1. Introduction
Uncertainty in estimates of equilibrium climate sensitivity (ECS)—the equilibrium surface temperature change in response to a doubling of CO2 above preindustrial levels—has long been linked to uncertainty in the radiative feedbacks λ that govern the efficiency with which the climate system radiates energy to space per degree of surface warming. The strength of λ is intrinsically set by blackbody radiation, which is further modulated by radiative feedbacks associated with changes in atmospheric lapse rate, water vapor, surface albedo, and clouds. Among these, the cloud feedback has been found to be the primary source of ECS uncertainty (Webb et al. 2006; Soden and Held 2006; Dufresne and Bony 2008; Webb et al. 2013; Caldwell et al. 2016; Zelinka et al. 2016; Ceppi et al. 2017; Caldwell et al. 2018; Zelinka et al. 2020). The low-cloud feedback is particularly uncertain (Bony and Dufresne 2005; Webb et al. 2006, 2015; Ceppi et al. 2017), leading to tremendous efforts in the community to constrain it (Bony et al. 2006).
Within global climate models (GCMs), ECS is often estimated based on a standard linear framework for global energy balance:
where F is the effective radiative forcing (with F2× representing forcing from CO2 doubling), and where the subscript “eq” denotes the equilibrium state when N approaches zero. All variables represent global-mean anomalies with respect to a preindustrial state. A useful method to derive λ and ECS from simulations of abrupt CO2 doubling or quadrupling is proposed by Gregory et al. (2004), regressing net TOA radiation imbalance N against surface air temperature change T (hereafter referred to as Gregory N–T regression, with the graphical illustration of this regression referred to as a Gregory plot). This method has been widely used to provide estimates of λ (regression slope), F2× (from the y-axis intercept), and ECS (from the x-axis intercept), but is only valid under the assumption that λ is constant over time (i.e., λ = λeq at any given time). This general assumption may be violated for several reasons. For example, a discrepancy between λ and λeq may arise from nonlinear state dependence of some feedbacks on global-mean or local temperature (e.g., Block and Mauritsen 2013; Andrews et al. 2015; Bloch-Johnson et al. 2015). For instance, sea ice albedo feedback will become less positive as the amount of sea ice decreases with warming (Goosse et al. 2018) while the water vapor feedback (Meraner et al. 2013) and cloud feedback (Caballero and Huber 2013) may both become more positive with warming. Most importantly, the majority of GCMs in phases 5 and 6 of the Coupled Model Intercomparison Project (CMIP5 and CMIP6) exhibit a weakening of the negative net feedback as time evolves after CO2 forcing is imposed, indicated by a curvature in the Gregory N–T regression (Andrews et al. 2015; Armour 2017; Proistosescu and Huybers 2017; Lewis and Curry 2018). The time dependence of λ has been found to arise primarily from its dependence on the spatial pattern of sea surface temperature (SST), which itself can evolve over time (Armour et al. 2013; Zhou et al. 2016; Haugstad et al. 2017; Ceppi and Gregory 2017; Andrews et al. 2018; Dong et al. 2019)—the so-called pattern effect (Stevens et al. 2016). An important implication is that the climate sensitivity inferred from the historical energy budget is biased low compared to the climate sensitivity estimated over longer time scales under CO2 forcing due to the evolution of surface warming patterns (Armour 2017; Proistosescu and Huybers 2017; Andrews et al. 2018; Marvel et al. 2018; Dong et al. 2019; Gregory et al. 2020; Rugenstein et al. 2020). What is less well understood, however, is what sets the magnitude of the pattern effect, as illustrated by the large intermodel spread in the degree of feedback curvature in the Gregory regression (Andrews et al. 2015; Armour 2017; Ceppi and Gregory 2017). Moreover, the contribution of model spread in feedback curvature to the model spread in ECS estimates has not yet been quantified. This work addresses these two key issues in both CMIP5 and CMIP6 models.
We first present an overview of net feedbacks in CMIP5 and CMIP6 models by showing the Gregory N–T regression for the 150-yr-long simulations of abrupt CO2 quadrupling (hereafter abrupt4×CO2) (Fig. 1). Following Andrews et al. (2015), we calculate radiative feedbacks based on regression over a fast time scale (years 1–20) and over a slow time scale (years 21–150), noted hereafter as λ1–20 and λ21–150, respectively. We calculate values of N and T in each model with respect to their preindustrial control simulations (piControl) after accounting for drift by subtracting the linear regression of piControl values over time segment corresponding to the abrupt4×CO2 simulation [following Forster et al. (2013) and Armour (2017)]. All of the anomalies used in this study are annual-mean quantities. Note that we use year 20 to separate the fast response on decadal time scales from the slow response on centennial time scales, following many existing studies, but results are insensitive to the year chosen (Andrews et al. 2015). ECS estimated using the regression method over the course of abrupt4×CO2 simulations is often referred to as the effective equilibrium climate sensitivity (Andrews et al. 2015; Andrews and Webb 2018; Andrews et al. 2018; Gregory et al. 2020), as it presumably differs from the true ECS of the Earth system that would be found by equilibrating over multiple millennia (Rugenstein et al. 2020). In this study, we use several measures of the effective ECS derived from extrapolation of the Gregory N–T regressions to the x axis (divided by 2 to account for CO2 quadrupling) and distinguish them with a subscript denoting the years over which the regression was performed. Specifically, we use ECS1–20, ECS21–150, and ECS1–150, corresponding to values derived from the regressions over years 1–20, years 21–150, and years 1–150, respectively. Of these three, ECS21–150 provides the most accurate estimate of the true ECS in eight GCMs analyzed by Rugenstein et al. (2020), so we will make this approximation and refer the effective ECS of each model to their ECS21–150 values here.
Gregory plots for (a) CMIP5 and (b) CMIP6: annual-mean change in global-mean net TOA radiation (W m−2) against annual-mean change in global-mean surface air temperature (K) from abrupt4×CO2 experiments. Gray dots denote each year from each model; black dots denote each year of multimodel means. Thin (thick) lines show regression fits for years 1–20 (blue) and for years 21–150 (red) for each model (multimodel means). The slope of blue line represents the feedback parameter on the fast time scale (λ1–20), and the slope of red line represents the feedback parameter on the longer time scale (λ21–150). (c)–(f) Box plots of λ1–20 (W m−2 K−1), Δλ (W m−2 K−1), ECS1–20 (K), and ECS21–150 (K) in CMIP5 (left box) and CMIP6 (right box) models. The box indicates interquartile range (IQR), the whiskers indicate 1.5 × IQR range, and the dashed line inside the boxes indicates the median value, for each quantity.
Citation: Journal of Climate 33, 18; 10.1175/JCLI-D-19-1011.1
Figure 1 shows that for both CMIP5 and CMIP6, the ensemble-mean (negative) net feedback weakens toward the longer time scales. That is, there is a positive change in the (negative) net feedback (Δλ = λ21–150 − λ1–20 > 0) across 23 of 24 CMIP5 models and 26 of 29 CMIP6 models (see Table 1 for model information), indicating that ECS1–20 is nearly always smaller than ECS21–150 in both CMIP5 and CMIP6. Comparing the two ensembles, we find that ECS1–20 and ECS21–150 on average are higher in CMIP6 relative to CMIP5, although they have larger variance in CMIP6 (Fig. 1; Tables 2 and 3). Several up-to-date studies of individual CMIP6 models [Gettelman et al. (2019) for CESM2; Golaz et al. (2019) for E3SM; Sellar et al. (2019) for UKESM1; Bodas-Salcedo et al. (2019) for HadGEM3; Andrews et al. (2019) for HadGEM3-GC3.1 and UKESM1] report that the higher values of ECS in their models are largely due to stronger positive cloud feedbacks, which is recently confirmed to be a common feature in the CMIP6 ensemble by Zelinka et al. (2020). Here, by quantifying λ on different time scales, we find that both λ1–20 (feedback strength on the fast time scale) and Δλ (feedback change over time) are, on average, different in CMIP6 relative to CMIP5 (Fig. 1). Key questions are 1) how do λ1–20 and Δλ contribute to the spread in ECS across models and between CMIP5 and CMIP6 ensembles, and how does the pattern effect over historical period change from CMIP5 to CMIP6, 2) what causes the differences in Δλ across models and between CMIP5 and CMIP6 ensembles, and 3) what physical mechanisms govern λ1–20 and Δλ.
The CMIP6 models used in this study.
Estimates of feedback parameter (W m−2 K−1) and effective climate sensitivity (K) from abrupt4×CO2 simulations for the CMIP6 GCMs and their multimodel mean. Shown from left to right are feedback parameter over the fast time scale (λ1–20), feedback parameter over the longer time scale (λ21–150), feedback evolution (Δλ = λ21–150 − λ1–20), effective climate sensitivity from regressions over years 1–20 (ECS1–20), and effective climate sensitivity from regressions over years 21–150 (ECS21–150). All regressions are calculated using the ordinary least squares regression method.
Motivated by the three questions, we assess the effective ECS, λ1–20, and Δλ within 24 CMIP5 models and 29 CMIP6 models (summarized in Table 1). In section 2, we investigate the source of model spread in the effective ECS relating the radiative response on fast time scale and the pattern effect on slow time scale, and also estimate the ECS bias relative to historical estimates in both ensembles. In section 3, we compare the ensemble-mean Δλ in the CMIP5 and CMIP6 models. In section 4, we investigate the intermodel spread in λ1–20 and Δλ separately, and track down the key regions of the pattern effect that are most responsible for driving the spread in Δλ across the CMIP5 and CMIP6 models.
2. The contribution of the pattern effect to the variance of ECS estimates
Figure 1d shows that Δλ is on average smaller in CMIP6 models (0.4 W m−2 K−1) than in CMIP5 models (0.53 W m−2 K−1), despite the fact that ECS21–150 is on average higher in CMIP6 (Fig. 1f) (corresponding to an overall less-negative λ). That is, higher CMIP6-mean effective ECS is not coming from a stronger pattern effect (it is weaker, in fact); it is likely due to less-negative feedbacks on the fast time scale and stronger radiative forcing (Zelinka et al. 2020). However, there remains the possibility that intermodel spread in Δλ may contribute to the spread in effective ECS. Therefore, we first estimate the degree to which Δλ affects the spread in ECS21–150 across models (section 2a). Then we use abrupt4×CO2 simulations as an analog for historical warming [following Lewis and Curry (2018)] to estimate the degree to which the pattern effect causes historical estimates of effective ECS to be less than ECS21–150 (or ECS1–150) in CMIP5 and CMIP6 models (section 2b).
a. Correlation between ECS21–150 and ECS1–20
Previous studies (Dufresne and Bony 2008; Caldwell et al. 2016) partitioning ECS into components associated with radiative feedbacks and radiative forcing have identified feedbacks as the dominant source of the ECS spread across models. To estimate the relative roles of λ1–20 and Δλ in setting ECS, we evaluate the correlation between ECS21–150 and ECS1–20. Without any pattern effect–induced variance, ECS21–150 and ECS1–20 would be highly correlated.
The correlation (r2) between ECS21–150 and ECS1–20 is 0.69 in CMIP5 and 0.70 in CMIP6, respectively; both correlations are statistically significant at 95% confidence level. This indicates that the total variance of ECS21–150 can be primarily explained by the spread in the radiative response on fast time scales, even without considering the feedback evolution due to the pattern effect. The degree to which feedbacks change over time (Δλ) thus explains, at most, 30% of the total variance in ECS in both model ensembles, given the fact that λ1–20 and Δλ are weakly correlated (r2 = 0.3 for CMIP5 and r2 = 0.2 for CMIP6).
These results suggest that the differences in feedback evolution on longer time scales contribute much less to the spread in ECS21–150 than do the differences in feedbacks on the fast time scales (λ1–20), even though this measure of ECS here is based on the latter period of the abrupt4×CO2 simulations (years 21–150). However, it is worth noting that both in ensemble means and in individual models, Δλ is generally positive (23 of 24 CMIP5 models and 26 of 29 CMIP6 models), therefore ECS21–150 is nearly always greater than that derived from early portion of the simulation (ECS1–20). Thus, while λ1–20 is the major driver of variance in ECS, ignoring Δλ and using an assumption of time-invariant feedbacks would lead to a low estimate of the true ECS (as estimated here by ECS21–150).
b. ECS-to-ECShist ratio
As many studies have revealed, the value of ECS estimated from historical energy budget constraints is lower than that based on the behavior of fully coupled and atmosphere-only GCM simulations (Armour 2017; Proistosescu and Huybers 2017; Andrews et al. 2018; Lewis and Curry 2018; Marvel et al. 2018; Gregory et al. 2020). Multiple factors have contributed to the spatial pattern of warming, and thus the pattern effect, over the historical period, including the inherent time scales of ocean adjustment to radiative forcings (e.g., Marvel et al. 2016; Armour 2017; Proistosescu and Huybers 2017) as well as unforced internal climate variability (e.g., Andrews et al. 2018; Marvel et al. 2018). The distinction between forced and unforced pattern effects is further discussed in Dessler (2020). In this section, we consider how the forced pattern effect may bias values of ECS inferred from historical warming based on the behavior of the CMIP5 and CMIP6 models’ response to CO2 forcing.
Following Armour (2017) and Andrews et al. (2018), we rewrite Eq. (2) as
where λhist is the feedback parameter estimated from historical energy budget constraints, and λ′ is the change in feedback at the equilibrium state relative to the historical period. Using λhist based on historical energy budgets, one can make an estimate of climate sensitivity (termed ECShist herein):
which will underestimate the value of ECS if λ′ > 0. Note that while λ′ is expected to have the same sign of Δλ (positive in most GCMs), their magnitudes will be smaller. The change Δλ is defined as the change in feedbacks between the first 20 years and the last 130 years of abrupt4×CO2 simulations, whereas λ′ is defined in terms of how feedbacks will change from historical warming to equilibrium warming under CO2 forcing. Armour (2017, hereafter A17) and Lewis and Curry (2018, hereafter LC18) proposed a ratio of ECS to ECShist (hereafter “ECS-to-ECShist ratio”) to quantify the difference in ECS estimates, and reported the CMIP5-mean ECS-to-ECShist ratio as 1.095 (LC18) or 1.26 (A17). The difference between these estimates is attributed to the differences in the method and time scale of regression used and to differences in assumptions about how CO2 forcing scales with CO2 concentration (LC18).
Ideally, estimates of λhist and ECShist require accurate estimates of historical energy budgets from observations or GCM simulations with all historical forcing agents included (e.g., historical simulations). In the latter case, additional simulations with the same historical forcings but fixed SSTs are needed to diagnose the magnitude of forcing, namely, the Radiative Forcing Model Intercomparion Project (RFMIP; Pincus et al. 2016). Given the absence of the RFMIP simulations for the majority of the current CMIP5 and CMIP6 models, several ways to approximate ECShist are proposed, for example, using abrupt4×CO2 or 1pctCO2 simulations as an analog for historical warming (A17, LC18), or estimating historical forcings based on empirical scaling (Gregory et al. 2020). Here, following LC18, we make use of the early portion of abrupt4×CO2 simulations as a historical analog to estimate ECShist by regressing N against T over years 2–50 of each model’s abrupt4×CO2 simulation. We also calculate F2× by scaling the y-axis intercept of the regression of N against T over years 2–10. Long-term ECS here is estimated from the regression of N against T over years 21–150 (equal to ECS21–150), which is the same period used in both A17 and LC18, but using Deming regression to be consistent with LC18 for comparison. We also provide the results using a more conventional estimate of ECS derived from the N–T regression over years 1–150 (ECS1–150; shown in parentheses in Table 4).
Estimates of ECShist, ECS-to-ECShist ratio, and λ′ (the change in feedback from historical period to equilibrium) for individual CMIP6 models and ensemble means of CMIP5 and CMIP6, to be compared with Table S2 in Lewis and Curry (2018). For ECS-to-ECShist ratio and λ′, the results shown are calculated with the values of effective ECS derived from regressions over years 21–150 (or years 1–150), using the Deming regression method.
The results of individual CMIP6 models and ensemble means are shown in Table 4. The pattern-effect induced feedback evolution from the historical period to equilibrium (λ′) is on average weaker in CMIP6 models (0.06 W m−2 K−1) relative to CMIP5 models (0.092 W m−2 K−1), so that the ECS-to-ECShist ratio is also reduced in the CMIP6 ensemble mean (6%) compared to the CMIP5 ensemble mean (9.5%; consistent with LC18). This suggests that the latest generation of GCMs produce an overall smaller ECS-to-ECShist ratio, consistent with results above that the pattern effect is slightly smaller in the abrupt4×CO2 simulations. However, there remains a large spread across CMIP6 models: λ′ varies from 0.3 to −0.23 W m−2 K−1, corresponding to ECS values that are 40% higher to 12% lower than ECShist.
We note an important caveat of this analysis regarding the calculation of ECShist. Making use of abrupt4×CO2 simulations as an analog for the historical energy budget is a useful approach as it enables intermodel comparison, but it may produce different values of ECShist than those estimated from historical simulations that include a more realistic time evolution of CO2 and non-CO2 forcings as well as an unforced pattern effect (Marvel et al. 2016: Gregory et al. 2020; Andrews et al. 2019). For example, Andrews et al. (2019) found that ECShist within historical simulations of HadGEM3-GC3.1-LL is 4.7 K, with a ECS-to-ECShist ratio of 1.21. For comparison, using HadGEM3-GC3.1-LL’s abrupt4×CO2 simulation, our calculation gives an ECShist of 5.2 K, and an ECS-to-ECShist ratio of 1.08 (Table 4), suggesting that the values reported here may underestimate the historical pattern effect. However, our main focus is to provide information on the difference in pattern effect between the CMIP5 and CMIP6 ensembles, rather than to provide a definitive ECShist metric for each model. Future work employing RFMIP simulations to accurately quantify radiative feedbacks in the historical simulations of CMIP6 models is needed to shed light on this in greater detail.
3. The consistency and difference in ensemble-mean Δλ between CMIP5 and CMIP6
Even though Δλ does not contribute as much as λ1–20 to the intermodel spread in ECS, it substantially affects ECS estimates for both CMIP5-mean and CMIP6-mean projections (comparing ECS1–20 to ECS21–150 in Figs. 1e and 1f). In this section, we first compare the global-mean Δλ and its individual components partitioned by radiative kernels. We then examine the spatial patterns of ensemble-mean Δλ from CMIP5 and CMIP6 models. A comparison of SST patterns is also provided to aid in uncovering the causes of ensemble differences.
Figure 2 shows global-mean net Δλ and its individual components associated with changes in atmospheric temperature, water vapor, lapse rate, surface albedo, and clouds, estimated using radiative kernels (Huang et al. 2017) as described in Zelinka et al. (2020). We calculate the cloud feedback using radiative kernels by removing cloud masking effects from the temperature-mediated change in net cloud radiative effect. An overall consistency between CMIP5 and CMIP6 is found in the fact that the dominant contribution to the ensemble-mean Δλ comes from the net cloud component (ΔλCLD), followed by the sum of lapse rate (ΔλLR) and water vapor (ΔλWV) components. Both CMIP5 and CMIP6 have a large spread in the net Δλ, primarily owing to the spread in ΔλCLD. However, the (positive) ensemble-mean net Δλ is slightly smaller in CMIP6, primarily due to a smaller surface-albedo feedback change (ΔλALB), particularly from the Northern Hemisphere (NH).
The Δλ for each individual CMIP5 models (blue circles), CMIP6 models (orange circles), and their multimodel means (black circles), decomposed into contributions of (from left to right) Planck (PL), surface albedo (ALB), the sum of lapse rate (LR) and water vapor (WV), net cloud (CLD), and residual (RES), respectively. The ΔλALB is further broken down into contributions from Northern Hemisphere (ALB_NH) and Southern Hemisphere (ALB_SH). The differences between CMIP5 means and CMIP6 means are printed at the bottom, with red numbers highlighting multimodel means that are significantly different (p < 0.05).
Citation: Journal of Climate 33, 18; 10.1175/JCLI-D-19-1011.1
We next show the spatial patterns of ensemble-mean feedbacks for the CMIP5 and CMIP6 models (Figs. 3 and 4). The feedback patterns are first calculated for each model by regressing the corresponding local N against global-mean T over the two separate time periods, and then averaging across models. The patterns of local contributions to the net feedback change are qualitatively consistent between the two ensemble means (Figs. 3 and 4, first row). That is, the positive changes in the net feedback primarily come from the tropical eastern Pacific. This is a region where a cool ocean and a strong capping inversion promote ubiquitous low clouds in the climatology. Because warmer surface temperatures and weaker low-level stability in this region both reduce low cloud cover, delayed warming in this region will yield a less-negative feedback during the approach toward equilibrium (Zhou et al. 2016; Ceppi and Gregory 2017). Indeed, among all individual components, cloud feedback and lapse-rate feedback contribute the most to the positive change in the net feedback over this region in both CMIP5 and CMIP6. The major difference between the two ensembles lies in the Arctic, where positive surface-albedo feedback strengthens with time in the CMIP5 models (Fig. 3, bottom row) but weakens over time in the CMIP6 models (Fig. 4, bottom row), consistent with the regional attribution results in Fig. 2.
CMIP5 ensemble-mean spatial patterns of the local radiative feedback components (calculated by regressing the local N against global-mean T). Shown from top to bottom are net feedback, net cloud feedback, lapse-rate feedback, water-vapor feedback, Planck feedback, and surface-albedo feedback, on time scales of (left) years 1–20 and (center) years 21–150, and (right) the change (late minus early).
Citation: Journal of Climate 33, 18; 10.1175/JCLI-D-19-1011.1
As in Fig. 3, but for CMIP6 ensemble means.
Citation: Journal of Climate 33, 18; 10.1175/JCLI-D-19-1011.1
Changes in the strength of the surface-albedo feedback may arise from changes in the sensitivity of local albedo to local surface temperature (a nonlinear state dependence; e.g., Goosse et al. 2018), or from differences in surface warming patterns acting on constant local surface-albedo feedbacks (e.g., Armour et al. 2013), or from a combination of these two factors. The state dependence can be identified through changes in the local surface-albedo feedback, which is defined by regressing local N onto local T (rather than global T), assuming that the local surface-albedo feedback is independent of the pattern of surface warming. We found that the local surface-albedo feedback over the Arctic slightly strengthens over time in both ensembles, indicating a nonlinear state dependence, but that the change in local surface-albedo feedback from fast to slow time scale is nearly identical in the CMIP5 and CMIP6 multimodel means. Moreover, while this nonlinear state dependence–induced strengthening of the local surface-albedo feedback over time may enhance the strengthening of the Arctic surface-albedo feedback within CMIP5 (Fig. 3, bottom row), it opposes to the weakening of the Arctic surface-albedo feedback within CMIP6 (Fig. 4, bottom row), suggesting that ΔλALB is primarily governed by changing warming patterns rather than by local state dependence. Indeed, the relative warming in the Arctic over the first 20 years is stronger in CMIP6 than CMIP5 (Fig. 5c), but it becomes weaker over the following decades in CMIP6 relative to CMIP5 (Fig. 5f). As a result of this change in the rate of Arctic warming, the Arctic surface-albedo feedback on average weakens over time (i.e., negative ΔλALB) within CMIP6 models (Fig. 4), which overcomes the positive ΔλALB arising from enhanced warming of the Southern Ocean on the slow time scale (Fig. 4 bottom row), leading to a slightly negative value of global-mean ΔλALB and an overall smaller value of global-mean Δλ in CMIP6 models (Fig. 2).
Spatial patterns of SST changes (SST*) over (top) years 1–20 and (middle) years 21–150, and (bottom) their changes (late minus early), for (a)–(c) CMIP5 multimodel mean, (d)–(f) CMIP6 multimodel mean, and (g)–(i) the difference (CMIP6 minus CMIP5). The values of SST* are calculated as the regression slope of local SST changes against global-mean SST changes, such that the global mean of (a), (b), (d), and (e) is one by construction. Note that the color scales in the left two columns and in the right column are different.
Citation: Journal of Climate 33, 18; 10.1175/JCLI-D-19-1011.1
4. The source of the intermodel spread in Δλ across CMIP5 and CMIP6
We next move away from the multimodel mean perspective, to consider why individual models have different values of Δλ. We find it conceptually helpful to consider that radiative feedbacks and their changes may be influenced by both atmospheric model physics and SST patterns. To separate the two factors, we make use of radiative feedback “Green’s functions” (Zhou et al. 2017; Dong et al. 2019), which will be introduced in section 4a. In sections 4b and 4c, we investigate the major source of the intermodel spread in Δλ across the CMIP5 and CMIP6 models, respectively.
a. Green’s functions
To separate the effect of SST patterns and the effect of model physics, we use radiative feedback Green’s functions, as they predict the radiative response based solely on SST anomaly patterns, given the atmospheric physics of the parent model from which they were derived. The basis of a Green’s function is a Jacobian matrix, representing the sensitivity of any regional response to regional SST anomalies, which consists of both local and nonlocal effects of changes in SST. The full Jacobian is calculated from a series of prescribed-SST simulations within an AGCM, each with a single patch of SST anomalies on the top of climatological SSTs. Then, convolving the Jacobian with a global SST anomaly pattern can predict the global response to the given SST pattern, based on the assumption of spatial linearity, which has been shown to be a good approximation (Zhou et al. 2017; Dong et al. 2019). Hence, applying the Green’s functions linearly separates the differences in SST patterns and the differences in the sensitivity of radiative feedbacks on SST patterns.
Here we employ two Green’s functions: one derived from the Community Atmosphere Model version 5 (CAM5) by Zhou et al. (2017), and one derived from CAM4 by Dong et al. (2019). The major difference between CAM4 and CAM5 Green’s functions lies in the representation of cloud properties within the two models, which are reported to be more realistic in CAM5 (Kay et al. 2012), although both models exhibit large biases in the subtropical marine boundary layer cloud regimes. Throughout this study, we use the two-dimensional global-mean Jacobians (denoted as
where X can be any response (e.g., R, T), and SST(r) denotes the global pattern of SST anomalies. Then λ1–20, λ21–150, and Δλ are calculated following the same regressions used to process model outputs. Note that the Green’s function can only predict the TOA radiative response R (= λT), which is different from the net TOA radiation imbalance N in fully coupled GCMs, because the latter includes the effective radiative forcing of CO2 quadrupling F4×: N = F4× + R. Indeed, the effective radiative forcing also varies slightly across models; but it is abruptly imposed and held constant over time. Therefore, while radiative forcing matters for ECS itself, its absence does not cause any inconsistency in the estimates of feedbacks (defined as the regression slope in Gregory plots) between Green’s functions and the GCM simulations.
b. Intermodel spread in Δλ across CMIP5 models
We first show the comparison of feedbacks from CMIP5 GCMs and those reconstructed by the CAM4/CAM5 Green’s functions (Fig. 6). Both Green’s functions poorly capture λ1–20 but approximately reproduce GCM values of Δλ, suggesting that λ1–20 and Δλ are governed by different processes. The failure of the Green’s functions in reconstructing λ1–20 may come from several factors; for example, the Green’s functions fail to account for the radiative response to land warming which emerges generally on fast time scales. However, we favor the interpretation that the spread in λ1–20 is primarily determined by each model’s atmospheric physics (e.g., cloud parameterizations). Therefore, the radiative responses from each model cannot be captured by Green’s functions derived from either CAM4 or CAM5, which have distinct atmospheric physics. On the other hand, the fact that both Green’s functions more accurately reproduce Δλ, even though they are built from different models, suggests that the spread in Δλ arises primarily from the changes in SST patterns and is largely insensitive to model physics.
Comparison of (top) λ1–20 and (bottom) Δλ from CMIP5 models and those from the (a),(c) CAM4 and (b),(d) CAM5 Green’s function, respectively. Gray lines are the y = x reference line. Variance explained is noted in the bottom-right corner of each panel.
Citation: Journal of Climate 33, 18; 10.1175/JCLI-D-19-1011.1
We next investigate what regions of SSTs drive the intermodel spread in Δλ across the CMIP5 models. Previous studies have pointed out the importance of tropical warming through changing cloud and lapse-rate feedbacks. Zhou et al. (2016) proposed the role of the tropical eastern Pacific, where relative cooling in recent decades is thought to be responsible for driving an increase in local low cloud and a more-negative cloud feedback. Andrews and Webb (2018) further established a mechanism associated with east–west tropical Pacific SST gradient that governs the change in tropospheric stability, and therefore the change in low clouds and lapse rate. Silvers et al. (2018) highlighted changes in low clouds throughout the tropics beyond the traditional stratocumulus regimes in driving decadal variability of feedbacks over the historical period. Recently, Dong et al. (2019) proposed that Δλ tracks the ratio of warming in the west Pacific warm-pool (WP) regions relative to warming in the rest of global ocean areas γ. Here we test this mechanism by examining the correlation of Δλ against the proposed WP warming ratio change Δγ across models.
To calculate Δγ for all CMIP5 and CMIP6 models, we define WP regions in this study as grid cells within 30°S–30°N, 30°E–160°W that have an upward vertical velocity at 500 hPa (ω500) in the piControl simulation. Unlike the fixed rectangular area in the west Pacific used in Dong et al. (2019), this updated metric takes into account mean-state biases, ensuring that in each model the WP regions capture the radiative responses in regions of deep convection. Note that results using the fixed region in Dong et al. (2019) are similar to those shown here. We also simplify γ to be the WP SST warming relative to global-mean surface air temperature changes, calculated as the regression slope of the averaged SST over the selected WP regions against global-mean T, over the two time periods used throughout this study (years 1–20 for γ1–20, years 21–150 for γ21–150, and Δγ =γ21–150 − γ1–20).
Figure 7a shows that Δλ is well correlated with Δγ for CMIP5 models (with r2 = 0.63). Although many approximations are made in the derivation (Dong et al. 2019), the simple metric Δγ, which includes no information about radiative response, explains over 60% of the variance in CMIP5 Δλ. The physical mechanism, as discussed in Dong et al. (2019), is the preeminent impact of WP warming on global TOA radiation change via deep convection. Over the WP regions, where the surface is tightly coupled to the free troposphere by deep convection, surface warming directly enhances upper tropospheric warming. This leads to a stronger negative lapse-rate feedback and a more-negative cloud feedback over low-cloud regions caused by increased lower tropospheric stability, which together promotes a more efficient radiative damping at TOA. On the other hand, the weaker coupling between surface and upper troposphere in all other regions results in a weak TOA radiation response to surface warming. This leads to a weaker negative lapse-rate feedback, and a more-positive low-cloud feedback, hence, resulting in an inefficient radiative damping (see Dong et al. 2019, their Figs. 4 and 5). The key importance of warm pool warming for TOA radiation changes is also supported by observational evidence (Zhou et al. 2016; Ceppi and Gregory 2017; Fueglistaler 2019).
The relation between the change in net feedback (Δλ) and the change in the west Pacific warm-pool warming ratio (Δγ), for (a) CMIP5 models and (b) CMIP6 models. The linear fit for CMIP5 models is plotted as the black line in (a) and the gray dashed line in (b). Variance explained is noted in the bottom-left corner of each panel.
Citation: Journal of Climate 33, 18; 10.1175/JCLI-D-19-1011.1
To further demonstrate the proposed mechanism, we select three representative models that have large positive Δλ (GISS-E2-R), small positive Δλ (IPSL-CM5B-LR), and small negative Δλ (CNRM-CM5), respectively. The term Δλ is demonstrated as the degree of curvature in the Gregory plots for each model (Figs. 8a–c). We then show their SST warming patterns defined as local SST changes regressed against global-mean SST changes, denoted by SST* (Figs. 8d–l). In this context, values above 1 (in red) indicate local warming exceeding the global-mean warming in the given period, and values below 1 (in blue) indicate local warming weaker than the global-mean warming. In GISS-E2-R, the warm-pool regions warm up relatively quickly during the first 20 years, but warming in the warm pool does not keep pace with warming in other oceans (e.g., the Southern Ocean) over the last 130 years. This sharp transition of surface warming from tropical ascent regions to all other regions is responsible for the large Δλ. In IPSL-CM5B-LR, the WP region does not warm substantially faster than the global average warming on the fast time scale, so that the change in the relative warming over WP regions is weaker, leading to a smaller Δλ. In CNRM-CM5, the WP region warms relatively fast on the longer time scales, leading to a nearly zero change in WP region in contrast to the other two models, driving a negative Δλ. This comparison shows that the CMIP5 values of Δλ can be well characterized by the ratio of warm-pool to global-mean warming (Fig. 7a), suggesting an important role of tropical convective regions in modulating the strength of radiative feedbacks in CMIP5.
(a)–(c) Gregory plots and (d)–(l) patterns of SST changes for (left) GISS-E2-R, (center) IPSL-CM5B-LR, and (right) CNRM-CM5. Colored lines in (a)–(c) show regression fits for years 1–20 (blue) and for years 21–150 (red). Also shown are the regression slopes of local SST changes against global-mean SST changes over years 1–20 in (d)–(f) and years 21–150 in (g)–(i), and the change between the two time periods (later minus early) in (j)–(l). The hatchings highlight the warm-pool ascent regions in each model.
Citation: Journal of Climate 33, 18; 10.1175/JCLI-D-19-1011.1
c. Intermodel spread in Δλ across CMIP6 models
For CMIP6 models, we first repeat the analysis applying the WP warming ratio. Interestingly, the above theory does not seem to hold as well for CMIP6 models (Fig. 7b), suggesting that the Δλ spread in the latest models may not directly trace to relative warm-pool warming. One may ask whether this is because the deep convection in other regions (e.g., Atlantic Ocean warm-pool regions) carry more weight in the CMIP6 ensemble. To identify the key regions for driving feedback changes, we regress global-mean Δλ onto local ΔSST* (the change in the relative warming rate from fast to slow time scale) across CMIP5 and CMIP6 models, respectively, and evaluate the local correlation coefficient (r). Note that SST* is calculated as the local SST change relative to global-mean SST change, and Δ is defined as the late period (years 21–150) minus the early period (years 1–20).
The resulting correlation maps (r) are shown in Fig. 9. The positive correlation indicates that models that have stronger positive global-mean Δλ tend to show a locally delayed warming as approaching to equilibrium, whereas the negative correlation indicates that models that have stronger positive global-mean Δλ tend to show a local warming predominately on the fast time scale. The magnitude of correlation coefficient illustrates the degree to which the intermodel spread in Δλ correlates with the differences in local warming rates. For example, Fig. 9a shows a strong negative correlation over Indo-Pacific deep convective regions, which indicates that in the CMIP5 models, Δλ is primarily governed by the difference in the relative warming in the west Pacific warm-pool regions where greater warming on the fast time scale gives rise to a stronger positive Δλ. This is achieved mostly through ΔλCLD (Fig. 9c) and ΔλLR (Fig. 9g). However, the results from the CMIP6 models highlight the tropical Indian Ocean, the equatorial eastern Pacific, and the SH midlatitudes (Fig. 9b), which are mostly reflected in the pattern of ΔλCLD (Fig. 9d). This comparison suggests that the CMIP5 values of Δλ may be primarily dominated by surface warming in the broad tropical convective regions, whereas the CMIP6 values of Δλ may be influenced more by surface warming in the tropical subsidence regions and extratropics. Indeed, we found that about half of the variance in Δλ in CMIP5 ensemble can be explained by the change in the estimated inversion strength (EIS) per unit of global warming, whereas the variance in Δλ explained by the EIS change in CMIP6 ensemble is slightly decreased (r2 = 0.4). Moreover, we found that both Green’s functions fail to reproduce CMIP6 Δλ (not shown), even though they largely capture Δλ in CMIP5 models (Figs. 6c,d). Multiple factors may contribute to the inability of the CAM4/CAM5 Green’s functions to capture the behavior of CMIP6 models, and we consider two of them here.
Correlation coefficients (r) for local regression of global-mean Δλ against local ΔSST* (local SST warming rate relative to global-mean SST change) across (left) CMIP5 models and (right) CMIP6 models for (a),(b) net Δλ, (c),(d) cloud Δλ, (e),(f) surface-albedo Δλ, (g),(h) lapse rate Δλ, and (i),(j) water vapor feedback. Hatching marks grids where correlations are significant (i.e., p < 0.05).
Citation: Journal of Climate 33, 18; 10.1175/JCLI-D-19-1011.1
First, we consider the possibility that the CAM4/CAM5 Green’s functions cannot capture feedback changes in the CMIP6 models, even assuming that the radiative response to SST patterns remain linear (section 4a). That is, the CMIP6 models may be systematically different from the CMIP5 models from which the Green’s functions are built. One example is the modifications made to extratropical clouds in CMIP6 models, whose feedbacks have strengthened in CMIP6 owing to changes in their sensitivities to local environmental conditions (Zelinka et al. 2020). These changes may give rise to a different dependence of cloud feedbacks on SST pattern, presumably with stronger cloud radiative response to Southern Ocean warming. In this case, the global TOA radiation change may no longer be dominated by the tropical warm-pool warming as seen in CAM4 Green’s function for example (see Dong et al. 2019, their Fig. 11), but could instead also be strongly influenced by the Southern Ocean warming. As a result, the delayed Southern Ocean warming would yield a stronger pattern effect on the cloud feedback (i.e., a greater positive ΔλCLD). Indeed, the Southern Ocean is highlighted in the CMIP6’s result in Fig. 9d with a stronger positive correlation, suggesting a stronger sensitivity of cloud feedback on the Southern Ocean warming rate. If this is the case, new Green’s functions with up-to-date GCMs may better capture the causes of feedback changes in CMIP6 models.
Apart from extratropical clouds, changes in CMIP6 models may also yield a different radiative response to the equatorial eastern Pacific, where delayed warming seems to drive a negative Δλ corresponding to a strengthening of global-mean (negative) feedback over time (Fig. 9b). However, there also remains a possibility that the correlation between the equatorial eastern Pacific warming and Δλ is not causal but comes about through correlations between the eastern Pacific and SH extratropical warming rates, for instance. Specific mechanisms need to be further uncovered.
A second possibility comes from the potential nonlinear state dependence of feedbacks in the CMIP6 models, in which case the Green’s functions can no longer apply as they rely on linear estimation. In particular, we consider a well-documented nonlinearity in the extratropical mixed-phase cloud feedback. The negative mixed-phase cloud feedback arises from the brightening of the clouds as they become increasingly composed of liquid droplets with warming. Therefore, it depends on the mean-state of ice/liquid fraction of the clouds, with more ice in the initial state leading to a stronger negative-feedback with warming (Tsushima et al. 2006; Storelvmo et al. 2015; McCoy et al. 2015). Many CMIP6 models now have higher climatological cloud liquid water fractions, in better agreement with observations (Bodas-Salcedo et al. 2019; Gettelman et al. 2019; Zelinka et al. 2020). Bjordal et al. (2020, manuscript submitted to Nat. Geosci.) shows that in CESM2, with the inclusion of a new mixed-phase ice nucleation scheme, the negative mixed-phase cloud feedback weakens with warming from the first 15 years to the last 15 years of abrupt4×CO2 simulation, particularly over the Southern Ocean, as the amount of ice decreases allowing for no further phase change to happen (see their Fig. 3). This weakening toward longer time scales in their simulations leads to a positive ΔλCLD over the Southern Ocean, which is primarily driven by the nonlinear state dependence rather than by the pattern effect. If this case holds more generally across the CMIP6 models, the nonlinear state dependence of ΔλCLD on the Southern Ocean warming may never be captured by any Green’s functions, as the method relies on linear estimation.
In summary, we found the CMIP5 and CMIP6 ensembles on average highlight different regions where surface warming can influence the magnitude of global-mean Δλ (Fig. 9). In CMIP5, intermodel differences in Δλ are overall driven by intermodel differences in the surface warming rates over the west Pacific warm-pool region, where surface warming has strong remote impact on global TOA radiation changes (Dong et al. 2019). In CMIP6, intermodel differences in Δλ (and the cloud component ΔλCLD in particular) appear to have more contributions from SH extratropical warming and tropical eastern Pacific warming. Specific physical mechanisms are under investigation. Here we speculate that the stronger sensitivity of feedbacks on the delayed extratropical warming may result either from a stronger pattern effect (stronger cloud radiative response to surface warming in this region) or from a nonlinear state dependence of extratropical cloud feedback on the mean state of the liquid fraction in the clouds.
5. Conclusions
In this study, we investigated the changes in radiative feedbacks over time and their contributions to climate sensitivity from abrupt4×CO2 simulations within 24 CMIP5 GCMs and 29 CMIP6 models. Comprehensive comparisons were made between the two CMIP generations and between individual models. To examine the time variation of feedbacks, we derived feedback parameters from the Gregory regressions between the net TOA radiation imbalance and surface air temperature change over years 1–20 as λ1–20 and years 21–150 as λ21–150, and use Δλ (= λ21–150 − λ1–20) to represent the feedback changes over time.
We found that on average the effective ECS derived from the regression is higher and Δλ is smaller in CMIP6 relative to CMIP5. We then evaluated the correlation between ECS21–150 (derived from years 21–150; featuring long-term response) and ECS1–20 (derived from years 1–20; featuring fast response governed primarily by λ1–20). The correlation (r2) is 0.69 for CMIP5 and 0.70 for CMIP6, suggesting that the variance in ECS (as estimated by ECS21–150) is dominated by the differences in radiative response on the fast time scale, rather than the differences in Δλ. This also explains the fact that a greater Δλ generally leads to a greater effective ECS within individual climate models, yet the higher effective ECS in the CMIP6 models occurs despite smaller Δλ. We also compared the ECS-to-ECShist ratio between CMIP5 and CMIP6, where ECShist is estimated from years 2–50 of abrupt4×CO2 simulations as an analog for historical warming. We found the difference in feedback estimates between the short-term abrupt4×CO2 (as the proxy for historical energy budget) and the long-term abrupt4×CO2 (as the proxy for equilibrium state) is on average smaller in CMIP6, and the CMIP6-mean ECS-to-ECShist ratio is also slightly reduced, on average, relative to CMIP5, suggesting a weaker forced pattern effect in CMIP6 abrupt4×CO2 simulations. Further work employing fully coupled historical simulation and RFMIP simulations are expected to provide a more accurate estimate on historical energy budget and the role of unforced pattern effect by internal variability over the historical period.
Although the spread in Δλ contributes less to the spread in ECS than does atmospheric model physics, understanding the magnitude of Δλ and the pattern effect is still of a great importance to constrain ECS on longer time scales. By comparing the multimodel mean Δλ in the CMIP5 and CMIP6 models, we see great similarities in the spatial patterns of Δλ, highlighting the cold tongue regions with delayed warming. An overall smaller ensemble-mean Δλ in the CMIP6 models is primarily due to the difference in surface-albedo feedback over the Arctic. While the positive Arctic surface-albedo feedback generally strengthens with time in CMIP5, it weakens over time in CMIP6, compensating the global-mean change in surface-albedo feedback. This is caused primarily by changes in surface warming patterns in CMIP6, which feature rapid Arctic warming on the fast time scale followed by slow Arctic warming on the slow time scale. But we caution that the differences between ensemble-mean Δλ are not statistically significant given the large spread across models, and the results may be subject to change as more models come in.
Because both model physics and surface warming patterns are important for driving Δλ, we employ Green’s functions to isolate their contributions and investigate why individual models produce different Δλ. The Green’s functions used in this study are derived from two GCMs, which intrinsically represent the given model physics of CAM4 or CAM5 but can be independently applied to different SST anomaly patterns. When applied to the CMIP5 models, the Green’s functions reproduce Δλ well but cannot capture λ1–20, suggesting that Δλ is primarily set by the differences in warming patterns, while λ1–20 is presumably determined by the differences in model physics. Building upon Dong et al. (2019), the spread in Δλ is found to be well correlated with the change in the warm-pool warming ratio, defined as the relative ocean warming from warm-pool ascent regions to global-mean surface air warming. Across CMIP5 models, this simple metric is able to explain over 60% variance of Δλ. Models showing greater Δλ generally have west Pacific warm-pool regions warming up more quickly than the rest of world oceans on the fast time scale, but more slowly on longer time scales. This transition, on the other hand, is less significant in models that produce smaller Δλ. Regression of global-mean Δλ against local warming rates also highlights the west Pacific warm-pool regions as the dominant control driving Δλ variance across CMIP5 models, consistent with recent observations identifying the warm-pool as a key region controlling global radiation (e.g., Fueglistaler 2019).
However, the correlation analysis across CMIP6 models show a different spatial distribution, with SH extratropics and equatorial eastern Pacific being highlighted in addition to the west Pacific warm-pool regions, suggesting that the CMIP6 values of Δλ may not be dominated by tropical warm-pool warming. The specific mechanism needs to be further uncovered; we speculate here that it may be partly attributable to a stronger sensitivity of extratropical clouds to surface warming. Future studies employing Green’s function approach built from the CMIP6 models may bring more insights on investigating the pattern effect within the latest generation of GCMs, but will have limitations in the case that nonlinear state dependence of feedbacks also contributes to the changes in feedbacks with time.
Acknowledgments
We thank Stephen A. Klein and Masahiro Watanabe for insightful discussions, and thank the editor Isaac Held and three anonymous reviewers for constructive comments. We acknowledge the World Climate Research Programme, which, through its Working Group on Coupled Modelling, coordinated and promoted CMIP6. We thank the climate modeling groups for producing and making available their model output, the Earth System Grid Federation (ESGF) for archiving the data and providing access, and the multiple funding agencies who support CMIP6 and ESGF. YD, KCA, and CP were supported by National Science Foundation Grant AGS-1752796. MDZ’s work was supported by DOE’s Regional and Global Model Analysis Program and was performed under the auspices of the U.S. Department of Energy under Contract DE-AC52-07NA27344. DSB was supported by the Tamaki Foundation. CZ was supported by NSFC 41875095. TA was supported by the Met Office Hadley Centre Climate Programme funded by Department for Business, Energy and Industrial Strategy (BEIS) and Department for Environment, Food and Rural Affairs (Defra).
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