Evaluating Observational Constraints on Intermodel Spread in Cloud, Temperature, and Humidity Feedbacks
Abstract
Uncertainty in climate feedbacks is the primary source of the spread in projected surface temperature responses to anthropogenic forcing. Cloud feedback persistently appears as the main source of disagreement in future projections while the combined lapse-rate plus water vapor (LR + WV) feedback is a smaller (30%), but non-trivial source of uncertainty in climate sensitivity. Here we attempt to observationally constrain the feedbacks in an effort to reduce their intermodel uncertainties. The observed interannual variation provides a useful constraint on the long-term cloud feedback, as evidenced by the consistency of global-mean values and regional contributions to the intermodel spread on both interannual and long-term timescales. However, interannual variability does not serve to constrain the long-term LR + WV feedback spread, which we find is dominated by the varying tropical relative humidity (RH) response to interhemispheric warming differences under clear-sky conditions and the RH-fixed LR feedback under all-sky conditions.
Key Points
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Observed interannual variation provides a useful constraint to narrow the uncertainty in long-term cloud feedback
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It is not possible to constrain the long-term LR + WV feedback uncertainty with available observations of interannual variability
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Disagreements in the response of tropical relative humidity are responsible for the long-term clear-sky LR + WV feedback spread
Plain Language Summary
How much the Earth warms in response to greenhouse gas increases depends on the Earth's efficiency in restoring radiative equilibrium. This efficiency differs significantly among climate models due to differences in feedback processes, particularly the responses of clouds, temperature and water vapor to the initial perturbation. One approach to narrowing the intermodel spread of feedbacks is to only consider models whose observable variability is consistent with available measurements. The magnitude of cloud feedbacks on interannual and long-term timescales are closely related, which allows us to employ this approach with observational estimates of the interannual cloud feedback to constrain the long-term cloud feedback. However, this approach does not work for the feedback resulting from changes in the vertical distribution of temperature and water vapor (the combined lapse-rate plus water vapor feedback).
1 Introduction
The projected surface temperature responses to anthropogenic forcing have a large spread among global climate models, primarily due to large uncertainties in climate feedbacks (Flato et al., 2013). The cloud feedback has persistently been identified as the largest source of intermodel spread in effective climate sensitivity (ECS) across several generations of climate models (Dufresne & Bony, 2008; Vial et al., 2013; Zelinka et al., 2020). Although the cloud feedback appears positive in most models and thereby acts to amplify global warming, its magnitude differs substantially among models (Colman, 2003; Soden et al., 2008; Soden & Held, 2006; Zelinka et al., 2020). Accurately simulating clouds and their radiative responses has long been a stubborn challenge for climate modeling, largely because clouds depend on fine-scale physical processes that cannot be explicitly represented by coarse model grids. Although the representation of cloud processes have been improved in state-of-the-art climate models, including more accurate representation of supercooled liquid cloud water, the range of global-mean cloud feedback in the most recent generation of models has actually increased slightly (Bjordal et al., 2020; Zelinka et al., 2020).
Another important contributor to the uncertainty in ECS is the temperature feedback induced by tropospheric warming, which includes contributions from vertically uniform warming (Planck feedback) and departures from vertically uniform warming (lapse-rate [LR] feedback). From a global-mean perspective, the latter constituent further leads to a large spread in the water vapor (WV) feedback, since atmospheric moistening responds via a nearly constant relative humidity (RH) and thus follows the Clausius-Clapeyron relation (Soden & Held, 2006). Since these two components are tightly coupled in models, it is physically logical to analyze the LR + WV feedback instead of each term individually (Held & Soden, 2000). Even though there is cancellation between LR and WV feedbacks in both magnitude and intermodel spread, the LR + WV feedback still possesses the second largest contribution (∼30% that of cloud feedback) to the intermodel spread of ECS (Dufresne & Bony, 2008; Soden et al., 2008; Vial et al., 2013). Soden and Held (2006) noted that, individually, the global-mean LR and WV feedbacks are strongly related to the ratio of tropical to global-mean surface warming. Meanwhile, a recent study found that the global-mean RH-fixed LR feedback (the sum of LR feedback and its corresponding WV feedback component under RH-fixed condition; 
feedback) is largely driven by local model differences over southern extratropics (Po-Chedley et al., 2018), highlighting the role of Southern Ocean heat uptake in determining the global-mean LR + WV feedback, by partitioning of surface warming between tropics and southern extratropics.
Here we reexamine the sources of intermodel spread in cloud and LR + WV feedbacks across climate models from Coupled Model Intercomparison Project Phase 6 (CMIP6; Eyring et al., 2016), using a local feedback definition with global-mean surface temperature anomalies. We find the global-mean clear-sky LR + WV feedback uncertainty largely comes from the tropics, where local relative humidity response exhibits the largest intermodel disagreement. Meanwhile, the 
feedback is the largest contributor to all-sky LR + WV feedback uncertainty. We find this contribution largely occurs over northern extratropics, instead of southern extratropics reported in CMIP5 analysis by Po-Chedley et al. (2018) using a local feedback parameter estimated with local surface temperature anomalies. Additionally, we extend the well-established emergent constraint method (e.g., Klein & Hall, 2015) to these long-standing climate feedback challenges to investigate its utility in narrowing the spread of these feedbacks, in an effort to ultimately refine the estimate of ECS.
2 Data and Methodology
Climate feedbacks represent the amplification or dampening of radiative flux anomalies to internal variability or externally forced changes in global-mean surface temperature. Using observationally based radiative kernels derived from CloudSat/CALIPSO data (Kramer et al., 2019), we decompose top-of-atmosphere radiative flux anomalies into radiation changes caused by variations in temperature, water vapor, surface albedo and cloud, following Soden et al. (2008). Here, cloud radiative response, which is the sum of its longwave and shortwave components, is diagnosed from change in cloud radiative effect corrected for cloud masking effects on non-cloud radiative responses. Based on documented relationships between longwave and shortwave components for different cloud types (Webb et al., 2006), we further separate the cloud radiative responses into contributions from high, low and mixed clouds, following Soden and Vecchi (2011). The LR + WV radiative response is the sum of LR and WV radiative responses. Since differences in cloud climatologies can influence analyses of the all-sky LR + WV feedback, we focus primarily on uncertainties in the clear-sky LR + WV feedback in the main text, while further details of the all-sky LR + WV feedback are provided in the supplemental material (Text S1).
Climate models with the r1i1p1f1 realization available for both pre-industrial control (piControl) and abrupt quadrupling CO2 (abrupt-4xCO2) experiments are evaluated in this work (Table S1). Following Dessler (2013), interannual climate feedbacks are calculated as the linear regression slope of monthly deseasonalized global-mean radiative flux anomalies against corresponding global-mean surface (air) temperature anomalies from piControl runs. To obtain the interannual climate feedbacks as accurately as possible, the longest simulation length available for all models (200 years) is used. Climate feedbacks in response to long-term climate change are calculated as the linear regression slope of annual global-mean radiative flux anomalies against corresponding global-mean surface temperature anomalies from standard 150-year abrupt-4xCO2 experiments. Although the time-invariant feedback assumption adopted here is undermined by evolving pattern effects (e.g., Andrews et al., 2015; Andrews & Webb, 2018; Chung & Soden, 2015; Dong et al., 2020), the assumption is still useful for investigating the intermodel spread, for instance, since no noticeable difference occurs between the spread of cloud feedbacks derived from regressions over years 1–150 and years 21–150 of CMIP5 abrupt-4xCO2 simulations (e.g., Zhou et al., 2015).
To evaluate the model-simulated global-mean feedbacks, observation-based interannual emergent constraints are adopted. The observed interannual feedbacks are calculated using radiative fluxes from CERES EBAF Edition 4.1 product (Loeb, Doelling, et al., 2018, Loeb et al., 2019), vertical profiles of temperature and humidity from ERA5 (Hersbach et al., 2020) and surface temperature from GISTEMP v4 (Lenssen et al., 2019). The corresponding 95% confidence intervals are calculated using standard deviations of the observed interannual feedbacks (i.e., linear regression slope) to provide observed uncertainty bounds. In addition, vertical profiles from Version 6 Level 3 AIRS retrievals (Aumann et al., 2003) and MERRA-2 reanalysis (Gelaro et al., 2017) are adopted for potential cross-validations. Because of the limited length of satellite observations, the observation-based estimates without (with) AIRS retrievals are conducted over the period of 2001 (2003) through 2019. To increase the credibility of the emergent constraints, we also evaluate whether these constraints work with the interannual feedback obtained from the same-period historical simulations. Since the historical simulations include period 2015–2019 from idealized 21st century scenario SSP2-4.5 (O’Neill et al., 2016) and are available for less models (Table S2), we present the interannual feedbacks from piControl runs for most of the manuscript.
3 Results
3.1 Emergent Constraints
The emergent constraint method has been applied to help reduce the persistent intermodel spread of climate feedbacks (e.g., Hall & Qu, 2006; Qu & Hall, 2014). One key principle of the emergent constraint idea is that models failing to reproduce observed characteristics in unforced or historical simulations should not be trusted for future climate projections, especially if that characteristic in question is physically and statistically related across interannual and centennial timescales (Klein & Hall, 2015). Here, comparisons between global-mean interannual and long-term feedbacks are conducted (Figure 1). As shown in Figure 1a, there is a strong correlation (
) between interannual and long-term cloud feedbacks. With a least-squares regression slope close to one (
), the intermodel spread of cloud feedback is comparable on these timescales, which differs from previous findings using CMIP5-era models (Colman & Hanson, 2017; Zhou et al., 2015). For instance, Zhou et al. (2015) found the global-mean long-term cloud feedbacks of CMIP5-era models are generally smaller than their interannual counterparts, especially for those models with relatively large interannual feedback. This leads to a smaller regression slope (0.50).
Scatterplots of global-mean interannual (a) cloud and (b) clear-sky LR + WV feedbacks versus their corresponding long-term feedbacks. The vertical lines denote observed interannual feedbacks, while the shadings show their corresponding 95% confidence intervals. The red horizonal dash lines highlight the spreads of long-term feedbacks constrained by the observed feedbacks using ERA5 vertical temperature and humidity profiles.
Since the global-mean long-term and interannual cloud feedbacks are closely related in both magnitude and intermodel spread, it is possible to observationally constrain the former by identifying models with interannual cloud feedbacks that fall within observed uncertainty. In this case, we find the models with small or negative cloud feedback are inconsistent with observed uncertainty estimates (Figure 1a). Compared to Zhou et al. (2015), the narrower uncertainty range could be attributed to the longer observations, which captured a shortwave absorption increase during post-hiatus years, associated with decreases in low cloud cover (Loeb, Thorsen, et al., 2018). If one only considers models that are consistent with observations (i.e., dots fall within shading), the intermodel spread of long-term cloud feedback could be narrowed by approximately one-third (0.55 out of 1.63 
). Since the ECS of a model is tied to the strength of its cloud feedback (e.g., Zelinka et al., 2020), our findings suggest a low ECS is unlikely, consistent with conclusions by Sherwood et al. (2020). However, a recent work by Wang et al. (2021), using an emergent constraint based on historical warming patterns, suggests low ECS models cannot be ruled out.
Figure 1b compares interannual and long-term clear-sky LR + WV feedbacks. Although the correlation between global-mean interannual and long-term clear-sky LR + WV feedbacks is statistically significant at the 99% level, observed interannual variation does not serve to constrain the long-term clear-sky LR + WV feedback spread. This is due to two reasons. First, the spread of long-term clear-sky LR + WV feedback (1.32–1.67 
) is only half of that of interannual feedback (1.07–1.80 
). Second, the observational-interannual uncertainty is nearly equal to the intermodel spread. Additionally, the observed interannual clear-sky LR + WV feedbacks differ considerably among different observational and reanalyses products, reflecting the large degree of uncertainty in available observations of temperature and humidity profiles (Kramer et al., 2021). Similar results are seen in all-sky LR + WV feedback (Figure S1), with a weaker correlation between global-mean interannual and long-term all-sky LR + WV feedback. Since the impact of profile uncertainties on cloud feedback is confined to the cloud masking effect, which is the secondary contribution to cloud radiative response, the observational uncertainties do not cause noticeable differences in the observed cloud feedback estimations. When we test these constraints using the CERES observational period from historical simulations, we find these constraints exhibit slightly weaker but consistently constraining effects on the intermodel spreads (Figure S2).
Surprisingly, the spread of tropical-mean long-term clear-sky LR + WV (1.61–2.37 
) is twice as large as the global-mean spread. This is counter-intuitive. Since the tropical atmosphere has long been known for following well-documented processes (i.e., moist adiabatic lapse-rate and radiative-convective equilibrium; e.g., Santer et al., 2005), one might expect the spread of tropical-mean LR + WV feedback to be smaller than the global-mean spread. This motivates us to further explore the sources of intermodel spread in these feedbacks.
3.2 Intermodel Spread Analyses
(1)Here, 
is the intermodel variation of local feedbacks, which is resolved at each grid point. The interannual (long-term) 
from each model is calculated by regressing monthly deseasonalized (annual) local radiative response against corresponding global-mean surface temperature anomalies. 
is the intermodel variation of global-mean feedbacks, which is the same for each grid. The “a” is the contribution from local intermodel uncertainty to the global-mean feedback spread. When 
spread is large and varies with 
, we can obtain a large value of “a,” suggesting a large contribution from local difference to the global-mean spread. The spatial distribution of this contribution will be referred to as “contribution pattern” hereafter. The “b” is the y-intercept of the linear regression, a meaningless parameter in this method.
Figures 2a and 2b highlight the contribution from local cloud feedback differences to the spread in global-mean cloud feedback. The contribution patterns for interannual and long-term cloud feedbacks exhibit similar characteristics. Specifically, local feedback differences over eastern Pacific and Southern Ocean contribute the most to the global-mean cloud feedback spread on both timescales. Additionally, most of regions with statistically significant contribution to the global-mean cloud feedback spread are associated with low clouds (Figures S3c and S3d). This supports the utility of the observed constraint on global-mean long-term cloud feedback, since an emergent constraint must be based on a coherent relationship between intermodel variations in an observable quantity and in its future projection (Klein & Hall, 2015). This consistency between interannual and long-term contribution patterns is also evident in both shortwave and longwave cloud feedbacks (Figures 2c–2f), although the magnitude of local contribution on long-term timescales is generally smaller than that on interannual timescales. As expected, the shortwave component dominates local contributions to global-mean, total cloud feedback (Figures 2a–2d and S3a–S3d), given the considerable importance of low cloud feedback.
Cross-model regressions of local (a and b) total, (c and d) shortwave, and (e and f) longwave cloud feedbacks against global-mean total cloud feedback on both (left) interannual and (right) long-term timescales. Hatching indicates area where regression is statistically significant at the 95% level.
A similar analysis is applied to the LR + WV feedback (Figures 3a, 3b, S4a and S4b). Generally, the spread of global-mean LR + WV feedback is driven by feedbacks over tropics on both interannual and long-term timescales, except the long-term all-sky LR + WV feedback is dominated by the northern extratropics (Figure S5). However, the contribution patterns are noticeably different on these timescales. For instance, the intermodel spread of long-term LR + WV feedback is driven by an interhemispheric asymmetric contribution pattern which is not observed on interannual timescales. This difference highlights the challenge in using observed variability to constrain global-mean long-term LR + WV feedback, since the difference suggests that the physical processes that shape these feedbacks are timescale dependent.
Cross-model regressions of local clear-sky (a and b) LR + WV, (c and d) WVuniform, (e and f) 
, and (g and h) relative humidity (RH) feedbacks against global-mean clear-sky LR + WV feedback on both (left) interannual and (middle) long-term timescales. Hatching indicates area where regression is statistically significant at the 95% level. (i) is a comparison between long-term clear-sky LR + WV and RH feedbacks, while (j) is same as Figure 1b except for clear-sky RH feedback.
Interestingly, the spread in global-mean long-term clear-sky LR + WV feedback is partly reduced due to compensation between northern and southern extratropics (Figures 3b and S5b–S5d), with a correlation of −0.74 between corresponding regional average of local feedbacks. Even though there is also substantial hemispheric cancellation in the tropics, a regional-mean regression coefficient of 1.40 presents over tropics. This explains why the spread of global-mean long-term clear-sky LR + WV feedback is considerably smaller than that of interannual counterpart, and why the spread of tropical-mean long-term clear-sky LR + WV feedback is twice as large as that of global-mean feedback.
feedback and RH feedback, as following:
(2)The contribution of local uncertainty to the spread of global-mean LR + WV feedbacks are shown for each component (Figures 3c–3h and S4c–S4h). The decomposition reveals that the large uncertainties in tropical LR + WV feedback comes from intermodel uncertainties in the RH feedback (e.g., Figures 3a, 3b, 3g and 3h). In particular, the spread of global-mean clear-sky feedback is dominated by differences in the tropical RH feedback, with a correlation of 0.94 (0.98) between long-term, global-mean (tropical-mean) clear-sky LR + WV and RH feedbacks (Figure 3i). The high correlation over tropics is consistent with Vial et al. (2013) and Po-Chedley et al. (2018). For the same reasons mentioned in Section 3.1 regarding the LR + WV feedback, the RH feedback also cannot be constrained with observations (Figures 3j and S7).
The local, offsetting extratropical contributions to the global-mean long-term clear-sky LR + WV feedback spread mostly come from local uncertainties of the WVuniform feedback (Figures 3b and 3d). The interhemispheric asymmetry of WVuniform contribution pattern also partly reflects a meridional warming asymmetry. Meanwhile, signals are weak in the contribution pattern of clear-sky 
feedback (Figures 3e, 3f and S6b). Similar patterns of local contribution occur under all-sky conditions (Figures S4c–S4h), except for the enhanced 
feedback contribution, which correspondingly weakens the offsetting extratropical all-sky LR + WV feedback contributions (Figures S4b and S5f–S5h). The enhanced 
feedback contribution is because the sensitivity of radiative flux to upper-tropospheric temperature and humidity anomalies amplifies under all-sky conditions (e.g., Soden et al., 2008). Especially, there are noticeably larger positive contributions from local uncertainties of long-term all-sky 
feedback over northern extratropics (Figure S4f), compared to those under clear-sky conditions (Figure 3f). This is due to a negative covariation (
) between warming extents over northern extratropics and tropics (Figures 3d and S4d). The negative covariation amplifies the all-sky 
feedback uncertainty over northern extratropics and its contribution to the global-mean all-sky LR + WV feedback spread (Text S1).
Our findings, in part, differ from the CMIP5 analyses by Po-Chedley et al. (2018). First, they showed that local feedback spread over southern extratropics drives the model variability in global-mean long-term all-sky 
feedback, while we find most of these uncertainties occur in northern extratropics across CMIP6-era models and contribute more to the global-mean all-sky LR + WV feedback spread. Additionally, the uncertainty in clear-sky LR + WV feedback largely comes from tropics (Figures 3a, 3b, 3g, and 3h), where local relative humidity responses exhibit the largest intermodel disagreement. The corresponding RH feedback uncertainty also plays a secondary role in determining all-sky LR + WV feedback spread (Figure S6f). However, it should be noted that the local feedback calculation is different, as their calculations use local surface temperature anomalies instead of global-mean surface temperature anomalies and thus are more strongly influenced by local warming asymmetries (Feldl & Roe, 2013; Text S2).
The question then arises: Do differences in warming patterns modify these climate feedbacks? To answer this question, we extend our analysis to uncertainties in local surface temperature sensitivities, which is calculated by regressing time-evolving abrupt-4xCO2 local surface temperature against global-mean surface temperature and will be referred to as “warming pattern” hereafter. By adopting the same analysis method (Equation 1) to warming patterns against the global-mean long-term feedbacks, we find the long-term cloud feedback spread has an interhemispheric-asymmetric dependence on the warming pattern uncertainty (Figure 4a). The positive contribution over southern extratropics is likely driven by low cloud thermodynamic and stability mechanisms affecting shortwave cloud feedback (Figures 2d and S3d; Bretherton, 2015; Klein & Hartmann, 1993; Qu et al., 2015; Wood & Bretherton, 2006), while the negative contribution over north Pacific could be attributed to divergent low cloud responses to different jet shifts (Zelinka et al., 2018), which are determined by local warming gradient (Yang et al., 2002). In contrast, the spread of long-term LR + WV feedbacks is driven by an opposite meridional asymmetry (Figures 4b, S8b, S9c and S9f). This is consistent with the above-mentioned uncertainty contribution pattern of the WVuniform feedback. The most noticeable contribution occurs over Southern Ocean (Figure 4b), where uncertainty in ocean heat uptake plays an essential role in manipulating the regional warming extent, as shown in Po-Chedley et al. (2018). Decomposing the LR + WV feedback further, we find warming pattern uncertainty modifies the overall LR + WV feedback largely via its effect on the RH feedback (Figures S8a, S8b, S8g and S8h). Its effect on the all-sky 
feedback also contribute to the LR + WV feedback spread, although there is a cancellation between its effect on WVuniform and 
feedbacks, caused by the opposite contribution from tropical warming extent (Figures S8a–S8f; Soden & Held, 2006). Finally, we note that the opposite dependences of cloud and LR + WV feedbacks on warming patterns ultimately lead to a statistically significant negative correlation between these two feedbacks (Caldwell et al., 2016). It mostly comes from the negative correlation between cloud and RH feedbacks (Figure S10).
Cross-model regressions of local surface temperature sensitivity to global-mean long-term (a) cloud and (b) clear-sky LR + WV feedbacks. Hatching indicates area where regression is statistically significant at the 95% level.
4 Conclusions and Discussion
Here we attempt to observationally constrain the long-term cloud and LR + WV feedbacks in an effort to reduce their intermodel uncertainties. The results indicate that observed interannual variation provides a useful constraint to narrow the uncertainty in global-mean long-term cloud feedback. Similar regional uncertainty contributions on both interannual and long-term timescales reflect a consistent behavior of low cloud changes and bolster the effectiveness of the observed constraint. In contrast, the long-term LR + WV feedback cannot be constrained with observations of interannual variability. This arises for two reasons: (a) the spread of global-mean long-term LR + WV feedback is only half as large as that of interannual feedback; and (b) the observed uncertainty from individual observation nearly equals to the intermodel spread of global-mean interannual LR + WV feedback. Additionally, there is a large discrepancy among different observations and reanalyses products on the value of interannual LR + WV feedback. The spread of global-mean long-term clear-sky LR + WV feedback is largely determined by the tropics, where the largest contribution comes from the uncertainties in the local RH feedback, with a remarkably high correlation between clear-sky LR + WV and RH feedbacks. The RH feedback spread, which also plays a secondary role in determining all-sky LR + WV feedback spread, is shown to be associated with model differences in interhemispheric warming asymmetry, induced primarily by Southern Ocean heat uptake differences. Meanwhile, the all-sky 
feedback uncertainty, which is larger than its counterpart under clear-sky conditions, largely determines the global-mean long-term all-sky LR + WV feedback spread and is substantially caused by the negative covariation between warming extents over northern extratropics and tropics.
While the pattern of local warming contribution to the global-mean long-term LR + WV feedback suggests Southern Ocean heat uptake plays a role in uncertainty, a direct connection is not immediately obvious. For example, less warming due to more Southern Ocean heat uptake should lead to a smaller local LR + WV feedback, not the larger global-mean LR + WV feedback as we find. Hence, Southern Ocean heat uptake likely exerts its impact on the global-mean LR + WV feedback in indirect ways, for instance by suppressing ocean heat uptake and leveraging a larger fraction of surface warming over northern extratropics via a weakened Atlantic meridional overturning circulation. This linkage is supported by a strong correlation of −0.84 between warming extents over southern and northern extratropics, suggesting a robust heatsink seesaw between these regions. Hence, the warming pattern shows broadly consistent signal over southern extratropics, instead of dipole pattern related to subdued warming (Armour et al., 2016). The warming pattern difference could be further attributed to salinity differences, which are primarily induced by varying difference between precipitation and evaporation (e.g., Liu et al., 2020). Finally, the amplifying meridional warming asymmetry could lead to a shift in Intertropical Convergence Zone, thereby modifying the LR + WV feedback (Text S3).
Acknowledgments
The authors thank Stephen Po-Chedley and two anonymous reviewers for providing helpful feedback on the manuscript. H. He and B.J. Soden are supported by NASA award 80NSSC18K1032. R.J. Kramer is supported by an appointment to the NASA Postdoctoral Program administered by Universities Space Research Association.
Conflict of Interest
Authors have no competing interests.
Open Research
Data Availability Statement
The CMIP6 data are available at https://esgf-node.llnl.gov/search/cmip6/. The CMIP6 models used in this work are listed in Tables S1 and S2. The CERES radiative flux observations are available at https://ceres.larc.nasa.gov/data/#ebaf-level-3. The GISTEMP is available at https://data.giss.nasa.gov/gistemp/. The ERA5 reanalysis data are available at https://cds.climate.copernicus.eu/cdsapp#!/dataset/reanalysis-era5-pressure-levels-monthly-means?tab=overview. The AIRS temperature and water vapor observations and the MERRA-2 reanalysis data are available at https://disc.gsfc.nasa.gov/datasets/AIRS3STM_006/summary?keywords=AIRS and https://disc.gsfc.nasa.gov/datasets/M2IMNPASM_5.12.4/summary?keywords=MERRA2, respectively. The CloudSat/CALIPSO radiative kernels used in this study and related code for applying them are available at https://climate.rsmas.miami.edu/data/radiative-kernels/.
