Extension of the Application of Classical Momentum Flux-profile Relationship in the Urban Roughness Sublayer

Eddy-correlation observations were carried out at different heights above the urban canopy in three cities, Nanjing, Changzhou, and Suzhou, China. At the site in Nanjing, the observations were conducted at 33.5 m and 48.5 m above ground level (AGL). At the site in Suzhou, the observations were conducted at 20 m, 23 m and 32 m AGL. And there are only one observation at 35 m AGL in Changzhou. At each height, the observation data are analyzed to derive the momentum flux-profile relationships, and the relationships are then compared to classical similarity relationships of Businger et al. (1971). The results show that the classical flux-profile relationships did not perform well in the urban roughness sublayer. The predicted momentum flux was found to be overestimated under unstable and near neutral conditions. And it gets closer to the observation values when the observation height gets higher. The reason is suggested to be the dependence of roughness length on the stability. The calculated roughness lengths are found to increase with observation heights under neutral conditions, while decrease with increasing instability/stability. The explanation based on the hypothesis that the roughness length can only be influenced by the buildings that lower than the observation level. Under neutral conditions, the calculated roughness length increases with normalized observation heights (z/z_H, z is observation height and z_H is mean building height). Because there are more buildings can be observed at higher observation height. Under unstable conditions, the mean flow will be influenced by the updraughts from the side walls, which means that the heights of roughness elements are the building heights together with their virtual extensions. There are some roughness elements that higher (including virtual extensions) than the observation level, comparing to neutral conditions. So the calculated roughness length decreases with increasing instability. Under stable conditions, denser-fluid occupies the lower part of the roughness layer, and the mean flow interacts only with the upper parts of the roughness elements, so the calculated roughness length decreases, suggested by Zilitinkevich et al. (2008). A parameterization of roughness length is made: z₀=z_0Ne^Ciζ, i=1,2 , where z_0N is the calculated roughness length under neutral conditions, ζ is the stability parameter, C1 and C2 are the coefficients under stable and unstable conditions. C1 and C2 are found to be related to observation height and standard deviation of building heights. The parameterization of roughness length is used in the classical momentum flux-profile relationship, and predicted momentum fluxes are close to the observation values.