Butterfly Effect and the Kinetic Energy Cascade in Probabilistic Machine Learning Weather Prediction Models
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.
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BibTeX
@misc{chen2026butterfly,
title = {{Butterfly Effect and the Kinetic Energy Cascade in Probabilistic Machine Learning Weather Prediction Models}},
author = {Jiakai Chen and Joel Oskarsson and Simon Driscoll and Sebastian Schemm},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.18489},
eprint = {2609.18489},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.18489},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Butterfly Effect and the Kinetic Energy Cascade in Probabilistic Machine Learning Weather Prediction Models
AU - Jiakai Chen
AU - Joel Oskarsson
AU - Simon Driscoll
AU - Sebastian Schemm
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2609.18489
UR - https://arxiv.org/abs/2609.18489
AB - 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.
ER -