Energy Gain Kernel for Climate Feedbacks. Part I: Formulation and Physical Understanding

Abstract This paper introduces a climate feedback kernel, referred to as the “energy gain kernel” (EGK). EGK allows for separating the net longwave radiative energy perturbations given by a Planck feedback matrix explicitly into thermal energy emission perturbations of individual layers and thermal radiative energy flux convergence perturbations at individual layers resulting from the coupled atmosphere–surface temperature changes in response to the unit forcing in individual layers. The former is represented by the diagonal matrix of a Planck feedback matrix and the latter by EGK. Elements of EGK are all positive, representing amplified energy perturbations at a layer where forcing is imposed and energy gained at other layers, both of which are achieved through radiative thermal coupling within an atmosphere–surface column. Applying EGK to input energy perturbations, whether external or internal due to responses of nontemperature feedback processes to external energy perturbations, such as water vapor and albedo feedbacks, yields their total energy perturbations amplified through radiative thermal coupling within an atmosphere–surface column. As the strength of EGK depends exclusively on climate mean states, it offers a solution for effectively and objectively separating control climate state information from climate perturbations for climate feedback studies. Given that an EGK comprises critical climate mean state information on mean temperature, water vapor, clouds, and surface pressure, we envision that the diversity of EGK across different climate models could provide insight into the inquiry of why, under the same anthropogenic greenhouse gas increase scenario, different models yield varying degrees of global mean surface warming. Significance Statement The wide range of 2.5°–4.0°C in global warming projections by climate models hinders our ability to predict its impacts. The newly introduced energy gain kernel (EGK) provides critical information for climate mean infrared opacity, which is collectively determined by climate mean temperature, water vapor, clouds, and surface pressure fields. EGK is directly derived from physical principles without additional definition. EGK captures the temperature feedback’s amplification of energy perturbations initiated from both external forcing and internal nontemperature feedback processes. EGK allows for disentangling positive and negative aspects of temperature feedback, rectifying the common misconception in existing temperature kernels that portray temperature feedback as predominantly negative. The diversity of EGK across different climate models may help explain their varying global warming degrees.