FIELD TESTING AND EVALUATION OF DUST DEPOSITION AND ...

where the subscript “G” is used to indicate that the dispersion coefficient is defined as in
the Gillette box model with units of m/s. Equation 4-27 is identical to Equation 4-20, and
forms the basis for the Gillette Box model. Note that the gravity resistance has been
included for the transport of material through the top of the box model (i.e. Equation
4-28).
Planetary Boundary Layer (PBL)
F = F(z)
C SL Surface Layer2
r a2
F Box-SL =V da2 [C SL -C Box ]=(1/r a1 ) [C SL2 -C SL1 ]
C Box ∆z
r Surface Layer1
a1 F dep = F QL = F Box-SL1 =V da2 [C Box -C QL ]=(1/r a2 ) [C Box -C QL ]
C QL
Quasi-laminar Layer
F r dep = F Box-SL1 = F QL =V db [C QL -C 0 ]=(1/r b ) [C QL -C 0 ]
b
C 0 = 0
Ground or Vegetative Surface
r c r c assumed = 0 for particles if particle rebound is
negligible
r g
Figure 4-2. Representation of the Gillette Box Model in the context of the resistance model to
transport. The dashed horizontal line effectively divides the resistance r a into two smaller resistances,
r a1 and r a2 . The equations for fluxes in the figure do not include the effect of gravity.
In arriving at Equation 4-27 we have made three assumptions that warrant closer
inspection. First, we have assumed that there is no resistance to deposition at the ground
or vegetative surface (r c =0, C 0 =0). This assumption is frequently invoked for particles
that are 10 µm in diameter or less, and we accept it as being reasonable (Seinfeld and
Pandis, 1999; Raupach et al., 1999). Second, we have assumed that the concentration
profile through the surface layer is sufficiently well-developed that F box-SL is constant
from the box to the top of the surface layer. The validity of this assumption depends on
the atmospheric stability. Under unstable conditions, most of the resistance to
aerodynamic transport resides near the surface (see Figure 4-3). When conditions are
stable, the resistance to transport does not drop off as dramatically with height.
Therefore, assuming that the constant flux layer is instantly well-developed is probably a
reasonable approximation for unstable conditions, less so for neutral conditions, and not
valid for stable conditions.
The magnitude of K G cannot be estimated for a stable atmosphere since r a does
not converge on a maximum value. Under unstable conditions, r a converges on a
maximum value, and we can in principle calculate K G . However, since r a is dependent on
height above ground, we must make an assumption about which height to use. Selection
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