Modeling surface water-groundwater interactions using numerical-soft computing simulation: an integrated approach

Effective water resource management requires a comprehensive understanding of hydrological processes, particularly the interactions between surface water and groundwater systems. In the Astaneh-Kouchesfahan region of northern Iran, strong hydraulic connections exist between rivers and aquifers, making it an ideal case for integrated modeling. This study proposes an innovative hybrid approach that combines numerical and soft computing techniques to simulate surface water–groundwater (SW–GW) interactions. First, the Soil and Water Assessment Tool (SWAT) model was employed to simulate surface hydrology and estimate aquifer recharge from rivers. The estimated recharge was then coupled with a groundwater model developed using MODFLOW to simulate subsurface flow and quantify river–aquifer exchanges. In the third stage, several machine learning models, including Gaussian Process Regression (GPR), Least Squares Support Vector Regression (LSSVR), Adaptive Neuro-Fuzzy Inference System (ANFIS), ANFIS-PSO, and ANFIS-RSA, were applied to predict the magnitude of SW–GW interactions using input variables such as topography, groundwater level, surface recharge, river leakage, riverbed properties, and river stage. The results demonstrated that SWAT provided reliable recharge estimates for groundwater modeling, while MODFLOW revealed stronger river–aquifer exchanges in the southern part of the basin, where rivers predominantly recharge the aquifer. Conversely, in much of the northern region, the aquifer discharged to rivers. Among the machine learning models, LSSVR achieved the best performance (RMSE = 2748.6 m3/month, MAE = 1884.1 m3/month, NRMSE = 0.36, NSE = 0.87). Although the standalone ANFIS model showed limited accuracy, its performance was significantly improved when optimized with RSA and PSO algorithms. Moreover, the extent of SW–GW interactions in a given cell was strongly influenced by the interactions in adjacent cells and by surface recharge. Overall, the proposed integrated numerical–soft computing framework offers a cost-effective and accurate tool for modeling surface water–groundwater interactions and can be effectively applied to similar hydrological systems.