Hydrodynamics of river-channel confluence: toward modeling separation zone using GEP, MARS, M5 Tree and DENFIS techniques

Abstract

Hydrodynamics of confluence as a natural component in river-channel networks is complicated. Having sufficient knowledge about erosion and sedimentation in the river-channel confluences requires determination of the separation zone dimensions. In this paper, we estimated dimension of separation zone (i.e. length and width) by utilizing data driven techniques: gene expression programming (GEP), M5 Tree model, multivariate adaptive regression spline (MARS), and dynamic evolving neural-fuzzy inference system (DENFIS) trained with hydraulics input variables including discharge ratio (Qr), downstream Froude number (Fr3), and side slope angle of main channel ( $$\sin \,\theta$$ ). Different splitting scenarios, 50–50%, 60–40% and 75–25%, for train-test parts after randomizing, were considered achieving more robust evaluation of the models. The estimated dimensionless length and width (i.e. $$\frac{L}{{B_{3} }}$$ and $$\frac{H}{{B_{3} }}$$ ) were compared with experimental results. In order to measure the accuracy of various models, different statistical criteria including root mean square error (RMSE), Nash–Sutcliffe model efficiency coefficient (NS), correlation coefficient (R), mean absolute error, Legates and McCabe index and Willmott Index of Agreement have been used. For 50–50% train-test scenario, there is a slight difference among the DENFIS, MARS and M5 Tree models while the GEP has the worst accuracy in estimating length of separation zone. The results indicated that by increasing the percentage of training data (i.e. from 50 to 75%), the accuracy of models in term of RMSE was improved as 22, 12, 14, and 15% for the DENFIS, GEP, M5 Tree and MARS models, respectively. Regarding estimation of separation zone width, adding $$\sin \,\theta$$ variable as input considerably increases the models’ performances. The results revealed that M5 Tree is more sensitive to data number in training phase.