Introduction:
The water crisis has become one of the fundamental challenges of the modern era, exacerbated by factors such as population growth, climate change, and uneven rainfall distribution. Iran, with its arid and semi-arid climate, faces significant limitations in water resource management, which impacts agriculture and the economy. Accurate runoff prediction is essential for sustainable water resource management and the design of water infrastructures. However, the complexity of nonlinear relationships and irregular flow distributions makes runoff prediction challenging. Various approaches, including physical, conceptual, and data-driven models, have been proposed. Data-driven models, leveraging machine learning, are particularly notable for their ability to analyze large datasets and uncover hidden patterns. Despite challenges (such as selecting suitable algorithms, determining effective inputs, and evaluating estimation accuracy), these models have been widely applied in hydrology. The aim of this research was to improve monthly runoff prediction in Mashhad basin by utilizing advanced machine learning approaches. In this regard, Variable Mode Decomposition (VMD) was employed as a data preprocessing method, and the Whale Optimization Algorithm (WOA) was used to enhance model accuracy. These methods were applied with the goal of achieving more accurate and efficient predictions in this field.
Methods:
The study area of Mashhad basin, located in Khorasan Razavi Province, is bordered by Hezar Masjid heights to the north and the Binalod heights to the south, with the longitudes of 59˚30' to 59˚42' East and the latitudes of 36˚12' to 36˚24' North. Meteorological and hydrometric data were provided for four stations (Ardak Band, Zoshk, Alang asadi and Kartian), from 1968 to 2022. The stationarity and stability of the time series for rainfall, evaporation, temperature, and discharge were first analyzed. Two distinct modeling approaches were employed to estimate runoff for the future month. In the first approach, three different combinations of parameters were used as model inputs. In the first scenario, all parameters with a three-month lag, determined based on the correlation coefficient of rainfall, temperature, evaporation, and discharge, were utilized. For the second scenario, after conducting sensitivity analysis on the first scenario, seven of the most influential parameters were selected. In the third scenario, the effect of using discharge with a three-month lag as the sole model input was evaluated. The Support Vector Machine (SVM) model and Long Short-Term Memory (LSTM) neural network, both in their basic and optimized forms, were applied to the data from each of the four studied stations. The accuracy of the developed models was assessed using statistical indices, including the Nash–Sutcliffe Efficiency (NSE), Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and Normalized Root Mean Square Error (NRMSE). In the second approach, the Variational Mode Decomposition (VMD) technique and the Whale Optimization Algorithm (WOA) were employed. Using this approach, the discharge time series was decomposed into several sub-series, each of which, with a three-month lag, was used as an input to both the basic and optimized SVM and LSTM models. Finally, the performance of the developed models was evaluated during the training and testing phases.
 Results
This study aimed to evaluate the performance of VMD-WOA-SVM-WOA hybrid model for runoff estimation at four stations within Mashhad study basin. In this study, two different approaches for modeling runoff were investigated. In the first method, data preprocessing was performed using normalization, the optimized LSTM and SVR models performed better than the base models; however, due to the structural complexity of the hydrological data, the models' ability to identify accurate patterns and estimate runoff was limited. In the second method, data preprocessing was performed using Variable Mode Decomposition. This technique allowed for the extraction of more accurate features by separating hydrological data into components with different frequencies. The primary approach involved using the Variational Mode Decomposition (VMD) method to decompose the runoff time series into modes and optimize their frequencies with the Whale Optimization Algorithm (WOA). These modes were then used as inputs to the Support Vector Machine (SVM) model to estimate runoff for the future month. To assess the proposed model, its performance was compared with a simple SVM model using different input configurations. The results demonstrated that the VMD-WOA-SVM-WOA model achieved mean RMSE and Nash–Sutcliffe 0.185 and 0.979, respectively, with the minimum input variables. These findings align with the principles of regression modeling, emphasizing simplicity and avoiding unnecessary complexity. Furthermore, the results confirmed that increasing the number of input variables does not necessarily enhance estimation accuracy and can even introduce noise and reduce the model's generalizability. This research showed that by employing data preprocessing (VMD) and optimizing model parameters with WOA, a simple, accurate, and interpretable model can be developed. Additionally, the proposed model is not only effective for runoff estimation but also has the potential to be applied to similar studies of hydrological processes such as evapotranspiration and sediment modeling in different regions.
 Conclusion:
This study investigated two approaches for runoff modeling. The first approach used data normalization and application of optimized LSTM and SVR models, which showed some improvement compared to base models. However, due to the complexity of hydrological data, the models demonstrated limited accuracy, and the overall performance based on low Nash–Sutcliffe values was not satisfactory. The second approach employed for processing, was Variational Mode Decomposition (VMD), which allowed better extraction of temporal features. With parameter optimization using the Whale Optimization Algorithm (WOA), the VMD-WOA-SVR-WOA model achieved significantly better accuracy and generalization. While VMD-WOA-LSTM also performed well, the superior results of VMD-WOA-SVR-WOA model highlighted it as an effective tool for runoff prediction and water resource management.