ABSTRACT
Today, river flow forecasting is one of the important topics in hydrology and water resources, water structures management, and flood forecasting. In this research, the performance of a combined model consisting of the slime mold optimizer algorithm and the support vector regression simulator algorithm (SVR-SMA) was evaluated in forecasting the average monthly discharge of the Volga River at the Volgograd hydrometric station during the statistical period of 1980–2020. In this research, various combinations of climatic observation data, including minimum temperature, maximum temperature, average rainfall, and sunshine hours, were used as input patterns to predict flow rate. The results obtained from this research indicate the better performance of the combined slime mold–support vector regression model, with a coefficient of determination equal to 0.80 (R² = 0.80), a root mean square error equal to 7.19 (RMSE = 7.19), and a mean absolute error equal to 0.56 (MAE = 0.56) in the validation stage for forecasting the monthly discharge of the Volga River at the Volgograd station, in comparison with genetic algorithms, artificial neural networks, and support vector regression alone. Therefore, the findings of this research indicate that the use of the slime mold algorithm together with the support vector regression algorithm has been able to improve its speed and accuracy.

1. INTRODUCTION
The Volga River is the main supplier of the Caspian Sea. It provides 90% of the water entering the Caspian Sea (Kalugin, 2022), which is of great importance for water resources and environmental studies. Therefore, predicting the discharge of the Volga River is one of the important topics of the hydrology of this basin, which needs more research and studies. The purpose of this research is to investigate the effectiveness of new solutions by combining the slime mold algorithm and support vector regression as a new model in predicting the monthly river discharge and finally comparing the results of other models and providing a suitable and accurate method.
2. MATERIALS AND METHODS
The Slime Mold Optimizer (SMA) is a new population-based meta-heuristic algorithm inspired by the intelligent behavior of a type of mold called slime mold. The mold has intelligent behavior and can perform very fast, without error. The Support Vector Machine (SVM) is an efficient learning system based on the theory of constrained optimization that uses the inductive principle of structural error minimization and leads to an overall optimal solution (Vapnik et al., 1996). Support vector machines include two categories: the support vector classifier and support vector regression. A support vector machine algorithm seeks a decision plane that separates data of different classes. In some cases, a complex and non-linear structure is needed for data separation, in which the support vector machine maps and recovers the original data in a new space by using a set of mathematical functions called kernel functions. In this research, the optimal values of hyper-parameters required by the model were obtained by trial and error. Often, data models are evaluated based on the correlation coefficient (Coefficient of Determination, R²), Root Mean Squared Error (RMSE), and Mean Absolute Error. In this study, the average daily rainfall data for 41 years from the Volgograd hydrometric station and the climate parameters of the Volgograd synoptic station were used between 1980 and 2020. From a total of 492 data points from the monthly hydrometric station and climatic parameters of the synoptic station, 369 data points were used for training and the remaining 123 data points were used for testing.
3. RESULTS
In this research, eight different models for predicting river discharge at the Volgograd hydrometric station were investigated. The evaluated models are based on the combination of parameters affecting the hydrometric station of Volgograd. The meteorological parameters used for modeling are: average monthly maximum temperature (Tmax), average monthly minimum temperature (Tmin), average monthly temperature (Tmean), average total monthly precipitation (P), and average total monthly sunshine hours (Rad). In this research, the slime mold algorithm was used as an optimization algorithm and the support vector regression algorithm was used as a simulation algorithm to predict the Volga River discharge.
4. DISCUSSION AND CONCLUSION
In this research, the performance of the combination of the slime mold optimizer and the support vector regression simulator was investigated in forecasting the monthly flow of the Volga River in the Caspian Sea catchment. In this regard, the average monthly discharge data of the Volgograd hydrometric station between 1980 and 2020 have been used. Different rainfall forecasting patterns with the influence of climatic variables were used for modeling. In the models used in this research, the best performance was related to the scenario of total rainfall, maximum and minimum temperatures, and monthly solar radiation using the RBF kernel. Also, the results of this research show that the use of the slime mold algorithm has been able to improve the speed and accuracy of the results of the support vector regression algorithm in predicting the monthly flow of the Volga River. The results of this research showed that the IHACRES model has good abilities in simulating the monthly discharge of the river, but the accuracy of data mining models was better than that of this model.
REFERENCES
Kalugin, A., 2022. Hydrological and Meteorological Variability in the Volga River Basin under Global Warming by 1.5 and 2 Degrees. Climate, 107(10), pp.1–23. Doi: 10.3390/cli10070107
Vapnik, V., Golwich, E.S. and Smola, A., 1996. Support vector method for function approximation, regression estimation and signal processing, Journal of Advances in Neural Information Processing Systems, 9, pp.281–287.