A note on quaternary climate modelling using Boolean delay equations

The Boolean delay equation model of Ghil et al. for the study of Quaternary ice ages has been re-examined and also extended to include a hydrological feedback mechanism that directly influences the thermohaline circulation. For the basic Ghil et al. model (with the original and with corrected time delays), we show that the maximum duration for a high ice volume state depends continuously but not monotonically on the time delays of the problem. In particular, both short spiky glacials and longer glacials can be obtained from identical parameter values by simply choosing different initial conditions. In the extended model, we find that an additional temperature-hydrology-ocean feedback mechanism tends to generate longer glacials, but in neither case do the average time scales of model variability compare favourably with those of the major Quarternary glacials.