Flow above the canopy

Surface roughness causes a drag on the wind expressed as a shear stress (where stress is force per unit surface area). The square root of the surface kinematic stress yjr0/p is the friction velocityg m . Dimensional arguments lead us to a logarithmic form for the wind profile such that  

For many situations, this is too restrictive and a modification must be made to account for the fact that exchanges between the atmosphere and the canopy occur at levels elevated from the ground surface by plant components. The common procedure is to introduce a quantity called the zero-plane displacement to adjust the level at which momentum, or the variety of scalar quantities, are exchanged. Whereas all levels within the canopy might be active and the various sources or sinks are distributed through the depth of the canopy, they are represented in this case by a single level. The wind profile can then be written  

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For continuity with flow within the canopy, the velocity is taken as a spatial and temporal average, (n), although above the canopy this spatial average is not needed. The effective momentum boundary is the vertical position within the canopy below which momentum from the overflow does penetrate. That is, for flow above the canopy, z = zm is an effective lower boundary and (H - zm) is the effective depth of the overflow. Friction velocity for the overflow may then be estimated as... 

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