Learning Spatiotemporal Precipitation Fields with Probabilistic Neural Processes

Reliable high resolution precipitation fields are essential for hydrology flood risk management agriculture and climate impact assessment yet remain difficult to reconstruct from sparse and irregular rain gauge networks. Reanalysis products such as ERA5 provide physically consistent estimates but are constrained by coarse effective resolution temporal smoothing and weak local observational constraints. By formulating interpolation of spatiotemporal precipitation fields as a probabilistic context to target regression problem using neural process (NP) models, this study assesses whether NP-based approaches can outperform reanalysis and classical interpolation for local to regional rainfall reconstruction. Using high quality UK rain gauge observations combined with gridded auxiliary variables from ERA5 we implement convolutional NPs within the DeepSensor framework and compare them with a transformer based NP variant.

Models are jointly conditioned on dense meteorological fields and sparse precipitation observations and output full predictive distributions using a Bernoulli–Gamma likelihood to capture intermittency and extremes. Training is performed using random sensor masking to enforce location agnostic learning and enable zero shot prediction at unseen coordinates. Performance is evaluated against ERA5 and Kriging using identical data splits with emphasis on interpolation accuracy as well as calibration robustness to sensor sparsity. Generalisation is further assessed through few shot and zero shot transfer across regions with contrasting regimes including England, Scotland and selected GHCN domains in the US.

Using NPs, this work aims to recover sharper spatial structure with improved uncertainty calibration and higher frequency precipitation estimates relative to ERA5 under sparse observation scenarios and also evaluates their potential as robust uncertainty aware additions to physics-based models for high resolution environmental monitoring.