PIXAL: a physics-inspired explainable machine learning architecture for Greenland ice albedo modeling

[en] Abstract. The Greenland ice sheet (GrIS) is a major contributor to global sea level rise. A significant portion of the GrIS' contribution can be attributed to increased ice surface melting, which is strongly controlled by ice albedo, a property that regulates the amount of absorbed solar radiation that leads to surface melting. Yet, we lack a comprehensive understanding of the complex and nonlinear relationships ice albedo has with its environment and is, therefore, often simplified or crudely parameterized in climate models. However, an accurate representation of future ice albedo evolution is essential for reducing uncertainties in sea level rise projections. This study presents PIXAL, a physics-inspired explainable machine learning architecture that significantly outperforms the Modèle Atmosphérique Régional (MAR), a state-of-the-art regional climate model, in modeling ice albedo on the southwestern GrIS. PIXAL is based on an Extreme Gradient Boosting (XGBoost) model and is trained on a suite of modeled topographic, atmospheric, radiative, and glaciologic variables from MAR to capture the complex and nonlinear relationships with ice albedo observations obtained from the Moderate Resolution Imaging Spectroradiometer (MODIS). Performance metrics show that PIXAL achieves an R2 of 0.563, a structural similarity index measure (SSIM) of 0.620, a mean squared error (MSE) of 0.005, and a mean absolute percentage error (MAPE) of 14.699 %, compared to MAR's R2 of 0.062, SSIM of 0.112, MSE of 0.032, and MAPE of 46.202 %. Explainable artificial intelligence analysis reveals that topographic features, specifically ice sheet surface height and slope, are important drivers of ice albedo variability due to their relationships with ice exposure duration and the effectiveness in accumulating meltwater and light-absorbing constituents (LACs) on flat ice surfaces. Near-surface air temperature and runoff further significantly impact ice albedo variability by affecting the ice metamorphic state and accumulation of meltwater and LACs. These findings highlight that understanding the complex physical processes underlying ice albedo variability is essential for accurate climate modeling and sea level rise predictions. PIXAL represents a crucial advancement in ice albedo modeling and paves the way for improved representation of ice sheets in Earth system models.

Research Center/Unit :

SPHERES - ULiège

Disciplines :

Earth sciences & physical geography

Author, co-author :

Antwerpen, Raf

Tedesco, Marco

Gentine, Pierre

van de Berg, Willem Jan

Fettweis, Xavier ; Université de Liège - ULiège > Département de géographie > Climatologie et Topoclimatologie

Language :

English

Title :

PIXAL: a physics-inspired explainable machine learning architecture for Greenland ice albedo modeling

Publication date :

29 May 2026

Journal title :

The Cryosphere

ISSN :

1994-0416

eISSN :

1994-0424

Publisher :

Copernicus GmbH

Volume :

Issue :

Pages :

3131-3149

Peer reviewed :

Peer Reviewed verified by ORBi

Tags :

CÉCI : Consortium des Équipements de Calcul Intensif

Additional URL :

https://tc.copernicus.org/articles/20/3131/2026/tc-20-3131-2026.pdf

Funders :

NSF - National Science Foundation
Heising-Simons Foundation
GSFC - Goddard Space Flight Center

Available on ORBi :

since 29 May 2026

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Akiba, T., Sano, S., Yanase, T., Ohta, T., and Koyama, M.: Optuna: A Next-generation Hyperparameter Optimization Framework, arXiv [preprint], https://doi.org/10.48550/arXiv.1907.10902, 2019.
Alexander, P. M., Tedesco, M., Fettweis, X., van de Wal, R. S. W., Smeets, C. J. P. P., and van den Broeke, M. R.: Assessing spatio-temporal variability and trends in modelled and measured Greenland Ice Sheet albedo (2000–2013), The Cryosphere, 8, 2293–2312, https://doi.org/10.5194/tc-8-2293-2014, 2014.
Amino, T., Iizuka, Y., Matoba, S., Shimada, R., Oshima, N., Suzuki, T., Ando, T., Aoki, T., and Fujita, K.: Increasing dust emission from ice free terrain in southeastern Greenland since 2000, Polar Sci. 27, 100599, https://doi.org/10.1016/j.polar.2020.100599, 2021.
Antwerpen, R. M., Tedesco, M., Fettweis, X., Alexander, P., and van de Berg, W. J.: Assessing bare-ice albedo simulated by MAR over the Greenland ice sheet (2000–2021) and implications for meltwater production estimates, The Cryosphere, 16, 4185–4199, https://doi.org/10.5194/tc-16-4185-2022, 2022.
Aschwanden, A., Fahnestock, M. A., Truffer, M., Brinkerhoff, D. J., Hock, R., Khroulev, C., Mottram, R., and Khan, S. A.: Contribution of the Greenland Ice Sheet to sea level over the next millennium, Sci. Adv., 5, eaav9396, https://doi.org/10.1126/sciadv.aav9396, 2019.
Badgeley, J. A., Steig, E. J., Hakim, G. J., and Fudge, T. J.: Greenland temperature and precipitation over the last 20000 years using data assimilation, Clim. Past, 16, 1325–1346, https://doi.org/10.5194/cp-16-1325-2020, 2020.
Batunacun, Wieland, R., Lakes, T., and Nendel, C.: Using Shapley additive explanations to interpret extreme gradient boosting predictions of grassland degradation in Xilingol, China, Geosci. Model Dev., 14, 1493–1510, https://doi.org/10.5194/gmd-14-1493-2021, 2021.
Bond, T. C., Doherty, S. J., Fahey, D. W., Forster, P. M., Berntsen, T., DeAngelo, B. J., Flanner, M. G., Ghan, S., Kärcher, B., Koch, D., Kinne, S., Kondo, Y., Quinn, P.K., Sarofim, M. C., Schultz, M. G., Schulz, M., Venkataraman, C., Zhang, H., Zhang, S., Bellouin, N., Guttikunda, S. K., Hopke, P. K., Jacobson, M. Z., Kaiser, J. W., Klimont, Z., Lohmann, U., Schwarz, J. P., Shindell, D., Storelvmo, T., Warren, S. G., and Zender, C. S.: Bounding the role of black carbon in the climate system: A scientific assessment, J. Geophys. Res.-Atmos., 118, 5380–5552, https://doi.org/10.1002/jgrd.50171, 2013.
Briner, J. P., Cuzzone, J. K., Badgeley, J. A., Young, N. E., Steig, E. J., Morlighem, M., Schlegel, N.-J., Hakim, G. J., Schaefer, J. M., Johnson, J. V., Lesnek, A. J., Thomas, E. K., Allan, E., Bennike, O., Cluett, A. A., Csatho, B., de Vernal, A., Downs, J., Larour, E., and Nowicki, S.: Rate of mass loss from the Greenland Ice Sheet will exceed Holocene values this century, Nature, 586, 70–74, https://doi.org/10.1038/s41586-020-2742-6, 2020.
Brun, E., David, P., Sudul, M., and Brunot, G.: A numerical model to simulate snow-cover stratigraphy for operational avalanche forecasting, J. Glaciol., 38, 13–22, https://doi.org/10.3189/S0022143000009552, 1992.
Calì Quaglia, F., Meloni, D., Muscari, G., Di Iorio, T., Ciardini, V., Pace, G., Becagli, S., Di Bernardino, A., Cacciani, M., Hannigan, J. W., Ortega, I., and di Sarra, A. G.: On the Radiative Impact of Biomass-Burning Aerosols in the Arctic: The August 2017 Case Study, Remote Sens., 14, 313, https://doi.org/10.3390/rs14020313, 2022.
Cathles, L. M., Abbot, D. S., Bassis, J. N., and MacAyeal, D. R.: Modeling surface-roughness/solar-ablation feedback: application to small-scale surface channels and crevasses of the Greenland ice sheet, Ann. Glaciol., 52, 99–108, https://doi.org/10.3189/172756411799096268, 2011.
Chen, T. and Guestrin, C.: XGBoost: A Scalable Tree Boosting System, Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 785–794, https://doi.org/10.1145/2939672.2939785, 2016.
Colkesen, I. and Ozturk, M. Y.: A comparative evaluation of state-of-the-art ensemble learning algorithms for land cover classification using WorldView-2, Sentinel-2 and ROSIS imagery, Arab. J. Geosci., 15, 942, https://doi.org/10.1007/s12517-022-10243-x, 2022.
Cook, J. M., Tedstone, A. J., Williamson, C., McCutcheon, J., Hodson, A. J., Dayal, A., Skiles, M., Hofer, S., Bryant, R., McAree, O., McGonigle, A., Ryan, J., Anesio, A. M., Irvine-Fynn, T. D. L., Hubbard, A., Hanna, E., Flanner, M., Mayanna, S., Benning, L. G., van As, D., Yallop, M., McQuaid, J. B., Gribbin, T., and Tranter, M.: Glacier algae accelerate melt rates on the south-western Greenland Ice Sheet, The Cryosphere, 14, 309–330, https://doi.org/10.5194/tc-14-309-2020, 2020.
Cranmer, M.: Interpretable Machine Learning for Science with PySR and SymbolicRegression.jl, ARXIV, https://doi.org/10.48550/ARXIV.2305.01582, 2023.
de Myttenaere, A., Golden, B., Le Grand, B., and Rossi, F.: Mean Absolute Percentage Error for regression models, Neurocomputing, Advances in Artificial Neural Networks, Machine Learning and Computational Intelligence, 192, 38–48, https://doi.org/10.1016/j.neucom.2015.12.114, 2016.
Descals, A., Verger, A., Yin, G., Filella, I., and Peñuelas, J.: Local interpretation of machine learning models in remote sensing with SHAP: the case of global climate constraints on photosynthesis phenology, Int. J. Remote Sens., 44, 3160–3173, https://doi.org/10.1080/01431161.2023.2217982, 2023.
Dikshit, A. and Pradhan, B.: Interpretable and explainable AI (XAI) model for spatial drought prediction, Sci. Total Environ., 801, 149797, https://doi.org/10.1016/j.scitotenv.2021.149797, 2021.
Evangeliou, N., Kylling, A., Eckhardt, S., Myroniuk, V., Stebel, K., Paugam, R., Zibtsev, S., and Stohl, A.: Open fires in Greenland in summer 2017: transport, deposition and radiative effects of BC, OC and BrC emissions, Atmos. Chem. Phys., 19, 1393–1411, https://doi.org/10.5194/acp-19-1393-2019, 2019.
Fan, J., Wang, X., Wu, L., Zhou, H., Zhang, F., Yu, X., Lu, X., and Xiang, Y.: Comparison of Support Vector Machine and Extreme Gradient Boosting for predicting daily global solar radiation using temperature and precipitation in humid subtropical climates: A case study in China, Energy Convers. Manag., 164, 102–111, https://doi.org/10.1016/j.enconman.2018.02.087, 2018.
Feng, S., Cook, J. M., Naegeli, K., Anesio, A. M., Benning, L. G., and Tranter, M.: The Impact of Bare Ice Duration and Geo-Topographical Factors on the Darkening of the Greenland Ice Sheet, Geophys. Res. Lett., 51, e2023GL104894, https://doi.org/10.1029/2023GL104894, 2024.
Fettweis, X., Box, J. E., Agosta, C., Amory, C., Kittel, C., Lang, C., van As, D., Machguth, H., and Gallée, H.: Reconstructions of the 1900–2015 Greenland ice sheet surface mass balance using the regional climate MAR model, The Cryosphere, 11, 1015–1033, https://doi.org/10.5194/tc-11-1015-2017, 2017.
Fettweis, X., Hofer, S., Séférian, R., Amory, C., Delhasse, A., Doutreloup, S., Kittel, C., Lang, C., Van Bever, J., Veillon, F., and Irvine, P.: Brief communication: Reduction in the future Greenland ice sheet surface melt with the help of solar geoengineering, The Cryosphere, 15, 3013–3019, https://doi.org/10.5194/tc-15-3013-2021, 2021.
Flanner, M. G. and Zender, C. S.: Linking snowpack microphysics and albedo evolution, J. Geophys. Res., 111, D12208, https://doi.org/10.1029/2005JD006834, 2006.
Flanner, M. G., Arnheim, J. B., Cook, J. M., Dang, C., He, C., Huang, X., Singh, D., Skiles, S. M., Whicker, C. A., and Zender, C. S.: SNICAR-ADv3: a community tool for modeling spectral snow albedo, Geosci. Model Dev., 14, 7673–7704, https://doi.org/10.5194/gmd-14-7673-2021, 2021.
Fox-Kemper, B., Hewitt, H. T., Xiao, C., Aðalgeirsdóttir, G., Drijfhout, S. S., Edwards, T. L., Golledge, N. R., Hemer, M., Kopp, R. E., Krinner, G., Mix, A., Notz, D., Nowicki, S., Nurhati, I. S., Ruiz, L., Sallée, J.-B., Slangen, A. B. A., and Yu, Y.: Ocean, cryosphere, and sea level change, in: Climate Change 2021: The Physical Science Basis, Contribution of Working Group I to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change, edited by: Masson-Delmotte, V., Zhai, P., Pirani, A., Connors, S.L., Péan, C., Berger, S., Caud, N., Chen, Y., Goldfarb, L., Gomis, M.I., Huang, M., Leitzell, K., Lonnoy, E., Matthews, J. B. R., Maycock, T. K., Waterfield, T., Yelekçi, Ö., Yu, R., and Zhou, B., Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA, 1211–1362, https://doi.org/10.1017/9781009157896.001, 2021.
Gallée, H.: Air-sea interactions over Terra Nova Bay during winter: Simulation with a coupled atmosphere-polynya model, J. Geophys. Res.-Atmos., 102, 13835–13849, https://doi.org/10.1029/96JD03098, 1997.
Gallée, H. and Schayes, G.: Development of a Three-Dimensional Meso-γ Primitive Equation Model: Katabatic Winds Simulation in the Area of Terra Nova Bay, Antarctica, Mon. Weather Rev., 122, 671–685, https://doi.org/10.1175/1520-0493(1994)122<0671:DOATDM>2.0.CO;2, 1994.
Ghafarian, F., Wieland, R., Lüttschwager, D., and Nendel, C.: Application of extreme gradient boosting and Shapley Additive explanations to predict temperature regimes inside forests from standard open-field meteorological data, Environ. Model. Softw., 156, 105466, https://doi.org/10.1016/j.envsoft.2022.105466, 2022.
Goelles, T. and Bøggild, C. E.: Albedo reduction of ice caused by dust and black carbon accumulation: a model applied to the K-transect, West Greenland, J. Glaciol., 63, 1063–1076, https://doi.org/10.1017/jog.2017.74, 2017.
Gorelick, N., Hancher, M., Dixon, M., Ilyushchenko, S., Thau, D., and Moore, R.: Google Earth Engine: Planetary-scale geospatial analysis for everyone, Remote Sens. Environ., 202, 18–27, https://doi.org/10.1016/j.rse.2017.06.031, 2017.
Hall, D. K., Salomonson, V. V., and Riggs, G. A.: MODIS/Terra Snow Cover Daily L3 Global 500m Grid. Version 6, Boulder, Colorado, USA: NASA National Snow and Ice Data Center Distributed Active Archive Center [data set], https://doi.org/10.5067/MODIS/MOD10A1.006, 2016.
Hersbach, H., Bell, B., Berrisford, P., Hirahara, S., Horányi, A., Muñoz-Sabater, J., Nicolas, J., Peubey, C., Radu, R., Schepers, D., Simmons, A., Soci, C., Abdalla, S., Abellan, X., Balsamo, G., Bechtold, P., Biavati, G., Bidlot, J., Bonavita, M., Chiara, G., Dahlgren, P., Dee, D., Diamantakis, M., Dragani, R., Flemming, J., Forbes, R., Fuentes, M., Geer, A., Haimberger, L., Healy, S., Hogan, R.J., Hólm, E., Janisková, M., Keeley, S., Laloyaux, P., Lopez, P., Lupu, C., Radnoti, G., Rosnay, P., Rozum, I., Vamborg, F., Villaume, S., and Thépaut, J.: The ERA5 global reanalysis, Q. J. Roy. Meteor. Soc., 146, 1999–2049, https://doi.org/10.1002/qj.3803, 2020.
Hofer, S., Tedstone, A. J., Fettweis, X., and Bamber, J. L.: Decreasing cloud cover drives the recent mass loss on the Greenland Ice Sheet, Sci. Adv., 9, https://doi.org/10.1126/sciadv.1700584, 2017.
Howat, I. M., Negrete, A., and Smith, B. E.: The Greenland Ice Mapping Project (GIMP) land classification and surface elevation data sets, The Cryosphere, 8, 1509–1518, https://doi.org/10.5194/tc-8-1509-2014, 2014.
Huang, L., Kang, J., Wan, M., Fang, L., Zhang, C., and Zeng, Z.: Solar Radiation Prediction Using Different Machine Learning Algorithms and Implications for Extreme Climate Events, Front. Earth Sci., 9, https://doi.org/10.3389/feart.2021.596860, 2021.
Huber, P. J.: Robust Estimation of a Location Parameter, Ann. Math. Stat., 35, 73–101, https://doi.org/10.1214/aoms/1177703732, 1964.
Ibrahem Ahmed Osman, A., Najah Ahmed, A., Chow, M.F., Feng Huang, Y., and El-Shafie, A.: Extreme gradient boosting (Xgboost) model to predict the groundwater levels in Selangor Malaysia, Ain Shams Eng. J., 12, 1545–1556, https://doi.org/10.1016/j.asej.2020.11.011, 2021.
Ishfaque, M., Salman, S., Jadoon, K. Z., Danish, A. A. K., Bangash, K. U., and Qianwei, D.: Understanding the Effect of Hydro-Climatological Parameters on Dam Seepage Using Shapley Additive Explanation (SHAP): A Case Study of Earth-Fill Tarbela Dam, Pakistan, Water, 14, 2598, https://doi.org/10.3390/w14172598, 2022.
Jonsell, U., Hock, R., and Holmgren, B.: Spatial and temporal variations in albedo on Storglaciären, Sweden, J. Glaciol., 49, 59–68, https://doi.org/10.3189/172756503781830980, 2003.
Keegan, K. M., Albert, M. R., McConnell, J. R., and Baker, I.: Climate change and forest fires synergistically drive widespread melt events of the Greenland Ice Sheet, P. Natl. Acad. Sci. USA, 111, 7964–7967, https://doi.org/10.1073/pnas.1405397111, 2014.
Khan, A. L., Xian, P., and Schwarz, J. P.: Black carbon concentrations and modeled smoke deposition fluxes to the bare-ice dark zone of the Greenland Ice Sheet, The Cryosphere, 17, 2909–2918, https://doi.org/10.5194/tc-17-2909-2023, 2023.
Klein, A. G. and Stroeve, J.: Development and validation of a snow albedo algorithm for the MODIS instrument, Ann. Glaciol., 34, 45–52, https://doi.org/10.3189/172756402781817662, 2002.
Koo, Y., Xie, H., Kurtz, N. T., Ackley, S. F., and Wang, W.: Sea ice surface type classification of ICESat-2 ATL07 data by using data-driven machine learning model: Ross Sea, Antarctic as an example, Remote Sens. Environ., 296, 113726, https://doi.org/10.1016/j.rse.2023.113726, 2023.
Lefebre, F., Gallée, H., van Ypersele, J.-P., and Greuell, W.: Modeling of snow and ice melt at ETH Camp (West Greenland): A study of surface albedo, J. Geophys. Res.-Atmos., 108, https://doi.org/10.1029/2001JD001160, 2003.
Li, J., Wu, C., Zhang, Y., Peñuelas, J., Liu, L., and Ge, Q.: Weakening warming on spring freeze–thaw cycle caused greening Earth's third pole, P. Natl. Acad. Sci. USA, 121, e2319581121, https://doi.org/10.1073/pnas.2319581121, 2024.
Liang, S.: Narrowband to broadband conversions of land surface albedo I: algorithms, Remote Sens. Environ., 76, 213–238, https://doi.org/10.1016/S0034-4257(00)00205-4, 2001.
Lundberg, S. and Lee, S. I.: A Unified Approach to Interpreting Model Predictions, ARXIV, https://doi.org/10.48550/ARXIV.1705.07874, 2017.
Ma, M., Zhao, G., He, B., Li, Q., Dong, H., Wang, S., and Wang, Z.: XGBoost-based method for flash flood risk assessment, J. Hydrol., 598, 126382, https://doi.org/10.1016/j.jhydrol.2021.126382, 2021.
Ma, X., Fang, C., and Ji, J.: Prediction of outdoor air temperature and humidity using Xgboost, IOP Conf. Ser. Earth Environ. Sci., 427, 012013, https://doi.org/10.1088/1755-1315/427/1/012013, 2020.
MacGregor, J. A., Fahnestock, M. A., Colgan, W. T., Larsen, N. K., Kjeldsen, K. K., and Welker, J. M.: The age of surface-exposed ice along the northern margin of the Greenland Ice Sheet, J. Glaciol., 66, 667–684, https://doi.org/10.1017/jog.2020.62, 2020.
McCutcheon, J., Lutz, S., Williamson, C., Cook, J. M., Tedstone, A. J., Vanderstraeten, A., Wilson, S. A., Stockdale, A., Bonneville, S., Anesio, A. M., Yallop, M. L., McQuaid, J. B., Tranter, M., and Benning, L. G.: Mineral phosphorus drives glacier algal blooms on the Greenland Ice Sheet, Nat. Commun., 12, 570, https://doi.org/10.1038/s41467-020-20627-w, 2021.
Meinander, O., Dagsson-Waldhauserova, P., and Arnalds, O.: Icelandic volcanic dust can have a significant influence on the cryosphere in Greenland and elsewhere, Polar Res., https://doi.org/10.3402/polar.v35.31313, 2016.
Moroni, B., Arnalds, O., Dagsson-Waldhauserová, P., Crocchianti, S., Vivani, R., and Cappelletti, D.: Mineralogical and Chemical Records of Icelandic Dust Sources Upon Ny-Ålesund (Svalbard Islands), Front. Earth Sci., 6, 415699, https://doi.org/10.3389/feart.2018.00187, 2018.
Moustafa, S. E., Rennermalm, A. K., Smith, L. C., Miller, M. A., Mioduszewski, J. R., Koenig, L. S., Hom, M. G., and Shuman, C. A.: Multi-modal albedo distributions in the ablation area of the southwestern Greenland Ice Sheet, The Cryosphere, 9, 905–923, https://doi.org/10.5194/tc-9-905-2015, 2015.
Munro, D. S.: Comparison of Melt Energy Computations and Ablatometer Measurements on Melting Ice and Snow, Arct. Alp. Res., 22, 153–162, https://doi.org/10.2307/1551300, 1990.
Nagatsuka, N., Goto-Azuma, K., Tsushima, A., Fujita, K., Matoba, S., Onuma, Y., Dallmayr, R., Kadota, M., Hirabayashi, M., Ogata, J., Ogawa-Tsukagawa, Y., Kitamura, K., Minowa, M., Komuro, Y., Motoyama, H., and Aoki, T.: Variations in mineralogy of dust in an ice core obtained from northwestern Greenland over the past 100 years, Clim. Past, 17, 1341–1362, https://doi.org/10.5194/cp-17-1341-2021, 2021.
Nkiruka, O., Prasad, R., and Clement, O.: Prediction of malaria incidence using climate variability and machine learning, Inform. Med. Unlocked, 22, 100508, https://doi.org/10.1016/j.imu.2020.100508, 2021.
Noël, B., van de Berg, W.J., Lhermitte, S., and van den Broeke, M. R.: Rapid ablation zone expansion amplifies north Greenland mass loss, Sci. Adv. 5, eaaw0123, https://doi.org/10.1126/sciadv.aaw0123, 2019.
Riahi, K., van Vuuren, D. P., Kriegler, E., Edmonds, J., O'Neill, B. C., Fujimori, S., Bauer, N., Calvin, K., Dellink, R., Fricko, O., Lutz, W., Popp, A., Cuaresma, J. C., Kc, S., Leimbach, M., Jiang, L., Kram, T., Rao, S., Emmerling, J., Ebi, K., Hasegawa, T., Havlik, P., Humpenöder, F., Da Silva, L. A., Smith, S., Stehfest, E., Bosetti, V., Eom, J., Gernaat, D., Masui, T., Rogelj, J., Strefler, J., Drouet, L., Krey, V., Luderer, G., Harmsen, M., Takahashi, K., Baumstark, L., Doelman, J. C., Kainuma, M., Klimont, Z., Marangoni, G., Lotze-Campen, H., Obersteiner, M., Tabeau, A., and Tavoni, M.: The Shared Socioeconomic Pathways and their energy, land use, and greenhouse gas emissions implications: An overview, Glob. Environ. Change, 42, 153–168, https://doi.org/10.1016/j.gloenvcha.2016.05.009, 2017.
Ridder, K. D. and Schayes, G.: The IAGL Land Surface Model, J. Appl. Meteorol. Climatol., 36, 167–182, https://doi.org/10.1175/1520-0450(1997)036<0167:TILSM>2.0.CO;2, 1997.
Rohmer, J., Thieblemont, R., Le Cozannet, G., Goelzer, H., and Durand, G.: Improving interpretation of sea-level projections through a machine-learning-based local explanation approach, The Cryosphere, 16, 4637–4657, https://doi.org/10.5194/tc-16-4637-2022, 2022.
Ryan, J. C., Smith, L. C., van As, D., Cooley, S. W., Cooper, M. G., Pitcher, L. H., and Hubbard, A.: Greenland Ice Sheet surface melt amplified by snowline migration and bare ice exposure, Sci. Adv., 5, eaav3738, https://doi.org/10.1126/sciadv.aav3738, 2019.
Shimada, R., Takeuchi, N., and Aoki, T.: Inter-Annual and Geographical Variations in the Extent of Bare Ice and Dark Ice on the Greenland Ice Sheet Derived from MODIS Satellite Images, Front. Earth Sci., 4, https://doi.org/10.3389/feart.2016.00043, 2016.
Silva, S. J., Keller, C. A., and Hardin, J.: Using an Explainable Machine Learning Approach to Characterize Earth System Model Errors: Application of SHAP Analysis to Modeling Lightning Flash Occurrence, J. Adv. Model. Earth Sy., 14, e2021MS002881, https://doi.org/10.1029/2021MS002881, 2022.
Stibal, M., Box, J. E., Cameron, K. A., Langen, P. L., Yallop, M. L., Mottram, R. H., Khan, A. L., Molotch, N. P., Chrismas, N. A. M., Calì Quaglia, F., Remias, D., Smeets, C. J. P. P., Broeke, M. R., Ryan, J. C., Hubbard, A., Tranter, M., As, D., and Ahlstrøm, A. P.: Algae Drive Enhanced Darkening of Bare Ice on the Greenland Ice Sheet, Geophys. Res. Lett., 44, 11463–11471, https://doi.org/10.1002/2017GL075958, 2017.
Stroeve, J.: Assessment of Greenland albedo variability from the advanced very high resolution radiometer Polar Pathfinder data set, J. Geophys. Res.-Atmospheres, 106, 33989–34006, https://doi.org/10.1029/2001JD900072, 2001.
Tan, W., Wei, C., Lu, Y., and Xue, D.: Reconstruction of All-Weather Daytime and Nighttime MODIS Aqua-Terra Land Surface Temperature Products Using an XGBoost Approach, Remote Sens., 13, 4723, https://doi.org/10.3390/rs13224723, 2021.
Tang, Y., Duan, A., Xiao, C., and Xin, Y.: The Prediction of the Tibetan Plateau Thermal Condition with Machine Learning and Shapley Additive Explanation, Remote Sens., 14, 4169, https://doi.org/10.3390/rs14174169, 2022.
Tedesco, M., Doherty, S., Fettweis, X., Alexander, P., Jeyaratnam, J., and Stroeve, J.: The darkening of the Greenland ice sheet: trends, drivers, and projections (1981–2100), The Cryosphere, 10, 477–496, https://doi.org/10.5194/tc-10-477-2016, 2016.
Tedstone, A. J., Cook, J. M., Williamson, C. J., Hofer, S., McCutcheon, J., Irvine-Fynn, T., Gribbin, T., and Tranter, M.: Algal growth and weathering crust state drive variability in western Greenland Ice Sheet ice albedo, The Cryosphere, 14, 521–538, https://doi.org/10.5194/tc-14-521-2020, 2020.
Temenos, A., Temenos, N., Kaselimi, M., Doulamis, A., and Doulamis, N.: Interpretable Deep Learning Framework for Land Use and Land Cover Classification in Remote Sensing Using SHAP, IEEE Geosci. Remote Sens. Lett., 20, 1–5, https://doi.org/10.1109/LGRS.2023.3251652, 2023.
Thomas, J. L., Polashenski, C. M., Soja, A. J., Marelle, L., Casey, K. A., Choi, H. D., Raut, J.-C., Wiedinmyer, C., Emmons, L. K., Fast, J. D., Pelon, J., Law, K. S., Flanner, M. G., and Dibb, J. E.: Quantifying black carbon deposition over the Greenland ice sheet from forest fires in Canada, Geophys. Res. Lett., 44, 7965–7974, https://doi.org/10.1002/2017GL073701, 2017.
Uetake, J., Naganuma, T., Hebsgaard, M. B., Kanda, H., and Kohshima, S.: Communities of algae and cyanobacteria on glaciers in west Greenland, Polar Sci., 4, 71–80, https://doi.org/10.1016/j.polar.2010.03.002, 2010.
Újvári, G., Klötzli, U., Stevens, T., Svensson, A., Ludwig, P., Vennemann, T., Gier, S., Horschinegg, M., Palcsu, L., Hippler, D., Kovács, J., Biagio, C. D., and Formenti, P.: Greenland Ice Core Record of Last Glacial Dust Sources and Atmospheric Circulation, J. Geophys. Res.-Atmos., 127, e2022JD036597, https://doi.org/10.1029/2022JD036597, 2022.
van Dalum, C. T., van de Berg, W. J., Lhermitte, S., and van den Broeke, M. R.: Evaluation of a new snow albedo scheme for the Greenland ice sheet in the Regional Atmospheric Climate Model (RACMO2), The Cryosphere, 14, 3645–3662, https://doi.org/10.5194/tc-14-3645-2020, 2020.
van den Broeke, M., Box, J., Fettweis, X., Hanna, E., Noël, B., Tedesco, M., van As, D., van de Berg, W. J., van and Kampenhout, L.: Greenland Ice Sheet Surface Mass Loss: Recent Developments in Observation and Modeling, Curr. Clim. Change Rep., 3, 345–356, https://doi.org/10.1007/s40641-017-0084-8, 2017.
van Kampenhout, L., Lenaerts, J. T. M., Lipscomb, W. H., Lhermitte, S., Noël, B., Vizcaíno, M., Sacks, W. J., and van den Broeke, M. R.: Present-Day Greenland Ice Sheet Climate and Surface Mass Balance in CESM2, J. Geophys. Res.-Earth Surf., 125, e2019JF005318, https://doi.org/10.1029/2019JF005318, 2020.
Vermote, E. and Wolfe, R.: MOD09GA MODIS/Terra Surface Reflectance Daily L2G Global 1km and 500m SIN Grid V006, NASA EOSDIS Land Processes DAAC [data set], https://doi.org/10.5067/MODIS/MOD09GA.006, 2015.
Vermote, E. F., Tanre, D., Deuze, J. L., Herman, M., and Morcette, J. J.: Second Simulation of the Satellite Signal in the Solar Spectrum, 6S: an overview, IEEE T. Geosci. Remote, 35, 675–686, https://doi.org/10.1109/36.581987, 1997.
Vermote, E. F., El Saleous, N. Z., and Justice, C. O.: Atmospheric correction of MODIS data in the visible to middle infrared: first results, Remote Sens. Environ., 83, 97–111, https://doi.org/10.1016/S0034-4257(02)00089-5, 2002.
Wang, S., Tedesco, M., Alexander, P., Xu, M., and Fettweis, X.: Quantifying spatiotemporal variability of glacier algal blooms and the impact on surface albedo in southwestern Greenland, The Cryosphere, 14, 2687–2713, https://doi.org/10.5194/tc-14-2687-2020, 2020.
Wang, X. and Zender, C.: MODIS snow albedo bias at high solar zenith angles relative to theory and to in situ observations in Greenland, Remote Sens. Environ., 114, 563–575, https://doi.org/10.1016/j.rse.2009.10.014, 2010.
Wang, Z., Bovik, A. C., Sheikh, H. R., and Simoncelli, E. P.: Image quality assessment: from error visibility to structural similarity, IEEE T. Image Process., 13, 600–612, https://doi.org/10.1109/TIP.2003.819861, 2004.
Ward, J. L., Flanner, M. G., Bergin, M., Dibb, J. E., Polashenski, C. M., Soja, A. J., and Thomas, J. L.: Modeled Response of Greenland Snowmelt to the Presence of Biomass Burning-Based Absorbing Aerosols in the Atmosphere and Snow, J. Geophys. Res.-Atmos., 123, 6122–6141, https://doi.org/10.1029/2017JD027878, 2018.
Warren, S. G. and Wiscombe, W. J.: A model for the spectral albedo of snow. II: Snow containing atmospheric aerosols, J. Atmos. Sci., 37, 2734–2745, https://doi.org/10.1175/1520-0469(1980)037<2734:AMFTSA>2.0.CO;2, 1980.
Warren, S. G., Brandt, R. E., and Grenfell, T. C.: Visible and near-ultraviolet absorption spectrum of ice from transmission of solar radiation into snow, Appl. Optics, 45, 5320, https://doi.org/10.1364/AO.45.005320, 2006.
Whicker, C. A., Flanner, M. G., Dang, C., Zender, C. S., Cook, J. M., and Gardner, A. S.: SNICAR-ADv4: a physically based radiative transfer model to represent the spectral albedo of glacier ice, The Cryosphere, 16, 1197–1220, https://doi.org/10.5194/tc-16-1197-2022, 2022.
Whicker-Clarke, C. A., Antwerpen, R., Flanner, M. G., Schneider, A., Tedesco, M., and Zender, C. S.: The Effect of Physically Based Ice Radiative Processes on Greenland Ice Sheet Albedo and Surface Mass Balance in E3SM, J. Geophys. Res.-Atmos., 129, e2023JD040241, https://doi.org/10.1029/2023JD040241, 2024.
Wientjes, I. G. M. and Oerlemans, J.: An explanation for the dark region in the western melt zone of the Greenland ice sheet, The Cryosphere, 4, 261–268, https://doi.org/10.5194/tc-4-261-2010, 2010.
Wientjes, I. G. M., Van De Wal, R. S. W., Schwikowski, M., Zapf, A., Fahrni, S., and Wacker, L.: Carbonaceous particles reveal that Late Holocene dust causes the dark region in the western ablation zone of the Greenland ice sheet, J. Glaciol., 58, 787–794, https://doi.org/10.3189/2012JoG11J165, 2012.
Williamson, C.J., Cook, J., Tedstone, A., Yallop, M., McCutcheon, J., Poniecka, E., Campbell, D., Irvine-Fynn, T., McQuaid, J., Tranter, M., Perkins, R., and Anesio, A.: Algal photophysiology drives darkening and melt of the Greenland Ice Sheet, P. Natl. Acad. Sci. USA, 117, 5694–5705, https://doi.org/10.1073/pnas.1918412117, 2020.
Wiscombe, W. J. and Warren, S. G.: A model for the spectral albedo of snow. I: Pure Snow, J. Atmos. Sci., 37, 2712–2733, https://doi.org/10.1175/1520-0469(1980)037<2712:AMFTSA>2.0.CO;2, 1980.
Yue, C., Zhao, L., Wolovick, M., and Moore, J. C.: Greenland Ice Sheet Surface Runoff Projections to 2200 Using Degree-Day Methods, Atmosphere, 12, 1569, https://doi.org/10.3390/atmos12121569, 2021.
Zuo, Z. and Oerlemans, J.: Modelling albedo and specific balance of the Greenland ice sheet: calculations for the Søndre Strømfjord transect, J. Glaciol., 42, 305–317, https://doi.org/10.3189/S0022143000004160, 1996.