Spherical Physics-informed Neural Operator with Multi-scale Coupling for Meteorological Downscaling

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.

We introduce a probabilistic diffusion-based method for global atmospheric downscaling implemented within the Anemoi framework. The approach transforms low-resolution ensemble forecasts into high-resolution ensembles by learning the conditional distribution of finer-scale residuals, defined as the difference between the high-resolution fields and the interpolated low-resolution inputs. The system is trained on reforecast pairs from ECMWF IFS, using coarse fields at 100 km to reconstruct fine-scale variability at 30 km resolution. The bulk of the training focuses on recovering small-scale structures, while fine-tuning in high-noise regimes enables the generation of extremes. Evaluation against the medium-range IFS ensemble target shows that the model increases probabilistic skill (FCRPS) for surface variables, reproduces target power spectra at small scales, captures physically consistent multivariate relationships such as wind-pressure coupling, and generates extreme values consistent with those of the target ensemble in tropical cyclones.

While AI-based numerical weather prediction (NWP) enables rapid forecasting, generating high-resolution outputs remains computationally demanding due to limited multi-scale adaptability and inefficient data representations. We propose the 3D Gaussian splatting-based scale-aware vision transformer (GSSA-ViT), a novel framework for arbitrary-resolution forecasting and flexible downscaling of high-dimensional atmospheric fields. Specifically, latitude-longitude grid points are treated as centers of 3D Gaussians. A generative 3D Gaussian prediction scheme is introduced to estimate key parameters, including covariance, attributes, and opacity, for unseen samples, improving generalization and mitigating overfitting. In addition, a scale-aware attention module is designed to capture cross-scale dependencies, enabling the model to effectively integrate information across varying downscaling ratios and support continuous resolution adaptation. To our knowledge, this is the first NWP approach that combines generative 3D Gaussian modeling with scale-aware attention for unified multi-scale prediction. Experiments on ERA5 show that the proposed method accurately forecasts 87 atmospheric variables at arbitrary resolutions, while evaluations on ERA5 and CMIP6 demonstrate its superior performance in downscaling tasks. The proposed framework provides an efficient and scalable solution for high-resolution, multi-scale atmospheric prediction and downscaling. Code is available at: https://github.com/binbin2xs/weather-GS.