Machine-Learning-Based Ensemble Prediction of the Snow Water Equivalent in the Upper Yalong River Basin

Abstract

The snow water equivalent (SWE) in high-altitude regions is crucial for water resource management and disaster risk reduction, yet accurate predictions remain challenging due to complex snowmelt processes, nonlinear meteorological factors, and time-lag effects. This study used snow remote sensing products from the Advanced Microwave Scanning Radiometer (AMSR) as the predictand for evaluating SWE predictions. It applied nine machine learning models—linear regression (LR), decision trees (DT), support vector regression (SVR), random forest (RF), artificial neural networks (ANNs), AdaBoost, XGBoost, gradient boosting decision trees (GBDT), and CatBoost. For each machine learning model, submodels were constructed to predict the SWE for the next 1 to 30 days. The 30 submodels of each machine learning model formed the prediction model for the snow water equivalent over the next 30 days. Through an accuracy evaluation and ensemble forecasting, the snow water equivalent prediction for the next 30 days in the Yalong River above the Ganzi Basin was finally achieved. The results showed that for all models, the average Nash–Sutcliffe Efficiency (NSE) rate was greater than 0.8, the average root mean square error (RMSE) was under 8 mm, and the average relative error (RE) was below 7% across three lead time periods (1–10, 11–20, and 21–30 days). The ensemble average model, combining ANNs, GBDT, and CatBoost, demonstrated superior accuracy, with NSE values exceeding 0.85 and RMSE values under 6 mm. A sensitivity analysis using the Shapley Additive Explanations (SHAP) model revealed that temperature variables (average, minimum, and maximum temperatures) were the most influential factors, while relative humidity (Rhu) significantly affected the SWE by reducing evaporation. These findings provide insights for improving SWE prediction accuracy and support water resource management in high-altitude regions.

1. Introduction

Snow, as an important component of the cryosphere, accounts for about 98% of seasonal snow, with the largest area reaching 4.7 × 10⁷ km² in the Northern Hemisphere [1,2,3]. It is highly sensitive to climate change and significantly impacts the climate, water cycle processes, and the structure and function of ecosystems [4,5,6]. Snowmelt water can alleviate seasonal water shortages, providing stable water resources during dry seasons. It is a crucial freshwater source for about one-sixth of the world’s population [7]. Spring snowmelt runoff typically accounts for 10–15% of the global annual runoff [8,9,10], playing an important role in global runoff. Accurate snow data can enhance the effective utilization of watershed water resources and can be used to assess the potential impact of climate change on hydrological processes in cold regions, providing important observational indicators for climate change monitoring and hydrological model construction [11,12]. Therefore, the acquisition and prediction of snow data are important for water resource management, ecosystem health, and early disaster warnings [13,14,15,16,17].

Currently, snow data acquisition mainly relies on ground-based observations, remote sensing inversion, and model simulations [18,19]. Ground-based observations can provide high-precision local data, including on the snow depth, density, and SWE. However, due to the sparse distribution of observation stations, it is difficult for ground-based observations to meet the needs of large-scale and fine-grained applications. Satellite remote sensing technology has distinct advantages in acquiring large-scale snow data, enabling snow data collection in data-scarce areas of cold regions. For instance, MODIS data from optical remote sensing and AMSR data from passive microwave remote sensing have been widely used for snow data acquisition [20,21,22,23,24]. Traditional optical remote sensing data are limited by cloud cover, resulting in significant errors. Although microwave remote sensing data can penetrate clouds, they are still influenced by surface features, and their transmission exhibits latency. Remote sensing data still face limitations in inversion accuracy and real-time acquisition, and there is a significant gap in future snow data predictions [25,26].

To further explore snow evolution mechanisms and predict future snow changes, many scholars have turned to physical or artificial intelligence models. These models use meteorological and surface data for the refined simulation and prediction of snow processes [27,28]. In current physical models, snowmelt mechanisms mainly include degree-day factors and energy balance models [29,30]. The degree-day factor model requires fewer data and can relatively simply simulate snowmelt runoff, although due to its simple mechanism, it is difficult to accurately predict future snow changes. Energy balance models, on the other hand, have complex parameters and high requirements for initial data, limiting their application in data-scarce high-altitude regions. For example, Bi et al. [31] used the upper Lancang River as the study area to compare the snowmelt runoff simulation processes under both the degree-day factor and energy balance methods, which partly reflected their simulation’s effectiveness for snow evolution. Grusson et al. [32] applied the SWAT model to simulate snow in the upper Shule River watershed. Zhao et al. [33] combined WRF model forecast data with the DHSVM model to achieve a 24 h snowmelt runoff forecast. However, the WRF model relies on high-quality initial and boundary conditions, which requires high data accuracy, and there are limitations in simulating long-term forecasts and complex meteorological phenomena. Therefore, due to the limitations of meteorological and hydrological data, there is still room for further research in predicting long-term snowmelt scenarios.

The limitations of the current methods have led to the application of machine learning in snowmelt inversion and snowmelt runoff simulations. Compared with traditional hydrological models, machine learning models do not require consideration of the complex and variable physical processes within the watershed. By using past meteorological datasets to explore the complex nonlinear relationships between input factors and target values, more accurate simulation results can be obtained. With the development of remote sensing and machine learning technologies, data-driven methods based on machine learning have gradually become some of the mainstream approaches for snow retrieval [34,35]. For example, Steel et al. [11] applied traditional machine learning algorithms such as random forests to capture the complex nonlinear relationship between environmental factors and the SWE for snowmelt inversion using remote sensing data. Moradizadeh et al. [36] used machine learning algorithms such as SVM and CNN models for the spatial downscaling of snow data in high-altitude areas. Wang et al. [37] used ANN and RF models to simulate runoff and capture snow change trends in the Xiying River basin in western Qilian. In addition to the machine learning algorithms commonly used in snowmelt assessments, such as ANN, random forest, and SVM models, existing models such as linear regression [38], decision trees [39], XGBoost [40], GBDT [41], AdaBoost [42], and CatBoost [43] have also been effectively applied in data inversion and analysis processes. However, machine learning algorithms depend on training data, which still leads to uncertainty in the model’s adaptability and prediction performance across domains. Moreover, differences in the sensitivity of various models to data features result in varying performance under specific conditions, increasing the difficulty of model selection and parameter optimization [44].

This study addresses this issue by using seven meteorological factors, including precipitation, temperature, wind speed, and sunshine hours, as driving data. We constructed 30 daily snow water equivalent prediction models for the next 1 to 30 days, and combined these 30 daily prediction models to form the snow water equivalent prediction model for the next 30 days. To comprehensively select machine learning models with better accuracy, our experiments compared the performance of nine common machine learning models—linear regression, decision trees, random forest, support vector machine, neural networks, AdaBoost, XGBoost, GBDT, and CatBoost—in snow data prediction. The top-performing models, CatBoost, ANNs, and GBDT, were then selected for ensemble forecasting to obtain the snow water equivalent prediction values for the next 30 days. This study selected the upper Yalong River Basin above the Ganzi Station as the typical research area, aiming to explore the complex relationships between meteorological factors and the SWE in a more comprehensive manner and conduct a comparative analysis of the simulation results. The SWE prediction model developed in this study can provide a reference for hydrological forecasting in cold regions. The experimental results show that different models perform differently under various time scales and meteorological conditions, providing a solid foundation for accurate SWE prediction. This study not only demonstrates the potential of machine learning in SWE prediction but also provides strong support for further optimizing snow water equivalent forecasting in the future, ultimately contributing to the sustainable utilization of water resources.

2. Study Area and Data

2.1. Study Area

The Yalong River originates from the southern slopes of the Bayan Har Mountains in Yushu Prefecture, Qinghai Province. The main stream stretches 1571 km, with a basin area of 136,000 km² and a natural elevation drop of 3830 m, with maximum topographic relief exceeding 5000 m. Among the key hydrological stations in the upper basin, the Ganzi Hydrological Station controls a drainage area of 32,500 km², with an average altitude of over 4500 m (Figure 1a). The region experiences a high-altitude, cold plateau climate characterized by intense sunlight and long winters, with significant spatiotemporal variations in snow cover and seasonal permafrost. Spring snowmelt and seasonal permafrost thaw play a critical role in runoff generation, confluence mechanisms, and hydrological processes during both flood and dry seasons [45].

From autumn to winter, the temperatures in the upper basin above Ganzi gradually drop below freezing, with snow accumulation starting in October and November. The snow cover peaks in March of the following year, and the snowmelt period primarily occurs in April and May. By early June, the snow is almost completely melted, with the annual average snow cover exceeding 50% of the basin (Figure 1b). The seasonal distribution of transient and seasonal permafrost follows a similar pattern to the snow cover. The permafrost typically begins to form around October, reaching its maximum depth between January and February of the following year. In spring, the permafrost thaws rapidly during April and May, with near-complete thawing by early June.

Under the influence of global climate change, the spatiotemporal variability of the snowmelt and seasonal permafrost in the basin has increased in recent years, leading to greater instability in the spring runoff [46,47]. This variability poses challenges to the scientific management of the cascade reservoir system and the efficient development and utilization of hydropower resources in the basin.

2.2. Data

2.2.1. Meteorological Data

The meteorological data used in this study were sourced from the CN05.1 [48,49] daily meteorological grid dataset released by the China Meteorological Administration. The dataset has a temporal resolution of 1 day and a spatial resolution of 0.25°. The CN05.1 dataset applies observational data from over 2400 stations within China, using the anomaly approximation method. The climate field and anomaly field are interpolated separately and then superimposed to obtain the data. The dataset includes daily precipitation (Pre), average temperature (Tm), maximum temperature (Tmax), minimum temperature (Tmin), wind speed (Win), sunshine duration (Ssd), and relative humidity (Rhu) data. The data are of good quality and are widely used in daily research. Area-averaged daily data for Pre, Tm, Tmax, Tmin, Win, Ssd, and Rhu from 2013 to 2022 for the Ganzi Basin were collected for this analysis and were used as driving data for the subsequent snow water equivalent prediction model. Figure 2 shows the spatial distribution map of CN05.1 precipitation, mean temperature, maximum temperature, minimum temperature, sunshine duration, relative humidity, and wind speed data.

2.2.2. Remote Sensing Snow Water Equivalent Data

The snow water equivalent (SWE) data were obtained from the AMSR2 daily snow water equivalent grid dataset. This dataset is based on satellite observations using passive microwave remote sensing technology to monitor the water content of surface snow. The SWE refers to the depth of water that would result from the melting of the snow on the surface, typically measured in millimeters, and is a key parameter for assessing snow water resources and predicting snowmelt runoff. The dataset, based on satellite remote sensing observations, has a temporal resolution of 1 day and a spatial resolution of 0.25°. To ensure the continuity and reliability of the data, after collecting and extracting the daily SWE raster data for the area above Ganzi, two steps were performed: removing outliers and imputing missing values. First, it was set that if the difference between the value of a grid on a given day and the values of the adjacent two days was greater than three times the value, the value was considered an outlier. The identified outlier grid values were then replaced with the average of the values from the preceding and following days. Similarly, when there were missing values for a grid, they were filled with the average of the values from the preceding and following days. After removing outliers and imputing missing values in the raster data, the area-averaged values for the basin above Ganzi were extracted. Daily snow water equivalent data for the period from 2013 to 2022 for the basin above Ganzi were collected and used for preliminary simulations and a forecast accuracy evaluation of the snow water equivalent prediction.

3. Methods

In recent years, machine learning models have been widely applied in fields such as snow remote sensing data inversion and snowmelt runoff numerical simulation. Different models have their own advantages under different simulation scenarios. To comprehensively compare the performance of various machine learning algorithms in simulation and prediction, we selected nine commonly used machine learning algorithms in snow accumulation and melting, and compared their accuracy in snow water equivalent prediction. The following is a brief introduction to these nine algorithms.

3.1. Machine Learning Algorithms

(1)

Linear Regression (LR)

Linear regression (LR) is a supervised machine learning model [50,51] suitable for numerical prediction tasks. Compared to other machine learning algorithms, linear regression has a short training time and performs well in datasets with few features and a strong linear relationship. The main calculation formula is as follows:

$$y={\beta }_0+{\beta }_1{x}_1+{\beta }_2{x}_2+\cdots +{\beta }_n{x}_n+\epsilon$$

(1)

where y is the predicted value; ${\beta }_{\mathrm{i}}$ is the predicted value; $x_{\mathrm{i}}$ are the features, i $\in$ [1, n]; $\epsilon$ is the error term.

(2)

Decision Trees (DT)

Decision trees represent a supervised machine learning model that uses a tree structure to recursively split data [52,53]. At each node, the model splits the dataset based on feature selection, typically by minimizing the impurity index to choose the best splitting feature. During training, for regression tasks, the model selects the optimal features for splitting based on the mean square error (MSE) criterion. The main calculation formula is as follows:

$$MSE={\displaystyle \frac{1}{n}}{\sum }_{i=1}^n{(y_i-{\widehat{y}}_i)}^2$$

(2)

where n is the number of samples; $y_i$ is the actual value of the i-th sample; ${\widehat{y}}_i$ is the predicted value of the sample.

(3)

Random Forest (RF)

The random forest (RF) model is a supervised machine learning model [54,55]. Compared with other machine learning algorithms, it has a short training time and high accuracy. The main calculation formula is as follows:

$$\widehat{y}={\displaystyle \frac{1}{T}}{\sum }_{t-1}^T h_t(x)$$

(3)

where ŷ is the output of the random forest; $h_t\left(x\right)$ is the prediction of the t-th decision tree; T is the number of decision trees.

(4)

Support Vector Machine (SVM)

A support vector machine (SVM) is a supervised machine learning model aimed at optimizing classification results by maximizing the margin of the hyperplane that separates the classes [56,57]. The SVM model performs well on data with a few outliers and high-dimensional data. By introducing a kernel function, the model can handle nonlinear data. The main formula is as follows:

$$\mathrm{Decision} \mathrm{Function}:\hspace{1em}\hspace{1em}\hspace{1em}f\left(x\right)=\mathrm{s}\mathrm{i}\mathrm{g}\mathrm{n}\left(w\cdot x+b\right)$$

(4)

$$\mathrm{Optimization} \mathrm{Objective}:\hspace{1em}\hspace{1em}\hspace{1em}\mathrm{m}\mathrm{i}\mathrm{n}{\displaystyle \frac{1}{2}}\Vert w{\Vert }^2$$

(5)

$$\mathrm{Constraints}:\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}{w}^T{x}_i+b\ge 1, y_i=+1$$

(6)

$$w^T{x}_i+b\le 1, y_i=-1$$

where f(x) is the decision function, representing the classification result, which outputs +1 or −1, corresponding to the positive and negative classes, respectively; w is the normal vector of the hyperplane; x is the feature vector; b is the bias term, which controls the position of the decision boundary and allows it to flexibly adapt to the data; $y_i$ is the label of the i-th sample, with values +1 or −1; $x_i$ is the feature vector of the i-th sample.

(5)

Artificial Neural Network (ANN)

Artificial neural networks (ANNs) are machine learning models inspired by biological neural networks, capable of modeling complex nonlinear relationships [58,59] They excel in handling large-scale data and complex relationships between features, but the training process can be relatively time-consuming. The main calculation formula is as follows:

$$y=f\left({\sum }_{i=1}^n w_i{x}_i+b\right)$$

(7)

where y is the output of the neuron, also known as the predicted value; f is the activation function, which introduces nonlinearity, enabling the neural network to model complex nonlinear mappings; $w_i$ is the weight associated with the i-th input feature, indicating the importance of the input feature in the output; $x_i$ is the value of the i-th input feature, representing the input data; $b$ is the bias term, used to adjust the output of the model, making it more flexible; n is the total number of input features.

(6)

AdaBoost

AdaBoost (adaptive boosting) is an ensemble learning algorithm that improves the accuracy of a classifier by combining multiple weak classifiers (e.g., decision trees) [60,61,62]. During training, the model progressively focuses on misclassified samples, increasing the weights of these samples to improve the model’s performance on them. The main calculation formula is as follows:

$$H(x)=\mathrm{s}\mathrm{i}\mathrm{g}\mathrm{n}\left({\sum }_{t-1}^T {\alpha }_t{h}_t(x)\right)$$

(8)

where H(x) is the final strong classifier’s prediction for sample x, which is the weighted sum of the predictions from multiple weak classifiers; T is the total number of weak classifiers; ${\alpha }_t$ is the weight of the t-th weak classifier, indicating its importance in the final decision, typically inversely proportional to the classifier’s error rate; $h_t\left(x\right)$ is the prediction of the t-th weak classifier for sample x.

(7)

XGBoost

XGBoost is an optimized version of the gradient boosting algorithm that incorporates a regularization term to control the model complexity, thereby reducing overfitting. XGBoost is known for its speed and high performance, making it suitable for handling large-scale data [63,64]. The main calculation formula is as follows:

$$\mathrm{Obj}={\sum }_{i=1}^n l\left(y_i,{\hat{y}}_i\right)+{\sum }_{k=1}^K \mathsf{\Omega }\left(f_k\right)$$

(9)

where Obj is the overall objective function; n is the number of training samples; $l\left(y_i,{\hat{y}}_i\right)$ is the loss function, which measures the error between the predicted value ${\hat{y}}_i$ and the true value $y_i$; K is the total number of decision trees; $\mathsf{\Omega }\left(f_k\right)$ is the regularization term for the k-th tree, which controls the complexity of the tree.

(8)

Gradient Boosting Decision Tree (GBDT)

A gradient boosting decision tree (GBDT) is an ensemble model that iteratively trains multiple decision trees, with each tree optimizing the residuals from the previous one. The GBDT method is suitable for both regression and classification tasks [65,66]. It effectively captures nonlinear relationships between features but requires longer training times. The main calculation formula is as follows:

$$r_i^{\left(m\right)}=y_i-F^{\left(m-1\right)}\left(x_i\right)$$

(10)

where $x_i$ is represents the feature vector of the i-th sample; $r_i^{\left(m\right)}$ is the residual for the i-th sample in the m-th iteration, indicating the model’s improvement direction for the target in this iteration; $y_i$ is the true value of the i-th sample; $F^{(m-1)}\left(x_i\right)$ is the prediction of the i-th sample from the model in the (m − 1)-th iteration.

(9)

CatBoost

CatBoost is an improved gradient boosting algorithm with a similar formula to XGBoost [67,68]. The main advantage of CatBoost lies in its unique handling of categorical features; by using ordered target encoding, it effectively prevents information leakage. Additionally, CatBoost employs a symmetric tree structure, enhancing both the model’s stability and training efficiency.

3.2. Sensitivity Analysis with the SHAP Model

The Shapley Additive Explanations (SHAP) model can measure the interaction of different features on the final prediction by separating the marginal contribution of each feature to the predicted value [69,70]. Let the i-th sample be x_i, the j-th feature of the i-th sample be x_ij, the model’s prediction for the sample be y_i, and the average value of the sample variables be y_base. The SHAP value is calculated as follows:

$$y_{ij}=y_{base}+f\left(x_{i1}\right)+f\left(x_{i2}\right)+f\left(x_{i3}\right)+\cdots +f\left(x_{ij}\right)$$

(11)

In this equation, $f\left(x_{ij}\right)$ represents the SHAP value of x_ij, which is the contribution of the j-th feature of the i-th sample to the final prediction y_i. The absolute value of the SHAP value reflects the impact of the predictor variable on the model’s prediction; the larger the absolute value, the more significant the influence of that predictor variable on the feature variable. When $f\left(x_{ij}\right)$ > 0, this indicates that the feature increases the predicted value and has a positive effect on the model’s prediction, meaning an increase in the factor value promotes an increase in the SWE value. Conversely, when $f\left(x_{ij}\right)$ < 0, this indicates that the feature decreases the predicted value and has a negative effect on the model’s prediction, meaning an increase in the factor value leads to a decrease in the SWE value. This study analyzed the marginal contribution of each feature in the snow water equivalent prediction model to the predicted values, obtaining the sensitivity levels of different feature values.

3.3. Model Construction

The input features for machine learning models are crucial for the accuracy of the model’s training results. To comprehensively simulate the correlation between various factors and snow, it is necessary to consider the basic elements across the watershed. In this study, machine learning algorithms were used to model the daily SWE in the upper Yalong River Basin above Ganzi. The algorithm takes into account not only the conventional meteorological elements but also the characteristics of snow in the watershed. The primary input features include the total precipitation, average temperature at 2 m, maximum temperature, minimum temperature, sunshine duration, wind speed, and relative humidity. Among the input features, the total precipitation is the daily cumulative value, while the average temperature, sunshine duration, wind speed, and relative humidity represent daily averages.

Since the SWE is related to the cumulative effect of meteorological factors such as precipitation and temperature, if the forecast start date is 1 January 2022, with a lead time of 1–30 days, the changes in the SWE during the lead times are related to the cumulative changes in meteorological factors (precipitation, temperature, etc.) over 1–30 days. Therefore, the input data for the model include the SWE on the start date, along with the cumulative values of the total precipitation, average temperature at 2 m, maximum temperature, minimum temperature, sunshine duration, wind speed, and relative humidity during the lead time.

This study applied nine machine learning models, with each model predicting the SWE for every day from the 1st day up to the 30th day, resulting in 30 SWE prediction models. Each model was applied for a different lead time ranging from 1 to 30 days, and the 30 models were combined into the final daily prediction model for the next 30 days. The expression is as follows:

$$\begin{gathered} y_{t,j}=f_j\left({SWE}_0; \sum _{i=1}^t{\displaystyle \frac{P_i}{t}}; \sum _{i=1}^t{\displaystyle \frac{T_{mi}}{t}}; \sum _{i=1}^t{\displaystyle \frac{T_{maxi}}{t}}\sum _{i=1}^t{\displaystyle \frac{T_{mini}}{t}}; \sum _{i=1}^t{\displaystyle \frac{{Rhu}_i}{t}}\sum _{i=1}^t{\displaystyle \frac{{Ssd}_i}{t}}; \sum _{i=1}^t{\displaystyle \frac{{Win}_i}{t}}\right), \\ t\in \left[1, 30\right],j\in [1, 9] \end{gathered}$$

(12)

where t is the lead time, $t\in \left[1, 30\right]$; j is the model number, $j\in \left[1, 9\right]$; $f_j$ is the j-th model; $y_{t,j}$ is the predicted SWE for the j-th model on the t-th day; ${SWE}_0$ is the SWE from the day before the forecast start date; $P_i$ is the precipitation on the i-th day; $T_{mi}$ is the average temperature on the i-th day; $T_{maxi}$ is the maximum temperature on the i-th day; $T_{mini}$ is the minimum temperature on the i-th day; ${Rhu}_i$ is the relative humidity on the i-th day; ${Ssd}_i$ is the sunshine duration on the i-th day; ${Win}_i$ is the wind speed on the i-th day.

The SWE prediction models were trained with the objective of maximizing the Nash–Sutcliffe Efficiency (NSE).

3.4. Ensemble Mean (EM) Model

The ensemble mean (EM) model is a statistical method that improves the overall prediction performance by combining the prediction results from multiple models [71]. In hydrological and meteorological forecasting, the EM method is widely used to reduce random errors and systematic biases that may exist in individual models. The core idea is to integrate the predictions of multiple models through simple averaging or weighted averaging, thereby generating more robust and accurate results.

The mathematical expression of the EM method is as follows:

$${\mathrm{E}\mathrm{M}}_{\mathrm{t}}={\displaystyle \frac{1}{N}}{\sum }_{j=1}^N y_{t,j}$$

(13)

where ${\mathrm{E}\mathrm{M}}_{\mathrm{t}}$ is the prediction result of the ensemble mean model; N is the number of models participating in the ensemble; $y_{t,j}$ is the prediction of the j-th model for the t-th day.

3.5. Snow Water Equivalent Prediction Model

This study used the period from 2013 to 2019 as the model calibration period for training and hyperparameter optimization, and the period from 2020 to 2022 as the validation period to assess the model’s generalization ability. During the calibration period, K-fold cross-validation combined with grid search cross-validation [72] was employed for hyperparameter tuning. Nine machine learning models were used to establish 30 individual snow water equivalent prediction models, forecasting the snow water equivalent for the next 1 to 30 days. These models were then combined to form a set of daily prediction models for the next 30 days. Finally, based on the combined NSE, RMSE, and RE rankings, the top three models were selected for ensemble forecasting, ultimately obtaining the snow water equivalent prediction values for the next 30 days (Figure 3).

3.6. Evaluation Metrics

Three evaluation metrics were used to assess the accuracy of the results: the Nash–Sutcliffe Efficiency (NSE), root mean square error (RMSE), and relative error (RE) [73].

The Nash–Sutcliffe Efficiency (NSE) is a commonly used parameter for evaluating the quality of hydrological models, with its value ranging from negative infinity to 1 [74]. The closer the value is to 1, the better the model quality and reliability. Values closer to 0 indicate that the model is close to the mean of the observed values, suggesting that while the overall results are reliable, significant errors exist in the simulation process; values far less than 0 indicate that the model is unreasonable. The specific mathematical formula for the NSE is as follows:

$$NSE=1-{\displaystyle \frac{{\sum }_{t=1}^T{\left(X_0^t-X_m^t\right)}^2}{{\sum }_{t=1}^T{\left(X_0^t-{\overline{X}}_0\right)}^2}}$$

(14)

where $T$ is the number of samples; $X_0^t$ is the observed value; $X_m^t$ is the predicted value; ${\overline{X}}_0$ is the mean of the observed values.

The root mean square error (RMSE) is a method for assessing the goodness of fit of a regression model to a dataset, displaying the average distance between the model’s predictions and the actual values in the dataset. The lower the RMSE, the better the model “fits” the dataset. A value closer to 0 is preferred. The formula for the RMSE is:

$$RMSE=\sqrt{{\displaystyle \frac{1}{n}}{\sum }_{i=1}^n{(y_i-{\widehat{y}}_i)}^2}$$

(15)

where $n$ is the number of samples; $y_i$ is the observed value; ${\widehat{y}}_i$ is the predicted value.

The relative error (RE) refers to the ratio of the absolute error of the measurement to the true value (or accepted value) of the quantity being measured, multiplied by 100%, and is expressed as a percentage. Generally, the relative error provides a better reflection of the reliability of the measurement. The unit of the RE is %, and the closer the RE value is to 0, the better [75].

$$RE={\displaystyle \frac{|y_i-{\widehat{y}}_i|}{y_i}}\times 100\mathrm{\%}$$

(16)

where $y_i$ is the observed value; ${\widehat{y}}_i$ is the predicted value.

4. Results

4.1. Comparison of Machine Learning Model Performance During the Testing Period

The performance of nine machine learning models was evaluated, and the results showed that the Nash–Sutcliffe Efficiency (NSE) for all models during the training period was greater than 0.87, indicating that the models had high capability to capture trends and changes in observed values. In hydrological forecasting, predictions are typically categorized based on lead time into short-term (0–3 days), medium-term (3–10 days), and long-term (over 10 days) forecasts. Based on historical training data, the SWE for the testing period from 1 January 2020 to 31 December 2022 was predicted for each of the 1st to 30th days. The lead time was further divided into three sub-periods: days 1–10, days 11–20, and days 21–30. A comparative analysis of the prediction performance for these nine models across each period is shown in Figure 4.

During the 1–10 day lead time, the average NSE for all nine machine learning models was greater than 0.9, indicating that the models fit the short-term SWE change trends with high accuracy (Figure 4a). Additionally, the average RMSE was less than 5.1 mm. Except for the SVR model, which exhibited larger fluctuations in RMSE, the other models had RMSE fluctuations of around 3 mm (Figure 4d). Furthermore, the average RE also showed a small error range for the models during the short-term lead time (Figure 4g). Therefore, for short-term SWE forecasting, models such as the ANN, GBDT, and RF demonstrated high accuracy and stability.

During the medium-term lead time (days 11–20), the average NSE for all nine models was greater than 0.85, showing that the models still maintained high accuracy in predictions over a longer period (Figure 4b). The average RMSE was less than 6.3 mm, with the decision tree model exhibiting relatively large fluctuations in RMSE (around 0.4 mm), while the RMSE fluctuations for the other models were all below 0.1 mm (Figure 4e). The average RE for all models was less than 5.5%, with small fluctuations (Figure 4h). In this period, models such as CatBoost, ANN, and GBDT performed particularly well, effectively capturing the SWE variation trends over the medium term.

In the long-term lead time (days 21–30), the average NSE for all models was greater than 0.8, with fluctuations in NSE being less than 0.2, demonstrating a certain level of stability (Figure 4c). The average RMSE was less than 6.8 mm, showing that the models maintained good forecasting capabilities over a longer time scale (Figure 4f). The average RE was below 6%, with minimal fluctuation (Figure 4i). A comprehensive analysis found that during the long-term forecast, models such as CatBoost, ANN, and GBDT continued to show relatively high prediction accuracy and stability, providing valuable insights for future long-term SWE forecasting.

To comprehensively evaluate the prediction performance of machine learning models under different SWE scenarios, this study selected three models with the best overall performance: ANN, GBDT, and CatBoost. Figure 5a–f presents the prediction results for the future 30 days of the SWE for several example initialized forecast dates, corresponding to high SWE values, low SWE values, and rapid accumulation and melt periods, in order to validate the model’s applicability under diverse scenarios.

The results show that the EM model exhibited stable and accurate prediction performance during the aforementioned typical periods. The RMSE for all periods was below 6 mm, reflecting high accuracy, especially in cases where the initial snow conditions were stable, such as on 1 January 2020 (Figure 5a) and 15 January 2022 (Figure 5d), which showed the lowest RMSE values, demonstrating the model’s good adaptability to initial snow conditions. The NSE exceeded 0.85 for all periods, indicating that the model could accurately capture the dynamic trends of SWE changes. Notably, during the rapid snowmelt phases on 26 March 2020 (Figure 5c) and 1 March 2022 (Figure 5e), the NSE approached 0.9, showing the model’s sensitivity to rapid changes. At the same time, for the snowmelt process during the period of 21 March 2020 (Figure 5b), the snow water equivalent monthly melt value was greater than 50 mm, and the NSE value of 0.87 indicated a good forecast of the melting trend. The RE values fluctuated within 10%, with the lowest RE values observed on 1 January 2020 (Figure 5a) and 25 April 2022 (Figure 5f), further confirming the robustness and reliability of the ensemble mean model for future SWE predictions.

Furthermore, the uncertainty range of the model predictions (represented by the pink shaded area) covered almost all observed true values, especially during the high SWE and rapid melt phases, where the prediction intervals effectively captured the trend changes. For instance, in the forecast initialized on 1 January 2020, during the middle period, the ensemble mean model overestimated the SWE by approximately 3–4 mm. However, considering the uncertainty, the model provided a range from the three models, which included the observed true value. These results further validate the applicability and advantages of the ensemble mean model in predicting the SWE in the dynamic and complex high-altitude regions.

4.2. Snow Sensitivity Analysis

Given the artificial neural network (ANN) model performs best in predicting SWE, this study further conducted a sensitivity analysis on the key influencing factors for the ANN using the SHAP method. The SHAP plots provide deep insights into the importance and directional influence of each meteorological factor on SWE prediction, offering an intuitive basis for understanding the model’s prediction logic.

The SHAP values reflect the contribution of each feature to the model’s prediction outcome. According to the SHAP analysis results (Figure 6), aside from the initial SWE value on the forecast start date, Tm, Tmin, and Tmax had SHAP values of 6.2, 5, and 3.3, respectively, making them the most influential meteorological factors with the highest sensitivity to the SWE. Following these, Rhu and Pre had SHAP values of 2 and 1.4, respectively, and also had considerable impacts on the SWE. In contrast, Ssd and Win had SHAP values of 0.6 and 0.3, indicating relatively lower sensitivity. Specifically (Figure 7), higher SHAP values (light yellow) contribute strongly in a positive direction to the prediction outcome, while lower values (dark green) exert a negative influence. The minimum temperature, relative humidity, and sunshine duration have a positive effect on the SWE, meaning their increase helps to increase the SWE. In contrast, the average temperature, maximum temperature, precipitation, and wind speed show a negative effect, where their increase leads to a decrease in SWE.

From the analysis of Figure 6 and Figure 8a–f, it can be further observed that the SWE exhibits a positive change when the following meteorological conditions are met: average temperature below −2.5 °C, minimum temperature below −12 °C, maximum temperature below 7.5 °C, precipitation less than 1 mm, relative humidity greater than 55%, sunshine duration exceeding 6 h, and wind speed below 2.5 m/s. These conditions collectively indicate the accumulation and retention process of the SWE. Low temperatures reduce the rate of snowmelt, high humidity minimizes evaporation losses, and longer sunshine durations may indirectly affect surface temperature and precipitation patterns in cold environments.

5. Discussion

5.1. Model Accuracy Evaluation

This study focused on the upper Yalong River Basin above Ganzi, an area with an average elevation exceeding 4500 m. The high altitude and high solar radiation characteristics make the snowmelt process highly sensitive to meteorological variables (such as temperature and humidity), and the relationship between meteorological variables and the SWE is relatively clear. These characteristics provide favorable conditions for machine learning models to capture the trends of SWE variations.

The CatBoost model [76], through optimizing the decision tree training process, can fully utilize mixed inputs of categorical and numerical features, significantly enhancing the model’s ability to model complex variable interactions. Its high sensitivity to outliers makes it particularly effective under the complex climate conditions of the study area. The ANN model automatically extracts nonlinear patterns of input features through hidden layers and can dynamically adjust feature weights. It is particularly sensitive to the impacts of key variables, such as temperature and humidity, meaning the simulation results closely align with actual trends. The GBDT model, by iteratively fitting residuals, can precisely model nonlinear relationships between variables, especially for complex but nonexplicit variable interactions within the study area. Furthermore, the GBDT model [65,66] shows greater robustness in handling outliers and missing values, with excellent performance in predicting extreme values.

An analysis of the EM model [77], which combines the predictions from CatBoost, ANN, and GBDT methods, shows that integrating these models’ results effectively reduces the bias of individual models, significantly improving the prediction accuracy and robustness of SWE forecasts for the next 30 days. This fusion method has shown good adaptability and universality under the high-altitude and complex climatic conditions of the study area. This indicates that the ensemble mean model not only provides high-precision daily forecasts but also offers a scientific basis for risk assessment and emergency management, helping decision-makers make more accurate and robust judgments when addressing snowmelt risks and water resource allocation needs.

From January to May, the SWE prediction accuracy is highest in January, followed by March and February, with the largest errors in May. In January, the snow accumulation peaks and SWE changes are stable, making predictions easier. In March, the snow remains abundant and melts slowly, keeping the impact of meteorological factors stable. In February, as melting begins and temperatures rise, the SWE becomes more sensitive to fluctuating weather, increasing the prediction difficulty. By April and May, accelerated snowmelt and more volatile conditions lead to greater prediction errors.

5.2. Sensitivity Analysis

Figure 6, Figure 7 and Figure 8 display the sensitivity analysis of the SWE, showcasing the sensitivity rankings and positive (negative) correlations of different meteorological factors, providing important insights for further discussion.

From Figure 6, it can be seen that Rhu is ranked higher in terms of sensitivity compared to the Pre. High-humidity environments reduce evaporation losses and help maintain snow cover, thereby increasing the SWE [78]. Conversely, low humidity accelerates the sublimation and evaporation of snow, leading to a significant reduction in the SWE. Particularly in high-altitude or cold regions, high humidity is typically accompanied by lower radiative evaporation demands, a phenomenon that is especially pronounced. Additionally, the relative humidity not only directly impacts the SWE by reducing evaporation but may also enhance its importance through interactions with other variables, such as temperature and radiation. In contrast, although precipitation has a direct contribution to the SWE, its sensitivity ranking may be lower due to the data distribution, time scale, or complexity of variable interactions in the model.

According to Figure 7 and Figure 8e, the Ssd has a significant positive impact on the SWE [79]. From a physical mechanism perspective, a longer sunshine durations mean that the snow surface absorbs more solar radiation energy, accelerating snowmelt. This melting process increases the surface SWE in a short time. Additionally, under low-temperature conditions, an increased sunshine duration may raise both surface and atmospheric temperatures, altering precipitation forms, such as converting solid precipitation (snow) into liquid precipitation (rain), further increasing the SWE. The interaction between the sunshine duration and Tm also significantly influences SWE. Under lower temperature conditions, increased sunshine duration has a more pronounced effect on snowmelt, while under higher temperature conditions, its effect is more apparent in changes in precipitation forms. These interaction effects are clearly presented in the SHAP dependence plots, showing the variation of SHAP values under different sunshine durations.

In conclusion, the relative humidity and sunshine duration not only have direct effects on the SWE but also amplify their influence through interactions with other key factors, such as temperature. These results provide important insights for understanding the mechanisms behind SWE variations and improving forecasting models.

5.3. Advantages Compared to Other Snow Water Equivalent Models

The snow water equivalent prediction method proposed in this study has the following three main advantages compared to some of the existing models [80,81]. First, nine machine learning models were selected and comprehensively evaluated, providing multiple model options and offering valuable references for related research [82]. Second, based on the prediction results of these models, an ensemble forecasting method was applied [71,77]. By combining the predictions of multiple models, a more reliable forecast range for snow water equivalent can be provided, better supporting early warning and prevention measures under uncertainties. Finally, the study introduced a rolling prediction method, where the snow water equivalent value at the initial time was assimilated into the model with each prediction, thereby continuously improving the accuracy of the model [83].

5.4. Model Future Improvement

This study used CN05.1 meteorological data and AMSR remote sensing SWE data for model training. In real-time forecasting, future SWE predictions for the next 30 days could be made by combining weather forecast data from climate forecasting agencies, such as the European Centre for Medium-Range Weather Forecasts (ECMWF) [84], which includes variables such as the temperature, precipitation, relative humidity, sunshine duration, and wind speed.

Although the model demonstrated high accuracy during lead times, the simulation accuracy still needs to be improved during periods of rapid SWE changes. Traditional machine learning models lack the ability to deeply model temporal dependencies in time series data. Additionally, some key surface factors, such as terrain variations, land use, and soil moisture, were not included in the models, which may have contributed to the prediction errors. Future research studies could be improved in the following ways:

(1)

Introduce time series modeling methods (e.g., LSTM or transformer) [85] to better capture the temporal dynamics of snowmelt processes;

(2)

Combine multi-model ensemble techniques to integrate the advantages of linear and nonlinear models to enhance the prediction accuracy and robustness;

(3)

Further expand the input features, such as the initial snow conditions, surface evaporation, and soil moisture, to improve the model’s explanatory power for SWE variation mechanisms.

These improvements could provide a more solid theoretical foundation for accurately forecasting the SWE during the snowmelt period in high-altitude regions.

6. Conclusions

This study focused on the variation characteristics of the SWE in high-altitude regions, and predicted and analyzed the future 30-day SWE using nine machine learning models. Based on a model performance evaluation and sensitivity analysis, the following conclusions were drawn:

(1)

Nine machine learning models were selected for predicting the future 30-day SWE: linear regression, decision trees, random forest, SVR, ANN, AdaBoost, XGBoost, GBDT, and CatBoost. From the results of the single-day predictions, all nine models demonstrated average NSE values greater than 0.8, average RMSE values less than 8 mm, and average RE values less than 7% during the 1–10 day, 11–20 day, and 21–30 day lead times. Among these, the CatBoost, ANN, and GBDT models performed well across the three lead times (1–10 days, 11–20 days, 21–30 days) and three evaluation metrics (RMSE, NSE, RE), showing excellent trend capture ability and low error values.

(2)

The results showed that the ensemble mean model (a fusion of the CatBoost, ANN, and GBDT models) was able to capture the SWE trend effectively for each forecast start date, especially during key periods (such as the spring snowmelt season), demonstrating strong trend simulation capabilities. Compared to the individual models, the ensemble mean model significantly reduced the error impacts of individual models, producing more robust and accurate predictions. This fusion method is adept at handling the nonlinear characteristics of climate variations in high-altitude regions, providing stable predictions for continuous SWE data over the next 30 days.

(3)

The sensitivity analysis revealed that the variation in the SWE is highly sensitive to meteorological factors. Among these, Tm, Tmin, and Tmax are the most significant drivers of the SWE, with a negative impact on the SWE. On the other hand, Rhu has a positive regulating effect on the SWE; high humidity reduces snow evaporation losses, thereby increasing SWE. Furthermore, Ssd and Win have lower sensitivity, although under specific conditions (such as high-radiation or low-temperature environments) they may still influence SWE. The interactions among these factors were well reflected in the model predictions, providing important insights into the mechanisms driving SWE variation.