Abstract

CAMPOS-ARANDA, Daniel Francisco. Fitting with L-moments of the non-stationary distributions GVE₁ and GVE₂ to PMD series. Tecnol. cienc. agua [online]. 2019, vol.10, n.5, pp.75-105.  Epub Feb 15, 2020. ISSN 2007-2422.  https://doi.org/10.24850/j-tyca-2019-05-03.

Design Floods allow the hydrological sizing of hydraulic works. When hydrometric data is not available, design floods are estimated using hydrological methods that are based on Design Rainfalls. The most common records used to estimate design rainfalls are the annual maximum daily precipitations (PMD), this, due to the scarcity of rainfall recorder stations. The impacts of climate change and/or the alteration of the geographic environment of rain-gauge stations cause PMD records to show trends and therefore these records become non-stationary. In order to estimate predictions of low probability of exceedance a probabilistic analysis of the non-stationary PMD records can be performed. A simple approach without computational difficulties is based on the extension of the method of L moments applied to the General of Extreme Values (GVE) distribution with its location parameter (u) variable with time (t) in years, which is entered as a covariate. When the trend in the PMD register is linear, the probabilistic model GVE1 is applied in which u t = μ 0 + μ 1· t and when the trend is curve the model GVE2 with u t = μ 0 + μ 1· t + μ 2·t 2 is used. Thus, the GVE1 distribution has four fit parameters (μ 0, μ 1, α, k) and five for the GVE2 distribution (μ 0, μ 1, μ 2, α, k). Four numerical applications are described and the analysis of their results shows the simplicity of the extension of the L moments method and its versatility to estimate predictions within the historical record and to the future.

Keywords : L moments; GEV distribution; standard error of fit; linear regression; parabolic regression; determinants; multiple linear regression.

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