Comparing a spatial propinquity extreme-value model with a simple univariate generalized Pareto approach for trends in extreme precipitation

Extreme weather and climate events such as heavy precipitation, drought, heat waves, and strong winds can cause extensive human lives and financial losses to society. As climate changes, it is essential to understand how trends in frequency and intensity of extreme precipitation may change as a result.

Most spatial statistical models measure spatial dependence between variables at different spatial locations directly, usually by their distance separation or via a Markov process. The current work is distinct from previous research because it examines the spatial aspect of essential field quantity (EFQ) conditioned on the occurrence of extreme events somewhere in the field. Although some spatial fields may not encounter any extreme events over time, applying positive or negative extreme field concepts (Kholodovsky and Liang (2021)) suggests that one or more extreme regions will exist. We refer to this modeling technique as the Propinquity (PQ) model.

Two approaches are employed to represent the spatial dependence of extreme fields. First, the traditional temporal generalized Pareto (GP) model is applied to individual grid cells with quantile-based thresholds. Second, rather than considering extreme values at individual sites and their temporal dependence, we consider an overall spatial field that is conditioned on being extreme by utilizing the PQ modeling framework represented by Heffernan and Tawn (2004) model.

We apply these models to an observed precipitation dataset over CONUS and compare resulting trends in probabilities and return levels. The results suggest that extreme caution must be taken if univariate model results are aggregated in space, and it is essential to consider the connectivity between individual grid cells for the trend calculation.

This work is the first step to utilize a novel approach in statistical model comparison to help deepen our understanding of added value (i.e., the connection between individual grid cells) that multivariate spatial models such as the PQ modeling framework represents for spatial dependence analysis of extremes fields that are not modeled in the traditional univariate case.