The erosive behavior and fundamentals of the black-box analysis of a catchment are briefly discussed, and the potentialities of functional series are considered as a model. Then a physically significant nonlinear functional model, called a "2D unit sediment graph," is developed for predicting the river suspended-sediment concentration or yield from the current and antecedent effective precipitation events. The model represents the overall behavior of the catchment, and hence, does not require separation of excess rainfall, direct runoff, and washload. Comparative applications are performed for the 2D unit sediment graph model and the first- and second-order functional series. Unusually good predictions are produced by the 2D unit sediment graph model. The model represents the factors affecting the erosive behavior by its response functions (unit sediment graphs); hence, it is expected to predict the sediment concentration or yield with sufficient accuracy if the catchment conditions in the calibration period do not change significantly in the prediction period.