Traditional and novel approaches to palaeoclimate modelling

Palaeoclimate archives contain information on climate variability, trends and mechanisms. Models are developed to explain observations and predict the response of the climate system to perturbations, in particular perturbations associated with the anthropogenic influence. Here, we review three classical frameworks of climate modelling: conceptual, simulator-based (including general circulation models and Earth system models of intermediate complexity), and statistical. The conceptual framework aims at a parsimonious representation of a given climate phenomenon; the simulator-based framework connects physical and biogeochemical principles with phenomena at different spatial and temporal scales; and statistical modelling is a framework for inference from observations, given hypotheses on systematic and random effects. Recently, solutions have been proposed in the literature to combine these frameworks, and new concepts have emerged: the emulator (a statistical, computing efficient surrogate for the simulator) and the discrepancy, which is a statistical representation of the difference between the simulator and the real phenomenon. These concepts are explained, with references to implementations for both time-slices and dynamical applications