Operator-Aware Posterior Sampling for Multivariate Weather Downscaling

Meteorological downscaling is crucial for high-resolution regional climate forecasting and disaster early warning. While neural operators have emerged as a promising paradigm for modeling complex spatiotemporal mappings, existing frameworks often struggle with spherical manifold geometric distortions, inherent atmospheric multi-scale coupling mismatches, and lack of explicit atmospheric laws. We propose the Spherical Physics-informed Neural Operator, which utilizes a Spherical Laplacian Decomposition to partition atmospheric fields into hierarchical frequency components, maintaining exact point-wise correspondence across scales. To evaluate these representations at arbitrary locations, we introduce a localized spherical integral operator that approximates continuous kernel transforms via geometry-aware attention. Dynamical consistency is further enforced by embedding differentiable constraints into the learning process. Extensive experiments demonstrate that our framework attains superior accuracy and zero-shot generalization across various meteorological variables and unseen queries, representing a robust and interpretable solution for global-to-regional meteorological downscaling.

Probabilistic downscaling models the conditional distribution of high-resolution fields given coarse inputs and is a core challenge in atmospheric science, climate modeling, and other multiscale physical systems. A widely used paradigm decomposes the problem into a deterministic mean predictor followed by a stochastic residual generator. While effective in idealized settings, this mean-residual approach frequently produces biased and underdispersive ensembles in real-world applications. We identify a fundamental source of this failure: residual target misspecification, where the residual distribution induced during training systematically differs from the correction distribution required at test time, a mismatch amplified by downscaling bias. We theoretically connect this misspecification to underdispersion through the spread-skill ratio and show that conditional residual distribution matching controls both residual-energy and conditional-mean mismatch. Motivated by this analysis, we introduce ReMatch (Residual Distribution Matching), which aligns training residual targets toward a held-out calibration regime via optimal transport. On a controlled synthetic benchmark with varying bias levels and a real-world HRRR-ERA5 wind-field downscaling task, ReMatch substantially reduces underdispersion, improves calibration, and outperforms strong mean-residual and super-resolution baselines. Our code is available at https://github.com/sdean-group/ReMatch.git.

Accurate high-resolution wind field simulations are critical for resolving fine-scale atmospheric dynamics, yet the simulation of wind fields in Earth System Models (ESMs) remains limited by coarse spatial resolution and systematic biases. To address this, data-driven down scaling techniques have been widely used to enhance coarse-resolution ESM outputs. However, existing methods are typically tied to fixed discretizations, limiting generalization across models with different native resolutions. Here we formulate global near-surface wind downscaling as an operator-learning problem on continuous atmospheric state fields and develop a downscaling neural operator that maps coarse-scale fields to fine-scale counterparts across heterogeneous discretizations. The operator learning-based neural downscaling framework outperforms dominant baselines, recovers fine-scale physical structures, and generalizes to previously unseen ESMs and future climate scenarios without retraining, while preserving long-term wind projection trends. These findings establish a generalizable paradigm for high-resolution climate downscaling across diverse simulation outputs and future scenarios.