Surface roughness

Inlet velocity profiles

Within the atmospheric boundary layer (ABL) the wind speed varies from zero at the ground to the gradient wind speed at the top, where surface friction is no longer affecting the wind. The actual shape of the vertical velocity profile depends on the upstream land surface and the thermal state (stability) of the boundary layer. The wind profile is often approximated by a semi-empirical logarithmic formulation:

$$ u_{z}={\frac {u_{*}}{\kappa }}\left[\ln \left({\frac {z-d}{z_{0}}}\right)+\psi (z,z_{0},L)\right] $$

where z is height above ground, $u_*$ is friction velocity, $\kappa$ is the von Kármán constant, $z_0$ is a surface roughness length scale and d is a displacement height. $\psi$ is a correction term for atmospheric stability, which is zero for neutral thermal stratification. This formulation is valid inside the surface layer which usually comprises the lowest 50-200 meters of the ABL.

In ArchiWind a neutrally stratified logarithmic wind profile is used. The wind inlet profile is determined individually for each wind direction. The dominating land cover class inside a sector extending 500 meters upstream of the simulation domain inlet is used to determine the surface roughness length ($z_0$). Offshore wind profiles are modeled using the Charnock relation relating $z_0$ to mean wind speed.

For an urban site, the inlet velocity profile mainly affects the wind speed close to the inlet edge of the domain and at high altitudes, since the building geometries would create strong mixing of the vertical layers further downstream. Tall buildings will contribute to the mixing of energy from the higher windspeeds aloft towards the ground.

Land cover data

Land cover data is retrieved from the ESA WorldCover project [2021]. The dataset contains land cover data, derived from Sentinel-1 and Sentinel-2 satellite data, with global geographic coverage and 10 meters spatial resolution.

The earth surface is categorized and divided into 11 land cover classes. For each class, a representative aerodynamic surface roughness length scale ($z_0$) is found from an empirical look-up table and used in the equations to calculate the average vertical wind profiles used in the simulations. The “Permanent water bodies” class is a special case, since the surface roughness depends on the wave conditions. For this case the Charnock relation is used to calculate the roughness length from the mean wind speed at the site. Some sites might have seasonal variations in land cover caused by e.g. snow cover or crops, but this is not reflected in the land cover data.

Terrain surface roughness

Surface roughness on the terrain surface inside the simulation domain is currently not implemented in ArchiWind.