Regional flood quantile estimation under linear transformation of the data

We examine some performance indices (PIs) that are used to compare regional and at-site flood quantile estimation methods. These include the relative bias, the regional average root-mean-square-error (RMSE), the regional average relative root-mean-square-error (RRMSE), and the average RMSE and RRMSE ratios of quantile estimators. We study the dependence of these Pls on the relative variability (coefficient of variation) of the data, This is done by examining the effect of a location shift in the data on these PIs. The aim is to bring awareness to the fact that when comparing hydrological quantile estimators, some PIs are more greatly affected than others by data shifts in Location. Among the PIs considered, we identify those that: are invariant to a location shift in the data and those that are not. This is done under both assumptions of homogeneous and heterogeneous hydrological region, The generalized extreme value distribution is used to demonstrate some of the results, but the conclusions are applicable to other distributions with a location parameter. It is argued that because of the lack of invariance to location shift of certain quantile estimation methods and PIs, additional precautions need to be taken when comparing these methods. Although we focus discussion around flood frequency analysis, the points raised should be viewed within the broader context of hydrological frequency analysis.