Inverse Transform of Duhamel Integral for Data Processing in Hydrology

Abstract

The inverse transform of Duhamel integral is a procedure to find the value of one of the integrands of a Duhamel integral knowing the other and the result of the integral. It corresponds to the determination of the function of influence or the inverse transform of the output to the input for a system. This paper compares the methods of the inverse transform which have been proposed as the general procedures for data processing in hydrology and the related fields. It is shown that the method of Kuchment gives a much better result than the least-square method, and that the Fourier transform method can give the best result when the optimal filter is designed according to the individual problem. In the example in which the method of Kuchment is applied to the analysis of data from the tracing of the overland flow in a model drainage basin, the mean velocity and the coefficient of dispersion of the tracer are evaluated to illustrate the effectiveness of this method as a general procedure for a detailed and quantitative analysis of hydrologic processes.