Displacement Height and Roughness Length of Forests – Are They Really Dependent on Stability?

Abstract:

Displacement height d and roughness length zo are two important parameters in a commonly used Obukhov-Monin similarity-theory wind-profile formulation. These parameters have historically been considered to be properties of the underlying surface. A few studies have pointed out that d and zo for tall vegetation, like forest, are also dependent on stability. Since d and zo are defined by the semi-logarithmic law, the most strict determination of them would be based on the upper part of the surface layer, which is free of roughness sublayer effects. Often the displacement height is determined from the wind profile inside the stand. The present study makes use of measurements with 14 3D sonic anemometers (Metek) in the Norunda forest in Sweden. This site is dominated by pine with trees up to 26 m tall. The sonics were mounted at 1.8, 4.4, 9.5, 14.8, 20.8, 26.6, 29.6, 32.7, 37.9, 44.7, 59.5, 74, 88.5 and 101.8 m heights. Data from two summer seasons, 2014 and 2015, were used in the current analysis. A serious complication was that the momentum and sensible heat fluxes were rarely constant with height. Also, during nighttime profiles appeared with nearly constant wind speed in the upper part of the profile. In our analysis, the Obukhov length was calculated from friction velocity and sensible heat flux averaged for 26.6, 29.6 and 32.7 m. The mean friction velocity and Obukhov length were then used in the profile formulation. Displacement height giving the best match to the measured data at 44.7, 59.5, 74, 88.5 and 101.8 m was searched for. This method gave extremely erratic results. Alternatively, d was estimated using the exponential law with measurement heights 9.5, 14.8, 20.8 and 26.6 m giving d close to 22 m with a tendency of slightly increasing d towards more stable situations, but with large uncertainty. We then used a constant d of 22 m in the upper part of the profile and this resulted in zo of about 2.5 m. A small tendency of lower zo could be observed for very stable conditions, but with large uncertainty. At present we cannot confirm that d and zo are dependent on stability. We need to extend our analysis by including the roughness sublayer effects and the full length of measured profiles.