Flexible nonstationary spatio-temporal modeling of high-frequency monitoring data

TL;DR

This paper introduces a flexible nonstationary spatio-temporal modeling framework for high-frequency monitoring data, enabling accurate representation of complex dynamic behaviors in physical datasets.

Contribution

It extends half-spectral covariance functions to nonstationary space-time data and develops efficient maximum likelihood estimation for high-frequency measurements.

Findings

Successfully models extreme nonstationarity in wind velocity data

Captures interactions across atmospheric boundary layers

Provides a tractable approach for complex spatio-temporal dynamics

Abstract

Many physical datasets are generated by collections of instruments that make measurements at regular time intervals. For such regular monitoring data, we extend the framework of half-spectral covariance functions to the case of nonstationarity in space and time and demonstrate that this method provides a natural and tractable way to incorporate complex behaviors into a covariance model. Further, we use this method with fully time-domain computations to obtain bona fide maximum likelihood estimators---as opposed to using Whittle-type likelihood approximations, for example---that can still be computed efficiently. We apply this method to very high-frequency Doppler LIDAR vertical wind velocity measurements, demonstrating that the model can expressively capture the extreme nonstationarity of dynamics above and below the atmospheric boundary layer and, more importantly, the interaction of the process dynamics across it.