Parameter estimation methods for non-stationary data using L-moments and TL-moments approaches

Abstract

Non-stationary flood frequency analysis (NFFA) plays an important role in defining the probabilities of flood occurrences by taking into account of the non-independence and non-stationary aspects of hydrological extreme events data. This analysis overcomes the issue of the stationary assumptions (independent and identically distributed flood series) applied in flood frequency analysis (FFA), which are no longer valid in infrastructure-designed methods. This is because ignoring the non-stationarity of hydrological records may result in inaccurate future flood event predictions. Flood estimation is one of the important components in frequency analysis. Thus, an appropriate parameter estimation method should be established to deal with flood frequency analysis in the likely case of non-stationary. The objective of this study is to propose a parameter estimation method to estimate the parameter of non-stationary distribution model. The proposed methods are Trimmed L-moments (TL-moments) method and performance comparison of TL-moments with L-moments method in NFFA study. The TL-moments method was applied to the Generalized Extreme Value (GEV) distribution model with time as covariate. Four GEV distribution models examined in this study were stationary model (GEV0) and three non-stationary models (GEV1, GEV2, and GEV3). Comparisons of the parameter estimation methods were carried out using Monte Carlo simulation and bootstrap techniques. The simulation study showed that TL-moments performed better than L-moments method for GEV1 and GEV3 models. Streamflow data for three of eleven rivers in Johor, Malayis were found to exhibit non-stationary behaviour in the annual maximum streamflow. These rivers showed decreased trend in the flood series based on the Mann-Kendall trend test and Spearman’s Rho test. From the bootstrap analysis, the TL-moments method performed better as compared to the L-moments method for GEV0, GEV1, and GEV3 models. The overall result concluded that the TL-moments method could provide an efficient prediction of the flood event estimated at quantiles of the higher return periods.