Flux-gradient profiles for momentum and heat over an urban surface

Abstract

In this paper, we evaluate the applicability of flux-gradient relationships for momentum and heat for urban boundary layers within the Monin-Obukhov similarity (MOS) theory framework. Although the theory is widely used for smooth wall boundary layers, it is not known how well the theory works for urban layers. To address this problem, we measured the vertical profiles of wind velocity, air temperature, and fluxes of heat and momentum over a residential area and compared the results to theory. The measurements were done above an urban canopy whose mean height zh is 7.3 m. 3-D sonic anemometers and fine wire thermocouples were installed at 4 heights in the region 1.5zh < z < 4zh. We found the following: (1) The non-dimensional horizontal wind speed has good agreement with the stratified logarithmic profile predicted using the semi-empirical Monin-Obukov similarity (MOS) function, when it was scaled by the surface friction velocity that is derived from the shear stress extrapolated to the roof-top level. (2) The scaled gradient of horizontal wind speed \(\phi_M =(dU/dz)kz^\prime/u_{\ast}\) followed a conventional semi-empirical function for a flat surface at a level (z/zh = 2.9), whereas, in the vicinity of the canopy height \({\phi_M}^{-1}\) was larger than the commonly-used empirical relationship. (3) The potential temperature profile above the canopy shows dependency on the atmospheric stability and the scaled gradient of temperature \((\phi_H=(d\theta/dz){kz^\prime/T_{\ast}})\) is in good agreement with a conventional shear function for heat. In the case of heat, the dependency on height was not found. (4) The flux-gradient relationship for momentum and heat in the region 1.5zh < z < 4zh was rather similar to that for flat surfaces than that for vegetated canopies.