Spatial variation of bed roughness in eroding rills and gullies

When overland flow concentrates rill and gully channels can be formed if a series of thresholds are exceeded. These thresholds are more or less explicitly linked to the erosion resistance of the topsoil. Moreover, flow velocity and channel width depend on total flow discharge. More recently also bed roughness in eroding channels has been attributed to the eroding effect of flow discharge while channel width was shown to be the result of the interplay between erosion resistance of the topsoil and flow discharge (see channel junction approach,Torri et al., 2006), which could be described by a modified Leopold and Maddock's relationship. The objective of this paper is to investigate the spatial variability of channel bed roughness in rills and gullies using an approach based on these findings. Field data confirm the various aspects reported so far. Hence these were used to develop a new equation allowing one to predict bed roughness in eroding rill and gully channels. Each of the new aspects introduced into the channel width–flow discharge equation by the channel junction approach is discussed and verified with new data. The validity of this approach is tested against channel data from Mars. Finally, an equation predicting bed roughness and based on stream power is developed and compared with measured rill and gully bed roughness successfully, confirming that 1) bed roughness, if generated by concentrated flow, increases with stream power; 2) channel width, local bed slope, topsoil cohesion at saturation, and grain size are all important factors controlling channel bed roughness; and 3) these variables as well as soil characteristics, all measurable in the field after a rill or gully forming event, are sufficient to determine channel bed roughness. Therefore one may expect that bed roughness of an eroded channel (and consequently hydraulic roughness or friction) will generally increase with bed gradient, erosion resistance of the soil and grain size, following a logic which is best expressed by the final equations described in this paper.status: publishe