An emergent constraint on future Arctic sea-ice albedo feedback

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Arctic sea ice has decreased substantially over recent decades, a trend projected to continue. Shrinking ice reduces surface albedo, leading to greater surface solar absorption, thus amplifying warming and driving further melt. This sea-ice albedo feedback (SIAF) is a key driver of Arctic climate change and an important uncertainty source in climate model projections. Using an ensemble of models, we demonstrate an emergent relationship between future SIAF and an observable version of SIAF in the current climate’s seasonal cycle. This relationship is robust in constraining SIAF over the coming decades (Pearson’s r = 0.76), and then it degrades. The degradation occurs because some models begin producing ice-free conditions, signalling a transition to a new ice regime. The relationship is strengthened when models with unrealistically thin historical ice are excluded. Because of this tight relationship, reducing model errors in the current climate’s seasonal SIAF and ice thickness can narrow SIAF spread under climate change.

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Fig. 1: Maps of seasonal cycle SIAF (SSIAF) across the Arctic.
Fig. 2: Heat map of historical Arctic SIT during the melt season.
Fig. 3: Comparison of simulated SIAF in the seasonal cycle and under climate change.
Fig. 4: Strength of the SIAF relationship between the seasonal cycle (always defined over MJJA) and various definitions of climate change time frames.
Fig. 5: Scatterplot of SIAF in the seasonal cycle and under climate change.

Data availability

The data that support the findings of this study are publicly available. The CMIP5 output is available from the Earth System Grid Federation ( Satellite albedo data are available from and The temperature reanalyses datasets are available from and The ice thickness data can be downloaded from Source data for Figs. 2, 4 and 5 is available online.

Code availability

The code relating to this study is available from the corresponding author on request.


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We acknowledge funding from the National Science Foundation grant (no. 1543268) titled ‘Reducing Uncertainty Surrounding Climate Change Using Emergent Constraints’. We also thank the World Climate Research Programme’s Working Group on Coupled Modeling and the individual modelling groups (listed in Extended Data Fig. 9) for their roles in making CMIP5 data available. For CMIP the US Department of Energy’s Program for Climate Model Diagnosis and Intercomparison provided coordinating support and led the development of software infrastructure in partnership with the Global Organisation for Earth System Science Portals. We thank X. Qu for helpful discussions about this research.

Author information

C.W.T. and A.H. conceived of the study and designed the analyses. C.W.T. conducted analyses and wrote the manuscript, while A.H. provided comments and feedback.

Correspondence to Chad W. Thackeray.

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The authors declare no competing interests.

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Peer review information Nature Climate Change thanks Mark Flanner and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data

Extended Data Fig. 1 Maps of model bias in SSIAF.

Similar to Fig. 1, spatial distributions of model bias relative to the OBS mean are shown. Note that the color bar on the left only applies to the OBS mean map (top left).

Extended Data Fig. 2 Scatterplots of SSIAF and various ice-related metrics from the CMIP5 models.

(a, b, c) The first three metrics breakdown the initial ice conditions (extent, albedo thickness), while (d) and (e) show the change in albedo and ice thickness across the melt season (defined as the May-Aug difference). (f) Lastly, we derive the seasonal change in ice concentration per degree of contemporaneous Arctic warming (defined ice cover sensitivity). The spatial domain for these metrics is limited to ocean areas polewards of 70°N, while ice thickness and ice-covered surface albedo are defined over areas with at least 10% sea ice concentration.

Extended Data Fig. 3 CMIP5 mean mid-century (2030-2050) monthly SIAF strength across the Arctic.

Shading illustrates ± one standard deviation from the ensemble mean. The percentage of annual feedback strength coming from the late spring and summer months (MJJA) is very high. This is why it can be used as a proxy for annual feedback strength.

Extended Data Fig. 4 Maps of mid-century CCSIAF across the Arctic in CMIP5 models.

Observations (from Fig. 1) and the CMIP5 mean (from Fig. 3) are shown for reference. The climate change feedback shown here is calculated as the average of May, June, July and August values for the period of 2030-2050 (with respect to 1980-2015).

Extended Data Fig. 5 Relationship between historical August ice thickness and the timing of ice-free Septembers.

Ice-free timing is shown with two different definitions. (a) The first ice-free September is defined as the first year in which the 5-year running mean SIE falls below 1 million km2, while (b) consistently ice-free conditions refers to the year when the 5-year running mean has been below 1 million km2 for 5 straight years. Each point is coloured by historical August sea ice extent.

Extended Data Fig. 6 Scatterplot of SSIAF and CCSIAF (as in Fig. 5a) with uncertainty shown (± 1 standard deviation).

Error bars are shown for models with at least 3 ensemble members under RCP8.5. In all cases the seasonal cycle variability is small between members, while the climate change variability can be larger. This illustrates that the choice of using only the first ensemble member does not impact our main conclusions.

Extended Data Fig. 7 Comparison of seasonal SIAF estimates derived from two different satellite-derived albedo datasets.

Observational SSIAF derived using two temperature datasets and (a) APP-x albedo (b) CLARA-A2 albedo. These estimates go into calculating the OBS mean used throughout the text. Note the slightly larger missing data region over the North Pole in b stems from the CLARA-A2 product.

Extended Data Fig. 8 Strength of the SIAF relationship between the seasonal cycle (defined over April-August) and various definitions of climate change.

As in Fig. 4, but with a different definition of seasonal SIAF. The similarity with Fig. 4 illustrates that changing the definition of SSIAF has little impact on the emergent constraint.

Extended Data Figure 9 CMIP5 models used in this study.

List of CMIP5 models analyzed here and their respective modelling centres.

Supplementary information

Source data

Source Data Fig. 2

Summer sea ice thicknesses from CMIP5 models and PIOMAS.

Source Data Fig. 4

Correlation values between SSIAF and CCSIAF for various collections of CMIP5 models.

Source Data Fig. 5

SIAF and SIT data for CMIP5 models.

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Thackeray, C.W., Hall, A. An emergent constraint on future Arctic sea-ice albedo feedback. Nat. Clim. Chang. 9, 972–978 (2019) doi:10.1038/s41558-019-0619-1

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