A mathematical model for nonlinear hydrologic systems

A new type of mathematical model for hydrologic systems is introduced. This decomposition model represents nonlinear time-lag systems, in decomposed form, by a series combination of parallel linear time-lag systems and parallel nonlinear no-time-lag systems. Thus the assumption that hydrologic systems are linear is no longer postulated. The theory of the decomposition model and its use in the prediction of the system output, given the input, are discussed. Computational algorithms for model construction and for its use in output prediction are given. A number of decomposition models have been constructed for a small watershed. These computational experiments established the applicability of the proposed method and its practicality in terms of ease of application and small computational cost. It is also shown how specific parameters of a given system can be determined. These parameters include length of the record that is needed to obtain a model of reasonable quality, length of the maximum time lag in a given system and its degree of nonlinearity, and details of the model structure. In particular, for a 2.33-acre watershed it was found that a record of 3000 hours suffices for model derivation, that the system maximum time lag was approximately 5 hours, and that three linear time-lag systems and up to fourth-order nonlinear, no-time-lag systems had to be included in the model.