From Drops to Grid: Noise-Aware Spatio-Temporal Neural Process for Rainfall Estimation
Authors: Rafael Pablos Sarabia, Joachim Nyborg, Morten Birk, Ira Assent
Abstract
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.
Accurate precipitation nowcasting is vital for disaster mitigation, but deep learning methods face a key trade-off: regression models produce over-smoothed, spectrally decaying predictions that blur convective details and violate turbulence power laws; diffusion models generate realistic yet unanchored hallucinations lacking physical grounding. We propose Spectral-Decoupled Iterative Refinement (SDIR), a deterministic framework that reformulates nowcasting as progressive frequency-decoupled refinement. SDIR first extracts a stable low-frequency synoptic skeleton, then iteratively refines high-frequency textures under physical constraints, eliminating both blurring and hallucinations. It features a dual-path design: the Synoptic Frequency-Guided Former (SFG-Former) with Scale-Adaptive Transformers for global structure, and the Fourier Residual Refiner (FR-Refiner) with Scale-Conditioned Fourier Neural Operators for fine residuals. A Physically Consistent Power Spectral Density (PCPSD) loss with dynamic masking enforces a turbulence-consistent spectral distribution. Experiments on three benchmarks show SDIR significantly outperforms SOTA methods in spatial accuracy while achieving spectral fidelity competitive with diffusion-based methods, enabling reliable high-resolution operational nowcasting. Code link: https://github.com/RuntimeWarning/SDIR.
Fine-scale rainfall reconstruction is critical for urban flood modeling, but real rainfall sensing systems observe the field through incompatible spatial supports: gauges measure points, microwave links measure paths, and radar/satellite products measure gridded areas. These differences in measurement support impose geometrically distinct constraints on the rainfall field, yet existing heterogeneous graph approaches reconcile such sources in feature space, giving each its own embedding while discarding the geometry of its support. We propose a geometry-aware multi-support heterogeneous graph neural network that represents each observation according to its support type (0D point, 1D line, or 2D grid) as a distinct node layer, and fuses them through cross-support message passing into a point-support prediction layer from which the field is reconstructed. An inductive masked-node formulation decouples prediction resolution from sensing resolution, allowing the same trained model to reconstruct the field at user-defined target locations or display grids. On Singapore data, the proposed method reduces RMSE by 23.2% over the classical interpolation baseline, inverse-distance weighting, and consistently outperforms other neural architectures such as convolutional fusion and support-agnostic heterogeneous graph baselines. A generalization study using data from Sydney, Australia lets us characterize when multi-support fusion helps: the available skill appears to depend on gauge spacing relative to the spatial correlation length of the field, so fusion delivers the largest gains where the field is under-sampled relative to its correlation length and little when it is already resolved. Code and models will be open-sourced upon paper acceptance.
Precipitation nowcasting is a vital spatio-temporal prediction task for meteorological applications but faces challenges due to the chaotic property of precipitation systems. Existing methods predominantly rely on single-source radar data to build either deterministic or probabilistic models for extrapolation. However, the single deterministic model suffers from blurring due to MSE convergence. The single probabilistic model, typically represented by diffusion models, can generate fine details but suffers from spurious artifacts that compromise accuracy and computational inefficiency. To address these challenges, this paper proposes a novel coarse-to-fine Vision Mamba Unet and residual Diffusion (VMU-Diff) based precipitation nowcasting framework. It realizes precipitation nowcasting through a two-stage process, i.e., a deterministic model-based coarse stage to predict global motion trends and a probabilistic model-based fine stage to generate fine prediction details. In the coarse prediction stage, rather than single-source radar data, both radar and multi-band satellite data are taken as input. A spatial-temporal attention block and several Vision mamba state-space blocks realize multi-source data fusion, and predict the future echo global dynamics. The fine-grained stage is realized by a spatio-temporal refine generator based on residual conditional diffusion models. It first obtains spatio-temporal residual features based on coarse prediction and ground truth, and further reconstructs the residual via conditional Mamba state-space module. Experiments on Jiangsu SWAN datasets demonstrate the improvements of our method over state-of-the-art methods, particularly in short-term forecasts.