New measures of multimodality for the detection of a ghost stochastic resonance

Large-amplitude (10-15 K) millennial-duration warming events, the Dansgaard-Oeschger (DO) events, repeatedly occurred in the North Atlantic region during ice ages. So far, the trigger of these events is not known. To explain their recurrence pattern, a ghost stochastic resonance (GSR) scenario has been suggested, i.e., a dynamical scenario in which the events represent the subharmonic response to centennial-scale solar forcing plus noise. According to this hypothesis a multimodal phase distribution of the events is expected, which should be tested on the basis of climate records by means of time series analysis. A major obstacle in these tests, however, is the need of a statistical measure of regularity that can distinguish between a random occurrence of DO events and a GSR scenario. Here we construct and compare three new measures of phase multimodality. In a Monte Carlo simulation with a simple conceptual model of DO events we simulate probability distributions of the measures under both scenarios for realizations of only 11 DO events. Based on these distributions we find that our measures are able to distinguish between a random occurrence and a GSR scenario. We further apply our measures to analyze the recurrence pattern of the last 11 DO events in the North Greenland Ice Core Project deep ice core from Greenland.