treasure valley road dust study: final report - ResearchGate

where ? is the von Karman constant and is equal to 0.4, z i is the mixed layer height assumed to be
200 m for wintertime conditions, and u * is the friction velocity, which can be calculated by the
boundary layer equation
u(
zref
) 1 z
? ln
(6-4)
*
u ? z
ref
*
0
where u(z ref ) is the wind speed at height z ref , and z 0 * is the roughness length for the surface. For
the purposes of illustration, the wind speed was assumed to be 1 m/s at a height of 10 m, and z 0
*
was assumed to be 0.01 m. This roughness height corresponds approximately to a surface that is
covered with lawn (Seinfeld, 1986; after McRae et al., 1982). Use of Eq (6-4) gives a value of
0.058 m/s for u * .
For stable atmospheric conditions,
*
? u z
K zz
?
0.74?
4.7( z
L)
f ( z,
u
*
)
(6-5)
where L is the Monin-Obukhov length scale and f is a correction term for the coriolis force. L was
assumed to be 10 m indicating stable to very stable conditions. The coriolis correction, f, was
assumed to be equal to unity since the modeling domain only extends to the modest height of 250
m AGL.
d
s
The total deposition velocity V d was assumed to be equal to the sum of two components,
V ? V ? V
(6-6)
i
where V s is the stokes settling velocity and V i is the removal rate of particles due to impaction on
surfaces. The Stokes settling velocity is given by
V
s
2
1 Dp? pg
? (6-7)
18 ?
Where D p is the diameter of the particle in m, ? p is the density of the particle (1000 kg/m 3 ), g is
the gravitational constant (9.81 m/s 2 ), and ? is the viscosity of air (1.7?10 -5 Kg?m/s at 20 ?C).
The impaction deposition velocity, V i was estimated from experimental curves (Seinfeld, 1986;
after McMahan and Denison, 1979). The impaction velocity was only applied to the first 20 cm
AGL of the modeling domain since in the absence of surfaces, impaction does not occur. The
values used in the model are shown in Table 6-1. At heights above 20 cm, the deposition velocity
was simply equal to the Stokes settling velocity, V s . Note that deposition, either by impaction or
by gravitational settling is negligible for particles with diameters less than 1.4 ?m and that the
model was not run for those small particle sizes.
6-3