The OML-SprayDrift model for predicting pesticide drift and deposition from ground boom sprayers

Introduction

Pesticide drift during field application to sensitive neighboring non-target biotopes or biotopes between fields is of much interest and has potential impacts on human health and livestock.^1–3) Several mechanistic models have been developed to predict the drift, deposition, and air concentrations of pesticides from various types of application equipment in order to understand the physical basics of spray drift as well as to develop a tool for regulatory assessment of unintended off-target exposure. However, the main concern has been habitats with no significant vertical component, e.g., water bodies.

Different types of model approaches have been taken all with advantages and disadvantages: Computational Fluid Dynamics (CFD) models,⁴⁾ random-walk trajectory models,^5–9) diffusion-advection models,¹⁰⁾ and Gaussian tilting plume models.^11,12)

CFD models can calculate the complicated flow and dispersion close to nozzles and spray equipment. These models are typically applied for distances up to 5 m, implying that they do not account for the cumulative effect of the numerous spray tracks farther away from the field edge. The cumulative effect is important, particularly for the vertical concentration profile and deposition to e.g., hedgerows. CFD models require expert skills, take much time to set up, are computationally demanding,⁴⁾ and are not suitable for fast and practical regulatory purposes,^9,12) but software¹³⁾ exists to quickly search tables produced from CFD calculations based on fixed turbulence intensity.

Trajectory models can deal with longer drift distances than CFD models, but they are still quite computationally expensive, particularly for longer distances where a large number of released droplets are needed in order to avoid discontinuities in deposition.¹¹⁾ These models either do not take atmospheric stability into account^6–8) or are calibrated to a particular atmospheric situation.⁹⁾ In addition, some models disregard the effects of evaporation of the droplets.⁹⁾

Gaussian tilting plume models are not directly able to model the special effects around the boom and nozzles, but they have the advantage of being easier to set up than CFD models. Gaussian models are more computationally efficient at longer distances than CFD and trajectory models⁹⁾ and are therefore favorable for management systems. A major disadvantage of tilting plume models without reflection at the ground is that when the water evaporates from the droplets and they become very small or even are reduced to dry pesticide particles, the terminal speed becomes almost zero and the calculated deposition almost stops. In reality, the atmospheric turbulence still maintains the deposition. This could explain the underestimation at the longest distances (20–30 m) of the tilting plume model by Lebeau et al.,¹²⁾ especially for low wind conditions, where the droplets have a long time to evaporate.

Another way of calculating deposition, commonly used in regional and local dispersion models, is based on the principle that deposition is directly proportional to the concentration at some reference height above the ground. The proportionality constant is called the deposition velocity,¹⁴⁾ v_d. The deposition velocity is calculated using the resistance method that, among other parameters, depends on the droplet fall speed and the atmospheric turbulence. This principle will ensure deposition in Gaussian plume models, also at far distances, even when the droplet terminal speed approaches zero. This method is used in the OML-SprayDrift model described in this paper. The model is developed in order to make a fast and easily usable tool for estimation of primary horizontal drift of pesticide application to hedgerows and is intended for use by authorities and agricultural advisors.

Materials and Methods

1. Spray-drift model

The OML-SprayDrift model (Operationelle Meteorologiske Luftkvalitetsmodeller, meaning Operational Meteorological Air Quality Model) is a combination of two Gaussian model principles. The Gaussian tilting plume method^11,12) determines the amount of spray deposited inside the directly sprayed zone. The remainder spray is treated as area sources located in the track and is dispersed applying a traditionally reflected Gaussian plume and the deposition beyond the track is calculated by deposition velocity. The model calculates the water and possible pesticide evaporation from the droplets and the resulting change in diameter and vertical velocity as a function of travel distance. Deposition outside the track is converted to negative surface sources following the principle of surface depletion described by Horst.¹⁵⁾ The negative surface sources ensure that the calculated vertical profiles of the horizontal drift at some distance from the edge of the field have a maximum above the ground, which also has been observed and modeled.⁹⁾ The model operates on droplet classes in size intervals of 10 µm.

1.1. Dispersion

The dispersion model is based on the Danish Gaussian plume model OML, which calculates the atmospheric dispersion of pollutants from multiple point and area sources and has been validated against many different datasets including non-buoyant surface releases.¹⁶⁾ The model is a regulatory model used by the Danish authorities, consultants, and industry. In OML, turbulence is described as continuous functions of micrometeorological parameters like friction velocity, heat flux from the surface, aerodynamic roughness, and the Monin–Obukhov length describing the atmospheric stability. The vertical and horizontal dispersion from a point source is described as a Gaussian (normal) distribution. For a point source placed at coordinates (0, 0, H) (m), the concentration c (g m⁻³) at the point (x, y, z) is calculated disregarding deposition as follows:

  

where Q is the emission rate (g sec⁻¹), u is the wind speed (m sec⁻¹), H is the height of the source (m), and σ_y and σ_z are the horizontal and vertical dispersion parameters (m), respectively. The reflection terms refer to the reflection from the ground surface of the plume and are active outside the track in the OML-SprayDrift model. In most cases, spray drift is a two-dimensional phenomenon, because the long spray track will smooth out the horizontal dispersion when estimating the average concentration. Therefore, the OML-SprayDrift model disregards the horizontal influence and is a 2D model.

1.2. Deposition inside the track

Inside the spray track, deposition is calculated using a Gaussian tilting plume or settling plume principle.^11,12) The height of the droplet plume centerline, H, in the concentration equation is decreased due to the descending droplets. The principle is applied to a number of droplet size classes. In this study, the classes consist of 10 µm droplet diameter intervals and are in the calculations represented by the median diameter of the interval center. In this case, the theoretical dispersion is not affected by the presence of the ground surface, and the plume is allowed to disperse under the surface; i.e., the reflection term in the concentration equation is neglected. At a given distance, the total deposition is equal to the part of the plume that is located beneath the surface.

The average deposition inside a track is represented by the droplets released at the center of the boom. At the edge of the boom, the deposition for each droplet class is calculated with the tilting plume where the vertical position of the droplet is calculated by the droplet model described in Section 1.4, taking into account the droplet exit speed from the nozzle, the evaporation, and the change in droplet size and speed.

1.3. Deposition beyond the track

After droplet release, the speed of the smaller droplets reaches a terminal speed within a few tenths of a second, which is not affected by the nozzle exit speed, but for boom heights of 0.5 m, the larger droplets will deposit inside the track. The smaller droplets, which will mainly deposit outside the track, have a terminal speed that is comparable to or less than the typical speed of turbulence eddies, i.e., in order of the friction velocity, u_*. This means that the rate of deposition due to turbulent transport will be comparable to the rate of deposition due to pure sedimentation.

The OML-SprayDrift takes this turbulent deposition into account using the surface depletion principle.¹⁵⁾ Deposition at a given distance downwind from a source is handled as a negative source with the same strength as the deposition rate.

The deposition rate Dep is calculated based on the principle of deposition velocity v_d. The deposition is proportional to the deposition velocity v_d(z) and the concentration c(z):

  

where z is the reference height, which is set to 0.5 m in the spray-drift model. The deposition velocity is parameterized analogous to electrical resistances and the dry deposition velocity of particles or droplets¹⁴⁾:

  

where v_s is the settling velocity of the drop as a function of its diameter, r_a (sec m⁻¹) is the aerodynamic resistance, and r_b is the laminar sublayer resistance close to the surface. The aerodynamic resistance in the mixing layer is defined as

  

where κ is the dimensionless von Karman’s constant, u_* (m/sec) is the friction velocity, z₀ (m) is the roughness length, and ψ is Businger’s corrections function for atmospheric stability.¹⁷⁾

For particles, the laminar sublayer resistance close to the surface is given as

  

where Sc is the dimensionless Schmidt number: ν/D, where D is the diffusivity, ν is the kinematic viscosity, and St is the dimensionless Stoke number: (u²_*v_s)/(g ν), where g is gravity (m sec⁻²). The settling velocity of the droplets is incorporated in the Stoke number.

1.4. Evaporation and fall velocity of droplets

The dispersion and deposition model is coupled with a droplet model describing droplet evaporation and the resulting changes in size and velocity. The model takes into account the droplet ejection velocity as well as the relative humidity and ambient temperature. The model is based on a model for pure water and further developed to deal with the pesticide content of the droplet and its possible evaporation. The model assumes no interaction between droplets and that the droplets have no influence on the air. The model does not take formulations and adjuvants into consideration, although it is known that formulations and adjuvants can influence the droplet size distribution^18–20) and thereby affect the drift potential. Although the results of Sanderson et al.²¹⁾ were related to specific experimental and meteorological conditions, they concluded that drift is considerably lower using water-dispersible granules or liquid-flowable formulations of Propanil compared to emulsifiable concentrates. Chapple et al.²²⁾ tested different adjuvants and found that six out of seven adjuvants shifted the droplet spectra relative to water, either to smaller or larger diameters.

The model describes droplet behavior after ejection. A droplet is affected by gravity, the drag force of the air, and the evaporation of water and pesticide. Fall velocity and evaporation are described by solving mass, moment and energy equations for a single droplet. These equations are transformed to equations for diameter, fall velocity, and temperature, respectively. Together with the ambient temperature and relative humidity, these equations determine the exchange and thereby the changes in size, velocity, and temperature of the droplet. A detailed description of the droplet model is found in Supplemental Material.

Droplet fall velocity is an important parameter for the deposition rate to the ground surface and primarily depends on the diameter. Even though the droplet exit speed at the nozzle outlet is in the range of about 15–25 m/sec,²³⁾ the smallest droplet reaches a much lower terminal velocity within a few tenths of a second after exit. However, a continued change in diameter and velocity occurs due to evaporation. For the smallest droplets, the change can be fast, as shown in Fig. 1. For a given diameter, the relative humidity of the air is the most important parameter for the evaporation rate, as shown in the figure.

Fig. 1. The rate of change in water droplet diameter as a function of initial size of 50, 100, and 200 µm for different values of relative humidity (full line 80%, broken line 60%, and dot-dash line 40%). Air temperature is 20°C and droplet initial speed is 20 m/sec.

When the droplets contain a pesticide with a low vapor pressure, the evaporation and change in diameter of the droplets almost stop, and they reach a minimum diameter. This occurs when the relative water content equals the relative humidity of the air. If the pesticide also evaporates, the minimum diameter decreases accordingly.

1.5. Calibration and validation

The model was calibrated and validated against the field measurements described in the next section. The field data were divided into data from the years 2005 and 2010, where a standard flat-fan and an air-injection nozzle were used, respectively. Calibration was performed using the 2005 data and validation was done on the 2010 data. Many spray-drift models have been calibrated, e.g., using field canopy porosity and velocity scaling parameters,⁹⁾ fitting horizontal and vertical eddy diffusivities K_y and K_z to the first trail in a series,¹²⁾ or adding empirical corrections to the evaporation rate that changed the deposition downwind with a factor of 2.⁶⁾ Teske et al.⁷⁾ describe the great variance between different empirical parameterizations of the nozzle-induced airstream velocity due to the entrainment of air. In this study, the calibration also involves the effects of the nozzle-induced airstream.

Calibration was based on the deposition inside the spray track. The droplet model only handles single droplets and does not take into account the effect of the whole continuous spray cloud on the airstream close to the nozzle. A droplet transfers momentum to the surrounding air and is slowed down. The droplet reaches the terminal speed at a certain fall distance, but all the droplets in the spray cloud together create a downward airstream that increases the fall distance compared to the calculated fall distance for a single droplet. Therefore, an algorithm for the empirical additional fall distance is established based on the 2005 data. It is anticipated that a high wind speed destroys the induced airstream. The additional fall distance, Δz (m), is a function of the wind speed at boom height u_B (m sec⁻¹):

  

The algorithm is applied for u_B below 4.4 m sec⁻¹, and Δz is 0 m for larger u_B, where u_B is calculated from the meteorological observations taking into account the atmospheric stability using Businger’s corrections¹⁶⁾ to the neutral logarithmic wind profile.

1.6. Model input and output

As input, the model needs meteorological information on wind direction, friction velocity (turbulence), Monin–Obukhov length (atmospheric stability), aerodynamic roughness, temperature, humidity, mixing height and boom height. The nozzle droplet spectra and ejection velocity are also needed together with pesticide tank concentration and application rate (L ha⁻¹). Driving speed is assumed to be around 7 km hr⁻¹.

The model calculates the ground-surface deposition and the vertical profile of the horizontal pesticide flux, in principle, at any distance downwind of any field size. Also, the droplet spectra can be calculated at any position.

2. Measurements

Most spray models are developed using deposition measurements. This type of measurement can be difficult to perform properly in order to measure the far-field drift deposition of small droplets using smooth horizontal surfaces, such as alpha-cellulose sheets, on a rough field surface.^8,11) To avoid this problem, this study measured the vertical profile of the horizontal drift. In the far field, the total amount of collected spray drift will be much larger than the horizontally deposited spray drift measured per unit area, which reduces uncertainty in measurements.

2.1. Field measurements

A series of spray experiments were carried out in order to determine pesticide droplet dispersion from spray tracks. These experiments were conducted so that horizontal flux at different heights and different distances from the spray boom was determined^24,25) using sodium fluorescein as a tracer. The tracer is assumed not to evaporate and has a molar mass of 376.3 g mol⁻¹, which is about the value of many pesticides.

Spraying was performed with a conventional tractor-mounted sprayer. Spray nozzles were either Hardi 4110-16 (flat fan; Hardi, Denmark) or TeeJet AI 110-04 (air induction; TeeJet, USA). The spray boom was 12 m wide with 24 nozzles, and boom height was adjusted to 50 cm above the vegetation. The tractor driving speed was about 7 km hr⁻¹. The conditions for each spraying are presented in Table 1. Before calibration and validation, all measurements were normalized to the same application rate, i.e., 300 L ha⁻¹ and 1.49 g L⁻¹.

Table 1. Meteorological conditions and settings for the spray equipment during spray events

	Parameter, unit	Trial
		April 05	May 05	June 05	Aug. 05	Sept. 05	June 10	June 10
Environmental conditions	Wind speed, m sec−1	5.5–6.2	2.0–3.6	2.9–3.8	3.7–4.5	2.4–3.3	4.6–5.8	4.8–5.6
	u*, m s−1 a)	0.51–0.61	0.19–0.28	0.39–0.45	0.34–0.53	0.29–0.58	0.45–0.62	0.51–0.61
	L, mb)	−57–−88	−5–−21	−58–−88	−21–−87	−24–−107	244	−116–−196
	Heat flux, W m−2	206–255	51–130	74–120	93–205	91–164	44–112	85–144
	Temperature, °C	10–11	11–12	17–18	17–18	22–24	12–15	15–16
	RH, %	42–50	53–59	65–79	47–60	45–65	67–77	63–65
Spraying equipment settings	Nozzle typec)	FF	FF	FF	FF	FF	AI	AI
	Pressure, MPa	0.55	0.55	0.30	0.30	0.30	0.30	0.30
	Flow rate, L min−1	1.6	1.6	1.1	1.1	1.1	1.6	1.6
	VDMd), µm	198	198	213	213	213	439	439
	Drop ejection speede), m sec−1	18.0	18.0	15.5	15.5	15.5	9.2	9.2
	Tractor speed, km hr−1	7	7	7	7	7	6.4	6.4
	Application rate, L ha−1	300	300	200	200	200	300	300
	Tank concentration, g L−1	1.49	2.23	1.63	1.99	1.83	2.23	1.93

^a) The parameter u* is the friction velocity, a measure of air turbulence. ^b) L (Monin–Obukhov number) is a parameter of atmospheric stability. ^c) FF=Hardi flat fan 4110-16 nozzles and AI=TeeJet Air Injection −110-04. ^d) Volume median diameter from measurement in laboratory. ^e) Value from centre of measured volumetric droplet velocity distribution from continuous scan in laboratory.

The experiments took place along a hawthorn hedgerow on seven occasions (April 2005, May 2005, June 2005, August 2005, September 2005, and twice in June 2010). The meteorological conditions for wind speed, wind direction, turbulence, temperature, and heat flux were measured with an ultrasonic anemometer at 4 m height on a mast in the center of the 200 m×200 m field, i.e., 100 m from the hedgerow. Relative humidity was also measured (Table 1). The calculated meteorological data during the individual trails are based on 10-min averages in correspondence with Bird et al.⁸⁾

Measurements were performed for five spray tracks parallel to the hedgerow with an increasing distance from the hedgerow (cf. Fig. 2). The hedgerow consisted almost entirely of hawthorn (Cartages laevigata (Poiret)) trees about 4–5 m high and 1–2 m wide, with a few gaps. Hawthorn is deciduous, and in Denmark leafing occurs in early May, flowering in May/June. Measurements of the vertical wind profile at 4 positions (1.0, 2.0, 3.5, and 5.1 m above the ground) in the hedgerow were compared with the wind measurements about 100 m upstream at the open field. These measurements indicated that the total horizontal flux from ground to 5.1 m was reduced by about 10% (data not shown). This indicates a small vertical component in the mean flow and is consistent with a measured average vertical wind component at 5.1 m of 8–9% of the horizontal component. Compared to other uncertainties, this is only a minor violation of the implicit assumption of horizontal mean flow.

Fig. 2. Sketch of the setup of the spray-drift trails for vertical profile measurements with tractor-carried boom sprayer and location of hedgerow and masts with height position of curlers. The masts are positioned in five rows with 12 m in between and with five masts in each row, totaling 25 masts.

Spray drift was collected using commercial plastic hair curlers (M-cosmetics, Denmark) mounted on masts 0.5, 1, 2, and 4 m above the ground. The curlers were covered with 3-mm-long “hair,” 0.15 mm in diameter, and were assumed to collect droplets with a diameter down to 10 µm and an effective crosswind area of 2 cm×6 cm. These assumptions were associated with some uncertainty due to the complex structure of the curler.

The masts were placed at five different distances to a hedgerow almost perpendicular to the wind direction. The mast spacing was 12 m, corresponding to the width of the spray boom. At each distance, five masts were set up at 10 m intervals, and the first row was placed just in front of the hedgerow, resulting in a total of 25 masts. In each mast, two hair curlers were placed upright at each of the four four sampling heights, giving 10 curler measurements at each height at each distance that were averaged and used in the model calibration and validation. Before spraying the next track, a new row of masts mounted with curlers was erected. In order to reduce the large variability in the measurements, some extra trails were performed where the tractor drove back and forth 10 times in the third track 24 m away from the hedgerow, and measurements were only made in the hedgerow.

2.2. Droplet size distributions

Three different droplet size distributions were applied during the field experiments, i.e., the standard flat-fan Hardi 4110-16 at 0.30 and 0.55 MPa and the TeeJet air-induction nozzle 110-04 at 0.30 MPa. The nozzle droplet spectra were experimentally determined using the PDPA laser-based measurement setup and protocol.^26,27) Cumulative droplet size distributions are shown in Fig. 3 together with the results of the flat-fan nozzle XR 110-02 at 0.30 MPa²⁸⁾ used for the sensitivity analysis in a later section.

Fig. 3. Measured drop spectra for the Hardi 4110-16 standard flat-fan nozzle (at 0.30 and 0.55 MPa), the TeeJet AI 110-04 air-inclusion nozzle (at 0.30 MPa), and the TeeJet XR 110-02 (at 0.30 MPa). Data for XR 110-02 are from Klein and Golus (2004).

Results and Discussion

1. Calibration

The calibration of the model was performed using data from the Hardi flat-fan 4110-16 nozzle spray experiments. As mentioned, the calibration was performed by adding an extra initial fall distance to the distance calculated by the droplet model. The wind speed at boom height was used as a scaling parameter. Calibration tests were performed replacing the measured wind speed with the relative wind speed at the moving boom by combining the driving velocity and the wind velocity. This did not improve the calibration. Baetens et al.⁴⁾ found only little influence by the tractor speed. This indicates that the turbulence related to the average wind speed might be the most important factor for low driving speeds.

The performance of the OML-SprayDrift model on the dependent data from 2005 is shown in Fig. 4. The values are shown on a log scale in order to differentiate between the smallest values. A group of points marked with a cross in a diamond indicates where modeled values are much lower than the measurements. These points all relate to measurements at 4 m height next to the boom at 0 m distance. The large difference may be due to the wake from the tractor that catches some of the spray and rapidly spreads it to a greater height. This phenomenon is not yet covered by the model. Except for this group of data, there is a reasonably good correlation between measured and model values for both near (high values) and far drift distances (low values). The points of 10 track averages (24 m distance) are, of course, less scattered. For all points, 82% are within a factor of four. This is actually quite good, taking into account that the model predicts deposition values based on 10-min meteorological data, while a spray experiment only represents about 30 sec (total time for 10 curlers collecting droplets passing by in about 3 sec from a 12 m boom in a wind speed of about 4 m sec⁻¹).

Fig. 4. Measured and modeled values of horizontal drift (ng cm⁻²) on data from 2005. Diamonds are single trail values (average of 10 curlers) and solid squares are averages of 10 sprays in the same track, giving a better ensemble average. The diamonds with a cross are for positions 0 m from boom and at a height of 4 m. The central line is the 1–1 curve, and the two others are a factor of four offset.

2. Validation

The model validation was done for the nozzle TeeJet air-injection 110-04 with a coarser droplet size spectrum (Fig. 3) with fewer small droplets than the Hardi flat-fan 4110-16 nozzle. The comparison between the modeled and measured values is shown in Fig. 5. Again, the group of points with a cross in a diamond represents measurements at 4 m height next to the boom, for which the modeled values are much too low. The explanation is again the effect of the tractor wake rapidly sending droplets upwards. For the other positions, the model performs well, with a tendency to overpredict the lower deposition values. The number of points within a factor of four is improved to 91%. The fact that the validation is performed with a completely different nozzle strengthens confidence in the model.

Fig. 5. Measured and modeled values of horizontal flux (ng cm⁻²). Validation on independent data from 2010. Crosses are for positions 0 m from boom and at a height of 4 m. See text with Fig. 4 for further explanation.

It is important to notice that the validation is performed for an air-injection nozzle using a model in which the additional droplet fall distance due to the airstream close to the nozzle is calibrated to a standard flat-fan nozzle. Teske et al.⁷⁾ used two different calibrations of the nozzle induced air stream for these two types of nozzles.

3. Sensitivity

In order to analyze the model behavior and identify important parameters affecting pesticide drift, some sensitivity runs have been performed, varying one parameter and keeping the others constant if nothing else is mentioned. The calculations were performed for multiple spray tracks of metsulfuron-methyl on a 240 m wide field including all drop sizes in opposite to the validation, where droplets less than 10 µm were excluded. The other parameters are pesticide 4 g ha⁻¹ (400 µg m⁻²), fluid 300 L ha⁻¹, boom height 0.5 m, sprayer speed 7 km h⁻¹, nozzle AI 110 04 at 0.3 MPa, wind speed 4 m s⁻¹ at 4 m, wind direction perpendicular to hedgerow, relative humidity 60%, air temperature 15°C, heat flux 100 W m⁻², and aerodynamic roughness 0.1 m. The considered pesticide had the following characteristics: vapor pressure 7.7 mPa (25°C), density 1.447 10³ kg m⁻³, and molar mass 381.37 g mol⁻¹.^28–30) Adapting values from other pesticides,^32,33) the binary diffusion coefficient in N₂ (25°C) was 5 10⁻⁶ m² sec⁻¹, and evaporation heat enthalpy was 98,000 J/mol. Heat capacity 4200 J kg⁻¹ K⁻¹ was assumed to be equal to that of air.

The model calculations are presented as vertical profiles of the horizontal pesticide flux at the edge of the sprayed field, i.e., at a possible hedgerow location. Results are also presented as the deposition drift to the ground as a function of the distance from the field edge, which is relevant for neighboring biotopes with a negligible vertical dimension.

Sensitivity calculations have been performed for spray-application parameters (nozzle type, spray pressure, and boom height), pesticide evaporation pressure, and meteorological conditions (wind speed, relative humidity, and air temperature).

3.1. Nozzle type and spray pressure

An important parameter is the droplet spectrum of the nozzle. In Fig. 6, the modeled drift is presented in two ways, as the vertical distributions of the airborne horizontal spray drift or horizontal flux at the edge of a field and as the deposition to the ground downwind of the field for three types of nozzles. As expected, the nozzle with the largest number of small droplets gives the highest horizontal drift and deposition. Deposition differs between the nozzles with a factor of 5–6, whereas the airborne drift values differ with a factor of about 10. The difference in factors is due to the fact that the spray cloud of the XR 110-02 nozzle contains a larger amount of small droplets that stay airborne and have a lower deposition velocity. At 10 m distance from the boom, the deposition ranges from 0.1 to 1.0% of the applied amount. A horizontal drift of 10 ng cm⁻² corresponds to 25% of the nominal application rate of 40 ng cm⁻². This number is extremely high compared to the ground deposits at 10 m distance, but as stated above the horizontal drift represents the cumulative dose from a 240-m wide field where most of the deposition to the ground occurs close to the sprayed track while the airborne horizontal drift moves over longer distances. The higher airborne drift values compared to deposition drift values are confirmed by Donkersley and Nuyttens.³²⁾

Fig. 6. Modeled vertical distributions of the airborne horizontal spray drift at the edge of a field (A) and deposition to the ground downwind of the field (B) for different types of nozzles: the standard flat-fans Hardi 4110-16 and XR 110-02 and the air-induction nozzle TeeJet AI 110-04. Values are the cumulated drift for a 240-m wide sprayed field. The value 10 ng cm⁻² corresponds to 25% of the applied pesticide of 400 µg m⁻². Other spray parameters and conditions are listed in the text.

The sensitivity of drift to differences in nozzle pressure is mainly caused by the effect on the droplet size spectrum and only slightly by the increased initial droplet speed. The calculated difference of the drift for the nozzle Hardi 4110-16 at 0.3 and 0.55 MPa is only about 7% (not shown).

Compared to the range of ground depositions reported from the databases referenced by Teske et al.,⁷⁾ our calculated deposition is underestimated at the first 0–5 m, but the setups in the scenarios may differ. The reason for this possible underestimation may be that the initial deposition calculated with the sinking plume is assumed only to occur inside the sprayed track.

3.2. Spray-boom height

The effect of boom height is calculated (not shown). Doubling the boom height from 0.5 to 1 m increased the horizontal flux at the hedgerow by a factor of about 2.3. Halving the height to 0.25 m only reduced the values by about 15%. These results should be considered with some caution, because they have not been validated.

3.3. Pesticide evaporation pressure

The evaporation pressures of common pesticides are extremely low and vary by orders of magnitude up to about 30 to 46 mPa.^33,34) Compared to water (vapor pressure of about 10 hPa), the evaporation of pesticides is about 10⁶ times lower. Runs of the model with metsulfuron-methyl with an increased evaporation pressure (77 mPa instead of 7.7 mPa) did not affect the amount of spray drift.

3.4. Wind speed, relative humidity, and air temperature

Wind speed is the most important meteorological parameter. In Fig. 7, drift values are shown for wind speeds of 2, 4, and 6 m sec⁻¹. As expected, increasing wind speed increases horizontal drift. The relative humidity of the air also plays a role in the amount of drift. Calculations (not shown) with relative humidity decreasing from 100 to 40% result in a gradual drift increase of about 70%. For low humidity, the droplets evaporate faster, and the reduced diameter results in lower fall speeds that increase the drift. Air temperature has the same effect on evaporation rate. Increasing temperature from 5 to 25°C increased drift by about 10–30% (not shown). Almost the same temperature dependence is calculated for the Hardi nozzle (not shown). The important effect of temperature and humidity on drift values corresponds with the results of Nuyttens et al.¹⁾

Fig. 7. Modeled spray drift at the edge of a field (A) and deposition to the ground downwind of the field (B) for different wind speeds. Other spray parameters and conditions are listed in the text.

4. Limitations

Although the model is based on reasonable physical principles, one should be cautious about changing the setup parameters too much, since only limited variations were available for calibration and evaluation. This concerns boom height, tractor speed, the minimum boom width of 12 m, and non-flat terrain. The effects of additives have not been addressed. The results will not be valid after the spray cloud has passed a possible hedgerow, as measured by De Schampheleire et al.²⁰⁾

Potential for Reduction of Exposures

The exposure of hedgerows and other neighboring biotopes to pesticides can be reduced by the introduction of spray-free buffer zones. The reduction of exposure depends on the width of the buffer zones, as demonstrated in Fig. 8, where deposition to the ground is calculated. The calculated values are the cumulative deposition from a 240-m wide field. The reduction of the deposition increases with increasing zone width. Compared to the standard situation without a buffer zone, the deposition at 40 m distance in biotopes with low vertical dimension is reduced by 33, 50, and 75% for buffer zone widths of 12 m, 24 m, and 48 m, respectively.

Fig. 8. Modeled spray deposition (% of field application) to the ground surface outside a 240-m wide field for different sizes of spray-free zones. The width of the zones is listed in the figure. Other spray parameters and conditions are listed in the text.

For the same situation, the exposure of a hedgerow is calculated in Fig. 9. The largest reduction occurs at the lowest levels as the width of the buffer zone increases. At the height of 8 m, the reduction is very limited. This is because it typically takes about 80 m before the airborne drift reaches a height of 8 m, and thus, the buffer zone of 48 m does not change the exposure at the top of a hedgerow. A maximum in the airborne drift profile appears just above the surface, which corresponds with our measurements. The same has been measured and modeled by Butler, Ellis and Miller¹⁰⁾ and supports the use of deposition velocity methods that assume this gradient to exist.

Fig. 9. Modeled vertical profile of the horizontal spray drift (ng m⁻²) for different sizes of spray-free zones at the border of a 240-m wide field. The width of the zones is listed in the figure. The value 1 ng cm⁻² corresponds to 2.5% of the applied pesticide of 400 µg m⁻². Other spray parameters and conditions are listed in the text.

Clearly, the meteorological parameters’ influence on the amount of spray drift emphasizes the importance of spraying during, e.g., the early morning hours, where speed and temperature are low and humidity is high. The type of nozzle, boom height, and pressure are, of course, also important.

Conclusion

The OML-SprayDrift model is developed using two well-tested principles, the Gaussian tilting plume and the traditional Gaussian reflected plume, with deposition calculated from deposition velocities depending on droplet fall speed and air turbulence. Model sensitivity to variation in meteorological and spray-application parameters behaves as expected from a physical point of view. The model’s initial droplet fall distance is calibrated for a standard flat-fan nozzle, and model performance is validated against an air-injection nozzle with a completely different droplet size spectrum. In spite of this challenge, the validation still shows a high accuracy of the model, and this strengthens confidence in the model.

In the model, the initial adjustment of droplet fall distance is solely dependent on wind speed at boom height. Other models use a correction independent of wind speed but use parameterizations of airstream velocity close to the nozzle that is fitted to the different types of nozzles. The accuracy of the OML-SprayDrift model should be further improved by applying this type of principle.

For the OML-SprayDrift model validation against existing experimental data for a wider span of meteorology, boom heights, additives, and crop types would be desirable in order to integrate these parameters in a future version. In general, there is a need for more accurate field trial experiments with a higher resolution. Additionally, scale-wind tunnel experiments under controlled and repeatable conditions can mean a step forward in further model refinement.

Acknowledgment

The authors thank technicians in the laboratory and in the field contributing to this study. The work of this paper was funded by the Danish Environmental Protection Agency.

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