A fluctuation-dissipation theorem perspective on radiative responses to temperature perturbations

Abstract: Radiative forcing drives warming in the Earth system, leading to changes in sea surface temperatures (SSTs) and associated radiative feedbacks. The link between changes in the top-of-the-atmosphere (TOA) net radiative flux and SST patterns, known as the "pattern effect", is typically diagnosed by studying the response of atmosphere-only models to SST perturbations. In this work, we diagnose the pattern effect through response theory, by performing idealized warming perturbation experiments from unperturbed data alone. First, by studying the response at short time scales, where the response is dominated by atmospheric variability, we recover results that agree with the literature. Second, by extending the framework to longer time scales, we capture coupled interactions between the slow ocean component and the atmosphere, yielding a novel "sensitivity map" quantifying the response of the net radiative flux to SST perturbations in the coupled system. Here, feedbacks are captured by a spatiotemporal response operator, rather than time-independent maps as in traditional studies. Both formulations skillfully reconstruct changes in externally forced simulations and provide practical strategies for climate studies. The key distinction lies in their perspectives on climate feedbacks. The first formulation, closely aligned with prediction tasks, follows the traditional view in which slow variables, such as SSTs, exert a one-way influence on fast variables. The second formulation broadens this perspective by incorporating spatiotemporal interactions across state variables. This alternative approach explores how localized SST perturbations can alter the coupled dynamics, leading to temperature changes in remote areas and further impacting the radiative fluxes at later times.