Exponential data fitting applied to infiltration, hydrograph separation, and variogram fitting

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Most lumped rainfall-runoff models separate the interflow and groundwater components from the measured runoff hydrograph in an attempt to model these as hydrologic reservoir units. Similarly, rainfall losses due to infiltration as well as other abstractions are separated from the measured rainfall hyetograph, which are then used as inputs to the various hydrologic reservoir units. This data pre-processing is necessary in order to use the linear unit hydrograph theory, as well as for maintaining a hydrologic budget between the surface and subsurface flow processes. Since infiltration determines the shape of the runoff hydrograph, it must be estimated as accurately as possible. When measured infiltration data is available, Horton’s exponential infiltration model is preferable due to its simplicity. However, estimating the parameters from Horton’s model constitutes a nonlinear least squares fitting problem. Hence, an iterative procedure that requires initialization is subject to convergence. In a similar context the separation of direct runoff, interflow, and baseflow from the total hydrograph is typically done in an ad hoc manner. However, many practitioners use exponential models in a rather ‘‘layer peeling’’ fashion to perform this separation. In essence, this also constitutes an exponential data fitting problem. Likewise, certain variogram functions can be fitted using exponential data fitting techniques. In this paper we show that fitting a Hortonian model to experimental data, as well as performing hydrograph separation, and total hydrograph and variogram fitting can all be formulated as a system identification problem using Hankel-based realization algorithms. The main advantage is that the parameters can be estimated in a noniterative fashion, using robust numerical linear algebra techniques. As such, the system identification algorithms overcome the problem of convergence inherent in iterative techniques. In addition, the algorithms are robust to noise in the data since they optimally separate the signal and noise subspaces from the observed noisy data. The algorithms are tested with real data from field experiments performed in Surinam, as well as with real hydrograph data from a watershed in Louisiana. The system identification techniques presented herein can also be used with any other type of exponential data such as exponential decays from nuclear experiments, tracer studies, and compartmental analysis studies.

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