  Here we use a very simple conceptual model in an attempt to reduce essential
parts of the complex nonlinearity of abrupt glacial climate changes (the
so-called Dansgaard-Oeschger events) to a few simple principles, namely (i) a
threshold process, (ii) an overshooting in the stability of the system and
(iii) a millennial-scale relaxation. By comparison with a so-called Earth
system model of intermediate complexity (CLIMBER-2), in which the events
represent oscillations between two climate states corresponding to two
fundamentally different modes of deep-water formation in the North Atlantic, we
demonstrate that the conceptual model captures fundamental aspects of the
nonlinearity of the events in that model. We use the conceptual model in order
to reproduce and reanalyse nonlinear resonance mechanisms that were already
suggested in order to explain the characteristic time scale of
Dansgaard-Oeschger events. In doing so we identify a new form of stochastic
resonance (i.e. an overshooting stochastic resonance) and provide the first
explicitly reported manifestation of ghost resonance in a geosystem, i.e. of a
mechanism which could be relevant for other systems with thresholds and with
multiple states of operation. Our work enables us to explicitly simulate
realistic probability measures of Dansgaard-Oeschger events (e.g. waiting time
distributions, which are a prerequisite for statistical analyses on the
regularity of the events by means of Monte-Carlo simulations). We thus think
that our study is an important advance in order to develop more adequate
methods to test the statistical significance and the origin of the proposed
glacial 1470-year climate cycle.
