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Modeling surface water quality using soft computing techniques is essential for the effective management of scarce water resources and environmental protection. The development of accurate predictive models with significant input parameters and inconsistent datasets is still a challenge. Therefore, further research is needed to improve the performance of the predictive models. This study presents a methodology for dataset pre-processing and input optimization for reducing the modeling complexity. The objective of this study was achieved by employing a two-sided detection approach for outlier removal and an exhaustive search method for selecting essential modeling inputs. Thereafter, the adaptive neuro-fuzzy inference system (ANFIS) was applied for modeling electrical conductivity (EC) and total dissolved solids (TDS) in the upper Indus River. A larger dataset of a 30-year historical period, measured monthly, was utilized in the modeling process. The prediction capacity of the developed models was estimated by statistical assessment indicators. Moreover, the 10-fold cross-validation method was carried out to address the modeling overfitting issue. The results of the input optimization indicate that Ca2+, Na+, and Cl− are the most relevant inputs to be used for EC. Meanwhile, Mg2+, HCO3−, and SO42− were selected to model TDS levels. The optimum ANFIS models for the EC and TDS data showed R values of 0.91 and 0.92, and the root mean squared error (RMSE) results of 30.6 µS/cm and 16.7 ppm, respectively. The optimum ANFIS structure comprises a hybrid training algorithm with 27 fuzzy rules of triangular fuzzy membership functions for EC and a Gaussian curve for TDS modeling, respectively. Evidently, the outcome of the present study reveals that the ANFIS modeling, aided with data pre-processing and input optimization, is a suitable technique for simulating the quality of surface water. It could be an effective approach in minimizing modeling complexity and elaborating proper management and mitigation measures.

Water pollution is an increasing global issue that societies are facing and is threating human health, ecosystem functions and agriculture production. The distinguished features of artificial intelligence (AI) based modeling can deliver a deep insight pertaining to rising water quality concerns. The current study investigates the predictive performance of gene expression programming (GEP), artificial neural network (ANN) and linear regression model (LRM) for modeling monthly total dissolved solids (TDS) and specific conductivity (EC) in the upper Indus River at two outlet stations. In total, 30 years of historical water quality data, comprising 360 TDS and EC monthly records, were used for models training and testing. Based on a significant correlation, the TDS and EC modeling were correlated with seven input parameters. Results were evaluated using various performance measure indicators, error assessment and external criteria. The simulated outcome of the models indicated a strong association with actual data where the correlation coefficient above 0.9 was observed for both TDS and EC. Both the GEP and ANN models remained the reliable techniques in predicting TDS and EC. The formulated GEP mathematical equations depict its novelty as compared to ANN and LRM. The results of sensitivity analysis indicated the increasing trend of input variables affecting TDS as HCO3− (22.33%) > Cl− (21.66%) > Mg2+ (16.98%) > Na+ (14.55%) > Ca2+ (12.92%) > SO42− (11.55%) > pH (0%), while, in the case of EC, it followed the trend as HCO3− (42.36%) > SO42−(25.63%) > Ca2+ (13.59%) > Cl− (12.8%) > Na+ (5.01%) > pH (0.61%) > Mg2+ (0%). The parametric analysis revealed that models have incorporated the effect of all the input parameters in the modeling process. The external assessment criteria confirmed the generalized outcome and robustness of the proposed approaches. Conclusively, the outcomes of this study demonstrated that the formulation of AI based models are cost effective and helpful for river water quality assessment, management and policy making.

The capillary length (λs) and time (ts) are dynamic scalars that emerge routinely in the infiltration problem when gravitational and pressure gradients forces are involved. During drainage, however, capillary gradients oppose gravity and retain soil moisture close to surface. In this case, the pull of capillary gradients increases with drainage time and offsets gravity resulting in a quasi‐hydrostatic pressure distribution and negligibly small drainage flux in the profile. In this paper, it is proposed to anchor the dynamic concept of field capacity—the attainment of a small negligible drainage flux—in the physics of soil moisture redistribution as influenced by gravity and capillary forces. Similar to infiltration, this dynamic approach grounds the concept of field capacity in soil hydrology and allows its estimation from readily measured intrinsic physical characteristics such as λs, ts, and Ks. Finally, we exploit an analytical solution by Broadbridge and White (1988, https://doi.org/10.1029/WR024i001p00145) to track the drainage front as soil water redistributes in an initially saturated soil profile. While initially large, the downward migrating drainage front decelerates with time reaching near steady state condition at t ≈ 1,000ts. Quasi‐hydrostatic pressure matric head and water content profiles develop above the drainage front.