Abstract

CAMPOS-ARANDA, Daniel Francisco. Fitting of non-stationary distribution GEV₁₁ through L moments. Tecnol. cienc. agua [online]. 2021, vol.12, n.3, pp.164-203.  Epub June 26, 2025. ISSN 2007-2422.  https://doi.org/10.24850/j-tyca-2021-03-05.

Hydrological dimensioning or revision of the hydraulic works and the elaboration of flood risk maps is based on the so-called Design Floods, which are maximum flows of the river associated with low probabilities of exceedance. The most reliable way of estimating such predictions is through Flood Frequency Analysis (FFA). Its fundamental assumption is that the stochastic process under study is stationary, i.e., it does not change with time. Construction of 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 Generalized Extreme Values (GEV), with parameters of location (u) and scale (α) varying with time (t), which is introduced as a covariate. In this work the L-moment 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 expected predictions in non-stationary annual maximum data series.

Keywords : Covariate; L-moments; GEV distribution; standard error of fit; trend; linear regression; residuals.

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