Dynamic Mode Decomposition of Extreme Events

Abstract. Most data-driven methods, among them Dynamic Mode Decomposition (DMD), focus on analysing and reconstructing the average behavior of a system. However, the primary interest often lies in the anomalous behaviour, known as extreme events. This is especially the case in climate research, where extreme events have significant economic and societal costs. Therefore, we extend a DMD method to account for extreme events by adding a penalisation term. This extension allows us to not only better reconstruct the extreme events, but also extract the spatio-temporal structures related to those extreme events. DMD was originally developed by Schmid and Sesterhenn (Schmid and Sesterhenn, 2008) to enable the fluid dynamics community to identify spatio-temporal coherent structures (called modes) from high-dimensional data. In its essence DMD uses most relevant modes to filter the noise and reconstruct the original signal. We ask "Is the noise really noise"? Or can we attribute some of these dynamic modes, that result from the DMD, to extreme events? We applied this new method to the climate system, well known for its high-dimensionality. We examined two heatwaves that occurred in Europe (HW 2003 and HW 2010). In both cases we were able to improve the accuracy of the reconstruction. This novel variation of the DMD, can also be applied to other dynamical systems across many disciplines, in which extreme events are of interest.