FITTING WITH L MOMENTS OF THE GEV, GLO AND GPA DISTRIBUTIONS NON-STATIONARY IN THEIR LOCATION PARAMETER, APPLIED TO EXTREME HYDROLOGICAL DATA

Abstract

The analysis of frequencies of extreme hydrological data such as floods, droughts, winds and maximum daily precipitation, is based on accepting that the maximum annual data of the available sample are independent and come from a random process that is stationary. This means that their statistical properties do not vary with time. Due to changes in land use and impacts of global warming, the hydrological data series show trends, indicating that they are non–stationary. The objective of this study was to expose the generalization of the L moments method, to estimate the fit parameters of the probability distribution functions: General Extreme Values (GVE), Generalized Logistics (LOG) and Generalized Pareto (PAG) of non–stationary type, by varying with time (t) its location parameter (u) in a linear and quadratic way. The probabilistic models GVE1 , LOG1 and PAG1 have four fitting parameters (d1 , d2 , a, k), since u = d1 + d2 ·t and their scale (a) and form (k) parameters are constant. The models GVE2 , LOG2 and PAG2 have five fitting parameters (d1 , d2 , d3 , a, k), due to the fact that u = d1 + d2 ·t + d3 ·t 2 . In series with trend it is used as a covariate t in years, but indicators of regional or global climate variability can also be used, such as the southern oscillation index. By means of the four numerical applications that are described, the simplicity of the operating procedure was demonstrated and the utility of the use of non–stationary GVE, LOG and PAG models is highlighted through their predictions in series with trend, or using a climatic covariate.