Exponential Data Fitting Applied to Environmental Data

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 serve as inputs to the various hydrologic reservoir units. 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. In a similar context, the separation of direct runoff, interflow, and baseflow from the total hydrograph is typically done using exponential models in a rather "layer peeling" fashion, which in essence also constitutes an exponential data fitting problem. In this paper we show that fitting a Hortonian model to experimental data, as well as performing hydrograph separation can be formulated as a system identification problem in the state-space domain. The main advantage is that the parameters can be estimated in a non iterative fashion, using robust numerical linear algebra techniques. 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.