Modeling and emulation of nonstationary Gaussian fields

TL;DR

This paper develops a convolution-based approach to model and efficiently simulate non-stationary Gaussian fields, especially useful for large geophysical datasets, by combining local stationary covariance estimates into a global model.

Contribution

It introduces a method to fit local stationary Matérn covariance models and assemble them into a global LatticeKrig model for non-stationary Gaussian processes.

Findings

LatticeKrig can reproduce non-stationary Matérn covariance functions.

The approach efficiently simulates fields at 105 locations.

Application to climate model data demonstrates practical utility.

Abstract

Geophysical and other natural processes often exhibit non-stationary covariances and this feature is important to take into account for statistical models that attempt to emulate the physical process. A convolution-based model is used to represent non-stationary Gaussian processes that allows for variation in the correlation range and vari- ance of the process across space. Application of this model has two steps: windowed estimates of the covariance function under the as- sumption of local stationary and encoding the local estimates into a single spatial process model that allows for efficient simulation. Specifically we give evidence to show that non-stationary covariance functions based on the Mat`ern family can be reproduced by the Lat- ticeKrig model, a flexible, multi-resolution representation of Gaussian processes. We propose to fit locally stationary models based on the Mat`ern covariance and then assemble these estimates into a single, global LatticeKrig model. One advantage of the LatticeKrig model is that it is efficient for simulating non-stationary fields even at 105 locations. This work is motivated by the interest in emulating spatial fields derived from numerical model simulations such as Earth system models. We successfully apply these ideas to emulate fields that de- scribe the uncertainty in the pattern scaling of mean summer (JJA) surface temperature from a series of climate model experiments. This example is significant because it emulates tens of thousands of loca- tions, typical in geophysical model fields, and leverages embarrassing parallel computation to speed up the local covariance fitting