Mellin Transform Applied to Uncertainty Analysis in Hydrology/Hydraulics

Abstract

In hydraulic and hydrologic design and analysis, engineers frequently face uncertainties involving quantities that cannot be assessed with absolute accuracy. Under such circumstances, uncertainty analysis is undertaken to examine the effects of uncertain factors on the results of design and analysis. The paper introduces a mathematical technique called the Mellin transform. The technique is analytically convenient in determining the exact statistical moments of a random variable that is a function of several nonnegative independent random variables in a multiplicative form. Two examples are given to demonstrate the application of the Mellin transform to uncertainty analysis of hydrologic and hydraulic problems.