Extremal dependence as given by the tail pairwise dependence matrix inprecipitation and temperature data

A better understanding of the dynamics and impacts of extreme weather events and their changes due to climate change is the subject of the ClimXtreme project (climxtreme.net) funded by the German Federal Ministry of Education and Research. 
The CoDEx project is investigating how data compression techniques can contribute to a better description and understanding of extremes. Various unsupervised learning approaches, such as clustering or principal component analysis, focusing on extremes have been developed recently and will be investigated and compared within the project. 
We use principal component analysis to study the spatial (co-)occurrence during extreme weather events such as heavy precipitation, heat waves or droughts. The focus on extreme events is done by using the tail pairwise dependence matrix (TPDM), proposed by Cooley and Thibaud (2019) as an analogue to the covariance matrix for extremes. Since the simultaneous occurrence of precipitation deficits and high temperature played an important role, especially in heat waves, we explore how Cooley and Thibaud's concept can be used in this regard. We propose an estimation of the TPDM based on pairwise dependencies of two variables. A singular value decomposition gives us insight into the spatial co-occurrence of extreme spatial patterns, which contributes to the understanding of so-called compound events. 
We use daily precipitation and temperature data, including observational stations and regional reanalyses in Germany and Europe. Using this method, we extract spatial patterns over Germany and Europe based on extreme dependencies. In addition, we identify historical events, and examine them in more detail in this context.