The three-dimensional structure of water flow at river confluences makes these zones of particular importance in the fields of river engineering, fluvial geomorphology, sedimentology and navigation. While previous research has concentrated on the effects of hydraulic and geometric parameters on the scour patterns at river confluences, there remains a lack of expert systems designed to predict the maximum scour depth (d sm ). In the present study, several soft computing models, namely multi-layer perceptron (MLP), radial basis function (RBF) and M5P model tree, were used to predict the d sm at river confluences under live-bed conditions. Model performance, assessed through a number of statistical indices (RMSE, MAE, MARE and R 2), showed that while all three models could provide acceptable predictions of d sm under live-bed conditions, the MLP model was the most accurate. By testing the models at three different ranges of scour depths, we determined that while the MLP model was the most accurate model in the low scour depth range, the RBF model was more accurate in the higher range of scour depths. adaptive neuro-fuzzy inference system artificial neural network depth of flow downstream from confluence (m) scour depth (m) maximum scour depth (m) maximum scour depth ratio (=d sm/w d ) median size of river bed material (m) densimetric Froude number feed-forward back propagation network gravitational acceleration (ms−2) specific gravity mean absolute error mean absolute relative error multi-layer perceptron, a type of ANN. a tree type model is the number of observations in the measured or predicted data set the ith observed value the ith model-predicted value number of observation data inputs in RBF model live-bed discharge (≡ sediment load) (m3 s−1) water discharge in channel downstream from confluence (m3 s−1) water discharge in main channel upstream of confluence (m3 s−1) water discharge of the tributary upstream of confluence (m3 s−1) ratio of live bed sediment discharge to discharge in channel downstream from confluence ratio of tributary discharge to main branch discharge linear correlation coefficient between measured and estimated d sm Reynolds number radial basis function, a type of ANN root mean square error channel bed slope set of examples in a model tree center of the jth radial basis function f in a RBF function river flow velocity (ms−1) river flow velocity downstream from confluence (ms−1) width of channel downstream from confluence (m) is the weight of the connection between the jth neuron in a layer with the ith neuron in the previous layer of an ANN width of main channel upstream of confluence (m) is the weight of the connection between the hidden and output nodes in a RBF network width of tributary channel upstream of confluence (m) ratio of tributary channel width to channel width below the confluence Weber number is the value of the ith neuron in the previous layer of an ANN is the output from the jth neuron in a given layer of an ANN bed elevation difference (m) the network output in RBF model flow viscosity (kgm−1 s−1) density of sediment (kgm−3) tributary-main branch confluence angle (°) force of surface tension (kgs−2) the size of the radius around the RBF center (U j ) the standard deviation of the reduction in M5P model tree 
Development of expert systems for the prediction of scour depth under live-bed conditions at river confluences: Application of different types of ANNs and the M5P model tree