Deep learning approaches have been widely adopted for precipitation nowcasting in recent years. Previous studies mainly focus on proposing new model architectures to improve pixel-wise metrics. However, they frequently result in blurry predictions which provide limited utility to forecasting operations. In this work, we propose a new Fourier Amplitude and Correlation Loss (FACL) which consists of two novel loss terms: Fourier Amplitude Loss (FAL) and Fourier Correlation Loss (FCL). FAL regularizes the Fourier amplitude of the model prediction and FCL complements the missing phase information. The two loss terms work together to replace the traditional L2 losses such as MSE and weighted MSE for the spatiotemporal prediction problem on signal-based data. Our method is generic, parameter-free and efficient. Extensive experiments using one synthetic dataset and three radar echo datasets demonstrate that our method improves perceptual metrics and meteorology skill scores, with a small trade-off to pixel-wise accuracy and structural similarity. Moreover, to improve the error margin in meteorological skill scores such as Critical Success Index (CSI) and Fractions Skill Score (FSS), we propose and adopt the Regional Histogram Divergence (RHD), a distance metric that considers the patch-wise similarity between signal-based imagery patterns with tolerance to local transforms.

Pretrained time series models have enabled inference-only forecasting systems that produce accurate predictions without task-specific training. However, existing approaches largely focus on univariate forecasting, limiting their applicability in real-world scenarios where multivariate data and covariates play a crucial role. We present Chronos-2, a pretrained model capable of handling univariate, multivariate, and covariate-informed forecasting tasks in a zero-shot manner. Chronos-2 employs a group attention mechanism that facilitates in-context learning (ICL) through efficient information sharing across multiple time series within a group, which may represent sets of related series, variates of a multivariate series, or targets and covariates in a forecasting task. These general capabilities are achieved through training on synthetic datasets that impose diverse multivariate structures on univariate series. Chronos-2 delivers state-of-the-art performance across three comprehensive benchmarks: fev-bench, GIFT-Eval, and Chronos Benchmark II. On fev-bench, which emphasizes multivariate and covariate-informed forecasting, Chronos-2's universal ICL capabilities lead to substantial improvements over existing models. On tasks involving covariates, it consistently outperforms baselines by a wide margin. Case studies in the energy and retail domains further highlight its practical advantages. The in-context learning capabilities of Chronos-2 establish it as a general-purpose forecasting model that can be used "as is" in real-world forecasting pipelines.

Benchmark quality is critical for meaningful evaluation and sustained progress in time series forecasting, particularly given the recent rise of pretrained models. Existing benchmarks often have narrow domain coverage or overlook important real-world settings, such as tasks with covariates. Additionally, their aggregation procedures often lack statistical rigor, making it unclear whether observed performance differences reflect true improvements or random variation. Many benchmarks also fail to provide infrastructure for consistent evaluation or are too rigid to integrate into existing pipelines. To address these gaps, we propose fev-bench, a benchmark comprising 100 forecasting tasks across seven domains, including 46 tasks with covariates. Supporting the benchmark, we introduce fev, a lightweight Python library for benchmarking forecasting models that emphasizes reproducibility and seamless integration with existing workflows. Usingfev, fev-bench employs principled aggregation methods with bootstrapped confidence intervals to report model performance along two complementary dimensions: win rates and skill scores. We report results on fev-bench for various pretrained, statistical and baseline models, and identify promising directions for future research.

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.

Deep learning approaches have been widely adopted for precipitation nowcasting in recent years. Previous studies mainly focus on proposing new model architectures to improve pixel-wise metrics. However, they frequently result in blurry predictions which provide limited utility to forecasting operations. In this work, we propose a new Fourier Amplitude and Correlation Loss (FACL) which consists of two novel loss terms: Fourier Amplitude Loss (FAL) and Fourier Correlation Loss (FCL). FAL regularizes the Fourier amplitude of the model prediction and FCL complements the missing phase information.

Wind power plays an increasingly significant role in achieving the 2050 Net Zero Strategy. Despite its rapid growth, its inherent variability presents challenges in forecasting. Accurately forecasting wind power generation is one key demand for the stable and controllable integration of renewable energy into existing grid operations. This paper proposes an adaptive method for very short-term forecasting that combines the generalised logit transformation with a Bayesian approach. The generalised logit transformation processes double-bounded wind power data to an unbounded domain, facilitating the application of Bayesian methods. A novel adaptive mechanism for updating the transformation shape parameter is introduced to leverage Bayesian updates by recovering a small sample of representative data. Four adaptive forecasting methods are investigated, evaluating their advantages and limitations through an extensive case study of over 100 wind farms ranging four years in the UK. The methods are evaluated using the Continuous Ranked Probability Score and we propose the use of functional reliability diagrams to assess calibration. Results indicate that the proposed Bayesian method with adaptive shape parameter updating outperforms benchmarks, yielding consistent improvements in CRPS and forecast reliability. The method effectively addresses uncertainty, ensuring robust and accurate probabilistic forecasting which is essential for grid integration and decision-making.

Most operational climate services providers base their seasonal predictions on initialised general circulation models (GCMs) or statistical techniques that fit past observations. GCMs require substantial computational resources, which limits their capacity. In contrast, statistical methods often lack robustness due to short historical records. Recent works propose machine learning methods trained on climate model output, leveraging larger sample sizes and simulated scenarios. Yet, many of these studies focus on prediction tasks that might be restricted in spatial extent or temporal coverage, opening a gap with existing operational predictions. Thus, the present study evaluates the effectiveness of a methodology that combines variational inference with transformer models to predict fields of seasonal anomalies. The predictions cover all four seasons and are initialised one month before the start of each season. The model was trained on climate model output from CMIP6 and tested using ERA5 reanalysis data. We analyse the method's performance in predicting interannual anomalies beyond the climate change-induced trend. We also test the proposed methodology in a regional context with a use case focused on Europe. While climate change trends dominate the skill of temperature predictions, the method presents additional skill over the climatological forecast in regions influenced by known teleconnections. We reach similar conclusions based on the validation of precipitation predictions. Despite underperforming SEAS5 in most tropics, our model offers added value in numerous extratropical inland regions. This work demonstrates the effectiveness of training generative models on climate model output for seasonal predictions, providing skilful predictions beyond the induced climate change trend at time scales and lead times relevant for user applications.

While numerical weather prediction (NWP) models are essential for forecasting thunderstorms hours in advance, NWP uncertainty, which increases with lead time, limits the predictability of thunderstorm occurrence. This study investigates how ensemble NWP data and machine learning (ML) can enhance the skill of thunderstorm forecasts. Using our recently introduced neural network model, SALAMA 1D, which identifies thunderstorm occurrence in operational forecasts of the convection-permitting ICON-D2-EPS model for Central Europe, we demonstrate that ensemble-averaging significantly improves forecast skill. Notably, an 11-hour ensemble forecast matches the skill level of a 5-hour deterministic forecast. To explain this improvement, we derive an analytic expression linking skill differences to correlations between ensemble members, which aligns with observed performance gains. This expression generalizes to any binary classification model that processes ensemble members individually. Additionally, we show that ML models like SALAMA 1D can identify patterns of thunderstorm occurrence which remain predictable for longer lead times compared to raw NWP output. Our findings quantitatively explain the benefits of ensemble-averaging and encourage the development of ML methods for thunderstorm forecasting and beyond.

Large-scale numerical simulations often produce high-dimensional gridded data that is challenging to process for downstream applications. A prime example is numerical weather prediction, where atmospheric processes are modeled using discrete gridded representations of the physical variables and dynamics. Uncertainties are assessed by running the simulations multiple times, yielding ensembles of simulated fields as a high-dimensional stochastic representation of the forecast distribution. The high-dimensionality and large volume of ensemble datasets poses major computing challenges for subsequent forecasting stages. Data-driven dimensionality reduction techniques could help to reduce the data volume before further processing by learning meaningful and compact representations. However, existing dimensionality reduction methods are typically designed for deterministic and single-valued inputs, and thus cannot handle ensemble data from multiple randomized simulations. In this study, we propose novel dimensionality reduction approaches specifically tailored to the format of ensemble forecast fields. We present two alternative frameworks, which yield low-dimensional representations of ensemble forecasts while respecting their probabilistic character. The first approach derives a distribution-based representation of an input ensemble by applying standard dimensionality reduction techniques in a member-by-member fashion and merging the member representations into a joint parametric distribution model. The second approach achieves a similar representation by encoding all members jointly using a tailored variational autoencoder. We evaluate and compare both approaches in a case study using 10 years of temperature and wind speed forecasts over Europe. The approaches preserve key spatial and statistical characteristics of the ensemble and enable probabilistic reconstructions of the forecast fields.

The rainfall-runoff relationship is a fundamental concept in hydrology. It describes how rainfall is transformed into surface runoff through interconnected hydrologic processes, such as infiltration, evapotranspiration, and the exchange of water between surface and subsurface flows (Beven & Kirkby, 1979). Thoroughly understanding these hydrologic processes and subsequently achieving accurate simulations of the rainfall-runoff relationship are critical for proactive flood forecasting and mitigation, efficient agricultural planning, and strategic urban development (Beven, 2012; Knapp et al., 1991; Moradkhani & Sorooshian, 2008). Physically-based hydrologic models (PBMs), grounded in physical laws that govern hydrologic dynamics, are the standard tools for simulating rainfall-runoff relationships (Beven, 1996). However, the highly nonlinear nature of various hydrologic processes often challenges PBMs, limiting their accuracy in diverse conditions (Beven, 1989; Clark et al., 2017). Consequently, there is a growing need for innovative approaches to address the limitations of PBMs. Deep learning (DL) has emerged as an alternative to PBMs, showing success in capturing the complex, nonlinear patterns in rainfall-runoff simulations. The hydrology community also explores the applicability of DL models in rainfall-runoff simulations across diverse temporal scales and geospatial locations.