Nonlinear behaviours that have been identified in the climate system include quadratic coupling in ENSO (e.g. Fischer 2017), and switching between multi-stable states on interdecadal timescales e.g. in Sahelian ranfall (Demaree and Nicolis 1990). The identification of nonlinear behaviours is important because whether a time series is linear or nonlinear governs how predictable it is. The identification of nonlinearities has been hampered by the relatively short instrumental record, and by the lack of an efficient nonlinearity test for time-irregular paleoclimate data. In order to test for nonlinear behaviours, it is necessary to generate a null distribution showing how likely is it that a particular nonlinear statistic could be generated by a finitely-sampled linear system? Fourier phase-randomisation methods can be used to produce null-hypothesis (or surrogate) time series that contain the same linear properties (e.g. variance, autocorrelation, fourier spectrum) as the observed time series, but phase-randomisation methods have so far proven difficult to apply to time series with time-irregular data. A new method, the CLLS method uses the harmonic regression of complex-valued variates to generate phase-randomised surrogates for irregularly-spaced time series. In this presentation, I apply the CLLS method to 20 high-resolution speleothem records, mainly from the tropics and subtropics, spanning the last two millenia. I test for nonlinear behaviours over interannual-interdecadal timescales, and examine the spatial distribution of various nonlinear statistics including bimodality, autoskewness and autocorrentropy. Nonlinear behaviours can be found in speleothems on climatic margins.

Fischer, M. (2016) Predictable components in global speleothem δ¹⁸O. Quat. Sci. Rev., 131, 380-392.
Fischer, M. (2017) Investigating nonlinear dependence between climate fields. J. Climate, 30, 5547-5562.