FIELD TESTING AND EVALUATION OF DUST DEPOSITION AND ...

downwind concentration profile is dependent on u * . In contrast, the ISC model
prescribes the concentration profile based on downwind distance only. In practice, this
means that the ISC does not allow for alteration of the concentration profile due to
variations in u * . This point is illustrated in the next chapter.
Figure 4-7 f. shows the fraction remaining in suspension according to the box
model for various values of the parameter A in Equation 4-29. The deposition velocity
for the box model was computed assuming a height of 1 meter and neutral stability. Note
that the box model gives a result that is independent of distance downwind of the source.
For all values of A, the box model captures the general behavior of particle deposition to
a surface; the greater the dispersion rate (as characterized by A and u * ), the smaller the
fraction of particles that deposit. However, comparison of Figure 4-7f. with the other
five panels in the figure (ADE and ISC3 model results) underscores the basic difficulty of
using the box model: Though in its derivation the box model does not depend on the
height of the box or the downwind distance, the parameter A used in the model depends
on both. A also depends on atmospheric stability.
It is clear from Figure 4-5 that for a line source, the concentration profile through
the surface layer is dynamic, becoming flatter in the vertical direction with downwind
distance. This means that the concentration at the top of the surface layer (C SL in the
previous section) is neither constant in time, nor is it negligibly small compared to the
concentration in the box (C Box ). Thus, the formulation for dispersion in the Box Model is
not valid for a plume that is expanding in the vertical direction with concurrent decay in
the concentration gradients within the surface layer.
In a dust storm (Gillette, 1974), the ground acts like an area source, which
behaves quite differently in the context of the Box Model from a line source for three
reasons. First, an area source is horizontally homogeneous. Therefore, the vertical
concentration profile is, on average, invariant with downwind distance. Second, the
ground is acting as a strong source and the net flux of material is always in the upward
direction. This means that we do not have to account for particles re-entering the Box
through the ceiling. Third, because in a dust storm, the ground is a very strong source,
the concentration near the ground is much higher than it is aloft (i.e. C Box >> C SL ), or at
least, the ratio C Box /C SL is constant over large distances in the horizontal. For these three
reasons, dispersion in a dust storm can be estimated based only on the concentration near
the ground (as in Equation 4-27), without considering the concentration profile aloft. For
a dust plume that is expanding while traveling downwind, the assumptions behind
Equation 4-27 do not hold as well.
4.3 Summary
For unpaved road dust emissions, the Box Model provides an order of magnitude
estimate of the dust particle removal due to deposition. For a more accurate assessment, a
model that accounts for changes in the concentration profile with downwind distance is
required. Among the models considered in this section, the algorithm of the ISC3 is most
suited for simulating near-source dispersion. The ADE performs poorly in the near field,
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