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The notion of climate sensitivity has become synonymous with equilibrium climate sensitivity (ECS), or the equilibrium response of the Earth system to a doubling of CO₂. But there is a hierarchy of measures of climate sensitivity, which can be arranged in order of increasing complexity and societal relevance and which mirror the historical development of climate modeling. Elements of this hierarchy include the well-known ECS and transient climate response and the lesser-known transient climate response to cumulative emissions and zero emissions commitment. This article describes this hierarchy of climate sensitivities and associated modeling approaches. Key concepts reviewed along the way include climate forcing and feedback, ocean heat uptake, and the airborne fraction of cumulative emissions. We employ simplified theoretical models throughout to encapsulate well-understood aspects of these quantities and to highlight gaps in our understanding and areas for future progress.▪There is a hierarchy of measures of climate sensitivity, which exhibit a range of complexity and societal relevance.▪Equilibrium climate sensitivity is only one of these measures, and our understanding of it may have reached a plateau.▪The more complex measures introduce new quantities, such as ocean heat uptake coefficient and airborne fraction, which deserve increased attention. 

Abstract A simple analytical model, the zero‐buoyancy plume (ZBP) model, has been proposed to understand how small‐scale processes such as plume‐environment mixing and evaporation affect the steady‐state structure of the atmosphere. In this study, we refine the ZBP model to achieve self‐consistent analytical solutions for convective mass flux, addressing the inconsistencies in previous solutions. Our refined ZBP model reveals that increasing plume‐environment mixing can increase upper‐troposphere mass flux through two pathways: increased cloud evaporation or reduced atmospheric stability. To validate these findings, we conducted small‐domain convection‐permitting Radiative‐Convective Equilibrium simulations with horizontal resolutions ranging from 4 km to 125 m. As a proxy for plume‐environment mixing strength, the diagnosed entrainment rate increases with finer resolution. Consistent with a previous study, we observed that both anvil cloud fraction and upper‐troposphere mass flux increase with higher resolution. Analysis of the clear‐sky energy balance in the simulations with two different microphysics schemes identified both pathways proposed by the ZBP model. The dominant pathway depends on the relative strengths of evaporation cooling and radiative cooling in the environment. Our work provides a refined simple framework for understanding the interaction between small‐scale convective processes and large‐scale atmospheric structure. 

Abstract The cooling-to-space (CTS) approximation says that the radiative cooling of an atmospheric layer is dominated by that layer’s emission to space, while radiative exchange with layers above and below largely cancel. Though the CTS approximation has been demonstrated empirically and is thus fairly well accepted, a theoretical justification is lacking. Furthermore, the intuition behind the CTS approximation cannot be universally valid, as the CTS approximation fails in the case of pure radiative equilibrium. Motivated by this, we investigate the CTS approximation in detail. We frame the CTS approximation in terms of a novel decomposition of radiative flux divergence, which better captures the cancellation of exchange terms. We also derive validity criteria for the CTS approximation, using simple analytical theory. We apply these criteria in the context of both gray gas pure radiative equilibrium (PRE) and radiative–convective equilibrium (RCE) to understand how the CTS approximation arises and why it fails in PRE. When applied to realistic gases in RCE, these criteria predict that the CTS approximation should hold well for H2O but less so for CO2, a conclusion we verify with line-by-line radiative transfer calculations. Along the way we also discuss the well-known “τ = 1 law,” and its dependence on the choice of vertical coordinate. 

Atmospheric radiative cooling is a fundamental aspect of Earth’s greenhouse effect, and is intrinsically connected to atmospheric motions. At the same time, basic aspects of longwave radiative cooling, such as its characteristic value of 2 K day-1, its sharp decline (or ‘‘kink’’) in the upper troposphere, and the large values of CO2 cooling in the stratosphere, are difficult to understand intuitively or estimate with pencil and paper. Here we pursue such understanding by building simple spectral (rather than gray) models for clear-sky radiative cooling. We construct these models by combining the cooling-to-space approximation with simplified greenhouse gas spectroscopy and analytical expressions for optical depth, and we validate these simple models with line-by-line calculations. We find that cooling rates can be expressed as a product of the Planck function, a vertical emissivity gradient, and a characteristic spectral width derived from our simplified spectroscopy. This expression allows for a pencil-and-paper estimate of the 2 K day-1 tropospheric cooling rate, as well as an explanation of enhanced CO2 cooling rates in the stratosphere. We also link the upper-tropospheric kink in radiative cooling to the distribution of H2O absorption coefficients, and from this derive an analytical expression for the kink temperature T_kink ~ 220 K. A further, ancillary result is that gray models fail to reproduce basic features of atmospheric radiative cooling. 

Abstract The linearity of global‐mean outgoing longwave radiation (OLR) with surface temperature is a basic assumption in climate dynamics. This linearity manifests in global climate models, which robustly produce a global‐mean longwave clear‐sky (LWCS) feedback of 1.9 W/m²/K, consistent with idealized single‐column models (Koll & Cronin, 2018,https//:doi.org/10.1073/pnas.1809868115). However, there is considerable spatial variability in the LWCS feedback, including negative values over tropical oceans (known as the “super‐greenhouse effect”) which are compensated for by larger values in the subtropics/extratropics. Therefore, it is unclear how the idealized single‐column results are relevant for the global‐mean LWCS feedback in comprehensive climate models. Here we show with a simple analytical theory and model output that the compensation of this spatial variability to produce a robust global‐mean feedback can be explained by two facts: (1) When conditioned upon free‐tropospheric column relative humidity (RH), the LWCS feedback is independent of RH, and (2) the global histogram of free‐tropospheric column RH is largely invariant under warming.