  Basin stability (BS) is a measure of nonlinear stability in multi-stable
dynamical systems. BS has previously been estimated using Monte-Carlo
simulations, which requires the explicit knowledge of a dynamical model. We
discuss the requirements for estimating BS from time series data in the
presence of strong perturbations, and illustrate our approach for two simple
models of climate tipping elements: the Amazon rain forest and the thermohaline
ocean circulation. We discuss the applicability of our method to observational
data as constrained by the relevant time scales of total observation time,
typical return time of perturbations and internal convergence time scale of the
system of interest and other factors.
