Flood frequency analysis with historic information

Abstract The series of annual peak flows obtained from a recent continuous flow record, together with any historic floods or information, are treated as a censored sample from a three-parameter lognormal population. The logarithmic likelihood function is derived in terms of the fully specified floods, the historic information with censoring threshold, and the distribution parameters to be determined. Maximum likelihood estimators of parameters are obtained as a set of three simultaneous transcendental equations and a solution method is given. Flood magnitudes for any required return period are then computed. The method is illustrated by its application to a river with historic data. Results are presented of a limited Monte Carlo experiment, the purpose of which was to compare this technique with the more conventional fitting method of historically weighted moments, in terms of bias and variability in estimates. Although both methods show bias to some degree, the maximum likelihood method gives estimates which are substantially less biassed, within the limits of the Monte Carlo experiment.