Development of design flood hydrographs using probability density functions

Abstract

Abstract: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 (EQ P ) and error of time to peak (ET P ) 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. Lognormalproduced 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.

Flash Flood Hazard Susceptibility Mapping Using Frequency Ratio and Statistical Index Methods in Coalmine Subsidence Areas

“…Hydrologic forcing is estimated using a rainfall-runoff model that quantifies flood peak discharges or a flow hydrograph for a given return period (T) [6,[11][12][13]. The hydraulic analysis can been performed using an Event Based Approach (EBA) [14,15], a Semi-Continuous Approach (SCA) [11][12][13], and a Fully Continuous Approach (FCA) [6]. The analysis is carried out using a one-dimensional (1D) surface water model or two-dimensional (2D) flood routing algorithm to simulate the spatially distribution of flow and velocity dynamics.…”

Toward creating simpler hydrological models: A LASSO subset selection approach

“…A greater number of g(t) functions is likely to be required for more complex hydrographs. A similar set of different inverse Gaussian distributions would have served equally well, as could other distributions discussed by various authors (Nadarajah, 2007;Pramanik et al, 2010;Muneepeerakul et al, 2010).…”

Evaluating Pre‐ and Post‐Fire Peak Discharge Predictions across Western U.S. Watersheds

“…We assess pre-fire model performance for both calibrated and uncalibrated models using flood frequency information from gaged watersheds. The Weibull method is commonly used to analyze streamflow and estimate expected frequency of flows based on the assumption that peak discharge is evenly distributed over a long period of time (Pramanik et al, 2010). The generated discharge values for each recurrence event are considered a reasonable approximation of the associated probability density of discharge values in a basin and allow comparison of modeled design storm simulations to an "observed" storm frequency (Clarke, 2002;Pramanik et al, 2010).…”

“…The Weibull method is commonly used to analyze streamflow and estimate expected frequency of flows based on the assumption that peak discharge is evenly distributed over a long period of time (Pramanik et al, 2010). The generated discharge values for each recurrence event are considered a reasonable approximation of the associated probability density of discharge values in a basin and allow comparison of modeled design storm simulations to an "observed" storm frequency (Clarke, 2002;Pramanik et al, 2010). In the current study, a Weibull frequency distribution is generated using the observed peak flow values for basins where long-term peak discharge exists (Andrews Creek To evaluate performance, we utilize two commonly used metrics, root mean square error (RMSE), and percent bias:…”