Stochastically Perturbed Weights: Ensembles from Deterministic Machine-Learning Weather Models

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.

Over the past few years, the rapid development of machine learning (ML) models for weather forecasting has produced deterministic models whose medium-range skill matches or exceeds that of the European Centre for Medium-Range Weather Forecasts (ECMWF)'s high-resolution forecast (HRES). However, when these models are integrated freely beyond the horizon they were trained for, they blow up, drift, or lose their seasonal cycle, and retraining them for stability is expensive. We therefore ask what can be recovered from a strictly frozen backbone. We present Rescene, a 0.4 M-parameter wrapper around a frozen 1.5 degree, 6-hourly vision-transformer operator, developed using ERA5 reanalysis data and comprising a deterministic "slow clock" (0.33 M) that blends the forecast toward a lead-aware day-of-year climatology and a generative head (0.06 M) that adds a spectrally shaped stochastic perturbation at every step. The performance evaluation demonstrates that the deterministic wrapper alone is stable for decades but collapses daily variability to 40% of ERA5. Adding the generative head restores 126% (Z500) and 130% (MSLP) of the observed daily variability with pattern correlations of 0.89 and 0.92, recovers 82% of the observed blocking frequency, keeps the ensemble calibrated (spread-skill ratio 0.78-0.97 from day 7 to day 90), and integrates for 100 years with no detectable drift (+0.008 +/- 0.014 K per century). Moreover, because the perturbation is band-limited to total wavenumber $k \le 20$, the small scales are never forced, yet realistic $k \ge 20$ power is sustained: a direct decomposition of the 6-hourly energy budget shows that the frozen operator supplies 28 times more energy than the perturbation at $k \ge 40$, with a fractional growth rate 247 times larger at the grid scale than at planetary scales.

End-to-end weather forecasting systems produce skillful global gridded and station forecasts directly from raw Earth observations, replacing the numerical weather prediction pipeline, including data assimilation, at a fraction of its cost. These systems are deterministic and issue no uncertainty. Here we render the Aardvark Weather model probabilistic by attaching one stochastic mechanism to each component: learned, input-dependent noise at the observation encoder, capturing aleatoric uncertainty inherited from the observing system, and Monte Carlo dropout in the processor, capturing epistemic uncertainty in the learned dynamics. The resulting nested ensemble attributes forecast spread to the two sources through a law-of-total-variance decomposition, cross-checked by withholding observation streams. Probabilistic finetuning significantly improves the mean forecast, by 4.2% on average across variables and lead times. The ensemble is calibrated against ERA5 through the medium range (spread-skill ratio 0.98), keeps station RMSE within 2.4% of the deterministic model while beating it in CRPS at every lead time, and trails the operational ECMWF ensemble. The encoder branch behaves as observation-driven uncertainty. Component-attributed uncertainty makes end-to-end forecasts more transparent, a step toward observation-driven digital twins of the atmosphere.