Agriculture Reference
In-Depth Information
x
2
(
1
)
−
1
D
=+
γ
(6.7)
L
2
Where
is related to the strength of the source of spores and
L
is a length scale
characteristic of the plant. The model adequately predicted the spread of phaseolus
bean rust (causal agent
Uromyces appendiculatus
) within 3 m of the source but
relied on averaging times long enough to give fairly uniform dispersal round the
source.
Two or three dimensional empirical or semi-empirical models have rarely been
used to describe plant pathogen dispersal. Tufto
et al
. (1997) compared exponential
and Weibull distribution models to two semi-empirical models using data for maize
pollen dispersal. One of the semi-empirical models was based on Brownian
diffusion and the other included a wind threshold for pollen release and a wind
direction. The Brownian diffusion model can be summarised as:
γ
1
.exp
{
1 (
r
}
Cxy
(,)
=
γτ
x y
+
τ
) 1
−
γ
+
τ
2
γ
2
+
τ
2
γ
2
(6.8)
x
y
x
y
2
πγ
r
Where
C(x, y)
is the concentration or deposition rate at position
x, y
from the source
and
r
is the distance from the source (
r
2
= x
2
+y
2
). The coefficient
γ
is related to the
variance of the distribution and
y
are related to the mean wind speeds in the
x
and
y
directions. The other model, also based on the idea of Brownian diffusion, can
be written as:
τ
x
and
τ
λ
Cxy
( ,
)
=
. exp{
−
λκ θθ
r
+
cos(
−
)}
(6.9)
0
23
2(
π
rI
)
( )
κ
0
are the polar co-ordinates of
x
and
y
(
r
2
= x
2
+y
2
and
= tan
-1
(
y/x
).
I
0
Where
r
and
θ
θ
is a modified Bessel function of the first kind. The coefficient
λ
is related to the
threshold wind speed,
0
to the
mean wind direction. Both semi-empirical models fitted the maize pollen deposition
data better than either exponential or Weibull models, partly because these two
models could not describe the effects of wind direction. Although both semi-
empirical models could describe experimental data better, they are relatively
difficult to fit to measured data. As with other empirical approaches, it is difficult to
estimate the values of model parameters
a priori
.
Three dimensional patterns of mean pollutant concentrations emitted from point
and line sources can be estimated using Gaussian Plume models (Pasquill and
Smith, 1983), which assume that concentration profile distributions are Gaussian in
both cross-wind and vertical directions. The standard deviations of the cross-wind
(
κ
is related to the variance of the distribution and
θ
z
) distributions are functions of distance and determine the shape
of down-wind gradients (McCartney and Fitt, 1985; Fitt and McCartney, 1986). For
a ground level point source, concentrations at the ground are given by:
σ
y
) and vertical (
σ
