Geostatistical analysis of the effects of stage and roughness on reach-scale spatial patterns of velocity and turbulence intensity

Abstract

Although previous research has documented well-organized interactions between the turbulent flow field and an irregular boundary, the spatial variability of turbulent flow characteristics at the reach-scale remains poorly understood. In this paper, we present detailed field measurements of three-dimensional flow velocities and turbulence intensities in a high-gradient, cobble-bed riffle from three discharges; additional data on sediment grain size and bed topography were used to characterize boundary roughness. An acoustic Doppler velocimeter was used to measure velocities along five cross-sections within a 6 m long reach of the North Fork Cache La Poudre River; vertical profiles were also measured along the channel thalweg. We adopted a spatially explicit stochastic hydraulic approach and focused not on coherent flow structures per se but rather time-averaged, reach-scale variability and spatial pattern. Scaling velocities and turbulence intensities by the reach-averaged friction velocity U ⁎ accounted for changes in flow depth and enabled comparisons among the three discharges. We quantified the effects of stage and roughness by assessing differences among probability distributions of hydraulic quantities and by examining geostatistical metrics of spatial variability. We computed semivariograms for streamwise and transverse directions and fit parametric models to summarize the spatial structure of each variable at each discharge. Cross-correlograms were also used to describe the local and lagged effects of boundary roughness on flow characteristics. Although the probability distributions yielded some insight, incorporating spatial information revealed important elements of stage-dependent flow structure. The development of secondary currents and flow convergence at higher stages were clearly documented in maps and semivariograms. In general, the spatial structure of the flow field became smoother and more continuous as stage increased and the effects of boundary roughness diminished. Although roughness elements do influence velocities and turbulence intensities, our data suggest that the flow primarily responds to the gross morphology of the channel and that flow depth is the primary control on flow structure. The geostatistical framework proved useful, and our results indicate that a complete stochastic description must also be explicitly spatial.