We compiled in situ SD data over the European Alps by combining stationary and point-based measurements with airborne photogrammetry snow surveys, sourced from multiple regional providers across the Alpine countries (Fig. ). Point-based measurements were collected for the time period 2015–2024, and include data from Austria (provided by Geosphere Austria, formerly ZAMG), France (from measurement stations operated by partners under agreement of MetéoFrance), Italy (collected in the autonomous regions of Valle d’Aosta, Trento and Alto-Adige, Piemonte, Lombardy and data provided by the International Center for Environmental Monitoring CIMA Research Foundation), and Switzerland (manual and automated point-based SD measurements collected and managed by the Swiss Federal Institute for Forest, Snow and Landscape Research (WSL) – Institute for Snow and Avalanche Research (SLF)). In addition, we augmented our SD dataset with measurement data sourced from the Synoptic Data platform and the National Oceanic and Atmospheric Administration's Global Historical Climatology Network-Daily database (GHCNd, ). With the addition of these data, our dataset also contained sites within Germany and Slovenia.

Next, we collected spatial SD measurements, derived from airborne photogrammetry over the Dischma valley, Switzerland (Fig. , red box). A total of nine photogrammetry SD surveys (snow surveys) were added to our dataset, with an original resolution of 0.5 m (6 maps, measured yearly near peak SD between 2017 and 2022) or 2 m (3 maps, collected on 3 distinct days in 2016). For both resolutions, we applied a linear averaging and reprojected all surveys to the target grid of our SD estimates, the 100 m WGS84 grid.

Within our research, we collected data from the European Space Agency (ESA) and Copernicus S1A and -B satellites, which operate at C-band and share the same orbital plane with a 180° orbital phasing difference. Both have a 12 d repeat cycle. Combined, they offer a repeat cycle of 6 d over the study area. S1B, however, has been out of operation since 24 December 2021, and thus does not cover the complete study period (2015–2024).

S1 dual-polarized PolSAR observations were acquired from interferometric wide swath (IW) single look complex (SLC) data in dual-polarization (VV and VH) mode. The data were processed into two dual-polarized PolSAR variables: the polarimetric scattering angle (α) and the first Stokes parameter (S0), using the Sentinel application platform (SNAP) toolbox, version 9, with processing steps described in . These processing steps included applying precise orbit file corrections, radiometric calibration, debursting TOPSAR bursts, and merging sub-swaths into a single image. This was followed by the generation of the 2×2 covariance matrix (C2-matrix). The C2-matrix was then used as input for two distinct processing chains. The first one involved an eigenvector/value decomposition of the C2-matrix, followed by the H/α decomposition , from which α was derived. The second processing chain utilized the compact-polarimetry Stokes parameter generation to derive S0 from the C2-matrix. Next, both variables were multilooked to ∼25 m to reduce speckle and finally, a Range Doppler terrain correction was applied to both variables, reducing (geometric) distortions due to topographical variations in the scene. For the latter, the Copernicus 30 m global digital elevation model (GLO-30 DEM) was used.

Next, co- (γVV0) and cross- (γVH0) polarized backscatter intensity variables were retrieved from ground range detected (GRD) amplitude data. Processing steps, described in and , were applied, including precise orbit file application, GRD border and thermal noise removal, radiometric calibration, terrain flattening to backscatter as γ0 and finally a Range Doppler terrain correction. As for the PolSAR variables, the Copernicus GLO-30 DEM was used during the processing steps. Additionally, local incidence angle (LIA) information was preserved and the cross-polarization ratio (γCR0; calculated as the ratio between γVH0 and γVV0 in linear scale) was calculated.

Finally, both the PolSAR and backscatter intensity observations were rescaled and summer-corrected, to reduce inter-orbital and interannual start-of-season differences, respectively. To this end, we first reprojected the satellite observations onto the 100 m WGS84 grid using linear averaging, and resampled to the 500 m WGS84 grid by taking the mean. Then, we performed a first and second-order moment scaling (to correct for differences in the mean and variance) between orbits. Finally, from each scaled time series for each snow season (September–June), we subtracted the mean summer value (July–September) of the summer preceding that snow season, thereby reducing interannual start-of-season differences that are not related to snow conditions (e.g., changing vegetation). To indicate that these variables have been rescaled, we further append a superscript “s” (^s) to the satellite variable notation.

Snow cover data were obtained from two sources: binary snow cover information from the interactive multisensor snow and ice mapping system (IMS; ) at 1 km resolution, and fractional snow cover (FSC) information from the moderate resolution imaging spectroradiometer (MODIS; ) at 500 m resolution. For the latter, we collected cloud gap-filled FSC data separately from the Terra and Aqua satellites, which we both reprojected onto the 500 m WGS84 grid using linear averaging. Subsequently, we combined the individual products using a weighted average, which accounted for the quality flags of each product, the time lag between the last cloud-free FSC observation and the current date, and the time lag of the individual satellite observations relative to each other (Appendix ). Next, a cutoff was set on the combined product, only allowing for FSC information less than 7 d before the current date. Finally, remaining gaps (3.95 % of the data points across the whole Alps and study period) were filled using IMS' binary snow cover information, reprojected to the same 500 m WGS84 grid using majority resampling. Hereby, a no-snow indication of IMS was set to an FSC value of 0 %, while an IMS snow covered pixel received a value of 100 %.

Additionally, a wet snow mask was acquired to differentiate between dry and wet snow periods. This dataset, based on S1 C-band satellite observations and obtained from the Copernicus Land Monitoring Service (CLMS) High Resolution Snow and Ice Monitoring (HRSIM) SAR Wet Snow in high mountains (SWS) product , provides a binary classification between wet snow conditions, and dry, patchy or snow-free conditions. The data, available at 60 m resolution from September 2016 onward, were first reprojected onto the 100 m WGS84 grid using majority resampling, whereby the most frequently occurring SWS value within each 100 m target pixel was selected while excluding any no-data values. Subsequently, all non-wet pixels were classified as dry, while quality flags were retained to identify locations and periods with no (reliable) classification.

We downscaled 3-hourly meteorological forcing data over the European Alps to a 500 m spatial resolution, to serve as additional input to the ML model. To this end, we first collected coarse three-hourly meteorological forcing data with a 0.1° spatial resolution. Precipitation data were sourced from the multi-source weighted-ensemble precipitation (MSWEP, ) dataset, which combines various state-of-the-art reanalysis products with gauge and satellite observations . Other variables, including downward shortwave and longwave radiation, 2 m air temperature, wind speed, and 2 m relative humidity, were obtained from the multi-source weather (MSWX, ) product. This dataset is derived from coarse-scale European centre for medium-range weather forecasts reanalysis version 5 (ERA5) data refined through bias correction and downscaling using monthly 0.1° reference climatologies .

Subsequently, we applied bilinear interpolation in combination with different downscaling techniques, explained below, to account for local terrain features. To this end, the Copernicus GLO-30 DEM was employed, linearly averaged to the 500 m WGS84 grid to match the target resolution for the meteorological forcings. First, coarse-scale precipitation (Pcoarse; [mm per 3 h]) was corrected as a function of elevation to account for orographic effects, using a rescaling function adapted from , who corrected in situ precipitation data for gauge undercatch in a glacier mass-balance study. Thus, for each location x within the 500 m grid at time step t, Pcoarsex,t was downscaled using the following equation: 1Px,t=(1-D)⋅Pcoarsex,t+D⋅Pcoarsex,t⋅0.75+0.5zx-zminzmax-zmin with  D=zmax-zminDdif,0≤D≤1 with zx the elevation [m] of the 500 m Copernicus GLO-30 DEM, zmin and zmax the minimum and maximum elevation [m] within an interpolation window – centered on the location x and spanning an area roughly matching the original 0.1° grid size – and Ddif a user defined difference in elevation, set to 250 m. The user defined difference was introduced to focus the corrections on the study area, with minor adjustments for areas with small elevation differences. Different from , Eq. () limits the downscaled precipitation values between 75 % and 125 % of the original Pcoarsex,t values.

The other forcings were adjusted as follows. The temperature was corrected using a seasonally varying lapse rate, following , to account for elevation-dependent temperature variations. For relative humidity, we first converted to dewpoint temperature, then applied a lapse rate correction similar as for the temperature, and finally converted the corrected dewpoint temperature back to relative humidity . Downward shortwave radiation was adjusted following the method of , which involved partitioning the radiation data into direct and diffuse components, accounting for the elevation effect on the direct component, and applying a topographic correction to both components. In contrast, downward longwave radiation and wind speed were not adjusted after bilinear interpolation.

Modeled SD estimates were obtained using Snowclim , a process-based enhanced single layer snow model utilizing a fully distributed energy and mass balance. We ran the model over the entire European Alps with the downscaled meteorological forcing data at a 500 m spatial and 3-hourly temporal resolution. To obtain daily values, the 3-hourly SD estimates were averaged to a daily time step. A description of the model's parameter settings, how they have been calibrated, and the model's performance when validated against in situ measurements, is provided in Appendix .

In addition to time-dependent data, we employed time-independent auxiliary data, sourced from various providers. As with the other datasets (except the meteorological forcing and Snowclim data), these data were first projected onto the 100 m WGS84 grid, using linear averaging for continuous variables and majority resampling for categorical data. Forest cover fraction (FCF) data and land cover information, including a water mask, were acquired from the 2018 epoch of the 100 m Copernicus PROBA-V global land cover dataset . Next, we used the Copernicus GLO-30 DEM to extract elevation and three topographic features: slope, aspect, and topographic position index (TPI), the latter quantifying the relative elevation of a grid cell concerning its surroundings within a predefined diameter. Slope and aspect were computed in MATLAB using the Geodetic and TopoToolbox toolboxes, while TPI was calculated following the methodologies of and . For this study, we computed the TPI using only the neighboring pixels of a specific grid cell, corresponding to a 3×3 grid window. Finally, we included a glacier mask, retrieved from the Randolph Glacier Inventory version 7.0 , and collected the snow classes.

Within this study, we deployed XGBoost to estimate SD across the European Alps. XGBoost is a tree-based traditional ML algorithm that constructs multiple decision trees in a sequential order, to minimize a differentiable loss function . Thereby, new trees are trained to fit the residual errors of the previously fitted trees, while incorporating regularization terms to reduce model complexity, and including additional mechanisms that contribute to its computational efficiency . We chose this ML algorithm after comparative experiments with other tree-based methods (including Random Forest, LightGBM and CatBoost) in which XGBoost showed the best performance and computational efficiency, as well as its use in recent snow studies (e.g., , or ).

We trained, validated, and tested XGBoost with various configurations on a dataset containing input features associated with each SD measurement (predictor variable) from the in situ measurement sites and snow surveys. To construct this dataset, we first excluded those stationary measurement sites located within glaciated areas, as well as those with less than 5 % non-zero SD observations. Subsequently, we identified the unique locations of the stationary sites within the 100 m WGS84 grid, and averaged time series from sites within the same grid cell. Furthermore, we excluded SD measurements during the summer months July and August, and resampled the data with a 500 m spatial resolution to the 100 m WGS84 grid using value replication.

The S1 data spatially and temporally coinciding with available SD measurements on the 100 m WGS84 grid include both ascending and descending orbits. This allows a single location to have two S1 observation values for the same SD measurement on a given date. Importantly, we chose not to exclude satellite observations with high or low LIA, as we assumed that XGBoost could effectively learn the relationships between these satellite observations and the corresponding SD. For each location and date with an available satellite observation, we also selected the corresponding (nearest) time-dependent non-satellite data and time-independent auxiliary data. This resulted in a dataset comprising 1022 measurement sites, with the distributions of observed SD and selected auxiliary variables shown in Fig. .

A similar procedure was applied for the photogrammetry snow survey data: for each SD measurement, the nearest input feature values within the 100 m WGS84 grid were selected and compiled into a dataset, linking each SD observation with its corresponding input features. Since satellite acquisitions did not always coincide with the exact date of the snow surveys, we used the most recent S1 observation prior to the survey, with a maximum offset of two days. Lastly, to represent the temporal component of our datasets, we computed the day of the year (DOY) for each instance. To account for the cyclic nature of the calendar year and prevent discontinuity between 31 December and 1 January, we transformed the DOY into two separate features using sine (DOYsin) and cosine (DOYcos) functions: 2DOYsin=sin(2⋅π⋅DOYn)3DOYcos=cos(2⋅π⋅DOYn) with n the number of days in the corresponding year.

The concept of nested cross-validation (nested CV) has been extensively utilized in other studies , as it enables a correct characterization of the generalization error of an ML model . Figure  illustrates that nested CV involves both inner and outer resampling to, respectively, train and tune the ML model (and its hyperparameters), and evaluate predictions on unseen and independent test data. Considering the susceptibility of SD measurements to spatial and temporal autocorrelation, we implemented the CV strategy described in within a threefold nested CV framework for the site data (excluding the snow surveys), in which subsets of the data are masked during training, validation and predicting (testing). To this end, the data of the site measurements were partitioned into spatial, temporal and spatio-temporal folds.

The spatial folds were constructed using a two-step approach: first, sites located within five km of one another were grouped into clusters, thereby preventing nearby sites with similar (climatic) characteristics and SD patterns from being split across training and test sets. Subsequently, these clusters were randomly assigned to five unique folds, ensuring that each fold contained a comparable amount of data and preserved a similar SD distribution. For the temporal folds, sites were not clustered; instead, all observations from a given snow season (September–June) and from across the study area were grouped into nine blocks (corresponding with the number of snow seasons for which SD data is available), which were then partitioned into five folds, again ensuring comparable fold sizes and a consistent SD distribution. Finally, by combining both fold-creation techniques, we constructed 25 unique spatio-temporal folds.

For each unique fold (five for spatial and temporal nested CV; 25 for spatio-temporal nested CV), we iteratively designated one fold as the test set during outer resampling, using the remaining folds for training and validation. To ensure independence of the test data, all data from the sites and/or years present in the test fold were excluded from the training and validation sets (Fig. ).

The same approach was applied during inner resampling, to split the training and validation data used for tuning XGBoost's hyperparameters. To tune the hyperparameters, we utilized Scikit-learn's RandomizedSearchCV algorithm, employing the mean squared error (MSE) as loss function. A different random seed was set for each outer resampling loop, introducing variability in the selection of optimal hyperparameter combinations. During each loop, 150 hyperparameter combinations were chosen from a predefined tuning grid, based on the one provided in PyCaret . The hyperparameters yielding the best mean MSE score across the validation folds were selected. This approach produced independent predictions for every instance in the dataset, enabling the calculation of performance metrics and the construction of FI scores.

We used both XGBoost's booster and Shapley additive explanations (SHAP; ) values to assess the feature's impact on the SD estimates. For the booster, we selected the gain FI, which informs about the contribution of each input feature in minimizing the loss function during model training. As such, for every outer resampling loop within the nested CV framework, we computed the gain FI of the individual features during model training.

SHAP values, on the other hand, quantify the contribution of each input feature to an individual (SD) prediction, measured relative to an expected prediction (SD) value. Within the nested CV framework, SHAP values thus indicate how each feature influences the SD predictions made for the outer resampling predicting sets, relative to the average (SD) prediction computed from the training set. Consequently, SHAP values can be both positive and negative. To assess the overall global SHAP value FI during SD prediction, mean absolute SHAP values were computed for each input feature during every outer resampling loop. The latter were converted into relative contributions by normalizing them with the sum across all features.

We further used SHAP values to assess the contribution of the S1 PolSAR and backscatter intensity observations to the SD predictions throughout the seasonal evolution of the snowpack. To this end, for each site and snow season in the test sets, we first identified the periods during which a snowpack was present, based on the measured SD. The season start date was identified as the first date with SD≥10 cm, that was followed by nine consecutive days with SD≥1 cm. For low elevation sites with (very) shallow snowpacks, where this condition was not met for an entire snow season, the start of the snow season was marked by the first date with SD≥10 cm. Conversely, we defined the end of a site's snow season as the first day of a 10 d period with 0 cm SD, near the end of snowpack presence. In addition, we used the CLMS SWS product to distinguish, where possible, between dry and wet snow conditions. As this product is only available from September 2016 onward, the 2015–2016 snow season was omitted from the corresponding analyses.

In addition to the FI and SHAP value analysis, several performance metrics were used to validate XGBoost SD predictions with measured SD. For each configuration and across all outer resampling predicting sets (thus the total dataset), we computed the spatio-temporal Pearson correlation coefficient (R), mean absolute error (MAE), root mean squared error (RMSE) and bias between predicted and measured SD (all averaged over time and space). Since cross-validation is conducted in both space and time, the performance metrics reflect the ML model’s ability to generalize across purely spatial, purely temporal, and combined spatio-temporal domains. Additionally, certain metrics were calculated on a per-site basis, such as the MAE.

Next, we evaluated XGBoost’s capability to generate spatial SD predictions by comparing them with the photogrammetry snow surveys conducted in the Dischma Valley, Switzerland. For this case, we trained XGBoost exclusively on stationary and point-based measurements, excluding spatial data from the snow surveys. Model training and hyperparameter tuning were performed using fivefold spatial CV, as this approach best reflects the intended application of the ML model: predicting SD on unseen locations across the European Alps within the time period of our S1 data collection. After training, XGBoost was applied to predict SD for each of the nine snow surveys, and performance metrics were computed.

We then repeated this process, but now incorporating all snow survey data except those of the targeted date into the training dataset. This resulted in nine independently trained and tuned XGBoost models, each applied to predict SD for the corresponding unseen snow survey. In this approach, we also employed spatial CV for training and tuning, where every training snow survey was randomly assigned to one of the five folds. This ensured that the distribution of training and validation data remained consistent across folds.

In general, all configurations (i.e., PolSAR_ML, Backscatter_ML and Combination_ML) achieve best results within the temporal nested CV framework (Table ), and performance progressively deteriorates in the spatial and spatio-temporal frameworks (Table ). This behavior is expected, as SD patterns within the same area (i.e., at the same sites) tend to recur across different years, such that SD prediction for an unseen snow season (i.e., the temporal framework) is inherently more favorable for XGBoost than prediction at unobserved locations (i.e., the spatial framework). Predicting at unobserved locations and during unseen snow seasons (i.e., the spatio-temporal framework), including times outside the study period is even more challenging, as XGBoost cannot exploit season-specific information from the training data nor rely on recurrent site-specific SD patterns. Consequently, because the intended application of XGBoost is to predict SD at previously unseen locations across the European Alps within the training dataset time period (e.g., Fig. a), reliance on the temporal framework would lead to an overly optimistic evaluation of model performance, whereas the spatio-temporal framework would provide a more conservative assessment.

The absolute improvements of using PolSAR observations, as a replacement for (or in combination with) backscatter intensities, are small within all nested CV frameworks, or even minimal within some CV frameworks. Within the spatial framework, the PolSAR_ML and Backscatter_ML configurations display marginal differences in overall performance metrics (Table ), which likely stems from the similar relationship of the variables with SD, and the spatial noise present in both types of S1 variables. The Combination_ML configuration also shows similar overall performance compared to the Backscatter_ML configuration, yet the improvements in MAE, computed per site, are significant (p≪0.05, 95 % confidence level), resulting in an overall MAE of 35 cm, a mean site-MAE of 29 cm, and a mean site-bias of -11 mm (excluding zero-measured SD). PolSAR observations moreover improve model performance for the spatio-temporal framework, with significant improvements in site-MAE for both the PolSAR_ML and Combination_ML configurations (p≪0.05, 95 % confidence interval). This improvement suggests that PolSAR observations, alone or in combination with backscatter intensities, more effectively capture the seasonal evolution of SD, a conclusion that is further supported by statistically significant gains in site-MAE (p≪0.05, 95 % confidence level) observed in the temporal nested CV framework. Nonetheless, also here the overall improvements remain limited, and the increased computational cost of processing S1 SLC data into PolSAR variables relative to deriving backscatter intensity from GRD data must be considered. Indeed, besides requiring separate processing chains to retrieve α and S0 from the C2-matrix (Sect. ), handling SLC data is more demanding, with raw images (∼5 Gb) substantially larger than GRD products (∼1 Gb).

Additionally, all three configurations exhibit difficulties in predicting high SD values at unobserved sites (Fig. ), which likely arises from the scarcity of high SD observations in the training dataset (Fig. a). For the spatial nested CV framework, the PolSAR_ML, Backscatter_ML and Combination_ML configurations exhibit a bias of -1.46, -1.51 and -1.48 m for observed SD≥2.5 m, which further deteriorates in the spatio-temporal framework. This is also visible in Fig. a, when comparing the observations (squares) with the SD prediction, and in Fig. b, that displays sites with a bias≤-0.5 m for the different configurations within the spatial nested CV framework (zero-measured SD excluded). Interestingly, many of the sites displayed in Fig. b also appear to have strong negative biases in Fig. 2a of . Consequently, the reduced ability of XGBoost models, trained with S1 variables to explain interannual and site-specific variability, to predict high SD values must be taken into account when deploying the model across the European Alps, particularly when applying it beyond the temporal range covered by the training data.

Across the configurations and nested CV frameworks, FSC and elevation consistently emerge as the most important features, similar to what has been reported by , indicated by both XGBoost’s internal gain metric and SHAP values (Fig. a and b). FSC is particularly important, which makes the predictions prone to potential errors in this input feature (e.g., the high-alpine area in the yellow box in Fig. a, where erroneously low FSC-values led to SD underestimation). The gain FI (Fig. a) moreover indicates an increasing FSC importance when transitioning from temporal to spatio-temporal nested CV frameworks (∼25 % to >40 %), with an opposite trend for elevation (∼20 % to ∼10 %). When predicting at unseen locations, XGBoost seems to rely more heavily on FSC to distinguish snow-covered periods, and cannot rely as much on recurring SD patterns that display a strong relationship with elevation. Finally, the DOY features, which help capturing the seasonal variations in the estimates, also emerge as important inputs, as reflected across the configurations in both Fig. a and b.

When used in the separate configurations, the S1 PolSAR and backscatter intensity features are similarly used during model training (Fig. a). However, the gain FI indicates a stronger importance of αs within the PolSAR_ML configuration over γCR0,s in the Backscatter_ML one. This observation is further confirmed in Fig. b across all nested CV frameworks, indicating that XGBoost seems to effectively extract more information from αs during model training and SD prediction. Consistent with this finding, the Combination_ML configuration also exhibits a clear preference of αs over γCR0,s. In addition, both the gain-based and SHAP value FI analyses reveal a less distinct separation between the S1 input features in the Backscatter_ML configuration, with the SHAP values even suggesting that γVV0,s contributes as much as, or slightly more than, γCR0,s during SD prediction at unseen locations and/or time periods.

Figure  illustrates the improvements when incorporating either regionally downscaled meteorological forcing data or Snowclim SD estimates (Table ; Weather_ML and Snowclim_ML configurations) when predicting at unseen locations (and time periods; Fig. a and b), with the most important improvements for high SD observations (≥2.5 m). The bias for observations ≥2.5 m improves by 28 cm when comparing the Weather_ML to the Combination_ML configuration within the spatial nested CV framework (Fig. a), decreasing from -1.48 to -1.20 m. Incorporating Snowclim SD estimates further reduces this bias to -1.12 m, likely reflecting a stronger correspondence between the Snowclim estimates and high SD observations than what is captured through derived meteorological variables. Despite these gains, the number of sites with a mean bias ≤-0.5 m remains similar in both the Weather_ML and Snowclim_ML configurations – with most of these sites again located in Switzerland (Fig. ) – reflecting the need for expanded high SD data collection. Furthermore, while the inclusion of meteorological forcing data or modeled SD estimates reduces the relative SHAP value FI of the S1 input features, these features continue to influence SD predictions (Fig. d), accounting in total for approximately 9 % and 7 % of the SHAP value FI in the Weather_ML and Snowclim_ML configurations, respectively, when predicting at unseen locations.

Overall, the Snowclim_ML configuration yields the best performance (Fig. a and b). Under the spatio-temporal nested CV framework, site-MAE during snow-covered periods decreases by at least 2.5 cm at 55 % of sites, while only 16 % exhibit an increase of 2.5 cm or more, relative to the Combination_ML configuration. Compared to the Weather_ML configuration, the difference in site-MAE is minimal, and only significant for the spatio-temporal framework. However, the Snowclim SD estimates appear to more accurately represent conditions at low-elevation sites (<1000 m) during the early snow season (Fig. c), highlighting the importance of reliable FSC information to correctly indicate snow-free conditions when relying solely on meteorological forcing data. In addition, while the Weather_ML configuration displays the lowest bias of the three configurations at medium-elevation (1000–2500 m) sites (Fig. c), the Snowclim_ML configuration still performs best at high-elevation sites (>2500 m) during peak SD and the ablation period. Nonetheless, both the Weather_ML and Snowclim_ML configurations seem to underestimate SD near March–May, with the differences being less pronounced for the 1500–2500 m elevation class. As such, the results indicate that directly using meteorological forcings can achieve comparable predictive performance within the applied XGBoost setup. This would eliminate the need to run a snow model, which reduces both computational cost and model complexity.

To address the findings of and , who emphasized that stationary and point-based SD measurements inadequately capture spatial snowpack variability, we trained the Combination_ML, Weather_ML and Snowclim_ML configurations with additional spatially distributed SD training (survey) data, and compared its impact over the Dischma valley. Figure a–c display the results of the 16 March 2017 snow survey (Fig. d), in which mountain ridges appear more distinctly in the predictions, and high SD estimates at steep locations and near ridges are more accurately corrected compared to Fig. a–e, which depict results obtained without spatial training data. Negative adjustments can be observed at high-elevation areas with (relatively) steep slopes for all configurations, but is most pronounced for the Combination_ML configuration (Appendix ). For the latter, the negative corrections are reflected in a reduced SHAP value FI of the topographic inputs (Fig. h, survey data; Appendix ). In contrast, the SHAP value FI of the topographic inputs increases in the Weather_ML and Snowclim_ML configurations (Fig. i and j). Here, the topographic features contributed less when the models were trained solely on point-based measurements but become increasingly influential once spatial training data are included, enabling improved representation of topographic controls on the SD estimates. Notably, αs remains among the more influential features for these configurations, indicating that despite its reduced relative importance, the inclusion of this S1 variable (and potentially other S1 variables) continues to affect the final SD predictions.

Despite the improvements, SD remains overestimated for the 16 March 2017 snow survey across all configurations. This overestimation is most pronounced for the Combination_ML configuration and exceeds the bias reported by . Although it is not the objective of this study to perform a direct comparison, the persistence of the Combination_ML bias indicates potential limitations in the current feature selection or training dataset. Nonetheless, both the Weather_ML and Snowclim_ML configurations outperform the results reported by . For the 9 March 2016 and 16 March 2017 snow surveys used by for model validation, the Weather_ML and Snowclim_ML configurations achieve higher correlation coefficients (0.68 and 0.64) and lower mean absolute errors (31 and 36 cm, respectively) than those reported by (0.56 and 41 cm). For the 16 March 2017 survey specifically, reported a mean SD difference (predicted minus observed) of 16 cm, whereas the Weather_ML and Snowclim_ML configurations exhibit differences of -5 and 15 cm, respectively. Thereby, the more pronounced overestimation of the Snowclim_ML configuration likely results from the systematic overestimation in the Snowclim SD estimates for this survey (Fig. d), which may also explain the 6 cm higher MAE compared to the Weather_ML configuration (Fig. b and c).

Across the nine snow surveys, the inclusion of spatially distributed SD training data primarily improves predictions for lower observed SD values (Fig.  and e–g), whereas differences for higher SD observations (≥2.5 m) remain less pronounced, albeit best captured by the Snowclim_ML configuration. Despite a persistent positive bias across all configurations, the Weather_ML configuration exhibits a bias reduction of approximately 10 cm relative to the Snowclim_ML configuration, suggesting that explicitly running Snowclim may not be required when the primary objective is to obtain accurate SD estimates across the European Alps. Indeed, XGBoost effectively learns the relationship between the meteorological forcing data and observed SD, without explicitly representing the physical processes governing snowpack evolution. For the Snowclim_ML configuration, the remaining overestimation largely originates from biases in the Snowclim SD estimates themselves (Figs. b and d). In contrast, the origin of the positive bias in the Weather_ML configuration is less straightforward and may reflect either an overestimation of cumulative snowfall (Ps,c) or limitations in XGBoost’s ability to implicitly represent variations in snow bulk density. In the latter case, even accurate snowfall forcing may still result in SD overestimation due to an implicit underrepresentation of snow densification processes. Further research should attempt to include factors or use ML models that govern variations in snow density, especially to enhance the potential of predicting short-term variations in SD. Finally, elevation mismatches within the relatively coarse 500 m meteorological forcing data may introduce temperature biases, thereby affecting snowfall estimates and the inferred number of melt days.

Figure  further illustrates the impact of the spatial training data outside the Dischma valley. The top row displays the SD estimates across the Ötztal region (Austria) on 29 January 2018, while the bottom row showcases the results for the Lötschental region (Switzerland), on the same date. For both valleys, the inclusion of spatial training data improved the spatial patterns, manifested by the appearance of mountain ridges and local depressions (Fig. b and f). These patterns also appear in the difference maps (Fig. c and g), and seem to be related to the TPI (Fig. d and h). Specifically, Fig. d and h indicate that SD estimates at areas situated below their surroundings (negative TPI) are positively corrected, whereas the opposite is true near mountain ridges. Figure d and h moreover indicate a dependency with the slope of the area, with steeper areas exhibiting more pronounced negative corrections, while flatter regions show the opposite tendency. The relationship with the other topographic features (e.g., aspect), however, is less clear.