This study evaluates standalone and hybrid soft computing models for predicting dissolved oxygen (DO) concentration by utilizing different water quality parameters. In the first stage, two standalone soft computing models, including multilayer perceptron (MLP) neural network and cascade correlation neural network (CCNN), were proposed for estimating the DO concentration in the St. Johns River, Florida, USA. The DO concentration and water quality parameters (e.g., chloride (Cl), nitrogen oxides (NOx), total dissolved solid (TDS), potential of hydrogen (pH), and water temperature (WT)) were used for developing the standalone models by defining six combinations of input parameters. Results were evaluated using five performance criteria metrics. Overall results revealed that the CCNN model with input combination III (CCNN-III) provided the most accurate predictions of DO concentration values (root mean square error (RMSE) = 1.261 mg/L, Nash-Sutcliffe coefficient (NSE) = 0.736, Willmott’s index of agreement (WI) = 0.919, R² = 0.801, and mean absolute error (MAE) = 0.989 mg/L) for the standalone model category. In the second stage, two decomposition approaches, including discrete wavelet transform (DWT) and variational mode decomposition (VMD), were employed to improve the accuracy of DO concentration using the MLP and CCNN models with input combination III (e.g., DWT-MLP-III, DWT-CCNN-III, VMD-MLP-III, and VMD-CCNN-III). From the results, the DWT-MLP-III and VMD-MLP-III models provided better accuracy than the standalone models (e.g., MLP-III and CCNN-III). Comparison of the best hybrid soft computing models showed that the VMD-MLP-III model with 4 intrinsic mode functions (IMFs) and 10 quadratic penalty factor (VMD-MLP-III (K = 4 and α = 10)) model yielded slightly better performance than the DWT-MLP-III with Daubechies-6 (D6) and Symmlet-6 (S6) (DWT-MLP-III (D6 and S6)) models. Unfortunately, the DWT-CCNN-III and VMD-CCNN-III models did not improve the performance of the CCNN-III model. It was found that the CCNN-III model cannot be used to apply the hybrid soft computing modeling for prediction of the DO concentration. Graphical comparisons (e.g., Taylor diagram and violin plot) were also utilized to examine the similarity between the observed and predicted DO concentration values. The DWT-MLP-III and VMD-MLP-III models can be an alternative tool for accurate prediction of the DO concentration values.

Accurate modeling for nonlinear and nonstationary rainfall-runoff processes is essential for performing hydrologic practices effectively. This paper proposes two hybrid machine learning models (MLMs) coupled with variational mode decomposition (VMD) to enhance the accuracy for daily rainfall-runoff modeling. These hybrid MLMs consist of VMD-based extreme learning machine (VMD-ELM) and VMD-based least squares support vector regression (VMD-LSSVR). The VMD is employed to decompose original input and target time series into sub-time series called intrinsic mode functions (IMFs). The ELM and LSSVR models are selected for developing daily rainfall-runoff models utilizing the IMFs as inputs. The performances of VMD-ELM and VMD-LSSVR models are evaluated utilizing efficiency and effectiveness indices. Their performances are also compared with those of VMD-based artificial neural network (VMD-ANN), discrete wavelet transform (DWT)-based MLMs (DWT-ELM, DWT-LSSVR, and DWT-ANN) and single MLMs (ELM, LSSVR, and ANN). As a result, the VMD-based MLMs provide better accuracy compared with the single MLMs and yield slightly better performance than the DWT-based MLMs. Among all models, the VMD-ELM and VMD-LSSVR models achieve the best performance in daily rainfall-runoff modeling with respect to efficiency and effectiveness. Therefore, the VMD-ELM and VMD-LSSVR models can be an alternative tool for reliable and accurate daily rainfall-runoff modeling.

This paper proposes a river stage modeling approach combining maximal overlap discrete wavelet transform (MODWT), support vector machines (SVMs) and genetic algorithm (GA). The MODWT decomposes original river stage time series into sub-time series (detail and approximation components). The SVM computes daily river stage values using the decomposed sub-time series. The GA searches for the optimal hyperparameters of SVM. The performance of MODWT–SVM models is evaluated using efficiency and effectiveness indices; and compared with that of a single model (multilayer perceptron (MLP) and SVM), discrete wavelet transform (DWT)-based models (DWT–MLP and DWT–SVM) and MODWT–MLP models. The conjunction of MODWT, SVM and GA improves the performance of the SVM model and outperforms the single models. The MODWT–based models using the SVM model enhance model performance and accuracy compared to those of using MLP model. Also, hybrid models coupling MODWT, SVM and GA improve model performance and accuracy in daily river stage modeling as compared with those combined with DWT. The MODWT–SVM model using the Coiflet 12 (c12) mother wavelet, MODWT–SVM-c12, produces the best efficiency and effectiveness among all models. Therefore, the conjunction of MODWT, SVM and GA can be an efficient and effective approach for modeling daily river stages.