Predicting water sorptivity coefficient in calcareous soils using a wavelet–neural network hybrid modeling approach

Sorptivity (S) coefficient is a measure of liquid absorption/desorption tendency of a porous medium by the capillary. It is a crucial component in hydrological modeling. Since its measurement is usually time-consuming and labor-intensive, the available data sets suffer from the lack of S coefficient. Therefore, its prediction through utilizing efficient numerical approaches (e.g., artificial neural networks, ANNs) has been received increased attention. For this purpose, the wavelet neural network (WNNs) with various wavelet types and decomposition levels was employed. The results were compared to that of two well-known NNs (multilayer perceptron, MLPNNs, and radial-basis function, RBFNNs) and multiple linear regression (MLR). Input attributes consisted of electrical conductivity, pH, initial water content, bulk density, mean weight diameter, geometric mean diameter, organic matter, and calcium carbonate equivalent of a 100-total data set. The performances of the approaches were demonstrated using the field data sets. Correlation-coefficient (R), root mean square error (RMSE), mean absolute percentage error (MAPE), and Nash–Sutcliffe efficiency coefficient (NSE) for test data set were 0.87, 0.015, 8.78, and 0.752 for RBFNNs; 0.92, 0.009, 7.19, and 0.798 for MLPNNs; 0.94, 0.005, 6.28, and 0.846 for WNNs, and 0.85, 0.097, 12.70, and 0.515 for MLR, respectively. The WNNs and in particular the ‘sym2′ wavelet function with decomposition level three was able to achieve accurate estimates. The NN models were ranked as RBF > MLP > WNN; WNN > MLP > RBF; MLP > WNN > RBF in terms of easy usability, accuracy and computational time, and cost-effectiveness, respectively. Regarding the predictions obtained, it can be concluded that the applied WNN model is a more efficient tool than the other models to predict S coefficient.