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Glaciers and ice caps are experiencing strong mass losses worldwide, challenging water availability, hydropower generation, and ecosystems. Here, we perform the first-ever glacier evolution projections based on deep learning by modelling the 21st century glacier evolution in the French Alps. By the end of the century, we predict a glacier volume loss between 75 and 88%. 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. Our results confirm an over-sensitivity of temperature-index models, often used by large-scale studies, to future warming. We argue that such models can be suitable for steep mountain glaciers. However, glacier projections under low-emission scenarios and the behaviour of flatter glaciers and ice caps are likely to be biased by mass balance models with linear sensitivities, introducing long-term biases in sea-level rise and water resources projections.
Average cumulative MB projections of French Alpine glaciers with a nonlinear deep learning vs. a linear Lasso model for 29 climate scenarios; a with topographical feedback (allowing for glacier retreat) and e without topographical feedback (synthetic experiment with constant mean glacier altitude). The projections without glacier geometry adjustment explore the behaviour of glaciers which cannot retreat to higher elevations (i.e. ice cap-like behaviour). b, c, d and f, g, h annual glacier-wide MB probability distribution functions for all n scenarios in each RCP. Vertical axes are different for the two analyses. Photographs taken by Simo Räsänen (Bossons glacier, European Alps, CC BY-SA 3.0) and Doug Hardy (Quelccaya ice cap, Andes, CC BY-SA 4.0).
We further assessed the effect of MB nonlinearities by comparing our simulated glacier changes with those obtained from other glacier evolution studies from the literature, which rely on temperature-index models for MB modelling. Previous studies on 21st century large-scale glacier evolution projections have covered the French Alps7,8. Here, we compare our results with those from a recent study that focused on the European Alps10. In that study, a temperature-index model with a separate degree-day factor (DDF) for snow and ice is used, resulting in piecewise linear functions able to partially reproduce nonlinear MB dynamics. Both the Lasso and the temperature-index MB model rely on linear relationships between PDDs, solid precipitation and MB. Therefore, their sensitivities to the projected 21st century increase in PDDs are linear. Despite the differences in the two modelling approaches (Table S2), 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. S7). Nonetheless, a close inspection of the annual glacier-wide MB rates from both models reveals similar patterns to those found when comparing deep learning and Lasso approaches (Figs. S5 and S6). Despite the existence of slightly different trends during the first half of the century, both the Lasso and the temperature-index model react similarly under RCP 4.5 and 8.5 during the second half of the century, compared to the deep learning model. 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. S6).
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. The temperature-index model includes up to three different DDFs, for ice, firn and snow, resulting in three parameters. Alternatively, the Lasso model used here includes 13 DDFs: one for the annual CPDDs and 12 for each month of the hydrological year. Due to the statistical nature of the Lasso model, the response to snowfall anomalies is also highly influenced by variations in PDDs (Fig. 3c). This results in a higher complexity of the Lasso compared to a temperature-index model. 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. 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. 3). 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. Interestingly, this matches the nonlinear, less sensitive response to summer snowfall in the ablation season of our deep learning model (Fig. 3c), which is directly linked to summer air temperatures and has a strong influence on surface albedo. 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. This translates into a more linear response to air temperature changes compared to the ablation season (Fig. 3b). Despite their limitations, temperature-index models, owing to their simplicity and parsimonious data requirements, have been widely used for large-scale glacier projections7,8. 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. 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. on various mass balance and radiation components) are opening the door for updated and better constrained projections.
Our results also highlight the important role played by glacier geometry adjustment under changing climatic conditions, which is typical of mountain glaciers38. 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. 4a). However, many glacierized regions in the world present different topographical setups, with flatter glaciers, commonly referred to as ice caps, covering the underlying terrain39. Such ice caps cannot retreat to higher elevations in a warming climate, which inhibits this positive impact on MB40 (Fig. 5). 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. In order to investigate the effects of MB nonlinearities on flatter glaciers, we conducted a synthetic experiment using the French Alps dataset. 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. With this setup, we reproduced the ice cap-like behaviour with a lack of topographical adjustment to higher elevations. The effect of glaciers shrinking to smaller extents is not captured by these synthetic experiments, but this effect is less important for flat glaciers that are dominated by thinning (Fig. 5). Additionally, glacier surface area was found to be a minor predictor in our MB models31. 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. This translates into more frequent extreme negative MB rates, and therefore greater differences due to nonlinearities for the vast majority of future climate scenarios (Fig. 4e).
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. Nonetheless, a better understanding of the underlying processes guiding these nonlinear behaviours at large geographical scales is needed. The machine learning models used in this study are useful to highlight and quantify how nonlinearities in MB affect climate-glacier interactions, but are limited in terms of process understanding. 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. Therefore, an alternative nonlinear parameterization for the reduction in MB sensitivity under increasing air temperatures would be useful. 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. 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. 59ce067264