Spatial early warning signals for tipping points using dynamic mode decomposition

Abstract

Tipping points are abrupt transitions in time-varying systems which may be driven by noise, changes in the underlying system, or some combination of the two. Early warning signals of tipping points are potentially valuable leading indicators of these transitions. In low-dimensional systems, it is possible to characterize these indicators based on the expected type of the tipping point. In spatial systems, indicators which take account of changes in the spatial structure are in principle able to capture more information, compared with aggregate measures, and thus provide stronger leading indicators. Here we propose the use of dynamic mode decomposition (DMD), a dimensionality reduction technique first developed in a fluid dynamics context, as a method for extracting useful information about critical slowing down in the leading mode of a spatial system approaching a tipping point. To demonstrate its potential utility for this purpose we employ two models: one drawn from the physiology literature for the study of spatially-patterned ventilation distributions in asthma, and the other an ecological model previously used for the study of spatial early warning signals of tipping points. Together these show that the DMD leading eigenvalue may be a useful spatially-informed early warning signal.