Optimal design of unit hydrographs using probability distribution and genetic algorithms

A nonlinear optimization model is developed to transmute a unit hydrograph into a probability distribution function (PDF). The objective function is to minimize the sum of the square of the deviation between predicted and actual direct runoff hydrograph of a watershed. The predicted runoff hydrograph is estimated by using a PDF. In a unit hydrograph, the depth of rainfall excess must be unity and the ordinates must be positive. Incorporation of a PDF ensures that the depth of rainfall excess for the unit hydrograph is unity, and the ordinates are also positive. Unit hydrograph ordinates are in terms of intensity of rainfall excess on a discharge per unit catchment area basis, the unit area thus representing the unit rainfall excess. The proposed method does not have any constraint. The nonlinear optimization formulation is solved using binary-coded genetic algorithms. The number of variables to be estimated by optimization is the same as the number of probability distribution parameters; gamma and log-normal probability distributions are used. The existing nonlinear programming model for obtaining optimal unit hydrograph has also been solved using genetic algorithms, where the constrained nonlinear optimization problem is converted to an unconstrained problem using penalty parameter approach. The results obtained are compared with those obtained by the earlier LP model and are fairly similar.