Dust Production Mechanisms - Mineral Dust: A Key Player in the Earth System - page 101

part of the surface must at least be equal to the shear stress corresponding to U t
in a “smooth” situation. This explains why U t measured in settings with roughness
elements are apparently higher than those in smooth surface settings. However, for a
given wind velocity at a fixed height, the surface wind shear stress and thus U * both
increase with Z 0 . The increase of the erosion threshold is generally predominant,
and a decrease of the soil losses due to wind erosion is generally observed when Z 0
increases (e.g. Fryrear 1985 ). This partition of wind shear stress can be theoretically
investigated by describing the forces exerted on the roughness elements, which is a
function of their surface exposed to the wind and their aerodynamic properties or
drag coefficients. This explains why the description of the drag partition generally
involves the roughness density or lateral cover, defined as the sum of the frontal
surface of the exposed roughness elements divided by a reference of unit horizontal
surface S: nbh =S, where n is the number of roughness elements, and b and h

are the mean width and height, of the roughness elements.
To determine predictive expressions for practical applications, Raupach ( 1992 )
proposed an analytical treatment of the drag partition on a rough surface based on
a dimensional analysis and physical hypothesis. The proposed equation gives the
ratio of the overall shear stress to the shear stress on the uncovered and erodible
surface as a function of the roughness density r , the ratio of the drag coefficients
of the roughness elements C R and of the erodible surface C S (ˇ r D

D

C R / C S ), r the
ratio of basal and frontal surfaces of the roughness elements and m r , a coefficient
accounting for the local shear stress acceleration (0> m r > 1).

r / 1=2 .1 m r ˇ r / 1=2 f R ./ D .1 C (5.6)

Predictions based on this equation agree well with the wind-tunnel dataset of
Marshall ( 1971 ), for ˇ r ranging from 0.0002 to 0.2 and other measurements
performed in wind tunnels or for natural sites (Raupach et al. 1993 ). Roughly,
the wind shear stress on the erodible part of the surface decreases as ˇ r increases
and becomes negligible for a value of 0.03. This provides an estimation of the
critical value of ˇ r for which the decrease of the wind shear stress on the uncovered
surface is such that it should inhibit erosion. When applied to field situations, this
formulation requires the introduction of an empirical parameter ( m r in Eq. 5.6 )that
reflects the differences between the average and the maximum stress on the surface
(Raupach et al. 1993 ). The practical use of this equation as a predictive tool is not
evident because of the difficulty in estimating the empirical parameter and the drag
coefficients of the obstacles. For example, to represent the shear stress partition
in sparsely vegetated desert canopies, Wolfe and Nickling ( 1996 ) tested various
combinations of values for these parameters and determined the appropriate values,
a posteriori, as those matching the experimental data.
Alternative approaches of the drag partition use a more integrative parameter
to represent the effect of roughness elements, Z 0 . In micrometeorology, Z 0 is
the length scale that characterises the loss of wind momentum attributable to
roughness elements. For aerodynamic roughness lengths ranging from 10 4 to