Stochastic Models for Glacial Cycles

Abstract

Despite recent achievements in understanding past climatic changes (Adern 1991b; Boulton et al. 1995; Huybrechts and Tsiobell 1995; Marsiat 1995; Berger and Loutre 1996, 1997; Muller and MacDonald 1997, etc.), there are still many difficulties in studying these extremely important natural processes. The causes of this situation are as follows: 1. Data on climatic changes in the past are imperfect and contradictory. We know that even data on climatic changes during the past 10–20 years cannot answer the crucial question of contemporary climatology: is the climate system warming or not? It is clear that paleoreconstructed data are much less accurate and give place to too many uncertainties. 2. Generally speaking, there is no established, unanimously adopted theoretical approach to the problem of paleoclimatic changes. Seemingly, there are hundreds of hypotheses trying to explain glacial cycles (for instance, see Verbitsky 1986). These hypotheses include different mechanisms of feedbacks within and/or between the components of the climate system, also external processes: astronomical, geophysical, processes in the mantle and the core of the earth, etc. As in the case of observational data, existing theories and proposed mechanisms do not cover (convincingly explain and attribute) even recent climatic changes. 3. Finally, many problems arise with respect to choice, identification, and assessment of parameters of mathematical models used for the description of glaciation-deglaciation processes. As in studies of contemporary climate, general circulation models of the atmosphere linked to the models of glaciers and oceans are the most popular in paleoclimatic studies. However, their shortcomings become serious obstacles for the studies of climatic variability at paleo-time scales. Artificial synchronization of oceanic and atmospheric model time and the problem of model drift make the direct using of GCMs in paleostudies questionable. Yet, GCMs cannot be integrated for hundreds of ka in hundreds of variants (usually needed for experiments with a model). Perhaps the most difficult problem for GCMs and detailed models of ice sheets and oceans (connected to these problems) is the difficulty in estimating the numerous parameters needed for these models. Accumulation of errors because of inadequate estimates of parameters can easily compromise large models and give results worse than those obtained on simpler but better-structured models. Convincing criticism of GCMs with respect to paleoclimate simulations was made recently in many papers: “GCMs seem to be unable to yield a reliable quantitative computation of the net snow accumulation” (Oglesby 1990); “coupling with oceanic GCMs and other complex climatic sub-system models (sea-ice, biosphere) is unrealizable for long simulations” (Marsiat 1995), etc.