A parameterization of heat and momentum fluxes in ... - LPAS - EPFL

The impact of the walls is modelled in a way similar to what it is done in vegetation canopy
models:
3
w drag ort
E = ρC U
⎡ SW
⎢
⎣V
−V
b
⎤
⎥
⎦
In the formulation by Bougeault and Lacarrere, the length scales used for the computation of
the dissipation and that for the turbulent diffusion coefficients, are function of the TKE value
in the point and the profile of potential temperature.
In the case of an urban surface, the presence of buildings can induce some circulation of a size
comparable with that of the roughness element. For this reason, below roof level we added a
second length scale (the roughness element size):
1 1 1
= +
l l hu
B
where hu is the building’s height and l B
is the length scale computed with the original
formulation.
Vertical profiles of TKE normalised by the square root of the Reynolds Stress at the roof
height are shown in Fig. 6.
Figure 6: Vertical profile of the ratio between the turbulent kinetic energy and the square root of the Reynolds
Stress computed by the model in the centre of the urban area at different time of the day.
Those values are consistent with the measurements of Rotach (1993) around roof height and
with that of Feigenwinter et al. at 2-3 times the building height.
As for momentum, also for TKE the most active surface is the walls.
4. Conclusions
A parameterisation for heat and momentum fluxes for mesoscale models in urban areas is
presented. The formulation takes into account separately the impact of the three active
surfaces of the roughness element: wall, street and roof. The modifications were introduced in
a mesoscale model and tested in a simple 2D case. A comparison with series of field