Spatio-temporal Dependency of Extremes: Some Results and a Study on Indian Summer Precipitation Data

Abstract:

Observations over spatial, temporal and spatiotemporal grids are expected to have
statistical dependencies, and modeling to account for such dependencies adds complexity,
but not necessarily value, in many cases of climate and other data analyses. Sometimes
however, there may not be any additional dependency beyond what can be accounted for
using covariates and fixed and random effects. Additionally, dependency patterns may not be
similar for different quantities of interest, for example, the dependency properties
while modeling for a mean may not be the same as those obtained while modeling an extreme 
quantile. Thus, there is a need to quantify the degree of dependency, and test for
different hypotheses including that of a lack of dependency, or structured patterns of dependency.
We study a classical Space-Time Index measure suggested for testing spatio-temporal associations and show that it has low
power in hypothesis tests and is generally unreliable. Newer, computation-driven statistical and machine learning methods for
quantifying and testing dependency patterns are presented, and some of their statistical
properties are studied in detail. We conduct a study of spatio-temporal dependency in Indian
summer precipitation data, and particularly the properties of extreme precipitation during
Indian monsoons. As expected, we find that the nature of extreme precipitations depend on some global and some local climate features. However, the spatio-temporal relationship between extreme precipitation events depends additionally on the threshold used to define an extreme event. This may be leveraged for a more precise modeling of extreme events, and for reducing uncertainty in predicting such events.