Weather Effects on Drift Meteorological Factors and Spray Drift: An Overview

Abstract

A summary is given of the meteorological factors that affect spray drift. The primary factors are wind speed and direction, humidity through its influence on droplet size, and atmospheric stability. It is difficult to generically quantify and rank the effects of meteorology on spray drift due to the complex interactions between spray material, the application system, the target and the ambient meteorology. An approach to dealing with this complexity is the development of computer models. Three types of models are discussed from the standpoint of the meteorology and dispersion algorithms.

Introduction

The amount of spray drift from a given application depends on many factors. These can roughly be broken down into factors related to the material properties of the sprayed material, factors related to the application mechanism and method, and finally, factors related to the ambient environment, including both the state of the atmosphere and the nature of the target.

Drift is enhanced or hindered based on the state of the ambient atmosphere through which the material traverses. The longer the material is in the atmosphere, the more important ambient atmospheric conditions become. Arguably, the single most important variable in drift is the size of the sprayed droplets. Sprayed droplets evaporate after release into the atmosphere, becoming smaller with time and more susceptible to drift. See Bache and Johnstone (1992) and Miller et al. (1995) for overviews of spray meteorology.

This paper discusses the role of the atmosphere on a droplet. This discussion focuses on the primary transport of the droplet, defined here as the movement of the droplet from its release into the atmosphere until it impacts a surface. Volatile chemicals will change phase and disperse as a gas. Though much of this discussion is relevant to gaseous dispersion, this phenomena is not discussed at length here. Other spray materials are not volatile and will not evaporate. Deposited material may, under some circumstances, be re-entrained by the atmosphere. This is known as secondary drift.

The objective of this discussion is to provide an overview of the effect of the state of the atmo-sphere on spray. It is directed to spray applicators and managers and attempts to provide a basic understanding of meteorological influences on spray drift and a conceptual framework that will aid in operational decision-making.

The Machine

This paper must begin with a discussion of the spray apparatus. The meteorological variables are often overwhelmed near the release by forces associated with the release mode and mechanism. In most cases of spray application, the spray material is emitted at high velocity from a pressurized system or injected into a high velocity air-stream. Sometimes it is chopped by a fan or screen. The object is not to give an exhaustive list of release modes, but to point out that the material often begins its traverse through the environment with an initial temperature, initial velocity, and in a turbulence field different from ambient conditions. In the case of aerial spraying, the material is greatly affected by the wake of the aircraft. In many row crop applications, the wake of the aircraft is used to push material into the crop canopy. Spray released from ground sprayers will be away from the energy associated with the release within a few meters. In aerial spraying, the size and strength of the wing-tip vortices depend on the weight of the airplane and the length of the wing (Teske et al., 1994). Such a wake may influence spray for tens of meters after ti has been released. Material still aloft beyond the influence of the release mechanism is available for drift. The extent and distance of drift depends on interaction of the material with the ambient environment as deter-mined by meteorological conditions.

Wind Speed and Wind Direction

Motion in a three-dimensional fluid is a vector quantity, meaning it has speed and direction. The familiar statement of wind speed and direction provide two of the most important meteorological variables when considering spraying conditions. Wind direction is a highly variable quantity in both time and space. Standard deviations of 20° are not uncommon in a wind direction record with measurements every second (1 Hz) at a point in space. However, a mean wind direction (10 minute average for instance) will adequately determine the mean direction of the movement of the spray cloud centerline and thus the direction of drift.

The wind supplies the horizontal transporting force while gravity supplies the downward force. The mean horizontal wind speed will determine how fast the droplet moves in the horizontal direc-tion. The velocity at which the droplet would fall in still air is known as droplet 'settling velocity'. Gravitational forces that act downward are opposed by drag forces that act to slow the fall rate. Very small droplets (< 100 m or so) fall so slowly because the downward gravitational force is almost equally opposed by drag forces. In the simplest representation of droplet movement in the atmo-sphere, we can draw a vector resultant between the downward settling velocity and the horizontal wind speed to yield a fall angle and approximate droplet speed (Figure 1). As discussed below; many factors complicate droplet movement in the atmosphere, but this simple resultant trajectory model is a beginning.

The wind speed can also be viewed as a dilution rate when the released material is considered as a volumetric cloud. The higher the wind speed, the more fresh material is mixed into the cloud vol-ume and the more dilute the material becomes, equating to an increase in dispersion of individual droplets. Due to the drag of the surface of the Earth and the obstacles on it, wind speed increases with height. The increase with height is generally approximated as logarithmic, so aerial applicators need to be aware that a wind speed measured near the surface may not represent that at the release height of the spray.

Humidity and Temperature

Humidity is defined as the amount of water vapor in the air. The direct statement of this quantity is absolute humidity, H,:

H = eMw/RT (1)

where a is water vapor pressure in Pascals (Pa), MW is the molecular weight of water (kg mol-¹), R is the universal gas constant (Pa m3 mol-¹ K-¹) and T is temperature (K). Working through the units shows that this results in a measure of humidity in mass per volume or kg m-³. Jones (1983) gives a complete overview of this topic. Since both MW and R are constants, the relationship for H can be written:

H = (2.17/T)e (2)

Relative humidity (RH) is the humidity measure most often used when discussing drift. RH is expressed as:

RH 100(e/es) (3)

Thus relative humidity is a measure of the ratio of a to the vapor pressure when the air is saturated with water vapor (es). The absolute humidity relationships shown previously indicate a problem with using RH, and that is that es is dependent on T. This can confuse discussion of temperature vs. humidity effects. The importance of relative humidity to spray drift derives from the dependence of spray drift on droplet size. After release into the atmosphere, the initial droplet size begins to shift towards smaller sizes. The rate of change of droplet sizes over the entire droplet size spectrum depends on the chemistry of the released material and the humidity of the air. Assume the spray droplets are spherical. The volume (and thus the mass of a uniformly mixed drop) varies with the cube of the sphere diameter. A water droplet of 200 m diameter has a settling velocity of 0.705 ms-¹ while a droplet of 40 m has a settling velocity of 0.047 ms-¹. This is a factor of five difference in droplet diameter and a factor of 15 difference in settling velocity. Consider a release height of 15 m and a wind speed of 1 ms-¹. If we ignore the effects of turbulence and assume for simplicity sake (unrealistically) that the wind is laminar, a droplet of 200 m diameter would move with the wind 21 m before reaching the surface while a droplet of 40 m would move 318m. It must be emphasized that this is an overly simplistic portrayal of droplet movement in the atmosphere. The point is that as the droplet evaporates, the location that the droplet impacts the surface is greatly altered and prediction of that point of impact becomes increasingly difficult. The physics of small droplet evaporation are discussed elsewhere (see Davies 1978 for a review article) and many aspects of this problem are still a matter of active research (some effects of turbulence are discussed below). It can generally be said that as the droplet becomes smaller, it will spend more time in the atmosphere, other things being equal because of lower settling velocity.

Atmospheric Stability

Atmospheric stability is simply the change of temperature in the atmosphere with height. The universal gas law:

PV=nRT (4)

where P is pressure, V is volume, n is moles, R is the universal gas constant and T is temperature dictates a relationship between pressure and temperature. The equation for this relationship in the atmosphere is more complex than equation 4 however the basic relationship holds. When the temperature/pressure relationship is the primary control of the temperature profile in the atmosphere, indicating that no other important sources or sinks of thermal energy are affecting it, the profile is said to be neutral and follows the adiabatic lapse rate which is a 3.6°F/1000ft temperature drop with increasing height in a dry atmosphere. The temperature profile is commonly expressed as dT/dz or temperature change with respect to change in height. Forecast meteorologists analyze a deep atmospheric layer to forecast weather. They use a term called potential temperature, that accounts for the pressure temperature relationship so that d /dz = 0 in a neutral atmosphere. In general, the near surface layer where pesticide spraying occurs is sufficiently shallow so that a conversion to is not useful and tends to complicate the discussion. If high release heights are necessary, conversion to may simplify interpretation.

Three primary factors cause the atmospheric stability to tend away from neutral. The first is direct input of air with different thermal properties moving laterally (advection), the second is phase changing of atmospheric moisture. Evaporation and melting store sensible heat, while condensation and freezing release sensible heat. These effects are so ubiquitous in the atmosphere that meteorologists define a moist adiabatic lapse rate (5.5°F/1000 ft) for saturated atmospheres.

The third factor is the thermal energy input by solar radiation. An introductory discussion of stability effects with regard to pesticide dispersion is given in Thistle (1996). Briefly, solar energy radiated from the sun is of a short wavelength as dictated by the temperature of the radiating body. The atmosphere of the Earth is relatively transparent to this short wavelength energy so it passes through the atmosphere and is absorbed at the surface. The surface then reradiates energy at a much longer wavelength than the sun due to its lower temperature. The atmosphere is a reasonably effective absorber at these longer wavelengths and the atmosphere is heated from below.

The relevance to the problem of pesticide drift is a result of the control that the resulting temperature profiles exert on atmospheric mixing. Warm air is not as dense as cold air and is therefore lighter. When the surface is heated, during a sunny afternoon for instance, the air near the surface wants to rise through the colder air over it. This is known as an unstable surface layer. At night, the surface is again the active radiation surface and loses heat faster than the air above it. Therefore, at night the surface is colder and air adjacent to it gets cold through conductive heat loss. This cold air is heavier than the air above it and tends to stay in place. This is known as a stable surface layer. Three states of atmospheric stability are defined:

1) Neutral - the temperature change with height follows the adiabatic lapse rate relationships.

2) Unstable - warm air under cold air (or slight cooling with height but less than the adiabatic rates)

3) Stable - cold air under warm air (cooling with height is greater than the adiabatic lapse rate)

In the air layer from 50 m above the surface to the surface, we will simplify this discussion by ignoring the lapse rate and discussing increasing temperature with height (stable), decreasing temperature with height (unstable) and no change (neutral). Consider a parcel of air at a given layer. In an unstable situation (Figure 2), the parcel is lighter than the air above it and heavier than the air below it. Therefore, if the parcel is moved up or down it will keep moving away from its point of origin. A small perturbation results in substantial mixing, and is characterized by large 'bubbles' of air lifting off the surface. These are the thermals that aviators are familiar with. This type of motion can result in cumulus formation (even initiating cumulonimbus or thunderhead formation). Near the surface, the liftoff of some air causes other air to rush in to replace it, resulting in the intermittent winds of variable direction characteristic of many summer afternoons.

Now consider a parcel of air in a stable layer (Figure 3). If this parcel is displaced upward it is heavier than the air in the layer above and will sink back to its layer of origin. If it is displaced downward, it is lighter than the air below it and will return to its layer of origin. Thus, a small perturbation in a stable layer will be damped out and mixing is suppressed. This situation typically exists on a cool, clear morning when the air is still.

With some exceptions, these conditions depend on two factors. These gradients will not establish themselves in strong winds. If there is macro-scale activity (such as a frontal passage) in the atmosphere and the wind is blowing, the surface layer tends to mix and the stability tends toward neutral. Surface heating and cooling are restricted by cloud cover. If cloud cover is present, surface heating will be damped and nocturnal surface cooling will also be lessened. The effectiveness of cloud cover in limiting surface temperature depends on the thickness and extent of cloud cover. The main exceptions to this rule are areas near large bodies of water (coastal settings) where the water provides a lateral source of air with markedly different characteristics, and sloped terrain where upslope and downslope flows develop in non-neutral atmospheres. (See Barr and Clements, 1984, for a discussion of both coastal and complex terrain effects on atmospheric dispersion.)

In conventional air pollution modeling, short term, single point maximum downwind concentrations typically occur under stable conditions. This is because the low mixing under stable conditions allows the pollutant plume to remain relatively concentrated. Other considerations affect spray droplets as well. The low velocity typical of the stable situations discussed above will give the droplets more time to settle out of the air and deposit. Thus, if the plume were integrated across a downwind vertical plane, the total amount still airborne would probably be less than in higher wind conditions. Increased residence time in the atmosphere leads to smaller drops. There is an explicit covariance with humidity because the stable layer is relatively cooler. Under low mixing conditions, humidity is typically higher near the surface around plant canopies. Higher humidity will reduce evaporation.

Turbulence

Turbulence can be loosely defined as the variance in a given fluid flow. If the mean wind speed is described as, the measurement of this speed at a given time will include the mean speed and some deviation from it. Thus, if the speed is u:

u = u+u' (5)

the term u' is the difference at any instant between the instantaneous wind speed and the mean wind speed (Figure 4). If we take the absolute value of this quantity ( |u'|) then a turbulence intensity (TI) can be stated as: TI =|u'|/u (6)

where the overbar indicates an average, alternatively, the u' term could be formulated as a standard deviation. Panofsky and Dutton (1984) is an excellent text discussing turbulence in the atmosphere. These authors state that a generally accepted definition of turbulence does not exist, so turbulence is described by its qualities. The system of fluid dynamics equations that describe a turbulent fluid are known as the fluctuating Navier-Stokes equations. Constantin and Foias (1988) provide a detailed mathematical treatment of these equations. These equations are the basis for much ongoing work in fluid dynamic research.

Turbulence can generally be thought of as overlying rotational motions that range in size in the atmosphere from a minimum of a few millimeters in diameter to a maximum wavelength determined by the system. For instance, in an unstable atmosphere the maximum vertical eddy size is on the order of the length of the highest rise of surface-generated thermals (that range up to thousands of meters in height). These big rotational motions break down in a very regular way (known as a cascade) into little eddies, the smallest of which are dissipated by the fluid (air in this case) viscosity.

The mean motion in the atmosphere away from the surface tends to be perpendicular to atmospheric isobars (lines of equal pressure). The turbulent eddies translate along with the larger motions. Turbulence tends to increase near the surface where the fluid encounters the drag of a rough surface. Plant canopies tend to have very high TI both because the canopy elements shed eddies and because mean flows () are relatively lower there because they lose energy to friction with the canopy.

Turbulence influences spray drift in various ways. Since the airflow is not in a straight line, the conceptual model of a vector resultant between the settling velocity and the mean wind speed needs to be modified to include rotational motions in the atmosphere. Because individual turbulent motions are random in time, the droplet will move up and down. The turbulent eddies tend to develop a relatively strong downward component in stronger winds and might be useful in pushing material into taller canopies. Also, the downward vertical component of the larger eddies may generally help to impact droplets onto a target surface. There is also a return flow from these eddies, but it tends to be composed of smaller eddies somewhat analogous to waves after they break on the beach. However, in an unstable atmosphere, strong updrafts may develop as discussed above. These may be capable of transporting droplets to remarkable heights. Spraying in very unstable conditions should .probably be avoided because these large thermal eddies make the spray hard to control.

Regarding the plume of droplets as a whole, the variance or turbulence controls the spread of the flow. In air pollution modeling, a dispersion coefficient of some type based on a measure of the atmospheric turbulence is used to calculate plume spread. Eddies bigger than the plume will move the plume in a meandering motion. Eddies very small relative to the plume will cause a small amount of `diffusive' plume spread, while eddies the size of the plume are probably most influential in determining plume width.

The final influence of turbulence on drift discussed here is more subtle. When considering droplet evaporation, the droplet can be considered as moving in the flow and the air around the droplet moves with it. The air adjacent to the droplet will thus have a higher humidity in the case of an evaporating water droplet than the free air away from the droplet. This layer of air with properties due to the droplet will slow evaporation. In more turbulent conditions, this boundary layer effect is weakened. Thus turbulence tends to facilitate droplet evaporation.

Canopy

A detailed discussion of canopy meteorology is beyond the scope of this paper (see Kaimal and Finnigan, (1994) and Stull(1988) for more complete discussions). Some generalizations can be made and are important to consider since the canopy is often the application target and, in the case of orchard spraying for instance, may influence most of the spray dispersion domain. Canopies are usually moister (higher humidity) than open areas. Wind speeds tend to be lower due to drag by the canopy elements. Turbulent intensity tends to be higher because of eddy shedding off of canopy elements. The canopy intercepts solar radiation. Under closed canopies, a stable layer (inversion) can exist in the middle of the day due to shading.

Modeling

There are generally three types of models currently widely used in pesticide dispersion and drift applications. The first is a Gaussian approach that follows an established, conventional method used in regulatory air pollution. It is most appropriate for gaseous diffusion. The second focuses on the machine energy, both of the pressurized system and of the release vehicle wake. It uses simple meteorological transition and transport models. The third is a physical approach often based on Navier-Stokes techniques applied in the atmosphere.

The first type of model assumes that the wind direction determines plume centerline and the crosswind distribution is a Gaussian or bell-shaped curve as shown in Figure 5 (See Turner (1970) for discussion of Gaussian techniques) . Gaussian models are mass conservative and steady state. The plume is narrower near the source and becomes wider downwind. The maximum airborne concentration is highest near the source and decreases downwind. A crosswind slice of equal thickness at any distance downwind will integrate to the same mass if no depletion of the plume material is considered. The rate of plume spread is determined by dispersion coefficients that vary with stability and also can be varied to consider cases of very large surface roughness such as tall buildings.

Gaussian models have proven very robust in dispersion applications. The model forces the concentrations to decrease with distance (at least away from source influences or source elevation effects) from the source and to decrease laterally from the plume centerline. This also helps these models show high correlations because correlation evaluates sameness of shape as opposed to a residual measure between observed and predicted. This type of model has never been of much interest to researchers because it is effectively a statistical model. The down and crosswind distribution of pollutant mass (expressed as concentration) is input a priori in the model so there is not much new to be learned from a theoretical standpoint from these models.

The second type of model focuses on the wake of the machine. The most commonly used model of this type is used in simulating aerial spraying and uses the weight of the airplane and wingspan to calculate the strength and location of wake vortices that entrain the spray droplets. (See Bilanin et al. (1989) for the basic formulation now widely used in pesticide dispersion work and Thistle et al.(1998) for a list and description of currently available models using this approach. ) The droplets then travel in the atmosphere in these swirling vortices until the vortical energy is dissipated either by the surface or by ambient wind and turbulence. This type of model focuses on the droplets and considers ambient temperature and humidity for a droplet evaporation algorithm. It explicitly considers droplet settling velocity and considers the ambient wind and turbulence to calculate vortice decay and to use as a transport mechanism after the machine energy has dissipated. These models are physically based. Some models used in the research community are full physics, numerical models incorporating the state-of-the-art in fluid dynamics theory. The models commonly used in agricultural spraying are greatly simplified, but are used in some research applications.

The final class of models generally use the Navier-Stokes equations to describe the atmospheric dynamics and interface those equations with a full physical description of the aircraft wake. The Navier-Stokes equations describe motion in a turbulent fluid and attempt to give a four-dimensional representation (three spatial dimensions and time). The equations use a velocity vector, pressure, fluid (air) viscosity and a stability term to calculate how the fluid will move and change with time. The equations cannot be solved without making assumptions about the flow that impart uncertainty into the solution. These assumptions and approaches to this problem are areas of ongoing research and there are a number of this type of model in existence (though only a few couple the ambient environment and the wake energy in a physical model).

Discussion

It is difficult to summarize this topic in a short review paper. The question of what is the most important meteorological variable depends on circumstances. In many situations, wind direction may be the most important variable as it is critical to keep spray out of sensitive areas that lie in a certain direction. When all the variables included in spraying are examined in a sensitivity study, droplet size may be important variable in determining the amount of drift. It follows from this that humidity plays a crucial role that is a controlling role in certain circumstances. Wind speed is of obvious import. Some of the more mysterious cases of off-target damage can be traced to stability or, more specifically, a concentration of fine droplets in a stable atmospheric layer.

Conclusions

Meteorological conditions will increasingly be considered in pesticide labeling so that constraints will be set from a regulatory perspective. Effective use of pest control agents requires that the material be on the target. Thus, off-target drift is a loss from both the standpoint of efficacy and economics and from the standpoint of the surrounding environment. The interactions of the variables involved are complicated. In response to this complexity, computer models have been developed and used to simulate spraying of pesticide. These models are used to plan, train and analyze completed application operations.

References

Bache D.H. and D.R. Johnstone. 1992. Microclimate and Spray Dispersion. Ellis Horwood Series in Environmental Management, Science and Technology.

Barr S. and W.E. Clements. 1984. 'Diffusion Modeling: Principles of Application', Atmspheric Science and Power Production. Ed. Darryl Randerson. DOE/TIC-27601.

Bilanin A.J., M.E. Teske, J.W. Barry and R.B. Ekblad. 1989. 'AGDISP: The Aircraft Spray Dispersion Model, code development and experimental validation'. 32.

Constantin P. and C. Foias. 1988. Navier-Stokes Equations. Chicago Lectures in Mathematics, University of Chicago Press. Chicago, IL.

Davies C.N. 1978. 'Evaporation of Airborne Droplets', Fundamentals of Aerosol Science Ed. D.T. Shaw. John Wiley and Sons. New York, NY.

Kaimal J.C and J.J. Finnigan. 1994. Atmospheric Boundary Layer Flows: Their Structure and Measurement. Oxford University Press. New York.

Jones H.G. 1983. Plants and Microclimate: A Quantitative Approach to Environmental Plant Physiology. Cambridge University Press. New York, NY.

Miller D.R., R.C. Reardon and M.L. McManus. 1995. An Atmospheric Primer for Aerial Spraying of Forests. USDA Forest Service FHM-NC-07-95. Morgantown, WV.

Panofsky H.A. and J.A. Dutton. 1984. Atmospheric Turbulence: Models and Methods for Engineering Applications. John Wiley and Sons. New York, NY.

Stull R.B. 1988. An Introduction to Boundary Layer Meteorology. Atmospheric Sciences Library, Kluwer Academic Publications. Boston, MA.

Teske M.E., J.W. Barry and H.W. Thistle. 1994. 'Aerial Spray Drift Modeling'. Environmental Modeling Vol. II: Computer Methods and Software for Simulating Environmental Pollution and its Adverse Effects. Ed. P. Zanetti. Computational Mechanics Publications. Boston MA.

Thistle H.W. 1996. 'Atmospheric Stability and the Dispersion of Pesticides'. Journal of the American Mosquito Control Association. 12(2).

Thistle H.W., M.E. Teske and R.C. Reardon. 1998. 'Modeling of Aerially Released Sprays'. Proceedings of the GIS'98/RT'98 Conference. GIS World, Inc. Ft. Collins CO.

Turner D.B. 1970. Workbook of Atmospheric Dispersion Estimates. PHS Publication No. 999-AP26. U.S. Department of Health, Education and Welfare. National Air Pollution Control Administration. Cincinnati, OH.

Figure 1. The simplest model of droplet fall angle calculates a resultant based on settling velocity (down) and mean horizontal wind speed (horizontal). Aircraft wake vortices and turbulence in the atmosphere cause the actual droplet trajectory to be much less regular.

Figure 2. In an unstable atmo-sphere, a parcel of air will move away from its level of origin, thus increasing turbulence and enhanc-ing mixing in the atmosphere.

Figure 3. In a stable atmosphere, a parcel of air will tend to return to its level of origin when perturbed vertically. This damps out turbu-lence and suppresses mixing in the atmosphere.

Figure 4. Turbulence can be described by the fluctuations in the wind speed. The magnitude of these fluctuations relative to the mean wind speed is referred to as turbulent intensity.

Figure 5. A simple family of dispersion models are known as Gaussian models. The direction of plume movement is determined by the wind direction and material distribution is Gaussian (normal or bell-shaped) in the crosswind direction. The vertical distribution is complicated by interaction with the ground surface but is usually also based on a Gaussian in this type of model. (Figure adapted from Turner (1970)).

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