Predicting instabilities in transient landforms and interconnected ecosystems.

Many parts of the Earth system are thought to have multiple stable equilibrium states, with the potential for catastrophic shifts between them. Common methods to assess system stability require stationary (trend- and seasonality-free) data, necessitating error-prone data pre-processing. Here, we use Floquet Multipliers to quantify the stability of periodically-forced systems of known periodicity (e.g., annual seasonality) using diverse data without pre-processing. We demonstrate our approach using synthetic time series and spatio-temporal vegetation models, and further investigate two real-world systems: mountain glaciers and the Amazon rainforest. We find that glacier surge onset can be predicted from surface velocity data and that we can recover spatially explicit destabilization patterns in the Amazon. Our method is robust to changing noise levels, such as those caused by merging data from different sensors, and can be applied to quantify the stability of a wide range of spatio-temporal systems, including climate subsystems, ecosystems, and transient landforms.