  The last glacial period was punctuated by a series of abrupt climate shifts,
the so-called Dansgaard-Oeschger (DO) events. The frequency of DO events varied
in time, supposedly because of changes in background climate conditions. Here,
the influence of external forcings on DO events is investigated with
statistical modelling. We assume two types of simple stochastic dynamical
systems models (double-well potential-type and oscillator-type), forced by the
northern hemisphere summer insolation change and/or the global ice volume
change. The model parameters are estimated by using the maximum likelihood
method with the NGRIP Ca$^{2+}$ record. The stochastic oscillator model with at
least the ice volume forcing reproduces well the sample autocorrelation
function of the record and the frequency changes of warming transitions in the
last glacial period across MISs 2, 3, and 4. The model performance is improved
with the additional insolation forcing. The BIC scores also suggest that the
ice volume forcing is relatively more important than the insolation forcing,
though the strength of evidence depends on the model assumption. Finally, we
simulate the average number of warming transitions in the past four glacial
periods, assuming the model can be extended beyond the last glacial, and
compare the result with an Iberian margin sea-surface temperature (SST) record
(Martrat et al., Science, vol. 317, p. 502, 2007). The simulation result
supports the previous observation that abrupt millennial-scale climate changes
in the penultimate glacial (MIS 6) are less frequent than in the last glacial
(MISs 2-4). On the other hand, it suggests that the number of abrupt
millennial-scale climate changes in older glacial periods (MISs 6, 8, and 10)
might be larger than inferred from the SST record.
