Effect of data length on estimation of peak flood discharge using L-moments of five probability distributions

Estimation of flood magnitude corresponding to a chosen risk of flooding or even failure of a structure is an important part of the engineering practices. For which, flood frequency analysis (FFA) approach is considered as one of the effective tools for estimation of peak flood discharge (PFD) for a given return period. This paper presented a study on effect of data length on estimation of PFD by adopting method of L-Moments (LMO) of Extreme Value Type-1 (EV1), Extreme Value Type-2 (EV2), Generalized Extreme Value (GEV), Generalized Pareto (PRT) and 2-parameter Log Normal (LN2) distributions. For this purpose, the stream flow data of river Tapi at Sarangkheda gauging site (1941–2020) was used to generate three annual maximum discharge (AMD) series with different data length say, D30 series with 30 years data (1941–1970), D60 series with 60 years data (1941-2000) and D80 series with 80 years data (1941–2020). Statistical characteristics of the data used in FFA was evaluated through statistical tests viz., Wald-Wolfowitz runs test for randomness, Mann–Whitney U test for data independency and Grubbs′ test for checking the outliers in the data. The adequacy of fitting distributions to the observed data was evaluated by Goodness-of-Fit (GoF) (viz., Chi-square and Kolmogorov–Smirnov) and diagnostic (D-index) tests. The quantum of uncertainty in the estimated PFD was measured through model performance indicators viz., correlation coefficient (CC) and relative error. Statistical tests results showed that the D30, D60 and D80 series are random and also independent. The Grubbs′ test results indicated that there are no outliers in the data series used in FFA. GoF tests results supported the LMO method of all five distributions for estimation of PFD using D30, D60 and D80 series. Based on qualitative and quantitative assessments, it was found that GEV is better suited distribution for estimation of PFD while using D30, D60 and D80 series in FFA. The standard error in the estimated PFD by GEV distribution is found as minimum when compared to the corresponding values of EV1, EV2, PRT and LN2. The results indicated that there is generally good correlation between the observed and estimated PFDs, and CC values vary between 0.946 and 0.995. The study showed that (i) the estimated PFDs are in increasing order when return period increases; (ii) the estimated PFDs for different return periods by five distributions are in decreasing order when data length increases; and (iii) the relative error computed by GEV is in decreasing order when the data length increases. The study suggested that the estimated PFD by LMO estimators of GEV distribution can be used as a design flood discharge while planning and design of civil and hydraulic structures.