Statistical characterization of bed roughness due to bed forms

Bed form geometry and dynamics in a straight section of the Elbe River in Germany is analyzed considering the measured bed surfaces as two-dimensional random fields of bed elevations. Statistically derived roughness parameters are evaluated from high-resolution digital elevation models, which were available for a range of flow rates from low flows to floods. The key results relate to the identification of characteristic scaling regions in the bed surface spectra, and to observed relationships between water discharge and both the standard deviation and a factor of the "-3" spectral law of bed elevations. Two-dimensional second-order structure functions of bed elevations are also analyzed to gain further insight into the spatial structure of sand wave beds. In addition, the interrelations between flow rate hysteresis and the statistical structure of bed forms, as well as effects of channel modification by groynes, are highlighted and discussed. The reported results demonstrate that statistical parameters of bed forms may be used for characterization and prediction of flow-dependent sand bed roughness.