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We previously demonstrated that this period is long enough to represent the secular trend of glacier dynamics in the region31. These are among the cascading effects linked to glacier loss which impact ecosystems and . Researchers analyzed almost 2 million satellite images of the glaciers and found that 94 . Our results also highlight the important role played by glacier geometry adjustment under changing climatic conditions, which is typical of mountain glaciers38. At this point, it is important to clarify the different ways of treating PDDs in the Lasso and the temperature-index MB models analysed in this study in order to justify analogies. This is particularly important for the ablation season and for ice DDFs, which need to accommodate the progressively decreasing role that shortwave radiation will play in the future glacier surface energy budget under warmer conditions. 48, 24872512 (2009). Both machine learning MB models were trained with exactly the same data coming from the 1048 annual glacier-wide MB values, and both were cross-validated using LSYGO. Res. Article This implies that specific climatic differences between massifs can be better captured by ALPGM than GloGEMflow. Alternatively, the Lasso model used here includes 13 DDFs: one for the annual CPDDs and 12 for each month of the hydrological year. Res. Moreover, these differences between nonlinear and linear models appear to come from an over-sensitivity of linear models to increasing ablation season air temperatures, when ice is exposed in a large fraction of glaciers. 4a, b) and negative (Fig. Glacier topography is a crucial driver of future glacier projections and is expected to play an important role in determining the magnitude that nonlinearities will have on the mass balance. Nature 568, 382386 (2019). Grenoble Alpes, CNRS, IRD, G-INP, Institut des Gosciences de lEnvironnement, Grenoble, France, INRAE, UR RiverLy, Lyon-Villeurbanne, France, Institute for Marine and Atmospheric research Utrecht, Utrecht University, Utrecht, Netherlands, Univ. To obtain Graphics inspired by Hock and Huss40. regularized multilinear regression. Park, and S. Beason. Tibshirani, R. Regression Shrinkage and Selection via the Lasso. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. 4). snowfall, avalanches and refreezing) and the mass lost via different processes of ablation (e.g. Millan, R., Mouginot, J., Rabatel, A., & Morlighem, M. Ice velocity and thickness of the worlds glaciers. The first main difference is related to the climate data used to force the models. Indeed, the projected 21st century warming will lead to increasing incoming longwave radiation and turbulent fluxes, with no marked future trends in the evolution of shortwave radiation37. 2) and RCP 8.5 by the end of the century. Model Dev. J. Hydrol. This behaviour is expected for mountain glaciers, as they are capable of retreating to higher altitudes, thus producing a positive impact on their glacier-wide MB (Fig. Article Zemp, M. et al. Bolibar, J. et al. The record, which was started in 1931, shows the glacier's dramatic responses to about half a century of small but significant climatic variations. Glacier-wide MB is simulated annually for individual glaciers using deep learning (i.e. 3). The processing chain for extracting glacier outlines from images is composed of four steps: (1) calculation of band ratio, (2) selection of threshold value, (3) creation of binary image and (4) manual digitization. Seasonal Arctic sea ice forecasting with probabilistic deep learning, Global glacier mass changes and their contributions to sea-level rise from 1961 to 2016, Two decades of glacier mass loss along the Andes, Centennial response of Greenlands three largest outlet glaciers, Accelerated global glacier mass loss in the early twenty-first century, High Mountain Asian glacier response to climate revealed by multi-temporal satellite observations since the 1960s, Rapid glacier retreat and downwasting throughout the European Alps in the early 21st century, Ice velocity and thickness of the worlds glaciers, Constraining glacier elevation and mass changes in South America, https://meetingorganizer.copernicus.org/EGU2020/EGU2020-20908.html, https://doi.org/10.5194/egusphere-egu2020-20908, https://doi.org/10.18750/MASSBALANCE.2019.R2019, https://doi.org/10.1016/B978-0-12-821575-3.00009-8, https://doi.org/10.1038/s41561-021-00885-z, http://creativecommons.org/licenses/by/4.0/, Unabated wastage of the Muz Taw Glacier in the Sawir Mountains during 19592021. Vincent, C. et al. A sensitivity analysis of both MB models revealed nonlinear relationships between PDDs, snowfall (in winter and summer) and glacier-wide MB, which the linear model was only able to approximate (r2=0.41 for the Lasso vs. r2=0.76 for deep learning in cross-validation31; Fig. S10). Our results show that the mean elevation is far more variable than the kinematic ELA ( Fig. This behaviour is not observed with the nonlinear model, hinting at a positive bias of linear MB models under RCP 2.6. These different behaviours and resulting biases can potentially induce important consequences in long-term glacier evolution projections. This creates a total of 34 input predictors for each year (7 topographical, 3 seasonal climate, and 24 monthly climate predictors). On top of that, they happen to be among the glacierized regions with the largest projected uncertainties8. Therefore, we were capable of isolating the different behaviours of the nonlinear deep learning model and a linear machine learning model based on the Lasso30. 10, 42574283 (2017). S6). The smallest best performing architecture was used, in order to find a good balance between predictive power, speed, and extrapolation outside the training data. With a secondary role, glacier model uncertainty decreases over time, but it represents the greatest source of uncertainty until the middle of the century8. Predicting future glacier evolution is of paramount importance in order to correctly anticipate and mitigate the resulting environmental and social impacts. J. Appl. New methods bridging the gap between domain-specific equations and machine learning are starting to arise42, which will play a crucial role in further investigating the physical processes driving these nonlinear climate-glacier interactions. A glacier is a large mass of snow and ice that has accumulated over many years and is present year-round. When comparing our deep learning simulations with those from the Lasso, we found average cumulative MB differences of up to 17% by the end of the century (Fig. Therefore, solid precipitation is projected to remain almost constant at the evolving glaciers mean altitude independently from the future climate scenarios, while air temperature is projected to drive future glacier-wide mass changes (Fig. MB rates only begin to approach equilibrium towards the end of the century under RCP 2.6, for which glaciers could potentially stabilize with the climate in the first decades of the 22nd century depending on their response time (Fig. Cauvy-Frauni, S. & Dangles, O. Overall, the evolving glaciers are expected to undergo rather stable climate conditions under RCP 4.5, but increasingly higher temperatures and rainfall under RCP 8.5 (Fig. Under warmer conditions (RCP 8.5), the differences between the linear and nonlinear MB model become smaller, as the topographical feedback from glacier retreat compensates for an important fraction of the losses induced by the late century warmer climate (Fig. Additionally, glacier surface area was found to be a minor predictor in our MB models31. By submitting a comment you agree to abide by our Terms and Community Guidelines. Ice thickness data for Argentire glacier (12.27km2 in 2015) was taken from a combination of field observations (seismic, ground-penetrating radar or hot-water drilling53) and simulations32. For intermediate and pessimistic climate scenarios, no significant differences were found (Fig. Rainier, Washington. We reduced these differences by running simulations with GloGEMflow using exactly the same 29 climate members used by ALPGM in this study (TableS1). ADS Geomorphology 350, 106913 (2020). longwave radiation budget, turbulent fluxes), in comparison with a future warmer climate. The same was done with winter snowfall anomalies, ranging between 1500mm and +1500mm in steps of 100mm, and summer snowfall anomalies, ranging between 1000mm and +1000mm in steps of 100mm. acknowledges the funding received from a EU Horizon 2020 Marie Skodowska-Curie Individual Fellowship (grant no. Article H.Z. is central to a glacier's response: Fig.2ashows 1L.t/for a warming trend of 1 C per century, for three glaciers with dierent (and fixed ). Since 2005, study finds that surface melt off glaciers in the North has risen by 900%. Lett. A dataset of 32 glaciers with direct annual glacier-wide MB observations and remote sensing estimates was used to train the models. In order to investigate the effects of MB nonlinearities on flatter glaciers, we conducted a synthetic experiment using the French Alps dataset. Earth Sci. J. Glaciol. Data 12, 19731983 (2020). Source: Mount Rainier National Park In order to simulate annual glacier-wide MB values, (a) topographical and (b) climate data for those glaciers and years were compiled for each of the 1048 glacier-year values. Dyn. A recent Northern Hemisphere temperature reconstruction indicates an oscillating temperature drop from A.D. 1000-1850 of about 0.2C with a subsequent and still continuing warming of nearly 0.8C ( 3 ). Toward mountains without permanent snow and ice: mountains without permanent snow and ice. S5h, j, l). A He uniform initialization45 was used for the network parameters. Massifs without glaciers by 2100 are marked with a cross, b Glacier ice volume distribution per massif, with its remaining fraction by 2100 (with respect to 2015), c Annual glacier-wide MB per massif, d Annual snowfall per massif, e Annual cumulative positive degree-days (CPDD) per massif. ice caps) that are found in other glacierized regions such as the Arctic, where the largest volumes of glacier ice (other than the ice sheets) are stored32, cannot retreat to higher elevations. Projected changes in surface solar radiation in CMIP5 global climate models and in EURO-CORDEX regional climate models for Europe. Another source of discrepancy between both models comes from the different MB data used to calibrate or train the MB models. Conversely, for RCP 8.5, annual glacier-wide MB are estimated to become increasingly negative by the second half of the century, with average MB almost twice as negative as todays average values (Fig. He, K., Zhang, X., Ren, S. & Sun, J. Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification. Nat Commun 13, 409 (2022). Our results confirm an over-sensitivity of temperature-index models, often used by large-scale studies, to future warming. Farinotti, D., Round, V., Huss, M., Compagno, L. & Zekollari, H. Large hydropower and water-storage potential in future glacier-free basins. 3 (2015). On the one hand, MB nonlinearities for mountain glaciers appear to be only relevant for climate scenarios with a reduction in greenhouse gases emissions (Fig. Annu. McKinley, Alaska, change in response to the local climate. S1a). A physically-based method for mapping glacial debris-cover thickness from ASTER satellite imagery: development and testing at Miage Glacier, Italian Alps Discovery - the University of Dundee Research Portal (Springer, New York, 2009). The performance of this parametrization was validated in a previous study, indicating a correct agreement with observations31. The high spatial resolution enables a detailed representation of mountain weather patterns, which are often undermined by coarser resolution climate datasets. For such cases, we assumed that ice dynamics no longer play an important role, and the mass changes were applied equally throughout the glacier. The ice thickness data for two of the largest glaciers in the French Alps were modified in order to improve data quality. The scheme simulates the mass balance as well as changes of the areal . Fundam. Hugonnet, R. et al. At present, using complex surface energy balance models for large-scale glacier projections is not feasible yet, mainly due to the lack of input data. Google Scholar. The model output data generated in this study have been deposited in netCDF and CSV format in a Zenodo repository under accession code Creative Commons Attribution 4.0 International. Reanalysis of 47 Years of Climate in the French Alps (19582005): Climatology and Trends for Snow Cover. We acknowledge the more than 50 years of glaciological monitoring performed by the GLACIOCLIM French National Observatory (https://glacioclim.osug.fr), which provided essential observations for our modelling study. ArXiv200104385 Cs Math Q-Bio Stat (2020). The source code of the glacier model can be freely accessed in the following repository: https://github.com/JordiBolibar/ALPGM. Correspondence to https://zenodo.org/record/5549758. Mt. Google Scholar. The glacier ice volume in the French Alps at the beginning of the 21st century is unevenly distributed, with the Mont-Blanc massif accounting for about 60% of the total ice volume in the year 2015 (7.06 out of 11.64km3, Fig. Glacier ice thickness observations are available for four different glaciers in the regions, which were compared to the estimates used in this model. These results revealed that the main uncertainties on glacier simulations arise from the initial ice thickness used to initialize the model.

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