Early warning skill, extrapolation and tipping for accelerating cascades

Abstract: We investigate how nonlinear behaviour (both of forcing in time and of the system itself) can affect the skill of early warning signals to predict tipping in (directionally) coupled bistable systems when using measures based on critical slowing down 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 realisations 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 evolvingdownstream'' system. If the upstream system crosses a tipping point, this can shorten the timescale of valid extrapolation. In particular, ``downstream-within-upstream'' tipping will typically have warnings only on a timescale comparable to the duration of the upstream tipping process, rather than the timescale of the original forcing.