Summary Statistics of Large-scale Model Outputs for Observation-corrected Outputs

TL;DR

This paper introduces Sig-PCA, a neural network-based framework that integrates statistical summaries of physics-based model outputs with observational data to improve the accuracy of large-scale model predictions, especially in terms of distributions and correlations.

Contribution

The paper presents a novel space-time framework that combines reduced-order model summaries with observations for bias correction, enabling efficient and effective data integration.

Findings

Successfully corrects model outputs to match observational data

Preserves probability distributions and space-time correlations

Works on datasets with different statistical properties

Abstract

Physics-based models capture broad spatial and temporal dynamics, but often suffer from biases and numerical approximations, while observations capture localized variability but are sparse. Integrating these complementary data modalities is important to improving the accuracy and reliability of model outputs. Meanwhile, physics-based models typically generate large outputs that are challenging to manipulate. In this paper, we propose Sig-PCA, a space-time framework that integrates summary statistics from model outputs with localized observations via a neural network (NN). By leveraging reduced-order representations from physics-based models and integrating them with observational data, our approach corrects model outputs, while allowing to work with dimensionally-reduced quantities hence with smaller NNs. This framework highlights the synergy between observational data and statistical summaries of model outputs, and effectively combines multisource data by preserving essential statistical information. We demonstrate our approach on two datasets (surface temperature and surface wind) with different statistical properties and different ratios of model to observational data. Our method corrects model outputs to align closely with the observational data, specifically enabling to correct probability distributions and space-time correlation structures.