Fitting of the non-stationary distribution GEV11 through L moments

Abstract

Hydrological dimensioning or revision of the hydraulic works and the elaboration of flood risk maps, is based on the so-called design floods, that are maximum flows of the river associated with low probabilities of exceedance. The most reliable way of estimating such predictions is through the Flood Frequency Analysis (FFA), its fundamental assumption is that the stochastic process under study is stationary, that is, it does not change with time. Construction of small reservoirs, urbanization and changes in land use in the basin, as well as global or regional climate change, alter the hydrological processes and generate records of annual flows that are non-stationary, showing trends and changes in variability. For the FFA of such registries, the extreme value theory has been extended to apply its classical distribution, the General of Extreme Values (GEV), with parameters of location (u) and scale (α) varying with time (t), introducing it as a covariate. In this work the L moments method is presented for the fit of the probabilistic model GVE₁₁ whose parameters u and α vary linearly over time. Three numerical applications are described. Conclusions highlight the simplicity of the exposed method and its importance in the estimation of the sought predictions in non-stationary annual maximum data series.