  Understanding and predicting environmental phenomena often requires the
construction of spatio-temporal statistical models, which are typically
Gaussian processes. A common assumption made on Gaussian processes is that of
covariance stationarity, which is unrealistic in many geophysical applications.
In this article, we introduce a deep-learning-inspired approach to construct
descriptive nonstationary spatio-temporal models by modeling stationary
processes on warped spatio-temporal domains. The warping functions we use are
constructed using several simple injective warping units which, when combined
through composition, can induce complex warpings. A stationary spatio-temporal
covariance function on the warped domain induces covariance nonstationarity on
the original domain. Sparse linear algebraic methods are used to reduce the
computational complexity when fitting the model in a big data setting. We show
that our proposed nonstationary spatio-temporal model can capture covariance
nonstationarity in both space and time, and provide better probabilistic
predictions than conventional stationary models in both simulation studies and
on a real-world data set.
