Bivariate simulation of river flow using hybrid intelligent models in sub-basins of Lake Urmia, Iran

In this study, the performance of continuous autoregressive moving average (CARMA), CARMA-generalized autoregressive conditional heteroscedasticity (CARMA-GARCH), random forest, support vector regression and ant colony optimization (SVR-ACO), and support vector regression and ant lion optimizer (SVR-ALO) models in bivariate simulating of discharge based on the rainfall variables in monthly time scale was evaluated over four sub-basins of Lake Urmia, located in northwestern Iran. The models were assessed in two stages: train and test. The results showed that the CARMA-GARCH hybrid model offered better performance in all cases than the stand-alone CARMA. The improvement percentages of the error rate in the CARMA model compared to the CARMA-GARCH hybrid model in the Mahabad Chai, Nazlu Chai, Siminehrood, and Zola Chai sub-basins were 9, 20, 17, and 6.4%, respectively, in the training phase. Among the models, the hybrid SVR models integrated with ACO and ALO optimization algorithms presented the best performance based on the Taylor diagram and evaluation criteria. Considering the use of ant colony and ant lion optimization algorithms to optimize the support vector regression model's parameters, these models offered the best performance in the study area to simulate the discharge. The improvement percentages of the error rate in the SVR-ACO model compared to the CARMA-GARCH hybrid model in the Mahabad Chai, Nazlu Chai, Siminehrood, and Zola Chai sub-basins were 11, 10, 19, and 21%, respectively, in the training phase. In contrast, the random forest model provided the lowest accuracy and the highest error in discharge simulation.