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Basin stability (BS) is a measure of nonlinear stability in multi-stabledynamical systems. BS has previously been estimated using Monte-Carlosimulations, which requires the explicit knowledge of a dynamical model. Wediscuss the requirements for estimating BS from time series data in thepresence of strong perturbations, and illustrate our approach for two simplemodels of climate tipping elements: the Amazon rain forest and the thermohalineocean circulation. We discuss the applicability of our method to observationaldata as constrained by the relevant time scales of total observation time,typical return time of perturbations and internal convergence time scale of thesystem of interest and other factors.

Estimating nonlinear stability from time series data