Abstract
Due to its geographical position, Mexico is exposed annually to cold fronts and tropical cyclones, registering extremely high values that are atypical in the series of maximum annual flows. Univariate mixed probability distribution functions have been developed based on the theory of extreme values, which require techniques to determine their parameters. Therefore, this paper explores a function that considers three populations to analyze maximum annual flows. According to the structure of the Generalized Extreme-Value Distribution (GEV), the simultaneous definition of nine parameters is required: three of location, three of scale, and three of probability of occurrence. Thus, the use of a meta-heuristic technique was proposed (harmonic search). The precision of the adjustment was increased through the optimization of the parameters, and with it came a reduction in the uncertainty of the forecast, particularly for cyclonic events. It is concluded that the use of an extreme value distribution (Type I) structured with three populations and accompanied by the technique of harmonic search improves the performance in respect to classic techniques for the determination of its parameters.
Highlights
IntroductionMathematical modeling of natural phenomena has become increasingly important due to the implications of global warming and associated climate modification, taking special relevance in public safety activities and economic aspects [1]
Mathematical modeling of natural phenomena has become increasingly important due to the implications of global warming and associated climate modification, taking special relevance in public safety activities and economic aspects [1].The modeling of extreme events is of great importance in countries affected by hurricanes.Countries in Asia and Latin America are affected by cyclones and hurricanes, new approaches to frequency analysis with extreme data sets are often sought
Having implemented an harmonic search (HS) meta-heuristic technique for the EV1-3P of Q, it is concluded that it is an effective and efficient option for the simultaneous determination of the three location, the three scale, and the three probability parameters, according to the structure of nine parameters that conform to the structure of the function
Summary
Mathematical modeling of natural phenomena has become increasingly important due to the implications of global warming and associated climate modification, taking special relevance in public safety activities and economic aspects [1]. A detailed study of the origin, characteristics, properties, and applications in hydrology for the function of the Generalized Extreme-Value Distribution (GEV) was presented in Mexico [5,6]. The presence of cold fronts or tropical cyclones generates atypical values in the series of maximum annual flows (Q) registered by hydrometric stations installed in the study basins [2] This behavior has been studied using the Gumbel probability distribution function of two populations (EV1-2P) [11], which later gave rise to the development of a new type of probability function named the mixed probability distribution function [12]. Extreme-Value Distribution, considering three populations in records for Q [14], showed the pertinence of its application in the hydrological area and the determination of the parameters through the use of maximum likelihood (ML) methodology. The objective is to explore the use of the meta-heuristic technique HS in the simultaneous optimization of the necessary parameters in the EV1-3P in I time series
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