Abstract

We review the fundamental basis of palaeoclimate theory : astronomical control on insolation, climate models as (stochastic) dynamical systems and statistical frameworks for model selection and model calibration, accounting for the specificities of the palaeoclimate problem : sparse data, dating uncertainties and phenomenological character.

In the spirit of the workshop, we emphasise the stochastic aspects of the theory. Stochastic methods intervene in model design, in order to parameterise climatic events at shorter time scales than the dynamics deterministically represented in the model. As stochastic parameterisations are introduced, the notions of synchronisation and climatic attractor have to be revisited, but modern mathematics provide the tools to this end (pullback and random attractors). In a specific example, we show how the synchronisation patterns on astronomical forcing evolve as the complexity of the astronomical forcing is gradually taken into account, and then when stochastic parameterisations are introduced.

Stochastic methods naturally occur in statistical problems of model calibration and selection, via Monte-Carlo Sampling methods. We give an overview of what has been attempted so far, including particle filter for state and parameter estimation methods, although we still are in uncharted territory.

Finally, we conclude on more philosophical attempts at understanding the meaning of stochastic parameterisations (‘sub-grid parameterisations’ or ‘model error’).