Fractal properties of simulated bed profiles in coarse-grained channels

Bed roughness characteristics in coarse-grained channels are fairly complex. A hierarchy of roughness elements can be observed, ranging from variable particle sizes and shapes and small-scale sedimentary structures, to large-scale bedforms such as riffle-pool sequences. The effects of these scales of roughness on the flow geometry still remain to be thoroughly investigated. The semivariogram has been suggested in the past as a means of quantifying bed roughness effects on streamflow, as well as for distinguishing between scales of roughness. However, field measurements are rather time-consuming. The low number of bed profiles measured in the field precludes the identification of generally applicable relationships between the statistical properties derived from the semivariograms (such as the Hausdorff dimensions and the scale of autocorrelation corresponding to each fractal band) and the bed configuration itself (geometrical and sedimentological properties). Simulation results of gravel-bed profiles are, therefore, presented in order to complement the original investigation of Robert (1988a). The simulation experiments, based on grain characteristics of sizes and shapes and on morphological properties of small-scale bedforms, yield very significant information on boundary roughness at the microscale and give insight into the interpretation of empirical semivariograms (derived from field measurements). Bed-material sorting, variable grain shapes, and height and spacing of cluster bedforms control the fractal dimensions obtained from the semivariograms, as well as the location of the break of slope and the range of the process.