The Karakoram region, spanning extensively across parts of Pakistan, India, and China, is bordered by some of the highest mountain systems on Earth, including the Himalayas, the Pamir Mountains, and the Hindu Kush mountain ranges (Fig. ). The study area encompasses the majority of Karakoram, covering an expansive geographical domain of approximately 450 000 km². This region extends from approximately 35 to 38° N latitude and 76 to 78° E longitude, characterized by a wide range of altitudes from around 2000 m a.s.l. (above sea level) in the valleys to well over 8000 m a.s.l. at the highest summits. The extreme topographic variation gives rise to rugged terrain, including steep valleys and towering mountain peaks.

Karakoram is situated upstream of both the Upper Indus Basin (UIB) and the Tarim River Basin. It covers three significant watersheds: Hunza, Shigar, and Shyok, as shown in Fig. . These basins serve as the upstream sources of the UIB and contribute 65 %–85 % of annual flows to the Indus River with the melting water from snow and glaciers, sustaining the livelihoods of millions of residents residing within these basins . The hydrological importance of Karakoram emphasizes the important role of mapping snow melting in the region.

With the pre-processed γ0 images, we derived the composite backscatter ratio (Rc) following the method proposed by . The Rc metric combines the backscatter ratios from both the VV and VH channels to comprehensively assess surface condition changes associated with snow melting. This approach incorporates a weighting factor W, which is determined by the local incidence angle (LIA, θ), to account for variations in backscatter due to differing incidence angles. This adjustment enables more robust snowmelt detection across varying terrain geometries.

To compute Rc, we first calculated the SAR backscatter ratio Ri for each polarization i∈vv,vh using the following equation: 1Ri=γi0/γi,ref0, where γi,ref0 represents a reference image constructed using the average of multiyear winter images. Note that this differs from other alpine regions, such as the Alps, where summer months are often used as the reference due to snow-free conditions. In Karakoram, due to the all-year-long snow cover at the higher elevations, we used winter images as a reference to leverage the dry snow conditions in winter for highlighting the contrast in backscattering intensity between summer wet snow (lower intensity due to water absorption) and winter dry snow.

With Ri for each polarization, the composite ratio Rc was calculated as a weighted sum of Rvv and Rvh: 2Rc=WRvv+(1-W)Rvh, where the weighting factor W is defined based on the LIA as 3W=0(θ<θ1)0.5(1+θ-θ1θ2-θ1)(θ1≤θ≤θ2)0.5(θ>θ2), with θ1=20° and θ2=45°.

While Rc alone effectively indicates surface condition changes, it can be sensitive to local variations and does not inherently incorporate adaptive boundaries for wet snow classification. Therefore, instead of directly applying a threshold to Rc for wet snow classification, we propose using a GMM to convert Rc into a wet snow index (WSI) to have a probabilistic measure that better captures the varying conditions of wet snow across different terrains. By leveraging the density distribution of Rc values, the WSI enables a dynamic scaling of the classification based on the underlying distribution of Rc values.

The GMM is an unsupervised probabilistic model for clustering and density estimation. We configured the GMM to identify two clusters corresponding to the wet snow pixels and the no-snow (or dry snow) pixels as 4P(Rc)=∑i=12πi⋅N(Rc|μi,σi), where P(⋅) the probability density function (PDF) of Rc, πi the ith Gaussian component's mixing coefficient for wet snow (i=1) and no-snow (or dry snow) (i=2) clusters, and N(Rc|μi,σi) the Gaussian distribution with mean μi and standard deviation σi. We used the full covariance structure in the GMM, i.e., each component has its own general covariance matrix, after testing different types of covariance structures.

To train the GMM and determine its parameters (πi, μi, and σi), we randomly sampled 106 unlabeled pixels from the summer Rc images of each basin and employed the expectation-maximization (EM) algorithm to fit the model for each basin with the sampled pixels . During the training, the maximum number of EM iterations was set to 100, and the convergence threshold was set to 10-3. With the estimated GMM parameters, the WSI can be determined using a modified logistic function: 5WSI=L1+ek(x-x0), with k=|μ1-μ2|σ1+σ2x0=μ1+μ22, where k is the slope factor, x0 the logistic curve's midpoint, and L the carrying capacity representing the supremum of the function. Here the carry capacity L was set to 10 to amplify the differences between pixels of different Rc values.

In the WSI logistic function, the slope factor k is determined by the separation between the two clusters, providing a flexible and adaptive control over the sensitivity of WSI to the difference between snow conditions. In the case when the two clusters are perfectly distinct from each other (i.e., |μ1-μ2|≫σ1+σ2), the WSI is transformed into a step function and thus effectively acts as a single-value hard threshold at x0. Therefore, Nagler's method can be taken as a special case under this assumption with x0=-2 dB. Contrarily, the mixed clusters (i.e., |μ1-μ2|≪σ1+σ2) would lead to progressively flattened WSI and soft segmentation boundaries. A similar form of logistic function was proposed by , which was determined with empirical parameters and used as a soft threshold to replace the hard threshold of -2 dB on Rc. In our approach, the GMM allows for an adaptive choice of the parameter k based on the distribution density of Rc, thereby enabling flexible and robust applications at large scale.

Given the strong impact of terrain properties on snow distribution, we introduce the TSI as a component of the proposed method to account for the terrain influence on snow presence.

Terrain properties, including the elevation, slope, and aspect, collectively influence the spatial and temporal distribution of snow. Compared to lower altitudes, regions of higher elevation experience lower temperatures and are conducive to more snow accumulation. The steepness of slopes and the orientation of aspects, on the other hand, impact the snow distribution through solar illumination and wind exposure. To take these factors into account, we calculated the TSI in two steps. First, we derived the discrete topographic bin maps using the COP-30 DEM by partitioning the terrain with its elevation, slope, and aspect. The partition was based on slope below or above 20°, elevation in every 100 m, and aspect in every 15°. The topographic bin map can effectively capture the localized terrain attributes that influence the occurrence of snow. The median WSI value within each topographic bin was then calculated to obtain the TSI so that the regional propensity of wet snow occurrence under the specific topographic conditions could be quantified.

An example TSI distribution for Hunza at different elevation, slope, and aspect is presented in Fig. . In this example, TSI values show different patterns across seasons and topographic conditions. In spring, strong TSI signals are found around 4000 m a.s.l. for east-facing slopes (aspect 0∼190°) over flat terrain (slope θ<20°), while no obvious TSI signal is observed for steep terrain (slope θ>20°). This can be explained by the limited snowmelt during the spring season of Karakoram. In summer, strong TSI signals are observed above ∼ 5000 m a.s.l. for all slope and aspect conditions, indicating the presence of wet snow. However, steep slopes showed an unevenly distributed TSI across slope aspects, which can be attributed to the shadowing effect of the surrounding terrain. In autumn, TSI signals generally decrease due to the absence of wet snow, and the snow line retreats to higher elevations. This example indicates that the dynamic influence of topography on snowmelt can be effectively captured by the designed TSI signal.

As illustrated in Fig. , the final step generated an integrated snow index (SI) map through pixel-wise multiplication of WSI and TSI. This multiplication scales the WSI by incorporating terrain characteristics, thereby linking the observed SAR backscattering ratio directly to terrain properties.

In order to classify the integrated SI into binary snow maps, it is crucial to apply an adaptive threshold that accounts for the variation in topographic features across different basins. The variation in SAR backscatter response within a basin is inherently handled by the GMM when deriving the WSI. In contrast, the TSI is time-varying and basin-specific, requiring an optimal coefficient to condition the SI for classification. This coefficient should moderate the influence of TSI in the SI formulation and compensate for the concentration of TSI values within a limited range so that the impact of TSI can be normalized to align with the traditional -2 dB reference. To determine this coefficient, we performed a sensitivity analysis, evaluating F1 score, precision, and recall across different values using the S2 validation snow map. The results (Fig. ) demonstrate that Hunza and Shyok exhibit similar responses, with optimal coefficients close to 3.5, while Shigar reaches its optimum at approximately 2.5. However, to avoid overfitting to specific basins or validation dates, we selected 3.5 as an overall coefficient to balance classification performance across all basins. This coefficient also reflects a moderate threshold applied to the TSI to determine the overall SI threshold for each basin.

The threshold was then calculated using the following equation: 6SI Threshold=3.5×WSI|Rc=-2, where WSI|Rc=-2 represents the WSI at a backscatter ratio of Rc=-2 dB for each basin. This value is basin-specific, allowing the threshold to adapt based on each basin’s distinct characteristics. Together, these conditions form an integrated, basin-adaptive thresholding mechanism, combining SAR backscatter and topographic information into a single index to determine the SI threshold.

Note that while the SI threshold is basin-specific, it is time-independent. The WSI is derived from a GMM trained on samples collected from multiple summer scenes over several years, ensuring that it represents an aggregated measure for each basin and is not tied to individual scenes or seasons. This design ensures robustness to seasonal variations in liquid water content and enables consistent application across different validation dates.

The proposed method was validated using S2 snow cover maps generated following the LIS algorithm proposed by . Before running the LIS algorithm, the input S2 multi-spectral bands were resampled to a pixel size of 20m×20m to match the resolution of different bands. The COP-30 DEM was also resampled to the same pixel size as the S2 images.

The LIS algorithm started by generating provisional snow masks by applying thresholds on the normalized difference snow index (NDSI) and the red band reflectance (ρred) with the condition 7(NDSI>ni)and(ρred>ri), where ni=0.4 and ri=0.2 . This step was designed to identify snow-covered areas while excluding non-snow surfaces such as vegetation and bare ground. However, this approach could sometimes exclude snow-covered pixels due to errors in cloud masking. To correct the errors, a refinement step was introduced to reassign dark cloud pixels that were initially misclassified. Following Gascoin et al. (2019), dark clouds were identified by applying a threshold of 0.3 on the bilinearly downsampled red band, which reduced the resolution of the red band from 20 to 240 m by a factor of 12. This process helped to exclude cloud shadows and high-altitude cirrus clouds from the snow classification. Afterwards, the provisional snow masks were further refined using the basin snow line calculated from the COP-30 DEM. We calculated the total snow cover fraction (SCF) within every 100 m elevation band using the provisional snow mask and defined the snow line using the lowest elevation band where the SCF exceeded 30 %. For pixels identified as dark clouds above the determined snow line, the conditions used in Eq. () were reapplied with adjusted thresholds to account for the unique conditions at high altitudes. Specifically, the relaxed thresholds of ni=0.15 and ri=0.04 were used to classify snow pixels, and dark cloud pixels with ρred>0.1 were reassigned as cloud, while other pixels were categorized as “no snow”. These adjusted thresholds help to differentiate snow from dark clouds in challenging high-altitude environments, ensuring a more accurate classification. Following the adjustment of the snow mask, we extended the LIS algorithm by further applying a threshold on the NIR band with ρNIR>0.4 to classify glacier ice and water bodies from snow .

The validation of snow classification results was carried out for three basins on specifically suited summer dates (Table ). These dates were chosen based on conditions of minimal cloud cover and the shortest possible intervals between acquisitions of S1 and S2 images. As S2 snow cover maps classify snow (both dry and wet) rather than only wet snow, we have chosen only the summer dates as listed in Table  to ensure that the S2 snow cover maps were mostly covered by wet snow. For Hunza and Shyok, two S2 images with an acquisition interval of 2 d were combined to achieve complete coverage of the basin, whereas same-day acquisitions of S1 and S2 were found for Shigar in 2019.

In the three basins, adaptive SI thresholds were used to generate the snow classification maps. The threshold values for each basin are also reported in Table . These thresholds provided basin-adaptive and time-independent classification boundaries to distinguish wet snow and dry snow or snow-free pixels.

Figure  shows maps of Rc and SI, as well as the SI snow map and the S2 snow map over the three basins. Compared to the Rc map, the SI map shows a much clearer boundary that separates wet snow pixels from no-snow or dry snow pixels. Over glacier surfaces and valley regions (shown with the zoomed-in insets), Rc falls in the value range of -4 to 0 dB, making it sensitive to the choice of threshold values. The Rc map over these regions presents noisy patterns, likely due to the complex scattering mechanisms on glacier surfaces. Over glacier surface, especially in the ablation zone, radar backscatter responses are highly variable due to refreezing, supraglacial features (e.g., crevasses, sun cups, debris cover), and the presence of wet debris or bare ice . These features contribute to significant spatial variability in backscatter within a single pixel, making it challenging to distinguish dry snow, wet snow, and ice with Rc alone. Additionally, glacier movement between winter and summer scenes introduces further variability, compounding the uncertainty in detection.

In Fig. b, it is observed that the variation of SI values is within different ranges across the three basins. This is due to the different density distributions of Rc, WSI, TSI, and SI in the three basins as shown in Fig. , underscoring the necessity of applying dynamically adaptive thresholds for each basin to generate classification results.

The snow maps in Fig. c and d offer a visual comparison between the snow maps produced by the proposed method and the S2 LIS algorithm. A detailed comparison is further illustrated in Fig. . Overall, the two methods show good agreement, demonstrating the effectiveness of the proposed approach. Notably, the SI-based classification exhibits reduced false positives and cleaner snow-free classifications in valleys and over glacier surfaces, as evident in the detailed comparison. This improvement is primarily attributed to the incorporation of topographic information through TSI, which smooths SI values within each topographic bin. However, a consistent mismatch in the ice/water category can be observed between the SAR (both the SI and ratio methods) and S2 results, particularly over glacier surfaces. This discrepancy arises from the differing detection principles of the two approaches: the S2 results classify glacier ice using thresholds on the NIR band, while the SAR-based methods do not explicitly resolve glacier ice. On the observed date, glacier ice in the ablation zone may have partially melted, reducing the SAR backscatter ratio and leading to its misclassification as wet snow in the SAR results. As discussed earlier, glacier surfaces present unique challenges for SAR-based methods due to their complex scattering mechanisms. While the inclusion of TSI improves the robustness of our method by integrating topographic controls, it does not explicitly account for the heterogeneity of glacier surfaces. Consequently, glacier-specific conditions, such as localized melting or scattering from mixed ice–snow surfaces, may lead to underestimation or misclassification.

We further quantified the comparison using a confusion matrix and the F1 score, as listed in Table . In the confusion matrix, S2 snow-free (S2-SF) and S2 snow (S2-S) pixels are used as negative and positive labels, respectively, while S1 snow classification maps designate no-snow or dry snow (S1-N/D) and wet snow (S1-WS) pixels as their counterparts. To minimize errors caused by the presence of dry snow at high altitudes, areas above 5500 m a.s.l. were excluded from the calculation. This elevation threshold, representing 11.08 % of pixels in Hunza, 12.95 % in Shigar, and 30.43 % in Shyok (19.60 % in total), was chosen because such areas are consistently classified as non-melting zones due to persistently low air temperatures that inhibit snowmelt. Across all three basins, the proposed method shows an improvement in classification performance. In Hunza and Shyok, both true negative and true positive rates increased, while in Shigar, the true negative rate improved by 0.11, though the true positive rate decreased slightly by 0.04. Despite this, the overall F1 scores improved for all three basins, highlighting the method’s enhanced precision and recall.

We also evaluated the accuracy of the classification map using the elevation profile of snow distributions. As illustrated in Fig. , the profile of snow coverage was analyzed along 100 m elevation bands. Below 4500 m a.s.l., snow coverage was overestimated by approximately 7 % when using the Rc thresholds, leading to a misrepresentation of the actual snow line, especially over the challenging conditions on glacier surfaces and valleys (Fig. ). In contrast, the SI method provided a snow classification closer to the S2 profiles in the low-elevation regions. Between 4500 and 5500 m a.s.l., the SI curve exhibited a noticeably steeper slope than the S2 curve, with an underestimation of snow coverage between 4000 and 5000 m and an overestimation from 5000 to 5500 m. This pattern suggests that the SI uncertainties in mixed snow conditions within transition zones might have led to a nonlinear exaggeration of the TSI response to snow cover. A more precisely calibrated TSI model could further align snow coverage profiles between the SI method and S2 results. Above 5500 m a.s.l., where expansive dry snow cover predominates, both Rc and SI maps showed a greater reduction in wet snow coverage compared to S2, highlighting the differing sensitivities of SAR signals to dry snow conditions in these methods compared to S2's multi-spectral data.

In this section, we further applied the proposed method to the collected S1 image time series between 2017–2021 to generate wet snow maps across all three basins. The generated wet snow maps were resampled from the original SAR image resolution of 14×14 to 30×30 m before the analysis to speed up the processing. The temporal interval of the time series was 12 d, the same as the acquisition interval of S1 images. We analyze two key properties of snow cover dynamics derived from the time series data: the wet snow extent (WSE) and the snow melting duration (SMD). It is worth noting that these properties represent just a subset of the potential insights that can be derived from this dataset.

Compared to the conventional methods where only a single-value threshold is used on the Rc map, the proposed method effectively improved the mapping accuracy in the validation. This is primarily attributed to the transformation of Rc into WSI and the incorporation of TSI.

The GMM enabled a data-driven approach that allowed adaptively transforming the Rc into WSI based on the local SAR signal responses. As shown in Fig. , the WSI function for each basin was characterized by distinct center (x0) and slope (k) parameters determined from the GMM, indicating that varied local responses of SAR backscattering were raised by the diverse nature of wet snow distribution in different basins. This provides the flexibility required for large-scale application and thus offers an approach for robust wet snow mapping in complex and diverse landscapes.

Furthermore, the proposed method enriched the terrain analysis in snow mapping by incorporating multiple topographical factors (i.e., elevation, slope, and aspect) beyond the traditional use of snow line elevation. The add-on information from slope and aspect enables accurate capture of snow spatial distribution over the complex terrain, which is particularly important in the Karakorum region. As exemplified in Fig.  for the Hunza basin, the TSI values vary with elevation, aspect, and slope across different times of the year. At the onset of snowmelt, flat and east-facing slopes at altitudes between 3500 and 5000 m a.s.l. exhibited higher TSI values than the other regions, suggesting that snow in such areas was more susceptible to melting, likely due to solar exposure. As the season progressed into summer, altitude increasingly dictated the snowmelt on flat terrains, while on steeper slopes, aspect also played a significant role. Approaching late autumn, the snow line stabilized at similar altitudes across the two slope classes, yet variations were observed across the aspect with higher TSI values on south-facing slopes (approximate aspect of 75–255°), indicating conditions more conducive to melting. This level of detail in our analysis demonstrated the potential of our method to provide a more comprehensive understanding of wet snow dynamics than analysis using only snow line elevations.

While the proposed method demonstrates strong performance across the three basins in Karakoram, several limitations should be acknowledged. First, the choice of the SI threshold relies on the coefficient determined through sensitivity analysis for the selected study areas. While this approach balances classification performance across the basins, it is not fully dynamic and may require adaptation for larger, more topographically diverse regions, such as global-scale applications. Future work could explore supervised learning models, such as random forests or neural networks, to capture more complex, nonlinear relationships between SAR backscatter, topography, and snow conditions, enabling dynamic threshold adaptation.

Second, glacier surfaces present unique challenges for SAR-based snow classification. As shown in the results, glacier-specific scattering mechanisms, including contributions from wet debris, bare ice, and supraglacial features, introduce variability in radar backscatter that is not explicitly modeled in the current method. This limitation may lead to underestimation of wet snow on glacier surfaces and highlights the need for further refinement of the method to better handle glacier-specific conditions, potentially by incorporating land surface type information.

Finally, the use of TSI introduces potential bias in regions where topographic conditions deviate significantly from the assumptions underlying its calculation. As shown in Fig. , the long-tailed distribution of TSI values reflects the cumulative statistical nature of TSI, which relies on using a single median value to represent each topographic bin. This approach may be inadequate in bins with strong terrain variations, especially when the TSI distribution of pixels within a bin is highly skewed. In such cases, using the median can lead to systematic overestimation or underestimation – overestimating in left-skewed distributions and underestimating in right-skewed ones – ultimately affecting precision and recall in the classification results (see Sect. S2 of the Supplement for detailed visualizations). For instance, low TSI values in ablation zones may lead to underestimation of wet snow, as noted in the comparison with S2 results. While the inclusion of TSI improves overall robustness by integrating terrain characteristics, future studies should evaluate strategies to mitigate these biases, especially in regions with complex topography or unique land surface characteristics.

It is also important to note that while we followed Nagler's method to generate the Rc image, we did not apply the same post-processing steps, such as median filtering and land cover masking. These smoothing and filtering steps may influence accuracy, and future work could incorporate them to further evaluate their impact and potentially improve snow mapping performance.

Large-scale wet snow maps, especially the ones with high spatial and temporal resolution, have significant implications for hydrological studies, water resource management, and climate impact assessments . Snow data obtained from remote sensing and field site stations have proven to be fundamental for the development, calibration, and validation of snowpack, hydrology, and runoff prediction models .

Using the wet snow maps generated from the proposed method, our study has extracted and analyzed two critical snow variables, i.e., WSE and SMD, which are crucial for understanding regional snow melting dynamics. The analysis of WSE uncovered detailed patterns of snowmelt changes over time and across elevations, which can provide valuable observations for calibrating snowpack models or forecasting runoff events . The interpretation of SMD highlighted the yearly differences in snow melting duration across the basins, with Hunza exhibiting relative stability and Shyok demonstrating the most variability. A long-term SMD observation record will provide key insights into the changes of the regional climate pattern.