Top of the Atmosphere Shortwave Arctic Cloud Feedbacks: A Comparison of Diagnostic Methods

The cloud feedback may result in amplification or damping of Arctic warming. Two common techniques used to diagnose the top‐of‐the‐atmosphere cloud feedback are the Adjusted Cloud Radiative Effect (AdjCRE) method and the Cloud Radiative Kernel (CRK) method. We apply both to CMIP5 and CMIP6 model data, finding that the AdjCRE calculated Arctic shortwave cloud feedback is twice as correlated with sea ice loss in CMIP5, and four times in CMIP6, as the CRK method. We find that the CRK method produces Arctic all‐sky residual percentages exceeding 20% in 15 of 18 models. We use the CRK method to decompose the feedback in CMIP5 and CMIP6 finding that its median value changed from negative to positive driven by a less‐negative cloud optical depth feedback. Despite its lack of closure, we conclude that the CRK method is better suited for Arctic SW feedbacks as it is less impacted by surface albedo changes.


Introduction
The Arctic region is and will continue to experience warming two to four times the magnitude of that seen at lower latitudes (P.C. Taylor et al., 2021;Rantanen et al., 2022).A warming Arctic can impact continental temperatures and weather conditions (Cohen et al., 2020), and will result in rising sea levels (Box et al., 2022).This phenomenon of exaggerated polar warming is called Arctic amplification.The uncertainty in Arctic climate projections is greater than that of any other region on Earth (D. M. Smith et al., 2019) and is largely due to difficulties in quantifying the cloud response to surface temperature warming, known as the cloud feedback (Hahn et al., 2021;Previdi et al., 2021).
The value of the Arctic cloud feedback is highly uncertain and may be positive or negative (Forster et al., 2021).Two contributors to the uncertainty in the modeled cloud feedback are the lack of reliable and consistent observations of both macrophysical and microphysical Arctic cloud properties, and, as we will demonstrate, uncertainty introduced by the feedback calculation method itself.Considering observations of Arctic cloud properties, the accuracy of passive satellite retrievals is impacted by a lack of thermal and visible contrast in the Arctic (Liu et al., 2009), and active observations suffer from reduced spatial and temporal coverage, beam attenuation (Winker et al., 2009) and ground clutter (Blanchard et al., 2014).Additionally, in situ field campaigns are limited due to harsh environmental conditions.These issues lead to disparate representations of microphysical processes that contribute to uncertainty in the modeled cloud feedback (Gettelman & Sherwood, 2016).In addition to these difficulties, the uncertainty in the modeled cloud feedback caused by the method used to diagnose it is not well quantified in the Arctic.For example, it is unclear whether the Arctic cloud feedback value of 0.01 ± 0.05 Wm 2 K 1 estimated in the IPCC AR6 is biased due to the combination of methods used to derive it (Forster et al., 2021).
Multiple ways to diagnose the cloud feedback exist.Two commonly used techniques are the Adjusted Cloud Radiative Effect (AdjCRE) method (Shell et al., 2008), and the Cloud Radiative Kernel (CRK) method (Zelinka et al., 2012).The AdjCRE method calculates the effect of clouds on the top-of-the-atmosphere (TOA) radiative balance and then modifies this cloud radiative effect (CRE) by the impact that clouds have on non-cloud feedbacks.This is an attempt to account for non-linear interactions between these variables.The CRK method uses joint histograms of cloud top pressure (CTP) and visible cloud optical depth (COD) in accordance with the International Satellite Cloud Climatology Project (ISCCP) data set to calculate the cloud feedback directly from cloud property changes.The AdjCRE method has the advantage of being applicable year round in the Arctic, while the CRK method is unavailable during polar night due to the absence of visible COD.The CRK method has the advantage of being able to decompose the cloud feedback into impacts of CTP, COD, and cloud fraction (CF), while the AdjCRE method cannot.Another method to calculate the cloud feedback is that of Partial Radiative Perturbation (PRP) (Wetherald & Manabe, 1988), which, while being more accurate than the methods considered in this study, is not feasible for intermodel comparison due to its high computational costs and storage requirements.Neural networks have recently been used to perform PRP calculations (Zhu et al., 2019), with potential applications for evaluating the non-linear interactions in the Arctic (Huang et al., 2021).
To our knowledge, there does not exist a dedicated comparison between the AdjCRE and CRK methods with a specific focus on the Arctic.Additionally to our knowledge, there has not yet been a dedicated comparison of Arctic cloud feedbacks in the fifth and sixth eras of the Coupled Model Intercomparison Project (CMIP5 and CMIP6).In this paper we first compare the shortwave (SW) cloud feedback in the Arctic as calculated by the AdjCRE and CRK methods, and investigate the influence of sea ice loss on this feedback in each method.Then, we evaluate the radiative closure provided by the CRK method in the Arctic.Finally, we use the CRK method to decompose the SW Arctic feedback in a suite of CMIP5 and CMIP6 models to investigate changes between eras.While Hahn et al. (2021) use the AdjCRE method to compare the cloud feedback in CMIP5 and CMIP6, our study differs in that we use the CRK method to decompose this feedback into constituent parts.

Methods
Our analysis is performed in 8 global climate models (GCMs) participating in CMIP5 and 10 GCMs from the more recent CMIP6 (Tables 1 and S1 in Supporting Information S1).All CMIP6 feedbacks were calculated over 150 years of simulated data comparing climate scenarios with pre-industrial levels of carbon dioxide (piControl) and an instantaneous quadrupling of that concentration (4 × CO 2 ).These levels were then held constant over the entire simulation (Eyring et al., 2016).In CMIP5 the feedbacks were calculated using 20 years of data at the beginning and end of a 140 year period due to the availability of simulated satellite cloud observations formatted according to ISCCP standards (K.E. Taylor et al., 2012).In HadGEM2 the two periods of available data were only 19 years long and in CCSM4 the end of the second period was only 104 years after the beginning of the first.Figure S8 in Supporting Information S1 tests the impact of having two 20 year periods instead of 150 years of continuous climate data and finds no qualitative difference in our results.The models included in this study were selected because they provide output generated by the Cloud Feedback Model Intercomparison Project (CFMIP) Observation Simulator Package (COSP) (Bodas-Salcedo et al., 2011), which offers a consistent definition of ISCCP simulated cloud observations.

The AdjCRE Method
We use the radiative kernel method (Shell et al., 2008) to calculate the non-negligible SW feedbacks (albedo and water vapor) in the Arctic from the TOA perspective.In the context of this study the Arctic is defined as the region northward of 60°N.The anomaly in the albedo and specific humidity between the 4 × CO 2 and piControl simulations are multiplied by the response in the TOA radiation budget to a unit change in these variables and then regressed against the global near-surface temperature change to calculate their respective feedback parameters (Gregory et al., 2004).These feedbacks are then summed with the SW cloud feedback and a residual term to obtain the full SW feedback parameter, as in Geophysical Research Letters where λ SW is the total SW feedback parameter in Wm 2 K 1 , R is the radiative budget at the TOA in Wm 2 , α is the albedo, T s is the globally averaged near-surface temperature in K, q is the specific humidity in gkg 1 , λ CSW is the SW cloud feedback in Wm 2 K 1 , and Re is the residual, also in Wm 2 K 1 , which includes higher order interactions between the other feedback parameters in the Taylor series expansion of λ SW .The natural logarithm is applied to the specific humidity as the radiative absorption of water vapor scales with this value (Raval & Ramanathan, 1989).The Δ indicates the warming perturbation anomaly, or the difference in each variable between 4 × CO 2 and piControl scenarios.The ∂R ∂x part of each term is the "radiative kernel" and encodes the radiative response to changes in the desired climate variable, x.The kernels calculated in Huang et al. (2017) are used in this analysis due to the smaller residual terms they produce (Zelinka et al., 2020).
We then use the albedo and water vapor feedbacks to diagnose the Arctic SW cloud feedback with the AdjCRE method at the TOA in each model in both CMIP5 and CMIP6.The AdjCRE feedback consists of two parts, the

Geophysical Research Letters
10.1029/2023GL107780 change in the CRE between the perturbed and control scenarios as can be seen in the first term on the right hand side (RHS) of Equation 2, and the adjustments to this ΔCRE, which are the second and third terms on the RHS of where ΔR CSW is the adjusted SW CRE at the TOA, the subscripts AS and CS indicate "all-sky" and "clear-sky" cases respectively, and the subscript SW indicates that we focus entirely on the SW cloud feedback.This focus is due to the larger magnitude of the SW feedback compared to the longwave (LW) feedback in sunlit seasons (spring and summer) when both the AdjCRE and CRK methods are available.Linear regression against the globally averaged ΔT S is then performed on ΔR CSW to obtain the cloud feedback (λ CSW , Equation 1).The adjustments represent the cloudy-sky albedo and SW water vapor feedbacks, and subtracting them from ΔCRE SW is an attempt to isolate and remove the cloud masking of non-cloud radiative feedbacks (Shell et al., 2008;Soden et al., 2008).There is no need to include the cloud masking of the CO 2 forcing, as this is primarily a LW radiative effect.Data during Arctic night is manually excluded from calculations using the AdjCRE method to make consistent comparisons with the CRK method.Partial data unavailability begins in September and increases until the winter solstice, and then decreases until late March.

The CRK Method
The CRK method bypasses the consideration of the CRE and treats directly with changes in CTP, COD, and CF by calculating the TOA radiative impact of changes in these properties as where ΔR CSW is the change in the TOA radiative balance as caused by the ΔC change in cloud properties between the 4 × CO 2 and piControl scenarios, multiplied by the kernel K, where all variables in this equation are formatted as ISCCP joint CF histograms of COD and CTP.The CRKs used in this study are originally provided on a latitude and surface albedo grid and must therefore be mapped to a latitude and longitude grid using the clear-sky albedo in the control scenario (Zelinka et al., 2012).This ΔR CSW is then linearly regressed against the globally averaged ΔT S to obtain the cloud feedback.

Radiative Closure Calculations
In order to evaluate the accuracy of our clear-sky feedback and CRK cloud feedback calculations, we diagnose the residual percentage provided by these calculations.The decomposition of the total SW feedback parameter in Equation 1 is predicated on the linearity of the individual climate feedbacks.The residual encapsulates errors in this decomposition where the cloud masking effect is the dominant source of non-linearity in the Arctic SW feedback, particularly in large perturbation experiments such as that considered here.While it is obvious how cloud masking manifests itself in the AdjCRE feedback (Equation 2), the CRK method does not avoid the impacts of cloud masking (Sections 2.2 and 3.2) so it is necessary to evaluate its ability to provide radiative closure at the TOA in the Arctic.This was done by comparing the sum of the individual feedback parameters in Equation 1 to the feedback parameter generated by the SW TOA radiative fluxes output by each model, following Jonko et al. (2012), where the subscript m refers to model fluxes and k to kernel derived.The SW Re% in the Arctic was calculated in both the clear-sky and all-sky cases, with the all-sky case using the CRK cloud feedback.The all-sky residual calculated with the AdjCRE is not included in this analysis as it reduces to the clear-sky residual.

The Influence of Sea Ice Anomaly on the Cloud Feedback
A main point of deviation between the two methods is their representation of the SW cloud feedback over the Arctic Ocean (Figure 1).This difference is pronounced in the spring and summer seasons due in part to the lack of available data in the autumn and winter seasons.Ensemble averages of the three terms on the RHS of Equation 2suggest that this deviation is caused by cloud masking of the albedo feedback (Figures S5, S6, S7 in Supporting Information S1).This is manifested in ΔCRE SW of Equation 2 where large and negative albedo anomalies introduce a negative bias to the CRE (Figure S5 in Supporting Information S1).The first adjustment term in Equation 2 seeks to mend this by subtracting the cloudy sky albedo feedback from the ΔCRE SW (Figure S6 in Supporting Information S1).However, in the Arctic this adjustment is too small to fully account for the negative bias introduced by the sea ice loss associated with the 4 × CO 2 perturbation.The cloud masking of the water vapor feedback is positive and too small to be responsible for the bias seen in the cloud feedback as calculated by the AdjCRE method (Figure S7 in Supporting Information S1).
We quantify the influence of surface albedo changes on the cloud feedback as calculated by the AdjCRE method for each model using Pearson product-moment coefficients of linear correlation between the cloud feedback and the sea ice anomaly (Table 1).Across models in the annual, spring (MAM), and summer (JJA) averages, the AdjCRE method provides more consistently large and positive covariance between the SW cloud feedback and sea ice anomaly than the CRK method.The largest exceptions to this are the HadGEM2 and CCSM4 models.In the AdjCRE feedback in HadGEM2 a large and negative correlation during the spring results in a near zero annual correlation, and in CCSM4 correlations across the annual, spring, and summer averages are positive but generally low.
HadGEM2 produces the largest annual clear-sky, all-sky, and cloudy-sky albedo feedbacks of any model across both CMIP5 and CMIP6, despite simulating a sea ice anomaly that is larger than other CMIP5 models but typical for the CMIP6 ensemble (not shown).The large magnitude of the cloudy-sky albedo feedback relative to the clear-sky term indicates a strong adjustment to the ΔCRE due to an increase in cloud reflectivity alongside sea ice loss.This may be linked to the high ratio of ice particles to liquid water in Arctic mixed phase clouds as represented by HadGEM2 (Cesana et al., 2015), which would result in a large cloud phase feedback, in which the supercooled liquid water content in mixed phase clouds increases in a warming climate, increasing their optical depths (Tan et al., 2016).The transition from ice in the piControl to liquid dominated Arctic mixed phase clouds in the 4 × CO 2 scenario increases the reflectivity and lifetime of these clouds, decreasing the amount of sunlight reaching the Arctic surface.CCSM4, on the other hand, produces the smallest annual clear and all-sky albedo feedbacks in both CMIP5 and CMIP6 as a result of having the smallest sea ice anomaly between piControl and 4 × CO 2 scenarios (not shown).These relatively small albedo feedbacks mean that cloud masking effects do not have as large of an impact on the CRE, resulting in generally low correlation coefficients between the cloud feedback and the sea ice anomaly.
The annual ensemble averaged Pearson coefficient for the AdjCRE method is twice as large as that of the CRK method in CMIP5, and four times as large in CMIP6, most likely due to the greater sea ice loss in CMIP6.Additionally, every AdjCRE ensemble average Pearson coefficient is larger than its seasonal counterpart for the CRK method, and the smallest average AdjCRE coefficient in the sunlit seasons (0.50 in CMIP5 spring) is larger than the largest CRK coefficient in any season (0.41 in CMIP6 spring).Such high correlation coefficients between the AdjCRE method and sea ice anomaly are unreasonable.Large and positive correlation coefficients imply that areas of sea ice loss are collocated with large and negative SW cloud feedback, and we are unaware of any strongly negative cloud feedback that encourages sea ice loss.
Conversely, sea ice loss can result in increases in cloud fraction and cloud optical depth (Tan et al., 2023) via local aerosol production (Ridley et al., 2016), or decreases in lower tropospheric stability (P.C. Taylor et al., 2022).However, the disparate representations of these processes in models (Schmale et al., 2021;P. C. Taylor et al., 2019) and the seasonality of the cloud response to sea ice loss (Kay & Gettelman, 2009) suggests that they would not result in a large bias.This leads us to the conclusion that the most plausible explanation for the observed correlation between the AdjCRE feedback and sea ice anomaly is the cloud masking of the albedo feedback.

Radiative Closure
We further evaluate the accuracy of our CRK feedback calculations by considering the radiative closure they provide at the TOA.Radiative closure is evaluated by examining the magnitude of the residual percentage, Re%, in Equation 4. Previous studies have shown that the Re% of the sum of the SW and LW feedback parameters in clear-sky conditions for a doubling of CO 2 has a value of approximately 10% on a global scale (Jonko et al., 2012;Soden et al., 2008).This is the threshold for clear-sky linearity, and has been used as a check for the accuracy of the radiative kernel decomposition in CO 2 doubling and quadrupling scenarios (Shell et al., 2008;Virgin et al., 2021).While this threshold was originally calculated for clear-sky conditions considering both SW and LW feedbacks, it has also been analogously used to check the linearity of all-sky rapid adjustments in the SW with no modification to its 10% value (C.J. Smith et al., 2020).We expect our calculations to result in Re% values that exceed 10% due to the regional focus of our analysis, however the Re% is still a relevant metric when considering the closure of the TOA energy budget.We calculated the clear and all-sky SW Re% in all models (Figure 2).
All CMIP6 clear-sky Re% values indicate acceptable closure of the TOA radiative budget, and the same can be said for all but the HadGEM2 and CCSM4 models in CMIP5.In HadGEM2 the kernel derived feedback parameter overestimates the model flux calculated parameter, while in CCSM4 the opposite is true.This discrepancy is driven by the clear-sky albedo feedback in each model, with HadGEM2 producing the largest feedback across all CMIP5 and CMIP6 models, and CCSM4 producing the smallest.The Re% values provided by the CRK method, which exceed 20% in 15 of 18 models across CMIP5 and CMIP6, indicate that the CRK calculated all-sky SW feedback parameter provides poor radiative closure in the Arctic in the majority of the models included in this study.
The poor radiative closure of the CRK method is expected in high climate forcing scenarios, and is due to inaccuracies in the kernel method and the CRK technique.Neglecting higher order terms in the Taylor series expansion of λ SW is inaccurate for large perturbations such as a quadrupling of CO 2 (Jonko et al., 2012).Additionally, the kernel is calculated using the control climate (Shell et al., 2008), and multiplying by an anomaly from the perturbed climate becomes less accurate for larger perturbations.Mapping the cloud kernels from their latitude/albedo space introduces extra inaccuracy to the CRK method specifically.Additionally, the CRK method relies on COSP simulator data which has the same limitations as actual satellite retrievals in the Arctic (Bodas-Salcedo et al., 2011;Schiffer & Rossow, 1983).Despite this, satellite simulators are necessary when using the CRK method due to the uncertainty introduced by overlap assumptions (Zelinka et al., 2012).These issues can result in poor radiative closure in high perturbation simulations in the Arctic using the CRK method.

Cloud Feedback Decomposition in CMIP5 and CMIP6
We use the CRK method to decompose the SW Arctic cloud feedback to gain insight into individual cloud property feedbacks bearing in mind that it results in poor radiative closure.For the purposes of this study we neglect discussion of the CTP feedback as it was near zero across models and seasons (Figure S2 in Supporting Information S1).In general, decreasing CF results in a positive SW feedback as reduced cloud cover allows for increased absorption of solar energy at the surface (Hansen et al., 1984).Also generally, increasing COD results in a negative SW feedback as clouds become more reflective at higher optical depths (Paltridge, 1980).
The median SW Arctic cloud feedback in the CMIP6 models included in this study is slightly positive, in contrast to its slightly negative value in CMIP5 (Figure 3).This agrees with previous work (Zelinka et al., 2020), that calculated the SW cloud feedback using the Approximate Partial Radiative Perturbation technique (K.E. Taylor et al., 2007).In Hahn et al. (2021), who used the AdjCRE method, the Arctic cloud feedback is found to be less negative in CMIP6 than CMIP5 and they speculate that this is driven by less negative SW COD and CF feedbacks, which is partially supported by our decomposition.
We find that the change from negative to positive is largely driven by an increase in the COD feedback from CMIP5 to CMIP6 in every season excluding winter during which the feedback is nearly nonexistent due to the lack of sunlight.The increase in the COD feedback may be linked to a less negative cloud phase feedback as discussed in Tan et al. (2016), resulting from the improved parameterization of supercooled liquid water in mixed phase clouds that are pervasive in the Arctic (Bodas-Salcedo et al., 2019;Kawai et al., 2019;Zhang et al., 2019).This link is supported by the large increase in the summer COD feedback, as the weakening of the cloud phase feedback is expected to be particularly intense in this season (Tan et al., 2022).

Geophysical Research Letters
10.1029/2023GL107780 The median value of the CF feedback increases from CMIP5 to CMIP6 in the sunlit seasons, but sees a slight decrease in the annual average.Aside from one outlier, the summer CF feedback is robustly positive across models in CMIP6, which is a change from CMIP5.Ensemble average polar plots of the CF feedback in CMIP5 and CMIP6 suggest that the summertime increase is mostly seen over Arctic landmasses rather than the Arctic ocean (Figure S3 in Supporting Information S1).Our results suggest that the process of tropospheric drying under global warming conditions that may reduce total tropical continental cloud amount (Kamae et al., 2016) could also apply in the Arctic.
There is no uniform change in intermodel spread from CMIP5 to CMIP6.In the COD feedback the total spread generally increases or has no change depending on the season, with the opposite being true for the CF feedback.In the total SW feedback as calculated by each method increases and decreases are seen depending on the season (Figure 3).Previous work has shown that there is an increase in the intermodel spread of both the equilibrium climate sensitivity and global SW cloud feedback from CMIP5 to CMIP6 (Zelinka et al., 2020), and while this

Geophysical Research Letters
10.1029/2023GL107780 may be borne out in the Arctic there is no signal of it in our work.However, this may be due to the relatively smaller sample size being considered, with Zelinka et al. (2020) employing 28 CMIP5 and 27 CMIP6 models while we use 8 and 10 models respectively.
Finally, the AdjCRE feedback underestimates the Arctic cloud feedback as compared to the CRK method across seasons in both model eras, except for in autumn of CMIP6 (Figure 3).This is due to the negative bias introduced to the AdjCRE method by the sea ice anomaly via cloud masking effects.This link is supported by the largest discrepancy between the median of the CRK and AdjCRE calculated feedbacks being seen in the spring of CMIP6, the season with the largest ensemble average sea ice anomaly across both model eras (Figure S1 in Supporting Information S1).This differs from the conclusion in Zelinka et al. (2012) where the AdjCRE method is found to generally overestimate the CRK method.This disagreement may be related to the fact that Zelinka et al. ( 2012) has a global focus and discards grid cells with 90th percentile and higher surface albedo anomalies.
Despite their disagreement on the value of the feedback, both methods show that the annual and summertime median total SW Arctic cloud feedback increased in CMIP6 as compared to CMIP5.

Conclusions
The Arctic SW cloud feedback as calculated by the AdjCRE technique spatially covaries with sea ice changes twice as strongly as that calculated by the CRK method in CMIP5 and four times as strongly in CMIP6.This is due to the influence of cloud masking effects, which result in a negative bias in the feedback as calculated by the AdjCRE method compared to the CRK method.Despite the fact that it is less impacted by sea ice changes, the CRK method does not provide closure of the TOA SW radiative budget in the Arctic, with all-sky Re% values larger than 20% in 15 of 18 models across CMIP5 and CMIP6.This is likely due to the strong non-linear interactions between the cloud and albedo feedbacks in the Arctic that are not completely eliminated even in the CRK method (Section 3.2).Considering the limitations of both methods, the CRK method is better suited to calculating SW Arctic cloud feedbacks because, while it has a variety of inaccuracies that are exaggerated in large perturbation scenarios, it is not as impacted by surface albedo changes as the AdjCRE method.
A potential avenue of improvement to the CRK method would be to develop a new set of kernels based on the Moderate Resolution Imaging Spectroradiometer (MODIS) histograms.While this instrument still relies on passive remote sensing techniques, its retrieval uses more spectral information than ISCCP which should result in improved accuracy (Pincus et al., 2012).MODIS also separates cloud retrievals by phase, however, this feature is not included in the MODIS simulator provided by COSP (Bodas-Salcedo et al., 2011).While some work has already been done in the development and usage of CRKs for the surface and TOA perspectives using MODIS (Wall et al., 2022;Zhou et al., 2022), a dedicated comparison between ISCCP and MODIS CRK calculated feedbacks could shed light on the accuracy of the CRK method in the Arctic.
Due to its ability to decompose the cloud feedback we still use the CRK method, with caveats in mind, to investigate changes in the SW Arctic cloud feedback between CMIP5 and CMIP6.Our work has shown that the median SW cloud feedback in the annual average is slightly positive in CMIP6, a change from slightly negative in CMIP5.This change is driven largely by a less-negative COD feedback, which may be tied to reduced supercooled liquid water biases in the model representation of Arctic mixed phase clouds.There is also an increase in the median value of the CF feedback during the sunlit months, with the summertime increase being largely driven by changes over Arctic landmasses.While the AdjCRE method has a negative bias as compared to the CRK method, it produces a similar increase in the annual and summertime median SW Arctic cloud feedback from CMIP5 to CMIP6.
The IPCC AR6 asserts that the cloud feedback is one of the largest sources of uncertainty in Arctic climate projections (Forster et al., 2021).Their estimates do not account for uncertainties and biases associated with the method of calculating this feedback.Our work demonstrates the need to exercise caution in interpreting cloud feedback values depending on the method employed in their estimate.

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The Cloud Radiative Kernel method provides poor radiative closure in a suite of global climate models • The median shortwave Arctic cloud feedback in recent climate models is slightly positive due to a weakened cloud optical depth feedback Supporting Information: Supporting Information may be found in the online version of this article.

Figure 1 .
Figure 1.Ensemble average total SW Arctic cloud feedback broken down by season in both CMIP5 and CMIP6.The magnitude of the spring and summer feedbacks are generally larger than autumn and winter, resulting in dissimilar colorbar ranges.The ensemble averaged Pearson pattern correlation coefficients of the depicted feedback and the same season's sea ice concentration anomaly are included at the top of each polar plot.

Figure 2 .
Figure2.Clear and all-sky SW residual percentages of the SW feedback parameter in CMIP5 and CMIP6 in the Arctic.The all-sky residual percentage was calculated using the SW cloud feedback as diagnosed with the CRK method.

Figure 3 .
Figure3.Cloud feedback decomposition performed by the CRK method, accompanied by the total cloud feedback calculated by both the CRK method and the AdjCRE method, broken down by season in both (a) CMIP5 and (b) CMIP6.The lower whisker of each box is the minimum value of the ensemble, while the upper whisker is the maximum, excluding outliers.The bottom edge of the box is the first quartile of the ensemble, and the top is the third quartile, while the middle line represents the median value.Outliers were defined as values exceeding 1.5 times the interquartile range, or distance between the first and third quartiles.