Nonstationary Spatial Modeling of Massive Global Satellite Data

TL;DR

This paper introduces a scalable nonstationary Gaussian process model using multi-resolution approximation for massive global satellite data, improving prediction accuracy over stationary models.

Contribution

It develops a novel multi-resolution approximation method tailored for nonstationary Gaussian processes on large-scale satellite data, incorporating land barriers and distributed computing.

Findings

Successfully analyzed over 43 million SST observations.

Nonstationary model outperforms stationary approaches in predictive accuracy.

Demonstrated scalability and efficiency in high-performance computing environments.

Abstract

Earth-observing satellite instruments obtain a massive number of observations every day. For example, tens of millions of sea surface temperature (SST) observations on a global scale are collected daily by the Moderate Resolution Imaging Spectroradiometer (MODIS) instrument. Despite their size, such datasets are incomplete and noisy, necessitating spatial statistical inference to obtain complete, high-resolution fields with quantified uncertainties. Such inference is challenging due to the high computational cost, the nonstationary behavior of environmental processes on a global scale, and land barriers affecting the dependence of SST. In this work, we develop a multi-resolution approximation (M-RA) of a Gaussian process (GP) whose nonstationary, global covariance function is obtained using local fits. The M-RA requires domain partitioning, which can be set up application-specifically. In the SST case, we partition the domain purposefully to account for and weaken dependence across land barriers. Our M-RA implementation is tailored to distributed-memory computation in high-performance-computing environments. We analyze a MODIS SST dataset consisting of more than 43 million observations, to our knowledge the largest dataset ever analyzed using a probabilistic GP model. We show that our nonstationary model based on local fits provides substantially improved predictive performance relative to a stationary approach.