Multivariable Flood Level Frequency Distribution

A graphical procedure is outlined for the determination of discrete values of a multivariable frequency distribution of three independent variables each with individual frequency distributions. The method is developed for the determination of the frequency of water levels at a dike structure due to the combined occurrence of adjacent channel flows, outlet lake level fluctuations, and wave action. The frequency distribution is defined as a function of the triple integral of the product of the individual marginal frequency distributions. A graphical solution for the integration is detailed. The integrand is rearranged to products of two functions according to the statistical principle of mutually exclusivity and solved using a rectangular coordinate system defined by the individual frequency distributions. This method may be used to find the frequency distribution of any multivariable function of two or more independent variables with known frequency distributions.