Nonstationary covariance models for global data

TL;DR

This paper introduces a flexible parametric covariance model tailored for global geophysical data, effectively capturing nonstationarity and latitude-dependent dependencies, with efficient likelihood computation using Fourier transforms.

Contribution

The paper presents a novel covariance model that accounts for nonstationarity in global data and utilizes Fourier transforms for scalable likelihood evaluation.

Findings

Successfully applied to global ozone data

Outperforms some existing covariance models

Efficient likelihood computation for large datasets

Abstract

With the widespread availability of satellite-based instruments, many geophysical processes are measured on a global scale and they often show strong nonstationarity in the covariance structure. In this paper we present a flexible class of parametric covariance models that can capture the nonstationarity in global data, especially strong dependency of covariance structure on latitudes. We apply the Discrete Fourier Transform to data on regular grids, which enables us to calculate the exact likelihood for large data sets. Our covariance model is applied to global total column ozone level data on a given day. We discuss how our covariance model compares with some existing models.