Abstract
SummarySuperstatistics 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 behavior. Our main example is time series as recorded in the River Chess in South East England. Specifically, we use seasonal detrending and empirical mode decomposition to separate trends from fluctuations for the measured data. With either detrending method, we observe heavy-tailed fluctuation distributions, which are well described by 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 -distributions.
Highlights
Superstatistical methods, as introduced in (Beck and Cohen, 2003; Beck et al, 2005), provide a general approach to describe the dynamics of complex nonequilibrium systems with well-separated timescales
SUMMARY 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
We observe heavy-tailed fluctuation distributions, which are well described by log-normal superstatistics for dissolved oxygen
Summary
Superstatistical methods, as introduced in (Beck and Cohen, 2003; Beck et al, 2005), provide a general approach to describe the dynamics of complex nonequilibrium systems with well-separated timescales These models generate heavy-tailed non-Gaussian distributions by a simple mechanism, namely the superposition of simpler distributions whose relevant parameters are random variables, fluctuating on a much larger timescale. The overview article (Metzler, 2020) provides a recent introduction to superstatistics and non-Gaussian diffusion In all these cases, an underlying simple distribution, typically Gaussian or exponential, is identified to explain the observed heavy tails of the marginal distributions when aggregated with the fluctuating parameter. Both approaches are equivalent and form standard examples of distributions generated by the (more general) superstatistical approach
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