Development of design flood hydrographs using probability density functions

Probability density functions (PDFs) are used to fit the shape of hydrographs and have been popularly used for the development of synthetic unit hydrographs by many hydrologists. Nevertheless, modelling the shapes of continuous stream flow hydrographs, which are probabilistic in nature, is rare. In the present study, a novel approach was followed to model the shape of stream flow hydrographs using PDF and subsequently to develop design flood hydrographs for various return periods. Four continuous PDFs, namely, two parameter Beta, Weibull, Gamma and Lognormal, were employed to fit the shape of the hydrographs of 22 years at a site of Brahmani River in eastern India. The shapes of the observed and PDF fitted hydrographs were compared and root mean square errors, error of peak discharge (EQP) and error of time to peak (ETP) were computed. The best‐fitted shape and scale parameters of all PDFs were subjected to frequency analysis and the quartiles corresponding to 20‐, 50‐, 100‐ and 200‐year were estimated. The estimated parameters of each return period were used to develop the flood hydrographs for 20‐, 50‐, 100‐ and 200‐year return periods. The peak discharges of the developed design flood hydrographs were compared with the design discharges estimated from the frequency analysis of 22 years of annual peak discharges at that site. Lognormal‐produced peak discharge was very close to the estimated design discharge in case of 20‐year flood hydrograph. On the other hand, peak discharge obtained using the Weibull PDF had close agreement with the estimated design discharge obtained from frequency analysis in case of 50‐, 100‐ and 200‐year return periods. The ranking of the PDFs based on estimation of peak of design flood hydrograph for 50‐, 100‐ and 200‐year return periods was found to have the following order: Weibull > Beta > Lognormal > Gamma. Copyright © 2009 John Wiley & Sons, Ltd.