On Generalized Langevin Dynamics and the Modelling of Global Mean Temperature

TL;DR

This paper introduces a generalized Langevin framework for climate modeling, connecting statistical mechanics with energy balance models to better capture long-range memory effects in global temperature fluctuations.

Contribution

It maps the Generalized Langevin Equation from physics to climate models, extending traditional energy balance models to include long-range memory effects.

Findings

GLE and FLE models describe climate fluctuations with long memory

Connections made between statistical mechanics and climate modeling

Relates to Lovejoy's Fractional Energy Balance Model

Abstract

Climate science employs a hierarchy of models, trading the tractability of simplified energy balance models (EBMs) against the detail of Global Circulation Models. Since the pioneering work of Hasselmann, stochastic EBMs have allowed treatment of climate fluctuations and noise. However, it has recently been claimed that observations motivate heavy-tailed temporal response functions in global mean temperature to perturbations. Our complementary approach exploits the correspondence between Hasselmann's EBM and the original mean-reverting stochastic model in physics, Langevin's equation of 1908. We propose mapping a model well known in statistical mechanics, the Mori-Kubo Generalised Langevin Equation (GLE) to generalise the Hasselmann EBM. If present, long range memory then simplifies the GLE to a fractional Langevin equation (FLE). We describe the corresponding EBMs that map to the GLE and FLE, briefly discuss their solutions, and relate them to Lovejoy's new Fractional Energy Balance Model.