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Regional flood quantile estimation under linear transformation of the data
Author(s) -
Arsenault Michel,
Ashkar Fahim
Publication year - 2000
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/2000wr900040
Subject(s) - quantile , estimator , mean squared error , statistics , flood myth , mathematics , context (archaeology) , quantile regression , econometrics , geography , archaeology
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 PIs 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.