TR(BR)-108 : Effects of errors in annual maximum peak floods on flood frequency estimates

Abstract

In this study, the effects of errors in annual maximum peak floods on flood frequency estimates have been examined. The ratio of annual maximum peak floods to the mean annual maximum peak

flood( Q./Q 1

) have been computed for the respective 22 bridge

sites of Mahanadi basin sub-zone

3 (d). The Q. /Q values of the

1 different sites have been considered together as a single sample for the region. The sample statistics viz. mean, standard deviation and skewness have been computed. The computed mean and standard deviation of the Q. /Q series have been utilised to generate the samples of size 30 for each of the 22 sites, using Extreme Value Type I(EV1) distribution.

Regional flood frequency analysis has been carried out with the samples of the EV1 generated data using (i ) USGS method, (ii ) EV1(PWM) method, (iii ) GEV(PWM) method and (iv) Wakeby (PWM) method. The values of growth factors ( Q ) have been obtained T/Q for various return periods using the above mentioned 4 different methods. The analysis has been repeated 1000 times with the generated data and the expected values of growth factors have been obtained. Similar analysis has been carried out with the generated data of Pearson Type III population considering the mean, standard

deviation and skewness of the historical region.

(Q./Q ) 1

values for the

Error analysis has been performed based on the expected values of flood estimates obtained from the analysis of the generated data for the different sets of statistical parameter values using EV1 and PT3 distributions following the above procedure. From the study, it is observed that there can be significant errors in the flood estimates due to errors in the annual maximum peak flood data. All the methods viz. USGS method(M1), PWM based EV1 method(M2), PWM based GEV method(M3) and PWM based Wakeby method(M4) over estimate the growth factors for larger values of coefficients of variation than that of the historical value of coefficient of variation; whereas all the methods under estimate the growth factors for the lower values of coefficient of variation than that corresponding to the historical value of-coefficient of variation. The percentage errors in growth factors are very much sensitive to the coefficient of variation for a specific value of coefficient of skewness and these are not much sensitive to the coefficient of skewness for a specific value

of coefficient of variation. The percentage errors in growthfactors are relatively low for the USGS method (MI) and PWM based EVI method (M2) when the generated populations of EVI distribution are fitted with these methods. PWM based GEV distribution in general results in less percentage errors in the growth factors as compared to the other three methods.