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Tecnología y ciencias del agua

On-line version ISSN 2007-2422


CAMPOS-ARANDA, Daniel Francisco. Non-stationary frequency analysis by linear regression and LN31, LP31 y GVE1 distributions. Tecnol. cienc. agua [online]. 2019, vol.10, n.6, pp.57-89.  Epub May 15, 2020. ISSN 2007-2422.

All hydraulic works required by society are planned and dimensioned based on Floods Design. The most reliable estimation is made through frequency analysis (FA), consisting of fitting a probability distribution function (PDF) to the available data of annual maximum flows, in order to obtain the predictions sought. The FDP Log-Normal of three parameters of fit (LN3) was the first one of extensive application in the hydrological analyzes; the other two used have been established under precept for the FA of floods; the Log-Pearson type III (LP3) in U.S.A. and the General of Extreme Values (GVE) in England. The effects of climate change and the physical alterations of the basins, due to urbanization and deforestation, originate ascending tendencies in the flood registers; on the other hand, the construction of reservoirs leads to descending tendencies. Because of the above, the aforementioned data is non-stationary and its FA requires PDF to change over time, as a covariate. When the location parameter and the mean vary with time, in the quantile function of the LN3 distribution, its non-stationary model called LN31 is obtained. If the mean and the variance change over time, in the quantile function of the probabilistic model LP3, its non-stationary version designated LP31 is developed. Instead, when the fit parameters of the GVE model change over time, its non-stationary version called GVE1 is obtained. In this study, two records with ascending tendencies are processed, one of 77 annual maximum flows and the other of 58 annual maximum daily precipitation values. The results are analyzed and a selection of predictions is based on the lowest standard error of fit. Conclusions regarding the FA of series of extreme hydrological data with tendency highlight the simplicity of the method exposed, through the LN31, LP31 and GVE1 models.

Keywords : Non-stationary hydrological data; bivariate linear regression; conditional moments; Log-Normal distribution; Log-Pearson type III distribution; General Extreme Value distribution; standard error of fit.

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