Agriculture Reference
In-Depth Information
sources (Yao
et al.,
1997; Aylor, 1999) and include terms describing horizontal
diffusion and advection.
To solve EAD equations, it is necessary to define diffusion coefficients (
K
),
wind speeds and the spore removal term (
S
) at all points in the model volume and to
define appropriate boundary conditions at the edges of the volume (i.e. at the ground
and some upper limit in the atmosphere).
K
and wind field values may be derived
from micro-meteorological measurements, or theoretically estimated for different
atmospheric flow conditions (McCartney and Fitt, 1985; McCartney, 1997; Yao
et al.
, 1997; D'Amours, 1998).
S
(
x, z
) has to account for deposition by both
sedimentation and inertial impaction (McCartney and Fitt, 1985; Aylor, 1986, 1990;
Yao
et al.
, 1997). In validations against observed measurements of the dispersal of
fungal spores (Legg and Powell, 1979; Aylor and Ferrandino, 1989), the model
over-estimated concentrations close to the source, through either underestimation of
diffusion or enhancement of deposition by gusts. EAD models make the assumption
that the length scales of vertical movement are small compared with the size of the
plume, which is generally invalid within crops, and cannot easily accommodate the
effects of gustiness (Aylor, 1990). However, this type of model can give useful
results for spore dispersal over distances far enough from the source such that the
dominant turbulent eddies are small compared with the vertical width of the plume
(Aylor, 1999). For example, EAD models are suitable for calculating dispersal from
the downwind edge of a field (Yao
et al.
, 1997), providing the initial spore profile
can be defined. EAD models have recently been combined with models of
atmospheric thermo-hydrodynamics to calculate pollutant dispersal over regional
scales taking into consideration orographic and thermal inhomogeneities and terrain
effects (Aloyan, 2004; D'Amours, 1998).
Lagrangian stochastic (LS) atmospheric dispersal models employ a different
approach to Gaussian plume or EAD models. LS models simulate the paths of
individual air parcels or particles as a pseudo-random walk using the turbulence
statistics of the air flow. Particle trajectories are represented by a series of discrete
steps determined partly by a correlation between successive velocities (representing
velocity 'memory') and partly by a random component to simulate turbulent
fluctuations. The formulation of LS models (reviewed by Wilson and Sawford,
1996) can be illustrated by considering dispersal from an infinite line source where
cross-wind diffusion can be ignored (McCartney and Fitt, 1985; Aylor, 1990, 1999;
Aylor
et al.,
2003; Jarosz
et al.
, 2004). Particle trajectories are simulated as a series
of short straight-line segments, each representing the motion of the air parcel over a
short time step
dt.
If the horizontal and vertical speeds of the air parcel at the start of
the step are
u
and
w,
the horizontal (
dx
) and vertical (
dz
) displacements of a spore
contained in the air parcel are (Aylor
et al.
, 2003; Jarosz
et al.,
2004):
dx
=
(
u
+
du
)
dt
and
dz
=
(
w
+
dw
−
v
s
)
dt
(6.13)
where
du
=
a
u
dt
+
b
u
d
u
and
dw
=
a
w
dt
+
b
w
d
ξ
ξ
w
(6.14)
