Seeking more robust early warning signals for climate tipping points: the ratio of spectra method (ROSA)

Potential tipping points in the Earth System present challenges for society and ecosystems, especially as the global warming thresholds at which these may be triggered remain uncertain. Fortunately, a theory of 'critical slowing down' has been developed which could warn of approaching tipping points. Applications of this theory often implicitly assume stationary white-noise forcing, itself requiring a clean separation between forced trends and variability, which is especially difficult under contemporary climate change. This paper proposes a modified method to derive early warning signal in a system, such as the climate, which is forced by time correlated processes. The method looks at the ratio of spectra (ROSA) of a system state variable relative to a forcing variable. We demonstrate the ROSA method on an idealised forced dynamical system, before applying it to a particular challenging example from the Earth System: dieback of the Amazon rainforest. We show that ROSA identifies more examples of abrupt transitions in the Amazon than conventional early warning signals in state-of-the-art CMIP6 Earth System Models.