A theory is developed to describe the dependence upon roughness density of the threshold friction velocity ratio Rt, the ratio of the threshold friction velocity of an erodible surface without roughness to that of the surface with nonerodible roughness present. The roughness density is quantified by the frontal area index λ. The prediction is Rt=(1-m&sgr;λ)-1/2(1+mβλ)-1/2 where β is the ratio of the drag coefficient of an isolated roughness element on the surface to the drag coefficient of the substrate surface itself; &sgr; is the basal-to-frontal area ratio of the roughness elements; and m (<1) is a parameter accounting for differences between the average substrate surface stress and the maximum stress on the surface at any one point. The prediction is well verified by four indepedent data sets.<