J.B. was supported by a NWO VIDI grant 016.Vidi.171.063. 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. All values correspond to ensemble means under RCP 4.5. 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, 168173 (2019). . Rainier, Washington. Geophys. This creates an interesting dilemma, with more complex temperature-index MB models generally outperforming simpler models for more climatically homogeneous past periods but introducing important biases for future projections under climate change. Jordi Bolibar. 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 The images or other third party material in this article are included in the articles Creative Commons license, unless indicated otherwise in a credit line to the material. Analyses were made of the annual photographs . 65, 453467 (2019). Glaciers are important for agriculture, hydropower, recreation, tourism, and biological communities. The application of a non-linear back-propagation neural network to study the mass balance of Grosse Aletschgletscher, Switzerland. 4a). Vertical axes are different for the two analyses. However, many glacierized regions in the world present different topographical setups, with flatter glaciers, commonly referred to as ice caps, covering the underlying terrain39. https://doi.org/10.1038/s41467-022-28033-0, DOI: https://doi.org/10.1038/s41467-022-28033-0. This implies that specific climatic differences between massifs can be better captured by ALPGM than GloGEMflow. deep artificial neural networks) glacier evolution projections by modelling the regional evolution of French alpine glaciers through the 21st century. Climatol. Our synthetic experiment does not account for glacier surface area shrinking either, which might have an impact on the glacier-wide MB signal. Since the climate and glacier systems are known to be nonlinear13, we investigate the benefits of using a model treating, among others, PDDs in a nonlinear way in order to simulate annual glacier-wide MB at a regional scale. Due to the statistical nature of the Lasso model, the response to snowfall anomalies is also highly influenced by variations in PDDs (Fig. 3). Toward mountains without permanent snow and ice: mountains without permanent snow and ice. Climate Change 2013: The Physical Science Basis. S7). 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). Overall, this results in linear MB models overestimating both extreme positive (Fig. Glaciers and ice caps are experiencing strong mass losses worldwide, challenging water availability, hydropower generation, and ecosystems. Particularly in Asia, water demand exceeds supply due to rapid population growth, with glacier . This creates a total of 34 input predictors for each year (7 topographical, 3 seasonal climate, and 24 monthly climate predictors). Alternatively, the comparisons against an independent large-scale glacier evolution model were less straightforward to achieve. As such, these values reflect both the climatic forcing and the changing glacier geometry. Res. The position of the front of the wave will be defined as the transverse line across the glacier where the flow of . The Cryosphere 13, 13251347 (2019). Climate variations change a glacier's mass balance by affecting ablation and accumulation amounts. Advances occurred from 1963-68 and from 1974-79. J.B. developed the main glacier model, performed the simulations, analysed the results, and wrote the paper. Glaciers are experiencing important changes throughout the world as a consequence of anthropogenic climate change1. Finally, there are differences as well in the glacier dynamics of both models, with ALPGM using a glacier-specific parameterized approach and GloGEMflow explicitly reproducing the ice flow dynamics. Mer de Glace, 29km2 in 2015), which did show important differences under RCP 8.5 (up to 75%), due to their longer response time. 799904) and from the Fonds de la Recherche Scientifique FNRS (postdoctoral grant charg de recherches). You are using a browser version with limited support for CSS. These are among the cascading effects linked to glacier loss which impact ecosystems and . 1). Nonlinear sensitivity of glacier mass balance to future climate change unveiled by deep learning, https://doi.org/10.1038/s41467-022-28033-0. Vis. We argue that such models can be suitable for steep mountain glaciers. J. Glaciol. Lett. 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. Roberts, D. R. et al. The Elements of Statistical Learning. 3c). Nonetheless, since they are both linear, their calibrated parameters establishing the sensitivity of melt and glacier-wide MB to temperature variations remain constant over time. Nature 577, 364369 (2020). 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. Ecol. Monitoring the Seasonal hydrology of alpine wetlands in response to snow cover dynamics and summer climate: a novel approach with sentinel-2. Gaining a better understanding of how warming ocean water affects these glaciers will help improve predictions of their fate. CoRR abs/1505.00853 (2015). 4). J. Glaciol. Anyone you share the following link with will be able to read this content: Sorry, a shareable link is not currently available for this article. 31, n/an/a (2004). Huss, M., Jouvet, G., Farinotti, D. & Bauder, A. These results are in agreement with the main known drivers of glacier mass change in the French Alps28. Source: Mount Rainier National Park We perform, to the best of our knowledge, the first-ever deep learning (i.e. Through synthetic experiments, we showed that the associated uncertainties are likely to be even more pronounced for ice caps, which host the largest reserves of ice outside the two main ice sheets32. Rveillet, M. et al. This adjustment represents a major improvement over most climate data used to force regional and global glacier models. 4). This is not the case for the nonlinear deep learning MB model, which captures the nonlinear response of melt and MB to increasing air temperatures, thus reducing the MB sensitivity to extreme positive and negative air temperature and summer snowfall anomalies (Fig. Hock, R. et al. J. Glaciol. By unravelling nonlinear relationships between climate and glacier MB, we have demonstrated the limitations of linear statistical MB models to represent extreme MB rates in long-term projections. a1 and an r2 of 0.3531. In order to investigate the effects of MB nonlinearities on ice caps, we performed the same type of comparison between simulations, but the glacier geometry update module described in the Glacier geometry evolution section was deactivated. This enables the recalculation of every topographical predictor used for the MB model, thus updating the mean glacier altitude at which climate data for each glacier are retrieved. Correspondence to These synthetic experiments suggest that, for equal climatic conditions, flatter glaciers and ice caps will experience substantially more negative MB rates than steeper mountain glaciers. "Their numbers have gone from regularly exceeding 50,000 adult salmon in the Nisqually to about 5,000 last year." The Nisqually River near its glacial origins. On the one hand, this improves our confidence in long-term MB projections for steep glaciers made by most GlacierMIP models for intermediate and high emissions climate scenarios. Pellicciotti, F. et al. Each one of these models was created by training a deep learning model with the full dataset except all data from a random glacier and year, and evaluating the performance on these hidden values. 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. The anomaly in snowfall was evenly distributed for every month in the accumulation (October 1April 31) and ablation seasons, respectively. 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. Park, and S. Beason. Across the globe, glaciers are decreasing in volume and number in response to climate change. Huss, M. & Hock, R. A new model for global glacier change and sea-level rise. Additionally, glacier surface area was found to be a minor predictor in our MB models31. P. Kennard, J. The maximum advance of Nisqually Glacier in the last thousand years was located, and retreat from this point is believed to have started about 1840. He, K., Zhang, X., Ren, S. & Sun, J. Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification. Glacier landscapes are expected to see important changes throughout the French Alps, with the average glacier altitude becoming 300m (RCP 4.5) and 400m (RCP 8.5) higher than nowadays (Fig. & Funk, M. A comparison of empirical and physically based glacier surface melt models for long-term simulations of glacier response. Positive degree-day factors for ablation on the Greenland ice sheet studied by energy-balance modelling. Since these two glaciers are expected to be some of the few large glaciers that will survive the 21st century climate, an accurate representation of their initial ice thickness has an important effect on the estimates of remaining ice. The Karakoram and the Himalayan mountain range accommodate a large number of glaciers and are the major source of several perennial rivers downstream. ALPGM uses a feed-forward fully connected multilayer perceptron, with an architecture (40-20-10-5-1) with Leaky-ReLu44 activation functions and a single linear function at the output. Farinotti, D., Round, V., Huss, M., Compagno, L. & Zekollari, H. Large hydropower and water-storage potential in future glacier-free basins. New research suggests that climate change-induced melting of the Nisqually Glacier near Seattle, Wash., and other high-elevation glaciers will offset seasonal declines in streamflow until. However, both the climate and glacier systems are known to react non-linearly, even to pre-processed forcings like PDDs13, implying that these models can only offer a linearized approximation of climate-glacier relationships. The training was performed with an RMSprop optimizer, batch normalization46, and we used both dropout and Gaussian noise in order to regularize it. Ten . By 2100, under RCP 4.5, these two high-altitude massifs are predicted to retain on average 26% and 13% of their 2015 volume, respectively, with most of the ice concentrated in a few larger glaciers (>1km2, Fig. Alluvial landscape response to climate change in glacial rivers and the implications to transportation infrastructure. 58, 267288 (1996). Nature Geosciences, https://doi.org/10.1038/s41561-021-00885-z (2022). Therefore, linear MB models present more limitations for projections of ice caps, showing a tendency to negative MB biases. In Climate Change 157176 (Elsevier, 2021). Global glacier mass changes and their contributions to sea-level rise from 1961 to 2016. Comput. Rev. Three different types of cross validation were performed: a Leave-One-Glacier-Out (LOGO), a Leave-One-Year-Out (LOYO) and a Leave-Some-Years-and-Glaciers-Out (LSYGO). Nisqually Glacier is perhaps the most visited, best-surveyed glacier on Mount Rainier. Google Scholar. Several aquatic and terrestrial ecosystems depend on these water resources as well, which ensure a base runoff during the warmest or driest months of the year6. Between 1857 and 1979, Nisqually Glacier receded a total of 1,945 meters and advanced a total of 294 meters. Nonlinear deep learning response and linear Lasso response to a Cumulative positive degree days (CPDD) anomalies, b winter snowfall, and c summer snowfall. 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. Ecography 40, 913929 (2017). Nature Communications (Nat Commun) 5). This dataset applies a statistical adjustment specific to French mountain regions based on the SAFRAN dataset, to EURO-CORDEX26 GCM-RCM-RCP members, covering a total of 29 different future climate scenarios for the 20052100 period. Res. volume13, Articlenumber:409 (2022) Deep artificial neural networks (ANNs) are nonlinear models that offer an alternative approach to these classic methods. Predicting future glacier evolution is of paramount importance in order to correctly anticipate and mitigate the resulting environmental and social impacts. 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. S10). Ser. 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. On top of that, they happen to be among the glacierized regions with the largest projected uncertainties8. 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. Nonetheless, since the main GCM-RCM climate signal is the same, the main large-scale long-term trends are quite similar. Gardent, M., Rabatel, A., Dedieu, J.-P. & Deline, P. Multitemporal glacier inventory of the French Alps from the late 1960s to the late 2000s. 41, 153160 (1995). In order to overcome these differences, some adaptations were performed to the GloGEMflow output, accompanied with some hypotheses to ensure a realistic comparison. 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. Huss, M. et al. Earth Sci. Previous studies on 21st century large-scale glacier evolution projections have covered the French Alps7,8. 1 and S1). Rabatel, A., Sanchez, O., Vincent, C. & Six, D. Estimation of glacier thickness from surface mass balance and ice flow velocities: a case study on Argentire Glacier, France. Nature 568, 382386 (2019). 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. These different behaviours and resulting biases can potentially induce important consequences in long-term glacier evolution projections. Maussion, F. et al. Annual glacier-wide mass balance (MB) is estimated to remain stable at around 1.2m.w.e. Here, with our newly presented approach, we were able for the first time to quantify the effect that stationary parameters in temperature-index mass balance models have on transient glacier evolution. Zemp, M. et al. Scand. For such cases, we assumed that ice dynamics no longer play an important role, and the mass changes were applied equally throughout the glacier. Steiner, D., Walter, A. 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. Rackauckas, C. et al. Mt. 47 (2020). The 29 RCP-GCM-RCM combinations available, hereafter named climate members, are representative of future climate trajectories with different concentration levels of greenhouse gases (TableS1). We previously demonstrated that this period is long enough to represent the secular trend of glacier dynamics in the region31. Bolibar, J., Rabatel, A., Gouttevin, I. et al. H.Z. With this study, we provide new predictions of glacier evolution in a highly populated mountain region, while investigating the role of nonlinearities in the response of glaciers to multiple future climate forcings. J. Hydrol. Changes in DDFs with respect to air temperature also strongly depend on albedo, with ice presenting a substantially more nonlinear response than snow. From this behavior, inferences of past climate can be drawn. The lower fraction of variance explained by linear models is present under all climate scenarios. Glaciers with the greatest degree of seasonality in their flow behavior, such as Nisqually and Shoestring glaciers, responded most rapidly. Res. 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. Change 120, 2437 (2014). Tour. 3). Reanalysis of 47 Years of Climate in the French Alps (19582005): Climatology and Trends for Snow Cover. Multiple copies of this dataset were created, and for each individual copy a single predictor (i.e. Winter tourism under climate change in the Pyrenees and the French Alps: relevance of snowmaking as a technical adaptation. The Cryosphere 14, 565584 (2020). This experiment enabled the exploration of the response to specific climate forcings of a wide range of glaciers of different topographical characteristics in a wide range of different climatic setups, determined by all meteorological conditions from the years 19672015 (Fig. In order to investigate the implications of these results for flat glaciers, we performed additional synthetic experiments in order to reproduce this lack of topographical feedback (Fig. McKinley, Alaska, change in response to the local climate. A glacier is a large mass of snow and ice that has accumulated over many years and is present year-round. Use the Previous and Next buttons to navigate the slides or the slide controller buttons at the end to navigate through each slide. Res. Braithwaite, R. J. 2013). energy balance), with differences increasing when the conditions considerably differ from the calibration period33. When using the linear MB model (Lasso), glaciers are close to reaching an equilibrium with the climate in the last decades of the century, which is not the case for the nonlinear MB model (deep learning). C.G. 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. 48, 24872512 (2009). Despite marked differences among regions, the generalized retreat of glaciers is expected to have major environmental and social impacts2,3. regularized multilinear regression. This approach is known as a cross-validation ensemble49. As we have previously shown, these models present a very similar behaviour to the linear statistical MB model from this study (Fig. Earths Future https://doi.org/10.1029/2019EF001470 (2020). Get the most important science stories of the day, free in your inbox. The largest snow depths measured this spring exceeded 10 meters on Nisqually Glacier and 7 meters on Emmons. Article The source code of the glacier model can be freely accessed in the following repository: https://github.com/JordiBolibar/ALPGM. provided glacier mass balance data and performed the glaciological analyses. These bulges, called kinematic waves, form when higher than normal snowfall builds up in the accumulation area of the glacier (c). 2a and S3). 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. A similar trend is under way. Lett. 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.

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