A First Principles Approach to the 100,000-year Problem

TL;DR

This paper demonstrates that a simple linear astronomical model can effectively reproduce 800,000 years of glacial cycles, challenging the necessity of complex non-linear feedback mechanisms in explaining the 100,000-year problem.

Contribution

The study introduces two linear models aligned with competing theories, showing that the astronomical model suffices to explain glacial cycles without complex non-linear dynamics.

Findings

The augmented Budyko model fails to reproduce the 100,000-year cycle.

Linearized ice volume models perform similarly to non-linear ones, indicating data does not require non-linearity.

The astronomical model explains the absence of the 400,000-year eccentricity cycle and suggests oceanic heat storage plays a key role.

Abstract

The 100,000-year problem concerns the dominant period of glacial-interglacial cycles over the past 800,000 years and their correlation with Earth's orbital eccentricity, despite eccentricity's weak influence on solar radiation. Two theories compete: the astronomical theory, in which orbital forcing drives the cycles with amplification from Earth system feedbacks, and the geochemical theory, in which internal dynamics dominate with orbital forcing synchronising oscillations. We investigate these theories using conceptual models. Augmentations to the Budyko energy balance model fail to reproduce the 100,000-year period, revealing formulation limitations. Linearised versions of existing non-linear ice volume models perform comparably to their full counterparts, indicating the data does not necessitate non-linear dynamics. We develop two simple linear models: a feedforward model aligned with the astronomical theory and a feedback model aligned with the geochemical theory. The feedforward model reproduces the ice volume record well and offers a novel explanation for the absence of eccentricity's 400,000-year period, arising from oceanic heat storage and tropospheric energy responding with differing phase lags. Conservative estimates show bulk ocean temperature variation can be explained by eccentricity alone, challenging the geochemical theory's core assumption. We also show that widespread use of Q65 may bias models towards geochemical explanations by underrepresenting eccentricity. The feedback model's improvement is concentrated around Marine Isotope Stage 11, suggesting this anomalous interglacial reflects Earth-based events rather than a general requirement for feedback mechanisms. We conclude that 800,000 years of glacial cycles can be largely reproduced by a linear astronomical model, emphasising the importance of parsimony when interpreting palaeoclimate data.