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. Despite marked differences among regions, the generalized retreat of glaciers is expected to have major environmental and social impacts2,3. A.R. 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. 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. Despite these differences, the average altitude difference of the glaciers between both models is never greater than 50m (Fig. 4e). 47 (2020). 3). J. Glaciol. 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. Geomorphology 350, 106913 (2020). Magnin, F., Haeberli, W., Linsbauer, A., Deline, P. & Ravanel, L. Estimating glacier-bed overdeepenings as possible sites of future lakes in the de-glaciating Mont Blanc massif (Western European Alps). We ran glacier evolution projections for both the deep learning and Lasso MB models, but we kept the glacier geometry constant, thus preserving the glacier centroid where the climate data is computed constant through time. S5 and S6). 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. Gabbi, J., Carenzo, M., Pellicciotti, F., Bauder, A. 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. 3a). Steiner, D., Walter, A. J. Glaciol. 3b). 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. a1 and a r2 of 0.69, explaining 69% of the total MB variance. Our results suggest that, except for the lowest emissions climate scenarios and for large glaciers with long response times, MB models with linear relationships for PDDs and precipitation are suitable for mountain glaciers with a marked topographical feedback. Cross-validation strategies for data with temporal, spatial, hierarchical, or phylogenetic structure. 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. This rapid glacier retreat is already having an environmental impact on natural hazards20, mountain ecosystems21, and biodiversity6. Zekollari, H., Huss, M. & Farinotti, D. On the Imbalance and Response Time of Glaciers in the European Alps. A globally complete, spatially and temporally resolved estimate of glacier mass change: 2000 to 2019. (2020) Therefore, linear MB models present more limitations for projections of ice caps, showing a tendency to negative MB biases. The Cryosphere 12, 13671386 (2018). 2015 IEEE Int. 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. All climate anomalies are computed with respect to the 19672015 mean values. 799904) and from the Fonds de la Recherche Scientifique FNRS (postdoctoral grant charg de recherches). 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. Deep artificial neural networks (ANNs) are nonlinear models that offer an alternative approach to these classic methods. 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. Geophys. Summer melt was also above average. The two models with linear MB responses to PDDs and accumulation simulate more positive MB rates under RCP 2.6, highlighting their over-sensitivity to negative air temperature anomalies and positive snowfall anomalies (Fig. 12, 1959 (2020). Previous studies on 21st century large-scale glacier evolution projections have covered the French Alps7,8. In summary, the linear approximations used by the Lasso manage to correctly fit the main cluster of average values but perform poorly for extreme values31. Geophys. Our results confirm an over-sensitivity of temperature-index models, often used by large-scale studies, to future warming. Reanalysis of 47 Years of Climate in the French Alps (19582005): Climatology and Trends for Snow Cover. 51, 313323 (2005). Universal Differential Equations for Scientific Machine Learning. Nature 577, 364369 (2020). Huss, M. et al. 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. This work was funded by the Labex OSUG@2020 (Investissements davenir, ANR10 LABX56) and the Auvergne-Rhne-Alpes region through the BERGER project. Because of easy access and prominent location the glacier has been studied since the mid 1850's. In 1857, Lt. August Kautz crossed Nisqually Glacier during an attempt to climb the summit. Annu. 282, 104115 (2003). Due to the statistical nature of the Lasso model, the response to snowfall anomalies is also highly influenced by variations in PDDs (Fig. 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 The initial glacier ice thickness data for the year 2003 also differs slightly between both models. 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. Park, and S. Beason. Nisqually Glacier is perhaps the most visited, best-surveyed glacier on Mount Rainier. You are using a browser version with limited support for CSS. b, c, d and f, g, h annual glacier-wide MB probability distribution functions for all n scenarios in each RCP. 60, 867878 (2014). (Photograph by Klaus J. Bayr, Keene State College, 1990) One method of measuring glaciers is to send researchers onto the ice with . 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). Atmospheres 121, 77107728 (2016). In the United States, glaciers can be found in the Rocky Mountains, the Sierra Nevada, the Cascades, and throughout Alaska. 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. Nonetheless, since the main GCM-RCM climate signal is the same, the main large-scale long-term trends are quite similar. Earths Future 5, 418435 (2017). 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. Kinematic waves on glaciers move as several times the speed of the ice as a whole, and are subtle in topographic expression. The scheme simulates the mass balance as well as changes of the areal . Hock, R. & Huss, M. Glaciers and climate change. This annual geometry adjustment accounts for the effects of glacier retreat on the climate signal received by glaciers. Earth Planet. 4a). 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. As previously mentioned, here these differences are computed at regional level for a wide variety of glaciers. 4a). Despite the differences in the two modelling approaches (TableS2), both regional glacier volume projections present relatively similar results by the end of the century, with volume differences ranging between 14% for RCP 2.6 to less than 2% for RCP 4.5 (Fig. I.G. Durand, Y. et al. Rainier, Washington. 3 (2015). Regarding air temperature, a specific CPDD anomaly ranging from 1500 PDD to +1500 PDD in steps of 100 PDD was prescribed to all glaciers for each dataset copy. 185, 235246 (2014). In recent years, shrinking glaciers have contributed to about 30% of global sea level rise 1. Monitoring the Seasonal hydrology of alpine wetlands in response to snow cover dynamics and summer climate: a novel approach with sentinel-2. Sign up for the Nature Briefing newsletter what matters in science, free to your inbox daily. The authors declare no competing interests. Predicting future glacier evolution is of paramount importance in order to correctly anticipate and mitigate the resulting environmental and social impacts. This synthetic experiment is an approximation of what might occur in other glacierized regions with ice caps. Spandre, P. et al. Earth Syst. 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. The record, which was started in 1931, shows the glacier's dramatic responses to about half a century of small but significant climatic variations. Huss, M., Jouvet, G., Farinotti, D. & Bauder, A. (Springer, New York, 2009). 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. GlacierMIP A model intercomparison of global-scale glacier mass-balance models and projections. 4 ). Conf. CoRR abs/1505.00853 (2015). Univ. Nature 575, 341344 (2019). 41, 153160 (1995). contributed to the extraction of nonlinear mass balance responses and to the statistical analysis. Swiss Glacier Mass Balance (release 2019). 3). 33, 645671 (2005). Bolibar, J. ALPGM (ALpine Parameterized Glacier Model) v1.1. Soc. This will reduce the importance of shortwave radiation for future ablation rates, and it is expected to result in a reduction in values of degree-day factors (DDFs) and therefore a significant change in melt sensitivity to air temperature variations36. 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 . A glacier flows naturally like a river, only much more slowly. (2019) Strong Alpine glacier melt in the 1940s due to enhanced solar radiation. Ice-surface altitude changes of as much as 25 meters occurred between 1944 and 1955. Winter tourism under climate change in the Pyrenees and the French Alps: relevance of snowmaking as a technical adaptation. Many studies have investigated the effects of climate change on glacier runoff using observations or modelling, with a recent focus on High Mountain Asia 14,16,17 and the Andes 18,19,20.The degree . This implies that current global glacier mass loss projections are too low for the lowest emissions climate scenarios and too high for the highest emissions ones, which has direct consequences for related sea-level rise and water resources projections. Lett. 4e). The Nisqually Glacier is one of the larger glaciers on the southwestern face of Mount Rainier in the U.S. state of Washington.The glacier is one of the most easily viewed on the mountain, and is accessible from the Paradise visitor facilities in Mount Rainier National Park.The glacier has had periods of advance and retreat since 1850 when it was much more extensive. Article Hock, R. et al. Our results also highlight the important role played by glacier geometry adjustment under changing climatic conditions, which is typical of mountain glaciers38. PubMedGoogle Scholar. Regarding air temperature forcings, the linear Lasso MB model was found to be slightly under-sensitive to extreme positive cumulative PDD (CPDD) and over-sensitive to extreme negative CPDDs. A small ablation increase may cause . & Galiez, C. A deep learning reconstruction of mass balance series for all glaciers in the French Alps: 19672015. 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. We argue that such models can be suitable for steep mountain glaciers. Glaciers smaller than 0.5km2 often display a high climate imbalance, with their equilibrium line being higher than the glaciers maximum altitude. 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. Consequently, a simple MB model with a single DDF (e.g. The main uncertainties in future glacier estimates stem from future climate projections and levels of greenhouse gas emissions (differences between RCPs, GCMs, and RCMs), whose relative importance progressively increases throughout the 21st century. 21, 229246 (2021). 31, n/an/a (2004). 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. These trends explored with energy balance models from the literature correspond to the behaviour captured by our deep learning MB model, with a clearly less sensitive response of glacier-wide MB to extreme climate forcings, particularly in summer (Fig. For these 32 glaciers, a total of 1048 annual glacier-wide MB values are available, covering the 19672015 period with gaps. 4). Mt. On the other hand, ice caps present a different response to future warming, with our results suggesting a negative MB bias by models using linear PDD and accumulation relationships. We acknowledge the more than 50 years of glaciological monitoring performed by the GLACIOCLIM French National Observatory (, which provided essential observations for our modelling study. Alpine glaciers, like this one near Mt. CAS Cauvy-Frauni, S. & Dangles, O. The performance of this parametrization was validated in a previous study, indicating a correct agreement with observations31. Geophys. Bolibar, J. et al. Since the neural network used here virtually behaves like a black box, an alternative way is needed to understand the models behaviour. This results in a higher complexity of the Lasso compared to a temperature-index model. 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 Such ice caps cannot retreat to higher elevations in a warming climate, which inhibits this positive impact on MB40 (Fig. Canada's glaciers and ice caps are now a major contributor to sea level change, a new UCI study shows. Res. Model Dev. longwave radiation budget, turbulent fluxes), in comparison with a future warmer climate. This means that these differences linked to MB nonlinearities observed in this experiment could be even greater for such ice caps. We reduced these differences by running simulations with GloGEMflow using exactly the same 29 climate members used by ALPGM in this study (TableS1). J. Clim. Greenland's melting glaciers, which plunge into Arctic waters via steep-sided inlets, or fjords, are among the main contributors to global sea level rise in response to climate change. IPCC. Both DEMs were resampled and aligned at a common spatial resolution of 25m. For each glacier, an individual parameterized function was computed representing the differences in glacier surface elevation with respect to the glaciers altitude within the 19792011 period. 2a and S3). "Seeing the rapid and devastating collapse of this incredible and critical salmon in the Nisqually River is heartbreaking," said Troutt. 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. Our results show that the mean elevation is far more variable than the kinematic ELA ( Fig. Nature 568, 382386 (2019). An increase in the thickness of ice in the higher portion of the Nisqually Glacier was first observed by Arthur Johnson Reference Johnson 1 about ten years ago, and the progress of this "wave" of increased ice thickness has been measured by Johnson each year since that time. The two recent iterations of the Glacier Model Intercomparison Project (GlacierMIP7,8) have proved a remarkable effort to aggregate, compare and understand global glacier evolution estimates and their associated uncertainties. However, to further investigate these findings, experiments designed more towards ice caps, and including crucial mechanisms such as ice-ocean interactions and thermodynamics, should be used for this purpose. The Cryosphere 13, 13251347 (2019). 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. Together with recent findings by another study41 highlighting the increased uncertainties in ice thickness distribution estimates of ice caps compared to mountain glaciers, our results raise further awareness on the important uncertainties in glacier projections for ice caps. The anomaly in snowfall was evenly distributed for every month in the accumulation (October 1April 31) and ablation seasons, respectively. For such cases, we assumed that ice dynamics no longer play an important role, and the mass changes were applied equally throughout the glacier. 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. Secure .gov websites use HTTPS A lock ( ) or https:// means you've safely connected to the .gov website. When working with spatiotemporal data, it is imperative to respect spatial and temporal data structures during cross-validation in order to correctly assess an accurate model performance48. 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. Roe, G. H. Orographic precipitation. 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. Glaciers in the European Alps have been monitored for several decades, resulting in the longest observational series in the world23,24. Correspondence to 48, 24872512 (2009). With this setup, we reproduced the ice cap-like behaviour with a lack of topographical adjustment to higher elevations. 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. 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. Conversely, during the accumulation season, glaciers are mostly covered by snow, with a much higher albedo and a reduced role of shortwave radiation in the MB that will persist even under climate change. Presentation at 2008 National Hydraulic Engineering . (Zenodo, 2020). 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. Our results serve as a strong reminder that the outcomes of existing large-scale glacier simulations should be interpreted with care, and that newly available techniques (such as the nonlinear deep learning approach presented here) and observations (e.g. P. Kennard, J. 1). The Karakoram and the Himalayan mountain range accommodate a large number of glaciers and are the major source of several perennial rivers downstream. H.Z. Years in white in c-e indicate the disappearance of all glaciers in a given massif. All authors provided inputs to the paper and helped to write it. Annual glacier-wide mass balance (MB) is estimated to remain stable at around 1.2m.w.e. A consensus estimate for the ice thickness distribution of all glaciers on Earth. 0.78m.w.e. 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. Six, D. & Vincent, C. Sensitivity of mass balance and equilibrium-line altitude to climate change in the French Alps. Arch. 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.
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