Entropy and Intermittency of River Bed Elevation Fluctuations

River beds evolve as a result of a complex interaction between strongly nonlinear processes such as near-bed turbulence, particle-particle interaction, and particle-bed interaction. This interaction contributes to the initiation and evolution of extremely variable river bed elevation patterns, commonly known as bedforms that span across a range of spatiotemporal scales. In this paper, we employ a refined definition of entropy, that is, the multiscale entropy (MSE), to characterize the observed variability in the fluctuations of bed elevation time series under variable discharges obtained from a field-scale laboratory flume. The MSE accounts for the sequence of data points in a series and quantifies the complexity and lack of information in a system. We show that the MSE of bed elevation fluctuations is higher for higher discharges. When compared with surrogates, which are the linearized series of a signal, the MSE provides across-scale information about the underlying nonlinearity and linear correlation in a signal. The MSE difference between the original and surrogate series is due to the inherent nonlinearity that is higher for higher discharge at the smaller scales and peaks at intermediate scales. These results indicate the presence of a heterogeneous arrangement of extreme fluctuations that enhances the underlying complexity in bed elevation, rendering them less predictable at higher discharges. We further investigate the role of asymmetry of the bed elevation increments in observed complexity. Our results of asymmetry together with entropy suggest that characteristics of both small- and large-scale features should be included for the accurate predictive modeling of sediment transport.