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Abstract:Spatial fields in the Earth and environmental sciences are often available at multiple scales or resolutions. While coarse-scale data (e.g., from global circulation models) are often abundant, they lack the local detail provided by fine-scale data (e.g., from regional climate models), which are typically computationally expensive to generate. Statistical downscaling and multi-scale data fusion address this challenge by predicting high-resolution fields from low-resolution or related inputs. We propose a highly scalable Bayesian approach that can learn the joint non-Gaussian distribution and nonlinear dependence structure of nonstationary spatial fields across multiple scales from a small number of training samples. Our method employs scale-aware autoregressive Gaussian processes with suitably chosen regularization-inducing priors to model the conditional distribution of fine-scale fields given coarse-scale data. Exploiting conjugacy, the integrated likelihood is available in closed form, enabling efficient parameter optimization via stochastic gradient descent. Once trained, the method provides a closed-form characterization of the posterior distribution of fine-scale fields given coarse-scale inputs. In numerical comparisons, we demonstrate that our approach substantially outperforms existing methods and effectively characterizes and simulates fine-scale climate behavior based on output from coarse global circulation models.

Submission history

From: Alejandro Calle-Saldarriaga [view email]
[v1] Fri, 26 Sep 2025 15:20:06 UTC (2,964 KB)
[v2] Tue, 31 Mar 2026 01:27:27 UTC (3,025 KB)
[v3] Tue, 16 Jun 2026 01:29:01 UTC (3,026 KB)