  In environmental science applications, extreme events frequently exhibit a
complex spatio-temporal structure, which is difficult to describe flexibly and
estimate in a computationally efficient way using state-of-art parametric
extreme-value models. In this paper, we propose a computationally-cheap
non-parametric approach to investigate the probability distribution of temporal
clusters of spatial extremes, and study within-cluster patterns with respect to
various characteristics. These include risk functionals describing the overall
event magnitude, spatial risk measures such as the size of the affected area,
and measures representing the location of the extreme event. Under the
framework of functional regular variation, we verify the existence of the
corresponding limit distributions as the considered events become increasingly
extreme. Furthermore, we develop non-parametric estimators for the limiting
expressions of interest and show their asymptotic normality under appropriate
mixing conditions. Uncertainty is assessed using a multiplier block bootstrap.
The finite-sample behavior of our estimators and the bootstrap scheme is
demonstrated in a spatio-temporal simulated example. Our methodology is then
applied to study the spatio-temporal dependence structure of high-dimensional
sea surface temperature data for the southern Red Sea. Our analysis reveals new
insights into the temporal persistence, and the complex hydrodynamic patterns
of extreme sea temperature events in this region.
