An analysis of the Chow-Kulandaiswamy GHS model

The Chow-Kulandaiswamy general hydrologic system (GHS) model is revisited. Based on a mathematical study by Singh and McCann the GHS model is simplified. Explicit solutions are obtained for special cases which can satisfactorily determine watershed surface runoff response due to given rainfall excess. A rational criterion is developed to determine the number of derivative terms to be retained in the model. In order to determine the coefficients in the GHS model the method of moments is proposed. Criteria are developed to determine complex roots and oscillations for these coefficients. By analysing Chow-Kulandaiswamy's results it is found that in a majority of cases which they studied roots are complex. Moreover, for the cases which have complex roots, a majority of the solutions oscillate. A brief sensitivity analysis of the GHS model is performed with regard to: (a) its leading coefficient, and (b) the order of the differential equation. Finally, the peak characteristics are specified for the second order case and their qualitative properties are shown for the third order case.