Braithwaite, R. J. CAS These different behaviours and resulting biases can potentially induce important consequences in long-term glacier evolution projections. Kinematic waves on glaciers move as several times the speed of the ice as a whole, and are subtle in topographic expression. A well-established parametrization based on empirical functions50 was used in order to redistribute the annually simulated glacier-wide mass changes over each glacier. J. Hydrol. 6 (2018). All authors provided inputs to the paper and helped to write it. Huss, M. & Hock, R. A new model for global glacier change and sea-level rise. Changes in DDFs with respect to air temperature also strongly depend on albedo, with ice presenting a substantially more nonlinear response than snow. The Cryosphere 13, 11251146 (2019). In fact, in many cases the surface lowering into warmer air causes this impact on the MB to be negative, further enhancing extreme negative mass balance rates. 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. Universal Differential Equations for Scientific Machine Learning. (Photograph by Klaus J. Bayr, Keene State College, 1990) One method of measuring glaciers is to send researchers onto the ice with . 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. 12, 1959 (2020). Front. These predictors are composed of: the mean glacier altitude, maximum glacier altitude, slope of the lowermost 20% altitudinal range of the glacier, glacier surface area, latitude, longitude and aspect. Climate variations change a glacier's mass balance by affecting ablation and accumulation amounts. All these glacier models, independently from their approach, need to resolve the two main processes that determine glacier evolution: (1) glacier mass balance, as the difference between the mass gained via accumulation (e.g. Univ. This synthetic setup allowed us to reproduce the climatic conditions to be undergone by most ice caps, with their mean surface altitude hardly evolving through time. Advances occurred from 1963-68 and from 1974-79. Res. The advantage of this method is that by only changing the MB model, we can keep the rest of the model components (glacier dynamics and climate forcing) and parameters the same in order to have a controlled environment for our experiment. Arch. Nisqually Glacier is well known for its kinematic waves ( Meier, 1962 ), but its mass balance has never been measured due to the difficulty of the glacier terrain. Future high-mountain hydrology: a new parameterization of glacier retreat. Tibshirani, R. Regression Shrinkage and Selection via the Lasso. The Cryosphere 14, 565584 (2020). These results revealed that the main uncertainties on glacier simulations arise from the initial ice thickness used to initialize the model. 4e) MB rates. 3). This reduced sensitivity is captured through the response to summer snowfall anomalies, since the sensitivity to positive CPDD anomalies is quite similar for the linear and nonlinear models, as it encompasses both the accumulation and ablation seasons (Fig. Paul, F., Kb, A., Maisch, M., Kellenberger, T. & Haeberli, W. Rapid disintegration of Alpine glaciers observed with satellite data: disintegration of alpine glaciers. Alternatively, the Lasso MB model displayed an RMSE of 0.85m.w.e. Water resources provided by glaciers sustain around 10% of the worlds population living near mountains and the contiguous plains4, depending on them for agriculture, hydropower generation5, industry or domestic use. With this setup, we reproduced the ice cap-like behaviour with a lack of topographical adjustment to higher elevations. ADAMONT provides climate data at 300m altitudinal bands and different slope aspects, thus having a significantly higher spatial resolution than the 0.11 from EURO-CORDEX. MATH Long-term historical interactions between French society and glaciers have developed a dependency of society on them for water resources, agriculture, tourism18particularly the ski business19and hydropower generation. Additionally, the specific responses of the deep learning and Lasso MB models to air temperature and snowfall were extracted by performing a model sensitivity analysis. Vis. 2015 IEEE Int. Consortium, R. G. I. Randolph Glacier Inventory 6.0 (2017) https://doi.org/10.7265/N5-RGI-60. (b) Climate predictors are based on climatic anomalies computed at the glaciers mean altitude with respect to the 19672015 reference period mean values. Relatively minor climate changes during the Little Ice Age (A.D. 1200-1850) impart significant glacial responses. 0.78m.w.e. "Seeing the rapid and devastating collapse of this incredible and critical salmon in the Nisqually River is heartbreaking," said Troutt. Ice-surface altitude changes of as much as 25 meters occurred between 1944 and 1955. Google Scholar. Jordi Bolibar. Our results confirm an over-sensitivity of temperature-index models, often used by large-scale studies, to future warming. Front. Article This translates into a more linear response to air temperature changes compared to the ablation season (Fig. 1). We performed a validation simulation for the 20032015 period by running our model through this period and comparing the simulated glacier surface area of each of the 32 glaciers with MB to observations from the 2015 glacier inventory16,52. Earth Syst. how climate change and glacier retreat are reshaping whole aquatic ecosystems, there is a need to develop an integrated understanding spanning multiple taxonomic groups and trophic levels in glacier-fed rivers (e.g., bacteria, protists, fungi, algae, diatoms, invertebrates, mammals, amphibians, and fish; Clitherow et al. In this study, we demonstrated the advantages of using deep learning to model glacier MB at regional scales, both in terms of variance and bias. The vast majority of glaciers in the French Alps are very small glaciers (<0.01km2), that are mainly remnants from the Little Ice Age, with a strong imbalance with the current climate15. Verfaillie, D., Dqu, M., Morin, S. & Lafaysse, M. The method ADAMONT v1.0 for statistical adjustment of climate projections applicable to energy balance land surface models. Glaciers are important for agriculture, hydropower, recreation, tourism, and biological communities. Across the globe, glaciers are decreasing in volume and number in response to climate change. A global synthesis of biodiversity responses to glacier retreat. Previous studies on 21st century large-scale glacier evolution projections have covered the French Alps7,8. McKinley, Alaska, change in response to the local climate. Other articles where Nisqually Glacier is discussed: Mount Rainier: from the broad summit, including Nisqually Glacier, whose retreat and advance over the last 150 years has helped scientists determine patterns in the Earth's climate. Thin lines represent each of the 29 individual member runs, while the thick lines represent the average for a given RCP. 2) and RCP 8.5 by the end of the century. Gaining a better understanding of how warming ocean water affects these glaciers will help improve predictions of their fate. 1gi)26 and glaciers shrinking to higher elevations where precipitation rates are higher as a result of orographic precipitation enhancement27. Glaciers smaller than 0.5km2 often display a high climate imbalance, with their equilibrium line being higher than the glaciers maximum altitude. Rackauckas, C. et al. Ecol. 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. Tom R. Andersson, J. Scott Hosking, Emily Shuckburgh, Shfaqat A. Khan, Anders A. Bjrk, Toni Schenk, Romain Hugonnet, Robert McNabb, Andreas Kb, Atanu Bhattacharya, Tobias Bolch, Tandong Yao, Christian Sommer, Philipp Malz, Matthias H. Braun, Romain Millan, Jrmie Mouginot, Mathieu Morlighem, Matthias H. Braun, Philipp Malz, Thorsten C. Seehaus, Nature Communications Taking into account that for several regions in the world about half of the glacierized volume will be lost during this first half of the 21st century, glacier models play a major role in the correct assessment of future glacier evolution. Photographs taken by Simo Rsnen (Bossons glacier, European Alps, CC BY-SA 3.0) and Doug Hardy (Quelccaya ice cap, Andes, CC BY-SA 4.0). H.Z. 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. 185, 235246 (2014). IPCC. S4). 36, L23501 (2009). Nat. If material is not included in the articles Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. By performing glacier projections both with mountain glaciers in the French Alps and a synthetic experiment reproducing ice cap-like behaviour, we argue that the limitations identified here for linear models will also have implications for many other glacierized regions in the world. Limnol. The French Alps, located in the westernmost part of the European Alps, experience some of the strongest glacier retreat in the world15,16,17. The original ice thickness estimates of the methods used by both models are different10,32, and for ALPGM we performed some additional modifications to the two largest glaciers in the French Alps (see Glacier geometry evolution for details). However, many glacierized regions in the world present different topographical setups, with flatter glaciers, commonly referred to as ice caps, covering the underlying terrain39. A He uniform initialization45 was used for the network parameters. An analysis of the climate signal at the glaciers mean altitude throughout the century reveals that air temperature, particularly in summer, is expected to be the main driver of glacier mass change in the region (Fig. Meteorol. a1), but when conditions deviate from this mean training data centroid, the Lasso can only linearly approximate the extremes based on the linear trend set on the main cluster of average values (Fig. Summer climate is computed between April 1st and September 30th and winter climate between October 1st and March 31st. Secure .gov websites use HTTPS A lock ( ) or https:// means you've safely connected to the .gov website. 3). However, the impact of different climate configurations, such as a more continental and drier climate or a more oceanic and humid climate, would certainly have an impact on the results, albeit a much less important one than the lack of topographical feedback explored here. Swiss Glacier Mass Balance (release 2019). & Funk, M. A comparison of empirical and physically based glacier surface melt models for long-term simulations of glacier response. Both MB models were trained with exactly the same data, and all other glacier model parameters were unchanged in order to allow isolating the effects of the nonlinearities in the MB. Deep learning captures a nonlinear response of glaciers to air temperature and precipitation, improving the representation of extreme mass balance rates compared to linear statistical and temperature-index models. 1a). A similar trend is under way. J. Glaciol. For small perturbations, the response time of a glacier to a perturbation in mass balance can be estimated by dividing the maximum thickness of the glacier by the balance rate at the terminus. With this cross-validation we determined a deep learning MB model spatiotemporal (LSYGO) RMSE of 0.59m.w.e. Zekollari, H., Huss, M. & Farinotti, D. Modelling the future evolution of glaciers in the European Alps under the EURO-CORDEX RCM ensemble. Lett. Tour. 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. The dataset of initial glacier ice thickness, available for the year 2003, determines the starting point of our simulations. & Galiez, C. A deep learning reconstruction of mass balance series for all glaciers in the French Alps: 19672015. The scheme simulates the mass balance as well as changes of the areal . 4a). Simulating these processes at a large geographical scale is challenging, with models requiring several parametrizations and simplifications to operate. Six, D. & Vincent, C. Sensitivity of mass balance and equilibrium-line altitude to climate change in the French Alps. Ice caps in the Canadian Arctic, the Russian Arctic, Svalbard, and parts of the periphery of Greenland are major reservoirs of ice, as well as some of the biggest expected contributors to sea level rise outside the two polar ice sheets7. Our analysis suggests that due to this positive impact on the MB signal, only relevant differences are observed between nonlinear and linear MB models for the lowest emission climate scenarios (Fig. Ecography 40, 913929 (2017). All values correspond to ensemble means under RCP 4.5. 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. The initial glacier ice thickness data for the year 2003 also differs slightly between both models. Overall, this results in linear MB models overestimating both extreme positive (Fig. Hugonnet, R. et al. provided glacier mass balance data and performed the glaciological analyses. ISSN 2041-1723 (online). To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/. In order to overcome these differences, some adaptations were performed to the GloGEMflow output, accompanied with some hypotheses to ensure a realistic comparison. Roe, G. H. Orographic precipitation. 5). Mer de Glace, 29km2 in 2015), which did show important differences under RCP 8.5 (up to 75%), due to their longer response time. Huss, M., Funk, M. & Ohmura, A. Simulations were then performed by averaging the outputs of each one of the 60 ensemble members. S10). For intermediate and pessimistic climate scenarios, no significant differences were found (Fig. Conversely, the linear MB model appears to be over-sensitive to extreme positive and negative snowfall anomalies. Spandre, P. et al. 60, 867878 (2014). Fundam. Geophys. Such glaciers are often remnants of the Little Ice Age, and mainly lose mass via non-dynamic downwasting51. This synthetic experiment is an approximation of what might occur in other glacierized regions with ice caps. In our model, we specifically computed this parameterized function for each individual glacier larger than 0.5km2, representing 80% of the total glacierized area in 2015, using two DEMs covering the whole French Alps: a photogrammetric one in 1979 and a SPOT-5 one in 2011. Our projections highlight the almost complete disappearance of all glaciers outside the Mont-Blanc and Pelvoux (Ecrins region) massifs under RCP 4.5 (Fig. Model Dev. In Climate Change 157176 (Elsevier, 2021). When it was built in the early 1900s, the road into Mount Rainier National Park from the west passed near the foot of the Nisqually Glacier, one of the mountain's longest . Swiss glaciers have displayed less negative MB rates than French glaciers during the last decades, thus likely introducing a bias in simulations specific to the French Alps. Bolibar, J. ALPGM (ALpine Parameterized Glacier Model) v1.1. We compare model runs using a nonlinear deep learning MB model (the reference approach in our study) against a simplified linear machine learning MB model based on the Lasso30, i.e. 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. Glaciers in the European Alps have been monitored for several decades, resulting in the longest observational series in the world23,24. Alluvial landscape response to climate change in glacial rivers and the implications to transportation infrastructure. Winter tourism under climate change in the Pyrenees and the French Alps: relevance of snowmaking as a technical adaptation. J.B. was supported by a NWO VIDI grant 016.Vidi.171.063. 4 ). 4e). 2a). 22, 21462160 (2009). S6). Here, we compare our results with those from a recent study that focused on the European Alps10. 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. Nonetheless, a better understanding of the underlying processes guiding these nonlinear behaviours at large geographical scales is needed. This work was funded by the Labex OSUG@2020 (Investissements davenir, ANR10 LABX56) and the Auvergne-Rhne-Alpes region through the BERGER project. creates a Nisqually Glacier response similar to those seen from its historical waves, suggesting that there are other factors contributing to kinematic wave formation, and 4) the Nisqually . To interactively describe to response of glaciers to climate change, a glacier parameterization scheme has been developed and implemented into the regional climate model REMO. 3c). 282, 104115 (2003). Atmospheres 121, 77107728 (2016). https://doi.org/10.1038/s41467-022-28033-0, DOI: https://doi.org/10.1038/s41467-022-28033-0.