We assess the impact of a multi-scale loss formulation for training probabilistic machine-learned weather forecasting models. The multi-scale loss is tested in AIFS-CRPS, a machine-learned weather forecasting model developed at the European Centre for Medium-Range Weather Forecasts (ECMWF). AIFS-CRPS is trained by directly optimising the almost fair continuous ranked probability score (afCRPS). The multi-scale loss better constrains small scale variability without negatively impacting forecast skill. This opens up promising directions for future work in scale-aware model training.
It has been observed empirically that the sum of medians of skewed distributions is sometimes smaller than the median of their sum. To date, however, there has been no conclusive formal demonstration of this fact. This note continues an initial investigation in Van Zwet (Stat Neerl 33(1):1–5, 1979). It establishes a number of median inequalities, for example that the sum of medians of right-skewed distributions is smaller than the median of the sum, for a specific definition of skewness, and that the product of the medians of positive symmetric distributions is greater than the median of their product.
Global ocean warming continued unabated in 2025 in response to increased greenhouse gas concentrations and recent reductions in sulfate aerosols, reflecting the long-term accumulation of heat within the climate system, with conditions evolving toward La Niña during the year. In 2025, global upper 2000 m ocean heat content (OHC) increased by ∼23 ± 8 ZJ relative to 2024 according to IAP/CAS estimates. CIGAR-RT, and Copernicus Marine data confirm the continued ocean heat gain. Regionally, about 33
Weather forecasting plays a vital role in today's society, from agriculture and logistics to predicting the output of renewable energies and preparing for extreme weather events. Deep learning weather forecasting models trained with the next state prediction objective on ERA5 have shown great success compared to numerical global circulation models. Here, we propose a methodology to leverage deterministic weather models in the design of probabilistic weather models, leading to improved performance and reduced computing costs. We design a probabilistic weather model based on flow matching, a modern variant of diffusion models, that is trained to project deterministic weather predictions to the distribution of ERA5 weather states. Our model ArchesWeatherGen surpasses IFS ENS and NeuralGCM on all WeatherBench headline variables (except for NeuralGCM's geopotential). Our work also aims to democratize the use of generative machine learning models in weather forecasting research.
