Discussion: 'Macroscalesurface roughness and frictional resistance in overland flow' by D. S. L. Lawrence

Lawrence argued that the inundation ratio Lambda, defined as the mean flow depth d divided by the roughness height k, is the dominant control of flow resistance f and should be used as the primary variable when evaluating the hydraulics of overland flow on rough surfaces. Lawrence defined three flow regimes on the basis of ii and developed an expression for f in terms of Lambda for each regime. Common sense, however, suggests that f is independent of Lambda where Lambda < 1 because when roughness elements protrude through the flow, the value of f for the flow is the same regardless of the height of the elements. The error appears to have crept in as a result of Lawrence's representation of roughness elements by hemispheres. Lawrence found that f proportional to d/k, which she interpreted to mean f proportional to Lambda. However, in her model the length dimension denoted by k is in fact half the breadth b/2 of the roughness elements. The distinction between k and b/2 is important, especially for roughness elements where k not equal b/2, Thus, contrary to Lawrence's claim, f is not generally a function of Lambda. Instead, f is a function of Lambda only where Lambda > 1. Where Lambda < 1, f is a function of d/(b/2) or d/b. (C) 1998 John Wiley & Sons, Ltd.