A theory for drag partition over rough surfaces

Abstract

We present a theory for drag partition over rough surfaces of arbitrary roughness density. The total drag is partitioned into a pressure drag, a ground‐surface drag, and a roughness‐element‐surface skin drag. The theory is simple but allows for the estimations of drag partition functions, friction velocity, zero‐displacement height, and roughness length. The model estimates of these quantities are compared with observations and the model is found to perform well. The theory explains several known facts from observations such as the dependency of aerodynamic roughness length on roughness density. It is shown that drag partition is governed entirely by two functions fr and fs which represent the dependencies of surface drag coefficient and the roughness drag coefficient on roughness density. Under the condition of fr = fs, the Raupach (1992) model is derived without assumptions in addition to the drag laws.