Estimating the resilience of non-stationary systems

A wide body of work has applied the concept of critical slowing down to estimate the stability of different Earth system components. Most of them – such as global vegetation – are inherently non-stationary, for example due to strong seasonal forcing that complicates the estimation of their resilience to external perturbations. Here, we introduce a method to account for non-stationarity in estimating the resilience of diverse synthetic and real-world systems via a regression-based formulation of the Langevin equation. Our method does not require extensive data pre-processing, is robust to gaps in the data record, and does not require regular time sampling. We further show that our method can incorporate time-varying data uncertainties, derive uncertainty bounds for stability estimates, and can be natively extended to examine spatial systems. Our method is a drop-in replacement for widely-used autocorrelation-based resilience estimates, and can be applied across diverse Earth system components.