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 damage to society in terms of human lives and financial losses.  As climate changes, it is important to understand how the spatial distribution of extreme weather events may change as a result. 

Most spatial statistical models measure spatial dependence between variables at different spatial locations directly, typically by their distance separation or via a Markov process. This study differs from previous research by examining the spatial aspect of essential field quantities, conditioned on the occurrence of extreme events somewhere in the field. Although some spatial fields may not encounter any extreme events over time, applying the Positive Extreme Field (PEF) concept (Kholodovsky and Liang (2021)) suggests that one or more extreme regions will exist. We refer to this modeling technique as the Propinquity (PQ) modeling framework.

Two different statistical approaches are utilized to model extreme events. First, the traditional univariate generalized Pareto (GP) model is applied to individual grid cells with quantile-based thresholds.  Second, rather than considering extreme values at individual locations and their temporal dependence, we consider an overall spatial field conditioned on being extreme by utilizing the Heffernan and Tawn model (2004) with PEFs from the STTC algorithm.

We apply these models to an observed precipitation dataset over CONUS and compare resulting trends in probabilities and return levels. The findings highlight the risks of aggregating univariate model results in space and emphasize the need to account for the connectivity between individual grid cells when calculating historical trends.

This work introduces a novel statistical methodology that enhances our understanding of added value —specifically, by conditioning on PEFs and accounting for the connectivity between individual grid cells—through the multivariate PQ modeling framework, which enables analysis of spatio-temporal dependence for extreme fields that traditional univariate approaches do not capture.