A model for the capture of aerially sprayed pesticide by barley

coriandercultureMechanics

Feb 22, 2014 (3 years and 6 months ago)

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A model for the capture of
aerially sprayed pesticide by
barley

S.J.Cox, D.W.Salt, B.E.Lee & M.G.Ford

University of Portsmouth, U.K.

Introduction



Chemicals in agriculture
-

problem of growing
environmental concern



Wind drift of spray chemicals
off target



Knowledge of spray deposition
patterns on plants can reduce
the volume of chemical used



Role of mathematical modelling

Introduction



This work aims to develop an
improved method of treating the
capture of pesticide spray by a
crop for use with a trajectory
model of droplet transport


Previous methods have relied
upon treating the crop in an
averaged, homogeneous manner

Introduction



Here we use a realistically
modelled crop which should
allow a more detailed
consideration of particular
elements of the crop structure
and capture process than
previously


Transport



the simulation follows the fate
of individual droplets at evenly
spaced points in time


movement of droplet controlled
by gravity and airflow


mean wind profile


logarithmic above crop


exponential within crop


statistical treatment of turbulence


initial transport modelled by a
combination of ballistic and
random
-
walk motion (Mokeba
et al.,

1997)

Ballistic Model



Marchant (1977) specifies the
instantaneous acceleration of a
droplet,






the Runge
-
Kutta algorithm is
simultaneously applied to
velocity and diameter of the
droplet to obtain the ballistic
velocity components

m
A
C
dt
d
a
D
2
)
(
v
V
v
V
g
v






Random Walk Model



simple Markov Chain model for
droplets moving with the
airflow except for the addition
of their sedimentation speed,






additional terms required to
correct for aspects of non
-
physical behaviour (Legg,
1983)



parameters from Walklate
(1987)



v
v
v
r
n
v
r
n
v
v




2
1
1




)
/
exp(
Lv
v
T
t




Combined Model



the ballistic and random
-
walk
models are combined via a
weighting parameter
b
,







this weighting accounts for the
increasing influence of
turbulence on the droplet as it
slows to its sedimentation speed

r
i
b
i
i
1
1
1
)
1
(






v
v
v
b
b
i
s
w
v

b
Crop Model




realistic barley
plants
determined by a
series of
parameters taken
from
measurements on
real plants


this allows the
effect of real
properties of the
crop to be
investigated in an
intuitive manner
and produces
detailed results

Crop Effect on Airflow



mean wind profile
-

affected by
the density of the crop normal
to the wind and its height
(Raupach, 1994), relative
magnitude determined by the
friction velocity



turbulence statistics (Walklate,
1987) related to the crop via its
height and the friction velocity



Crop Effect on Airflow


Reynolds stress gradient with
height
-

affected by the density
of the crop normal to the wind
at each height (Raupach &
Thom, 1981)

Droplet Trajectories


10 x 150
m
m

10 x 100
m
m

Capture



Interception
-

comparison of
positions in space of droplet and
crop



Deviation
-

around plant elements
caused by local deviation of
airflow, impaction efficiencies of
May & Clifford (1967) are used



Capture



Rebound
-

droplets of the size
considered here are prone to
rebound rather than to be retained
by the leaf, critical speed
approach of Lake & Marchant
(1983) is used,


19
.
1
2
29
.
0
7
10
43
.
2





















d
x
u
crit
Plant Distribution


0
10
20
30
40
50
60
70
80
90
0
1 00
20 0
30 0
droplet diameter / µm
percentage caught by ground
r eb oun d
n o re bou nd
0
1
2
3
4
0
1 0 0
2 0 0
3 00
droplet diameter / µm
normalized proportion captured
g ro u n d
b o t t o m
ce n t r e
t o p
Plant Distribution


0
0.5
1
1.5
2
2.5
0
10 0
20 0
30 0
droplet diameter / µm
mean number of rebounds
0
0.5
1
1.5
2
2.5
0
1 0 0
2 0 0
3 00
droplet diameter / µm
normalized proportion captured
g ro u n d
b o t t o m
ce n t r e
t o p
Field Distribution




off
-
target drift when spraying a
square area of field with wind angles
of 0
°

and 60
°

0
10
20
30
40
50
60
70
0
10
20
30
40
50
parallel to tractor path, m
perpendicular to tractor path, m
wind
0
10
20
30
40
50
60
70
80
90
0
10
20
30
40
50
60
parallel to tractor path, m
perpendicular to tractor path, m
wind
Field Distribution




amount of drift outside the spraying
area and 5 m buffer zone


the direction of the wind affects
more than just the location of off
-
target drift; it can also affect the total
amount of this drift

0
1
2
3
0
60
120
180
angle of wind to direction of tractor
% deposited outside field + 5m
Conclusions



Possible improvements to
model:



use more refined transport model


include more interaction between
crop and airflow including
coherent crop waving


use of a more widely applicable
model of rebound would allow
greater confidence in the results
for the smallest droplets and
perhaps allow better account to be
taken of leaf characteristics

Conclusions



Possibilities opened up by
method:


an investigation of the detailed
effects of plant structure


to see detail of droplet distribution
on plant
-

use as input to further
models of pesticide action


The role of rebound in the
preferential penetration of
certain droplet sizes through the
crop may be as important as
differences in impaction
efficiencies