Precipitation

Data assimilation (DA) estimates the state of an evolving dynamical system from noisy, partial observations, and is widely used in scientific simulation as well as weather and climate science. In practice, filtering methods rely on frame-to-frame transition models. However, these models are fragile when observations are non-Markovian (when they form only a partial slice of a higher-dimensional latent state as in real-world weather data): they tend to accumulate errors over long horizons. At the same time, learned DA methods typically commit to a single regime, either filtering (nowcasting, real-time forecasting) or smoothing (retrospective reanalysis), which splits what should be a shared prior across application-specific pipelines. To address both issues, we introduce ForcingDAS, a unified and robust DA framework. Built on Diffusion Forcing with an independent noise level assigned to each frame, ForcingDAS learns a joint-trajectory prior instead of frame-to-frame transitions. This allows it to capture long-horizon temporal dependencies and reduce error accumulation. In addition, the same trained model spans the full filtering to smoothing spectrum at inference time. Specifically, nowcasting, fixed-lag smoothing, and batch reanalysis are selected through the inference schedule alone, without retraining. We evaluate ForcingDAS on 2D Navier-Stokes vorticity, precipitation nowcasting, and global atmospheric state estimation. Across all settings, a single model is competitive with or outperforms both learned and classical baselines that are specialized for individual regimes, with the largest gains observed on real-world weather benchmarks.

Existing precipitation nowcasting methods typically adopt an autoregressive formulation, where future states are predicted from previous outputs. However, such an approach accumulates errors over long rollouts, causing forecasts to drift away from physically plausible evolution trajectories. Although various studies have attempted to alleviate this problem by improving step-wise prediction accuracy, they largely neglect the global temporal evolution of meteorological systems and lack mechanisms to actively correct drift during rollouts. To address this issue, we propose McCast, a memory-guided latent drift correction method for precipitation nowcasting. Rather than treating memory as an unordered dictionary of latent states for passive conditioning, McCast leverages temporally organized memory to actively correct autoregressive latent evolution. Specifically, McCast introduces a Drift-Corrective Memory Bank (DCBank) that explicitly estimates the temporally consistent drift corrections to calibrate the divergent trajectory. DCBank performs drift correction in two stages: a Corrective Latent Extractor first predicts an initial correction from the current prediction and a reference latent state, and a Correction-Aware Memory Retrieval module then refines the initial correction using temporally organized historical memory. By explicitly correcting latent evolution, instead of improving step-wise prediction accuracy only, McCast produces more temporally coherent and reliable long-horizon forecasts. Experiments on two widely used benchmarks, SEVIR and MeteoNet, show that McCast achieves state-of-the-art performance, particularly in challenging long-horizon forecasting scenarios.

Precipitation nowcasting remains challenging due to the highly localized, rapidly evolving, and heterogeneous nature of atmospheric dynamics. Although recent methods increasingly adopt attention-based architectures in both unimodal and multimodal settings, they mainly emphasize stronger representation learning and prediction capacity, while paying less attention to the stability of attention responses across samples. In this work, we show that cross-sample instability of attention-response energy is an important and previously underexplored source of forecasting unreliability. Empirically, inaccurate forecasts are associated with larger attention-response energy variance across heads and layers. Theoretically, we show that cross-sample variability can propagate through self-attention, and enlarge a lower bound on prediction error. Based on this insight, we propose HARECast, a Head-wise Attention Response Energy-regulated framework for precipitation nowcasting. HARECast explicitly models head-wise attention-response energy and stabilizes it through a group-wise regularization objective that reduces cross-sample fluctuations. The proposed formulation is generic and applicable to both unimodal and multimodal nowcasting architectures. We instantiate HARECast in a standard forecasting pipeline with reconstruction branches and a diffusion-based predictor, and evaluate it on commonly used benchmarks--SEVIR and MeteoNet. Experimental results demonstrate that HARECast achieves state-of-the-art performance.

Precipitation nowcasting aims to forecast short-term radar echo sequences for extreme weather warning, where both prediction fidelity and inference efficiency are critical for real-world deployment. However, diffusion-based models, despite their strong generative capability, suffer from slow inference due to multi-step sampling trajectories, limiting their practical usability. Conditional Flow Matching (CFM) improves efficiency via straightened trajectories, but relies on latent space compression, which inevitably discards high-frequency physical details and degrades fine-grained prediction quality. To address these limitations, we propose PixelFlowCast, a two-stage probabilistic forecasting framework that achieves both high-efficiency and high-fidelity prediction without latent compression. Specifically, in the first stage, a deterministic model first produces coarse forecasts to capture global evolution trends. In the subsequent stage, the proposed KANCondNet extracts deep spatiotemporal evolution features to provide accurate conditional guidance. Based on this, a latent-free, few-step Pixel Mean Flows (PMF) predictor employs an $x$-prediction mechanism to generate high-quality predictions, effectively preserving fine-grained structures while maintaining fast inference. Experiments on the publicly available SEVIR dataset demonstrate that PixelFlowCast outperforms existing mainstream methods in both prediction accuracy and inference efficiency, particularly for long sequence forecasting, highlighting its strong potential for real-world operational deployment.

Accurate four-dimensional (4D) precipitation information is essential for understanding the Earth's energy and water cycles, yet remains observationally unresolved at global scales. Conventional theory holds that geostationary infrared observations primarily sense cloud-top properties, with limited sensitivity to sub-cloud precipitation. Here we show that cloud-top infrared measurements nevertheless encode sufficient information to recover the four-dimensional structure of precipitation, revealing a previously unexploited observability of sub-cloud processes. We introduce a physically constrained deep learning framework, 4DPrecipNet, in which a moisture-first constraint requires the latent representation to recover precipitable water vapour, anchoring the model in thermodynamic consistency. By integrating multi-channel infrared radiances with these constraints and radar-derived precipitation profiles, we reconstruct the vertical and temporal evolution of precipitation systems from geostationary orbit. The framework captures deep convective structures and their evolution, with robust performance across large samples and independent radar comparisons. These results demonstrate that sub-cloud precipitation is physically encoded in cloud-top infrared observations, establishing a new pathway for continuous global monitoring of precipitation structure.

High-resolution rainfall observations are crucial for weather forecasting, water management, and hazard mitigation. Traditional operational measurements are often biased and low-resolution, limiting their ability to capture local rainfall. Accurate high-resolution rainfall maps require integrating sparse surface observations, yet existing deep learning densification methods are hindered by rainfall's skewed, localized nature, noise, and limited spatio-temporal fusion. We present DropsToGrid, a Neural Process-based method that generates dense rainfall fields by fusing temporal sequences from noisy, irregularly distributed private weather stations with spatial context from radar. Leveraging multi-scale feature extraction, temporal attention, and multi-modal fusion, the model produces stochastic, continuous rainfall estimates and explicitly quantifies uncertainty. Evaluations on real-world datasets demonstrate that DropsToGrid outperforms both operational and deep learning baselines, generating accurate high-resolution rainfall maps with well-calibrated uncertainty, even when only few stations are available and in cross-regional scenarios.

Commercial Microwave Links (CMLs) offer dense spatial coverage for rainfall sensing but produce path-integrated measurements that make accurate ground-level reconstruction challenging. Existing methods typically oversimplify CMLs as point sensors and neglect line integration relating rainfall to signal attenuation, resulting in degraded performance under heterogeneous precipitation. In this work, we view rain field reconstruction as a Bayesian inverse problem with Diffusion Models (DMs) as high-fidelity spatial priors. We show that diffusion models better preserve key rainfall statistics compared to censored Gaussian processes. Framing rainfall estimation as a Bayesian inverse problem with a DM prior enables training-free posterior sampling using a broad family of methods, including Plug-and-Play, Sequential Monte Carlo, and Replica Exchange methods. Experiments on synthetic and real-world datasets demonstrate consistent improvements over established CML-based reconstruction baselines.

Folk meteorological proverbs encode centuries of empirical observation by agricultural communities. Two Hebrew proverbs link lunar calendar anchor days to monthly winter rainfall: (i) "If Rosh Chodesh is rainy, the whole month is rainy" and (ii) "If it rains on Shabbat Mevarechim, the whole month is rainy." Shabbat Mevarechim is the last Saturday before each new Hebrew month, preceding Rosh Chodesh by one to seven days. The first proverb is widely known; the second circulates in Hasidic oral tradition with no identified written source. Both have never been formally tested. We analyse 75 years (1950-2024) of daily precipitation data from seven Israeli cities across three climatic regions, comprising 191,758 station-days and 2,422 Hebrew-month observations during the winter rainy season (Marcheshvan-Adar). A rainy Rosh Chodesh increases the probability of a rainy month from 22.2% to 38.6% (lift +16.4 percentage points; chi-square = 57.8, p = 2.9e-14; Bayes factor 1.81). A rainy Shabbat Mevarechim produces a similar effect (lift +16.5 percentage points, p = 8.0e-13), despite preceding Rosh Chodesh by up to seven days. The effect decays with lag and mirrors daily rainfall autocorrelation (r = 0.35-0.44 at lag 1; ~0 at lag 7), consistent with Mediterranean cyclone persistence. A bootstrap permutation test (p < 1e-4) and a 15-year rolling analysis show declining predictive power (-0.20 percentage points per year, p < 0.001), consistent with shortening precipitation events under warming climate conditions. Both proverbs encode real but probabilistic meteorological signals whose reliability is decreasing over time.

ML climate model emulators are useful for scenario planning and adaptation, allowing for cost-efficient experimentation. Recently, the diffusion model Climate in a Bottle (cBottle) has been proposed for generation of atmospheric states compatible with boundary conditions of solar position and sea surface temperatures. Crucially, cBottle can be guided to generate extreme events such as Tropical Cyclones (TCs) over locations of interest. Diffusion models such as cBottle work by approximating the probability density of the training data. Here, we show use cases of the probability density estimates of atmospheric states obtained from this climate emulator. Most importantly, these estimates allow us to calculate likelihoods of extreme events under guidance. When guiding the model towards states including TCs, comparing the probability density under the guided and unguided model enables us to quantify how much more likely the guidance has made the TC. We show how these odds ratios allow us to importance-sample from the TC distribution, reducing the standard error of the probability estimate compared to simple Monte Carlo sampling. Furthermore, we discuss results and limitations of the application of model probability densities to extreme event attribution-like experiments. We present these early but encouraging results hoping they will spur more research into probabilistic information that can be gained from diffusion models of the atmosphere.

Understanding how vegetation loss alters rainfall remains a major challenge in climate and hydrological science, as deforestation modifies precipitation through heterogeneous, seasonal and nonlinear land-atmosphere feedbacks. Existing models struggle to capture these dynamics: convection is parameterised at coarse scales, tipping behaviour is poorly constrained, and rainfall-deforestation analyses are limited to multi-decadal timescales. Therefore, many approaches resolve correlations rather than causal effects, limiting our ability to anticipate hydrological disruption. Using a neural-network model for hourly rainfall prediction, combined with pathway diagnostics and sensitivity analyses, we examine how vegetation perturbations reorganise rainfall across space, intensity regimes, and timescales under deforestation. We assess whether the model captures physically consistent dependencies linking vegetation, atmospheric state, and precipitation, and whether sustained canopy loss induces threshold behaviour. The model accurately predicts rainfall occurrence and intensity (Spearman = 0.84, F1 = 0.93, ROC-AUC = 0.98) and learns temporally ordered dependencies aligned with ecohydrological theory. Sensitivity analyses reveal rapid, asymmetric responses to vegetation loss: heavy rainfall (20-50 mm/h) declines by up to 7% under sustained deforestation, while light rainfall (0.1-1 mm/h) increases by 4%. Rainfall entropy rises by 1.3%, and dry-season intensity increases by 0.3-0.5% per 0.5% forest-cover loss, with strongest impacts in the north-western Amazon and Andean foothills. Threshold analysis reveals a sharp decline in precipitating area fraction after 2-3 months of sustained vegetation change in sensitive regions. These results demonstrate that data-driven approaches uncover process-relevant land-atmosphere coupling and highlight growing hydrological vulnerability in the Amazon.

Short-range prediction of convective precipitation from weather radar observations is essential for severe weather warnings. However, deep learning models trained with pixel-wise error metrics tend to produce overly smooth forecasts that suppress intense echoes critical for hazard detection. This issue is exacerbated by insufficient multi-scale feature interaction and suboptimal fusion of heterogeneous geophysical inputs. We propose IMPA-Net (Integrated Multi-scale Predictive Attention Network), a deterministic 0-2 hour nowcasting framework that addresses these limitations through meteorologically-informed designs at the input, architecture, and loss function levels. A parameter-free Spatial Mixer reorganizes heterogeneous input channels at the mesoscale-$γ$ neighborhood (~2 km) via deterministic channel permutation, providing a structured cross-field prior. An integrated multi-scale predictive attention module serves as the spatiotemporal translator, capturing dynamics from mesoscale-$β$ to mesoscale-$γ$ scales. A Meteorologically-Aware Dynamic Loss employs three-level asymmetric weighting -- adapting across training epochs, storm intensity, and forecast lead time -- to counteract regression-to-the-mean. Evaluated against seven baselines on a multi-source radar dataset over eastern China, IMPA-Net raises the Heidke Skill Score at $\geq$45 dBZ from 0.049 (SimVP baseline) to 0.143 under matched settings. Relative to pySTEPS, it provides a better trade-off between severe-event detection and false-alarm control. Spectral analysis confirms preserved energy across mesoscale bands where competing methods show progressive smoothing. These improvements are shown within a single domain and convective regime; generalizability to other orographic and climatic regions remains to be tested.

Systematic biases in General Circulation Model (GCM) outputs limit their direct applicability in regional planning, making bias correction a technically demanding but necessary step for both short-term and long-term impact assessment. Correcting precipitation is particularly challenging due to its non-Gaussian distribution, intermittent nature, and heavy-tailed extremes. However, traditional statistical bias-correction methods have limited ability to learn systematic patterns from large datasets or generalize to new locations. While machine learning (ML) provides greater flexibility, it can produce unpredictable and difficult-to-interpret results, limiting generalization across GCMs and locations. In this study, we propose a differentiable bias-adjustment framework called dCLIMBA, that learns a spatiotemporally adaptive parametric bias-adjustment procedure, rather than corrected precipitation directly, between historical CMIP6 model outputs and a gridded observation-based dataset, Livneh. Results demonstrate that the proposed method corrects the magnitude and distribution of extreme precipitation with particularly strong performance in the upper tail. The quantile distribution of precipitation was well reproduced across diverse U.S. cities, and spatial patterns were comparable to those from the widely used LOCA2 statistical downscaling product. In addition, the framework showed partial future trend preservation and promising attenuation of marginal biases in unseen regions. This work presents a modular and efficient bias-correction approach. The differentiable approach provides an easy-to-use option for connecting atmospheric-model outputs to on-the-ground impacts.

Deep-learning video super-resolution has progressed rapidly, but climate applications typically super-resolve (increase resolution) either space or time, and joint spatiotemporal models are often designed for a single pair of super-resolution (SR) factors (upscaling spatial and temporal ratio between the low-resolution sequence and the high-resolution sequence), limiting transfer across spatial resolutions and temporal cadences (frame rates). We present a scale-adaptive framework that reuses the same architecture across factors by decomposing spatiotemporal SR into a deterministic prediction of the conditional mean, with attention, and a residual conditional diffusion model, with an optional mass-conservation (same precipitation amount in inputs and outputs) transform to preserve aggregated totals. Assuming that larger SR factors primarily increase underdetermination (hence required context and residual uncertainty) rather than changing the conditional-mean structure, scale adaptivity is achieved by retuning three factor-dependent hyperparameters before retraining: the diffusion noise schedule amplitude beta (larger for larger factors to increase diversity), the temporal context length L (set to maintain comparable attention horizons across cadences) and optionally a third, the mass-conservation function f (tapered to limit the amplification of extremes for large factors). Demonstrated on reanalysis precipitation over France (Comephore), the same architecture spans super-resolution factors from 1 to 25 in space and 1 to 6 in time, yielding a reusable architecture and tuning recipe for joint spatiotemporal super-resolution across scales.

Storm surge forecasting remains a critical challenge in mitigating the impacts of tropical cyclones on coastal regions, particularly given recent trends of rapid intensification and increasing nearshore storm activity. Traditional high fidelity numerical models such as ADCIRC, while robust, are often hindered by inevitable uncertainties arising from various sources. To address these challenges, this study introduces StormNet, a spatio-temporal graph neural network (GNN) designed for bias correction of storm surge forecasts. StormNet integrates graph convolutional (GCN) and graph attention (GAT) mechanisms with long short-term memory (LSTM) components to capture complex spatial and temporal dependencies among water-level gauge stations. The model was trained using historical hurricane data from the U.S. Gulf Coast and evaluated on Hurricane Idalia (2023). Results demonstrate that StormNet can effectively reduce the root mean square error (RMSE) in water-level predictions by more than 70% for 48-hour forecasts and above 50% for 72-hour forecasts, as well as outperform a sequential LSTM baseline, particularly for longer prediction horizons. The model also exhibits low training time, enhancing its applicability in real-time operational forecasting systems. Overall, StormNet provides a computationally efficient and physically meaningful framework for improving storm surge prediction accuracy and reliability during extreme weather events.

This study aims to develop and improve machine learning-based post-processing models for precipitation, temperature, and wind speed predictions using the Mesoscale Model (MSM) dataset provided by the Japan Meteorological Agency (JMA) for 18 locations across Japan, including plains, mountainous regions, and islands. By incorporating meteorological variables from grid points surrounding the target locations as input features and applying feature selection based on correlation analysis, we found that, in our experimental setting, the LightGBM-based models achieved lower RMSE than the specific neural-network baselines tested in this study, including a reproduced CNN baseline, and also generally achieved lower RMSE than both the raw MSM forecasts and the JMA post-processing product, MSM Guidance (MSMG), across many locations and forecast lead times. Because precipitation has a highly skewed distribution with many zero cases, we additionally examined Tweedie-based loss functions and event-weighted training strategies for precipitation forecasting. These improved event-oriented performance relative to the original LightGBM model, especially at higher rainfall thresholds, although the gains were site dependent and overall performance remained slightly below MSMG.

Decision-makers rely on weather forecasts to plant crops, manage wildfires, allocate water and energy, and prepare for weather extremes. Today, such forecasts enjoy unprecedented accuracy out to two weeks thanks to steady advances in physics-based dynamical models and data-driven artificial intelligence (AI) models. However, model skill drops precipitously at subseasonal timescales (2 - 6 weeks ahead), due to compounding errors, systemic model biases, and the chaotic nature of the atmosphere. To counter this degradation, we introduce probabilistic bias correction (PBC), a machine learning framework that substantially reduces systematic error by learning to correct historical probabilistic forecasts. When applied to the leading dynamical and AI models from the European Centre for Medium-Range Weather Forecasts (ECMWF), PBC doubles the modest subseasonal skill of the AI Forecasting System and improves the skill of the operationally-debiased dynamical model for 91% of pressure, 92% of temperature, and 98% of precipitation targets. We designed PBC for operational deployment, and, in ECMWF's 2025 real-time forecasting competition, its global forecasts placed first for all weather variables and lead times, outperforming the dynamical models from six operational forecasting centers, an international dynamical multi-model ensemble, ECMWF's AI Forecasting System, and the forecasting systems of 34 teams worldwide. These probabilistic skill gains translate into more accurate prediction of extreme events and have the potential to improve agricultural planning, energy management, and disaster preparedness in vulnerable communities.

Machine learning forecast systems are moving beyond point predictions to full predictive distributions for future outcomes y conditional on complex inputs x. However, these distributions are often locally miscalibrated, especially for high-stakes tail events where accurate uncertainty quantification is most needed to establish trust in models. Local miscalibration occurs because training data often lack examples of low-frequency events. The goal of this paper is to describe a simple, yet flexible framework that, at deployment, produces interpretable diagnostics and a robust correction mechanism of predictive distributions when train examples are limited. With this goal in mind, we introduce a semiparametric version of the Local Amortized Diagnostic and Reshaping (LADaR) framework that posits a covariate-dependent parametric model for a diagnostic transport map regressed nonparametrically on inputs to describe how to correct tail probabilities across the feature space to match calibration data. These maps provide the user with local, real-time diagnostics and a reshaped predictive distribution that can be related back to physical processes in the input space. We apply these semiparametric diagnostic transport maps to short-term tropical cyclone intensity forecasting to detect evolutionary modes linked to local miscalibration in the National Hurricane Center's forecasts and improve predictions for severe weather hazards.

Until recently, numerical weather prediction (NWP) models have stood rivalless in operational forecasting despite a few limitations. Namely, physically-based models are computationally demanding and struggle at short lead times, reducing their utility for nowcasting. Motivated by these shortcomings, recent work proposes AI-weather prediction (AI-WP) alternatives that emulate analysis data with neural networks. While these data-driven approaches have achieved high skill for medium-range forecasting-applications of AI-WP to precipitation and to nowcasting are less explored. To these ends, this paper discusses \textit{SaTformer}: a video transformer adapted for precipitation nowcasting. To ameliorate some problems related to what is essentially a fat-tailed regression task, we find it prudent to formulate nowcasting as a classification problem and employ a frequency-weighted loss. This straightforward approach scored first on the NeurIPS Weather4Cast 2025 ``Cumulative Rainfall'' challenge. Code and model weights are available: \texttt{\href{github.com/leharris3/w4c-25}{github.com/leharris3/satformer}}.

Accurate medium-range precipitation forecasting is essential for hydrometeorological risk management but remains challenging for both numerical weather prediction (NWP) systems and data-driven models. We present CSU-PCAST, a deep learning-based ensemble forecasting framework for global precipitation prediction. The model is trained using ERA5 atmospheric and surface variables at 0.25° resolution with precipitation labels from NASA's IMERG dataset. CSU-PCAST uses 57 prognostic variables and static geographical fields to predict both atmospheric states and 6-h accumulated precipitation. The framework employs a Swin Transformer backbone with stochastic noise conditioning, temporal embeddings, and a dual-branch decoder for precipitation and non-precipitation variables. During inference, CSU-PCAST is initialized from operational GFS analyses and generates 30 ensemble members out to 15 days using an autoregressive strategy. Evaluation against GEFS over the full year of 2023 shows improved precipitation forecast skill at short lead times, including higher Critical Success Index (CSI) and lower RMSE during the first several forecast days. CSU-PCAST also reduces GEFS wet bias for light precipitation and dry bias at heavier precipitation thresholds. Probabilistic verification demonstrates lower CRPS, higher Brier Skill Scores at several thresholds, and improved ensemble reliability relative to GEFS, although both systems remain underdispersive. A case study of the Sanba extreme precipitation event further shows improved spatial structure and exceedance-probability guidance. These results demonstrate the potential of CSU-PCAST for short-to-medium-range ensemble precipitation forecasting while highlighting remaining challenges in extreme precipitation prediction and ensemble calibration.

Machine learning-based precipitation nowcasting relies on high-fidelity radar reflectivity sequences to model the short-term evolution of convective storms. However, the development of models capable of predicting extreme weather has been constrained by the coarse resolution (1-2 km) of existing public radar datasets, such as SEVIR, HKO-7, and GridRad-Severe, which smooth the fine-scale structures essential for accurate forecasting. To address this gap, we introduce Storm250-L2, a storm-centric radar dataset derived from NEXRAD Level-II and GridRad-Severe data. We algorithmically crop a fixed, high-resolution (250 m) window around GridRad-Severe storm tracks, preserve the native polar geometry, and provide temporally consistent sequences of both per-tilt sweeps and a pseudo-composite reflectivity product. The dataset comprises thousands of storm events across the continental United States, packaged in HDF5 tensors with rich context metadata and reproducible manifests.

Artificial intelligence weather prediction systems now surpass state-of-the-art physical models for medium-range forecasting. However, because these models are trained almost exclusively on historical climate reanalyses, they inherit pervasive structural biases, particularly for precipitation. Here we fine-tune a global graph-transformer architecture directly on high-resolution, satellite-derived precipitation observations. The resulting model reduces global medium-range probabilistic forecasting errors by up to 19% and improves extreme rainfall prediction accuracy by 57% over current operational models. It additionally demonstrates superior skill for tropical storms and drizzle events, though a physics-based operational model remains more reliable for the heaviest precipitation events. Our results demonstrate that incorporating observation-based data directly into training can substantially improve precipitation forecasts.

Imbalanced labels can cause frequent samples to dominate AI-based quantitative remote sensing, degrading rare-event retrieval. In rain-rate retrieval based on satellite infrared brightness temperatures, this imbalance leads to systematic underestimation of rare high-intensity rainfall. In this study, Hurdle-Retrieval Model Imbalanced Learning (RMIL) is proposed. Following a divide-and-conquer strategy, Hurdle-RMIL separates zero inflation from the long-tailed distribution of positive rain. A hurdle model handles zero inflation, whereas RMIL exploits invariance under fixed observation conditions of the rainfall-to-satellite forward process to derive a Bayes-based transformation linking conditional distributions under naturally long-tailed and hypothetical balanced rainfall. This transformation enables the balanced-distribution model to be learned from natural samples without constructing a balanced dataset. Comparisons with conventional learning, classification-regression modeling, cost-sensitive learning, and generative learning using test data from multiple regions in China show that Hurdle-RMIL mitigates systematic underestimation and improves detection of rare high-intensity and extreme rainfall without markedly degrading lower-threshold accuracy. At 0.1-10 mm per hour, its root mean square error remains close to those of the best baselines, and it yields the highest equitable threat score (ETS) at most evaluated thresholds, with its advantage becoming more pronounced at high thresholds. At 30 mm per hour, its ETS is 0.051 versus 0.015 for the best baseline, and its mean error is -25.41 mm per hour versus -28.98 mm per hour. Case studies further show improved representations of rainfall intensity and spatial extent, demonstrating that Hurdle-RMIL effectively addresses rainfall-distribution imbalance and improves the retrieval of rare high-intensity rainfall.

Rainfall is an important environmental driver of water-quality variations through processes such as runoff, pollutant transport, dilution, and resuspension. Traditional mechanistic models can explicitly describe these processes but often require substantial process specification and site-specific calibration, limiting their flexibility under changing hydrological conditions. In this work, we explore a data-driven alternative by proposing RaiNet to jointly model multiscale water-quality dynamics and station-specific rainfall effects across relative lags and temporal scales. RaiNet employs LocTrend to capture irregular water-quality dynamics, constructs station-oriented rainfall events from gridded precipitation, and introduces XGateFusion for conditional lag-aware fusion across scales. We further release three real-world multimodal datasets comprising over 150,000 temporally aligned water quality observations and gridded precipitation raster images. Experiments show that RaiNet outperforms general time-series, water quality, diffusion-based, and spatiotemporal models by over 20%, while component-wise analyses confirm the distinct contribution of each module.