Change of terrain roughness and the wind profile

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Abstract
To describe the distribution of wind with height in hydrostatically‐neutral air following a change in terrain roughness, a theory is constructed by assuming that only the air below an internal boundary is affected by the change and that air above the boundary is moving with the speed and Reynolds stress that it had upwind of the change of roughness. Unlike in the closely related theory of Elliott, the assumed velocity distribution in the lower layer is consistent, not with stress independent of height, but with continuous variation of stress from the surface to the boundary where the stress is that in the original layer. the condition of overall conservation of momentum then leads to relations between surface stress, boundary height and fetch. the theory is compared with observations at a variety of locations, and the agreement with measurements is satisfactory. In particular, a fairly sharp boundary separates the masses of air influenced by the two types of terrain; for micrometeorological distances, the slope of this interface is of order 1/10.

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