Estimating the scale parameter of the norming constants method in analysing nonstationary annual maximum floods

Abstract

AbstractIn frequency analysis of annual maximum flood series (AMFS), it is mechanism‐based and significant to incorporate the information of the underlying “ordinary” daily streamflow events for improving accuracy of flood risk estimation and appropriate management. In previous studies related to flood nonstationarity, the classical norming constants method (C‐NCM) has been used to derive statistical parameters of annual maximum flood distribution from daily streamflow distribution. However, C‐NCM does not flexibly consider the feasible range of the scale parameter of annual maximum flood distributions, which can result in the inability to provide sufficient and reliable models to fit AMFS. This paper aims to investigate the potential of two alternative norming constants methods in fitting annual maximum floods, namely the Hall's norming constants method (H‐NCM) and the Fisher and Tippetts' norming constants method (FT‐NCM) respectively. A comparative study of these three methods was carried out using hydrological streamflow series of 77 stations in the Yangtze and Yellow River basins, China. The results found that H‐NCM outperforms both C‐NCM and FT‐NCM for the stations with relatively low‐skewness coefficient of AMFS. Therefore, H‐NCM is recommended to prioritize for practical applications when considering daily streamflow rather than small samples of flood events. Furthermore, if the skewness coefficient exceeds Cs,Gumbel≈1.14, the overall modelling performance of these three methods is significantly deteriorated. This can provide some reference for the applicability of the norming constants method in flood frequency analysis.