Performance of Different Sub-Grid-Scale Surface Flux Parameterizations for Urban and Rural Areas - Meteorological and Air Quality Models for Urban Areas - page 19

Fig. 3.1 Land use in the
model domain (See also
Colour Plate 6 on page 173)

using e.g. an effective roughness length z 0 .This z 0 is an artificial homogeneous
roughness length representative for each grid box.

n

z 0 = f i z 0i (3.1)

i = 1

The same averaging is applied for the other surface characteristics. This method
has the advantage of being very cost-efficient and it performs well as long as the
surface characteristics are not too distinct. Problems may arise when an area with a
large fractional coverage connected with a marginal flux is next to a small area with
a large flux. In these cases, the grid box flux based on averaged parameters might
be overestimated or have a direction counter the area-averaged vertical temperature
gradient.
This problem should be solved when applying the more expensive flux aggre-
gation method using a blending height concept (von Salzen et al., 1996). Here the
sub-grid-scale surface fluxes are calculated for each land-use class i based on the
class specific roughness lengths for momentum z 0 i , temperature and humidity ( z 0qi ).
As an example the latent heat flux is given:

i = 1

n

ρ l 21 q ∗ u ∗ = ρ l 21 f i q ∗ i u ∗ i

2 U

= ρ l 21 κ ( z 1 )

ln z 1

z 0 i

− ψ m z L i

ln z 1

z 0 qi

− ψ q z L i − 1
(3.2)

i = 1

n

f i · q q z 0 qi ·

· ( z 1 ) − ·