Machine-learning emergent constraints on surface albedo feedback over Arctic land regions

Domain: neuroscience
Published: 2026-04-10
Editorial outcome: major_revision

Abstract
Surface albedo feedback (SAF) amplifies warming in northern high latitudes, affecting the Arctic climate system, ecosystems, infrastructure, and global trade routes. However, Earth system models (ESMs) exhibit large uncertainties in SAF projections, complicating future Arctic warming estimates. Here, we develop a machine-learning method based on emergent constraints (ECs) and use in-situ observations to constrain SAF projections over Arctic land regions. Our approach leverages a physical relationship between historical albedo-temperature dynamics (1985–2014) and future SAF (2070–2099) across ESM ensembles. The constrained SAF is reduced by 0.29–0.52 W m-2 K-1 across emission scenarios, with uncertainties decreased by 45–55% compared to unconstrained projections. These findings enhance confidence in regional climate projections, offering more precise insights for climate adaptation and policy in vulnerable high-latitude communities.

Introduction
The Arctic is undergoing warming at rates more than twice the global average. This phenomenon is referred to as Arctic amplification; it is reshaping ecosystems, economies, and geopolitics with unprecedented speed1−4. As a result, there is widespread thawing permafrost that destabilizes critical infrastructure—roads, pipelines, and buildings—causing ground subsidence threatening indigenous communities and incurring economic losses projected to reach tens of billions of dollars by 20505,6.

Although the dramatic Arctic sea ice retreat observed since the 1970s has seemingly come to a halt since around 2005, the larger open water regions of the Arctic Ocean provide new opportunities for maritime pathways, such as the Northern Sea Route, potentially slashing transit times between Europe and Asia but raising risks of oil spills, ecosystem disruption, and increased greenhouse gas emissions from shipping2,3. These cascading changes underscore the urgency of understanding the drivers of Arctic warming to improve predictive capabilities to inform adaptation and mitigation strategies.

Arctic warming is driven by several interconnected mechanisms, including surface albedo feedback (SAF), ocean heat transport, lapse rate feedback, cloud feedback and other processes7−9. Central to Arctic amplification is the SAF, which is a critical mechanism amplifying warming over both land and ocean10−13. As global temperatures rise, melting snow and ice reduce surface reflectivity (albedo), allowing darker surfaces—open water or bare soil—to absorb more solar radiation, which further accelerates warming in a self-reinforcing loop12−17. Over northern high-latitude land areas, this feedback is driven by shrinking snow cover and vegetation changes, such as the greening of tundra into shrublands, which darken the surface and enhance absorption of solar radiation increasing the surface temperature18−21. SAF plays a critical factor in projections of Arctic land warming, yet its representation in Earth system models (ESMs) remains fraught with uncertainty20. ESMs struggle to accurately simulate complex processes and feedback mechanisms like snow metamorphosis, cloud-surface interactions, and vegetation dynamics, often overestimating or underestimating SAF’s strength due to sparse observational data and simplified parameterizations18. These uncertainties translate into divergent warming projections, undermining confidence in model results and complicating policy decisions for vulnerable Arctic regions, where even small temperature changes can trigger tipping points in permafrost stability or sea ice loss.

Emergent constraints (ECs) have proven to be a promising technique for reducing ESM uncertainties by exploiting physically based relationships between observable climate variables and future projections across model ensembles22,23. By anchoring projections to real-world data, ECs can refine estimates of climate processes like SAF, offering a path to more reliable projections22,24. However, traditional EC approaches often assume linear relationships between predictors and predictands,22−24, failing to capture the nonlinear complexities of the Arctic climate system. Moreover, many of these EC methods rely on gridded observational datasets (i.e., satellite or reanalysis products), which suffer from inconsistencies in remote regions like the Arctic due to limited sensor coverage and data interpolation errors9,25, particularly for land surface albedo26−28. As such, a low coefficient of determination (R2) less than 0.5 is often reported by previous ECs23,29−37. Lack of out-of-sample tests and verifications also cast doubt on the confidence of the constraints24,38−40. These limitations reduce the robustness and effectiveness of conventional ECs, leaving significant gaps in our ability to constrain SAF and predict accurate warming trajectories.

In this study, we address these challenges by developing a machine-learning method based on emergent constraints (ECs) to constrain SAF projections over Arctic land areas (defined by latitudes larger than 60°N). We identify physical and robust relationships between historical surface albedo-temperature dynamics and future SAF across ESMs from Coupled Model Intercomparison Project Phase 6 (CMIP6), based on which future SAF is constrained by leveraging high-quality in-situ observations of surface albedo and near-surface air temperature. Our approach overcomes the shortcomings of linear ECs and gridded observational datasets by using machine-learning to capture complex interactions and by basing our constraints on direct measurements from flux networks, which avoid the uncertainties related to satellite retrievals or reanalysis products. The revealed emergent relationships are carefully confirmed via out-of-sample tests, leave-one-out tests and verified against in-situ observations. By significantly reducing model uncertainty, we provide more precise estimates of SAF projections, which has great implications for climate impact assessment and adaptation planning for policymakers, indigenous communities, and stakeholders in northern high-latitude regions.

Results
Projected changes and uncertainties in surface albedo feedback (SAF)
SAF is driven by two key components: the sensitivity of planetary albedo α to land surface albedo α changes (∂α /∂α ), and the response of α to air temperature T changes (∂α /∂T )10,18. We analyzed these components across four emission scenarios (SSP1-2.6, SSP2-4.5, SSP3-7.0, SSP5-8.5) using a 30-year moving window from 35 CMIP6 ESMs (Supplementary Table 1). The strength of the SAF fluctuates around 1 W m-2 K-1, with statistically significant differences in averages between scenarios (Fig. 1a; Supplementary Fig. 1). In the low-emission scenario (i.e., SSP1-2.6), SAF weakens significantly (p < 0.05) by the late 21st century due to declines in both ∂α /∂α and ∂α /∂T (Figs. 1b, c). Conversely, under SSP2-4.5, a decrease in ∂α /∂T dominantly drives SAF (Fig. 1c). For high-emission scenarios (SSP3-7.0, SSP5-8.5), SAF variations are primarily governed by ∂α /∂T , reflecting changes in snow cover and vegetation dynamics (Figs. 1a–c; Supplementary Fig. 2). These differences arise from scenario-specific greenhouse gas concentration affecting temperature and albedo dynamics after 2035 (Supplementary Figs. 3–5).

Spatially, SAF exhibits positive signals across the region, peaking in Alaska, the Canadian Arctic Archipelago, central and eastern Russia (>1.4 W m-2 K-1 under SSP1-2.6 and SSP2-4.5; Figs. 1d, e). Under SSP3-7.0 and SSP5-8.5, SAF weakens in these areas but intensifies in northwestern Siberia, driven by enhanced vegetation greening and snowmelt (Figs. 1f, g; Supplementary Figs. 6, 7). Similar patterns of SAF were found for the near future period 2040−2069 and projections from Coupled Model Intercomparison Project Phase 5 (CMIP5) (Supplementary Figs. 8, 9). However, ESM uncertainties are substantial, with inter-model standard deviations of 0.46–0.74 W m-2 K-1 (43–81% of ensemble means), particularly in Alaska, eastern Russia, and Greenland (Figs. 1d–g). These uncertainties highlight the need for observational constraints to refine SAF projections.

Emergent constraints on future SAF and the resulting warming rate
To address uncertainties in ESM projections, we developed an emergent constraints (ECs) framework leveraging in-situ observations to refine future SAF estimates over Arctic land areas. We identified a robust negative relationship between historical (1985–2014) response of land surface albedo (α ) to air temperature changes (∂α /∂T ) and future (2070–2099) SAF across the CMIP6 ESM ensemble. Linear regression (LR) yields R² values of 0.28–0.48 (p < 0.05), indicating a moderate correlation, whereas random forest regression (RF) achieves R2 of 0.70–0.88 (p < 0.05), uncovering a stronger, nonlinear connection (Fig. 2a; Supplementary Figs. 10a–c) across different emission scenarios. This suggests that models simulating a higher ∂α /∂T in the history—reflecting greater albedo sensitivity to past air temperature changes—tend to project lower SAF in the future, likely due to stabilizing vegetation dynamics or snow cover limits. This relationship’s strength across SSP1-2.6, SSP2-4.5, SSP3-7.0, and SSP5-8.5 scenarios underscores its robustness, offering a pathway to constrain future projections using in-situ observations of α and air temperature.

The representativeness of in-situ observations is critical for effective constraints. We validated that local ∂α /∂T , derived from flux network sites41−43, correlates strongly with regional ∂α /∂T (R² = 0.59 for LR, 0.85 for RF; Fig. 2b), confirming that these sites capture regional albedo-temperature dynamics44,45. This correlation holds across diverse land cover types, from tundra to boreal forests, enhancing confidence in their applicability. Furthermore, historical ∂α /∂T from flux network sites exhibits a significant (p < 0.05) relationship with future SAF, consistent across emission scenarios (Fig. 2c; Supplementary Figs. 10d–f). The RF model effectively captures sharp transitions in surface albedo, reflecting nonlinear interactions among snow cover, vegetation dynamics, and radiative forcing (r = 0.63−0.83, p < 0.05; Supplementary Figs. 11–13). These transitions are physically plausible, aligning with substantial inter-model spread in temporal variability and thresholds for snowmelt and vegetation greening, where vegetation fluctuations and vegetation–snow interactions emerge as dominant drivers (Supplementary Note 1 and Fig. 14). Subgrouping analysis confirms that removing a small subset of “sharp transition” models would not substantially alter our major conclusions (Supplementary Note 2 and Figs. 15−17). By basing our ECs on high-quality in-situ measurements, we avoid uncertainties inherent in gridded satellite or reanalysis datasets. These findings establish a reliable bridge between past observations and future SAF projections.

Our machine-learning-based ECs using random forest (EC ) transforms SAF estimates and the probability density functions (PDFs) of constrained SAF are statistically different from the raw projections (Kolmogorov−Smirnov test, Supplementary Note 3). Raw CMIP6 models project future SAF at 1.06–1.21 W m-2 K-1 by 2070–2099 across the four scenarios. After applying EC , it decreases to 0.60–0.92 W m-2 K-1, a reduction of 24–46%, revealing systematic ESM overestimation (Fig. 3a). This correction aligns with model biases in snowmelt and vegetation parameterizations (Supplementary Fig. 18), which amplify SAF in unconstrained models. EC also slashes uncertainty by 45–55%, far surpassing linear EC (14–25%) methods (EC ) (Fig. 3b), due to RF’s ability to capture nonlinear interactions. Leave-one-out (LOO) sensitivity tests confirm that neither the emergent relationships nor the constrained SAF estimates are heavily influenced by any individual model, demonstrating strong robustness to model selection (Supplementary Note 4 and Figs. 19−21). These adjustments narrow the range of expected temperature increases32,46−49, offering a clearer picture of future Arctic climate.

Physical mechanisms underlying the emergent constraints
To elucidate the physical basis of the ECs, we applied a piecewise structural equation model (pSEM) based on land surface energy balances (see Methods and Supplementary Note 5). In pSEM, a positive standardized path coefficient (ρ) indicates that an increase in the independent variable drives an increase in the dependent variable, and vice versa. During the historical period, rising greenhouse gas concentrations (CO₂, CH₄, N₂O) significantly increased surface net (downward minus upward) irradiances (R , comprising net surface shortwave radiation; ρ = 0.89, p < 0.05), amplifying near-surface air temperature (ρ = 0.93, p < 0.05; Fig. 4a). This warming altered land surface properties, boosting vegetation (leaf area index, LAI; ρ = 0.96, p < 0.05) and reducing snow cover fraction (SCF; ρ = -0.96, p < 0.05).

These changes drove SAF via α . Decreased snow cover strongly lowered α (ρ = 0.80, p < 0.05), while increased vegetation had a weaker effect (ρ = -0.23, p > 0.05), trapping more energy (R sensitivity to α : -1.79 W m-2 %-1) and further warming the surface, forming a positive feedback loop (Fig. 4a). By 2070–2099, this loop persists across SSP1-2.6 to SSP5-8.5 scenarios (Supplementary Fig. 22), with vegetation’s influence on α strengthening (ρ = -0.33, p < 0.05) and snow’s weakening (ρ = 0.69, p < 0.05; Fig. 4b). Thus, historical and future SAF share consistent physical drivers—snowmelt and greening—explaining the robust EC relationship across diverse ESM parameterizations (Figs. 4c, d).

Out-of-sample tests, alternative periods (1975−2004, 2040–2069), choice of flux stations and CMIP5 ensembles confirm EC’s robustness (Supplementary Note 6, Figs. 23–26, Table 2). By capturing these mechanisms, EC corrects future SAF overestimations by 24–46%, enhancing Arctic warming projection accuracy.

Verification of the emergent constraints
Debates on EC’s robustness have intensified due to limited validation24,38−40, since there are no observations for the future climate. To address this, we conducted a two-stage cross-validation, training ECs on ESMs output during 1985–1999 and verifying their performance against in-situ observations during 2000–2014. We compared our machine-learning-based EC (EC ) with the traditional linear EC (EC ), which assumes a linear predictor-predictand relationship as previously developed22,31. Both EC (R² = 0.80) and EC (R² = 0.39) show strong predictive skill for 2000–2014, and the constrained local albedo−temperature sensitivity (∂α /∂T ) aligns more closely with in-situ measurements (Figs. 5a, b). EC tends to surpass EC ’s performance in terms of uncertainty reductions. To further validate the robustness of our methodology and results, we conducted a hindcast experiment spanning 2000–2014, benchmarking our approach against ERA5 reanalysis data. The results show that the EC -constrained SAF estimates align more closely with ERA5 than both the unconstrained and linearly constrained variants (Supplementary Fig. 27). This demonstrates the robustness of our proposed ECs for constraining future SAF projections using historical observations.

When the ECs trained on 1985–2014 data are applied to future projections, both EC and EC lead to smaller SAF estimates with reduced uncertainty. EC lowers the mean SAF estimates by 0.29–0.52 W m-2 K-1 and reduces the uncertainty by 45–55%, which more than double that by EC (Figs. 5c, d). These results validate EC ’s effectiveness, enhancing confidence in future SAF projections across SSP1-2.6 to SSP5-8.5 scenarios. By leveraging nonlinear random forest regression, EC better captures complex albedo dynamics, offering a superior approach to constrain Arctic warming projections.

Methods
Observations and CMIP6 simulations
We analyzed the outputs of CMIP6 Earth system model (ESM) ensemble (35 models; Supplementary Table 1), covering SSP1-2.6, SSP2-4.5, SSP3-7.0, and SSP5-8.5 scenarios from 1985–2099. Monthly outputs included downward shortwave radiation, upward shortwave radiation, shortwave radiation incoming at the top of the atmosphere, shortwave radiation outgoing at the top of the atmosphere, near-surface air temperature (T ), snow cover fraction (SCF), and leaf area index (LAI). Greenhouse gas concentrations (CO₂, CH₄, N₂O), cloud area fraction, convective/stratiform cloud optical depth were sourced from scenario forcings. The first realization (r1i1p1f1) of each model is used and an equal weight is assigned to each model in the multi-model analysis. Simulations from ESMs are commonly interpolated to a 1°×1° resolution using the bilinear interpolation method.

In-situ observations of daily mean air temperature, incoming shortwave (solar) radiation and outgoing shortwave radiation from 38 flux network sites (Alaska, Canada, Russia; Supplementary Table 3) are obtained from the FLUXNET 2015, AmeriFlux and ICOS (Integrated Carbon Observation System) (Supplementary Fig. 33a)41−43. We focus on the historical period from 1985 onward, when reliable and continuous observational data become readily available. In-situ measurements were quality-controlled, and missing values are filled using over 10,000 meteorological stations including Global Historical Climatology Network-Daily (GHCNd)67 (Supplementary Fig. 33b), satellite-based (GLASS and CLARA-A3)68,69 and reanalysis products (ERA5 and MERRA-2)70,71 (Supplementary Table 4). Missing air temperature records were filled using the nearest neighbor method, while α is constructed via a regression model. All the simulations and observations are aggregated to the annual scale to be consistent with SAF constraint. Details on the data filling process can be found in Supplementary Note 8 and Figs. 34 and 35.

SAF calculation
Following previous studies18,20,25, the strength of SAF is quantified by the additional net shortwave (solar) radiation at the top of atmosphere (TOA), as land surface albedo (𝛼 ) decreases in response to a 1 K increase in near-surface air temperature (𝑇 ), as follows:
𝑆𝐴𝐹 = 𝜕𝑄𝑛𝑒𝑡 / 𝜕𝑇𝑎 = (𝜕𝑄𝑛𝑒𝑡 / 𝜕𝛼𝑝) * (𝜕𝛼𝑝 / 𝜕𝛼𝑠) * (𝜕𝛼𝑠 / 𝜕𝑇𝑎) = −𝑄 * (𝜕𝛼𝑝 / 𝜕𝛼𝑠) * (𝜕𝛼𝑠 / 𝜕𝑇𝑎) (1)
where 𝑄 and 𝑄 are the incoming and net solar radiation at the TOA associated with decreases (increases) in land surface albedo (𝛼 ), respectively, 𝛼 is the planetary albedo.

Eq. (1) indicates that the strength of SAF is primarily determined by two factors: a coefficient representing the variations in planetary albedo with 𝛼 (𝜕𝛼 /𝜕𝛼 ) and the change in 𝛼 associated with a 1 K increase in 𝑇 (𝜕𝑎 /𝜕𝑇 )10,18.

To estimate 𝜕𝛼 /𝜕𝛼 , we adopted a physically based regression model for planetary albedo72, which is expressed as a function of 𝛼 , cloud cover, cloud optical thickness, and clear-sky planetary albedo:
𝜕𝛼𝑝 / 𝜕𝛼𝑠 = 𝑇𝑐𝑟 − 𝜀 ∙ 𝑐 ∙ 𝑙𝑛(𝜏+1) (2)
where 𝑇𝑐𝑟 is an effective clear-sky atmospheric transmissivity, which can be calculated as the ratio of land surface shortwave radiation to net shortwave radiation at TOA; 𝑐 is the cloud cover; 𝑙𝑛(𝜏+1) is the logarithm of cloud optical thickness; 𝜀 indicates the linear coefficient relating the logarithm of cloud optical thickness to the effective cloudy-sky atmospheric transmissivity (𝑇𝑐𝑑):
𝑇𝑐𝑑 = 𝑇𝑐𝑟 − 𝜀 ∙ 𝑙𝑛(𝜏+1) (3)

Regarding 𝜕𝑎 /𝜕𝑇 , we focused on the interannual variation of near surface (2 m) air temperature anomaly after excluding its trend component, and examined its response to the interannual fluctuation of α anomaly by:
𝐿𝑆𝐴 = 𝛾 + 𝛾 ∙ 𝑇 + 𝛾 (4)
where 𝑇 and 𝐿𝑆𝐴 represent the detrended air temperature and α for year i, respectively. Detrending is accomplished by subtracting the linear trend from the time series. 𝛾 represents the regression coefficient, which is used to measure 𝜕𝑎 /𝜕𝑇 . 𝛾 and 𝛾 indicate the intercept and residual of the regression model, respectively.

Emergent constraint framework
To constrain future SAF (2070–2099), we developed an emergent constraint (EC) framework linking historical (1985–2014) ∂α /∂T (predictor) to future SAF (predictand). Like previous studies12,22,23,29, the ECs are used to adjust SAF projections post-hoc rather than modifying model parameterizations during simulations. Two EC methods were applied: a linear EC (EC ), assuming a linear predictor-predictand relationship like previous studies21,23,32, and a machine-learning-based EC (EC ) using random forest regression to capture nonlinearities. For EC , we trained random forests on CMIP6 outputs of ∂α /∂T and SAF. The 10-Fold cross-validation is adopted to test the potential overfitting issue of RF (Supplementary Note 9). EC was fitted using ordinary least squares (Supplementary Note 10). Both methods were evaluated with R² and p-values (p < 0.05 threshold).

Following previous studies32,73, the difference between simulated and observed local mean ∂α /∂T is used to adjust regional mean SAF. This allows us to estimate the constrained SAF for each ESM and calculate the inter-model uncertainty:
𝑆𝐴𝐹 ′ = 𝑆𝐴𝐹 − {𝑓[(𝜕𝛼𝑠 / 𝜕𝑇𝑎) ] − 𝑓[(𝜕𝛼𝑠 / 𝜕𝑇𝑎) ]} (5)
where 𝑆𝐴𝐹 and 𝑆𝐴𝐹 ′ represent the unconstrained and constrained regional mean SAF (i.e. the average over Arctic land areas >60°N), respectively, (𝜕𝛼𝑠 / 𝜕𝑇𝑎) refers to local mean for model i, which is derived from model grid cells corresponding to the exact locations of eddy covariance flux sites, (𝜕𝛼𝑠 / 𝜕𝑇𝑎) refers to local mean in-situ observations of 𝜕𝛼𝑠 / 𝜕𝑇𝑎. 𝑓 indicate the linear regression or random forest model.

The PDFs of unconstrained and constrained SAF are derived from Eq. (6), by assuming that all ESMs are equally likely and sampled from a Gaussian distribution:
𝑃𝐷𝐹(𝑆𝐴𝐹) = 1 / (√2𝜋∙𝜎2) * 𝑒𝑥𝑝{− (𝑆𝐴𝐹𝑖 − 𝑆̅𝐴𝐹)2 / 2𝜎2} (6)
where 𝑆𝐴𝐹 indicates the simulated SAF from model i; 𝑆̅𝐴𝐹 denotes the multi-model ensemble mean SAF; 𝜎2 refers to the variance of SAF across models (Eq. (7)), describing the uncertainty in the SAF from all models.
𝜎 = √ [∑(𝑆𝐴𝐹𝑖 − 𝑆̅𝐴𝐹)2] / 𝑁 (7)

Attribution analysis
To explore SAF’s physical drivers, we constructed a piecewise structural equation model (pSEM)74, linking greenhouse gases, R , T , LAI, SCF, and α (Supplementary Note 5). Path coefficients (ρ) were estimated using standardized regressions, with significance at p < 0.05. A positive ρ suggests that an increase in the independent variable results in a rise of the dependent variable, while a negative ρ suggests that an increase in the independent variable leads to a decrease in the dependent variable. The direct effect refers to the immediate impact of one variable on another without involving intermediaries, while the indirect effect indicates the influence mediated through one or more intermediate variables. The pSEM has been widely adopted for decomposition of complex causal relationships74. Here, it was fitted using the R package ‘piecewiseSEM’ (v2.3.0.1).

Sensitivity tests
The robustness of our proposed emergent constraints (ECs) was evaluated across multiple dimensions. We applied both EC and EC to all SSP scenarios, alternative historical (1985–2014) and future (2040–2069) periods, and CMIP5 ensembles (Supplementary Table 2). In addition, we conducted model community-based evaluations using ensemble means from models developed by the same institutions, assessing both the strength of fit and the consistency of SAF estimates (Supplementary Fig. 24). Out-of-sample tests with randomly selected 20% holdout sets confirmed the stability of the constraints, demonstrating that the RF-based emergent relationship is robust and outperforms the LR model (Supplementary Note 6 and Fig. 23). Leave-one-out sensitivity tests were used to assess whether the constrained estimates are disproportionately influenced by any individual CMIP6 model or flux station (Supplementary Note 4 and Figs. 15, 17, 19−21, 26). Collectively, these evaluations confirm the applicability and reliability of the ECs under a wide range of conditions.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "In this study, the authors developed a machine-learning method to constrain surface albedo feedback over Arctic land regions. They try to offer more precise insights for climate adaptation. I highly recommend the English writing and figures plotting in this manuscript, which are impressive. However, I am sorry to give them a reject decision. This study is lack of robust theoretical diagnose. The authors are lack of necessary understanding to Arctic warming. I agree that variations in incoming shortwave radiation (SAF in this study) can easily change the result of climate prediction. However, we need a precise prediction instead of variations in prediction. Without a correct understanding to Arctic surface warming mechanisms, the methods and results have low credibility. Major comments 1. The authors have a wrong concept to Arctic warming mechanisms. The previous studies (Stuecker et al., 2018) concluded that Arctic warming is mainly a result of local forcing and feedback, and surface albedo feedback dominated in all mechanisms (Graversen et al., 2019). This conclusion is true for the whole Arctic region, while it is wrong for the continent only. As we know, the surface albedo feedback mainly offers the additional shortwave radiation to Arctic surface in summer. In cold seasons, the shortwave radiation and SAF are low, and the additional energy mainly come from the ocean (Dai et al., 2019), where the additional energy is stored and released in summer and cold seasons, respectively. In spring, there still be another mechanism to determine the Arctic warming. Back to the continent, there is no ocean to store the additional energy in summer, which means the Arctic continent warming in cold season may not be a result of local surface albedo feedback. Above all, the authors have wrong concept to Arctic continent warming mechanisms, which largely decrease the credibility and importance of the rest work. 2. If the authors try to continue this study, they need to prove the surface albedo feedback dominate the Arctic warming over the continent in the whole year. Otherwise, it is wrong to drive the model with the constrained SAF over the continent only. However, based on my understanding (we made large number of calculations with ERA5 reanalysis data and CMIP6 data), the primary mechanisms to determine the annual Arctic continent warming is not surface albedo feedback only. 3. The authors train the deep learning model with data between 1985 to 1999, and test the parameterization with data between 2000 to 2014. Later the authors estimate the future SAF and employed in the climate prediction. Please clarify why you choose data between 1985 to 1999 instead of data between 1850 to 1999. Why don’t you verify your parameterization in the model first before you employ it to climate prediction? For example, you can make climate prediction during 2000 to 2014 by inputting your EC into CMIP models, and compared with the model results and ERA5. I think a better model simulation is more important than a “better” parameterization (EC in this study). 4. The CMIP models have different sensitivities responding to SAF, whether a \"better\" parameterization can highly improve the climate prediction is still a big question.", "reviewer_2": "Surface albedo feedback (SAF) is one of the primary mechanisms amplifying Arctic warming, yet its large inter-model spread has limited confidence in projections of the region’s future climate. By combining flux-station observations with a machine-learning (random-forest regression) based emergent constraint method, this study markedly reduces both the magnitude and the uncertainty of projected surface albedo feedback over Arctic land and the associated warming. The new approach outperforms traditional emergent constraint techniques that assume a simple linear link between observable variables and future projections. Major comments: (1) The non-linear relationships identified by the machine-learning approach hinge on the training data, and because the flux stations are sparse and unevenly distributed, the constrained results may be sensitive to station selection. How sensitive are the results to the stations used? (2) Are the abrupt changes in the machine-learned, non-linear relationships physically credible? Sharp transitions appear in Figures 2c, S9d–f, S14, S15 and S17, yet their shapes differ markedly among cases, and the constrained result for any individual model is highly sensitive to these kinks. What physical mechanisms produce these disparate non-linear structures? Minor comments: Line 91: “western Russia”, central Russia? Line 92: “intensifies in northern Russia”, this is not evident from the figure. Line 201: How the emergent constraints were trained on 1985–1999 data is unclear. Lines 209-211: Does “the trained ECs” (Line 209) denote the same constraints trained on 1985–1999 data (Line 201)? It yields the same 45–55 % reduction in SAF uncertainty reported in Line 138. Text S1: The description of how the SAF-driven warming rate is estimated is too brief and requires additional detail.", "reviewer_3": "This manuscript presents analysis of historic and future surface albedo feedback (SAF) in the Arctic/boreal using a combination of CMIP6 models and observational data. The Emergens Constrains (EC)analysis framework is used to evaluate Arctic SAF under future climate scenarios. The use of EC reduces uncertainty in SAF between models, and lowers estimates of associated surface warming. The methods are sound, and the findings help improve predictive understanding of high latitude climate feedbacks. There are several aspects of the manuscript that can be improved before it is considered further for publication. Broadly, the research focuses on terrestrial SAF and so the brief inclusion of ocean/sea ice SAF (i.e. Figure 1) seems a little out of place. It would be good to either contextualize this a little more in the introduction/discussion, or just focus exclusively on the land. On a more specific note, differences between the regional and local quantification of SAF or the response of surface albedo to temperature are a little unclear given the inclusion of both observational and model data. For example, are the local feedbacks derived from model data (e.g. Figure S9 or L137 in the supplementary material) grid cells corresponding to the location of eddy covariance towers, or something different? Similarly, do regional values correspond to the entire study area, or some larger region around the location of observational sites? I think it is the former, but it is not explicitly mentioned. Lastly, I think that the explicit consideration of the limitations of model simulations, specifically related to LAI, are necessary. As I note in a specific comment below, some of the projected LAI increases effectively amount to a doubling of current LAI values *every decade*. This may be realistic, but it would be quite dramatic, and is worth discussing. For example, some of my own work highlights poor model representation of vegetation (Loranty et al 2014), and the invariance of LAI across large structural (i.e. albedo) differences (Bendavid 2023). Fire is another important driver of LAI/vegetation structure, and therefore albedo (e.g. Potter et al in Arctic and boreal ecosystems, and it is not mentioned at all. This is not to diminish the importance of these results presented here, but it is worth noting that the results rely on the assumption that models accurately represent vegetation dynamics, which is not necessarily the case. Bendavid, N. S., Alexander, H. D., Davydov, S. P., Kropp, H., Mack, M. C., Natali, S. M., et al. (2023). Shrubs Compensate for Tree Leaf Area Variation and Influence Vegetation Indices in Post-Fire Siberian Larch Forests. Journal of Geophysical Research: Biogeosciences, 128(3), e2022JG007107. https://doi.org/10.1029/2022JG007107 Loranty, M. M., Berner, L. T., Goetz, S. J., Jin, Y., & Randerson, J. T. (2014). Vegetation controls on northern high latitude snow-albedo feedback: observations and CMIP5 model simulations. Global Change Biology, 20(2), 594–606. https://doi.org/10.1111/gcb.12391 Potter, S., Solvik, K., Erb, A., Goetz, S. J., Johnstone, J. F., Mack, M. C., et al. (2020). Climate change decreases the cooling effect from postfire albedo in boreal North America. Global Change Biology, 26(3), 1592–1607. https://doi.org/10.1111/gcb.14888 Lastly, I think the manuscript could use thorough proofreading. There are some missing commas, typos, etc. Minor comments L104: It appears there are no significant differences? L186: Panel d in this figure looks more like a temperate ecosystem landscape, rather than a high-latitude one. Including evergreen conifers would be useful. L283: Is this true? In many cases warming and thaw is already occurring. In many cases these impacts will be associated with thresholds, which may be crossed regardless of SAF strength. LS137: To clarify, does the local mean for a model simply the modeled value for a specific grid cell corresponding to the location of an observation (i.e. an eddy covariance site)? LS208: The black points indicating significance are hard to discern (same for Figure S6). Related, some of the trends amount to very substantive increases in LAI. At present LAI values for many of these ecosystems is ~1-2 m2/m2, so it is hard for me to imagine what decadal increases of 1.5 m2/m2 over three decades would look like in these systems."}, "author_response": "Response to Reviewer Comments We sincerely thank the reviewers for their insightful and constructive feedback, which has significantly improved our manuscript, “Surface albedo feedback constraints imply one-third lower warming rates over Arctic land regions”. We all co-authors have conducted series of intensive discussions on the revision and tried our best to address all the concerns raised from the respected reviewers. Key revisions include: (1) expanded discussions of Arctic warming mechanisms in the Introduction (Lines 46–54) and Discussion (Lines 266–298); (2) new analyses quantifying SAF’s seasonal and annual contributions (new Supplementary Figs. 5–6) in the Results (Lines 105−113); (3) a sensitivity analysis for flux station selection (new Supplementary Fig. 22); (4) detailed explanations of nonlinearities and model limitations (new Supplementary Note 2, Supplementary Figs. 12–15); and (5) discussions on model limitations (Lines 288−298), particularly regarding leaf area index (LAI) and fire impacts. Our responses to reviewer comments are presented in black font, and all line numbers referenced correspond to the revised manuscript in track-changes mode for clarity. We believe these revisions fully address the reviewers’ concerns and enhance the manuscript’s scientific rigor and clarity. Thanks again for your time! Reviewer #1 In this study, the authors developed a machine-learning method to constrain surface albedo feedback over Arctic land regions. They try to offer more precise insights for climate adaptation. I highly recommend the English writing and figures plotting in this manuscript, which are impressive. However, I am sorry to give them a reject decision. This study is lack of robust theoretical diagnose. The authors are lack of necessary understanding to Arctic warming. I agree that variations in incoming shortwave radiation (SAF in this study) can easily change the result of climate prediction. However, we need a precise prediction instead of variations in prediction. Without a correct understanding to Arctic surface warming mechanisms, the methods and results have low credibility. Response: We sincerely thank you for the kind words regarding the manuscript’s writing and figures, and for your critical feedback, which has helped us strengthen the study. Below, we would like to first clarify our objectives and then address your valuable comments to enhance the study’s robust theoretical foundation and comprehensive understanding of Arctic warming mechanisms. We hope our revisions could meet your expectations. 1. Research background and gaps: As we know, Arctic warming is driven by several interconnected mechanisms, including surface albedo feedback (SAF), atmospheric and oceanic heat transport, changes in atmospheric circulation, changes in cloud cover, water vapor feedback, etc (Stuecker et al., 2018; Dai et al., 2019; Graversen et al., 2019). By conducting a theoretical analysis using a simplified energy balance model, we quantify SAF’s contribution to Arctic land warming rate, confirming that it accounts for 37–56% of annual warming trend during 2070−2099. However, Earth System Models (ESMs), which are the indispensable tools for Arctic climate projections, show large spread in SAF (0.10−2.50 W m-2 K-1 for SSP1-2.6, 0.42−2.32 W m-2 K-1 for SSP2-4.5, 0.62−1.94 W m-2 K-1 for SSP3-7.0 and 0.40−1.82 W m-2 K-1 for SSP5-8.5) and the resulting warming rate over land (0.02−0.40 K decade-1 for SSP1-2.6, 0.03−0.44 K decade-1 for SSP2-4.5, 0.08−0.83 K decade-1 for SSP3-7.0 and 0.17−1.23 K decade-1 for SSP5-8.5), largely because they struggle to accurately simulate complex processes and feedback mechanisms such as snow metamorphosis and vegetation dynamics due to sparse observational data and simplified parameterizations (Fig. R1). 2. Research goals: Our study aims to reduce such uncertainties of ESMs in SAF projections over Arctic land regions, rather than asserting that SAF is the sole driver of Arctic land warming. We acknowledge the complexity of Arctic warming, which involves multiple feedbacks (e.g., SAF, lapse rate, cloud) and forcings (e.g., ocean heat transport). Our study focuses on SAF due to its significant contribution (37–56% of annual warming trend), large uncertainty in ESMs, and availability of flux observations to constrain ESMs. To further clarify this, we have revised the Introduction (Lines 46−54) and Discussion (Lines 266−277) to explicitly frame SAF as an important but not exclusive contributor to Arctic land warming, citing Stuecker et al. (2018), Graversen et al. (2019), and Dai et al. (2019), as suggested. 3. Robust Theoretical Diagnosis: Clarification of Theoretical Framework: Our study is grounded in the well-established theory of surface albedo feedback (SAF), which amplifies Arctic land warming through changes in snow cover and vegetation that reduce surface reflectivity (e.g., Serreze and Barry, 2011; Callaghan et al., 2011; Barrere et al., 2018). Following previous studies (Thackeray and Fletcher, 2016; Qu and Hall., 2014; Thackeray et al., 2021), SAF is generally described within the standard climate feedback framework, where variations in albedo and temperature are linked to the corresponding changes in shortwave radiation fluxes. The magnitude of SAF is mainly determined by two components: (1) the sensitivity of planetary albedo to land surface albedo changes ( ), and (2) the dependence of land surface albedo variations on air temperature ( ): where and a𝑆𝑆r𝑆𝑆e 𝑆𝑆th=e incom=ing and ne=t −so𝑄𝑄lar radiation at the Top-of-Atmosphere associated with variations of land surface albedo ( ), respectively, is the planetary albedo. Manuscript Revisions: To strengthen the theoretical diagnosis, we have added a new section in the supplementary Note 1-2 that explicitly outlines the physical basis of SAF, including its dependence on snow cover fraction (SCF), leaf area index (LAI), and shortwave radiation, supported by equations for radiative forcing, referencing key studies (e.g., Qu and Hall, 2006; Thackeray and Fletcher, 2016). The Results (Lines 105−113) include a discussion of the energy balance model results, supported by new Supplementary Figs. 5−6, which validate the theoretical consistency of our constrained SAF estimates. 4. Understanding of Arctic Warming Mechanisms: Comprehensive Consideration of Mechanisms: We recognize that Arctic warming is driven by multiple mechanisms, including SAF, ocean heat transport, lapse rate feedback, and cloud feedbacks (e.g., Pithan and Mauritsen, 2014; Bengtsson et al., 2004; Previdi et al., 2021). Our study focuses on land SAF due to its significant contribution (37–56% of annual land warming trend), large uncertainty in ESMs, and availability of flux observations to constrain ESMs, but we explicitly acknowledge the role of other mechanisms. Our analysis confirms that SAF is an important contributor to annual warming trend over land, particularly in spring and summer, though other drivers (e.g. ocean heat transport) is more significant in winter (Fig. R2 and R3). Manuscript Revisions: We have expanded the Introduction (Lines 46−54) and Discussion (Lines 266−277) to provide a comprehensive overview of Arctic warming mechanisms, citing additional references (e.g., Stuecker et al., 2018; Graversen et al., 2019; Dai et al., 2019) to contextualize SAF’s role. The new Supplementary Figs. 5 and 6 quantify the relative contributions of SAF in different seasons, reinforcing our understanding of Arctic warming dynamics. 5. Credibility of Methods and Results: Precision in Predictions: You emphasizes the need for precise predictions rather than variations. Our machine learning-based emergent constraint approach (EC ) is developed to address this issue, which can significantly reduce SAF uncertainty by 45–55% (Fig. 3a), providing more precise projections than unconstrained ESMs. To further validate the credibility of our methods and results, we conducted a hindcast experiment for 2000–2014 to evaluate our approach against ERA5 reanalysis. Results indicate that the constrained SAF by EC is much closer to ERA5 data than both the unconstrained and linearly constrained SAF (Fig. R4). Accordingly, based on EC , the constrained SAF significantly improves warming rate predictions across different SSP scenarios. Additionally, we tested the robustness of EC to station selection using leave-one-out validation approach, finding that SAF estimates remain stable (new Supplementary Fig. 22). Physical Credibility of Nonlinearities: The nonlinear relationships in EC are physically credible, reflecting thresholds in snowmelt and vegetation greening (new Supplementary Note 2 and Supplementary Figs. 12−15). These relationships are validated against in-situ observations (R² = 0.80, Fig. 5a) and gridded datasets of ERA5 (R² = 0.75, new Supplementary Fig. 23). Manuscript Revisions: We have added a new paragraph in the Discussion (Lines 318−323) to emphasize the credibility of our methods, highlighting the station choice, hindcast validation and robustness tests (new Supplementary Fig. 11, 17, 19−23, 25). The Results (Lines 244−248) now include a detailed discussion of the hindcast experiment, reinforcing the precision and reliability of our predictions. [Comment 1]: The authors have a wrong concept of Arctic warming mechanisms. Previous studies (Stuecker et al., 2018; Graversen et al., 2019) concluded that Arctic warming is mainly a result of local forcing and feedback, with surface albedo feedback dominating in all mechanisms. This conclusion is true for the whole Arctic region, but wrong for the continent only. SAF mainly offers additional shortwave radiation in summer, while in cold seasons, shortwave radiation and SAF are low, and additional energy mainly comes from the ocean (Dai et al., 2019). In spring, another mechanism determines Arctic warming. On the continent, there is no ocean to store energy in summer, so Arctic continent warming in cold seasons may not be a result of local SAF. This decreases the credibility and importance of the work. Response: We appreciate the reviewer’s concern regarding the role of surface albedo feedback (SAF) and the seasonal dynamics of Arctic warming mechanisms. We emphasize that while ocean heat transport is significant in winter, SAF’s role in snowmelt and vegetation changes makes it an important contributor to Arctic land warming at the annual mean scale (as detailed below), which is the focus of our study. We aim to constrain ESMs in representing such local feedbacks at the annual scale, considering the availability of flux observations over land. To further address your concern, we have conducted additional analyses to clarify and quantify the role of SAF in Arctic land warming at the seasonal and annual scales. 1. Evidence of SAF’s Role in Annual Arctic Land Warming Rate: We acknowledge that SAF is most pronounced in summer due to higher incoming shortwave radiation, but its influence persists annually through snow cover changes and vegetation dynamics, particularly in spring and early autumn when snowmelt and greening occur. To substantiate this, we performed a seasonal decomposition of SAF’s contribution to warming using CMIP6 model outputs. Our analysis confirms that SAF contributes significantly to annual warming over Arctic land region (Fig. R2 and R3). This is driven by snowmelt in spring (March–May) and vegetation changes in summer (June–August), with residual effects in autumn due to delayed snow onset. While ocean heat transport dominates in winter (December–February), SAF remains a critical driver of Arctic land warming, with a contribution of 37−56% at the annual scale. 2. Revised Manuscript: We have expanded the Introduction (Lines 46−54) and Discussion (Lines 266−277) to provide a comprehensive overview of Arctic warming mechanisms. We have added a new section in the Results (Lines 105−113) to quantify the seasonal and annual contributions of SAF to Arctic land warming trend (new Supplementary Figs. 5 and 6), explicitly addressing your point about ocean-driven energy in cold seasons. We emphasize that while ocean heat transport is significant in winter, SAF’s role in snowmelt and vegetation changes makes it an important contributor (37–56%) to annual warming trend over land. 3. References to Previous Studies: We have incorporated the suggested references (Stuecker et al., 2018; Graversen et al., 2019; Dai et al., 2019) to contextualize SAF’s role relative to other mechanisms, such as ocean heat transport and lapse rate feedback, in the Introduction (Lines 46−47) and Discussion (Lines 266−267). This ensures a balanced discussion of Arctic warming mechanisms. [Comment 2]: If the authors try to continue this study, they need to prove the surface albedo feedback dominate the Arctic warming over the continent in the whole year. Otherwise, it is wrong to drive the model with the constrained SAF over the continent only. However, based on my understanding (we made large number of calculations with ERA5 reanalysis data and CMIP6 data), the primary mechanisms to determine the annual Arctic continent warming is not surface albedo feedback only. Response: We agree that Arctic warming is driven by several interconnected mechanisms, and we didn’t assert that surface albedo feedback (SAF) is the sole driver of Arctic warming. Here, our study focuses on constraining SAF at the annual mean scale, due to its significant contribution to Arctic land warming, the large uncertainties in Earth system models (ESMs) and the availability of flux observations for constraining ESMs. To address this concern: 1. Quantifying SAF’s Contribution: As described in our response to Comment 1, we quantify SAF’s role in Arctic land warming trend at the seasonal and annual mean scales. Our results show that SAF contributes 37−56% to annual warming trend over Artic land areas, with peaks in spring and summer (Fig. R2 and R3). While other mechanisms, such as ocean heat transport and lapse rate feedback, are important, SAF’s substantial contribution justifies its focus in our study at the annual scale, especially given its large uncertainty in ESMs (43–81% of ensemble means, Fig. 1a). 2. Clarification in Manuscript: We have further clarified in the Introduction (Lines 46−47) and Discussion (Lines 266−267) that SAF is an important but not exclusive driver of Arctic land warming trend. We explicitly state that our constrained SAF estimates improve the accuracy of warming projections by reducing uncertainties in this critical feedback, while acknowledging the role of other mechanisms. A new paragraph in the Results (Lines 105−113) is added to quantify the seasonal and annual contributions of SAF to Arctic land warming trend (new Supplementary Figs. 5 and 6). [Comment 3]: The authors train the deep learning model with data between 1985 to 1999, and test the parameterization with data between 2000 to 2014. Later the authors estimate the future SAF and employed in the climate prediction. Please clarify why you choose data between 1985 to 1999 instead of data between 1850 to 1999. Why don’t you verify your parameterization in the model first before you employ it to climate prediction? For example, you can make climate prediction during 2000 to 2014 by inputting your EC into CMIP models, and compared with the model results and ERA5. I think a better model simulation is more important than a “better” parameterization (EC in this study). Response: We appreciate the reviewer’s questions regarding the choice of periods and verification strategy. We address these points as follows: 1. Choice of Period: The selection of 1985–1999 for training is driven by the availability of high-quality in-situ observations from flux networks (e.g., FLUXNET, AmeriFlux, ICOS), which provide reliable albedo and air temperature data starting around 1985. Earlier periods (e.g., 1850–1999) lack sufficient in-situ measurements, and gridded datasets (e.g., satellite or reanalysis) suffer from uncertainties in Arctic regions due to sparse coverage and interpolation errors. To test the sensitivity to this period, we’ve conducted additional analyses using 1975–2004 data, confirming that the emergent relationship remains robust (new Supplementary Fig. 21). We have added a detailed justification in the Methods (Lines 358−362), explaining why 1985–1999 was chosen and its robustness across alternative periods. 2. Verification Strategy: We verified our EC framework using a two-stage cross-validation (1985–1999 training, 2000–2014 testing), which showed high predictive skill (R² = 0.80 for EC , Fig. 5a). To further address the reviewer’s suggestion, we conducted an additional hindcast experiment for 2000−2014 against ERA5 data. Results indicate that the EC effectively reduces the uncertainty in SAF, and the constrained SAF is much closer to ERA5 data (Fig. R4). The additional hindcast analysis is now included in the Results (Lines 244−248) and new Supplementary Information (new Supplementary Fig. 23). 3. Clarification on Model Application: Our EC framework adjusts SAF projections post-hoc rather than modifying model parameterizations during simulations. This is a standard approach in EC studies (e.g., Shiogama et al., 2022 Nature; Petrova et al., 2024 Nature; Thackeray and Hall, 2019 Nat. Clim. Change; Tokarska et al., 2020 Sci. Adv.; Zhang et al., 2022 Nat. Commun), as it leverages observational constraints to correct model biases without requiring full model reruns, which are computationally intensive. We have clarified this in the Methods (Lines 414−416). [Comment 4]: The CMIP models have different sensitivities responding to SAF, whether a \"better\" parameterization can highly improve the climate prediction is still a big question. Response: We agree that CMIP models exhibit varying SAF sensitivities (Fig. 1a), which is why our EC framework is designed to reduce inter-model spread and correct biases. To address this concern: 1. Impact of Constrained SAF: Our results show that the machine-learning-based EC (EC ) reduces SAF uncertainty by 45–55% (Fig. 3b), demonstrating significant improvements in prediction accuracy. The new hindcast experiment against ERA5 reanalysis for 2000–2014 (new Supplementary Fig. 23) further confirms that constrained SAF improves warming rate predictions across models with different sensitivities. 2. Model Sensitivity Analysis: We performed leave-one-out test to assess how model-specific SAF sensitivities affect our results, finding that the constraint consistently reduces SAF estimates and uncertainties across all groups (new Supplementary Fig. 19−23, 25). This is discussed in the Discussion section (Lines 306−325) and Supplementary Information (new Supplementary Note 5). 3. Manuscript Revisions: We have added a paragraph in the Discussion (Lines 306−325) to address the variability in model SAF sensitivities, emphasizing that our EC approach accounts for these differences by leveraging nonlinear relationships and in-situ observations, thus enhancing the reliability of climate predictions. Reviewer #2 Surface albedo feedback (SAF) is one of the primary mechanisms amplifying Arctic warming, yet its large inter-model spread has limited confidence in projections of the region’s future climate. By combining flux-station observations with a machine-learning (random-forest regression) based emergent constraint method, this study markedly reduces both the magnitude and the uncertainty of projected surface albedo feedback over Arctic land and the associated warming. The new approach outperforms traditional emergent constraint techniques that assume a simple linear link between observable variables and future projections. Response: We sincerely thank the reviewer for their insightful summary of our study and for recognizing the significance of our machine-learning-based emergent constraint (EC ) approach in reducing the magnitude and uncertainty of surface albedo feedback (SAF) projections over Arctic land regions. We appreciate the acknowledgment of our method’s ability to outperform traditional emergent constraint techniques, which rely on linear assumptions. Major comments: [Comment 1]: The non-linear relationships identified by the machine-learning approach hinge on the training data, and because the flux stations are sparse and unevenly distributed, the constrained results may be sensitive to station selection. How sensitive are the results to the stations used? Response: We appreciate the reviewer’s concern about the potential sensitivity of our results to flux station selection. To address this: 1. Sensitivity Analysis: We conducted a new sensitivity analysis using the leave-one-out cross-validation approach. Specifically, one flux station was excluded during the training of EC and the constrained estimates were recalculated. The results show that SAF estimates remain stable, with variations in constrained SAF of less than 5% and uncertainty reductions of 43–50% across all subsets (Fig. R5). Specifically, the reduction of SAF is -0.51 [-0.53, -0.48], -0.29 [-0.31, -0.28], -0.42 [-0.46, -0.39], and -0.48 [-0.53, -0.48] W m-2 K-1 for SSP1-2.6, SSP2-4.5, SSP3-7.0, and SSP5-8.5, respectively, while the corresponding uncertainty reduction is -55% [-57, -53%], -45% [-47, -43%], -55% [-57, -53%], and -54% [-56, -52%]. This stability is attributed to the strong correlation between local and regional albedo-temperature dynamics (R² = 0.85, Fig. 2b), confirming the representativeness of our flux sites. 2. Manuscript Revisions: We have added a new description of station sensitivity in the Results (Lines 216−217) and Discussion (Lines 318−321), highlighting the robustness of our findings to station selection. The new Supplementary Fig. 22 provide detailed results of the sensitivity analysis. [Comment 2]: Are the abrupt changes in the machine-learned, non-linear relationships physically credible? Sharp transitions appear in Figures 2c, S9d–f, S14, S15, and S17, yet their shapes differ markedly among cases, and the constrained result for any individual model is highly sensitive to these kinks. What physical mechanisms produce these disparate non-linear structures? Response: Thank you for raising this important point about the nonlinear relationships in our EC . We have conducted additional analyses to investigate the physical credibility of these relationships and their variability: 1. Physical Basis of Nonlinearities: The sharp transitions in the emergent relationships reflect nonlinear interactions between snow cover, vegetation dynamics, and albedo responses, which are captured by the random forest (RF) model. These transitions are physically credible, as they correspond to thresholds in snowmelt and vegetation greening. Similar threshold-like behaviors in Arctic feedbacks have been reported in previous studies, for instance in the context of snow–albedo feedback (Qu and Hall, 2006; Thackeray and Fletcher, 2016) and vegetation–albedo interactions (Bonfils et al., 2012; Pearson et al., 2013). Our RF model’s ability to capture these nonlinearities explains its superior performance (R² = 0.70–0.88) compared to linear ECs (R² = 0.28–0.48). 2. Attribution analysis of Nonlinearities: We analyzed the interannual variability (standard deviation, SD) of LAI (leaf area index, LAI ), SCF (snow cover fraction, SCF ), and LSA (land surface albedo, LSA ) in each model’s output during the historical and future periods (Figs. R6 and R7). The results reveal pronounced inter-model differences in temporal variability, supporting the interpretation that variations in the representation of vegetation and snow dynamics strongly shape the non-linear emergent relationships. We found significant (p < 0.05) correlations LSA versus SAF, with r (correlation coefficient) ranging from 0.63 to 0.83, across all scenarios (Fig. R8). These demonstrate that interannual LSA variability is a key factor driving the non-linear emergent relations across models. Since vegetation and snow cover are the two dominant factors controlling land surface albedo in the Arctic (Qu and Hall, 2006; Loranty et al., 2014; Thackeray and Fletcher, 2016), we further quantified their relative influences on interannual LSA variability using partial regression models with LSA regressed against LAI , SCF and their interaction: (Eq. 1) where , and represent the partial regression coefficient, is the residual, indicates the interaction between and . The regression models performed well across scenarios (R2 = 0.60–0.69 for 2040–2069; R2 = 0.67–0.71 for 2070–2099). In the near future (2040–2069), both vegetation and snow cover fluctuations contributed comparably to LSA variability, with relative contributions of 33.2–51.9% and 32.0–50.2%, respectively (Fig. R9a). In the far future (2070–2099), vegetation fluctuations and vegetation–snow interactions tend to dominate, with relative contributions of 34.0–62.0% and 33.0–65.2%, respectively (Fig. R9b). These findings indicate that, under strong Arctic warming, vegetation dynamics increasingly emerge as the dominant driver of albedo variability, consistent with the growing role of shrub expansion and boreal forest encroachment reported in recent observational and modeling studies (Pearson et al., 2013; Bonfils et al., 2012; Sturm et al., 2005). 3. Manuscript Revisions: We have added a new section in the Results (Lines 153−159) to explain the physical mechanisms behind the nonlinear relationships, supported by new Supplementary Note 2 and Supplementary Figs. 12−15. Minor comments: Line 91: “western Russia”, central Russia? Response: Thank you for pointing out this potential confusion. We have checked the spatial maps in Fig. 1 and revised it to “central and eastern Russia”. Line 92: “intensifies in northern Russia”, this is not evident from the figure. Response: We apologize for the lack of clarity. The statement refers to the intensification of SAF in northern Russia (e.g., Siberian tundra regions) under SSP3-7.0 and SSP5-8.5, driven by enhanced vegetation greening and snowmelt (new Supplementary Figs. 7 and 8). To make this clearer, we have revised this sentence to describe the spatial patterns more precisely (Line 116). Line 201: How the emergent constraints were trained on 1985–1999 data is unclear. Response: We conducted a two-stage cross-validation, training ECs on ESMs output during 1985–1999 and validating their performance against in-situ observations during 2000–2014. First, the emergent constraints are trained on ESMs outputs during 1985-1999. The constrained simulations during 2000−2014 are then compared with in-situ observations to verify the ECs. The close agreement between the simulated and observed values in the validation period demonstrates the robustness and reliability of our EC method. This is further clarified in the Results (Lines 237−239). Lines 209–211: Does “the trained ECs” (Line 209) denote the same constraints trained on 1985–1999 data (Line 201)? It yields the same 45–55% reduction in SAF uncertainty reported in Line 138. Response: No, “the trained ECs” in Line 209 refers to the constraints trained on 1985–2014 data, which are used for future projections. The trained ECs during 1985–1999 are used to verify their performance in the validation period (2000–2014) when in-situ observations are available. To avoid confusion, we have revised this sentence to explicitly state “ECs trained on 1985–2014 data” (now Line 250). The substantial uncertainty reduction reflects the robustness of EC across both validation and projection periods. Text S1: The description of how the SAF-driven warming rate is estimated is too brief and requires additional detail. Response: We have expanded Supplementary Note S1 to provide a more detailed explanation of the SAF-driven warming rate estimation, including step-by-step derivations of Equations 1–6 and assumptions about the climate feedback parameter. In brief, our approach first diagnoses the top-of-atmosphere net radiation and effective radiative forcing using Gregory regression, then quantifies the shortwave perturbation induced by SAF, and finally links this perturbation to surface air temperature trends through the climate feedback parameter. This framework allows us to isolate the SAF-driven component of warming and evaluate its relative contribution to the total warming rate. For full methodological details, please see the updated Supplementary Note 1. Reviewer #3 This manuscript presents analysis of historic and future surface albedo feedback (SAF) in the Arctic/boreal using a combination of CMIP6 models and observational data. The Emergens Constrains (EC) analysis framework is used to evaluate Arctic SAF under future climate scenarios. The use of EC reduces uncertainty in SAF between models, and lowers estimates of associated surface warming. The methods are sound, and the findings help improve predictive understanding of high latitude climate feedbacks. There are several aspects of the manuscript that can be improved before it is considered further for publication. Response: We sincerely thank you for your thoughtful evaluation of our manuscript and for recognizing the strengths of our analysis, which combines CMIP6 models and observational data to evaluate surface albedo feedback (SAF) in Arctic and boreal regions. We are encouraged by your acknowledgment that our emergent constraint (EC) framework effectively reduces uncertainty in SAF projections and lowers estimates of associated surface warming, thereby improving the predictive understanding of high-latitude climate feedbacks. We also appreciate your assessment that our methods are sound. Broadly, the research focuses on terrestrial SAF and so the brief inclusion of ocean/sea ice SAF (i.e. Figure 1) seems a little out of place. It would be good to either contextualize this a little more in the introduction/discussion, or just focus exclusively on the land. Response: We appreciate your suggestion to focus on terrestrial SAF. Following your suggestion, we have deleted the ocean-related estimates in Figure 1 and modified the manuscript accordingly. On a more specific note, differences between the regional and local quantification of SAF or the response of surface albedo to temperature are a little unclear given the inclusion of both observational and model data. For example, are the local feedbacks derived from model data (e.g. Figure S9 or L137 in the supplementary material) grid cells corresponding to the location of eddy covariance towers, or something different? Similarly, do regional values correspond to the entire study area, or some larger region around the location of observational sites? I think it is the former, but it is not explicitly mentioned. Response: We apologize for the lack of clarity and have revised the manuscript to explicitly define local and regional quantifications: 1. Local Feedbacks: Local mean in Fig. S9 and Line S137 refers to the albedo-temperature sensitivity derived from model grid cells corresponding to the exact locations of eddy covariance flux sites (e.g., FLUXNET, AmeriFlux, ICOS). This is now clarified in the Methods (Lines 429−430) and Figure captions (Lines 182−184). 2. Regional Values: Regional mean SAF refers to the average SAF across the entire Arctic land region (latitudes >60°N), calculated from CMIP6 model outputs. We have clarified this in the Methods (Lines 427−428) and Figure captions (Lines 182−184) In brief, regional estimates encompasses the whole study area, while local estimates are site-specific but representative of regional dynamics (R2 = 0.85, Fig. 2b). Lastly, I think that the explicit consideration of the limitations of model simulations, specifically related to LAI, are necessary. As I note in a specific comment below, some of the projected LAI increases effectively amount to a doubling of current LAI values *every decade*. This may be realistic, but it would be quite dramatic, and is worth discussing. For example, some of my own work highlights poor model representation of vegetation (Loranty et al 2014), and the invariance of LAI across large structural (i.e. albedo) differences (Bendavid 2023). Fire is another important driver of LAI/vegetation structure, and therefore albedo (e.g. Potter et al in Arctic and boreal ecosystems, and it is not mentioned at all. This is not to diminish the importance of these results presented here, but it is worth noting that the results rely on the assumption that models accurately represent vegetation dynamics, which is not necessarily the case. Response: We agree that model limitations in simulating vegetation dynamics, particularly leaf area index (LAI), are critical to address. We have incorporated the following: 1. LAI Limitations: We added a new paragraph in the Discussion (Lines 288−293) to discuss the limitations of ESMs in simulating LAI (see supplementary Fig. 16 for comparisons against gridded observations), citing Loranty et al. (2014) and Bendavid (2023). We acknowledge that some models project dramatic LAI increases, which may overestimate vegetation greening due to unaccounted ecological constraints like nutrient availability, water limitations, and permafrost stability. 2. Fire Impacts: We recognize the importance of fire as a driver of LAI and albedo, as highlighted by Potter et al. (2020). We have added a discussion in the Discussion section (Lines 293−296) noting that fires, which are poorly represented in many ESMs, can reduce LAI and increase albedo by exposing snow or bare soil. 3. Manuscript Revisions: The Discussion now includes a detailed section on model limitations (Lines 288−298), citing the suggested references and discussing the impact of fires and ecological constraints on LAI projections. Lastly, I think the manuscript could use thorough proofreading. There are some missing commas, typos, etc. Response: Thank you for your suggestion. We have conducted a comprehensive review, correcting typos, adding missing commas. All changes are marked in track changes for clarity. Response: We thank the reviewer for suggesting relevant references to strengthen the manuscript. We have incorporated the provided references (Bendavid et al., 2023; Loranty et al., 2014; Potter et al., 2020) in the revised manuscript to support our discussion of model limitations. These citations are included in the Discussion section (Lines 291−297), ensuring a robust and well-supported scientific context. Minor comments L104: It appears there are no significant differences? Response: We apologize for the ambiguity. In line with your suggestion, we have removed ocean-related estimates from Figure 1 and revised the manuscript accordingly. L186: Panel d in this figure looks more like a temperate ecosystem landscape, rather than a high-latitude one. Including evergreen conifers would be useful. Response: Thank you for the observation. We have replaced the image in Fig. 4d with a new photograph of a high-latitude Arctic landscape featuring tundra and sparse evergreen conifers, ensuring it accurately represents the study region. The caption for Fig. 4 has been updated to reflect this change. L283: Is this true? In many cases warming and thaw are already occurring. In many cases these impacts will be associated with thresholds, which may be crossed regardless of SAF strength. Response: We agree that warming and permafrost thaw are already occurring and that some thresholds may be crossed regardless of SAF strength. We have clarified that our constrained SAF estimates reduce projected warming rates, which may delay but not prevent threshold crossings in vulnerable systems like permafrost. This is further discussed in the Discussion (Lines 351−356), emphasizing the interplay between SAF and other feedbacks in driving tipping points. LS137: To clarify, does the local mean for a model simply the modeled value for a specific grid cell corresponding to the location of an observation (i.e., an eddy covariance site)? Response: Yes, the local mean refers to the modeled value for the grid cell corresponding to the location of an eddy covariance site. We have clarified this in new Supplementary Note 8 and the Methods (Lines 429−430) to ensure precision. LS208: The black points indicating significance are hard to discern (same for Figure S6). Some trends amount to very substantive increases in LAI. At present, LAI values for many of these ecosystems are ~1–2 m²/m², so it is hard to imagine decadal increases of 1.5 m²/m² over three decades. Response: We have addressed these concerns as follows: 1. Figure Clarity: We have revised Fig. S6 and Line S208 to increase the size and contrast of black points indicating statistical significance, ensuring they are clearly visible. The updated figures are included in the revised Supplementary Information (new Supplementary Figs. 7 and 8). 2. LAI Increases: We acknowledge the concern about large projected LAI increases. We have added a discussion (Lines 288−298) about these projected increases, citing ecological constraints and model limitations (Loranty et al., 2014; Bendavid, 2023)."}, {"round": 2, "reviewer_comments": {"reviewer_1": "I commend the authors for their considerable effort in revising the manuscript. However, after careful re-evaluation, I find that fundamental issues persist, which unfortunately lead me to a recommendation of rejection. The core problem lies in an inconsistency between the study's title and its stated primary objective. Furthermore, the revision does not adequately address the primary concern raised in the previous review round. The specific points are detailed below. Major comments 1.On the discussion of Arctic land warming mechanisms: My previous comment requested a more thorough explanation beyond the brief introduction. The revision, which only cites a few general papers, does not constitute an adequate response to this fundamental concern. 2.The necessity for a comprehensive understanding of warming mechanisms: While the Surface Albedo Feedback (SAF) is a dominant mechanism of Arctic amplification on annual or longer timescales, its contribution during cold seasons is minimal, as evidenced by the authors' own figures. Therefore, relying solely on SAF within the deep learning model is incongruent with the observed seasonal data and limits the model's explanatory power. A more complete mechanistic framework is required. 3.“Our study aims to reduce such uncertainties of ESMs in SAF projections over Arctic land regions, rather than asserting that SAF is the sole driver of Arctic land warming.” The manuscript's title, which suggests a broad investigation of Arctic land warming, is inconsistent with its actual scope and focus on optimizing the Surface Albedo Feedback (SAF). A more accurate title reflecting the specific methodological contribution is warranted. Furthermore, while the application of deep learning to SAF optimization is of interest, I question its novelty and broad impact for a journal of Nature Communications's standing. The work may be more appropriately suited for a specialized journal such as Remote Sensing of Environment (RSE), Journal of Advances in Modeling Earth Systems (JAMES), or Geoscientific Model Development (GMD). 4. On methodological rigor and novelty: My understanding is that the core experiment involves artificially reducing the SAF in a model to demonstrate a corresponding temperature decrease. This approach is conceptually simplistic and lacks the mechanistic insight expected for a rigorous scientific investigation; it primarily demonstrates a known correlation rather than probing underlying processes. Furthermore, the key finding that SAF contributes to approximately 40% of Arctic warming was established in prior literature (e.g., Graversen et al., 2014). Therefore, a study focused solely on reaffirming this relationship, without introducing a significant conceptual advance, does not meet the high novelty threshold required for publication in Nature Communications.", "reviewer_2": "Major comments: Several studies highlight the interconnections between surface albedo feedback and other regional climate feedbacks in the Arctic, particularly the compensatory interplay between surface albedo feedback and atmospheric heat transport (Alexeev and Jackson, 2013; Feldl et al., 2017; Hahn et al., 2021). This interplay complicates estimating the impact of constraining surface albedo feedback alone on Arctic land warming rates using model outputs, as individual feedbacks don't operate in isolation and anomalies from one can be offset by others. The physical mechanisms behind the sharp transitions in regional surface albedo feedback, caused by minor changes in land surface albedo responses to air temperature changes, are still unclear, especially around the value of -1.0 % K⁻¹ (Figure 2a, c). These sharp transitions appear to be largely driven by models near this value. What physical processes correspond to this? Would removing several models around the sharp transition zone near -1.0 % K⁻¹ significantly alter the transitions? In addition, the random forest regression relationship shows a markedly different strength compared to the linear regression relationship when the response of land surface albedo to air temperature changes is around -1.5 % K⁻¹ under SSP2-4.5 and SSP5-8.5 (Figure S20b, d). These discrepancies appear to be closely associated with the models in the vicinity. Does this suggest that the random forest regression relationship is heavily influenced by these models in this particular zone? If this is the case, does it imply that the observationally constrained surface albedo feedback is significantly influenced by models whose land surface albedo response to air temperature changes are close to the observation-derived values? Technical issue: Supplementary information, Lines 36 & 44: Please change “Seden and Held, 2006” to “Soden and Held, 2006”. References: Alexeev and Jackson 2013: Polar amplification - is atmospheric heat transport important? Feldl et al., 2017: Coupled High-Latitude Climate Feedbacks and Their Impact on Atmospheric Heat Transport Hahn et al., 2021: Contributions to Polar Amplification in CMIP5 and CMIP6 Models", "reviewer_3": "The authors have largely addressed my previous comments and the revised manuscript is improved as a result. There is still a disconnect between the emphasis on ocean/sea ice albedo feedbacks in the introduction and the focus of the analyses on terrestrial SAF dynamics. At the very least, it is necessary to frame terrestrial SAF/warming in the context of regional dynamics, but it would also be helpful to very briefly describe the terrestrial processes driving variability/uncertainty in SAF dynamics. L34: The Arctic is… L220: Indirect negative is listed twice, in red and blue, below panels a & b L479: A link to a GitHub repository or some other open access version of the code is preferable."}, "author_response": "Point-by-Point Response to Reviewers Reviewer #1 I commend the authors for their considerable effort in revising the manuscript. However, after careful re-evaluation, I find that fundamental issues persist, which unfortunately lead me to a recommendation of rejection. The core problem lies in an inconsistency between the study’s title and its stated primary objective. Furthermore, the revision does not adequately address the primary concern raised in the previous review round. The specific points are detailed below. Response: Thank you for your time and comments. In this study, we first develop a machine-learning based emergent constraint (EC) approach to reduce the uncertainty of surface albedo feedback (SAF) in Earth system models (ESMs), which contributes to 37–56% of Arctic land warming rate. We then quantify Arctic land warming rates driven by the unconstrained and constrained SAF, and compare their differences. We find that Arctic land warming rates are approximately one-third lower after constraining SAF projections, compared to the unconstrained estimates. Therefore, we believe the original title “Surface albedo feedback constraints imply one-third lower warming rates over Arctic land regions” can basically reflect the primary objective of our study. To address your concern, we propose revising the title to: “Machine-learning emergent constraints on surface albedo feedback reduce one-third of projected warming over Arctic land regions”. We hope this better reflects the primary objective. Below, we provide point-by-point responses, detailing revisions that strengthen the manuscript’s rigor and impact. Major comments: [Comment 1] On the discussion of Arctic land warming mechanisms: My previous comment requested a more thorough explanation beyond the brief introduction. The revision, which only cites a few general papers, does not constitute an adequate response to this fundamental concern. Response: We thank the reviewer for this comment. We did acknowledge the complexity of Arctic warming, which involves multiple feedbacks (e.g., SAF, lapse rate, cloud) and forcings (e.g., atmospheric heat transport). In our last revision, we briefly introduced other warming mechanisms because: 1) we focus on SAF (linked to vegetation and snow dynamics) over the land rather than oceans; 2) Reviewer #3 also suggests we focus on terrestrial SAF dynamics in the introduction. In this round of revision, considering both your and Reviewer #3’s suggestions, we have added the following statements in the Discussion section to provide a systematic overview, positioning SAF within the full spectrum of Arctic amplification processes. “Moreover, we implement ECs to SAF only, without constraining other related feedbacks like atmospheric heat transport, permafrost carbon release, or cloud radiative effects, which amplify Arctic warming in complex ways. For instance, although sea-ice retreat boosts local shortwave absorption, it often triggers a compensatory reduction in poleward atmospheric heat transport (Alexeev and Jackson, 2013; Feldl et al., 2017; Liang et al., 2022). Comparable offsets occur vertically: heightened humidity and low-cloud formation enhance longwave trapping, while increased ocean heat uptake tempers the lapse-rate feedback, redistributing SAF-induced heat anomalies across seasons and altitudes (Pithan and Mauritsen, 2014; Previdi et al., 2021). Such interdependencies highlight the challenges in mechanistic attribution and accurate projection of Arctic warming. Developing multi-feedback ECs could provide a more holistic view of Arctic climate, though this would require sophisticated modeling to disentangle overlapping signals.” [Comment 2] The necessity for a comprehensive understanding of warming mechanisms: While the Surface Albedo Feedback (SAF) is a dominant mechanism of Arctic amplification on annual or longer timescales, its contribution during cold seasons is minimal, as evidenced by the authors’ own figures. Therefore, relying solely on SAF within the deep learning model is incongruent with the observed seasonal data and limits the model's explanatory power. A more complete mechanistic framework is required. Response: Thank you for your comment. Please find our detailed responses below: 1. Response to the comment “While the Surface Albedo Feedback (SAF) is a dominant mechanism of Arctic amplification on annual or longer timescales, its contribution during cold seasons is minimal, as evidenced by the authors’ own figures” We quantified the contribution of SAF to Arctic land warming rate at the seasonal and annual scales, following your suggestion in your first round of review “If the authors try to continue this study, they need to prove the surface albedo feedback dominate the Arctic warming over the continent in the whole year.” Here we did show that SAF plays a major role in Arctic warming over the continent on annual scale, with minimal contribution during cold seasons. That’s exactly why we focus on annual SAF over land in this study. 2. Response to the comment “relying solely on SAF within the deep learning model is incongruent with the observed seasonal data and limits the model's explanatory power” We would like to clarify that we focus on SAF at the annual scale, and thus the observed seasonal data are aggregated to the annual scale accordingly. In addition, we did show a high explanatory power (R2 = 0.78) of the deep learning model (Fig. 2c in the Manuscript), which is much higher than the linear counterparts (R2 = 0.28) and most of prior works using ECs (Table R1 below). 3. Response to the comment “A more complete mechanistic framework is required.” We would like to emphasize that our estimate of SAF is grounded in the well-established theory, following previous mechanistic framework (Thackeray and Fletcher, 2016; Qu and Hall., 2014; Thackeray et al., 2021). Specifically, SAF is determined by two components: (1) the sensitivity of planetary albedo to land surface albedo changes ( ), and (2) the dependence of land surface albedo variations on air temperature ( 𝜕𝜕𝛼𝛼):𝑝𝑝 /𝜕𝜕𝛼𝛼𝑠𝑠 𝜕𝜕𝑎𝑎𝑠𝑠/𝜕𝜕𝜕𝜕𝑎𝑎 (1) 𝜕𝜕𝑄𝑄𝑛𝑛𝑛𝑛𝑛𝑛 𝜕𝜕𝑄𝑄𝑛𝑛𝑛𝑛𝑛𝑛𝜕𝜕𝛼𝛼𝑝𝑝 𝜕𝜕𝛼𝛼𝑝𝑝𝜕𝜕𝛼𝛼𝑠𝑠 where and are th𝑆𝑆e𝑆𝑆 i𝑆𝑆nc=omi𝜕𝜕n𝑇𝑇g𝑎𝑎 a=nd n𝜕𝜕𝛼𝛼et𝑠𝑠 s𝜕𝜕o𝑇𝑇l𝑎𝑎ar= ra−di𝑄𝑄ati𝜕𝜕o𝛼𝛼n𝑠𝑠 a𝜕𝜕t𝑇𝑇 𝑎𝑎the top-of-atmosphere (TOA) associat 𝑄𝑄 𝑄𝑄𝑛𝑛𝑛𝑛𝑛𝑛 ed with v𝑎𝑎ri𝑎𝑎tions of land surface albedo ( ), respectively, is the planetary albedo. 𝛼𝛼𝑠𝑠 𝛼𝛼𝑝𝑝 To quantify SAF-driven warming rate over Arctic land regions, we first computed the TOA net radiative flux ( ) as the sum of net shortwave and longwave fluxes: 𝑁𝑁 (2) where is TOA downwelling s𝑁𝑁ho=rtw𝑆𝑆↓av−e 𝑆𝑆r↑a−dia𝐿𝐿t↑ion, is TOA upwelling shortwave radiation𝑆𝑆,↓ and is TOA upwelling longwave radiation (G𝑆𝑆re↑gory et al., 2004; Trenberth et al., 2009). Positive𝐿𝐿 ↑ indicates energy gain by the Earth system. Annual means of were calculated using 3𝑁𝑁0-year moving windows for each CMIP6 model. 𝑁𝑁 Next, the effective radiative forcing ( ) and climate feedback parameter (λ) were estimated using the Gregory regression method𝑆𝑆 (Gregory et al., 2004), based on the energy-balance equation: (3) ′ where is the near-surface air tem𝑁𝑁pe=rat𝑆𝑆ure− a n𝜆𝜆oTm𝑎𝑎 aly relative to 1985–2014 (Gregory et al., ′ 2004; TTr𝑎𝑎enberth et al., 2009). For each SSP scenario, we regressed annual against over ′ the 30-year window; the intercept yielded (W m-2), and the slope provi𝑁𝑁ded λ (W mT𝑎𝑎-2 K-1), incorporating fast adjustments like cloud an𝑆𝑆d atmospheric responses without separate forcing data. λ encompasses multiple feedbacks, including atmospheric heat transport, water vapor feedback, cloud feedback and lapse-rate feedback (Knutti et al., 2017; Sherwood et al., 2020). Assuming SAF and λ vary slowly within the window (Hall, 2004; Soden and Held, 2006), the SAF-driven warming rate (ΔT ) is derived as: SAF (4) 𝑆𝑆𝑆𝑆𝑆𝑆 ∙ ΔT𝑛𝑛𝑡𝑡𝑛𝑛𝑎𝑎𝑡𝑡 ΔT𝑆𝑆𝑆𝑆𝑆𝑆 = 𝜆𝜆 where is the total warming rate (K decade-1) estimated via ordinary least squares. This approacΔhT 𝑛𝑛i𝑡𝑡s𝑛𝑛o𝑎𝑎l𝑡𝑡ates SAF’s contribution while accounting for the broader climate system’s response. 4. Summary of our revisions In the revision, we’ve added more details on the mechanistic framework used for estimating SAF and its driven land warming rate (Methods section: SAF calculation; SAF-driven warming rate), with strong theoretical foundations. We’ve also clarified in the Methods section that the observed seasonal data are aggregated to the annual scale accordingly (Lines 369−370 in the revised Manuscript). Please check the revised Methods section for details. [Comment 3] “Our study aims to reduce such uncertainties of ESMs in SAF projections over Arctic land regions, rather than asserting that SAF is the sole driver of Arctic land warming.” The manuscript’s title, which suggests a broad investigation of Arctic land warming, is inconsistent with its actual scope and focus on optimizing the Surface Albedo Feedback (SAF). A more accurate title reflecting the specific methodological contribution is warranted. Furthermore, while the application of deep learning to SAF optimization is of interest, I question its novelty and broad impact for a journal of Nature Communications's standing. The work may be more appropriately suited for a specialized journal such as Remote Sensing of Environment (RSE), Journal of Advances in Modeling Earth Systems (JAMES), or Geoscientific Model Development (GMD). Response: Thank you for your comment. In this study, we first develop a machine-learning based emergent constraint (EC) approach to reduce the uncertainty of SAF in ESMs, which contributes to 37–56% of Arctic land warming. We then quantify Arctic land warming rates driven by the unconstrained and constrained SAF, and compare their differences. We find that Arctic land warming rates are approximately one-third lower after constraining SAF projections, compared to the unconstrained estimates. Therefore, we believe the original title “Surface albedo feedback constraints imply one-third lower warming rates over Arctic land regions” can basically reflect the primary objective of our study. Our machine-learning EC approach has several novelties, addressing the limitations of prior ECs including linear assumptions, uncertain observations, insufficient validation (Shiogama et al., 2022 Nature; Petrova et al., 2024 Nature; Thackeray and Hall, 2019 Nat. Clim. Change; Tokarska et al., 2020 Sci. Adv.; Zhang et al., 2022 Nat. Commun): 1) Nonlinear Modeling: Random Forest effectively captures complex relationships (R2 = 0.70–0.88 vs. linear R2 = 0.28–0.48), yielding 45–55% uncertainty reduction—superior to prior ECs (as summarized in Table R1 above); 2) In-Situ Observational Fusion: Integrates low-uncertainty flux-tower data (FLUXNET 2015, ICOS and AmriFlux) with gridded products, enhancing constraint fidelity; 3) Multi-Type Validations: Novel tests for scenario/period/model-generational robustness (Supplementary Notes 2, 4, 6 and Figs. 16, 17, 20−22, 24−28, 30), filling gaps in EC literature (Williamson & Sansom, 2019). In the revision, we have revised title to: “Machine-learning emergent constraints on surface albedo feedback reduce one-third of projected warming over Arctic land regions”, which we hope can better reflect our methodological advance and key finding. [Comment 4] On methodological rigor and novelty: My understanding is that the core experiment involves artificially reducing the SAF in a model to demonstrate a corresponding temperature decrease. This approach is conceptually simplistic and lacks the mechanistic insight expected for a rigorous scientific investigation; it primarily demonstrates a known correlation rather than probing underlying processes. Furthermore, the key finding that SAF contributes to approximately 40% of Arctic warming was established in prior literature (e.g., Graversen et al., 2014). Therefore, a study focused solely on reaffirming this relationship, without introducing a significant conceptual advance, does not meet the high novelty threshold required for publication in Nature Communications. Response: Thanks for your comments. Our responses to each point are detailed below: 1. Response to the comment “My understanding is that the core experiment involves artificially reducing the SAF in a model to demonstrate a corresponding temperature decrease. This approach is conceptually simplistic and lacks the mechanistic insight expected for a rigorous scientific investigation” We would like to clarify that we did not artificially adjust SAF in a CMIP6 model. Instead, we constrain SAF projections by CMIP6 model ensemble and reduce the associated uncertainty, using the well-established emergent constraint (EC) approach (Shiogama et al., 2022 Nature; Petrova et al., 2024 Nature; Thackeray and Hall, 2019 Nat. Clim. Change; Tokarska et al., 2020 Sci. Adv.; Zhang et al., 2022 Nat. Commun). Recently, many ECs have been successfully applied to reduce the uncertainty of various indicators in the Earth system (Table R1). In this study, we develop a novel machine-learning based EC, addressing the methodological limitations of prior ECs (i.e. linear assumptions, uncertain observations, insufficient validation) by: 1) Nonlinear Modeling: Random Forest effectively captures complex relationships (R2 = 0.70–0.88 vs. linear R2 = 0.28–0.48), yielding 45–55% uncertainty reduction—superior to prior ECs (as summarized in Table R1 above); 2) In-Situ Observational Fusion: Integrates low-uncertainty flux-tower data (FLUXNET 2015, ICOS and AmriFlux) with gridded products, enhancing constraint fidelity; 3) Multi-Type Validations: Novel tests for scenario/period/model-generational robustness (Supplementary Notes 2, 4, 6 and Figs. 16, 17, 20−22, 24−28, 30), filling gaps in EC literature (Williamson & Sansom, 2019). Based on the constrained SAF, we then estimate Arctic land warming rate, which has strong theoretical foundations. Specifically, we first computed the top-of-atmosphere (TOA) net radiative flux ( ) as the sum of net shortwave and longwave fluxes: 𝑁𝑁 (5) where is TOA downwelling s𝑁𝑁ho=rtw𝑆𝑆↓av−e 𝑆𝑆r↑a−dia𝐿𝐿t↑ion, is TOA upwelling shortwave radiation𝑆𝑆,↓ and is TOA upwelling longwave radiation (G𝑆𝑆re↑gory et al., 2004; Trenberth et al., 𝐿𝐿↑ 2009). Positive indicates energy gain by the Earth system. Annual means of were calculated over 30𝑁𝑁-year moving windows for each CMIP6 model. 𝑁𝑁 Next, the effective radiative forcing ( ) and climate feedback parameter (λ) were estimated using the Gregory regression method𝑆𝑆 (Gregory et al., 2004), based on the energy-balance equation: (6) ′ where is the near-surface air tem𝑁𝑁pe=rat𝑆𝑆ure− a n𝜆𝜆oTm𝑎𝑎 aly relative to 1985–2014 (Gregory et al., ′ 2004; TTr𝑎𝑎enberth et al., 2009). For each SSP scenario, we regressed annual N against over ′ the 30-year window; the intercept yielded F (W m-2), and the slope provided λ (W mT𝑎𝑎-2 K-1), incorporating fast adjustments like cloud and atmospheric responses without separate forcing data. λ encompasses multiple local and nonlocal feedbacks, including ocean heat transport, atmospheric circulation anomaly, water vapor feedback, cloud feedback and lapse-rate feedback (Knutti et al., 2017; Sherwood et al., 2020). Assuming SAF and λ vary slowly within the window (Hall, 2004; Soden and Held, 2006), the SAF-driven warming rate ( ) is derived in trend form as: ∆T𝑆𝑆𝑆𝑆𝑆𝑆 (7) 𝑆𝑆𝑆𝑆𝑆𝑆 ∙ ∆T𝑛𝑛𝑡𝑡𝑛𝑛𝑎𝑎𝑡𝑡 ∆T𝑆𝑆𝑆𝑆𝑆𝑆 = 𝜆𝜆 where is the total warming rate (K decade-1) estimated via ordinary least squares. This approac∆hT 𝑛𝑛i𝑡𝑡s𝑛𝑛o𝑎𝑎l𝑡𝑡a tes SAF’s contribution while accounting for the broader climate system's response. Therefore, our approaches are not “artificially reducing SAF”. Instead, our approach has strong theoretical and mechanistic foundations as stated above. More details on the methodology can be found in the Methods and Supplementary texts. Mechanistic diagnosis can be found in the Results section: Physical mechanisms underlying the emergent constraints. Our methods are also carefully validated and verified against observations via multiply tests (Results section: Verification of the emergent constraints; Supplementary Notes 2, 4, 6 and Figs. 16, 17, 20−22, 24−28, 30). 2. Response to the comment “it primarily demonstrates a known correlation rather than probing underlying processes. Furthermore, the key finding that SAF contributes to approximately 40% of Arctic warming was established in prior literature (e.g., Graversen et al., 2014).” We would like to clarify that we quantify the contribution of SAF to Arctic land warming rate at the seasonal and annual scale, following your suggestion in the first round of review “If the authors try to continue this study, they need to prove the surface albedo feedback dominate the Arctic warming over the continent in the whole year.” Consistent with the literature (e.g., Graversen et al., 2014), we show that SAF has a significant contribution to annual warming trend (37–56%) (Fig. 1e in the Manuscript and Supplementary Figs. 5, 6). We show this not for demonstrating a known correlation, but following your prior suggestion to better justify our focus on annual SAF in this study. Reviewer #2 Major comments: Several studies highlight the interconnections between surface albedo feedback and other regional climate feedbacks in the Arctic, particularly the compensatory interplay between surface albedo feedback and atmospheric heat transport (Alexeev and Jackson, 2013; Feldl et al., 2017; Hahn et al., 2021). This interplay complicates estimating the impact of constraining surface albedo feedback alone on Arctic land warming rates using model outputs, as individual feedbacks don’t operate in isolation and anomalies from one can be offset by others. Response: Thanks for your comments. Please find our detailed responses to your concerns below: 1. Accounting for interconnections between SAF and other climate feedbacks We would like to clarify that our estimate of SAF-driven warming rate follows the energy-balance framework, which does account for interconnections and interplays between SAF and other climate feedbacks, as illustrated in Fig. R1. Here, the climate feedback parameter (λ) is used to represent the integrated effect of multiple feedbacks, including atmospheric heat transport, water vapor feedback, cloud feedback and lapse-rate feedback (Gregory et al., 2016; Knutti et al., 2017; Sherwood et al., 2020). Specifically, to quantify SAF-driven warming rate over Arctic land regions, we first computed the top-of-atmosphere (TOA) net radiative flux ( ) as the sum of net shortwave and longwave fluxes: 𝑁𝑁 (1) where is TOA downwelling s𝑁𝑁ho=rtw𝑆𝑆↓av−e 𝑆𝑆r↑a−dia𝐿𝐿t↑ion, is TOA upwelling shortwave radiation𝑆𝑆,↓ and is TOA upwelling longwave radiation (G𝑆𝑆re↑gory et al., 2004; Trenberth et al., 2009). Positive𝐿𝐿 ↑ indicates energy gain by the Earth system. Annual means of N were calculated over 30𝑁𝑁-year moving windows for each CMIP6 model. Next, the effective radiative forcing ( ) and climate feedback parameter (λ) were estimated using the Gregory regression method𝑆𝑆 (Gregory et al., 2004), based on the energy-balance equation: (2) ′ where is the near-surface air tem𝑁𝑁pe=rat𝑆𝑆ure− a n𝜆𝜆oTm𝑎𝑎 aly relative to 1985–2014 (Gregory et al., ′ 2004; TTr𝑎𝑎enberth et al., 2009). For each SSP scenario, we regressed annual against over ′ the 30-year window; the intercept yielded F (W m-2), and the slope provi𝑁𝑁ded λ (W mT𝑎𝑎-2 K-1), incorporating fast adjustments like cloud and atmospheric responses without separate forcing data. λ encompasses multiple feedbacks, including atmospheric heat transport, water vapor feedback, cloud feedback and lapse-rate feedback (Knutti et al., 2017; Sherwood et al., 2020). Assuming SAF and λ vary slowly within the window (Soden and Held, 2006; Hall, 2004), the SAF-driven warming rate (ΔT ) is derived as: SAF (3) 𝑆𝑆𝑆𝑆𝑆𝑆 ∙ ΔT𝑛𝑛𝑡𝑡𝑛𝑛𝑎𝑎𝑡𝑡 ΔT𝑆𝑆𝑆𝑆𝑆𝑆 = 𝜆𝜆 where is the total warming rate (K decade-1) estimated via ordinary least squares. This approacΔhT 𝑛𝑛i𝑡𝑡s𝑛𝑛o𝑎𝑎l𝑡𝑡ates SAF’s contribution while accounting for the broader climate system’s response. 2. Further clarification of our research goal (i.e. to demonstrate the importance of constraining SAF for more accurate Arctic climate projections) To constrain all related feedbacks is infeasible, so we focus on SAF, which contributes to 37–56% of annual warming rate over Arctic land areas. Specifically, we use the emergent constraint (EC) approach to constrain SAF projections (Brient, 2019; Hall et al., 2019), which has been successfully applied to reduce the uncertainty of a single indicator in the Earth system (e.g. Shiogama et al., 2022 Nature; Petrova et al., 2024 Nature; Thackeray and Hall, 2019 Nat. Clim. Change; Tokarska et al., 2020 Sci. Adv.; Zhang et al., 2022 Nat. Commun). Although we follow the framework of prior ECs, our approach is novel in addressing their limitations (e.g. linear assumptions, uncertain observations, insufficient validation), yielding high explanatory power of SAF—superior to prior ECs (Table R2 below). We then compare Arctic land warming rates driven by the constrained and unconstrained SAF, to demonstrate the importance of constraining SAF for more accurate Arctic climate projections (Fig. R1). 3. Summary of our revisions In the revision, we’ve described the approach for estimating SAF-driven warming rate (Methods section: SAF-driven warming rate), which accounts for the interconnections between SAF and other climate feedbacks. In addition, we’ve added a new paragraph in the Discussion section to acknowledge the limitation of not constraining all related feedbacks. “Moreover, we implement ECs to SAF only, without constraining other related feedbacks like atmospheric heat transport, permafrost carbon release, or cloud radiative effects, which amplify Arctic warming in complex ways. For instance, although sea-ice retreat boosts local shortwave absorption, it often triggers a compensatory reduction in poleward atmospheric heat transport (Alexeev and Jackson, 2013; Feldl et al., 2017; Liang et al., 2022). Comparable offsets occur vertically: heightened humidity and low-cloud formation enhance longwave trapping, while increased ocean heat uptake tempers the lapse-rate feedback, redistributing SAF-induced heat anomalies across seasons and altitudes (Pithan and Mauritsen, 2014; Previdi et al., 2021). Such interdependencies highlight the challenges in mechanistic attribution and accurate projection of Arctic warming. Developing multi-feedback ECs could provide a more holistic view of Arctic climate, though this would require sophisticated modeling to disentangle overlapping signals.” The physical mechanisms behind the sharp transitions in regional surface albedo feedback, caused by minor changes in land surface albedo responses to air temperature changes, are still unclear, especially around the value of -1.0 % K-1 (Figure 2a, c). These sharp transitions appear to be largely driven by models near this value. What physical processes correspond to this? Would removing several models around the sharp transition zone near -1.0 % K⁻¹ significantly alter the transitions? Response: Thank you for your comment. In Figure 2a, c, each dot indicates a CMIP6 model. The nonlinear relations shown in Figure 2a, c emerge when we analyze the ensemble of all available CMIP6 models, following prior EC studies (e.g., Shiogama et al., 2022 Nature; Petrova et al., 2024 Nature; Thackeray and Hall, 2019 Nat. Clim. Change; Tokarska et al., 2020 Sci. Adv.; Zhang et al., 2022 Nat. Commun). Therefore, it may be inappropriate to interpret that the sharp transitions in surface albedo feedback are caused by minor changes in land surface albedo responses to air temperature changes. Rather, it reflects an important structural feature of the CMIP6 model ensemble. Detailed explanations and sensitivity tests are shown below: 1. Explanations of the sharp transitions The sharp transition of near -1.0% K-1 is unlikely to reflect a single, abrupt physical threshold or tipping poin𝜕𝜕t𝛼𝛼 c𝑠𝑠r/o𝜕𝜕ss𝜕𝜕e𝑎𝑎d simultaneously by all Earth system models (ESMs). Instead, it emerges from the coexistence of two distinct model clusters within the CMIP6 ensemble, representing divergent but physically plausible depictions of Arctic land surface processes. To substantiate this interpretation, we conducted a quantitative diagnosis of the physical mechanisms driving the transition. Our findings reveal that models on either side of the transition exhibit systematic differences in the components of their SAF (e.g., snow-cover fraction changes, vegetation dynamics, and surface albedo sensitivity). Here we classified the CMIP6 ensemble into two groups based on their SAF values: • Group A: Models with lower (below -1.1% K-1). • Group B: Models with higher 𝜕𝜕𝛼𝛼𝑠𝑠/𝜕𝜕𝜕𝜕𝑎𝑎 (above -0.9% K-1). 𝜕𝜕𝛼𝛼𝑠𝑠/𝜕𝜕𝜕𝜕𝑎𝑎 We then decomposed SAF into its core physical components using available ESMs outputs. The snow-cover fraction contribution ( ) and vegetation contribution ( ) were quantified as follows: 𝑆𝑆𝑆𝑆𝑆𝑆𝑐𝑐𝑡𝑡𝑛𝑛 𝐿𝐿𝑆𝑆𝐿𝐿𝑐𝑐𝑡𝑡𝑛𝑛 = ( ) × ( ) (4) 𝑆𝑆𝑆𝑆𝑆𝑆𝑐𝑐𝑡𝑡𝑛𝑛 = 𝜕𝜕(𝛼𝛼𝑠𝑠/𝜕𝜕𝑆𝑆𝑆𝑆𝑆𝑆) × (𝜕𝜕𝑆𝑆𝑆𝑆𝑆𝑆/𝜕𝜕𝜕𝜕𝑎𝑎) (5) where represents l𝐿𝐿a𝑆𝑆nd𝐿𝐿𝑐𝑐 𝑡𝑡s𝑛𝑛urface𝜕𝜕 𝛼𝛼al𝑠𝑠b/e𝜕𝜕d𝐿𝐿o𝑆𝑆 r𝐿𝐿espon𝜕𝜕s𝐿𝐿e𝑆𝑆 to𝐿𝐿/ c𝜕𝜕h𝜕𝜕a𝑎𝑎nges in snow cover fraction, 𝜕𝜕𝛼𝛼𝑠𝑠 /i𝜕𝜕s 𝑆𝑆th𝑆𝑆e𝑆𝑆 temperature sensitivity of snow cover, is the albedo response to 𝜕𝜕ve𝑆𝑆g𝑆𝑆e𝑆𝑆ta/t𝜕𝜕io𝜕𝜕nₐ changes, and represents vegetation𝜕𝜕 𝛼𝛼s𝑠𝑠e/n𝜕𝜕si𝐿𝐿ti𝑆𝑆v𝐿𝐿ity to temperature. In this framework, qu an𝜕𝜕ti𝐿𝐿fi𝑆𝑆es𝐿𝐿 /t𝜕𝜕he𝜕𝜕 ₐcryosphere contribution linked to snow cover loss, while reflec𝑆𝑆t𝑆𝑆s 𝑆𝑆t𝑐𝑐h𝑡𝑡e𝑛𝑛 biospheric contribution associated with vegetation dynamics. 𝐿𝐿𝑆𝑆𝐿𝐿𝑐𝑐𝑡𝑡𝑛𝑛 We compared these feedback components between Groups A and B. The analysis reveals significant intergroup differences in both and , showing stronger snow and vegetation feedbacks in Group A. This con𝑆𝑆t𝑆𝑆ra𝑆𝑆𝑐𝑐s𝑡𝑡t 𝑛𝑛suggest𝐿𝐿s𝑆𝑆 t𝐿𝐿h𝑐𝑐a𝑡𝑡𝑛𝑛t the sharp divergence in SAF values originate from differences in the key physical parameterizations across CMIP6 models. As illustrated in Fig. R2 below, the sharp transitions around -1.0% K-1 are primarily associated with contrasting cryosphere and biospheric components. During the historical period, the transitions are jointly controlled by differences in the parameterization of snow cover and vegetation feedbacks (Fig. R2a). In future projections, these transitions are increasingly dominated by cryosphere feedback differences among models (Fig. R2b–i). Together, these results demonstrate that the abrupt transitions near -1.0% K-1 stem from nonlinear interactions between snow cover retreat and vegetation dynamics in CMIP6 models. The grouping analysis offers a clear physical interpretation, linking the apparent model bifurcation to structural differences in cryosphere and biospheric feedback parameterizations among CMIP6 models. We believe this additional analysis directly addresses your concern and enhances the physical interpretation of the observed transition. 2. Sensitivity tests by removing models around the sharp transition zone To further address your concern about the sensitivity of the constraint to models near the transition zone (-1.1 to -0.9% K-1), we performed a targeted sensitivity test. Specifically, we conducted a leave-one-out (LOO) sensitivity analysis focusing on models located near the -1.0% K-1 transition point to evaluate the robustness of our results. This analysis aimed to determine whether removing a small subset of “sharp transition” models would substantially alter our major conclusions. We excluded models within the range of -1.1% K-1 to -0.9% K-1 and refitted the emergent relationships. For example, under the SSP5-8.5 scenario during 2070–2099, excluding these models slightly modified the correlation strength (R2=0.78 vs R2=0.84) but did not alter the overall relationship or key conclusions. The results indicate that the multi-model ensemble mean continues to overestimate future SAF, while our machine learning–based emergent constraint consistently corrects this bias and reduces the associated uncertainty (Fig. R3), reinforcing the robustness of this finding. In summary, our sensitivity tests confirm that excluding models near -1.0% K-1 does not impact our major conclusions. The evidence suggests that the apparent sharp transition is fundamentally driven by structural differences between the two CMIP6 model clusters. 3. Summary of our revisions In the revision, we have added a new section in the supplementary on the sharp transitions and sensitivity test results (i.e. Supplementary Note 2: Explanation of sharp transition of SAF across CMIP6 models). A corresponding summary on this point is also included in the Result section (Lines 139−141 in the revised Manuscript). In addition, the random forest regression relationship shows a markedly different strength compared to the linear regression relationship when the response of land surface albedo to air temperature changes is around -1.5 % K-1 under SSP2-4.5 and SSP5-8.5 (Figure S20b, d). These discrepancies appear to be closely associated with the models in the vicinity. Does this suggest that the random forest regression relationship is heavily influenced by these models in this particular zone? If this is the case, does it imply that the observationally constrained surface albedo feedback is significantly influenced by models whose land surface albedo response to air temperature changes are close to the observation-derived values? Response: Thank you for your comment. The emergent relations emerge when we analyze an ensemble of models, and it is a common practice to include all available models to derive the relations, like previous EC works (Table R2). To address your concern, we conducted the leave-one-out (LOO) sensitivity test, in which each model was sequentially excluded and the emergent relationship was recalculated using both linear and random forest methods (see Fig. R4). The coefficients of determination (R2) for both regressions remain within a narrow and stable range across four climate scenarios and two future periods (2040–2069 and 2070–2099), indicating no heavy influence from individual models, even those close to the observation-derived values (Fig. R4). To further address your concern, we applied the EC derived from each LOO-fitted regression to estimate SAF during the near- and far-future periods (Figs. R5 and R6). The results reveal that (i) the unconstrained ensemble consistently overestimates SAF; (ii) the EC method, even when derived from LOO-fitted regressions (colored curves), produces a tightly constrained projection; and (iii) the constrained SAF distributions and their uncertainty metrics ( and ) remain highly consistent with the original results. Importantly, the random for𝛥𝛥e𝛥𝛥st EC c𝛥𝛥o𝛥𝛥ntinues to substantially reduce SAF projection uncertainty ( ) under all scenarios. 𝛥𝛥𝛥𝛥 These findings demonstrate that our EC is inherently robust to model selection and not heavily influenced by models near the observationally derived values. This robustness is consistently observed across all SSP scenarios and time periods. Together, this confirms the reliability of random forest–based EC in reducing the uncertainty of SAF projections. In the revision, we’ve added a new section in the supplementary to include the sensitivity tests (i.e. Supplementary Note 4: Leave-one-out (LOO) sensitivity tests). A corresponding summary on this point is also included in the Result section (Lines 153−156). Reviewer #3 The authors have largely addressed my previous comments and the revised manuscript is improved as a result. There is still a disconnect between the emphasis on ocean/sea ice albedo feedbacks in the introduction and the focus of the analyses on terrestrial SAF dynamics. At the very least, it is necessary to frame terrestrial SAF/warming in the context of regional dynamics, but it would also be helpful to very briefly describe the terrestrial processes driving variability/uncertainty in SAF dynamics. Response: Thank you for your positive comment. In the first round of review, Reviewer #1 asks for more descriptions of ocean related feedbacks, and so we expanded the introduction accordingly. We appreciate your recognition on our focus on terrestrial SAF dynamics. Considering both your and Reviewer #1’s suggestions for a thorough description of ocean related feedbacks in this round of review, the ocean related feedbacks are incorporated in the Discussion section. We hope this can achieve a balance between your and Reviewer #1’s contradictory suggestions. L34: The Arctic is… Response: Corrected. Thank you. L220: Indirect negative is listed twice, in red and blue, below panels a & b Response: Corrected. Thank you. L479: A link to a GitHub repository or some other open access version of the code is preferable. Response: We have deposited our code in a public repository and updated the “Code Availability” section."}, {"round": 3, "reviewer_comments": {"reviewer_2": "General comments: The authors’ attempt to constrain surface albedo feedback with a machine-learning approach is novel. Yet, because Arctic land warming is shaped by the combined effect of all feedbacks and related processes, isolating the influence of surface albedo feedback alone is problematic. Within a linear framework each feedback may appear to act independently, but their cross-correlations are usually non-negligible. Warming attributable to surface albedo feedback can be partially offset by cooling contributions from turbulent sensible and latent heat-flux feedbacks from a surface-energy-balance perspective (Hu et al., 2022) or by atmospheric heat transport from a top-of-atmosphere perspective (Alexeev & Jackson, 2013; Feldl et al., 2017; Hahn et al., 2021). Models that yield a large albedo-driven warming typically exhibit a compensating cooling from enhanced turbulent fluxes. Therefore, correcting surface albedo feedback induced warming biases alone does not imply an equivalent reduction in overall warming. It is recommended that the paper highlights the novelty of constraining surface albedo feedback, rather than emphasizing its isolated impact on Arctic land warming. Comments on the authors’ explanations of the abrupt transitions: Because the machine-learning regression maximizes nonlinear fit quality, dropping the models in the sharp-transition zone will not materially weaken the correlation, yet it could markedly alter the apparent shape of the transition. It would be interesting to see what Figure 2a and 2c look like after excluding models whose values lie between −1.1 % K⁻¹ and −0.9 % K⁻¹.", "reviewer_3": "The authors have satisfactorily addressed my previous comments. There are just a few minor points for clarification. L72: “...proving help for actionable insights for policymakers,", "reviewer_110": "To be clear, there are no statistically significant differences between scenarios? L118: Land surface albedo is defined differently above (L77)"}, "author_response": "Point-by-Point Response to Reviewers Reviewer #2 General comments: The authors’ attempt to constrain surface albedo feedback with a machine-learning approach is novel. Yet, because Arctic land warming is shaped by the combined effect of all feedbacks and related processes, isolating the influence of surface albedo feedback alone is problematic. Within a linear framework each feedback may appear to act independently, but their cross-correlations are usually non-negligible. Warming attributable to surface albedo feedback can be partially offset by cooling contributions from turbulent sensible and latent heat-flux feedbacks from a surface-energy-balance perspective (Hu et al., 2022) or by atmospheric heat transport from a top-of-atmosphere perspective (Alexeev & Jackson, 2013; Feldl et al., 2017; Hahn et al., 2021). Models that yield a large albedo-driven warming typically exhibit a compensating cooling from enhanced turbulent fluxes. Therefore, correcting surface albedo feedback induced warming biases alone does not imply an equivalent reduction in overall warming. It is recommended that the paper highlights the novelty of constraining surface albedo feedback, rather than emphasizing its isolated impact on Arctic land warming. Response: Thank you for your time and thoughtful comments. Following your recommendation, we have revised the manuscript to highlight the novelty of our machine-learning approach for constraining surface albedo feedback (SAF), rather than emphasizing its isolated impact on Arctic land warming. Specifically, we have deleted all statements related to the reduced Arctic warming in the Abstract (lines 13-14), Results (lines 89-94, 155-156), Discussion (lines 259-261; 337-339) and Methods sections (lines 401-421), and updated Figs. 1 and 3 accordingly. We have retained only a brief, balanced discussion of SAF’s potential role in Arctic land warming in the Discussion section (lines 247-249), to provide necessary context without overstatement. Additionally, we have added the following statements in lines 325-328 to explicitly acknowledge the compensating effects from other feedbacks: “SAF’s induced warming can also be partially offset by cooling contributions from turbulent sensible and latent heat-flux feedbacks from a surface-energy-balance perspective or by atmospheric heat transport from a top-of-atmosphere perspective (Alexeev and Jackson 2013; Feldl et al., 2017; Hahn et al., 2021; Hu et al., 2022).” The title of the paper has also been modified to “Machine-learning emergent constraints on surface albedo feedback over Arctic land regions” to better reflect our primary focus on constraining SAF. With these changes, claims related to reduced Arctic warming have been sufficiently toned down, and we have highlighted the limitations and interdependencies with other processes more transparently throughout the Discussion section. We hope these revisions meet your expectations and strengthen the manuscript's scientific rigor. Comments on the authors’ explanations of the abrupt transitions: Because the machine-learning regression maximizes nonlinear fit quality, dropping the models in the sharp-transition zone will not materially weaken the correlation, yet it could markedly alter the apparent shape of the transition. It would be interesting to see what Figure 2a and 2c look like after excluding models whose values lie between −1.1 % K⁻¹ and −0.9 % K⁻¹. Response: Thank you for your insightful comment. To address your concern, we have re-plotted Figure 2a and 2c by excluding models whose values lie between −1.1 % K⁻¹ and −0.9 % K⁻¹, as shown in Fig. R1a, b below. Although removing these models results in a modest change in the shape of the transition (compared to Figure 2a and 2c), it does not alter our main conclusions. Notably, whether we include or exclude the transition-zone models, our emergent constraints lead to similar reductions in SAF and its uncertainty (Supplementary Fig. 17), suggesting systematic overestimations in ESMs. In our previous submission, we added a new section in the Supplementary Information detailing the explanations for these transitions, supported by multiple sensitivity tests (Supplementary Note 2, Figs. 15, 17, 19, 20, 21). In this revision, we have incorporated Fig. R1 into the Supplementary Information (now as Supplementary Fig. 16) to further elaborate on this point and enhance transparency. Reviewer #3 The authors have satisfactorily addressed my previous comments. There are just a few minor points for clarification. Response: Thank you for your time, support, and positive assessment of our revisions! L72: “...proving help for actionable insights for policymakers,"}, {"round": 4, "reviewer_comments": {"reviewer_4": "I was asked to review the author's response to reviewer comments and specifically the comment to Reviewer 2 since they are not available. I have reviewed the comments and relevant portion of the manuscript. In my assessment the authors have satisfactorily addressed all reviewer comments and specifically the comments of Reviewer 2. While the points made by reviewer 2 with regards to the non-negligible interactions between multiple feedback processes are well-received and correct, I think that there is value is the quantification of individual feedback contributions to warming. The authors have adequately acknowledged the non-linear, coupled feedback processes. Lastly, the only major comment from reviewer 2 was with regards to the influence of models in the \"sharp transition zone\" on the ML regression results. The authors show that this has a minimal influence and does not alter conclusions. In my assessment, the article should be accepted."}, "author_response": ""}]

Decision letter