Intrinsic Non-stationary Covariance Function for Climate Modeling

TL;DR

This paper introduces a generalized intrinsic non-stationary covariance function for Gaussian process regression, improving modeling of complex, non-stationary global climate data such as sea level changes.

Contribution

It proposes a novel intrinsic non-stationary covariance function that adapts to local correlation structures using intrinsic statistics of positive definite matrices.

Findings

Enhanced regression accuracy on synthetic data

Improved error metrics on real sea level data

Better modeling of non-stationary geospatial processes

Abstract

Designing a covariance function that represents the underlying correlation is a crucial step in modeling complex natural systems, such as climate models. Geospatial datasets at a global scale usually suffer from non-stationarity and non-uniformly smooth spatial boundaries. A Gaussian process regression using a non-stationary covariance function has shown promise for this task, as this covariance function adapts to the variable correlation structure of the underlying distribution. In this paper, we generalize the non-stationary covariance function to address the aforementioned global scale geospatial issues. We define this generalized covariance function as an intrinsic non-stationary covariance function, because it uses intrinsic statistics of the symmetric positive definite matrices to represent the characteristic length scale and, thereby, models the local stochastic process. Experiments on a synthetic and real dataset of relative sea level changes across the world demonstrate improvements in the error metrics for the regression estimates using our newly proposed approach.