Forecasting runoff using statistical methods, artificial intelligence, and meteorological models (case study: Amirkabir Dam)

Introduction
The runoff generation in a watershed is mainly influenced by the hydrological, geomorphological, and climatic conditions of the region. Regarding rainfall-runoff models, the problem becomes very complicated due to the non-linear response of the watershed to the rain event. Prediction of daily river flow is one of the most important hydrological issues, which is very important for flood management. River flow rates can be estimated by several methods, each of which has strengths and weaknesses. Regarding rainfall-runoff models, the problem becomes very complicated due to the non-linear reaction of a watershed to the rain event. In addition, due to the spatial changes of precipitation in an area, this complexity increases. In this research, the rainfall and runoff model is analyzed with the help of statistical methods and multivariate regression. The purpose of this study predict the inflow to Amirkabir Dam using multivariate regression methods and artificial intelligence (AI) methods, including the network model. It is an artificial neural network (ANN).
 
Materials and Methods
To investigate the relationship between rainfall and runoff and to estimate the water entering the dam due to the rainfall upstream of the watershed, the rainfall of all the stations of the watershed upstream was received. The 7-year statistics of Karaj river flow (2016-2022) were used. After checking the rainfall data of the upstream stations, the homogeneity of the data was checked and the stations that had a suitable correlation in terms of climate were selected. At this stage, stations with appropriate conditions were selected by using factor analysis between upstream precipitation and runoff and water entering the dam downstream of the watershed. Then, to more properly analyze the relationship between rainfall and runoff, two-day and three-day cumulative rainfall at the selected stations was calculated. Then, the relationship between rainfall and runoff to the dam was investigated using statistical methods of multivariable regression and artificial intelligence. To get more accurate results, different seasons of the year were divided and the relationship between rainfall and runoff entering the dam in different seasons was investigated. Error statistics were calculated for calibration and verification during the test and training period. Finally, the final analysis of the data and the prediction of the runoff entering the dam was estimated using the upstream rainfall.
 
Results and Discussion
Determining the effective stations in the runoff generation entering the dam as well as the delay time of their precipitation was achieved using multivariable regression and four stations of Nesa, Sira, Shahristanak, and Amirkabir Dam., the model of the volume of inflow to the dam, and precipitation in the catchment area of Amirkabir Dam. The coefficient of determination (R²) of the calibrated model was calculated as 76%, which is an acceptable coefficient in the relationship between precipitation and runoff. Based on the calibration and validation models of rainfall-runoff evaluation of rainfall forecasting models in July 2022, good rains are predicted for the watershed of Amir Kabir Dam. The rain system entered the country on July 28^th and 29^th and until July 31^th it had relatively good coverage in the whole country, and on August 1^st and 2^nd this system weakened and only operates in limited parts of the country such as the Amir Kabir watershed. The results of evaluating the performance of the models with indicators such as coefficient of explanation (R²), mean absolute value of error (MAE), and root mean square error (RMSE) showed that the ANN model in both calibration (training) and validation (testing) stages ) has performed better than the multivariate regression model. The accuracy indices of the model for the ANN model training stage were equal to R²=0.77 and RMSE=0.27 m³ s^-1, while these indices for the testing stage were equal to R²=0.87 and RMSE=0.46 m³ s^-1. It indicates the better performance of the ANN model.
 
Conclusion
The research results of this article showed that due to the presence of 5 rain gauge stations in the catchment area of Amir Kabir Dam, all the stations can not have the same effect on the water entering the dam. Using the cluster cluster method, the effect of all the stations on the inflow to Amirkabir Dam was investigated and suitable rain gauge stations were selected. Also, the results showed that the relationship between the rainfall of the watershed and the runoff entering the Amirkabir dam is different in different seasons and it has the highest correlation in the winter season because it is less affected by other factors affecting the runoff of the basin, including water from melting snow or thunderstorms. One of the other results of this study was that the calibrated and validated model had a slightly higher yield in the three seasons of winter, spring, and autumn, and a slightly lower yield in the autumn season.