In this paper, a modeling method of the input-output relation of river runoff phenomena by Volterra functional series is studied. When the higher order Volterra model (3rd order Volterra Model is discussed in this study) is applied to river runoff phenomena, derived model does not give good simulation results, and can not represent the input-output relation. So, for a long time, the method can not become general method.
In this study, considering the source of the inaccuracy to be ill condition of the coefficient matrix of normal equation, the rank reduction method of SVD of M-P generalized inverse in performing the least-squares with a constraint conditions has been applied. As the results, it has been shown that the method is the very effective scheme to derive the faithful model representing the physical input-output characteristic, and the general modeling method of wide range natural nonlinear phenomenon whose input output data contain measuring errors has seemed to be established.
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