Linear Response and Optimal Fingerprinting for Nonautonomous Systems

TL;DR

This paper links response theory and optimal fingerprinting to improve attribution of time-dependent system anomalies, with applications to climate change detection and numerical validation on energy balance models.

Contribution

It derives formulas for linear response in nonautonomous systems and extends optimal fingerprinting for complex, time-varying backgrounds.

Findings

Response theory accurately predicts CO2 impact on temperature.

Optimal fingerprinting attributes climate change to multiple forcings.

Numerical validation confirms theoretical predictions.

Abstract

We provide a link between response theory, pullback measures, and optimal fingerprinting method that paves the way for a) predicting the impact of acting forcings on time-dependent systems and b) attributing observed anomalies to acting forcings when the reference state is not time-independent. We derive formulas for linear response theory for time-dependent Markov chains and diffusion processes. We discuss existence, uniqueness, and differentiability of the equivariant measure under general (not necessarily slow or periodic) perturbations of the transition kernels. Our results allow for extending the theory of optimal fingerprinting for detection and attribution of climate change (or change in any complex system) when the background state is time-dependent amd when the optimal solution is sought for multiple time slices at the same time. We provide numerical support for the findings by applying our theory to a modified version of the Ghil-Sellers energy balance model. We verify the precision of response theory - even in a coarse-grained setting - in predicting the impact of increasing CO$_2$ concentration on the temperature field. Additionally, we show that the optimal fingerprinting method developed here is capable to attribute the climate change signal to multiple acting forcings across a vast time horizon.