Abstract
A widely used morphometric method (Macdonald et al. 1998) to calculate the zero-plane displacement (zd) and aerodynamic roughness length (z0) for momentum is further developed to include vegetation. The adaptation also applies to the Kanda et al. (2013) morphometric method which considers roughness-element height variability. Roughness-element heights (mean, maximum and standard deviation) of both buildings and vegetation are combined with a porosity corrected plan area and drag formulation. The method captures the influence of vegetation (in addition to buildings), with the magnitude of the effect depending upon whether buildings or vegetation are dominant and the porosity of vegetation (e.g. leaf-on or leaf-off state). Application to five urban areas demonstrates that where vegetation is taller and has larger surface cover, its inclusion in the morphometric methods can be more important than the morphometric method used. Implications for modelling the logarithmic wind profile (to 100 m) are demonstrated. Where vegetation is taller and occupies a greater amount of space, wind speeds may be slowed by up to a factor of three.
Highlights
During neutral atmospheric stratification, the mean wind speed (Uz) at a height z, above a surface can be estimated using the logarithmic wind law (Tennekes, 1973): Uz 1⁄4u* κ ln z À zd z0 (1)where u* is the friction velocity, κ ~ 0.40 (Ho€gstro€m, 1996) is von Karman's constant, z0 is the aerodynamic roughness length, and zd is the zero-plane displacement
Report CDv for three poplar tree crowns varying from 1.1 to 0.1 with wind speeds between 1 and 15 m sÀ1. These results indicate at high wind speeds the relative drag of an individual tree (CDv ~ 0.1–0.2) is small compared to that of buildings, but during some flow conditions CDv can approach that of a solid structure of similar shape (i.e. 1.2) and exert similar drag to buildings
The influence of vegetation and buildings upon geometric parameters depends upon the dominant roughness elements: when buildings dominate (CC_lv and CC_hv), height based geometric parameters for all roughness elements are determined by buildings (Table 1); and, if vegetation is taller than buildings (SB_hv and Pa), the Hav, Hmax and σH of all roughness elements become noticeably larger than Hav,b, Hmax,b and σH,b (Table 1, subscript b denotes buildings only)
Summary
The mean wind speed (Uz) at a height z, above a surface can be estimated using the logarithmic wind law (Tennekes, 1973): Uz. where u* is the friction velocity, κ ~ 0.40 (Ho€gstro€m, 1996) is von Karman's constant, z0 is the aerodynamic roughness length, and zd is the zero-plane displacement. Uncertainties in wind-speed estimations arise from using idealised wind-speed profile relations, as well as representing the surface using only two roughness parameters (zd and z0), which are based upon a simplification of surface geometry. An uncertainty of >2.5 m sÀ1 exists (>25% of the mean wind speed) due to the flow variability throughout the profile (Kent et al, 2017a; their Fig. 7). Standard deviation of roughness-element heights σv Standard deviation of lateral wind velocity (crosswind) τ
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