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Superstatistics is a general method from nonequilibrium statistical physicswhich has been applied to a variety of complex systems, ranging fromhydrodynamic turbulence to traffic delays and air pollution dynamics. Here, weinvestigate water quality time series (such as dissolved oxygen concentrationsand electrical conductivity) as measured in rivers, and provide evidence thatthey exhibit superstatistical behaviour. Our main example are time series asrecorded in the river Chess in South East England. Specifically, we useseasonal detrending and empirical mode decomposition (EMD) to separate trendsfrom fluctuations for the measured data. With either detrending method, weobserve heavy-tailed fluctuation distributions, which are well described by alog-normal superstatistics for dissolved oxygen. Contrarily, we find a doublepeaked non-standard superstatistics for the electrical conductivity data, whichwe model using two combined $\chi^2$-distributions.

Fluctuations of water quality time series in rivers follow superstatistics