Dust Production Mechanisms - Mineral Dust: A Key Player in the Earth System - page 105

Greeley et al. ( 1994 ) allowed tests of these different expressions. These authors
found that Bagnold's ( 1941 ) model and White's ( 1979 ) formulations most closely
agree with the experimental data. However, as noted by Shao ( 2000 ), regarding the
uncertainties associated with the estimation of the erosion threshold, it is difficult
to determine the agreement of different expressions of the saltation flux with field
measurements. White's equation, which includes a threshold term, is given here as
a typical example for the vertically integrated horizontal flux, Q:

1

!

g U 3 1

U t 2
U 2

U t
U

c

D C

Q (5.8)

where c is an adjustment constant.
The problem in applying this formulation to natural situations is that the soil
grains are generally not characterised by a uniform diameter. As the equation of
U t is non-linearly dependent on particle diameter, the adequate size-dependent
threshold value will be affected by each size range, and thus the soil grain size
distribution must be represented by a continuous function. Both Marticorena and
Bergametti ( 1995 ) and Shao et al. ( 1996 ) included a size-dependent expression of
the erosion threshold in the horizontal flux equation. The flux produced by each
particle size range is weighted by its relative mass (Shao et al. 1996 ) or relative
basal surface (Marticorena and Bergametti 1995 ). An illustration of the influence
of the soil size distribution on the computed horizontal flux is given in Fig. 5.4 .
The horizontal flux is according to Marticorena and Bergametti ( 1995 ) for a soil
mass size distribution composed of two log-normal populations: a fine and a coarse
mode representing, respectively, 30 and 70 % of the soil mass size distribution.
The comparison between the relative mass and surface size distribution shows that
weighting the flux by the relative surface distribution increases the contribution of
the finer mode compared to the coarse mode. This predominance of the finer mode is
reinforced by the fact that this size range has a lower erosion threshold. As a result,
when U * is close to the minimum erosion threshold, only the fine mode contributes
to the erosion flux. When the wind friction velocity increases, the size distribution of
the horizontal flux broadens and progressively tends towards the size distribution of
the parent soil. This parameterisation reproduces the change in size distribution
between the eroding soil and the horizontal flux as a function of U * observed
in wind-tunnel experiments (Williams 1964 ) for simple soil size distributions
(Marticorena and Bergametti 1995 ). However, its application in the field, with
poly-disperse soil size distribution reveals some difficulties in reproducing the size
distribution of the horizontal flux. As an example, Flores-Aqueveque et al. ( 2010 )
noted that the model satisfyingly retrieved the total mass flux, while the measured
size distribution of the horizontal mode was much coarser than the predicted one.
Reproducing the size distribution of the horizontal flux is a key issue in representing
dust emission because the energy required for releasing fine dust particles from the
surface or from soil aggregates will be supplied mainly by the kinetic energy of the
saltating soil particles. The size distribution of the saltation flux and its dependence