A comparison of use of L- moment and LH- moment methods of parameter estimation for the regional flood frequency analysis in semi-arid areas: the case of Limpopo catchment, Botswana

Abstract

Design flood estimation is an important task that is required in the planning and design of many hydraulic structures. This study was therefore aimed at developing the regional growth curves for estimation of floods of various return periods in the Limpopo catchment at either gauged or ungauged sites. Finding the most suitable distribution to flood sample and selecting the appropriate parameter estimation method are of great importance for flood frequency analysis. In this study, the newer methods of the L-moments and LH-moments using the Regional Flood Frequency Analysis (RFFA) technique have been used to characterise the flood data of this region. The study focussed on the RFFA of the Limpopo catchment, Botswana, which comprises of 13 hydrometric stations. The heterogeneity test has revealed that the Limpopo catchment using LH-moments has been identified as “acceptably homogeneous” through all levels , = 1, 2, 3, 4, that is, (L1 to L4); and therefore, this method was found the best technique to characterize the Limpopo flood data. Three extreme value distributions, that is, generalized extreme value (GEV), generalized logistic (GLO) and generalized Pareto (GPA), through different levels of the LH-moments (L to L4) have been applied to develop the regional parameters and describe the annual maximum flood data obtained from 13 sites in the Limpopo catchment. The Z-statistic criteria were used in the distribution selection, considering the respective LH-moments (L to L4) and as such the GEV distribution using LH-moments at level 2 (L2) has been found the best distribution of all other distributions. For final selection of the appropriate method of parameter estimates, the performances of GEV distribution using L-moments and LHmoments (L2) have been assessed by evaluating the relative Root Mean Square Error (RMSE). The results of the RMSE showed that the LH-moments of level 2 (L2) based on GEV has been found most suitable and more efficient with minimum RMSE for obtaining improved values of flood peaks than the L-moments. Regional flood frequency relationships are developed for estimation of floods of various return periods for ungauged sites using the LH-moment (L2) based on the GEV distribution. A general relationship between mean annual peak flood, drainage area and rainfall has been developed.