Abstract

CAMPOS-ARANDA, Daniel Francisco. Application of the Unbounded Probability Distribution of the Johnson System for Floods Estimation. Ing. invest. y tecnol. [online]. 2015, vol.16, n.4, pp.527-537. ISSN 2594-0732.

Floods designs constitute a key to estimate the sizing of new water works and to review the hydrological security of existing ones. The most reliable method for estimating their magnitudes associated with certain return periods is to fit a probabilistic model to available records of maximum annual flows. Since such model is at first unknown, several models need to be tested in order to select the most appropriate one according to an arbitrary statistical index, commonly the standard error of fit. Several probability distributions have shown versatility and consistency of results when processing floods records and therefore, its application has been established as a norm or precept. The Johnson System has three families of distributions, one of which is the Log-Normal model with three parameters of fit, which is also the border between the bounded distributions and those with no upper limit. These families of distributions have four adjustment parameters and converge to the standard normal distribution, so that their predictions are obtained with such a model. Having contrasted the three probability distributions established by precept in 31 historical records of hydrological events, the Johnson system is applied to such data. The results of the unbounded distribution of the Johnson system (SJU) are compared to the optimal results from the three distributions. It was found that the predictions of the SJU distribution are similar to those obtained with the other models in the low return periods (< 50 years) and in general are of the same order of magnitude in higher recurrence intervals (> 1000 years). Because of its theoretical support, the SJU model is recommended in flood estimation.

Keywords : distributions Log-Pearson type III; General Extreme Values; Generalized Logistic; percentiles; standard error of fit; Rosenbrock algorithm.

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