FIELD TESTING AND EVALUATION OF DUST DEPOSITION AND ...

κu
( )
*
z
8 fz
K zz
=
exp
−
0.74
+ 4.7 z L u*
Equation 4-7
where z i is the mixing height, L is the Monin-Obukhov length scale for turbulence, u * is
the friction velocity, f is the Coriolis parameter, κ is the Von Karman constant (0.41), and
w * is the convective velocity scale given approximately by
w
1
3
zi
*
= u*
− L
(L is negative for unstable conditions).
Equation 4-8
To solve Equation 4-4, it is necessary to specify boundary conditions on z and
initial conditions for t=0. The top of the modeling domain is set high enough (z top > 2×z i )
so that there is no net flux of particles. That is,
∂c
K
zz
= 0 , z = z top
.
∂z
Equation 4-9
At the ground, the downward flux of particles by dispersion must equal the removal by
deposition
∂c
K
zz
= vd
c, z = 0
∂z
Equation 4-10
where v d is calculated from Equations 2-3, 2-25, and 2-26 with r a set to zero, since the
depositing particles are already at the ground (z=0).
The initial condition is simply that the concentration of particles is uniform up to
a specified injection height. That is
c z)
= c , z < IH
(
0
c(
z)
= 0, z ≥ IH
Equation 4-11
In practice, the transition across z=IH is made mathematically smooth to avoid
difficulties in the numerical solution. With these initial and boundary conditions, the
ADE is solved numerically at 1,000 time steps spaced logarithmically from 1 second to
10,000 seconds.
4-3