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.

💡 Research Summary

The paper provides a comprehensive review of the three classical frameworks used to model palaeoclimate data—conceptual, simulator‑based, and statistical—and discusses recent advances that integrate these approaches. Conceptual models aim for parsimonious representations of specific climate phenomena, using a minimal set of variables and simple equations to capture the essential physics. While they are valuable for hypothesis generation and parameter sensitivity studies, their oversimplification limits their ability to reproduce the full complexity of the Earth system. Simulator‑based frameworks encompass General Circulation Models (GCMs) and Earth System Models of Intermediate Complexity (EMICs). GCMs resolve climate processes on fine spatial grids with detailed physical, chemical, and biogeochemical equations, offering high fidelity but at prohibitive computational cost. EMICs reduce dimensionality and employ parameterizations to retain key dynamics while enabling long‑term simulations. Both types allow direct comparison with proxy records but suffer from uncertainties in initial conditions, boundary forcing, and structural model errors. Statistical frameworks treat palaeoclimate reconstruction as an inference problem, combining observations with hypotheses about systematic and random effects. Bayesian hierarchical models, regression techniques, and state‑space formulations provide rigorous uncertainty quantification and are especially useful when data are sparse or noisy, yet they do not directly encode physical mechanisms.

Recent literature has focused on bridging these paradigms through two key concepts: emulators and discrepancy. An emulator is a computationally cheap surrogate that learns the input‑output relationship of an expensive simulator. Techniques such as Gaussian Process regression, polynomial chaos expansions, and deep neural networks are employed to build emulators that can predict model outputs for new parameter sets in seconds, enabling efficient Bayesian calibration and uncertainty propagation. The discrepancy term acknowledges that even a perfectly calibrated simulator cannot fully capture reality; it is modeled statistically (often as a spatial‑temporal Gaussian process) to represent systematic model bias. By explicitly estimating discrepancy, researchers can separate structural model error from parameter uncertainty, leading to more credible palaeoclimate reconstructions.

The authors illustrate these integrated approaches with examples from both time‑slice and dynamical applications. In a Last Glacial Maximum (LGM) study, an emulator of a GCM was used to explore a wide range of CO₂ concentrations, while a discrepancy model corrected the simulated sea‑surface temperatures against marine sediment proxies. In another case, an EMIC coupled with an emulator was employed to assess long‑term carbon cycle feedbacks, with discrepancy accounting for mismatches between simulated and observed carbon isotope records. These case studies demonstrate that the combined framework can efficiently explore high‑dimensional parameter spaces, quantify uncertainties, and improve the fidelity of palaeoclimate reconstructions.

The paper concludes by outlining future research directions: extending emulators to handle high‑dimensional, non‑linear input spaces; developing more flexible discrepancy models that capture non‑stationary and non‑Gaussian behavior; and integrating multi‑model ensembles to propagate structural uncertainty across different modelling paradigms. Such advancements are expected to strengthen the link between past climate evidence and projections of future climate change, providing a more robust basis for assessing anthropogenic impacts on the Earth system.