Fractal analysis of persistence in fluctuation of levels of the Magdalena River

Abstract

The measures of water level in a river contributes to understand the dynamic of the discharge in a specific point of the catchment. With this kind of information, it is possible to predict and study future flooding events. The official entity CORMAGDALENA with support of IDEAM report every two days the water level along the Magdalena River. The Hurst coefficient H generates a new statistic methodology, which is based on the tendencies of data series, determining the persistence a dataset and consequently its fractality. This research applies this methodology to a dataset of time, registered by CORMAGDALENA in the municipality of Barrancabermeja, in the Department of Santander. The time has been taken between September 29th of 2011 and March 31st of 2017. According to the value of H we can say if the series of behaviours taken has persistence in the case that H is greater than 0.5, if H is less than 0.5 we will say that the series is anti-persistent. With these values of H it is possible to calculate the fractal dimension associated to the comportment and thus to determine the volatility for the analysis of the risk in terms of the fluctuation of the Magdalena River.