Machine learning for weather prediction increasingly relies on ensemble methods to provide probabilistic forecasts. Diffusion-based models have shown strong performance in Limited-Area Modeling (LAM) but remain computationally expensive at sampling time. Building on the success of global weather forecasting models trained based on Continuous Ranked Probability Score (CRPS), we introduce CRPS-LAM, a probabilistic LAM forecasting model trained with a CRPS-based objective. By sampling and injecting a single latent noise vector into the model, CRPS-LAM generates ensemble members in a single forward pass, achieving sampling speeds up to 39 times faster than a diffusion-based model. We evaluate the model on the MEPS regional dataset, where CRPS-LAM matches the low errors of diffusion models. By retaining also fine-scale forecast details, the method stands out as an effective approach for probabilistic regional weather forecasting

In recent years, machine learning has established itself as a powerful tool for high-resolution weather forecasting.

Tropical cyclones (TCs) are highly destructive and inherently uncertain weather systems. Ensemble forecasting helps quantify these uncertainties, yet traditional systems are constrained by high computational costs and limited capability to fully represent atmospheric nonlinearity. FuXi-ENS introduces a learnable perturbation scheme for ensemble generation, representing a novel AI-based forecasting paradigm. Here, we systematically compare FuXi-ENS with ECMWF-ENS using all 90 global TCs in 2018, examining their performance in TC-related physical variables, track and intensity forecasts, and the associated dynamical and thermodynamical fields. FuXi-ENS demonstrates clear advantages in predicting TC-related physical variables, and achieves more accurate track forecasts with reduced ensemble spread, though it still underestimates intensity relative to observations. Further dynamical and thermodynamical analyses reveal that FuXi-ENS better captures large-scale circulation, with moisture turbulent energy more tightly concentrated around the TC warm core, whereas ECMWF-ENS exhibits a more dispersed distribution. These findings highlight the potential of learnable perturbations to improve TC forecasting skill and provide valuable insights for advancing AI-based ensemble prediction of extreme weather events that have significant societal impacts.

This paper demonstrates the feasibility of trajectory learning for ensemble forecasts by employing the continuous ranked probability score (CRPS) as a loss function. Using the two-scale Lorenz '96 system as a case study, we develop and train both additive and multiplicative stochastic parametrizations to generate ensemble predictions. Results indicate that CRPS-based trajectory learning produces parametrizations that are both accurate and sharp. The resulting parametrizations are straightforward to calibrate and outperform derivative-fitting-based parametrizations in short-term forecasts. This approach is particularly promising for data assimilation applications due to its accuracy over short lead times.

In recent years, machine learning has established itself as a powerful tool for high-resolution weather forecasting.

Ensemble forecasting systems have advanced meteorology by providing probabilistic estimates of future states, supporting applications from renewable energy production to transportation safety. Nonetheless, systematic biases often persist, making statistical post-processing essential. Traditional parametric post-processing techniques and machine learning-based methods can produce calibrated predictive distributions at specific locations and lead times, yet often struggle to capture dependencies across forecast dimensions. To address this, multivariate post-processing methods-such as ensemble copula coupling and the Schaake shuffle-are widely applied in a second step to restore realistic inter-variable or spatio-temporal dependencies. The aim of this study is the multivariate post-processing of ensemble forecasts using a graph neural network (dualGNN) trained with a composite loss function that combines the energy score (ES) and the variogram score (VS). The method is evaluated on two datasets: WRF-based solar irradiance forecasts over northern Chile and ECMWF visibility forecasts for Central Europe. The dualGNN consistently outperforms all empirical copula-based post-processed forecasts and shows significant improvements compared to graph neural networks trained solely on either the continuous ranked probability score (CRPS) or the ES, according to the evaluated multivariate verification metrics. Furthermore, for the WRF forecasts, the rank-order structure of the dualGNN forecasts captures valuable dependency information, enabling a more effective restoration of spatial relationships than either the raw numerical weather prediction ensemble or historical observational rank structures. By contrast, for the visibility forecasts, the GNNs trained on CRPS, ES, or the ES-VS combination outperform the calibrated reference.

Over the last few years, probabilistic machine-learned weather prediction models have begun to rival physics-based numerical weather prediction (NWP) systems in skill (Kochkov et al., 2024; Price et al., 2023; Lang et al., 2024c,b). AIFS-CRPS (Lang et al., 2024b) is based on the machined-learned weather forecasting model AIFS (Lang et al., 2024a), developed at the European Centre for Medium-Range Weather Forecasts (ECMWF). AIFS-CRPS produces skilful predictions by directly optimising a score based on a proper scoring rule, the almost fair continuous ranked probability score (afCRPS). The model learns to shape Gaussian noise to represent uncertainty in the atmospheric state and achieves ensemble forecast skill that is competitive with, or superior to, the physics-based IFS ensemble (Molteni et al., 1996; Leutbecher and Palmer, 2008; Lang et al., 2021, 2023) at ECMWF. The afCRPS loss function used in AIFS-CRPS is computed point-wise on the full output field. However, atmospheric processes are inherently multi-scale, and different scales contribute to a different degree to the loss function.

Climate change is increasing the occurrence of extreme precipitation events, threatening infrastructure, agriculture, and public safety. Ensemble prediction systems provide probabilistic forecasts but exhibit biases and difficulties in capturing extreme weather. While post-processing techniques aim to enhance forecast accuracy, they rarely focus on precipitation, which exhibits complex spatial dependencies and tail behavior. Our novel framework leverages graph neural networks to post-process ensemble forecasts, specifically modeling the extremes of the underlying distribution. This allows to capture spatial dependencies and improves forecast accuracy for extreme events, thus leading to more reliable forecasts and mitigating risks of extreme precipitation and flooding.

Machine learning methods have been shown to be effective for weather forecasting, based on the speed and accuracy compared to traditional numerical models. While early efforts primarily concentrated on deterministic predictions, the field has increasingly shifted toward probabilistic forecasting to better capture the forecast uncertainty. Most machine learning-based models have been designed for global-scale predictions, with only limited work targeting regional or limited area forecasting, which allows more specialized and flexible modeling for specific locations. This work introduces Diffusion-LAM, a probabilistic limited area weather model leveraging conditional diffusion. By conditioning on boundary data from surrounding regions, our approach generates forecasts within a defined area. Experimental results on the MEPS limited area dataset demonstrate the potential of Diffusion-LAM to deliver accurate probabilistic forecasts, highlighting its promise for limited-area weather prediction. The frequency and cost of extreme weather events appear to be increasing (NOAA NCEI, 2025; IPCC, 2023; Whitt & Gordon, 2023), driven by climate change (IPCC, 2023). Therefore, accurate and reliable weather forecasts have become increasingly crucial for a variety of downstream applications.

We introduce the open-source Python package NABQR: Neural Adaptive Basis for (time-adaptive) Quantile Regression that provides reliable probabilistic forecasts. NABQR corrects ensembles (scenarios) with LSTM networks and then applies time-adaptive quantile regression to the corrected ensembles to obtain improved and more reliable forecasts. With the suggested package, accuracy improvements of up to 40% in mean absolute terms can be achieved in day-ahead forecasting of onshore and offshore wind power production in Denmark. Abbreviations Table 2. 1. Motivation and significance Quantifying predictive uncertainty is a key challenge in many scientific fields that depend on model-based forecasts [1]. Code metadata description Metadata C1 Current code version 0.1 C2 Permanent link to code/repository https://github.com/bast0320/