In the present study, six meta-heuristic schemes are hybridized with artificial neural network (ANN), adaptive neuro-fuzzy interface system (ANFIS), and support vector machine (SVM), to predict monthly groundwater level (GWL), evaluate uncertainty analysis of predictions and spatial variation analysis. The six schemes, including grasshopper optimization algorithm (GOA), cat swarm optimization (CSO), weed algorithm (WA), genetic algorithm (GA), krill algorithm (KA), and particle swarm optimization (PSO), were used to hybridize for improving the performance of ANN, SVM, and ANFIS models. Groundwater level (GWL) data of Ardebil plain (Iran) for a period of 144 months were selected to evaluate the hybrid models. The pre-processing technique of principal component analysis (PCA) was applied to reduce input combinations from monthly time series up to 12-month prediction intervals. The results showed that the ANFIS-GOA was superior to the other hybrid models for predicting GWL in the first piezometer (RMSE:1.21, MAE:0.878, NSE:0.93, PBIAS:0.15, R²:0.93), second piezometer (RMSE:1.22, MAE:0.881, NSE:0.92, PBIAS:0.17, R²:0.94), and third piezometer (RMSE:1.23, MAE:0.911, NSE:0.91, PBIAS:0.19, R²:0.94) in the testing stage. The performance of hybrid models with optimization algorithms was far better than that of classical ANN, ANFIS, and SVM models without hybridization. The percent of improvements in the ANFIS-GOA versus standalone ANFIS in piezometer 10 were 14.4%, 3%, 17.8%, and 181% for RMSE, MAE, NSE, and PBIAS in training stage and 40.7%, 55%, 25%, and 132% in testing stage, respectively. The improvements for piezometer 6 in train step were 15%, 4%, 13%, and 208% and in test step were 33%, 44.6%, 16.3%, and 173%, respectively, that clearly confirm the superiority of developed hybridization schemes in GWL modelling. Uncertainty analysis showed that ANFIS-GOA and SVM had, respectively, the best and worst performances among other models. In general, GOA enhanced the accuracy of the ANFIS, ANN, and SVM models.

The determination of scour characteristics in the downstream of sluice gate is highly important for designing and protection of hydraulic structure. The applicability of modern data-intelligence technique known as extreme learning machine (ELM) to simulate scour characteristics has been examined in this study. Three major characteristics of scour hole in the downstream of a sluice gate, namely the length of scour hole (Ls), the maximum scour depth (Ds), and the position of maximum scour depth (Lsm), are modeled using different properties of the flow and bed material. The obtained results using ELM were compared with multivariate adaptive regression spline (MARS). The dimensional analysis technique was used to reduce the number of input variable to a smaller number of dimensionless groups and both the dimensional and non-dimensional variables were used to model the scour characteristics. The prediction performances of the developed models were examined using several statistical metrics. The results revealed that ELM can predict scour properties with much higher accuracy compared to MARS. The errors in prediction can be reduced in the range of 79%–81% using ELM models compared to MARS models. Better performance of the models was observed when dimensional variables were used as input. The result indicates that the use of ELM with non-dimensional data can provide high accuracy in modeling complex hydrological problems.