A model for the capture of aerially sprayed pesticide by barley

1
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.

2
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

3
Introduction

• improved method of treating the capture of
  pesticide spray by a crop for use with a
  trajectory model of droplet transport
• previous methods have treated the crop in an
  averaged, homogeneous manner
• realistically modelled crop allows a more
  detailed consideration of the crop structure and
  capture process

4
Transport

• simulation follows the fate of individual
  droplets at evenly spaced points in time
• droplet controlled by gravity and airflow
• mean wind profile
• logarithmic above crop
• exponential within crop
• statistical treatment of turbulence
• combined transport model

5
Ballistic Model

• Marchant (1977) specifies the instantaneous
  acceleration of a droplet,
• Runge-Kutta algorithm simultaneously applied to
  velocity and diameter of droplet to obtain the
  ballistic velocity

6
Random Walk Model

• simple Markov Chain model for droplets moving
  with the airflow except for the addition of their
  sedimentation speed,
• additional terms to correct for aspects of
  non-physical behaviour (Legg, 1983) with
  parameters from Walklate (1987)

7
Combined Model

• ballistic and random-walk models are combined via
  a weighting parameter b,
• weighting accounts for the increasing influence
  of turbulence on the droplet as it slows to its
  sedimentation speed

8
Crop Model

• realistic plants determined by parameters taken
  from measurements made on barley plants
• effect of real properties of crop can be
  investigated in an intuitive manner and detailed
  results produced

9
Crop Effect On Airflow

• mean wind profile - affected by density of crop
  normal to wind and its height (Raupach, 1994),
  relative magnitude determined by the friction
  velocity
• turbulence statistics related to the crop via
  crop height and friction velocity
• Reynolds stress gradient with height - determined
  by the density of the crop normal to the wind at
  each height

10
Droplet Trajectories

• trajectories of ten 100 mm diameter droplets

11
Determining Capture

• interception - comparison of positions in space
  of droplet and crop
• deviation - around plant elements caused by local
  deviation of airflow, impaction efficiencies (May
  Clifford, 1967) used
• rebound - droplets of size considered here are
  prone to rebound rather than to be retained by
  leaf, critical speed approach of Lake Marchant
  (1983) is used

12
Capture by Plant

• capture with different droplet diameters at a
  range of heights in crop - with rebound

13
Capture by Plant

• effect of rebound on droplet penetration to
  ground for a range of diameters

14
Capture by Plant

• mean number of rebounds per droplet for a range
  of droplet diameters

15
Capture by Plant

• capture with different droplet diameters at a
  range of heights in crop - without rebound

16
Possible Improvements

• use of a more refined transport model
• include more interaction between crop and airflow
  including crop waving
• use a more widely applicable model of rebound to
  allow greater confidence in the results for the
  smallest droplets and perhaps allow better
  account to be taken of leaf characteristics

17
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 models of pesticide action
  
• rebound has a major role to play in determining
  the differing canopy penetration of different
  sized droplets