Statistical Roughness Parameter as Indicator of Channel Flow Resistance

Abstract

In an analysis of field data of four natural rivers a statistical, large‐scale roughness parameter has proved effective as an indicator of the channel resistance to the flow when the Froude number based on the mean annual flow is larger than about 0.2. The parameter is derived from the concept that the irregular shape and slope of an irregular alluvial channel may be considered as a result of the random walk of imaginary ‘particles’ along the channel bed. It is the so‐called diffusion coefficient which, according to the stochastic theory of the diffusion process, is normally defined in a diffusion equation as the mean square or the variance of the displacement of the particles during a step of random walk over a constant time interval of length Δt divided by 2 Δt. In the present study, however, Δt represents a constant distance interval instead. The parameter proved to have characteristics similar to those of another large‐scale roughness parameter that is derived by other investigators from concepts other than the statistical. This roughness parameter provides a new statistical geometric measure of the irregularities along the entire channel bed and sides that is related to the probability of channel geometry through the diffusion equation, which provides the conceptual basis for its use as a roughness parameter.