Subexponential Memory of Water Environmental Varia bles through the Superstatistics

Abstract

Water environmental variables have been reasonably described as subexponentially decaying processes. In this short paper, we apply a theory of superstatistics, the statistics of doubly random variables, to recently obtained experimental data of the benthic algae detachment in water flows created in a laboratorial flume. We show that the survival curve of the algae cover (i.e., the percentage of the surface of a gravel covered by benthic algae at each time) decays subexponentially in time in each experiment with different parameter values, even under the same experimental condition. We explain the obtained experimental results through the (bivariate) superstatistics.