Agriculture Reference
In-Depth Information
where
can vary from -2 to +2 (or more rarely +6), depending on the rain type
(Table 2 in Ulbrich, 1983). The gamma distribution was used in a simulation study
to quantify amounts of rain-splash from leaves (Huber
et al.
, 1997).
The gamma distribution takes account of short time variations better but the
Marshall-Palmer function may be satisfactory for long time and space averaging. If
the 'instant' spectrum (less than 10 min) is a gamma distribution, the time-averaged
spectrum (over a few hours) is a Marshall-Palmer distribution (i.e. negative
exponential) (Yangang, 1993). The Marshall-Palmer distribution can generally be
used to represent drop size variability if the time scale of the epidemiological
processes studied is longer than 20-30 min but the gamma distribution should be
used if the time scale is shorter.
From the DSD, integral parameters can be calculated using the generalized
expression:
µ
P
=
a
P
∫
0
∞
D
p
N
(
D
) d
D
(16.5)
in which
a
p
and
p
depend on the integral parameter of interest (Madden
et al
., 1998;
Ulbrich, 1983). With
D
in cm and
N
(
D
) in m
-3
cm
-1
, the values of
a
p
and
p
can be
easily calculated for any integral parameter: for drop number flux density (m
-2
s
-1
),
a
p
= 17.67 and
p
= 0.67; for rainfall intensity (mm h
-1
),
a
p
= 33.31
and
p
= 3.67; for
rainfall power (W m
-2
),
a
p
= 1.44 and
p
= 5.01; and for the back-scattering
coefficient (mm
6
m
-3
),
a
p
= 10
6
and
p
= 6.
Although the DSD can be measured directly with an accuracy in drop diameter
measurements of
6% (Salles and Poesen, 1999), the distribution can also be
estimated using two integral parameters measured independently (Madden
et al
.,
1998; Torres
et al.
, 1994). For instance, measurements at ground level (rain intensity
and rain power) can be used to predict the shape parameter of an assumed gamma
distribution before calculating the term of direct interest for rain-splash. The
atmospheric measurements used by meteorologists to characterise raindrop size
distribution, such as liquid water content and the radar back-scattering coefficient,
may be applied to splash dispersal at a regional scale since radar is used routinely
for assessing the spatial distribution of rainfall. Drops less than 1-2 mm in diameter
are of minor importance for splash dispersal because of their small velocity and
kinetic energy. Therefore, if a drop diameter threshold is known (or assumed) for a
given type of target or canopy, this lower limit can be used in the integration for
P
to
determine an integrative parameter that relates to splash dispersal (Walklate, 1989).
Since the angle between the target normal and the impact directions greatly
influences the splash process, it is important to characterise the variations in both
angle and direction of rainfall. This can be done with an instrument consisting of a
vertical grooved cylinder with the flow-off partitioned into the four cardinal sectors
as designed by Crockford
et al.
(1991). Volumes of water collected in each of the
four cardinal sectors can be used to derive rough estimates of rain angle and
direction at low wind speeds and without significant gusts or a bimodal wind
direction spectrum. Caution is required when using this type of instrument because
no standard exists.
≤
