Agriculture Reference
In-Depth Information
known to be present and estimates the risk that disease will develop in other areas.
A Gaussian puff model (RIMPUFF) was one of the dispersal models used to
investigate the UK 2001 FMD outbreak (Mikkelsen
et al.
, 2003). Four atmospheric
dispersion models (AEROMOD, HPDM, PCCOSYMA and HYSPLIT), based on
Gaussian plume or Gaussian puff principles, have recently been reviewed by Caputo
et al.
(2003).
Other physical models developed to describe spore and pollen dispersal
(McCartney and Fitt, 1985; Fitt and McCartney, 1986; Aylor, 1990; Aylor
et al.
,
2003; Di Giovanni and Kevan, 1991) have not been widely used in spore dispersal
or disease progress studies. This is perhaps because they are perceived to be
complex and need detailed micro-meteorological information to operate them.
However, recent advances in computer technology and in mathematical computing
make such models more accessible for general use. Two modelling approaches
based on the physical description of the dispersal process have been used to model
spore dispersal: Eulerian Advection-Diffusion models (EAD) (gradient transfer
or K-theory models) and Lagrangian Stochastic models (LS) (random walk models),
(McCartney and Fitt, 1985; Fitt and McCartney, 1986; Aylor, 1990, 1999;
McCartney, 1997).
EAD models assume that atmospheric diffusion is analogous to molecular
diffusion and obeys Fick's Law (i.e. the rate of diffusion is proportional to the
concentration gradient of the diffusing material). The approach can be illustrated by
considering dispersal from an infinite line source orientated at a right angle to the
prevailing wind direction and releasing particles continuously. For an infinite line
source, cross-wind diffusion (y-direction) can be ignored, and along-wind diffusion
(x-direction) is assumed to be negligible relative to down-wind transport. The model
is based on the number balance of particles entering or leaving small volumes of air
(i.e. dispersed spores are neither created nor destroyed). The difference between the
rates at which particles enter or leave the volume horizontally (by wind, LHS in
Equation 6.12) is balanced by the difference between the rates at which particles
enter or leave the volume vertically (by diffusion and sedimentation, terms 1 and 2,
RHS in Equation 6.12) and the rate of loss of particles by deposition onto surfaces
within the volume (term 3, RHS in Equation 6.12). This can be expressed by the
differential equation:
∂
C
(
x
,
z
)
∂
∂
C
(
x
,
z
)
∂
C
(
x
,
z
)
u
=
(
K
)
+
v
+
S
(
x
,
z
)
(6.12)
∂
x
∂
z
z
∂
z
s
∂
z
where
C
(
x, z
) is the particle concentration at height
z
and distance
x
down-wind of
the source. The wind speed
u
determines the rate of horizontal advection of spores
into and out of the volume. The rate of vertical diffusion is determined by
K
z
,
the
vertical diffusion coefficient. The rate of settling of particles depends on the fall
speed,
v
s
, and
S
(
x, z
) defines the rate of removal of particles by deposition.
Additional terms can be added to account for loss of viable spores by spore death or
wash-out by rain (Aylor 1999). EAD models can be formulated for point and area
