Aerodynamic roughness length

aerodynamic roughness length

(Also called the roughness length, z₀.) The height above the displacement plane at which the mean wind becomes zero when extrapolating the logarithmic wind- speed profile downward through the surface layer.

It is a theoretical height that must be determined from the wind-speed profile, although there has been some success at relating this height to the arrangement, spacing, and physical height of individual roughness elements such as trees or houses. The average wind speed

in the surface layer can be written using Monin–Obukhov similarity theory as

where z is height above ground, d is height of the displacement plane above ground, L is the Monin–Obukhov length scale, k is von Kármán's constant, ψ is a stability correction factor (= 0 for statically neutral conditions), and u_* is the friction velocity. To determine aerodynamic roughness, most experimentalists prefer to make wind profile measurements during statically neutral conditions (windy, overcast, negligible temperature advection) so that ψ = 0 in the equation above.
Compare Charnock's relation.

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