Mathematical modelling of climate has matured as a discipline to the point that it can be useful in palaeoclimatology. As an example a new two-dimensional energy balance model is described and applied to several problems of current interest. The model includes the seasonal cycle and the detailed land-sea geographical distribution. By examining the changes in the seasonal cycle when external perturbations are forced upon the climate system, it is possible to construct hypotheses about the origin of mid-latitude ice sheets and polar ice caps. In particular, the model predicts a rather sudden potential for glaciation over large areas when the earth’s orbital elements are only slightly altered. Similarly, the drift of continents or the change of atmospheric carbon dioxide over geological time can induce radical changes in continental ice cover. With the advance of computer technology and our improved understanding of the individual components of the climate system, it should be possible to test these ideas in far more realistic models in the near future:

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