Reply: ‘Macroscale surface roughness and frictional resistance in overland flow’

Abstract

The model for characterizing frictional resistance in overland flow as a function of surface roughness inundation presented in Lawrence (1997, Earth Surface Processes and Landforms, 22, 365–382) is neither in error nor at odds with physical intuition. The proposed model provides a simple, physically derived explanation for the relationship between frictional resistance and flow depth during the progressive inundation of surface roughness and is applicable to data acquired under a variety of field and experimental conditions. In maintaining these objectives, the model uses a single length scale for characterizing the surface roughness and it is assumed that the size of the roughness elements can be represented by this one measure. This is the only approach that can be physically justified for the range of data considered. Abraham's alternative model for the case of partial inundation (1998, Earth Surface Processes and Landforms, this issue) requires that the surface roughness elements be quantified in terms of two distinct length scales. Although this may be feasible within the context of laboratory and some very detailed field studies, it is not compatible with data more widely available. The alternative model Abrahams proposes is actually only useful for the case of circular cylindrical roughness elements and cannot be applied to objects of arbitrary shape as it is based on an implicit assumption requiring the two principal axes in the horizontal plane to be of equivalent lengths. The correct scaling for non-equidimensional shapes is given by f ∼ d/c (where c is the horizontal axis parallel to the direction of flow), rather than the scaling f ∼ d/b suggested by Abrahams. The generalization of the proposed heuristic model of Lawrence (1997) to a more precise description of surface geometry should, however, be undertaken with caution, as variations in other equally important factors (e.g. the coefficient of drag, the free surface elevation, and the size distribution of the surface roughness elements) also need to be taken into account in developing a more detailed model. © 1998 John Wiley & Sons, Ltd.