Evaluating the Performance of Multiple Machine Learning and Deep Learning Models on Glacier Mass Balance Estimation

Abstract

Glacier mass balance estimation is important for understanding glacier responses to climate change and for assessing mountain water resources. Data-driven methods are widely used, but their cross-regional transferability remains unclear, especially in High Mountain Asia (HMA), where observations are limited. This study develops a unified framework to compare 16 machine learning and deep learning models across the European Alps and HMA. A degree-day-based monthly decomposition scheme is used to generate physically constrained monthly mass balance estimates. These are used as intermediate supervision signals. All models are trained at the monthly scale, and the outputs are aggregated to annual values for evaluation against observations. In transfer experiments, models are trained on Alpine data and tested in HMA. In joint-training experiments, different proportions of HMA samples are gradually added to the training set to assess the role of target-region information. Results show that machine learning models outperform deep learning models in cross-regional settings. Random Forest and K-Nearest Neighbors remain relatively stable under limited HMA data, while deep learning models are more sensitive to distribution shifts. Adding a small amount of HMA data improves annual prediction performance, highlighting the value of region-specific information. Overall, this study provides guidance for modeling glacier mass balance in data-scarce regions.

1. Introduction

Glaciers are important indicators of climate change. They strongly influence global and regional hydrological cycles, sea-level change, and terrestrial ecosystems [1,2]. Over the past six decades, glaciers worldwide have lost approximately 9.6 ± 3.5 trillion tons of ice, contributing roughly 27 ± 9 mm to global mean sea-level rise, and since the 1990s the rate of mass loss has increased by nearly 50% [3,4]. In mountainous regions, glacier meltwater supports irrigation, hydropower generation, and domestic water supply [5,6,7,8]. Accurate estimation of glacier mass balance is therefore essential for projecting future glacier evolution, runoff, and sea-level rise [9,10,11]. However, glacier mass balance estimation remains challenging. Glacier mass balance is controlled by temperature, precipitation, radiation, and other environmental factors that show strong spatial heterogeneity. In addition, in situ observations remain sparse and unevenly distributed worldwide [12,13].

From the perspective of physical modeling, glacier mass balance models are commonly divided into two categories: temperature-index models and physically based energy-balance models. Temperature-index models use air temperature and precipitation to represent ablation and accumulation processes. These models estimate melt as a linear function of air temperature above the freezing point. They also use a degree-day factor to relate temperature to melt rate and estimate accumulation from precipitation [14,15]. Because these models require relatively few input variables and have high computational efficiency, they are widely applied at regional scales [7]. However, the degree-day factor is not constant. Its value changes with elevation, albedo, and solar radiation [12,15]. As a result, the parameter must be calibrated for different glaciers or climatic regions. This parameter sensitivity limits the transferability of temperature-index models in data-scarce catchments [16]. In contrast, energy-balance models explicitly calculate radiative and turbulent heat fluxes at the glacier surface. These models also account for albedo evolution and variations in snow and firn conditions [17,18]. Models such as Coupled Snowpack and Ice surface energy and mass balance model for Python 3 (COSIPY) can quantitatively simulate glacier ablation and surface energy exchange through physical processes [19]. However, these models require high-resolution meteorological forcing data and substantial computational resources. These requirements limit their application in many high-mountain regions, including High Mountain Asia.

In recent years, machine learning and deep learning have provided new approaches for glacier mass balance (GMB) simulation [11,20]. These methods rely on nonlinear fitting and data-driven learning rather than complex physical parameterizations. Unlike physical models, machine learning and deep learning approaches do not explicitly describe physical processes. Instead, they infer glacier mass balance patterns directly from observations and reanalysis datasets [8]. These methods can also partially account for uncertainties and biases in climatic and glaciological variables. Previous studies have demonstrated the potential of machine learning methods for glacier mass balance estimation. Anilkumar et al. showed that gradient boosting regression outperformed several other algorithms in the Central European Alps [12]. Their model achieved a coefficient of determination of 0.713 and an RMSE of 1.071 water equivalent in meters (m w.e.). Bolibar et al. developed the Alpine Glacier Model (ALPGM) using deep neural networks for glacier surface mass balance simulation in the Alps [20]. Van der Meer et al. proposed the miniML-MB model based on extreme gradient boosting [11]. Their model achieved high simulation accuracy at 28 glacier stations in the Swiss Alps using only two predictors: summer mean temperature and winter cumulative precipitation. These studies demonstrate that data-driven methods are effective tools for glacier mass balance estimation. These approaches also show strong potential for glacierized regions with sparse or uneven observational coverage.

Meanwhile, data-driven methods have increasingly been applied to glacier studies in High Mountain Asia (HMA), which contains the largest concentration of glaciers outside the polar regions and is characterized by strong spatial climatic heterogeneity. Recent studies have demonstrated the potential of machine learning for glacier mass balance estimation in this region. For the Tibetan Plateau, ensemble learning models that integrate climatic, topographic, and glacier dynamic variables have been shown to improve mass balance simulation accuracy compared with traditional linear models. Explainable machine learning approaches have further revealed the spatial distribution of dominant controlling factors and their nonlinear interactions with glacier dynamic processes [21]. In the Tian Shan and Pamir regions, Peng et al. applied several machine learning algorithms to reconstruct the spatiotemporal variability of glacier mass balance during 2000–2020. Their results showed that XGBoost performed best in capturing nonlinear relationships between annual mass balance and meteorological–topographic variables [22]. Comparative studies across different HMA subregions have also shown that their performance is more regionally variable for maritime glaciers with more complex ablation processes [8]. Overall, these studies demonstrate the promise of data-driven methods for glacier mass balance estimation in HMA.

Despite this growing body of work, several important limitations persist. First, cross-regional generalization has not been systematically assessed. Most glacier mass balance models are calibrated and validated within a single geographic region, and few studies have conducted extrapolation experiments across regions with markedly different climatic backgrounds. A unified cross-regional benchmark encompassing both the European Alps and High Mountain Asia is therefore still lacking. Second, many studies aggregate input variables into seasonal or annual means, which discards monthly scale process information that is essential for capturing how accumulation and ablation jointly determine annual mass balance. This aggregation masks intra-annual accumulation–ablation dynamics and may reduce the accuracy of annual mass balance prediction. It may also hinder model transfer from precipitation-limited mid-latitude Alpine glaciers to monsoon-influenced or westerly dominated glaciers in High Mountain Asia. Third, methodological comparisons across studies are often based on inconsistent experimental settings. Differences in feature selection, temporal resolution, sample definition, and validation schemes make it difficult to determine whether deep learning models truly outperform ensemble machine learning methods under comparable conditions.

To address these gaps, the main contributions of this study are summarized as follows. First, we develop a unified benchmarking system for machine learning and deep learning models. All models are evaluated using consistent monthly input features and physically constrained monthly mass balance labels as intermediate supervisory signals, and final performance is assessed at the annual scale by aggregating monthly predictions. The evaluated deep learning models include Long Short-Term Memory (LSTM), Bidirectional Long Short-Term Memory (BiLSTM), Convolutional Neural Network (CNN), Deep Feedforward Neural Network (DNN), and Transformer-based attention models. The machine learning baselines include Ordinary Least Squares (OLS), Least Absolute Shrinkage and Selection Operator (Lasso), Least Angle Regression (LARS), K-Nearest Neighbors (KNN), Support Vector Regression (SVR), Classification and Regression Trees (CART), Random Forest (RF), Gradient Boosting, Extreme Gradient Boosting (XGBoost), and Light Gradient Boosting Machine (LightGBM). All models follow the same training, validation, and testing protocol to assess their relative performance under comparable conditions [8,20]. Second, we assess cross-regional transferability from the European Alps to High Mountain Asia. Models are first trained exclusively on Alpine glacier samples and evaluated on both an independent Alpine test set and unseen HMA glaciers. Joint-training experiments then progressively incorporate different proportions of HMA samples to quantify how much target-region information is needed to recover prediction accuracy under different climatic backgrounds. Third, we provide model selection guidance for data-scarce glacierized catchments. Model performance is compared across regions and training strategies using the coefficient of determination, root mean square error, and mean absolute error. These comparisons provide practical evidence for selecting suitable glacier mass balance prediction models when in situ observations are limited.

2. Study Area and Data

2.1. Study Area

This study selects two representative glacierized regions as research domains: the European Alps and High Mountain Asia (HMA). These regions differ in moisture sources and degrees of continentality. Such differences provide a suitable basis for evaluating model applicability under different climatic conditions.

The European Alps are located between 44° N and 47° N and 5–8° E. Although the region covers a relatively small geographic area, it contains complex topography and strong climatic gradients. Climate conditions can change over short spatial distances. The western and southwestern Alps are strongly influenced by Atlantic westerlies and show maritime climate characteristics. In contrast, the northern and eastern Alps experience more continental climatic conditions [23,24]. The Alps also contain a dense glacier mass balance observation network. Several glaciers provide continuous annual mass balance records spanning multiple decades [25]. These characteristics make the region suitable for model training and internal consistency evaluation. This study selects 32 glaciers from the Alps as research targets. Most glacier mass balance records cover the period from 1984 to 2018. For several glaciers, including Mer de Glace, Saint-Sorlin, Sarennes, and Argentière, older observations are also available. These additional records extend back to 1959. This study further groups Alpine glaciers according to their center-of-mass latitude (φ) to evaluate hydroclimatic differences across latitudinal gradients. Figure 1A divides the glaciers into three categories: northern glaciers (φ ≥ 45.6°), middle glaciers (45.3° ≤ φ < 45.6°), and southern glaciers (φ < 45.3°).

High Mountain Asia contains large elevation differences and complex climate regimes. The southern and southeastern margins are strongly affected by the Asian monsoon and receive abundant precipitation. In contrast, the northern and western interior regions extend deep into the Eurasian continent and experience cold and arid climatic conditions [26]. Compared with the Alps, HMA shows stronger spatial variability and more pronounced precipitation seasonality. These characteristics make HMA an appropriate region for evaluating model generalization under extrapolation conditions. This study separates glacier samples in HMA at the individual-glacier level. The dataset includes 19 glaciers in the training set and 3 glaciers in the test set. In addition, this study selects three fixed test glaciers and keeps them unchanged across all experiments. The first glacier is Urumqi Glacier No. 1 in the Tianshan Mountains, which represents a typical continental climate environment. The second glacier is Xiaodongkemadi Glacier in the Tanggula Mountains, which represents transitional climatic conditions between inland continental and monsoon influences. The third glacier is Palong Glacier No. 94 in the Palong Tsangpo River Basin. This glacier is located on the southeastern margin of HMA and is strongly influenced by the monsoon climate. These three glaciers are excluded from the HMA training dataset.

2.2. Data

This study uses ERA5-Land hourly reanalysis data as the main meteorological forcing dataset. The data are obtained from the Copernicus Climate Data Store. This study extracts air temperature and precipitation variables and aggregates them into monthly glacier-scale datasets. Monthly meteorological variables for each glacier are calculated through linear interpolation based on glacier locations. This study also includes a month index as an auxiliary predictor to represent seasonal variability in machine learning tasks. This study obtains glacier mass balance data from the World Glacier Monitoring Service (WGMS) [25]. These annual mass balance records serve two main purposes. First, they are used as target variables for supervised learning during model training and evaluation. Second, they provide annual-scale closure constraints for the monthly decomposition results generated by the degree-day model. This constraint ensures that the sum of monthly mass balance estimates exactly matches the observed annual mass balance for each glacier and year. This study also retrieves additional Alpine glacier mass balance series from the ALPGM project repository. These data supplement the WGMS observations and improve data coverage in the Alpine region. This study further uses Randolph Glacier Inventory version 6.0 (RGI 6.0) to obtain glacier coordinate information for both the Alps and HMA. These data provide a unified and reliable spatial basis for subsequent spatial analysis and regional classification. The summary table of data sources is shown in

Table 1. Summary of data sources used in this study.

Dataset	Resolution	Period	Source
ERA5-Land Reanalysis	monthly	1959–2023	Copernicus CDS
WGMS Mass Balance	Annual	1959–2023	https://wgms.ch
ALPGM Repository	Annual	1959–2018	https://github.com/JordiBolibar/ALPGM (accessed on 24 May 2025)
RGI 6.0	Static	-	https://glims.org/RGI (accessed on 28 May 2025)

below.

3. Methodology

The overall workflow consists of three stages: data preparation, model training, and model performance assessment (Figure 2). In the data preparation stage, observed annual glacier mass balance, daily precipitation, and daily air temperature are used to construct monthly scale predictors and physically constrained monthly mass balance labels. Specifically, a degree-day model and residual redistribution procedure are applied to derive monthly mean temperature, total precipitation, snowfall, positive degree-day sum, ablation, and monthly glacier mass balance. The monthly resolution is used as an intermediate modeling step to preserve intra-annual accumulation and ablation signals that would otherwise be lost when using only seasonal or annual aggregates. In the model training stage, the dataset is divided into training and test sets using a glacier-wise strategy. This strategy ensures that all glacier-year records from the same test glacier are excluded from the training dataset, thereby reducing dependence among repeated annual observations from the same glacier and preventing information leakage between training and test samples. Machine learning and deep learning models are then trained under consistent experimental settings. Machine learning models are optimized through hyperparameter tuning, whereas deep learning models are trained with early stopping to reduce the risk of overfitting.

In the performance assessment stage, monthly model outputs are aggregated into annual mass balance values and compared with observed annual glacier mass balance. Model performance is evaluated using standard regression metrics, including the coefficient of determination (R²), Pearson correlation coefficient (R), mean squared error (MSE), root mean squared error (RMSE), and mean absolute error (MAE). The overall workflow is illustrated in Figure 2.

Following the terminology of transfer learning, the source domain refers to the domain that provides labeled data for model training, whereas the target domain refers to the domain where the trained model is applied and evaluated [27,28]. In this study, the European Alps are defined as the source domain, and High Mountain Asia (HMA) is defined as the target domain. This design follows the data availability and application context of the study. The European Alps have relatively dense and long-term glacier mass balance records from the WGMS database, making them suitable for source-domain calibration. In contrast, HMA contains sparser and more heterogeneous observations but represents an important application region where glacier mass balance estimation remains challenging. The Alps-to-HMA transfer direction was selected to evaluate whether models trained in a data-rich glacier region can generalize to a data-scarce and climatically heterogeneous region. In principle, the transfer direction can be reversed by using HMA as the source domain and the European Alps as the target domain. However, such a setting would address a different research question and would be more strongly constrained by the limited sample size, uneven spatial coverage, and high climatic heterogeneity of HMA observations. Therefore, the present study focuses on the Alps-to-HMA transfer direction.

To quantify the effect of target-region information on model transferability, this study defines five joint-training configurations with different proportions of HMA training samples. In the 0% HMA configuration, models are trained only on Alpine data and are directly applied to HMA without any target-region training information. In the 30%, 50%, and 80% HMA configurations, the corresponding proportions of HMA training glacier-year records are added to the Alpine training dataset. In the 100% HMA configuration, all available HMA training samples are incorporated into the training process. In all configurations, the fixed HMA test glaciers and their corresponding annual records are kept completely independent and are never used during model training. For the Alpine dataset, a fixed subset of glaciers is reserved for testing. For the HMA dataset, the 22 monitored glaciers are divided into fixed training and test subsets, and the test glaciers remain unseen during model fitting. This glacier-wise split ensures that no glacier-year samples from test glaciers appear in the training dataset. As a result, the reported evaluation metrics reflect model generalization ability on unseen glaciers rather than interpolation among repeated records from the same glacier.

3.1. Monthly Decomposition Algorithm

To turn yearly glacier mass balance values into physically relevant monthly mass balance labels, this work employs a monthly decomposition technique based on a degree-day model and a residual allocation approach [29]. This approach provides monthly weak labels for later data-driven models while keeping the yearly mass balance identical to the observed values. Monthly resolution allows the model to resolve intra-annual accumulation–ablation dynamics that are masked when training directly on yearly aggregates. These monthly weak labels, therefore, serve as process-level supervision signals, yielding more physically accurate annual predictions.

3.1.1. Daily Melt Estimation Based on Positive Degree Days

Surface melt is estimated using the positive degree-day (PDD) method [13,30]. This approach assumes that when the air temperature exceeds the melting point, the melt rate scales linearly with the accumulated positive temperature. For each day $d$, given the daily 2 m air temperature $T_d$ (°C), the daily positive degree days are defined as:

$${\mathrm{PDD}}_d=\mathrm{m}\mathrm{a}\mathrm{x}\left(0,T_d\right).$$

The daily melt rate $M_d$ (mm w.e. day⁻¹) is then expressed as:

$$M_d=\alpha ·{\mathrm{PDD}}_d,$$

where $\alpha$ is the degree-day factor (mm w.e./°C · day). By minimizing the sum of squared residuals (SSR) between simulated annual mass balance and observed values, the optimal α is independently determined. It is important to emphasize that α is calibrated independently for each individual glacier using only that glacier’s own observed annual mass balance records from the WGMS database. Specifically, the calibration is performed by minimizing the sum of squared residuals between the degree-day-simulated and observed annual mass balance across all available years for that glacier. This per-glacier calibration relies solely on that glacier’s own historical observations, and the resulting melt coefficient carries a physically interpretable meaning.

Daily melt is accumulated to the monthly melt for glacier $g$ in year $y$ and calendar month $m$:

$$M_m\left(g,y,m\right)=\sum _{d\in m}{M}_d\left(g,y,d\right).$$

In parallel, daily positive degree days are accumulated to obtain the monthly total:

$${\mathrm{PDD}}_m\left(g,y,m\right)=\sum _{d\in m}{\mathrm{PDD}}_d\left(g,y,d\right),$$

which is later used as a weighting term in the residual redistribution step.

3.1.2. Temperature-Based Phase Partitioning of Precipitation and Accumulation Estimation

Total precipitation is partitioned into solid (snow) and liquid (rain) to estimate monthly accumulation [31]. For each day $d$, the daily air temperature $T_d$ is used to define a snowfall fraction $f_s\left(T_d\right)$:

$$f_s\left(T_d\right)=\{\begin{array}{ll}1,& T_d\le T_{\min }\\ {\displaystyle \frac{T_{\max }-T_d}{T_{\max }-T_{\min }}},& T_{\min }<T_d<T_{\max }\\ 0,& T_d\ge T_{\max }\end{array}$$

Here, the temperature thresholds are fixed to $T_{\min }=-2^{\circ }\mathrm{C}$ and $T_{\max }=2^{\circ }\mathrm{C}$ [32]. Let $P_d$ (mm) denote the daily total precipitation. The portion of that precipitation that is treated as solid accumulation on the glacier surface is then

$$S_d=f_s\left(T_d\right)P_d.$$

Daily snowfall is summed to obtain the monthly accumulation:

$$S_m\left(g,y,m\right)=\sum _{d\in m}{S}_d\left(g,y,d\right),$$

and the monthly total precipitation is recorded as

$$P_m\left(g,y,m\right)=\sum _{d\in m}{P}_d\left(g,y,d\right).$$

The raw (i.e., unconstrained) monthly net mass balance is then defined as

$$B_m^{\mathrm{raw}}\left(g,y,m\right)=S_m\left(g,y,m\right)-M_m\left(g,y,m\right).$$

If $B_m^{\mathrm{raw}}\ge 0$, that month is classified as accumulation-dominated (cold month); if $B_m^{\mathrm{raw}}<0,$ the month is classified as ablation-dominated (warm month).

3.1.3. Annual Residual Redistribution

Since $B_m^{\mathrm{raw}}$ is derived from a simplified positive degree-day model; its sum over 12 months does not necessarily match the observed annual mass balance for that glacier and year. Let the observed annual mass balance of glacier $g$ and year $y$ be $B_{\mathrm{yr}}^{\mathrm{obs}}\left(g,y\right)$ (mm w.e.), and let the annual sum of the raw monthly values be

$$B_{\mathrm{yr}}^{\mathrm{raw}}\left(g,y\right)={\displaystyle \sum _{m=1}^{12}}{B}_m^{\mathrm{raw}}\left(g,y,m\right).$$

The required annual correction (residual) is then

$$\Delta \left(g,y\right)=B_{\mathrm{yr}}^{\mathrm{obs}}\left(g,y\right)-B_{\mathrm{yr}}^{\mathrm{raw}}\left(g,y\right).$$

A positive residual $\Delta \left(g,y\right)>0$ means that the raw estimate is too negative, and mass must be added back. A negative residual $\Delta \left(g,y\right)<0$ means that the raw estimate is too positive, and mass must be removed. Uniformly distributing $\Delta \left(g,y\right)$ across all 12 months does not reflect physical processes, so the residual is redistributed based on physical reasoning as follows:

If $\Delta \left(g,y\right)>0$: the residual is primarily assigned to cold months (those with $B_m^{\mathrm{raw}}\ge 0$) and weighted by monthly snowfall $S_m$. This reflects that the underestimation of the annual mass balance is likely associated with accumulation processes that are not fully captured. If total snowfall across all cold months is near zero, $\Delta \left(g,y\right)$ is evenly distributed among cold months. If no cold months exist, $\Delta \left(g,y\right)$ is evenly distributed across all 12 months. If $\Delta \left(g,y\right)<0$: the residual is primarily assigned to warm months (those with $B_m^{\mathrm{raw}}<0$), and weighted by the monthly cumulative positive degree days ${\mathrm{PDD}}_m$. This reflects that overestimation of the annual mass balance is typically linked to underestimation of ablation during melt-dominated months. If the total PDD across all warm months is very small, $\Delta \left(g,y\right)$ is evenly distributed among warm months. If no warm months exist, $\Delta \left(g,y\right)$ is evenly distributed across all 12 months.

$$B_m^{\mathrm{*}}\left(g,y,m\right)=B_m^{\mathrm{raw}}\left(g,y,m\right)+{\delta }_m\left(g,y,m\right),$$

and it is guaranteed that

$${\displaystyle \sum _{m=1}^{12}}{B}_m^{\mathrm{*}}\left(g,y,m\right)=B_{\mathrm{yr}}^{\mathrm{obs}}\left(g,y\right).$$

Positive corrections are mainly applied during months with snow accumulation, and negative corrections during months with melt.

3.1.4. Output and Application

For each glacier–year–month combination, the method produces the adjusted monthly mass balance $B_m^{\mathrm{*}}$ (mm w.e.). In this study, $B_m^{\mathrm{*}}$ is treated as a physically constrained monthly mass balance estimate. It is not a direct monthly observation, but it carries physical meaning. Compared with training on only annual mass balance values, these physically constrained monthly mass balance estimates enable the model to learn month-scale statistical relationships between climate drivers and glacier mass balance, thereby producing more accurate annual estimates. For final performance evaluation, the monthly glacier mass balance values are summed into annual values and compared with the observed annual mass balance. Annual mass balance is therefore the ultimate prediction target throughout this study.

3.2. Machine Learning Algorithms

We evaluated ten machine learning algorithms commonly used in geoscience and glacier studies. They cover five categories: linear regularization, approximate nearest neighbors, kernel methods, single decision trees, and ensemble learners. Algorithm selection was based on recent glacier modeling studies [8,12,20].

Ordinary Least Squares (OLS) models linearly connect variables and predict continuous outcomes by fitting a linear function. It reduces the sum of squared residuals between observed and anticipated values, providing interpretability and a standard for correlations [12,33]. Lasso penalizes OLS to generate sparse models, minimizing multicollinearity and finding the most useful predictors. When predictors are highly correlated, Lasso may select one variable while ignoring others. Least Angle Regression (LARS), like Lasso, adds variables progressively based on their association with the residuals, resulting in a complete regularization path [34]. LARS is used for exploratory analysis and variable ranking, with predictive performance similar to Lasso. K-Nearest Neighbors (KNN) forecasts outcomes by averaging the target values of the k most comparable samples in feature space [35]. It is appropriate for data-scarce areas or transmitting spatial patterns. Still, it needs distance calculations for all samples, is sensitive to feature scaling, and performs poorly in high-dimensional environments. Support Vector Regression (SVR) uses kernel functions to transform data into a high-dimensional space and identify the linear hyperplane with the greatest margin [36]. SVR detects somewhat nonlinear correlations but is largely reliant on hyperparameters, trains slowly on big datasets, and has poor interpretability. Classification and Regression Trees (CART) divide data iteratively to optimize impurity reduction, resulting in tree-like prediction structures [37]. Single trees are mostly utilized for data exploration and rule extraction due to overfitting and large variation. Random Forest (RF) builds many trees using bagging, random feature selection, and bootstrap sampling to reduce variance [38]. RF is frequently used in glacial mass balance modeling because it provides feature significance rankings, but it is computationally intensive and difficult to interpret. Gradient Boosting Regression (GBR) trains weak learners sequentially, with each weak learner focusing on the negative gradient of the prior residuals [39]. GBR can achieve excellent accuracy, particularly on medium-sized datasets, but it is susceptible to overfitting and requires careful hyperparameter tuning. Extreme Gradient Boosting (XGBoost) incorporates regularization to manage complexity and employs acceleration approaches to speed up training [40]. It is very accurate and automatically handles missing data, but it has a large number of hyperparameters and requires substantial customization. LightGBM uses a histogram-based decision tree technique designed for categorical features and parallel computing [41]. It handles large-scale, high-dimensional datasets well, but it may overfit small datasets and requires parameter adjustment.

3.3. Deep Learning Algorithms

Deep learning algorithms learn features and patterns from data through many nonlinear transformations and are used to understand long-term correlations in glacier mass balance sequences. This research compares six deep learning architectures: recurrent neural network (RNN), long short-term memory (LSTM), bidirectional long-term memory (BiLSTM), convolutional neural network (CNN), deep neural network (DNN), and transformer. RNNs are used to learn cross-seasonal correlations between accumulation and ablation periods; they may exhibit gradient vanishing or explosion in extended sequences [20,42]. LSTM addresses long-term dependency via gating methods and cell states, retaining information over long time spans despite increased parameter count and computational cost [42]. BiLSTM combines forward and backward LSTM layers, capturing dependencies in both temporal directions [43]. This architecture is suited for modeling seasonal transitions where mass balance depends on both antecedent and subsequent climatic conditions. CNN extracts local patterns through convolution and pooling operations. It is effective for gridded spatial data but has limited capacity for temporal sequence modeling [44]. DNN maps input features to targets through multiple fully connected layers but lacks explicit mechanisms for capturing temporal or spatial structure [20]. The Transformer uses self-attention to model global dependencies across the full input sequence without recurrence or convolution [45]. However, its large parameter count makes it prone to overfitting on small datasets.

3.4. Performance Measures

When using predictive models, predictive accuracy is assessed using standard evaluation metrics. For regression, four commonly used metrics are R², R, RMSE, and MAE.

(1)

Coefficient of Determination (R²)

R² is a standard statistic for regression that measures goodness of fit. It describes how well the regression line approximates the observed data; a value of 1 indicates a perfect fit. It quantifies the proportion of variance in the dependent variable explained by the independent variables. Typically, R² ranges from 0 to 1; a negative R² indicates performance worse than predicting the mean (i.e., a horizontal line) [46].

$$R^2=1-{\displaystyle \frac{{\displaystyle {\sum }_{i=1}^n}{\left(y_{\mathrm{obs},i}-y_{\mathrm{sim},i}\right)}^2}{{\displaystyle {\sum }_{i=1}^n}{\left(y_{\mathrm{obs},i}-{\overline{y}}_{\mathrm{obs}}\right)}^2}}$$

(2)

Pearson Correlation Coefficient (R)

R is a classic statistical measure used to quantify the strength and direction of linear relationships between two continuous variables. It describes the degree of linear association between two variables, where a larger absolute value indicates a stronger linear relationship. A positive sign denotes a positive correlation, while a negative sign indicates a negative correlation [47]. The formulation for calculating R is

$$R={\displaystyle \frac{{\displaystyle {\sum }_{i=1}^n}\left(y_{\mathrm{sim},i}-{\overline{y}}_{\mathrm{sim}}\right)\left(y_{\mathrm{obs},i}-{\overline{y}}_{\mathrm{obs}}\right)}{\sqrt{{\displaystyle {\sum }_{i=1}^n}{\left(y_{\mathrm{sim},i}-{\overline{y}}_{\mathrm{sim}}\right)}^2{\displaystyle {\sum }_{i=1}^n}{\left(y_{\mathrm{obs},i}-{\overline{y}}_{\mathrm{obs}}\right)}^2}}}$$

(3)

Root Mean Squared Error (RMSE)

The root mean square error is intuitive and closely related to the least-squares loss used by many models. It measures the square root of the average squared error between predictions and observations. RMSE is scale-dependent and sensitive to outliers; large errors contribute disproportionately [46].

$$\mathrm{RMSE}=\sqrt{{\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^n}{\left(y_{\mathrm{obs},i}-y_{\mathrm{sim},i}\right)}^2}$$

(4)

Mean Absolute Error (MAE)

The mean absolute error measures the average magnitude of the errors without considering their direction. It sums the absolute deviations and divides by the number of samples [48].

$$\mathrm{MAE}={\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^n}\left|y_{\mathrm{obs},i}-y_{\mathrm{sim},i}\right|$$

3.5. Hyperparameter Selection

Hyperparameter selection influences the prediction performance and generalizability of machine learning and deep learning models [49]. Hyperparameters for standard machine learning models were adjusted using GridSearchCV, which performs cross-validation to exhaustively search predefined parameter combinations and find the optimal configuration [50]. The coefficient of determination (R²) was used to assess the model’s capacity to explain interannual variations in glacier mass balance. Ordinary Least Squares (OLS) regression does not require hyperparameter tuning, as its parameters are computed directly via least squares [33]. The essential hyperparameters of other machine learning models were adjusted to reduce complexity and improve generalization. Given the small sample size and relatively high noise in glacier mass balance measurements, each model’s search space was confined to decrease the danger of overfitting [49]. Empirical considerations guided the design of network architectures and parameters for deep learning models such as Deep Neural Networks (DNN), Convolutional Neural Networks (CNN), Recurrent Neural Networks (RNN), Long Short-Term Memory (LSTM) networks, Bidirectional LSTM (BiLSTM), and Transformer models. Monthly climatic variables and auxiliary characteristics were handled as fixed-length vectors, and all inputs were normalized using z-score normalization to eliminate the effects of different scales [50]. The Adam optimizer was utilized with an initial learning rate of 0.001, and L2 regularization was used to minimize overfitting [51]. An early stopping method regulated training to increase generalization [51]. Model performance was evaluated using five-fold cross-validation, a method frequently used in geoscientific investigations [33,49]. As shown in Appendix A,

Table A1. Hyperparameter settings of regression algorithms used in this study.

Algorithm	Hyperparameter	Param Grids
Lasso	alpha	[0.001, 0.01, 0.1, 0.5, 1.0, 2.0, 5.0, 10.0]
LARS	n_nonzero_coefs	[4, 6, 8, 10, 12, 15, 20, None]
OLS	/	/
KNN	n_neighbors	[3, 5, 7, 10, 15, 20, 30]
SVR	kernel	‘rbf’
	C	[0.1, 1.0, 10.0, 50.0, 100.0, 500.0]
	epsilon	[0.001, 0.01, 0.05, 0.1, 0.2]
	gamma	[‘scale’, ‘auto’, 0.001, 0.01, 0.1, 1.0]
CART	max_depth	[3, 5, 8, 10, 12, 15, 20, None]
	min_samples_split	[2, 5, 10, 20]
RF	n_estimators	[100, 200, 300, 500]
	min_samples_split	[2, 5, 10]
	max_depth	[10, 15, 20, 30, None]
GBR	n_estimators	[100, 200, 300]
	max_depth	5 [3, 5, 8, 10]
	learning_rate	[0.01, 0.05, 0.1, 0.2]
XGB	n_estimators	[100, 200, 300, 500]
	max_depth	[3, 5, 7, 10]
	learning_rate	[0.01, 0.05, 0.1, 0.2]
LightGBM	n_estimators	[100, 200, 300, 500]
	max_depth	[5, 7, 10, −1]
	learning_rate	[0.01, 0.05, 0.1, 0.2]
LSTM	hidden_size	[32, 64, 128, 256]
	num_layers	[1, 2, 3]
	dropout	[0.0, 0.2, 0.3, 0.5]
BiLSTM	hidden_size	[32, 64, 128, 256]
	num_layers	[1, 2, 3]
	bidirectional	True
	dropout	[0.0, 0.2, 0.3, 0.5]
Transformer	d_model	[32, 64, 128, 256]
	nhead	[2, 4, 8]
	num_layers	[1, 2, 3, 4]
	dim_feedforward	[128, 256, 512]
	dropout	[0.1, 0.2, 0.3]
RNN	hidden_size	[32, 64, 128, 256]
	num_layers	[1, 2, 3]
	dropout	[0.0, 0.2, 0.3, 0.5]
CNN	kernel_size	[2, 3, 5]
	out_channels	[32, 64, 128]
	num_conv_layers MaxPool	[1, 2, 3] AdaptiveAvgPool1d
DNN	layers (neurons)	[256, 128, 64, 32]
	activation	ReLU
	dropout	[0.4, 0.3, 0.2, 0.1]

lists the hyperparameters of all models.

4. Results

The European Alps served as the source domain, and High Mountain Asia (HMA) was defined as the target domain for cross-regional transferability evaluation. Annual glacier mass balance, derived by aggregating monthly model outputs, constituted the primary prediction target throughout all experiments.

4.1. Annual Prediction Performance in the Alps Test Region

Annual prediction performance in the Alpine test region was evaluated for all sixteen models under the zero HMA training ratio condition, i.e., models trained exclusively on Alpine source-domain data. Figure 3 presents sixteen forest plots, each displaying the point estimates of annual prediction performance (R² and RMSE) alongside 95% bootstrap confidence intervals, with machine learning models shown in teal and deep learning models in orange. Confidence intervals were constructed via bootstrap resampling, whereby test–glacier–year pairs were drawn with replacement and R² and RMSE were recomputed on each resample. The number of iterations was set to 50, primarily on grounds of computational efficiency, as each iteration requires re-evaluating all sixteen models across five HMA training proportions and two test regions.

Ensemble tree-based models yielded the highest annual prediction accuracy. Among all models evaluated, Random Forest (RF) achieved the highest R² of 0.69 and the lowest RMSE of 632 mm w.e., demonstrating strong alignment between predicted and observed annual glacier mass balance. This result is consistent with the variance-reduction properties of the bagging mechanism in RF, which mitigates overfitting while capturing nonlinear climate–mass balance relationships. KNN also performed competitively (R² = 0.60, RMSE = 715 mm w.e.), followed by CART (R² = 0.57, RMSE = 745 mm w.e.) and XGBoost (R² = 0.52, RMSE = 787 mm w.e.). LightGBM and GBR both achieved R² = 0.51, with RMSEs of 790 and 792 mm w.e., respectively.

Deep learning models showed comparatively lower reliability at the annual scale in the Alpine test region. BiLSTM and DNN both achieved R² = 0.42, with RMSEs of 865 and 860 mm w.e., respectively. The Transformer model achieved R² = 0.34 (RMSE = 922 mm w.e.), while LSTM (R² = 0.32, RMSE = 933 mm w.e.) and CNN (R² = 0.33, RMSE = 930 mm w.e.) showed relatively greater scatter. RNN recorded the lowest R² among the deep learning models at 0.30 (RMSE = 950 mm w.e.). The relatively wider bootstrap confidence intervals observed for most deep learning models suggest greater prediction instability, likely reflecting the sensitivity of these architectures to the limited sample sizes available in the Alpine training set. Linear models (OLS, Lasso, LARS) and SVR exhibited the weakest Alpine performance (R² ≈ 0.26–0.27, RMSE ≈ 970–975 mm w.e.), reflecting their limited capacity to represent nonlinear accumulation and ablation dynamics.

4.2. Cross-Regional Transfer Performance in the HMA Test Region

Cross-regional annual prediction performance at the zero HMA training ratio is presented in Figure 4 for all sixteen models, reflecting the capacity of each model to transfer knowledge acquired exclusively from Alpine training data to the climatologically distinct High Mountain Asia domain. Among all models, Lasso achieved the best cross-regional annual prediction performance (R² = 0.54, RMSE = 361 mm w.e.). The strong cross-regional transferability of Lasso can be attributed to its L1 regularization, which promotes sparse feature selection and retains only climatologically transferable predictors, thereby maintaining predictive skill under domain shift. DNN ranked second (R² = 0.46, RMSE = 390 mm w.e.), capturing the primary variance structure of HMA annual mass balance despite receiving no HMA-specific training samples. RF achieved R² = 0.39 (RMSE = 418 mm w.e.), ranking third among all models. OLS and LARS both achieved R² = 0.30 (RMSE = 447 mm w.e.), suggesting that simple linear relationships can partially generalize across regions in the absence of target-domain calibration data. XGB (R² = 0.29) and LightGBM (R² = 0.22) showed moderate transferability, while SVR (R² = 0.19), CART (R² = 0.18), and KNN (R² = 0.05) performed progressively worse. GBR produced a slightly negative R² (−0.17) and RNN also yielded a negative R² (−0.24), indicating predictions below the mean baseline.

Deep learning models performed substantially worse at the annual scale under zero-shot cross-regional transfer. LSTM yielded an annual R² of −5.49 (RMSE = 1358 mm w.e.), CNN failed severely (R² = −15.53, RMSE = 2168 mm w.e.), BiLSTM yielded R² = −28.48 (RMSE = 2895 mm w.e.), and the Transformer produced the most extreme failure (R² = −41.61, RMSE = 3481 mm w.e.). These results indicate that deep learning architectures are highly sensitive to distributional shifts between source and target domains. Trained exclusively on Alpine data, these models failed to encode the distinct precipitation seasonality, glacier hypsometry, and elevation gradients characteristic of HMA glaciers, leading to systematic and severe annual prediction errors. The substantially wider bootstrap confidence intervals for deep learning models further confirm their instability under domain shift conditions.

4.3. Effect of HMA Training Data Proportion on Annual Prediction Performance

Figure 5 presents four heatmaps summarizing the annual-scale prediction performance of all sixteen models across five HMA training data proportions (0%, 30%, 50%, 80%, and 100%), evaluated separately for the Alps test region (panels a,b) and the HMA test region (panels c,d), using R² and RMSE (mm w.e.) as performance metrics.

In the Alpine test region, annual prediction performance remained highly stable across all training configurations. R² values for each model showed virtually no systematic change as the HMA training proportion increased from 0% to 100% (panels a,b). For example, RF maintained R² = 0.69 throughout all five training ratios, and KNN showed only marginal fluctuations (R² ranging from 0.60 to 0.70). Similarly, RMSE values for most models remained consistent, with changes generally within the natural range of bootstrap uncertainty. These results confirm that the dominant interannual variability in the Alpine region is already well captured by the source-domain data, and that Alpine predictive skill is largely insensitive to the inclusion of HMA samples.

A clear pattern appears in the HMA test region (panels c,d). As the proportion of HMA training data increases from 0% to 100%, most models show a monotonic increase in R² and a decrease in RMSE. This indicates consistent improvements in cross-regional prediction with more target-domain data. The largest improvements occur when moving from 0% to 30% HMA data. Even a small amount of HMA samples greatly reduces prediction errors. For example, OLS improves from R² = 0.30 to 0.56, and CART from 0.18 to 0.49. Deep learning models also improve substantially. CNN increases from −15.53 to 0.28, BiLSTM from −28.48 to −0.15, and the Transformer from −41.61 to −4.09. When HMA training proportion exceeds 50%, performance differences among models become smaller. This suggests that model architecture becomes less important when sufficient target-domain data are available. At 100% HMA training, most models converge to R² values between 0.50 and 0.66. Linear models stabilize around R² ≈ 0.56, while ensemble tree-based models such as KNN and Random Forest reach up to about 0.66.

Table 2. Annual prediction performance of the best-performing model for each training configuration on the Alpine and HMA test sets.

Train Sample	Area	Best Model	RMSE (mm w.e.)	MAE (mm w.e.)	R2
0%	Alps	RF	632.44	478.11	0.69
	HMA	Lasso	361.16	270.81	0.54
30%	Alps	KNN	630.42	473.09	0.69
	HMA	OLS	354.91	261.37	0.56
50%	Alps	KNN	623.56	467.85	0.70
	HMA	KNN	340.48	258.45	0.59
80%	Alps	KNN	623.96	468.53	0.70
	HMA	KNN	314.34	231.71	0.65
100%	Alps	KNN	624.15	469.17	0.70
	HMA	RF	313.10	205.51	0.66

summarizes the best-performing model and corresponding annual metrics for each training configuration in both test regions. In the Alpine test set, RF or KNN consistently achieved the highest performance across all configurations (R² ≈ 0.69–0.70, RMSE ≈ 623–633 mm w.e.), confirming their stability under varying training conditions. In the HMA test set, optimal model selection shifted systematically from linear models (Lasso at 0%, R² = 0.54) to nonlinear ensemble models (KNN at 50–100%, R² = 0.59–0.66; RF at 100%, R² = 0.66, RMSE = 313.10 mm w.e.) as more HMA training data became available. This transition reflects the increasing capacity of ensemble methods to exploit region-specific nonlinear patterns once sufficient local data are provided, whereas linear models were favored under data-scarce conditions due to their regularization-driven generalizability.

5. Discussion

5.1. Cross-Regional Advantages of Ensemble Machine Learning Models

Across all experiments, ensemble machine learning models, particularly Random Forest and K-Nearest Neighbors (KNN), consistently outperformed deep learning architectures in both in-domain and cross-regional annual prediction tasks. This finding is consistent with previous glacier mass balance studies. For example, Anilkumar et al. reported that Gradient Boosting Regression outperformed neural networks in glacier mass balance modeling in the Central European Alps. Similarly, Van der Meer et al. demonstrated that an XGBoost model using only two predictor variables could still achieve high prediction accuracy in the Swiss Alps.

The present study extends these findings to a cross-regional framework. The results show that Random Forest and KNN maintain relatively stable annual prediction performance even in climatically distinct target regions with limited training data. The robust performance of these models is closely related to their structural characteristics and lower sensitivity to regional distribution shifts. Random Forest reduces prediction variance through bootstrap aggregation and random feature selection. By constructing multiple decorrelated decision trees, the model can effectively mitigate overfitting to source-domain-specific patterns [38]. This ensemble strategy also improves model robustness under heterogeneous climatic conditions. KNN shows a different but equally effective mechanism. As an instance-based learning method, KNN predicts glacier mass balance by retrieving the most similar samples in feature space. The model does not impose explicit parametric assumptions on the relationship between climate variables and glacier mass balance. This property enables KNN to exploit statistically transferable patterns between source and target regions.

The cross-regional advantage of tree-based ensembles observed here is also consistent with several recent in-region benchmarks. Ren et al. compared multiple ML algorithms across maritime and continental HMA glaciers and reported that Gradient Boosting Decision Trees achieved R² values of 0.72 and 0.67 for the continental Manas River Basin and the maritime Niyang River Basin, respectively, substantially outperforming linear baselines under heterogeneous climate forcing [8]. The Mass Balance Machine framework based on XGBoost similarly reconstructed seasonal and annual point mass balances across 32 glaciers spanning heterogeneous climate settings in mainland Norway using approximately 4000 measurements, and the authors interpreted its skillful winter mass balance reconstruction as evidence that tree-based learners can downscale and bias-correct mountain reanalysis forcing [52]. The study by Anilkumar et al., which is most closely aligned with our Alpine setup, achieved an R² of 0.713 with Gradient Boosting in the Central European Alps using ERA5-Land meteorological inputs and hyperparameter tuning [12], a value comparable to our RF performance (R² = 0.69, RMSE = 632 mm w.e.).

In contrast, deep learning models generally require larger amounts of target-domain data to adapt effectively to new climatic distributions. In glacierized regions with limited observations, these models are therefore more vulnerable to underfitting or overfitting. Their weaker performance is likely related to the inherently small sample size of available glacier mass balance observations, which may limit the ability of complex neural networks to learn transferable representations across climatically distinct regions. As model complexity increases, dependence on sufficient target-domain data also becomes stronger. These characteristics reduce the cross-regional generalization capability of deep learning models under data-scarce conditions.

Results at the individual glacier scale further corroborate the above findings. In the Alpine test region (Random Forest model, 100% HMA training proportion), as shown in Figure 6, all four glaciers exhibit Pearson correlation coefficients exceeding 0.80. Among them, Glacier de la Gurraz shows the best agreement with observations (R² = 0.81, RMSE = 518.09 mm w.e., MAE = 343.00 mm w.e.). Glacier des Quirlies (R² = 0.69, RMSE = 480.32 mm w.e.), Glacier de Talefre (R² = 0.68, RMSE = 769.64 mm w.e.), and Glacier du Vallon de la Pilatte (R² = 0.56, RMSE = 704.92 mm w.e.) exhibit larger interannual variability; however, the model generally captures the direction of long-term trends.

In the HMA test region (Figure 7), Urumqi Glacier No. 1 (Tianshan, continental climate) achieves the best performance (R² = 0.82, RMSE = 160.08 mm w.e., MAE = 124.37 mm w.e.), with the model accurately reproducing the intensifying negative mass balance trend after 2010. Xiaodongkemadi Glacier (Tanggula Mountains) yields an R² of 0.41; despite its relatively small interannual variability, the model captures the overall trend direction with acceptable bias. Palong Glacier No. 94 (Parlung Zangbo basin, monsoon-dominated) is constrained by a shorter observational record and larger interannual fluctuations, resulting in a lower R² of 0.22, although the model is still able to capture part of the variability signal.

5.2. Cross-Regional Transferability and Regional Climate Regime Differences

The performance gap between the Alpine and High Mountain Asia (HMA) regions primarily reflects differences in climatic conditions and glacier mass balance regimes between the two regions. Alpine glaciers are predominantly influenced by moisture transport associated with the mid-latitude westerlies from the Atlantic, resulting in relatively stable seasonal patterns of winter accumulation and summer ablation. In contrast, HMA glaciers exhibit spatial heterogeneity: the southeastern margin is affected by monsoonal systems (e.g., Palong Glacier No. 94), the central plateau represents a transitional climatic zone (e.g., Xiaodongkemadi Glacier), and the Tianshan region is characterized by a continental arid climate (e.g., Urumqi Glacier No. 1). Models trained solely on Alpine data are therefore unable to capture the diverse accumulation and ablation processes driven by these distinct climatic regimes.

In the absence of High Mountain Asia (HMA) training data, Lasso outperforms other models in cross-regional transferability due to the nature of L1 regularization: it shrinks most coefficients to zero, forcing the model to rely only on the limited climatic features common to both the European Alps and HMA, and automatically discards region-specific predictors that are effective solely in the source domain. This sparsification process serves as feature selection that retains only transferable climatic predictors.

In contrast, deep learning models exhibit the opposite tendency. Sequence architectures such as LSTM and BiLSTM learn region-specific temporal dependency patterns during training, such as the phase relationship between winter accumulation and summer ablation in Alpine glaciers. While these patterns serve as effective predictive signals within the Alpine domain, they are not transferable to HMA glaciers. When directly applied to HMA, the models continue to infer accumulation and ablation cycles based on Alpine-specific temporal logic, despite the differing climatic drivers across HMA subregions. This mismatch leads to substantial deviations in annual mass balance predictions. Their weaker performance is likely attributable to the inherently small sample size of available glacier mass balance observations, which may limit the effective capacity of complex sequence models to generalize across climatically distinct domains. A similar issue arises in Transformer-based models with attention mechanisms. As model complexity increases and the fit to source-domain temporal structures becomes deeper, transfer performance degradation also tends to increase. In the absence of labeled data in the target domain, increasing model capacity does not improve transferability; instead, it exacerbates errors induced by distributional shifts. This observation is consistent with findings reported in previous studies.

6. Conclusions

This study established a cross-regional evaluation framework that benchmarked sixteen ML and DL models for glacier mass balance prediction, using the European Alps as the source domain and High Mountain Asia as the target domain. All models were trained at a monthly resolution using physically constrained monthly mass balance labels derived from a degree-day decomposition scheme, and monthly predictions were aggregated into annual totals for evaluation against observed annual mass balance. The principal findings are as follows:

(1) Ensemble tree-based models achieved the strongest in-domain performance. In the Alpine test region, KNN attained the highest annual accuracy (R² = 0.70, RMSE = 623.56 mm w.e. at 50% HMA configuration), and RF delivered comparable results (R² = 0.69, RMSE = 632.44 mm w.e.). Both models remained stable across all training configurations, confirming their robustness when driven by reanalysis-derived monthly climate features. (2) Under zero-shot cross-regional transfer to HMA, DL models were sensitive to distributional shifts, with LSTM and Transformer failing to generalize. In contrast, Lasso achieved the best zero-shot transfer accuracy (R² = 0.54, RMSE = 361.16 mm w.e.), benefiting from L1 regularization that retains only climatologically transferable predictors, while RF also maintained reasonable generalization (R² = 0.39). (3) Progressive incorporation of HMA training data improved target-region predictions. The largest accuracy gains occurred between 0% and 30% HMA inclusion (best model shifting from Lasso at R² = 0.54 to OLS at R² = 0.56). As data availability increased, optimal model selection transitioned to nonlinear ensemble methods, with KNN achieving R² = 0.65 at 80% and RF reaching R² = 0.66 (RMSE = 313.10 mm w.e.) at 100% HMA inclusion. (4) Training at a monthly resolution using degree-day-derived mass balance labels preserved intra-annual accumulation–ablation signals as learning targets, enabling models to capture seasonal climate–mass balance relationships that are obscured under direct annual input aggregation, and yielding more physically faithful annual predictions upon temporal summation.

These findings demonstrate that, under sparse in situ observations and pronounced inter-regional climate heterogeneity, ensemble ML models provide more reliable cross-regional transferability than DL architectures. The proposed framework is applicable to remote sensing-based glacier monitoring and regional climate impact assessment in data-scarce glacierized environments.