Abstract Brownian motion is a physical phenomenon studied by biologist Robert Brown through which it is possible to describe the random irregular motion of pollen particles suspended in a fluid using the probability of finding a particle at a specific time. In a fractional way, the Brownian movement describes the random fluctuation of continuous stochastic processes which can be characterized by the Hurst coefficient whose initial utility was the observation of the levels of the Nile River to predict the persistence of future phenomena and thus prepare for the drought or flood. Fractional Brownian motion has been used for study in various areas such as hydrodynamics. Water is a vital natural resource for the preservation of species and less than 1% of fresh water is available for human consumption. Turbidity in a measure of the degree of transparency that water loses, the greater the number of solids suspended in the water, the greater the degree of turbidity. With the data provided by the “Acueducto Metropolitano”, Bucaramanga, Colombia between January 2008 and August 2019, volatility and persistence of turbidity were established in the Colombia municipalities of Bucaramanga, Floridablanca and Girón. In the latter, persistent behavior and extreme volatilities are observed. law.