1. Introduction
Snowmelt is one of the major sources of fresh water in the world. Billions of people living in river basins originating from the snow-dominated Hindu Kush Himalayan (HKH) region, directly or indirectly rely on rivers for food, water, and electricity [
1]. In this region, the accurate prediction of snowmelt runoff is crucial for effective water resource planning and management. However, the paucity of snow monitoring networks in the HKH region, due to geographical conditions and extreme weather, leads to inadequate ground truth information available for developing strategies for optimum water resource utilization. Remotely sensed snow cover and meteorological data are invaluable assets for snowmelt runoff modeling in the data-scant mountainous watersheds.
A number of models have been developed for accurate snowmelt runoff prediction based on various approaches. These models can be broadly classified into energy balance (EB) models, temperature index (TI) models, and data-driven (DD) models. EB models work on the principle of energy and mass conservation and require a profound understanding of complex processes including net radiation and heat exchange in a snowpack [
2]. These models are computationally intensive and demand more data inputs [
3], therefore, not suitable for operational forecasting in the data-scarce mountainous region. TI models use easily available air temperature data as a proxy to energy sources involved in the snowmelt process [
4]. Therefore, TI models are simple and often used in operational forecasting, but they are not as good as sophisticated EB models [
5]. Moreover, parameters of the TI models should be approximated through calibration. The process of finding suitable model parameters is tedious and also requires sufficient knowledge of the hydrological processes as well as catchment characteristics [
6]. DD models such as machine learning (ML) can learn complex associations between inputs and outputs instantly and work with high model accuracy even without prior knowledge of the underlying processes [
7]. However, despite its advantages, the application of ML models in snowmelt modeling is still scarce.
The history of ML and its applications, especially in different domains of water resource modeling, is well investigated in previous studies [
7,
8]. The majority of the ML applications are concentrated on artificial neural networks (ANNs), however, alternative ML methods, such as decision trees, support vector machines, and Gaussian process regression are also in practice. In a study, Callegari et al. [
9] employed support vector regression (SVR) models for monthly snowmelt driven discharge forecasting in the Italian Alps using snow cover area (SCA) along with antecedent discharge and meteorological data. The SVR model predicted better than the benchmark linear autoregressive model. The applicability of SVR models in operational river discharge forecasting in Alpine catchments was further demonstrated by Gregorio et al. [
10]. In a study, Uysal et al. [
11] successfully employed a simple ANN model in the upper Euphrates basin of Turkey for one day ahead snowmelt forecasting. In the study, SCA, along with antecedent discharge, temperature, and precipitation as inputs showed excellent model efficiency (>93%). Moreover, the performance of the ANN model and the snowmelt runoff model (SRM) was compared. SRM [
12] is a popular TI model which has been successfully applied to more than 100 basins for snowmelt modeling. The outcomes of the study [
11] revealed that ANN models perform better than the widely-used SRM model.
Although traditional ANNs were very popular in the past, they were unable to retain temporal information, which is important in the case of time-series problems, such as hydrological forecasting. This drawback was solved by the recurrent neural network (RNN) [
13]. However, RNNs were also not problem-free. The primary challenges to RNNs are exploding and vanishing gradient problems. A deep learning (DL) approach, known as long short-term memory (LSTM), overcomes the issues encountered by RNNs as well as preserves the long-term temporal information of the time-series data [
14]. Due to the advancement in computer technology and the availability of remotely sensed data, DL methods are gaining popularity within the research and modeling community. Recent studies have shown great potentiality of the DL models, such as the LSTM model in rainfall-runoff modeling [
15,
16,
17,
18]. In the study by Kratzert et al. [
15], two-layered LSTM with a dense layer was employed for rainfall-runoff modeling in the contiguous US catchments and among other things, they argued that the model could also mimic the snowmelt process by learning the relationship between precipitation during winter (cold temperature) and runoff in spring (warm temperature). However, in the Himalayan basins, where there is lack of sufficient meteorological stations and even if present, precipitation gauges considerably underestimate (up to 40%) the solid precipitation in high altitude region [
19], precipitation data only may not be adequate for reproducing snow accumulation and melting process accurately. Moreover, precipitation and river discharge have no significant correlation whereas snow cover area (SCA) and river discharge are significantly correlated in the Central Himalayas [
20]. Therefore, we utilized SCA as a key input to the LSTM model for predicting snowmelt runoff accurately; however, we also used precipitation data and compared the model performance for various inputs. Furthermore, Kratzert et al. [
15] did not investigate the influence of hyperparameters (e.g., the number of LSTM layers and window size) on model performance but rather used some arbitrary values. Le et al. [
17] and Fan et al. [
16] emphasized the window size as an important hyperparameter to be tuned for best model performance, however, the effect of other hyperparameters, such as the number of LSTM layers and optimizers, were not evaluated.
This study aims to scrutinize the ability of the state-of-the-art deep learning LSTM network in modeling daily snowmelt runoff in a Himalayan basin. Furthermore, we evaluated the effect of various hyperparameters, including the number of LSTM layers and optimizers to achieve the best model performance. We developed three other ML models, namely, nonlinear autoregressive exogenous model (NARX), support vector regression (SVR), and Gaussian process regression (GPR) models and compared their performance. In this study, remotely sensed daily precipitation, temperature, and snow products along with the antecedent discharge data were used as inputs for one day ahead river discharge forecasting. The Gamma test (GT) was carried out to determine a suitable input combination for the model. The ML approach for operational river discharge forecasting will be useful in estimating water availability for reservoir management, water supply, irrigation, and hydroelectricity projects in the data-scarce mountain basins.
4. Discussion
In this study, the model efficiency (in terms of NSE) of LSTM, NARX, GPR, and SVR models were found to be 99.5%, 99.1%, 97.3%, and 97.1%, respectively. In a previous study by Pradhananga et al. [
49], a positive degree day TI model employed in the Langtang basin for river discharge prediction achieved model efficiency (in terms of NSE) up to 80%, which is much lower than that of all ML models used in this study. Moreover, the ANN model employed by Uysal et al. [
11] for 1 day ahead snowmelt runoff prediction in the Upper Euphrates Basin of Turkey achieved the model efficiency (in terms of NSE) up to 93%, which is also lower than that of ML models used in this study. In the study by Le et al. [
17], the LSTM model for rainfall-runoff modeling showed the model efficiency (in terms of NSE) up to 99.2%, which is comparable to the result of LSTM model used in this study.
Kratzert et al. [
15] employed a two-layered LSTM whereas Le et al. [
17] and Fan et al. [
16] used the single-layered LSTM, however, these studies did not evaluate the effect of the number of hidden layers on the predictive power of the LSTM model for runoff modeling. In this study, we compared the performance of the LSTM model for several hidden layers (1, 2, and 3 layers) and noticed that the LSTM layer with one hidden layer performed better than the LSTM model with multiple hidden layers. Similar to this, Kratzert et al. [
18] also reported that a single-layered stacked LSTM model performs better than two-layered stacked LSTM. From this result, we realized that a single hidden layer LSTM model is adequate, and deeper LSTM models are not essential for streamflow prediction. In their study, Le et al. [
17] used SGD optimizer whereas Fan et al. [
16] used Adam optimizer. Both studies did not evaluate the influence of optimizer on model performance. In a study by KC et al. [
35], the performance of three optimizers was compared and they found that Nadam optimizer was more accurate than SGD and Adam for plant disease detection. In this study, we compared the performance of seven optimizers (Adam, Nadam, Adamax, Adadelta, Adagrad, SGD, RMSprop) and found that Adamax optimizer is superior to other optimizers for runoff modeling.
Kratzert et al. [
15] and Kratzert et al. [
18] argued that the LSTM model could mimic snow accumulation and melting process by learning the linkage between precipitation during winter and runoff in spring. In this study, we compared the performance of the LSTM model with different input combinations (see
Table 6). It is well noticed that SCA as input gives better snowmelt runoff prediction than precipitation as input. The results achieved by the previous studies [
15,
18] were good enough but could have been better (in the case of snow-influenced catchments) if they had incorporated snow-related data in the input.
Several studies [
39,
40] used the LM algorithm for training the NARX model. We compared the performance of LM, BR, and SCG algorithms, and the results showed that the BR algorithm performs better than LM and SCG algorithms. The superiority of the BR algorithm over the LM algorithm was also shown by Guzman et al. [
38]. In a study, Alsumaiei [
39] employed the NARX model for groundwater level forecasting and the results showed the model efficiency up to 99.3%, which is comparable to the performance of the NARX model in this study.
In most of the studies employing ML models [
9,
11,
15,
16,
18], inputs were determined on an ad-hoc basis or by trial and error method. Input selection is an important task in the model development process for the DD models, however, it is often neglected. The application of GT during the initial phase of the model development process to determine the appropriate input combination reduced the workload which otherwise would have required several experiments. LSTM models used in rainfall-runoff modeling used precipitation data as a key input [
15,
16,
17,
18]. Since precipitation is the prime source of river discharge in those catchments, it is obvious to utilize rainfall as input for modeling in those cases. However, in the Himalayan basins, due to low temperature, precipitation is stored in the form of snow and therefore, does not instantly contribute to total runoff. In a study by Thapa et al. [
20], it was found that precipitation and river discharge has no significant correlation whereas SCA and river discharge are significantly correlated in the Langtang basin. From the results of sensitivity analysis, it is clear that the models are sensitive to snow cover than precipitation data in the Himalayan basins, which demonstrates the ability of ML techniques to learn the complex physical linkage between input and output.
Due to the sparsity of ground stations, it is hard to obtain ground truth observation in Himalayan basins. Even if available, the ground truth data are not representative of the whole basin due to high elevation difference, as most of the stations are located at lower elevation zones within the Himalayas. In such cases, remotely sensed SCA and meteorological products are invaluable assets for the water resource modeling. The result of this study proves the applicability of ML models in operational streamflow forecasting using remotely sensed products in the data-scant mountainous basins.
5. Conclusions
In this study, four ML models, including LSTM, NARX, SVR, and GPR models are employed for snowmelt driven streamflow prediction. Langtang basin is one of the snow-glacier dominated basins in the Himalayas, therefore, this study area was chosen for the study. The performance of models is assessed by KGE’, NSE, R2, RMSE, and MAE. The SCA extracted from MODIS snow products and remotely sensed meteorological data are utilized as inputs to the models. A suitable input combination was selected based on GT.
The LSTM model (KGE’ = 0.99, RMSE = 0.173) outperformed NARX (KGE’ = 0.974, RMSE = 0.486), GPR (KGE’ = 0.95, RMSE = 0.812), and SVR (KGE’ = 0.949, RMSE = 0.851) models. All four ML models achieved good results in discharge prediction (KGE’ > 0.94). However, NARX, GPR, and SVR models slightly underestimated the high flows. While scrutinizing the potentiality of LSTM architecture in snowmelt-runoff prediction, we found the shallow LSTM model with a single hidden layer performing better than deeper models with multiple hidden layers. Out of seven optimizers tested, Adamax was found to be the most suitable optimizer for this study. The results of the GT and sensitivity analysis revealed that the ML models were more sensitive to SCA than precipitation data in the Langtang basin. Therefore, ML models enriched with snow data are appropriate for river discharge prediction in snow-dominated basins.
This study demonstrates the successful application of the LSTM, NARX, GPR, and SVR models in predicting snowmelt driven streamflow. This approach can be easily replicated on other snow-dominated mountainous basins with diverse characteristics where sufficient past river discharge data are available. This work will be useful for estimating water availability for reservoir management, water supply, irrigation, and hydroelectricity projects in the data-scanty mountainous basins.