Spatial models generated by nested stochastic partial differential equations, with an application to global ozone mapping

TL;DR

This paper introduces a new class of nested stochastic partial differential equation models that are computationally efficient, flexible for various manifolds, and capable of modeling nonstationary and oscillating covariance structures, demonstrated through global ozone mapping.

Contribution

The paper develops a novel nested SPDE framework that enhances modeling flexibility and computational efficiency for spatial fields on manifolds, including nonstationary and oscillating covariance structures.

Findings

Efficient parameter estimation via direct numerical optimization.

Successful application to global ozone data.

Model encompasses Gaussian Matérn and oscillating covariance fields.

Abstract

A new class of stochastic field models is constructed using nested stochastic partial differential equations (SPDEs). The model class is computationally efficient, applicable to data on general smooth manifolds, and includes both the Gaussian Mat\'{e}rn fields and a wide family of fields with oscillating covariance functions. Nonstationary covariance models are obtained by spatially varying the parameters in the SPDEs, and the model parameters are estimated using direct numerical optimization, which is more efficient than standard Markov Chain Monte Carlo procedures. The model class is used to estimate daily ozone maps using a large data set of spatially irregular global total column ozone data.