Abrupt climate change: chaos and order at orbital and millennial scales

Abstract

Successful prediction of future global climate is critically dependent on understanding its complex history, some of which is displayed in paleoclimate time series extracted from deep-sea sediment and ice cores. These recordings exhibit frequent episodes of abrupt climate change believed to be the result of nonlinear response of the climate system to internal or external forcing, yet, neither the physical mechanisms nor the nature of the nonlinearities involved are well understood. At the orbital (10 4–10 5 years) and millennial scales, abrupt climate change appears as sudden, rapid warming events, each followed by periods of slow cooling. The sequence often forms a distinctive saw-tooth shaped time series, epitomized by the deep-sea records of the last million years and the Dansgaard–Oeschger (D/O) oscillations of the last glacial. Here I introduce a simplified mathematical model consisting of a novel arrangement of coupled nonlinear differential equations that appears to capture some important physics of climate change at Milankovitch and millennial scales, closely reproducing the saw-tooth shape of the deep-sea sediment and ice core time series, the relatively abrupt mid-Pleistocene climate switch, and the intriguing D/O oscillations. Named LODE for its use of the logistic-delayed differential equation, the model combines simplicity in the formulation (two equations, small number of adjustable parameters) and sufficient complexity in the dynamics (infinite-dimensional nonlinear delay differential equation) to accurately simulate details of climate change other simplified models cannot. Close agreement with available data suggests that the D/O oscillations are frequency modulated by the third harmonic of the precession forcing, and by the precession itself, but the entrained response is intermittent, mixed with intervals of noise, which corresponds well with the idea that the climate operates at the edge between chaos and order. LODE also predicts a persistent ∼1.5 ky oscillation that results from the frequency modulated regional climate oscillation.