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Boundary-Layer Meteorol (2012) 145:423437 DOI 10.1007/s10546-012-9747-0
ARTICLE
Equations for the Drag Force and Aerodynamic Roughness Length of Urban Areas with Random Building Heights
Richard D. Crago Winnie Okello Michael F. Jasinski
Received: 13 July 2011 / Accepted: 14 June 2012 / Published online: 10 July 2012 Springer Science+Business Media B.V. 2012
Abstract We use a conceptual model to investigate how randomly varying building heights within a city affect the atmospheric drag forces and the aerodynamic roughness length of the city. The model is based on the assumptions regarding wake spreading and mutual sheltering effects proposed by Raupach (Boundary-Layer Meteorol 60:375395, 1992). It is applied both to canopies having uniform building heights and to those having the same building density and mean height, but with variability about the mean. For each simulated urban area, a correction is determined, due to height variability, to the shear stress predicted for the uniform building height case. It is found that u/uR, where u is the friction velocity and uR is
the friction velocity from the uniform building height case, is expressed well as an algebraic function of and h/hm, where is the frontal area index, h is the standard deviation of the building height, and hm is the mean building height. The simulations also resulted in a simple algebraic relation for z0/z0R as a function of and h/hm, where z0 is the aerodynamic roughness length and z0R is z0 found from the original Raupach formulation for a uniform canopy. Model results are in keeping with those of several previous studies.
Keywords Buildings Aerodynamic roughness length Shear stress Urban
1 Introduction
Urban areas are characterized by their very rough surfaces (Liu et al. 2008), relatively low evaporation rates, high sensible heat uxes and high surface temperatures during the day. Regional climates in and around cities are known to differ from the surrounding areas for these and other reasons, resulting in urban heat islands, altered precipitation patterns (Shepherd and Burian 2003) and other impacts. Cities have complex roughness element
R. D. Crago (B) W. Okello
Department of Civil and Environmental Engineering, Bucknell University, Lewisburg, PA 17837, USA e-mail: [email protected]
M. F. JasinskiHydrological Sciences Branch, NASA/Goddard Space Flight Center, Greenbelt, MD, USA
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geometries (Ratti et...