Application of a hybrid approach in nonstationary flood frequency analysis – a Polish perspective

Abstract. The alleged changes in rivers' flow regime resulted in the surge in the methods of non-stationary flood frequency analysis (NFFA). The maximum likelihood method is said to produce big systematic errors in moments and quantiles resulting mainly from bad assumption of the model (model error) unless this model is the normal distribution. Since the estimators by the method of linear moments (L-moments) yield much lower model errors than those by the maximum likelihood, to improve the accuracy of the parameters and quantiles in non-stationary case, a new two-stage methodology of NFFA based on the concept of L-moments was developed. Despite taking advantage of the positive characteristics of L-moments, a new technique also allows to keep the calculations "distribution independent" as long as possible. These two stages consists in (1) least square estimation of trends in mean value and/or in standard deviation and "de-trendisation" of the time series and (2) estimation of parameters and quantiles by means of stationary sample with L-moments method and "re-trendisation" of quantiles. As a result time-dependent quantiles for a given time and return period can be calculated.

The comparative results of Monte Carlo simulations confirmed the superiority of two-stage NFFA methodology over the classical maximum likelihood one. Further analysis of trends in GEV-parent-distributed generic time series by means of both NFFA methods revealed big differences between classical and two-stage estimators of trends got for the same data by the same model (GEV or Gumbel). Additionally, it turned out that the quantiles estimated by the methods of traditional stationary flood frequency analysis equal only to those non-stationary calculated for a strict middle of the time series. It proves that use of traditional stationary methods in conditions of variable regime is too much a simplification and leads to erroneous results. Therefore, when the phenomenon is non-stationary, so should be the methods used for its interpretation.