Statistical modeling of extreme value behavior in North American tree-ring density series

Many analyses of the paleoclimate record include conclusions about extremes, with a focus on the unprecedented nature of recent climate events. While the use of extreme value theory is becoming common in the analysis of the instrumental climate record, applications of this framework to the spatio-temporal analysis of paleoclimate records remain limited. This article develops a Bayesian hierarchical model to investigate spatially varying trends and dependencies in the parameters characterizing the distribution of extremes of a proxy data set, and applies it to the site-wise decadal maxima and minima of a gridded network of temperature sensitive tree ring density time series over northern North America. The statistical analysis reveals significant spatial associations in the temporal trends of the location parameters of the generalized extreme value distributions: maxima are increasing as a function of time, with stronger increases in the north and east of North America; minima are significantly increasing in the west, possibly decreasing in the east, and exhibit no changes in the center of the region. Results indicate that the distribution varies as a function of both space and time, with tree ring density maxima becoming more extreme as a function of time and minima having diverging temporal trends, by spatial location. Results of this proxy-only analysis are a first step towards directly reconstructing extremal climate behavior, as opposed to mean climate behavior, by linking extremes in the proxy record to extremes in the instrumental record.