1 Spatial Modelling of the Terrestrial Environment - Georeferencial

142 Spatial Modelling of the Terrestrial Environment
Table 7.1 Variations in F a /Q Tot as a function of soil texture
(from Gillette et al. (1997))
Log of F a /Q tot (cm −1 )
Number of
Texture Average Minimum Maximum samples
Clay −6.4 −6.5 −6.3 2
Loam −5.7 −5.7 −5.7 1
Sandy loam −3.7 −4.1 −3.5 2
Loamy sand −4.5 −5.9 −4.2 7
Sand −5.7 −6.6 −5.1 28
c○1997 American Geophysical Union, reproduced with permission
(cm −1 ) that is typically of order of 10 −4 −10 −5 cm −1 that varies with soil texture (see
Table 7.1) (Gillette et al., 1997). F a is envisioned as the mass leaving the surface per unit
time.
The shear velocities, u ∗ and u ∗t , are related to wind speed at height z, U(z) (cm s −1 ),
by:
U(z) = u ( )
∗ z − D
k ln , (2)
z 0
where k is von Karmann’s constant (unitless), z 0 is the roughness height (cm) and D is
the displacement height (cm). If D > 0, then turbulent flow in wakes predominates and no
wind erosion can occur.
Kaimal and Finnigan (1994, p. 68) have suggested that D is approximately related to
canopy height, h c (cm) by:
D = 0.75h c . (3)
While this relationship may hold when considering boundary layer phenomena that take
place above the canopy, equation (3) dictates a non-zero D and therefore no wind erosion,
for all vegetated surfaces (surfaces with h c ≠ 0). Modelling approaches to wind erosion
must assume that D = 0, so that wind erosion is allowed on vegetated surfaces and roughness
height, z 0 , must be assumed to be the determinant of the relationship between U(z)
and u ∗ .
Several authors have proposed relations to predict z 0 as a function of surface roughness.
Lettau (1969) and Wooding et al. (1973) have suggested parameterization of z 0 by:
z 0 = 0.5h c λ, (4)
where λ is a unitless parameter known as ‘lateral cover’ (Raupach et al., 1993) or ‘roughness
density’(Marticorena et al., 1997). Lateral cover is equal to the average frontal area of plants
multiplied by their number density, N (cm −2 ). Number density is related to fractional cover
of vegetation, C (unitless) by:
where A p is the average footprint of individual plants (cm 2 ).
N = C A p
, (5)