning weather prediction (MLWP) models: NeuralGCM-ENS, FourCastNet 3, AIFS-ENS, and GenCast. Results are compared with those from the physics-based numerical weather prediction model IFS-ENS. While NeuralGCM-ENS successfully reproduces the expected upscale transfer of KE, noise injection at its encoder stage underestimates mesoscale KE. Conversely, AIFS-ENS, GenCast, and FourCastNet 3 produce realistic KE spectral magnitudes but do not capture the expected upscale transfer of KE. In particular, AIFS-ENS and GenCast, which employ spatially uncorrelated stochastic perturbations, exhibit enhanced accumulation of KE at high wavenumbers. All examined models exhibit upscale error growth, reflected by the progressive shift of the DKE spectral peak toward larger wavelengths over time. However, the MLWP models struggle to reproduce the rapid initial growth of ensemble spread at small spatial scales associated with the butterfly effect. The results show that MLWP models can misrepresent the known scale transfer of kinetic energy despite producing skilful weather forecasts.
Atmospheric and Oceanic Physics (physics.ao-ph); Machine Learning (cs.LG)
arXiv:2609.18489 [physics.ao-ph]
(or arXiv:2609.18489v1 [physics.ao-ph] for this version)
https://doi.org/10.48550/arXiv.2609.18489 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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