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Overview of the Morteratsch glacier complex and stakes for SMB measurements in the ablation area. The eight stakes used in the multiple linear regression analysis (MLRA) are shown in blue (Vadret da Morteratsch) and red (Vadret Pers), the other stakes are represented in light grey. The terminus is at ∼2100 m a.s.l., while the highest mountain peaks are ∼4000 m. The SwissTopo Digital Elevation Model (DEM) used to produce this figure is from 2001 (i.e. start of the field campaign). Figure created with TopoZeko toolbox (Zekollari, 2017). 

Overview of the Morteratsch glacier complex and stakes for SMB measurements in the ablation area. The eight stakes used in the multiple linear regression analysis (MLRA) are shown in blue (Vadret da Morteratsch) and red (Vadret Pers), the other stakes are represented in light grey. The terminus is at ∼2100 m a.s.l., while the highest mountain peaks are ∼4000 m. The SwissTopo Digital Elevation Model (DEM) used to produce this figure is from 2001 (i.e. start of the field campaign). Figure created with TopoZeko toolbox (Zekollari, 2017). 

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Article
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In this study we analyse a 15-year long time series of surface mass-balance (SMB) measurements performed between 2001 and 2016 in the ablation zone of the Morteratsch glacier complex (Engadine, Switzerland). For a better understanding of the SMB variability and its causes, multiple linear regressions analyses are performed with temperature and prec...

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Context 1
... Morteratsch glacier complex is situated on the southern side of the European Alps (Engadine, SE Switzerland) and consists of two glaciers, the Morteratsch glacier (Vadret da Morteratsch) and the Pers glacier (Vadret Pers) (Fig. 1). Until 2015, Vadret Pers was the main tributary of the Vadret da Morteratsch ( Zekollari and Huybrechts, 2015), but now both glaciers have disconnected and act as inde- pendent ice bodies. At present, the glacier complex covers an area of ∼16 km 2 and has a volume of ∼1.1 km 3 (Zekollari and others, ...
Context 2
... the 15-year period, a total of 232 annual mass-balance point measurements are available for the ablation area and around the Equilibrium Line Altitude (ELA) of the Morteratsch glacier complex (Fig. 3). These readings result from annual visits to the glacier, which occur at the very end of September -beginning of October, corresponding to a floating-date system that is very close to the fixed-date system (Cogley and others, 2011). Of the 232 readings, eight have a positive mass balance (up to +0.6 m ice eq a −1 ) (Fig. 3). A total of 128 readings were performed on Vadret da Morteratsch and 104 on Vadret Pers (see Fig. 1). These readings were obtained from 31 separate stakes (17 on Vadret da Morteratsch, 14 on Vadret Pers), of which 12 stakes have a series of at least 10 years and eight stakes cover the full 15-year period. The entire dataset is available as Supplementary material. For Vadret da Morteratsch, the ele- vation of the stakes ranges from the front (∼2030-2100 m a.s.l. over this period) to ∼2600 m a.s.l. (just underneath the icefall, the 'labyrinth'). Most of this range is covered with stakes, roughly at 100 m height intervals (see also Fig. 1). For Vadret Pers, two SMB observations were taken at the front (∼2450 m a.s.l.), but all other measurements are situated between 2600 and 3050 m a.s.l. (∼ the ELA). The SMB is sig- nificantly lower on Vadret Pers compared with Vadret da Morteratsch (Fig. 3), which is likely related to the orientation and resulting daily insolation cycle for both glaciers. The abla- tion area of the Pers glacier is oriented towards the WNW (tongue)-NW (upper ablation area) and is more exposed to direct insolation than the Morteratsch glacier, which is exposed to the N and strongly shielded by the high mountain peaks (see also Fig. 1). A simple approach in which a best linear fit (i.e. linear regression) through all stakes is taken clearly illustrates the higher SMB for Morteratsch in the 2000-3000 m elevation range (ablation area): ...
Context 3
... the 15-year period, a total of 232 annual mass-balance point measurements are available for the ablation area and around the Equilibrium Line Altitude (ELA) of the Morteratsch glacier complex (Fig. 3). These readings result from annual visits to the glacier, which occur at the very end of September -beginning of October, corresponding to a floating-date system that is very close to the fixed-date system (Cogley and others, 2011). Of the 232 readings, eight have a positive mass balance (up to +0.6 m ice eq a −1 ) (Fig. 3). A total of 128 readings were performed on Vadret da Morteratsch and 104 on Vadret Pers (see Fig. 1). These readings were obtained from 31 separate stakes (17 on Vadret da Morteratsch, 14 on Vadret Pers), of which 12 stakes have a series of at least 10 years and eight stakes cover the full 15-year period. The entire dataset is available as Supplementary material. For Vadret da Morteratsch, the ele- vation of the stakes ranges from the front (∼2030-2100 m a.s.l. over this period) to ∼2600 m a.s.l. (just underneath the icefall, the 'labyrinth'). Most of this range is covered with stakes, roughly at 100 m height intervals (see also Fig. 1). For Vadret Pers, two SMB observations were taken at the front (∼2450 m a.s.l.), but all other measurements are situated between 2600 and 3050 m a.s.l. (∼ the ELA). The SMB is sig- nificantly lower on Vadret Pers compared with Vadret da Morteratsch (Fig. 3), which is likely related to the orientation and resulting daily insolation cycle for both glaciers. The abla- tion area of the Pers glacier is oriented towards the WNW (tongue)-NW (upper ablation area) and is more exposed to direct insolation than the Morteratsch glacier, which is exposed to the N and strongly shielded by the high mountain peaks (see also Fig. 1). A simple approach in which a best linear fit (i.e. linear regression) through all stakes is taken clearly illustrates the higher SMB for Morteratsch in the 2000-3000 m elevation range (ablation area): ...
Context 4
... the 15-year period, a total of 232 annual mass-balance point measurements are available for the ablation area and around the Equilibrium Line Altitude (ELA) of the Morteratsch glacier complex (Fig. 3). These readings result from annual visits to the glacier, which occur at the very end of September -beginning of October, corresponding to a floating-date system that is very close to the fixed-date system (Cogley and others, 2011). Of the 232 readings, eight have a positive mass balance (up to +0.6 m ice eq a −1 ) (Fig. 3). A total of 128 readings were performed on Vadret da Morteratsch and 104 on Vadret Pers (see Fig. 1). These readings were obtained from 31 separate stakes (17 on Vadret da Morteratsch, 14 on Vadret Pers), of which 12 stakes have a series of at least 10 years and eight stakes cover the full 15-year period. The entire dataset is available as Supplementary material. For Vadret da Morteratsch, the ele- vation of the stakes ranges from the front (∼2030-2100 m a.s.l. over this period) to ∼2600 m a.s.l. (just underneath the icefall, the 'labyrinth'). Most of this range is covered with stakes, roughly at 100 m height intervals (see also Fig. 1). For Vadret Pers, two SMB observations were taken at the front (∼2450 m a.s.l.), but all other measurements are situated between 2600 and 3050 m a.s.l. (∼ the ELA). The SMB is sig- nificantly lower on Vadret Pers compared with Vadret da Morteratsch (Fig. 3), which is likely related to the orientation and resulting daily insolation cycle for both glaciers. The abla- tion area of the Pers glacier is oriented towards the WNW (tongue)-NW (upper ablation area) and is more exposed to direct insolation than the Morteratsch glacier, which is exposed to the N and strongly shielded by the high mountain peaks (see also Fig. 1). A simple approach in which a best linear fit (i.e. linear regression) through all stakes is taken clearly illustrates the higher SMB for Morteratsch in the 2000-3000 m elevation range (ablation area): ...
Context 5
... the MLRA, 120 SMB measurements are considered, which correspond to the eight stakes that cover the whole observational period (i.e. the 15-year record). All eight stakes are in the ablation zone and are in debris-poor areas. Four of these stakes are located on Vadret da Morteratsch and four on Vadret Pers (see Fig. 1). Including SMB measurements from stakes that do not cover this entire period would introduce bias in the anomalies due to the gap in their data record. Since SMB data from the eight stakes covering the full period would be needed to solve these biases, this approach would not add information about total SMB ...
Context 6
... Morteratsch glacier complex is situated on the southern side of the European Alps (Engadine, SE Switzerland) and consists of two glaciers, the Morteratsch glacier (Vadret da Morteratsch) and the Pers glacier (Vadret Pers) (Fig. 1). Until 2015, Vadret Pers was the main tributary of the Vadret da Morteratsch ( Zekollari and Huybrechts, 2015), but now both glaciers have disconnected and act as inde- pendent ice bodies. At present, the glacier complex covers an area of ∼16 km 2 and has a volume of ∼1.1 km 3 (Zekollari and others, ...
Context 7
... at the very end of September -beginning of October, corresponding to a floating-date system that is very close to the fixed-date system (Cogley and others, 2011). Of the 232 readings, eight have a positive mass balance (up to +0.6 m ice eq a −1 ) (Fig. 3). A total of 128 readings were performed on Vadret da Morteratsch and 104 on Vadret Pers (see Fig. 1). These readings were obtained from 31 separate stakes (17 on Vadret da Morteratsch, 14 on Vadret Pers), of which 12 stakes have a series of at least 10 years and eight stakes cover the full 15-year period. The entire dataset is available as Supplementary material. For Vadret da Morteratsch, the ele- vation of the stakes ranges from ...
Context 8
... 15-year period. The entire dataset is available as Supplementary material. For Vadret da Morteratsch, the ele- vation of the stakes ranges from the front (∼2030-2100 m a.s.l. over this period) to ∼2600 m a.s.l. (just underneath the icefall, the 'labyrinth'). Most of this range is covered with stakes, roughly at 100 m height intervals (see also Fig. 1). For Vadret Pers, two SMB observations were taken at the front (∼2450 m a.s.l.), but all other measurements are situated between 2600 and 3050 m a.s.l. (∼ the ELA). The SMB is sig- nificantly lower on Vadret Pers compared with Vadret da Morteratsch (Fig. 3), which is likely related to the orientation and resulting daily insolation ...
Context 9
... likely related to the orientation and resulting daily insolation cycle for both glaciers. The abla- tion area of the Pers glacier is oriented towards the WNW (tongue)-NW (upper ablation area) and is more exposed to direct insolation than the Morteratsch glacier, which is exposed to the N and strongly shielded by the high mountain peaks (see also Fig. 1). A simple approach in which a best linear fit (i.e. linear regression) through all stakes is taken clearly illustrates the higher SMB for Morteratsch in the 2000-3000 m elevation range (ablation area): ...
Context 10
... the MLRA, 120 SMB measurements are considered, which correspond to the eight stakes that cover the whole observational period (i.e. the 15-year record). All eight stakes are in the ablation zone and are in debris-poor areas. Four of these stakes are located on Vadret da Morteratsch and four on Vadret Pers (see Fig. 1). Including SMB measurements from stakes that do not cover this entire period would introduce bias in the anomalies due to the gap in their data record. Since SMB data from the eight stakes covering the full period would be needed to solve these biases, this approach would not add information about total SMB ...

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... Continuous seasonal monitoring at a dense stake network is performed since 1991 on Ghiacciaio del Basòdino, southern Switzerland (Fig. 6). On Vadret Pers, southeastern Switzerland, a network of stakes in the ablation area has been 370 observed since 20 years (Zekollari and Huybrechts, 2018). ...
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... www.nature.com/scientificreports/ The stake's elevation changes with time due to the melting of ice and glacial downward flow [56][57][58] . During seven years, the total elevation change is around 253 m for stake 1, 210 m for stake 2, and 183 m for stake 3 (kindly refer Statistical Analysis under Results and Discussion for Stake 1, 2 and 3 description). ...
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... MLRA does not include those SMB measurements which are from the stakes that were not able 147 to survive for the whole study period. The involvement of these kinds of measurements will surely 148 raise the biases due to the gap in their dada record [55]. ...
... The stakes elevation change with time due to glacier flow and changes in local ice thickness [55][56][57] ...
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We present a novel approach to simulate and reconstruct annual glacier-wide surface mass balance (SMB) series based on a deep artificial neural network (ANN; i.e. deep learning). This method has been included as the SMB component of an open-source regional glacier evolution model. While most glacier models tend to incorporate more and more physical processes, here we take an alternative approach by creating a parameterized model based on data science. Annual glacier-wide SMBs can be simulated from topo-climatic predictors using either deep learning or Lasso (least absolute shrinkage and selection operator; regularized multilinear regression), whereas the glacier geometry is updated using a glacier-specific parameterization. We compare and cross-validate our nonlinear deep learning SMB model against other standard linear statistical methods on a dataset of 32 French Alpine glaciers. Deep learning is found to outperform linear methods, with improved explained variance (up to +64 % in space and +108 % in time) and accuracy (up to +47 % in space and +58 % in time), resulting in an estimated r2 of 0.77 and a root-mean-square error (RMSE) of 0.51 m w.e. Substantial nonlinear structures are captured by deep learning, with around 35 % of nonlinear behaviour in the temporal dimension. For the glacier geometry evolution, the main uncertainties come from the ice thickness data used to initialize the model. These results should encourage the use of deep learning in glacier modelling as a powerful nonlinear tool, capable of capturing the nonlinearities of the climate and glacier systems, that can serve to reconstruct or simulate SMB time series for individual glaciers in a whole region for past and future climates.
... This is also the case in the European Alps (Fischer et al., 2015;Berthier et al., 2016;Dehecq et al., 2016), where glaciers have been subject to strongly negative mass balances (e.g. Charalampidis et al., 2018;Thibert et al., 2018;Vincent et al., 2018;Zekollari & Huybrechts, 2018). By retreating, glaciers lose ice at their lower elevations which has a stabilizing feedback on their mass balance, hence reducing the imbalance between glacier geometry and the climatic conditions (hereafter referred to as 'glacier-climate imbalance'). ...
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Glaciers in the European Alps rapidly lose mass to adapt to changes in climate conditions. Here, we investigate the relationship and lag between climate forcing and geometric glacier response with a regional glacier evolution model accounting for ice dynamics. The volume loss occurring as a result of the glacier‐climate imbalance increased over the early 21st century, from about 35% in 2001 to 44% in 2010. This committed loss reduced to ~40% by 2018, indicating that temperature increase was outweighing glacier retreat in the early 2000s but that the fast retreat effectively somewhat diminished glacier imbalances. We analyze the lag in glacier response for each individual glacier and find mean response times of 50 ± 28 years. Our findings indicate that the response time is primarily controlled by glacier slope and secondarily by elevation range and mass balance gradient, rather than by glacier size.