Roughness Lengths for Momentum and Heat Derived from Outdoor Urban Scale Models

Abstract

Urban climate experimental results from the Comprehensive Outdoor Scale Model (COSMO) were used to estimate roughness lengths for momentum and heat. Two different physical scale models were used to investigate the scale dependence of the roughness lengths; the large scale model included an aligned array of 1.5-m concrete cubes, and the small scale model had a geometrically similar array of 0.15-m concrete cubes. Only turbulent data from the unstable boundary layers were considered. The roughness length for momentum relative to the obstacle height was dependent on wind direction, but the scale dependence was not evident. Estimated values agreed well with a conventional morphometric relationship. The logarithm of the roughness length for heat relative to the obstacle height depended on the scale but was insensitive to wind direction. COSMO data were used successfully to regress a theoretical relationship between B Ϫ1 , the logarithmic ratio of roughness length for momentum to heat, and Re*, the roughness Reynolds number. Values of B Ϫ1 associated with Re* for three different urban sites from previous field experiments were intercompared. A surprising finding was that, even though surface geometry differed from site to site, the regressed function agreed with data from the three urban sites as well as with the COSMO data. Field data showed that B Ϫ1 values decreased as the areal fraction of vegetation increased. The observed dependency of the bulk transfer coefficient on atmospheric stability in the COSMO data could be reproduced using the regressed function of Re* and B Ϫ1 , together with a Monin-Obukhov similarity framework.

Trade-offs and responsiveness of the single-layer urban canopy parametrization in WRF: An offline evaluation using the MOSCEM optimization algorithm and field observations

“…However, since the ratio of roughness length for momentum to heat is considerably larger over urbanized surfaces than vegetated ones (Voogt and Grimmond, 2000), a specific approach to the modelling of Z 0HR and Z 0HC needs to be taken for the SLUCM. The relation derived by Kanda et al (2007) using an outdoor scale model and evaluated against field data is chosen because it was developed specifically for urban conditions and has recently been applied to the Simple Urban Energy Balance Model for Mesoscale Simulations (SUMM), which is very similar to the SLUCM in its approach (Kanda et al, 2005;Kawai et al, 2009). It links the roughness length for heat to that for momentum using the roughness Reynolds number and an empirical constant a K (Table II, Eqs 24, 25).…”

“…It links the roughness length for heat to that for momentum using the roughness Reynolds number and an empirical constant a K (Table II, Eqs 24, 25). The formula is applied to both the roof surfaces and canyon space using the best-fit value of a K = 1.29 identified by Kanda et al (2007) as well as two distinct values of the roughness Reynolds number (Table II, Eq. 26).…”

“…In that sense they do not relate to any objectively measurable quantity and can only be determined with regard to a given experiment (e.g. Kanda et al (2007) found a K varied (1.24-1.41) depending on dataset in their study). Although not an input, coefficients α m and β m from MacDonald et al (1998) are in the same Table V.…”

Parametrisation of the variety of human behaviour related to building energy consumption in the Town Energy Balance (SURFEX-TEB v. 8.2)

“…The aerodynamic roughness length is assumed to be the building height divided by 10. The roughness length for scalar quantities is calculated following Kanda et al (2007).…”

On the Relevance of ln(z0/z0T) = kB-1

“…1 The variation with surface roughness Reynolds number of the boundary-layer resistance factor kB −1 = ln(z 0 /z 0T ), as determined for the case of heat transfer and as reported by G&H. The solid circles (•) represent the average results from datasets originally available to G&H. Two additional averages are plotted, both discussed below: black up-pointing triangle daytime results obtained over natural fallow in Zimbabwe, and black down-pointing triangle the average of daytime measurements made over grazed pasture in Alabama. The curves drawn are due to, (1) Zhang et al (2001), (2) Owen and Thomson (1963), (3) Brutsaert (1975), and (4) Kanda et al (2007). Curve (5) has been created using random numbers kB −1 decreases uniformly from a maximum value of about 2 at Re * = 10 2 to about zero at Re * = 10 5 , much as might be concluded from Fig.…”