Evaluating the performance of artificial intelligence models in predicting monthly runoff in Karkheh basin using SISO and MISO models

Predicting runoff is a crucial aspect of preventing floods and droughts, safeguarding reservoirs, and managing water resources. The exceptional accuracy of artificial intelligence models in predicting hydrological parameters has attracted considerable attention from researchers. Consequently, this study employed Support Vector Machine models optimized by Simulated Annealing (SVM-SA) and Particle Swarm Optimization algorithms (SVM-PSO), as well as Linear Regression (LR) and Multiple Linear Regression (MLR) models utilizing Single Input-Single Output (SISO) and Multiple Input-Single Output (MISO) patterns to predict monthly runoff at 25 hydrometric stations in the Karkheh basin, located in Iran. For this purpose, the statistical data were divided into 80% calibration and 20% validation. The statistical analysis of the results utilized the coefficient of determination (R²), Standard Error (SE), and Root Mean Square Error (RMSE), Nash–Sutcliffe Efficiency (NSE), Kling Gupta Efficiency (KGE), and Percent Bias (PBIAS) as indicators. Among the SISO models assessed, the LR model demonstrated the most favorable performance, achieving an average Standard Error of 0.41, a R² and NSE of 0.87, a PBIAS close to zero, and a KGE of 0.90. These metrics indicate a robust capability to replicate monthly runoff patterns effectively. The SVM-PSO and SVM-SA models also exhibited commendable performance, with SE values ranging from approximately 0.41 to 0.42 and NSE values between 0.87 and 0.88. The KGE scores for these models were 0.88 and 0.87, respectively. It is noteworthy that SVM-SA exhibited narrower prediction intervals and lower sensitivity, as indicated by an Average Relative Interval Length (ARIL) of 0.07, whereas SVM-PSO produced wider prediction intervals with an ARIL of 2.16. In the MISO configuration, the MLR model outperformed all other models, recording the lowest SE of 0.39, a PBIAS of 0, a KGE of 0.90, and the most compact ARIL of 0.03. These results reflect high accuracy, stability, and reliability in predicting monthly runoff. The SVM-SA model demonstrated balanced performance with a higher KGE of 0.93, while the SVM-PSO model displayed a lower KGE of 0.88 and broader uncertainty coverage, albeit with wider prediction intervals (ARIL = 2.46). The SVM-PSO model provided broader uncertainty coverage but at the expense of wider intervals, while the SVM-SA model showed moderate performance with acceptable sensitivity and prediction accuracy. Overall, the MLR model under the MISO structure proved to be the most effective approach for monthly runoff prediction due to its combination of high predictive accuracy, computational simplicity, stable sensitivity profile, and reliable uncertainty quantification.