Devicing early-warning signals using linear response: A Koopman operator approach

Tipping points in the climate system mark abrupt, irreversible dynamic transitions, posing difficulties for prediction and risks for mitigation. Developing reliable early-warning indicators is therefore essential. Linear response has long been used for predicting a system's change with respect to external perturbations. The stability of the predictions depend on how far the system from tipping and, hence, it provides a candidate measure to detect tipping events. Here, we propose using the Koopman operator spectrum to quantify linear response stability through the spectral gap, which shrinks near bifurcation. We apply this approach to Veros, an ocean general circulation model, and demonstrate that spectral-gap narrowing precedes critical transitions— providing the basis for Koopman-based response prediction in complex climate models.