Fluctuations of water quality time series in rivers follow superstatistics

Superstatistics is a general method from nonequilibrium statistical physics which has been applied to a variety of complex systems, ranging from hydrodynamic turbulence to traffic delays and air pollution dynamics. Here, we investigate water quality time series (such as dissolved oxygen concentrations and electrical conductivity) as measured in rivers, and provide evidence that they exhibit superstatistical behaviour. Our main example are time series as recorded in the river Chess in South East England. Specifically, we use seasonal detrending and empirical mode decomposition (EMD) to separate trends from fluctuations for the measured data. With either detrending method, we observe heavy-tailed fluctuation distributions, which are well described by a log-normal superstatistics for dissolved oxygen. Contrarily, we find a double peaked non-standard superstatistics for the electrical conductivity data, which we model using two combined $\chi^2$-distributions.