Treatment of Hydrological Variables in Non-Linear Systems
In the background of the need for simulation or forecast modelling the catchment is considered as an engineering system that transforms rainfall input into streamflow output. In the mathematical methods shown above, this kind of application is possible only for linear systems. To apply linear models to problems in practice, the data have to be modified so that a linear behaviour can be approximated. Base-flow substraction or determination of the effective rain are used to obtain corresponding functions of a linear system. Leaving out of account the problem of obtaining accurate measurements of the involved quantities, the linear model does not represent the catchment behaviour, because the catchment behaves non-linearity. The first systematic treatment of the non-linear effects was reported by Minshall (1986), who demonstrated the dependency of the unit hydrograph on rain fall intensity. In accordance with the hydrodynamic equations describing hydrological processes, a non-linear behaviour of the catchment can be taken for granted. A useful non-linear representation of the rainfall runoff relationship is the second-order Volterra series model.
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