Relationship of tropospheric stability to climate sensitivity and Earth’s observed radiation budget

We first consider the SST evolution during the first 150 y following a quadrupling of CO₂ concentration in a set of 15 coupled climate models (Materials and Methods and Table S1). The changes over the course of the simulations are defined as the difference in responses between years 1–20 (hereafter “early period”) and years 21–150 (“late period”). As the planet warms, the pattern of SST response per unit global warming evolves toward enhanced warming in the tropical East Pacific, the Southern Ocean, the North Atlantic, and, to a lesser extent, the Northeast Pacific, while the tropical West Pacific, Northwest Pacific, tropical Atlantic, and much of the Indian Ocean experience reduced warming relative to the global average (Fig. 1A). The global-mean difference between patterns of SST change is very close to zero. (The global-mean difference between patterns of surface temperature change, including land areas, would be exactly zero by construction.) The overall spatial structure of the SST evolution is reasonably robust among models (hatching in Fig. 1A). The characteristics of the SST evolution are also similar to those found in previous studies using different sets of climate models (7, 9, 21). The delayed warming in the East Pacific and the Southern Ocean is broadly consistent with the effects of upwelling (22, 23), but additional coupled ocean–atmosphere processes likely contribute to the evolution of the SST pattern (22, 24).

We now provide evidence that the evolution of the SST warming pattern favors a decrease in tropospheric stability. As a stability metric, we use the estimated inversion strength [EIS (25)], a measure of the strength of the inversion at the top of the boundary layer based on the difference in potential temperature between the surface and 700 hPa. EIS accounts for the temperature dependence of the moist adiabat to quantify the effective stability of the lower troposphere and is traditionally defined over ocean regions only. In observations, EIS is strongly correlated with marine low cloud cover in subsidence regions (25), consistent with the notion that a stronger inversion is more effective at trapping moisture in the boundary layer.

How do we expect the SST pattern to affect tropospheric stability? At any point in space, the stability change depends on the relative change in surface and free-tropospheric temperature. In the tropics, free-tropospheric temperature is largely set by the evolution of SST in warm, convective regions, such as the West Pacific warm pool, where the lapse rate is pegged to a moist adiabat owing to moist convection (26, 27). This constraint implies that the warmest regions should always remain nearly neutrally stable. Away from warm convective regions, however, the stability response will roughly depend on the ratio of local SST change to SST change in the warm pool (15). If local SST increases more than in the warm pool, stability will decrease because the free-tropospheric temperature will increase less than predicted by a local moist adiabat; the opposite would be true if local SST increased less than in the warm pool. While strictly speaking, the constraint on free-tropospheric temperature applies to the tropics only, extratropical free-tropospheric temperature should be influenced by SST changes in warmer convective regions, so that a similar argument can be applied to qualitatively interpret extratropical stability changes. Although we argue that the SST pattern is the main control on the time evolution of tropospheric stability in our model simulations, additional processes can also affect stability as quantified by EIS—for example, land–sea temperature contrasts and CO₂ concentrations (28).

The differences in stability response between the early and late periods in Fig. 1B are consistent with the above reasoning. The EIS difference in the warm pool around the Maritime Continent is small. Because the warm pool is warming less than average, the EIS response becomes more negative in most other regions; the larger the relative warming, the larger the stability decrease. This yields a global-mean decrease in the response of tropospheric stability to warming. It is noteworthy that the global-mean EIS response becomes more negative as time passes in all models included in this analysis (Fig. S2A).

We will now show that the evolution of climate feedbacks is consistent with the changes in tropospheric stability over the course of the transient response to CO₂ forcing. Fig. 2 shows the changes in global-mean feedback parameter decomposed into the contributions of temperature, water vapor, surface albedo, and clouds (using radiative kernels; Materials and Methods). On average, the total feedback increases by 0.50 W⋅m⁻²⋅K⁻¹ ($-1.38$ to $-0.88$ W⋅m⁻²⋅K⁻¹), consistent with previous findings (9). Consequently, the estimated ECS increases by 0.57 K on average (2.83–3.40 K; Fig. S2B). The change in feedback is primarily due to the effect of clouds (0.21 W⋅m⁻²⋅K⁻¹), followed by the lapse-rate feedback (0.14 W⋅m⁻²⋅K⁻¹), with smaller contributions of changes in surface albedo (0.09 W⋅m⁻²⋅K⁻¹) and relative humidity (0.06 W⋅m⁻²⋅K⁻¹). The increase in cloud feedback is almost entirely due to a change in shortwave reflection (0.20 W⋅m⁻²⋅K⁻¹). Since the mean residual is near zero, it does not contribute to the change in total feedback parameter.

The results in Fig. 2 are thus consistent with the expected effect of a stability decrease following hypothesis 2: a decrease in low cloud amount (causing a more positive shortwave cloud feedback) and a less negative lapse-rate feedback, these two effects jointly accounting for most of the increase in feedback parameter and climate sensitivity. While changes in factors other than stability—particularly local SST, subsidence, and free-tropospheric humidity—may also affect the evolution of the cloud response to global warming (29, 30), previous evidence from climate model experiments suggests that the stability effect dominates the cloud response to evolving tropical SST patterns (15). In further support for this conclusion, the relationship between tropospheric stability and feedbacks broadly holds across models: A larger stability decrease is associated with a larger increase in feedback parameter (Fig. S3, Supporting Information). Stability changes account for less than half of the intermodel spread in net feedback changes, however ($r^2=0.40$; Fig. S3A), indicating that effects other than stability must also contribute to this spread (Supporting Information).

The joint effect of cloud and lapse-rate feedbacks accounts for ∼70% of the change in net feedback in our set of models, leaving part of the change unexplained. We calculate how much of the evolution in global feedback parameter can be ascribed to a change in spatial weighting of local feedbacks as the warming pattern evolves, following hypothesis 1 (Fig. S4). The results suggest that hypothesis 1 can explain only a minor part of the change in the global net feedback parameter, through pattern effects on surface albedo and relative humidity feedbacks (0.05 and 0.04 W⋅m⁻²⋅K⁻¹, respectively; Supporting Information). While the increase in surface albedo feedback is consistent with the evolution toward enhanced high-latitude warming (Supporting Information and ref. 7), the mechanisms of change in global relative humidity feedback (via either of the hypotheses or alternative mechanisms) remain unknown.

The linkage between climate feedbacks and tropospheric stability is particularly striking when considering the spatial distribution of the changes. Generally speaking, the feedbacks become more positive in regions where the EIS response decreases (compare Figs. 1B and 3) and vice versa. The largest increase in feedback parameter occurs in the tropical Central and East Pacific, where the EIS response becomes substantially more negative as the planet warms. Although the EIS change over the Southern Ocean is comparable or larger in magnitude, the local change in cloud feedback is generally small; this may be because processes unrelated to tropospheric stability dominate the cloud response to warming at high southern latitudes. Comparing Fig. 3 C and D confirms that the feedback decomposition accurately captures the actual evolution of changes in top-of-atmosphere (TOA) net radiation, so that the spatial feedback patterns are not artifacts of the methodology.

We show the existence of a relationship between SST pattern, tropospheric stability, and the radiative budget in climate models. Can a similar link be observed in the real world to confirm the realism of the modeled responses? Reliable satellite observations of the Earth’s radiative budget are too short to allow for meaningful trend calculations. However, the proposed relationship between long-term changes in stability and radiative balance may also hold in the context of interannual variations. Climate models show qualitatively similar interannual relationships between SST, EIS, and the radiative budget in the context of unforced variability to those found at decadal time scales under abrupt CO₂ quadrupling (compare Figs. 1 and 3 and Fig. S5). In the following, we will demonstrate from observations that real-world year-to-year fluctuations in tropospheric stability are associated with SST and radiative anomalies consistent with the evolution of these variables in climate models.

Fig. 4 shows the patterns of SST, EIS, cloud-radiative effect (CRE; defined as all-sky minus clear-sky net downward TOA radiation), and net downward TOA radiation, all regressed onto annual- and global-mean EIS anomalies, using 16 y of gridded observational and reanalysis data (note that global-mean EIS excludes regions poleward of 50°; Materials and Methods). Since the regression coefficients would represent changes consistent with a 1-K global-mean EIS increase, we multiply the coefficients by the multimodel mean change in the derivative of EIS with respect to global-mean surface temperature ($-0.16$ K⋅K⁻¹; Fig. 1B) to obtain observed anomalies comparable in sign and magnitude with the model ensemble. Note that the impact of any changes in global-mean surface temperature has been regressed out (Materials and Methods) to minimize the contribution of the Planck response to the global-mean radiative anomalies. The observed SST pattern associated with an EIS decrease features positive SST anomalies in the tropical and subtropical East Pacific (Fig. 4A). Although no substantial cooling is observed in the warm pool, the anomalous east–west SST gradient across the tropical Pacific is in broad qualitative agreement with the difference between patterns of SST change in climate models (Fig. 1A), causing a decrease in stability in the East Pacific (Fig. 4B).

Consistent with observed relationships between EIS and low cloud, the EIS decrease coincides with a region of positive CRE anomaly, which is reflected in the net TOA radiative change (Fig. 4 C and D). The net observed global radiative anomaly (0.62 W⋅m⁻²⋅K⁻¹) is larger than the multimodel-mean radiative response associated with a $-0.16$ K⋅K⁻¹ EIS change (0.50 W⋅m⁻²⋅K⁻¹); however, considering the differences in observed SST and EIS patterns relative to the forced climate change signal in models (compare Fig. 1 with Fig. 4 A and B), and given the relatively low signal-to-noise ratio in the short observational record of 16 y, the agreement between observations and models should be interpreted qualitatively, rather than quantitatively. In further support of our findings, similar relationships between tropical SST pattern and low cloud amount have been observed in the context of decadal trends over the 1983–2005 period (15).

CRE anomalies can be affected not only by changes in clouds, but also by noncloud anomalies in temperature, moisture, and surface albedo. By adjusting the CRE anomalies for noncloud factors (Materials and Methods), we confirm the contribution of clouds to the stability-induced interannual radiative anomalies in observations and models (Figs. S6A and S7A). Decomposing the stability-induced radiative changes into individual components using kernels, we find that lapse-rate changes also contribute to the positive radiative anomalies in the East Pacific and in the global mean (Figs. S6B and S7B), but note that the total kernel-derived radiative changes overestimate the actual observed radiative anomalies by ∼13% (Fig. S6 C and D). Differences between kernel-derived and observed anomalies could be associated with errors in reanalysis temperature and moisture data, inaccuracies in the radiative kernel method (31, 32), or errors in satellite radiances (33). Despite these limitations, our observational analysis does qualitatively support the notion that decreasing tropospheric stability promotes a decrease in radiative cooling to space through changes in clouds and tropospheric lapse rate, consistent with the evolution toward higher effective climate sensitivity in CO₂-forced climate model experiments.

The evolution of SST, EIS, and climate feedbacks is analyzed in Coupled Model Intercomparison Project Phase 5 (CMIP5) climate model output during the 150 y following abrupt quadrupling of atmospheric CO₂ concentrations starting from preindustrial conditions (the “abrupt4xCO2” experiment). We analyze monthly mean values of temperature, specific humidity, surface albedo, and upward and downward radiative fluxes at the TOA for both all- and clear-sky conditions. The 25 models with available data are listed in Table S1. To remove any potential model drift, anomalies are calculated by subtracting the preindustrial (piControl) integration from the corresponding parallel abrupt4xCO2 integration. Only the first ensemble member is used for each model.

The contributions of temperature, moisture, surface albedo, and clouds to changes in TOA radiation are diagnosed separately for each month of the abrupt4xCO2 integration by using radiative kernels (31, 32). Kernels are partial derivatives of the TOA radiative flux relative to temperature, water vapor mixing ratio, and surface albedo at each model grid point. Multiplying the kernels by the changes in each of these variables provides an estimate of their contributions to TOA flux changes. Water vapor changes are partitioned into changes consistent with constant relative humidity (included in the temperature feedbacks) and changes in relative humidity (35). The kernels are also used to adjust CRE anomalies for changes in noncloud effects to obtain an estimate of the radiative changes due to clouds only (31). In this study, we use kernels calculated with the Community Atmospheric Model version 5 (36).

The kernel-derived contributions to TOA flux anomalies are aggregated into annual-mean values for each model and converted to feedbacks by regressing the radiative flux time series onto global-mean surface air temperature (1, 37). Ordinary least-squares regressions are calculated separately for years 1–20 and 21–150 of the abrupt4xCO2 experiment (9). We verify the accuracy of the kernel-derived feedbacks by a clear-sky linearity test (32, 37), whereby we compare the kernel-based sum of clear-sky TOA feedbacks with the actual clear-sky feedback obtained by regressing clear-sky net TOA radiation onto global-mean surface temperature. In our results, we only include the 15 models for which the error in kernel-based clear-sky feedback is <15% of the actual value in both regression periods [bolded model names in Table S1 (37)]. [Since CRE anomalies are based on model output, testing the kernel decomposition with clear-sky feedbacks ensures that only kernel-derived quantities are used in the test (32).] The results of the feedback analysis remain qualitatively unchanged if we include models with clear-sky errors >15% in the calculations (Table S1) or if we use an alternative set of radiative kernels (31). The feedback residuals are computed as actual minus sum of kernel-derived feedbacks (where the actual feedback is the regression slope of net TOA radiation against global-mean temperature). ECS values (Fig. S2B) are calculated as the $x$-intercepts of the least-squares fits over years 1–20 and 21–150.

The impact of year-to-year variations in tropospheric stability on the radiative budget is assessed by regression analysis in observations and preindustrial model integrations (using 50 y of data for each model). As a simple measure of large-scale stability changes, we use global-mean EIS, but exclude grid points poleward of 50°; including those grid points tends to emphasize high-latitude changes at the sea ice margins in climate models, likely related to sea ice variability. Since global-mean surface temperature anomalies associated with EIS variability will not generally be zero, a component of the associated radiative changes will be due to a Planck response that is not a direct result of the stability-driven cloud and lapse-rate responses. Therefore, the fields are jointly regressed onto annual global-mean temperature and EIS anomalies to isolate the EIS effect, and we present results for the regression slopes associated with EIS only.

We use Clouds and the Earth’s Radiant Energy System monthly gridded global satellite observations of all- and clear-sky TOA radiative fluxes during December 2000–November 2016. Before analysis, the values are detrended at each grid point by removing a linear trend estimated by least-squares regression. To estimate the relationship between SST, EIS, and the observed radiative budget, we use ERA-Interim (38) reanalysis fields of surface and atmospheric temperature, with which we compute annual detrended SST and EIS anomalies. In addition to reanalysis temperature, we use moisture and surface albedo reanalysis values in combination with radiative kernels to decompose the TOA radiative flux anomalies and to adjust the CRE anomalies for noncloud effects.