Evaluation of Segmented Iuh from Derivatives

A new method is presented for the analysis of rainfall excess hyetographs and direct surface runoff hydrographs and for the derivation of instantaneous unit hydrographs. The method assumes that the IUH can be approximated by a segmented polygon composed of straight lines and that the duration of the rainfall excess is shorter than or equal to the duration of the shortest of the straight line segments composing the polygon. Other assumptions are that the watershed system for which the input and output curves are available is a linear time invariant system and that it is initially relaxed. The method is based on a theorem for the convolution of derivatives of functions and shows how the derivatives of the assumed instantaneous unit hydrograph can be obtained from an analysis of the shapes of the available rainfall excess hyetograph and direct surface runoff hydrograph. Numerical examples accompany the development of the method and a final example illustrating the application of the method is also included.