Predicting precipitation maps is a highly complex spatiotemporal modeling task, critical for mitigating the impacts of extreme weather events. Short-term precipitation forecasting, or nowcasting, requires models that are not only accurate but also computationally efficient for real-time applications. Current methods, such as token-based autoregressive models, often suffer from flawed inductive biases and slow inference, while diffusion models can be computationally intensive. To address these limitations, we introduce BlockGPT, a generative autoregressive transformer using batched tokenization (Block) method that predicts full two-dimensional fields (frames) at each time step. Conceived as a model-agnostic paradigm for video prediction, BlockGPT factorizes space-time by using self-attention within each frame and causal attention across frames; in this work, we instantiate it for precipitation nowcasting. We evaluate BlockGPT on two precipitation datasets, viz. KNMI (Netherlands) and SEVIR (U.S.), comparing it to state-of-the-art baselines including token-based (NowcastingGPT) and diffusion-based (DiffCast+Phydnet) models. The results show that BlockGPT achieves superior accuracy, event localization as measured by categorical metrics, and inference speeds up to 31x faster than comparable baselines.

Quantifying and predicting rare and extreme events persists as a crucial yet challenging task in understanding complex dynamical systems. Many practical challenges arise from the infrequency and severity of these events, including the considerable variance of simple sampling methods and the substantial computational cost of high-fidelity numerical simulations. Numerous data-driven methods have recently been developed to tackle these challenges. However, a typical assumption for the success of these methods is the occurrence of multiple extreme events, either within the training dataset or during the sampling process. This leads to accurate models in regions of quiescent events but with high epistemic uncertainty in regions associated with extremes. To overcome this limitation, we introduce Extreme Event Aware (e2a or eta) or $η$-learning which does not assume the existence of extreme events in the available data. $η$-learning reduces the uncertainty even in `uncharted' extreme event regions, by enforcing the extreme event statistics of an observable indicative of extremeness during training, which can be available through qualitative arguments or estimated with unlabeled data. This type of statistical regularization results in models that fit the observed data, while enforcing consistency with the prescribed observable statistics, enabling the generation of unprecedented extreme events even when the training data lack extremes therein. Theoretical results based on optimal transport offer a rigorous justification and highlight the optimality of the introduced method. Additionally, extensive numerical experiments illustrate the favorable properties of the $η$-learning framework on several prototype problems and real-world precipitation downscaling problems.

High-resolution (HR) precipitation prediction is essential for reducing damage from stationary and localized heavy rainfall; however, HR precipitation forecasts using process-driven numerical weather prediction models remains challenging. This study proposes using Wasserstein Generative Adversarial Network (WGAN) to perform precipitation downscaling with an optimal transport cost. In contrast to a conventional neural network trained with mean squared error, the WGAN generated visually realistic precipitation fields with fine-scale structures even though the WGAN exhibited slightly lower performance on conventional evaluation metrics. The learned critic of WGAN correlated well with human perceptual realism. Case-based analysis revealed that large discrepancies in critic scores can help identify both unrealistic WGAN outputs and potential artifacts in the reference data. These findings suggest that the WGAN framework not only improves perceptual realism in precipitation downscaling but also offers a new perspective for evaluating and quality-controlling precipitation datasets.

Effective hydrological modeling and extreme weather analysis demand precipitation data at a kilometer-scale resolution, which is significantly finer than the 10 km scale offered by standard global products like IMERG. To address this, we propose the Wavelet Diffusion Model (WDM), a generative framework that achieves 10x spatial super-resolution (downscaling to 1 km) and delivers a 9x inference speedup over pixel-based diffusion models. WDM is a conditional diffusion model that learns the learns the complex structure of precipitation from MRMS radar data directly in the wavelet domain. By focusing on high-frequency wavelet coefficients, it generates exceptionally realistic and detailed 1-km precipitation fields. This wavelet-based approach produces visually superior results with fewer artifacts than pixel-space models, and delivers a significant gains in sampling efficiency. Our results demonstrate that WDM provides a robust solution to the dual challenges of accuracy and speed in geoscience super-resolution, paving the way for more reliable hydrological forecasts.

Precipitation nowcasting -- the short-term prediction of rainfall using recent radar observations -- is critical for weather-sensitive sectors such as transportation, agriculture, and disaster mitigation. While recent deep learning models have shown promise in improving nowcasting skill, most approaches rely solely on 2D radar reflectivity fields, discarding valuable vertical information available in the full 3D radar volume. In this work, we explore the use of Echo Top Height (ETH), a 2D projection indicating the maximum altitude of radar reflectivity above a given threshold, as an auxiliary input variable for deep learning-based nowcasting. We examine the relationship between ETH and radar reflectivity, confirming its relevance for predicting rainfall intensity. We implement a single-pass 3D U-Net that processes both the radar reflectivity and ETH as separate input channels. While our models are able to leverage ETH to improve skill at low rain-rate thresholds, results are inconsistent at higher intensities and the models with ETH systematically underestimate precipitation intensity. Three case studies are used to illustrate how ETH can help in some cases, but also confuse the models and increase the error variance. Nonetheless, the study serves as a foundation for critically assessing the potential contribution of additional variables to nowcasting performance.

To this day, accurately simulating local-scale precipitation and reliably reproducing its distribution remains a challenging task. The limited horizontal resolution of Global Climate Models is among the primary factors undermining their skill in this context. The physical mechanisms driving the onset and development of precipitation, especially in extreme events, operate at spatio-temporal scales smaller than those numerically resolved, thus struggling to be captured accurately. In order to circumvent this limitation, several downscaling approaches have been developed over the last decades to address the discrepancy between the spatial resolution of models output and the resolution required by local-scale applications. In this paper, we introduce RainScaleGAN, a conditional deep convolutional Generative Adversarial Network (GAN) for precipitation downscaling. GANs have been effectively used in image super-resolution, an approach highly relevant for downscaling tasks. RainScaleGAN's capabilities are tested in a perfect-model setup, where the spatial resolution of a precipitation dataset is artificially degraded from 0.25$^{\circ}\times$0.25$^{\circ}$ to 2$^{\circ}\times$2$^\circ$, and RainScaleGAN is used to restore it. The developed model outperforms one of the leading precipitation downscaling method found in the literature. RainScaleGAN not only generates a synthetic dataset featuring plausible high-resolution spatial patterns and intensities, but also produces a precipitation distribution with statistics closely mirroring those of the ground-truth dataset. Given that RainScaleGAN's approach is agnostic with respect to the underlying physics, the method has the potential to be applied to other physical variables such as surface winds or temperature.

This work introduces GPTCast, a generative deep-learning method for ensemble nowcast of radar-based precipitation, inspired by advancements in large language models (LLMs). We employ a GPT model as a forecaster to learn spatiotemporal precipitation dynamics using tokenized radar images. The tokenizer is based on a Quantized Variational Autoencoder featuring a novel reconstruction loss tailored for the skewed distribution of precipitation that promotes faithful reconstruction of high rainfall rates. The approach produces realistic ensemble forecasts and provides probabilistic outputs with accurate uncertainty estimation. The model is trained without resorting to randomness, all variability is learned solely from the data and exposed by model at inference for ensemble generation. We train and test GPTCast using a 6-year radar dataset over the Emilia-Romagna region in Northern Italy, showing superior results compared to state-of-the-art ensemble extrapolation methods.

Climate change exacerbates extreme weather events like heavy rainfall and flooding. As these events cause severe losses of property and lives, accurate high-resolution simulation of precipitation is imperative. However, existing Earth System Models (ESMs) struggle with resolving small-scale dynamics and suffer from biases, especially for extreme events. Traditional statistical bias correction and downscaling methods fall short in improving spatial structure, while recent deep learning methods lack controllability over the output and suffer from unstable training. Here, we propose a novel machine learning framework for simultaneous bias correction and downscaling. We train a generative diffusion model in a supervised way purely on observational data. We map observational and ESM data to a shared embedding space, where both are unbiased towards each other and train a conditional diffusion model to reverse the mapping. Our method can be used to correct any ESM field, as the training is independent of the ESM. Our approach ensures statistical fidelity, preserves large-scale spatial patterns and outperforms existing methods especially regarding extreme events and small-scale spatial features that are crucial for impact assessments.

Accurate and high-resolution Earth system model (ESM) simulations are essential to assess the ecological and socio-economic impacts of anthropogenic climate change, but are computationally too expensive. Recent machine learning approaches have shown promising results in downscaling ESM simulations, outperforming state-of-the-art statistical approaches. However, existing methods require computationally costly retraining for each ESM and extrapolate poorly to climates unseen during training. We address these shortcomings by learning a consistency model (CM) that efficiently and accurately downscales arbitrary ESM simulations without retraining in a zero-shot manner. Our foundation model approach yields probabilistic downscaled fields at resolution only limited by the observational reference data. We show that the CM outperforms state-of-the-art diffusion models at a fraction of computational cost while maintaining high controllability on the downscaling task. Further, our method generalizes to climate states unseen during training without explicitly formulated physical constraints.

This paper presents a convolutional neural network model for precipitation nowcasting that combines data-driven learning with physics-informed domain knowledge. We propose LUPIN, a Lagrangian Double U-Net for Physics-Informed Nowcasting, that draws from existing extrapolation-based nowcasting methods and implements the Lagrangian coordinate system transformation of the data in a fully differentiable and GPU-accelerated manner to allow for real-time end-to-end training and inference. Based on our evaluation, LUPIN matches and exceeds the performance of the chosen benchmark, opening the door for other Lagrangian machine learning models.