The definition of the formulas (5)–(8) variables is So (stream-flow observed records), Sp (stream-flow predicted records). So and Sp are the mean values. N is the number of the data set. It is even worth to brief the formation structure of the modeling before proceeding with the discussion of the results. Since neural networks topology affects the complexity of the computational models and most importantly the level of the accuracies. Remarkably, RBFNN algorithm has been observed to be quite simple compared with the others (i.e. FFNN or MLP). The most significant parameters that should be obtained (as described in Sect. 2) are the spread values and the number of radial basis function. The spread values and the number of RBF are achieved by using trail-and-error procedure until the desired accuracies aim (MSE) is accomplished. This is for the reason that there is no general methodology or guideline to obtain them. The optimum spread values were established (0.35, 0.6, and 0.8) for daily, weekly, and monthly time scale,