Early warning skill, extrapolation and tipping for accelerating cascades

We investigate how nonlinear behaviour (both of forcing in time and of the system itself) can affect the skill of early warning signals (EWS) to predict tipping in (directionally) coupled bistable systems when using measures based on critical slowing down (CSD) due to the breakdown of extrapolation. We quantify the skill of early warnings with a time horizon using a receiver-operator methodology for ensembles where noise realizations and parameters are varied to explore the role of extrapolation and how it can break down. We highlight cases where this can occur in an accelerating cascade of tipping elements, where very slow forcing of a slowly evolving 'upstream' system forces a more rapidly evolving 'downstream' system. If the upstream system crosses a tipping point, this can shorten the time scale of valid extrapolation. In particular, 'downstream-within-upstream' tipping will typically have warnings only on a time scale comparable to the duration of the upstream tipping process, rather than the time scale of the original forcing.