A canopy model of mean winds through urban areas

An urban canopy model is developed for spatially averaged mean winds within and above urban areas. The urban roughness elements are represented as a canopy-element drag carefully formulated in terms of morphological parameters of the building arrays and a mean sectional drag coefficient for a single building. Turbulent stresses are represented using a mixing-length model, with a mixing length that depends upon the density of the canopy and distance from the ground, which captures processes known to occur in canopies. The urban canopy model is sufficiently simple that it can be implemented in numerical weather-prediction models. The urban canopy model compares well with wind tunnel measurements of the mean wind profile through a homogeneous canopy of cubical roughness elements and with measurements of the effective roughness length of cubical roughness elements. These comparisons give confidence that the basic approach of a canopy model can be extended from fine-scale vegetation canopies to the canopies of large-scale roughness elements that characterize urban areas. The urban canopy model is also used to investigate the adjustment to inhomogenecus canopies. The canonical case of adjustment of a rural boundary layer to a uniform urban canopy shows that the winds within the urban canopy adjust after a distance x(0) = 3L(c) ln K, where L-c is the canopy drag length-scale, which characterizes the canopy-element drag, and In K depends weakly on canopy parameters and varies between about 0.5 and 2. Thus the density and shape of buildings within a radius x(0) only determine the local canopy winds. In this sense x(0) gives a dynamical definition of the size of a neighbourhood. The urban canopy model compares well with observations of the deceleration of the wind associated with adjustment of a rural boundary layer to a canopy of cubical roughness elements, but only when the sectional drag coefficient is taken to be somewhat larger than expected. We attribute this discrepancy to displacement of streamlines around the large-scale urban roughness elements, which yields a stress that decelerates the wind. A challenge for future research is to incorporate this additional 'dispersive stress' into the urban canopy model.