Turbulent Transport in the Atmospheric Surface Layer - Transport in the Atmosphere-Vegetation-Soil Continuum - page 121

Roughness Length and Displacement Height: Values
For a particular surface the roughness length needs to be determined locally (using
the method described in the previous subsection). The roughness length for momen-
tum can be considered to be a constant surface property, although for some surfaces
(e.g., long grass, water) the roughness may depend on wind speed. At higher wind
speeds grass bends and becomes smoother, whereas on water waves will develop that
make the surface rougher.
However, local observations are usually not available and therefore one has to
revert to tabulated values or simple models. The simplest model is that the z 0 would
be proportional to the canopy height h c , or better, the height of that part of the canopy
that extends above the displacement height (Garratt, 1992 ):

( ) z = γ c hd (3.41)

0 1

γ 1 is of the order of 0.2 to 0.4. With the rule of thumb that d = 2/3 h c , this gives z 0 /h c
in the range 0.07 to 0.14 (i.e., order 0.1).
The proportionality will depend on the density and distribution of the roughness
elements. If there are only few elements per unit area, or if they are very narrow,
the low will hardly be affected by the roughness elements and the constant of
proportionality will be smaller than at a medium element density. On the other
hand, at high obstacle density (e.g., a dense forest) the low will no longer enter
the region between the roughness elements and will 'skim' the surface, yielding
again a lower constant of proportionality (Garratt, 1992 ). This is illustrated in
Figure 3.19 .
For the displacement height similar arguments hold with respect to the relationship
to obstacle density: at low obstacle density d/h c will be close to zero since the low
will hardly be lifted. On the other hand for high densities the low 'skims' the surface
and will experience the surface as a rather smooth, lifted surface: d/h c will tend to one.
Typical values for displacement height and aerodynamic roughness length are given
in Table 3.3 .
Regarding the roughness length for scalars (in particular temperature) a distinction
needs to be made with respect to surface type:

• For permeable surface cover (dense packing of small individual elements, e.g., vegeta-

tion fully covering the ground) a commonly used value for to κ B -1 = 2, corresponding to
z 0 / z 0h is 7.4 (see, e.g., Garratt and Francey, 1978).
For bluff body surface cover (nearly impermeable obstacles, or sparse vegetation with •

patches of bare soil in between) κ B -1 can be of the order of 4-12 and thus z 0 / z 0h of the
order of 55 to 10 5 (Stewart et al., 1994 ). For bluff body surfaces the roughness length
ratio also depends on wind speed (see, e.g., Malhi, 1996 ). For sparse vegetation on dry
bare soil the large difference between z 0 and z 0h can be understood as follows. The main