Energy Gain Kernel for Climate Feedbacks. Part III: Reconciliation of the Apparent “Negative” Nature of Lapse-Rate Feedback

Abstract In Part I of this three-part series, we derive the energy gain kernel (EGK) to represent energy amplification by temperature feedback. We here demonstrate that due to the amplification, the vertically integrated total energy perturbations from input energy at a single layer can be 2–15 times greater than the input energy. The lower the level where input energy is placed, the greater the total energy perturbations are. Temperature feedback alone amplifies the vertically integrated global mean anthropogenic radiative forcing nearly 14 times, compared to 5.2 times by nontemperature feedbacks. Such great amplification arises from the continuous back-and-forth relay of warming-induced thermal emissions from individual layers to absorption by other layers throughout the atmosphere–surface column until the system reaches a new equilibrium state. Outgoing longwave radiation reflects the vertically integrated net cooling rate and cannot capture the absorption/emission at individual layers. The lapse-rate feedback mainly reflects the level where input energy is placed, rather than the physical nature of air temperature feedback. Its sign changes from positive for input energy at lower levels to negative for input energy at upper levels. Because energy perturbations due to radiative processes tend to have vertically decreasing profiles, their lapse-rate feedback tends to be predominantly positive. When also considering nonradiative feedbacks, such as enhanced vertical convection, the net effect of nontemperature feedbacks tends to be weak or even negative at the surface but strongly positive in the upper atmosphere in the tropics. This explains why the lapse-rate feedback is predominantly negative in the tropics.