When quadrupling the atmospheric CO$_{2}$ concentration in relation to pre-industrial levels, most global climate models show an initially strong net radiative feedback that significantly reduces the energy imbalance during the first two decades after the quadrupling. Afterwards, the net radiative feedback weakens, needing more surface warming than before to reduce the remaining energy imbalance. Such weakening radiative feedback has its origin in the tropical oceanic stratiform cloud cover, linked to an evolving spatial warming pattern. In the classical linearized energy balance framework, such variation is represented by an additional term in the planetary budget equation. This additional term is usually interpreted as an ad-hoc emulation of the cloud feedback change, leaving unexplained the relationship between this term and the spatial warming pattern. I use a simple non-linearized energy balance framework to justify that there is a physical interpretation of this term: the evolution of the spatial pattern of warming is explained by changes in the ocean’s circulation and energy uptake. Therefore, the global effective thermal capacity of the system also changes, leading to the additional term. In reality, the clouds respond to what occurs in the ocean, changing their radiative effect. In the equation, the term is now a concrete representation of the ocean’s role. Additionally, I derive for the first time an explicit mathematical expression of the net radiative feedback and its temporal evolution in the linearized energy balance framework. This mathematical expression supports the new proposed interpretation. As a corollary, it justifies the twenty-year time scale used to study the variation of the net radiative feedback.

The tropical temperature in the free troposphere deviates from a theoretical moist-adiabat. The overall deviations are attributed to entrainment of dry surrounding air. The deviations gradually approach zero in the upper troposphere, which we explain with a buoyancy-sorting mechanism: the height to which individual convective parcels rise depends on parcel buoyancy, which is closely tied to the impact of entrainment during ascent. In higher altitudes, the temperature is increasingly controlled by the convective parcels that are warmer and more buoyant, because of weaker entrainment effects. We represent such temperature deviations from moist-adiabats in a clear-sky one-dimensional radiative-convective equilibrium model. Compared with a moist-adiabatic adjustment, having the entrainment-induced temperature deviations leads to higher climate sensitivity. As the impact of entrainment depends on the saturation deficit which increases with warming, our model predicts even more amplified surface warming from entrainment in a warmer climate.

An atmospheric composition feedback mechanism modulates the global equilibrium climate sensitivity (ECS) through changes in the tropical upper-tropospheric and lower-stratospheric (UTLS) water vapor. The feedback mechanism is caused by the acceleration of the Brewer-Dobson circulation. This process changes the ozone (O$_{3}$) concentration, resulting in a drier and cooler UTLS region than without O$_{3}$ changes. Thus, the planetary long-wave emissivity increases, and the ECS decreases. However, the BDC alone already provides dynamical cooling through the tropical stratospheric upwelling, potentially impacting the ECS. Here, we analyze the implications of this effect from a tropical clear-sky perspective, applying a one-dimensional radiative-convective equilibrium (RCE) model that explicitly accounts for the adiabatic cooling by the BDC and includes an interactive representation of O$_{3}$. We study how increasing upwelling modifies the change of the tropical energy budget resulting from a doubling of CO$_{2}$. An increase in upwelling reduces the tropical ECS mainly through an increased tropical energy export related to the adiabatic cooling. The atmospheric composition feedback through O$_{3}$ contributes less than 30\% to the tropical ECS reduction. Due to the dominance of the energy export, any impact on the global ECS will depend on the redistribution of the energy in the extratropics. We show that GCMs simulate similar changes of the tropical energy export under increased upwelling which corroborates that the findings obtained with the RCE approach bear relevance for the global climate.