Climate Sensitivity Derived from First-Principles Temperature Feedback Circuits

Abstract

A long-standing challenge in climate science since the Charney Report in 1979 is to determine how much the Earth's climate warms in response to a unit external energy input at the top of the atmosphere (TOA). In this study, we show from first principles that temperature feedback within an atmosphere-surface column operates as a set of feedback circuits, each governed by an intrinsic gain less than unity, leading to geometric amplification of energy through successive feedback cycles. In particular, the surface-centered temperature feedback circuit determines the amplification of surface energy per unit TOA forcing. The surface energy amplification by non-temperature feedback is estimated from the amplification of solar energy absorption by downward longwave radiation at the surface in the climate mean state. Climate sensitivity then emerges as the product of these two amplifications scaled by the surface Planck feedback parameter. The climate sensitivity derived from the 1980-2000 climate mean state is 1.15 K (W m$^{-2}$)$^{-1}$. It yields a warming of 0.44 K from 1980-2000 to 2000-2020, consistent with the observed warming of 0.41 K, and equilibrium warmings of 3.02 and 5.83 K for CO$_2$ doubling and quadrupling, respectively, the former consistent with the Charney estimate near 3 degrees C. The framework provides a basis for predicting global surface temperature responses to other external forcing scenarios from the climate mean state.