A comparison of three approaches to non-stationary flood frequency analysis

Abstract

Non-stationary flood frequency analysis (FFA) is applied to statistical analysis of seasonal flow maxima from Polish and Norwegian catchments. Three non-stationary estimation methods, namely, maximum likelihood (ML), two stage (WLS/TS) and GAMLSS (generalized additive model for location, scale and shape parameters), are compared in the context of capturing the effect of non-stationarity on the estimation of time-dependent moments and design quantiles. The use of a multimodel approach is recommended, to reduce the errors due to the model misspecification in the magnitude of quantiles. The results of calculations based on observed seasonal daily flow maxima and computer simulation experiments showed that GAMLSS gave the best results with respect to the relative bias and root mean square error in the estimates of trend in the standard deviation and the constant shape parameter, while WLS/TS provided better accuracy in the estimates of trend in the mean value. Within three compared methods the WLS/TS method is recommended to deal with nonstationarity in short time series. Some practical aspects of the GAMLSS package application are also presented. The detailed discussion of general issues related to consequences of climate change in the FFA is presented in the second part of the article entitled ''Around and about an application of the GAMLSS package in non-stationary flood frequency analysis''.Keywords Non-stationary flood frequency analysis Á Maximum likelihood Á Two-stage methodology Á GAMLSS Á Multimodel approach Á Monte Carlo simulations

Can we still predict the future from the past? Implementing non‐stationary flood frequency analysis in the UK

“…In recent years non‐stationary techniques of frequency analysis have been a very active area of research (Cunderlik & Burn, ; Debele, Strupczewski, & Bogdanowicz, ; El Adlouni, Ouarda, Zhang, Roy, & Bobee, ; Milly et al, ; Prosdocimi, Kjeldsen, & Svensson, ; Rootzén & Katz, ; Šraj, Viglione, Parajka, & Blöschl, ; Yan et al, ; Yu, Cohn, & Stedinger, ). Such methods have not yet been generally adopted in standard UK flood estimation.…”

An Overview of Flood Risk Analysis Methods

“…Based on existing data, new models have been created for areas with similar characteristics [107][108][109]. Statistics were used as soon as the databases allowed their processing with good results [110][111][112][113][114]. The development of GIS techniques has allowed the spatialization of these methodologies, leading to combined methods.…”

Quantile Mixture and Probability Mixture Models in a Multi-Model Approach to Flood Frequency Analysis

“…Since this variant of aggregation has been presented in detail in our previous papers and also used for non-stationary flood analysis by Debele et al [39], here only the basic principles of MM aggregation are briefly recalled.…”

“…matching to each data series of two selected (in point 2) distributions, determining the weights of both distributions, the values of the aggregated quantile (Equation (1)), its asymptotic standard error (Equations (17) and (19)) and the confidence interval with a confidence level of 68.3%, called a one-sigma confidence interval [39,51].…”