ML modelling is a data-driven set of modelling techniques. Here, we used a supervised learning framework for regression, where inputs are in the form of monthly meteorological variables, and targets are in the form of point measurements of glacier mass balance. The actual point mass balance measurements are the target data vital to tuning the model parameters. We do this parameter tuning by designing a loss function defining the variation between the actual mass balance measurements, i.e. the target data, and the point mass balance estimates, i.e. the model's output. We start with random initialization of model parameters and fine-tune the parameters to minimize the loss function. For each of the ML models used in the study, we used the mean squared error (MSE) as the loss function. Further, we obtained the features of importance by assessing permutation importance. Figure  depicts the complete workflow used for the study. The Supplement files include runs of such experiments that impact all the ML models in an equivalent manner.

The RF model is an ensemble-based algorithm where the base learner used is a decision (regression or classification) tree . It relies on the principle of bootstrap aggregating or bagging (proposed by ) for the generation of multiple training datasets to be used by each base learner . To illustrate this, assume there are Ndata samples in the training dataset D, and a new dataset D^ is generated by sampling Ndata samples with repetition. In addition to the generation of bootstrapped datasets, the decision trees are generated using a random subset of input features at every impure node of the tree instead of a complete set of features that standard regression trees use.

Like the RF model, the GBR model is an ensemble-based algorithm where aggregated base learners of decision (classification or regression) trees provide an estimate. However, it differs from the RF model because it uses boosting instead of bagging to construct ensembles. In boosting-based ensembles, base learners are typically weak learners, and the design of subsequent learners is such that the overall error reduces .

The SVM model is a powerful ML tool that relies on Cover's theorem. The theorem suggests that data that might not be linearly separable in a lower dimensional space can be linearly separable when transformed into a higher dimensional space. In the context of classification, the SVM model uses a kernel to transform the data into a higher dimensional space where linear separability is feasible in the form of a hyperplane and decision boundaries. For this purpose, we use kernels such as polynomial kernel and radial basis function kernel . In the case of regression, the hyperplane represents the best-fit line. Thus, unlike empirical risk minimization, where the difference between the actual and predicted model is optimized, the SVM model for regression uses structural risk minimization by identifying the best-fit line.

proposed the NN models as mathematical representations of biological neuron interconnections. showed that neural networks with as few as a single hidden layer with a sufficiently large number of neurons, when used with a non-constant unbounded activation function, can function as universal function approximators. Presently, several applications using multiple-layered NN models demonstrate that NNs can infer abstract relationships between features. NN models use weighted combinations of input features in tandem with non-linearities provided by activation functions such as sigmoid, tanh, and rectified linear unit (ReLU), resulting in the model output. The weights of the NN model are the model parameters obtained by optimization of the loss function.

The most crucial component in ML modelling is the availability of target data to train the model. The target data used for training should be representative of the entire population. Hence, we chose the Fluctuations of Glaciers (FoG) database that contains measured point mass balance information (46 356 data points) globally. The study area is the Randolph Glacier Inventory (RGI) version 6 second-order region Alps under the first-order region 11: Central Europe. This consisted of 15 727 glacier mass balance point measurements. We performed a first-level preprocessing where we considered only annual mass balance measurements (10 102 data points) and measurements from 1950 (9595 data points) onward. We then performed an outlier removal where we considered only those points within 2 standard deviations of the median. This was to avoid the effects of noisy data. We finally used 9166 data points to apply our model.

The second aspect is the input features used by the model to make predictions. The network of weather stations is sparse over much of the Alpine terrain; hence, reanalysis datasets are recommended . We used the ERA5-Land reanalysis dataset . This dataset was chosen primarily due to its comparatively high spatial resolution. This is in line with the findings of and that suggest that datasets with higher spatial resolution effectively represent the orographic drag and mountain valley circulation, which in turn results in improved performance for orographically complex terrain. The choice of variables reflected the contribution of the same to the energy balance equation that drives mass balance modelling from a physical standpoint. We considered the following 14 variables for the modelling: the temperature at 2 m, snow density, snow temperature, surface net solar radiation, total precipitation, forecast albedo, surface pressure, surface net solar radiation downwards, snowfall, surface net thermal radiation, snowmelt, surface sensible heat flux, snow depth, and surface latent heat flux (for details, see ). We consider these meteorological variables because of their effect and representation of the accumulation and ablation process and define the variables expected to represent accumulation processes as accumulation variables (e.g. snowfall, forecast albedo) and melt processes as ablation variables (e.g. temperature, solar radiation). The monthly mean of each of the accumulation and ablation variables was considered. Thus, we have 168 total input parameters. For each of these variables, we extracted the data using the nearest neighbour algorithm, using latitude, longitude, and year of the glacier mass balance measurement from the FoG database. Thus, the final dataset has 168 input features and 9166 data points.

We then normalized the data points using a min–max scaling to ensure the absence of user-conceived bias in the model. We have split the dataset using a random split, where 70 % of the total dataset is used for training the model and 30 % is used for testing the model performance. The training split is used in a 3-fold cross-validation process for tuning the hyperparameters, as described further in Sect. . Finally, we rescaled the model's predictions to assess the model metrics, such as root mean squared error (RMSE), mean absolute error (MAE), normalized mean squared error (nRMSE), and normalized mean absolute error (nMAE) in the measured point mass balance units.

In typical ML workflows, we split the complete dataset (set of features and target data) into training, validation, and testing. We fit the model to the data using the training subset, tune the hyperparameters using the validation subset, and report the independent performance metrics using the testing subset. In our case, we used a 70 %–30 % split for training and testing. We have considered a hyperparameter grid with all combinations of values that each hyperparameter can take (see Table ). Rather than using a fixed ratio subset for validation, as was the case with the testing, we divided the training data subset into three equal folds. Two folds are randomly selected as the training set, and the third fold is used for validation. The validation score is noted, and the process is then repeated for the other fold combinations. The mean validation score for each hyperparameter setting obtained from the grid is used for the selection of the optimal hyperparameters. We compute the validation score as the negative of the RMSE after scaling the target data to a range between 0 and 1. Thus, a more negative validation score results in a more significant error.

For the RF model, we tuned the number of trees. We maintained the maximum depth as indefinite, leading to tree expansion until all nodes were pure. We considered all features to obtain the best split, ensuring minimum bias. As computation for absolute error is slow at each split, we used the squared error as the splitting criterion. This ensured the minimization of the variance after each split. For the GBR model, we tuned the number of trees, maximum depth of each tree (which affects the randomness in the choice of features in each tree), and subsampling ratio (for stochastic gradient boosting). Larger values of maximum depth, such as the indeterminate depth of the RF model, are not used as GBR functions with weak learners to increase the randomness. The SVM model hyperparameter fine-tuning involved kernel selection and a choice of the regularization parameter. Further, in the case of polynomial kernels, the degree of the polynomial was also tuned. For the NN model, we used a fully connected feedforward network where the hyperparameters of the number of layers and number of neurons in a layer were tuned. The activation function ReLU was used to incorporate non-linearity. We used the Adam optimizer to minimize the loss function. The training process was performed for 500 iterations with early stopping in the event of convergence before completing the iterations. The NN models for each set of hyperparameters converged before the completion of the 500 iterations.

The testing dataset evaluation metrics used to assess the models' performances are the coefficient of determination (R2) which represents the percentage deviation between the target and model predictions, the RMSE which represents the absolute deviations between the target, and the model predictions. Lower R2 values suggest that the model does not represent the targets well. Values close to 1 indicate a strong linear correlation. Lower RMSE values are preferable, as this quantifies the variance between the targets and predicted values. Additionally, we report the slope and additive bias using reduced major axis (RMA) regression. We used RMA regression slope and bias to ensure symmetry about the y=1 line. This is preferable, as there exist uncertainties in both target data and outputs.

ML models are heavily reliant on the availability of training data. To understand the effect of data availability on the model performance, we perform an experiment on varying the training sizes. We split the original dataset into subsets of iteratively increasing sizes. We partition each subset into training and testing partitions using a 70:30 ratio. For each subset, we trained all the models using the training partition and computed the evaluation metrics over the testing partition.

The feature importance is represented using permutation importance described in . Here, we disregard individual features from the model at each iteration and recorded the reduction in evaluation score. This is repeated for each input feature. We normalize the obtained permutation importance for each model and express the importance of each input meteorological variable as a percentage. A comparative analysis of the obtained feature importance is performed on percentage importance associated with the accumulation months (November to March) and the ablation months (June–September) is summed and graphically represented for each model in Fig. .

The number of samples required for training the ML models depends upon the complexity of the model. Thus, each of the models used in this study is variably sensible to the number of training samples. We use the evaluation metrics of RMSE and the correlation coefficient to assess the requirement of training samples for each of the models. Figure  depicts the training and testing metrics varying with the size of the training dataset. The training metrics do not show significant change after 20 %–30 % of the training dataset size for the LR, RF, GBR, and SVM models and after 40 % for the NN model. This illustrates the larger number of trainable parameters, resulting in the requirement of larger datasets for artificial neural networks for training. The testing performance of each of the models does not show significant change for training dataset sizes larger than 50 %. We observe that, while a downward trend is evident with the addition of new data, the rate of improvement is slower.

It is interesting to note that RF, GBR, and LR models see an increase in training MAE as opposed to a consistent decrease in testing MAE with increasing training samples. This depicts the tendency of these models to overfit the training samples in the case of smaller datasets. This is evident when observing the order of variation in the training and testing evaluation metric for smaller datasets; e.g. GBR depicts a training MAE of 357 mm w.e. and a testing MAE of 1183 mm w.e. at 10 % training dataset size and training MAE of 659 mm w.e. and a testing MAE of 774 mm w.e. at 100 % training dataset size. Thus, care must be taken when using RF and GBR for smaller datasets, as they are susceptible to overfitting. The performance of the LR model deteriorates for training, and testing performance is also poor. This is not due to overfitting but due to the inability of the model to explain the complex relationship between the inputs and the target. NN requires larger datasets for the training of the model. Figure 2b depicts the superior performance of RF, GBR, and SVM in the event of limited dataset availability. However, we have seen that RF and GBR show a marked increase in training MAE with increasing training samples, which suggests overfitting to limited datasets. Thus, SVM is more robust to smaller datasets.

The best-performing RF model resulted in a testing RMSE value of 1083 mm w.e. and an R2 value of 0.71. The testing MAE value is 782 mm w.e., and the testing nRMSE and nMAE values are 0.55 and 0.40 respectively. The training RMSE value is 934 mm w.e., MAE value is 672 mm w.e., nRMSE is 0.48, nMAE is 0.34, and R2 value is 0.80. We observe that hyperparameter tuning is not important, and no major variations were observed upon changing the number of estimators. The slope of RF was closest to 1, with a value of 0.752 for the training samples and 0.744 for the testing samples. Both the training and testing additive bias were negative, suggesting the model underestimated the point mass balance (Fig. ).

Feature importance analysis using permutation importance considering the 17 (10 % of all features) most essential features indicates that the RF model is highly influenced by downward solar radiation in January; net solar radiation in July; downward thermal radiation in June; temperature at 2 m in June; forecast albedo in February and December; snow depth in January and July; snow density and snowmelt in July; sensible heat flux in December, January, March, and May; latent heat flux in August; and surface pressure in June and July. Permutation importance for the RF model summed over the accumulation months had the highest importance scores for sensible heat flux followed by downward solar radiation and forecast albedo. Each of these variables depict a summed percentage importance between 6 %–9 %. Snow depth and pressure are also important, with a summed percentage importance between 3 %–6 %. For the ablation months, only pressure is observed to have a summed percentage importance greater than 6 %. Sensible heat flux, net solar radiation, latent heat flux, snow depth, forecast albedo, snow density, and temperature at 2 m display a summed percentage importance between 3 %–6 %.

Tuning the maximum depth permitted for each weak learner tree was important in estimating the best model, and varying the number of weak learner trees during hyperparameter tuning improved performance in the case of smaller depths of the weak learners. Deeper tree structures did not significantly change the model's performance upon changing the number of trees. Stochastic gradient boosting (subsampling at 0.7) resulted in reduced performance. The hyperparameter combination of the best-performing GBR model is 100 trees with a maximum depth of five nodes (Fig. a). The best-performing GBR model resulted in a testing RMSE value of 1071 mm w.e. and an R2 value of 0.71. The testing MAE value is 774 mm w.e., and the testing nRMSE and nMAE are 0.55 and 0.39 respectively. The training RMSE value is 759 mm w.e., MAE value is 659 mm w.e., nRMSE is 0.39, nMAE is 0.34, and R2 value is 0.80.

The most important meteorological inputs for the GBR model are snowfall in July; downward solar radiation in January and December; forecast albedo in December, January, February, March, and May; sensible heat flux in January, March, May, November, and December; temperature at 2 m in June and August; snow depth in June; and surface pressure in August. Note the marked importance associated with ablation meteorological variables and the months associated with ablation. Permutation importance expressed as a percentage and summed over the accumulation months depicts the most importance to forecast albedo, followed by sensible heat flux, with both variables depicting a summed percentage importance greater than 10 %. Among other meteorological variables, downward solar radiation, net solar radiation, and snow depth in the accumulation months are also important. The ablation months depict higher summed importance values, with forecast albedo in these months prominent. Sensible heat flux, latent heat flux, surface pressure, snowfall, snow depth, and temperature at 2 m above the surface are also important.

The SVM model depicted large fluctuations in the validation score with changes in the hyperparameters. This is represented in Fig. b. We considered the hyperparameters of the kernel, degree (for polynomial kernel), and regularization (penalty) factor. The sigmoid kernel resulted in evaluation metrics markedly poorer than the radial basis function (RBF) kernel and polynomial kernels. The sigmoid kernel was excluded from the graphical representation of the validation score to emphasize the variations observed in the other kernels. The polynomial kernel at larger degrees consistently performed better than the RBF kernel in the case of regularization tuning lower than 1. For larger regularization parameters, the RBF kernels demonstrated better performance. The best-performing model in this study is the RBF kernel (penalty factor: 10.0). Figure b depicts the results of hyperparameter tuning for the SVM kernel. The testing RMSE values for the model are 1085 mm w.e., and the R2 value is 0.70. The testing MAE value is 836 mm w.e., and the testing nRMSE and nMAE are 0.56 and 0.43 respectively. The training RMSE value is 727 mm w.e., MAE value is 727 mm w.e., nRMSE is 0.37, nMAE is 0.37, and R2 value is 0.76.

The permutation importance associated with the sensible heat flux in March is most important, as is the sensible heat flux associated with April, May, June, and December. Latent heat flux in August and October is important. Snowfall in October and snow density for the months of November, December, and January are important. The temperature at 2 m above the surface in June and July; downward solar radiation in December; and forecast albedo in August, October, and December are important. Summing the percentage importance over the accumulation and ablation months, we observe that sensible heat flux in the accumulation months is most important, followed by snow density and downward solar radiation. These three variables depict a summed percentage importance of more than 6 %. The temperature at 2 m a.g.l. and forecast albedo depict an importance between 3 %–6 % for the accumulation months. For the ablation months, sensible heat flux continues to depict a summed percentage importance of more than 6 %. Latent heat flux, snow density, forecast albedo, and temperature at 2 m above the surface also depict a summed percentage importance between 3 %–6 %.

The NN model performance is highly susceptible to hyperparameter selection. We varied the number of hidden layers in the network and the number of neurons in each hidden layer. Figure c and d depict the variation in performance of the model for each of these cases. On the left is the variation in the number of neurons for a single hidden layer. A larger number of hidden neurons permits more combinations of the inputs that can affect the targets. The improved performance with the increasing size of neurons illustrates the role of the complexity of the model in estimating mass balance. Increasing the number of layers also affects the performance of the NN model, with the best performance obtained using two hidden layers. This further emphasizes the importance of incorporating non-linear elements in estimating point mass balance. A larger number of hidden layers did not significantly improve performance, as the larger number of parameters demanded a larger training dataset to avoid overfitting and to complete the training. The testing RMSE values for the best-performing model are 1096 mm w.e. and R2 value is 0.70. The testing MAE value is 836 mm w.e., and the testing nRMSE and nMAE are 0.56 and 0.43 respectively. The training RMSE value is 773 mm w.e., MAE value is 773 mm w.e., nRMSE is 0.39, nMAE is 0.39, and R2 value is 0.76.

The most important meteorological variables in terms of the percentage permutation importance for the NN model are the sensible heat flux for March, April, and May; latent heat flux in July; surface pressure in February; net solar radiation in May and September; downward solar radiation in December; and forecast albedo in July. The snow density in December and the snow depth in January, February, April, July, September, October, and December are important. We see that snow depth across the year dominates the important meteorological inputs for this model. Upon summing the percentage importance for the accumulation and ablation months, we observe that snow depth is the most important for both accumulation and ablation months. Snow density, pressure, sensible heat flux, and downward solar radiation are also important in the accumulation months, with a summed percentage importance value between 3 %–6 %. For the ablation months, net solar radiation is also important. Snow density, forecast albedo, latent heat flux, and sensible heat flux are also important, with summed percentage importance values between 3 %–6 %.

The testing RMSE values for the LR model are 1248 mm w.e. and R2 value is 0.58, and the training RMSE values are 1197 mm w.e. and R2 value is 0.61 (Fig. ). The testing MAE value is 941 mm w.e., and the nRMSE and nMAE are 0.64 and 0.48 respectively. The training MAE value is 935 mm w.e., nRMSE is 0.61, and nMAE is 0.48.

Snow depth over most of the year is the most important feature for the model, with surface pressure also playing an important role. Other features do not depict as high an importance value. However, relative importance varies across the months.

The performance of each of the models was evaluated using an independent test dataset. The GBR model resulted in the best testing performance MAE, RMSE, and R2 values, outperforming the RF model and SVM and NN models. Neural networks resulted in better bias performance. RF, GBR, SVM, and NN significantly improve upon the LR model's metrics. The ability of all non-linear models to outperform the linear model is further depicted in each model's scatter plot (Fig. ). This is in agreement with similar studies in other domains, such as , who showed that tree-based models such as RF were preferable to LR models for the bias correction of snow water equivalent, and , who depicted the efficacy of non-linear models in estimation of streamflow when compared to linear models.

The performance of all models is affected by the uncertainties associated with the input features and targets. Inherent errors exist in point mass balance estimates, as heterogeneity is not captured sufficiently by the available measurements . Of the 727 locations with uncertainty estimation performed, we note a mean uncertainty of 62 mm w.e., which can adversely impact performance evaluation. The uncertainty estimates for the remaining point locations are unknown; hence, their impact is not constrained. In this study, we did not consider the effect of topography and debris cover for the models. This can lead to inflated RMSE values.

Further, the use of input meteorological reanalysis data can result in bias, especially in locations without sufficient ground stations . Specifically for the use of ERA5-Land data in complex terrain, report that while ERA5-Land represents the intra-annual variations in precipitation characteristics, there is a positive bias in the precipitation variables. Similarly, in the case of temperature, show through correlation and RMSE analysis that while the ERA5-Land dataset captures the temperature trends effectively, the magnitude of the values is not well represented. Thus, we suggest using a bias correction step such as that proposed by in the case of RF, GBR, and SVM models. Moreover, the reanalysis data do not fully reflect point scale data, as they have a coarse resolution. depict the impact of resolution in simulating drivers of local weather in complex terrain and show that coarser resolutions do not account for orographic drag. Approaches such as using a scaling factor or lapse rates have been attempted in studies (e.g. ). However, these studies largely utilize precipitation and temperature as inputs, the scaling of which with elevation is fairly straightforward. Choosing appropriate scaling factors for other meteorological variables that drive glacier mass balance (e.g. sensible and latent heat fluxes, albedo) is not intuitive. We note that the effects of the larger scale of the input variable will persist in the model. However, these effects will be consistent across all the models. Thus, the effect of the input variable scale is represented by the uncertainty of all models, and a relative analysis of the performance of models will remain well founded.

The testing performance improves by increasing the number of training samples. We observe that for a larger number of data points, marginal improvement is observed upon increasing the number of samples further. The reduction in the rate of improvement for all models suggests that all models have been successfully trained. However, the marginal improvements observed suggest that a potential improvement in model performance is possible when including more data samples. The RF and GBR models overfit the training samples in the case of smaller datasets. The NN model training and testing metrics depict improved performance with training size. The NN model had the most trainable parameters and hence is the most data intensive. A larger number of training samples is essential for models with a larger number of trainable parameters. The training performance of the LR model deteriorates with increasing training samples. While the graph (LR model of Fig. ) appears similar to the RF and GBR training graphs, the relatively close training and testing metric values suggest that overfitting is not the likely cause. Rather, it suggests that the model cannot explain the non-linear relationship between the inputs and the target.

Further, Fig.  represents each model's variation in training and testing evaluation metrics. Each model was trained and tested over each dataset size. For each model, the box plots are generated by utilizing the outcome of the models developed using varying training dataset sizes. The training performance, as expected, is better than the testing performance, as the model parameters are tuned to fit this dataset. The range of values is more extensive for the testing errors as a result of overfitting in the case of smaller datasets. In such cases, the use of the SVM model yields better results.

Assuming a winter accumulation-type glacier, we expect the months of November to March to be dominated by accumulation processes and June to September to be dominated by ablation processes. Analysis of the permutation importance (by percentage) of the features of each model was studied month-wise based on a physical understanding of which season-specific features will be most important. Figure  represents the summed feature importance for each input variable in the accumulation and ablation months. We sum the percentage importance rather than the feature importance values to permit comparison between models. We expect temperature (2 m) for ablation seasons to be significant compared to temperatures in the accumulation season. This is not well reflected when using the LR model. While all the ML models show the reduced importance of temperature in the accumulation months, it is most pronounced in the case of the RF and GBR models. A similar trend is expected for the downward thermal radiation and snowmelt. Here too the LR model does not reflect the expected outcome. All ML models depict reduced importance in the accumulation months, with a pronounced reduction observed in the RF and GBR models. In the case of snowmelt, all ML models and the LR model follow the expected response. Snow depth throughout the year is important when considering snow density. We expect the depth in the ablation months to be important. All models portray this except the SVM model. We observe that the LR model relies heavily on snow depth to estimate the mass balance. The SVM model reports the exaggerated importance of snow density in the accumulation months. While we expect more importance regarding precipitation terms such as total precipitation and snowfall in the accumulation months, we do not observe this for any model. The LR model did show a weak reduction in the importance of total precipitation and snowfall. However, the ML models showed only a weak reduction or a weak increase in importance. This is possibly a result of the scale of the meteorological variables used not sufficiently representing the influence of orographic water vapour transport that results in precipitation .

Net solar radiation and albedo are important ablation components. Albedo over snow-covered regions is higher than that of exposed ice or firn. At higher elevations and in summer months, we expect lower albedo values. Thus, variations in albedo are significant. In the case of ERA5-Land, the forecast albedo variable represents both the direct and diffuse radiation incident on the surface, with values dependent on the land cover type. It is calculated using a weight applied to the albedo in the UV–visible and infrared spectral regions. The albedo of snow and ice land covers differs in the UV–visible and infrared spectral regions. This makes forecast albedo more important than broadband albedo, which depends only on the surface net solar radiation and the surface solar radiation downwards. The expected importance of the albedo is observed in the RF, GBR, NN, and SVM model. LR models, in contrast, depict very low importance of albedo for the accumulation months. Thus, we see that the ML models represent the importance of the ablation features well. This is in agreement with the predominantly negative mass balance observed in in situ measurements.

We can observe that the importance associated with the meteorological variables is not dominated solely by total precipitation and temperature, as with temperature index models. Thus, ML modelling can represent the contributions of a complete set of variables with lesser complexity and ease of use than physical models. This also emphasizes the requirement for ML models to use all meteorological variables of interest, as opposed to a subset of them. This is the case with studies such as . Further, our results agree with the studies conducted by and in that artificial neural networks capture the complexity of the mass balance estimation using non-linear relationships between inputs. However, we propose that other ML models, notably ensemble tree-based methods, can be used as an equivalent to improved estimates in the case of fewer real-world data samples for training. This has also been observed in other studies (e.g. ) For this case, feature importance derived using permutation importance for the ensemble-based models, RF and GBR, represented the expected role of meteorological variables in determining feature importance. The evaluation metrics also emphasize the performance of these models.

With the emergence of artificial intelligence techniques, a number of studies have employed deep learning algorithms for numerous applications. A majority of these studies use neural networks to incorporate non-linearity in the modelling of various Earth observation applications. However, a host of ML techniques exist which remain under-utilized. This is being studied in the ML community (e.g. , studied 179 classification models), and it has been observed that for tabular datasets, tree-based models remain state of the art for both classification and regression problems for medium-sized datasets (training samples under 10 000). Our study also depicts the improved performance of GBR models, which aligns with these recent findings. While it largely follows the assumptions made by , we demonstrate the case of regression with heterogeneous and interdependent input features, and a voided assumption of the identical and independent distribution of samples also depict a better performance by ensemble tree-based models. With glacier mass balance datasets being typically medium-sized datasets with correlated input features, we recommend that studies aiming to use ML for modelling the Earth system consider the ensemble-based techniques. Many ensemble-based techniques exist, including bagging as used by RF and boosting as used by AdaBoost and GBR. Further, studies that combine ensemble trees models with deep learning are also being used effectively (e.g. , used XGBoost in tandem with an ensemble of deep models). utilize a leave-one-year-out and leave-one-glacier-out mode of testing the performance of the model. This is in line with , who suggest that spatially and temporally structured datasets would benefit from a manually designed blocking strategy. As the testing and validation splits will result in similar effects in all the models, performing the grouped splitting does not provide immense value to this study. However, for cases where a single model is to be used to estimate glacier mass balance, the leave-one-glacier-out and leave-one-year-out techniques are useful.

An aspect not considered in this study is a transfer learning approach to the ML modelling, where glacier mass balance datasets from other locations can be used to pre-train the neural network and generate an initialization of weights to be tuned by the dataset of the region of interest (see ). In line with utilizing datasets from other locations, another aspect to consider with glacier mass balance datasets is the generalizability of the models. Understanding which machine learning model can be used for local, regional, and global analysis is important and will be a useful study to take up. Feature importance associated with the local, regional, and global analysis will also provide new insights into the changes in the glacier mass balance at these scales. An important factor to note is that through this study, we have considered annual mass balance measurements as opposed to seasonal measurements due to the paucity of sufficient datasets to train a multi-parameter machine learning model fully. The role of ablation and accumulation variables will be better represented in the case of seasonal measurements and is an avenue to explore through future studies.