Spatio-temporal Frameworks of Extreme Value Analysis: Applications to 
Understanding and Modeling the Current California Drought and Rainfall 
Extremes 

In this presentation, a spatio-temporal framework for modeling extreme 
values is presented. The framework has two hierarchical components – 
(i) the generalized extreme value (GEV) distributions are fitted to 
the block maxima (e.g., seasonal maximum rainfall) at each 
gauge/location, and (ii) a Copula is applied to pool at-site extremes 
together to capture the spatial correlation. Furthermore, the 
parameters of the GEV distributions are modeled as a function of time 
and additional climate covariates, such as ENSO and PDO etc. This 
hierarchy is implemented in a Bayesian realm to estimate posteriors of 
distribution parameters of extremes with quantifying the uncertainties 
more rigorously at the same time. The proposed framework is 
illustrated on modeling seasonal rainfall extremes over Arizona. The 
results skillfully capture the spatial and temporal features of the 
rainfall extremes, and it offers an attractive approach to forecast 
seasonal extremes across spatio-temporal scales with considerably 
reduced uncertainties.
In the second part, related to the above method, the Copula in 
particular is applied to understand the feature of the current 
California drought. The impact of the ongoing drought on California’s 
water and agriculture is well known. One of the scientific questions 
being hotly debated is - how has human-induced climate change affected 
CA drought risk? Here we apply multivariate Copula to drought metrics 
including duration, cumulative precipitation deficit and soil moisture 
depletion, from observations and climate model experiments to 
characterize the risk/return period of the current CA drought. We find 
that droughts characterized using bivariate indicators of 
precipitation and 10-cm soil moisture become more frequent because 
shallow soil moisture responds most sensitively to increased 
evaporation driven by warming. However, when using 1-m soil moisture 
droughts become less frequent because deep soil moisture responds most 
sensitively to increased precipitation. These interesting insights 
will be of immense help in managing water and agricultural resources.