a) The surface roughness of the sea depends on the wind speed, see (7).

It should be noted that the surface roughness is not constant in agricultural areas, but depends on the heights of the crops, which vary during a year. The surface roughness length for the open sea is not constant either, but is a function of the wind speed (Lindfors et al., 1991):

where n is the kinematic viscosity of air (~ 1.5x10^-5 m² s^-1) and g is the gravitation (9.81 m s^-2). In the wind speed range of 0-3 m s^-1 the roughness length decreases with wind speed, for larger wind speeds the roughness length increases, mainly because the wave height increases.

Effect of surface roughness on wind speed profile

The surface roughness varies with the nature of the terrain. For that reason the wind speed near the surface will be a function of the surface roughness.

This means that under the same meteorological conditions (i.e. same wind speed at greater height) the wind speed near the surface will be different for e.g. bare soil, crops, forest and water. The friction velocity u_*, which is a measure of the mechanical turbulence, is in that case larger for a more rough surface like a crop than for bare soil. As a result the wind speed near the surface will decrease with surface roughness. Figure 5 shows some vertical wind profiles for two different surfaces under neutral conditions: a crop and an almost bare soil. The surfaces are chosen so that they represent typical situations encountered in agricultural areas on or near fields where pesticides are applied.

Figure 5
Vertical wind speed profile over a crop with a surface roughness length of 0.1 m and almost bare soil with a surface roughness length of 0.006 m. It is assumed that in both cases the wind speed at 60 m height is the same.

Effect of wind speed profile on atmospheric transport

The existence of a wind speed profile influences the average speed at which a released compound is transported in the atmosphere. At some distance from the source part of the released compound has been transported upward by diffusion and encounters a higher wind speed than near the surface. This means that the average speed at which a compound is transported increases with the distance to the source until it is mixed over the whole mixing layer (see below).

Effect of surface roughness on atmospheric transport

Figure 5 shows that the wind speed is higher in the case of the bare soil. This means that a compound released from a field with almost bare soil is transported at a greater speed, than a compound released from a field with a crop. At some distance from the released point, however, this difference is not any longer so large, because the air has been transported over areas with other surface roughness lengths. Moreover, the compound is then transported higher up in the atmosphere where the wind speed is less influenced by the surface.

Wind direction profile

Not only the wind speed is influenced by the presence of the surface, but also the wind direction. Usually the wind direction is veering with height in the Northern Hemisphere. This means that the origin of the air at greater heights is different from that at ground-level.

Mixing height

In some parts of the atmosphere stable layers may exist, where vertical air movements are suppressed. This means that air originating from below cannot be transported across this layer and this layer is than functioning as a "lid" on the atmosphere below, where mixing can occur. Air from above this layer can also not be transported downward. In case of tall stacks that emit pollution above this lid, this is a favourable situation, because the pollution cannot reach the earth’s surface where humans live. In case of emission of pollution from low or ground level sources, as is the case for pesticides, this is an unfavourable situation, where very high concentrations can occur near the ground. This can especially be the case during night time when temperature inversions close to the ground are observed frequently.

The "mixing layer" is the layer nearest to the earth’s surface where mixing takes place. It is bounded by the surface and the first layer where vertical movements are suppressed. The height of the mixing layer is called "mixing height", It is important to know the mixing height, at least when transport of pollutants at some distance from the source has to be described, because the pollution plume may then have come so wide that it has reached the mixing layer height. Further dilution in the vertical is then not any longer possible and this will influence the concentrations at the surface.

The mixing height shows large diurnal variations. During a cloudless night, radiative cooling may cause the temperature near the surface may to drop so much that a temperature inversion is observed. As we have seen before this leads to high concentrations at ground-level near low sources. If the atmosphere is also cloudless after sunrise the next day, the earth’s surface will be heated and the inversion disappears. Also wind can have an effect on the mixing height. If there is much wind during a cloudless night, the air is well-mixed and air that is cooled down near the surface is transported upward so that the mixing height will not be close to the surface. It must be noted here that water bodies (lakes, seas) do not show the large diurnal temperature variations as the upper layer of the soil. For that reason the mixing height over sea will generally be different than over land.

During night time the mixing height is often below 200 m, whereas it is often higher than 500 m during day time. If the atmosphere is very unstable the mixing height can be indefinite (i.e. over 2000 m).

For neutral and stable conditions there is a relation between the friction velocity and the mixing height:

where z_mix = mixing height (m); c₁ = a constant; f_cor = Coriolis parameter (s^-1) and is given by 2W sin(lat), where W = angular velocity of the earth (radians s^-1) and lat = latitude (radians), for a latitude of 50° N the f is 1.11x10^-4 s^-1. Van Jaarsveld (1995) uses a value of 0.08 for c₁. This value is chosen so that reasonable results are obtained for compounds that are transported over long distances. It should be noted, that other scientists use different values. In the short range dispersion model OML developed at the National Environmental Research Institute, Roskilde, Denmark a value of 0.25 is used for c₁ (Berkowicz, National Environmental Institute, Roskilde, Denmark, personal communication). The reason for using this much higher value is that otherwise observed concentrations near power plants with high stacks cannot be reproduced by the OML model. So there is considerable uncertainty in the function for the mixing height. Equation (8) shows that the mixing height increases with the friction velocity u_*, i.e. with the wind speed. As u_* also depends on the surface roughness, the mixing height is in principle a function of the surface roughness. This is, however, not a local surface roughness, but a surface roughness of the whole landscape as "seen" from the mixing height.

The mixing height under unstable conditions can only be found from measurements (vertical temperature profile) or from a more complicated model that describes the development of the mixing height during the day as a function of e.g. solar radiation.

Atmospheric diffusion near a point source

The diffusion near a point source produces a normally distributed timeaveraged concentration perpendicular to the plume axis. Such a Gaussian distribution can be described with a standard deviation, just as the normal distribution used in statistics. In this case, however, the standard deviation is not constant, but is a function of the distance to the source. As there is diffusion in all directions, the concentration can be described with a normal distribution in all directions. If the point source is continuous, the diffusion in the wind direction can be neglected, because the effect of diffusion at subsequent time steps will compensate each other in this case. Figure 6 illustrates how the concentration distribution at ground-level as a function of distance from a point source looks like. It can be seen that the plume becomes wider and the maximum concentration lower as a function of the distance to the source. In this case the x direction is parallel to the wind direction (the wind blows from left to right), the y direction is in the horizontal perpendicular to the wind direction. On the vertical axis the concentration is shown.

Figure 6
Ground-level concentration due to a point source for several downwind cross-wind sections.

Mathematical description

The diffusion of airborne material from a point source can be described mathematically with the Gaussian distribution:

In this model it is assumed that the wind direction is parallel to the x axis, that the y axis is perpendicular to the plume axis in the horizontal direction, and that the z axis is perpendicular to the plume axis in the vertical direction. The coordinate system starts at ground level at the position of the point source (there x,y and z are 0); c(x,y,z) is the concentration (kg m^-3); Q is the source strength (kg s^-1);is the average wind speed at stack height (m s^-1); h is the stack height (m), s _y(x) and s _z(x) are the standard deviations of the concentration distribution in the y and z direction (m). The second exponential function within the brackets results from reflection of the plume at the earth’s surface. c(x,y,z), , s _y(x) and s _z(x) should reflect the same averaging time. The standard deviations of the concentration s _y(x) and s _y(x) are determined experimentally and depend on meteorological conditions (atmospheric stability), surface roughness, averaging time and to some extent on the source height.

Standard deviations for concentration

For neutral conditions s _y(x) (m) and s _z(x) can be described by estimates of Briggs for a rural situation (equations (10) and (11); Pasquill and Smith, 1983).

It should be noted here that these equations are, in fact, only valid for elevated releases. The values for surface releases can be up to a factor 2 larger. s _y(x) and s _z(x). For other than neutral conditions there are also equations for s _y(x) and s _z(x) available (Pasquill and Smith, 1983).

Figure 7 and equation (11) show how s _z(x) increases as a function of distance to the source. Close to the source it increases linearly with x and at greater distance proportionally with . This is important to notice, because that means that the diffusion close to a source is not the same as the diffusion at some distance from the source.

Figure 7
Standard deviation for concentration in the vertical (s _z(x)) according to Briggs as a function of distance to a point source.

Area source

A field onto which pesticides have been applied does not act as a point source, but as an area source because the whole area is covered with pesticides. The diffusion from an area source can be described in the same way as the diffusion from a point source. For that reason it can be simulated in a model by putting many small point sources on the field. Another method to simulate an area source in a model is by using one point source that is at such an upward distance from that s _y(x) has the same width at the position of the field in the model as the field itself ("virtual point source"). These approaches give good results at some distance from the field, but near the field and especially on the field itself they do not give an accurate description.

K-model

There exists another type of diffusion model, a so called "K-model". In such a model the atmosphere is divided into cubic air parcels and the diffusive transport between these air parcels in all directions is described with so called "eddy diffusivity coeffcients". We will here only focus on the diffusion in the vertical, which is described in the following way: The atmosphere is divided into vertical layers. Between these layers the diffusion is described by an eddy diffusivity coefficient (m² s^-1), which for a neutral atmosphere is:

From the equation it can be seen that the K_Heat(z) increases with height. This assumption is, in fact, not entirely correct as K_Heat(z) decreases short before the mixing height is reached, but the above equation leads nevertheless to good simulations of ground-level concentrations. It can be seen from (12) that K_Heat(z) is a function of the friction velocity u_*. This type of model is called a K-model, because it uses eddy diffusivity coefficients K to describe the diffusion. For other than neutral conditions (12) can still be used, but then some corrections have to be made.

Difference between a K- model and a Gaussian plume model

It should be noted, that there is a difference in how a K-model and a Gaussian plume model describe the diffusion as a function of distance to the source. The results of a K-model for which K_Hear(z) does not vary with height as in (12) behaves in the same fashion a Gaussian plume model for which the s _z(x) increases is everywhere with. This is different from the description of a real plume, where s _z(x) increases with x close to the source and with at greater distance. If a K-model is applied where K_Heat(z) increases with height the diffusion will increase with distance to a ground-level source. The reason is that an increasing fraction of the released compound is transported upward, where the diffusivity is greater than near the surface. This effect will be enhanced if also the wind speed is made a function of the height. So the approach in the two types of models is different and for that reason they will also give somewhat different results.

A K-model can adequately describe area sources and even concentrations within the area source (a field onto which pesticides are applied) can be modelled well. Gaussian plume models are not able to describe concentrations within area sources well. A K-model can also better handle dry deposition, i.e. deposition that takes place at the surface (see also the next section). As a result of dry deposition the concentration near the surface decreases, which is more difficult to reproduce with a Gaussian plume model.

Equation (12) shows that the diffusion depends u_*. As was noted before u_* increases with surface roughness. Consequently the diffusion increases also with the surface roughness.

1.4 Surface exchange

Exchange of material between the atmosphere and the surface is caused by eddies in the atmosphere. The simplest way of describing the process is using a "big leaf model". In this model the surface is treated as one big leaf on a tree and not as a very complicated surface with differences in surface properties as in reality.

Big leaf model

The transport is considered to consist of three distinct steps. These steps can be described with resistances in series by analogy with electrical circuits. The first part is the transport by turbulent diffusion from a certain height in the atmosphere (reference height) to a very thin (~ 1 mm) layer just above the surface. The resistance belonging to this part is called aerodynamic resistance (r_a). The second part of the transport is through the thin layer. In this layer the flow is laminar (= not turbulent) and the transport has to occur by non-turbulent diffusion. For gases this is the molecular diffusion, for small particles this is the Brownian diffusion. For larger particles inertial and gravitational effects become important, the latter characterised by the settling velocity. The thin layer is called laminar boundary layer and the resistance is called laminar boundary layer resistance (r_b). Then the material arrives at the surface. The properties of the surface: solubility, reactivity/degradation, transport velocity into the surface determine how much of the material that arrives at the surface is taken up. This resistance associated with this step is called surface resistance (r_c). It is in fact an over-all resistance category describing many processes. The best thing to do is, in fact, not to use just a value for the surface resistance in the big leaf model, but to model the surface resistance by modelling all relevant processes that take place in the surface. In that way it is also possible to understand the underlying mechanisms and to model e.g. temporal variations in the surface resistance. This is especially necessary for pesticides, because there are no measurements of the exchange of pesticides between the atmosphere and the surface and because some pesticides can be re-emitted once they have been deposited. If models that describe the fate of pesticides in soil, vegetation and water bodies are coupled to models for the atmospheric part of the exchange, it will be possible not only to model deposition, but also emission from e.g. bare soil, crops etc.

Big leaf model for gases

Figure 8 shows the big leaf model for gases, which describes the dry deposition to land surfaces. Highly soluble/reactive gases like nitric acid (HNO₃) are immediately taken up by the surface, the surface resistance will be negligible and the over-all transport is determined by the aerodynamic and laminar boundary layer resistance. An inert gas like helium (He) is not at all taken up in the surface. The surface resistance will in that case be indefinitely large and determines the over-all transport: although He is transported to the surface it is also transported from the surface so that no net transport occurs. We can conclude that the exchange velocity depends both on the properties of the gas and the properties of the surface and that depending on theses properties either the atmospheric processes (characterised by the aerodynamic and laminar boundary layer resistance) dominate the velocity or the surface processes or both.

Figure 8
"Big leaf" model for dry deposition of gases.

"Big leaf" model for tørdeposition af gasser.
   

Aerodynamic resistance for gases and particles

The aerodynamic resistance is the same for gases and particles. For neutral   conditions it is given by:

where r_a = the aerodynamic resistance (s m^-1) and z_r is the reference height (m). Equation (13) shows that r_a decreases with u_*. This means that the exchange increases with u_* and therefore also with the wind speed. This way of expressing the exchange gives exactly the same results as the eddy diffusivity concept presented in the previous section. The same type of function but then with correction factors can be used to describe the aerodynamic resistance for other than neutral conditions.

Laminar boundary layer resistance for gases

For gases the laminar boundary resistance is given by Hicks et al. (1987):

where r_b = laminar boundary layer resistance (s m^-1); Pr = Prandtl number (dimensionless = 0.72); Sc = Schmidt number (dimensionless) which can be found from Sc = n /D_g, where n = kinematic viscosity of air (m² s^-1) and D_g is the diffusivity of the gas in air (m² s^-1). Sc is not a function of temperature, so for n and D_g the values for 25° C can be taken; n at 25° C is 1.55x10^-5 m² s^-1 and D_g depends on molecular mass of the gas. The larger the molecule the smaller the diffusivity, because large molecules do not move so fast. If D_g is not known, it can be estimated by:

where D_g is in m² s^-1 and M_g is the molecular mass of the gas (g mol^-1). This description of r_b is still somewhat uncertain. It is important to note that pesticides have much higher molecular masses (typical 200-300 g mol^-1) than more frequently studied atmospheric gases. Equations (14) and (15) show us that r_b decreases with the molecular mass of the compound that is exchanged.

Gaseous flux

The exchange of gases between the atmosphere and the surface depends on both the concentration in the atmosphere and the concentration in the surface and is given by:

where F_g = flux (kg m^-2 s^-1), which is by definition negative if the material is removed from the atmosphere; v_e is the exchange velocity (m s^-1) and is equal to 1/(r_a + r_b) ; c_g,air is the concentration of the compound in the air at reference height (kg m^-3); c_g,surf^* is the (theoretical) gas phase concentration in the surface. If the gas phase concentration in the surface is not known it can be calculated from the concentration in the water phase and the Henry’s law coefficient: c_g,surf^* = Hc_w, where c_w is the water phase concentration (kg m^-3). If c_g,air is larger than c_g,surf^* dry deposition will occur. If c_g,surf^* is larger than c_g,air emission will occur. Pesticides like lindane can be re-emitted after being dry or wet deposited. So it is important that both ways can be described, but then processes in the surface that influence the concentration in that surface should be described as well. Both r_a and r_b decrease with u_*. This means that the flux increases with wind speed.

For compounds for which reemission is not important and for which the surface resistance has been measured (or can be modelled), the flux is described by:

In this equation v_d is the dry deposition velocity (m s^-1), which is equal to 1/(r_a + r_b + r_c); r_c is the surface resistance (s m^-1). In this case not only atmospheric processes are described as with (16), but also surface processes. The flux increases also in this case with the wind speed. It should be noted here that both r_a and r_b are a function of the wind speed, but r_c is not. If the surface resistance r_c is small compared to r_a and r_b (almost all material is taken up by the surface) the flux increases relatively much with wind speed. If the surface resistance r_vc is relatively large, the flux does not increase much with wind speed.

The exchange of gases between the atmosphere and water surfaces depends on turbulence in the air, solubility of the gas,and also on the turbulence in the water (Liss and Slinn, 1983; Asman et al., 1994). As this deposition is beyond the scope of this report it will not be discussed here.

Maximum dry deposition velocity for gases to land surfaces

As can be seen from (17) the dry deposition velocity v_d has a maximum value if the surface resistance r_c is 0, i.e. the dry deposition velocity is then totally determined by the atmospheric processes. This maximum dry deposition velocity will be a function of the friction velocity, which can vary appreciably. The friction velocity depends on the wind speed at greater height and the surface roughness. It is possible, however, to calculate an average maximum dry deposition velocity for a area and surface roughness. For Danish conditions this average maximum dry deposition velocity will be of the order of 2´ 10^-2 m s^-1 for cropland (surface roughness length of 0.1 m) and of the order of 4´ 10^-2 m s^-1 for forests (surface roughness length of 1 m). Assuming that the concentration of the compound is the same everywhere over a mixing height of 500 m, only 13% and 25% of the compound is removed after 1 hour with dry deposition over cropland respectively forests (22). This shows that dry deposition is not a fast process, even not for the fastest depositing gas. The only exception is close to a low source where the compound is not yet mixed over the whole mixing layer and the concentration is relatively high for that reason.

Determination of the uptake rate by dry deposition of gaseous compounds in the laboratory

The dry deposition velocity for many organic compounds, like pesticides, is not so high and is more determined by the processes that play a role in the surface. This gives the possibility to study uptake by dry deposition in the  laboratory, where it is difficult to generate realistic atmospheric turbulence.  The only condition is then that there is enough turbulence in the experiment, created e.g. by a ventilator, that the diffusion in the atmosphere does not limit the uptake rate. In that case the uptake rate is only determined by processes in the surface. These processes in the surface are diffusion into the surface, adsorption and degradation. For water also mixing in the water itself plays a role. The uptake rate will not be constant in such experiments, but will decrease with time because the surface gets saturated with the pesticide.

Duyzer and van Oss (1997) performed laboratory experiments where they measured the uptake rate of organic chemicals by soil, fresh water, sea water and by grass as a function of time. They developed also simple models for uptake as a function of time and were in most cases able to obtain reasonable agreement between modelled and measured uptake rates.

Effective dry deposition velocities for soils for field conditions can be obtained by using the model developed for the laboratory experiments and then taking into account the occurrence of precipitation. The uptake rate by dry deposition in the field also decreases also with time due to saturation, just as in the laboratory. Rainfall will wash down compounds that are for a large part present dissolved in soil water. The surface will then become less saturated and can then again take up gas at a higher rate. In some cases also re-emission will occur. A more complicated of this type was presented by van Jaarsveld (1996). Van Pul et al. (1998) give also some useful parameterizations taking the degradation rate in the surface into account.

Big leaf model for particles

Particles of many different sizes are found in the atmosphere. Most particles  are so small that gravitational settling is negligible compared to the vertical transport caused by turbulent diffusion in the atmosphere. As a result, most particles are transported and diffused in the atmosphere in the same fashion as gases. Once particles are deposited, they are usually not re-emitted to the atmosphere again. As a result, the surface resistance can usually be omitted in exchange models for particles, because it is zero. The dry deposition velocity is in that case given by:

Particles have some properties that cause their laminar boundary layer resistance to be much higher than for gases, because their transport through the laminar layer is much slower. Only very small particles with radius less than 0.1 m m, which do not contribute much to the total atmospheric aerosol mass, have reasonable Brownian diffusivities and are transported with a reasonable speed through the laminar boundary layer. For particles with a radius larger than about 1 m m, transport through the laminar boundary layer is more efficient because then impaction and interception at the surface are also important. But a large fraction of the particles has a radius between 0.1 and 1 m m and are only transported very slowly through the laminar boundary layer. The velocity at which particles are transported through the laminar boundary layer varies highly with their size an as a result the dry deposition velocity for particles varies also highly with their size. For particles with a radius > 5 m m gravitational settling is important and should be taken into account. As this mechanism is active at the same time as the other atmospheric transport mechanisms the big leaf model can be modified by adding an additional gravitational settling resistance r_vg to transport parallel to the other resistances (Figure 9).

Figure 9
"Big leaf" model for dry deposition of particles over land.

"Big leaf" model for tørdeposition af partikler over land.

An important fraction of the atmospheric particles has a radius in between 0.1 and 1 m m. For these particles the laminar boundary layer resistance r_b is usually is larger than r_a and dominates the overall resistance to transport from the atmosphere to the surface. As a result the dry deposition velocity of particles is relatively low, because they do not cross the laminar boundary layer fast (Ruijgrok et al., 1995). For particles of a particular size the dry deposition velocity increases wind speed (u_*), mainly because the thickness of the laminar boundary layer is reduced. The dry deposition velocity for particles is also highly dependent on the properties of the surface. The knowledge on particle dry deposition is still insufficient.

Primitive model for dry deposition of particles to vegetation

For particles with a radius between 0.1 and 1 m m the estimated dry deposition velocity for neutral atmospheric conditions is (Erisman et. al, 1994):

These equations show that the dry deposition velocity increases with the wind speed.

Dry deposition of particles to the sea

The dry deposition velocity of particles to the sea is generally thought to be   less than the dry deposition velocity of particles to land surfaces, because the sea is relatively smooth. The deposition velocity is also influence by the fact that the particles are mostly hygroscopic, take up water and consequently grow if they come very near the water surface. Figure 10 shows how the dry deposition velocity of particles varies with particle size for various wind speeds (Slinn and Slinn, 1980).

Figure 10

Tørdepositionshastighed for partikler for havområder som funktion af størrelse og ved forskellige vindhastigheder.

Atmospheric lifetime of particles the dry deposition

As a result of the relatively low dry deposition velocity, particles have a relative long atmospheric residence time (~ 5 days). They are only removed well when they meet precipitation on their way. Particles can also coagulate and as a result larger particles are formed that are removed at another speed by dry and wet deposition than the particles they were formed of. Moreover, the pesticides bound in particles can volatilise if the particles are exposed to higher temperatures or to lower concentrations of pesticides in the gas phase.

Field measurements of velocity for pesticides

There almost no field measurements of the dry deposition velocity of gase ous of particulate pesticides. Some estimates have been made of the dry deposition velocity by using measured concentrations in the air and exchange models. For particles it is generally very difficult to measure the dry deposition velocity because it is so low. It has usually to be derived from very small concentration differences and the measurements are for that reason very uncertain. The same holds for the classical non-polar gaseous pesticides. But for the more soluble gases it would perhaps be possible to measure the dry deposition velocity. The dry deposition velocity of gaseous pesticides is not only determined by properties of the compound, the properties of the surface and the meteorological conditions, but also by the concentration in the surface. As a result the dry deposition velocity measured under the same meteorological and surface conditions at one site is not necessarily the same as the dry deposition velocity measured somewhere else, because the concentration in the surface can be different. For that reason it is also necessary to specify the surface concentration when a dry deposition velocity of a gaseous pesticide is reported. Only for highly soluble gases it can presumably be assumed that the concentration in the surface is so low that it has no influence on the flux and it is for that reason not necessary to report it. But most gaseous pesticides are not highly soluble.

Even in the case of highly soluble gases it is not likely that the dry deposition rate is measured continuously, because these measurements are extremely expensive. For such gases the dry deposition rate is usually estimated from a dry deposition velocity measured during a limited number of campaigns for different atmospheric conditions and continuous meteorological measurements.

Change in concentration in air due to dry deposition

If the compound is distributed homogeneously over the whole mixing layer  the change in concentration c(t) due to dry deposition as a function of time t (s) is given by:

where v_d is the dry deposition velocity (m s^-1) and z_mix the mixing height (m). Close a source the compound will not yet be mixed over the whole mixing layer. This means that in the case of a low source the concentration near the surface can be very high and the removal rate close to the source can for that reason be much higher. In that case the change in concentration due to dry deposition will be much greater than that one derived from (22).

1.5 Intermezzo: Main conclusions on meteorology and surface exchange

In this section the information in the previous sections on meteorology and surface exchange is summarised.

Neutral atmosphere

Mechanical turbulence is generated due to friction exerted on the wind by the surface. This friction is caused by the roughness of the surface. A measure of the friction is the friction velocity. The friction velocity depends on the wind speed at greater height and the surface roughness. The friction velocity increases with the surface roughness. Under neutral atmospheric conditions the turbulence is entirely mechanical. In northwestern Europe the atmosphere is most frequently neutral. The friction velocity is a very important parameter. If influences the following:

	Wind speed. The wind speed increases with the friction velocity at one particular height (6). The wind speed itself increases with height.
	Atmospheric diffusion. The atmospheric diffusion increases with the friction velocity (12) and therefore also with the wind speed. The atmospheric diffusion increases with height in the lower part of the atmosphere.
	Surface exchange. The surface exchange increases also with the friction velocity (13,14,16,17) and therefore also with the wind speed. It does not only depend on the friction velocity, but also on processes in the surface, characterised by the surface resistance (see section 1.4). If the surface resistance is low, the exchange is mainly governed by atmospheric turbulence, characterised by the friction velocity. In this case the surface exchange will show a relatively large increase with wind speed. If the surface resistance is high, the surface exchange will be mainly dominated by processes in the surface an will only slow a relatively small increase with wind speed. If the net flux is from the atmosphere to the surface the surface exchange is also called dry deposition. If the net flux is from the surface to the surface the surface exchange is also called emission.
	Mixing height. The mixing height increases with the friction velocity (8).

Non-neutral atmosphere

If the atmosphere is stable or unstable thermal turbulence plays also an important role. The wind speed, atmospheric diffusion, surface exchange and to some extent the mixing height will in this situations also increase with the friction velocity and therefore also with the wind speed. The functions used to describe the increase are, however, somewhat modified. Under these conditions the heat and moisture flux at the surface play also a role. These heat and moisture fluxes also influence the emission of pesticides from the soil (see section 1.6). For this reason it is also important to describe these fluxes in the same fashion in the meteorological part of a pesticide surface exchange model as in the soil part of such a model.

Surface gas exchange: both directions possible

The rate of exchange between the atmosphere and the surface depends on  the friction velocity and on processes that occur in the surface. The direction of the flux depends on the difference of the concentration in the air and the gas phase concentration that would be in equilibrium with the concentration in the surface. If the concentration in the air is higher than the equilibrium gas concentration in the surface, the net flux will be from the atmosphere to the surface. Is the equilibrium concentration in the surface higher than the concentration in the air, net emission from the surface will occur. This is the case on a field after application of pesticides.

Highly soluble volatile pesticides can also be emitted from a field, but when they are transported to areas where no emission has taken place the surface concentration will so low that the surface can be considered as a perfect sink for these gaseous pesticides i.e. the concentration in the surface is rather low and the flux is always from the atmosphere to the surface.

For slightly soluble pesticides the surface is not a perfect sink. The concentration in the surface can be relatively high. Their net deposition flux will be lower for that reason. As a result they have a lower dry deposition velocity than highly soluble gases. Their concentration in the soil can even become so high that no net deposition occurs, but net emission. This means that they can be re-emitted again after deposition. Several cycles of dry deposition and re-emission result in a transport over considerable distances. For these pesticides is it extremely important to describe the processes in the surface in the same way as for emission (section 1.6). For slightly soluble pesticides it is possible to conduct laboratory measurements that give information on uptake by dry deposition.

Dry deposition of  particles

Particles are usually not re-emitted again after they have been dry deposited.   The dry deposition velocity of particles depends on the friction velocity, size and properties of the particles and properties of the surface (presence of "hairs" on plants etc. It is usually much lower than the dry deposition velocity for highly soluble gases. The dry deposition velocity of particles is very different for particles of different size.

Measurements of the dry deposition velocity

It is in principle very difficult to measure the dry deposition rate (= flux) at all, both for gaseous as well as particulate pesticides. The only exception is presumably for highly soluble gases. In that case it is also not likely that it is monitored continuously, but that it is estimated from a limited number of measurements and continuous meteorological measurements.

Potential for long-range transport

The average dry deposition velocity cannot become higher for a certain combination of climate and surface roughness than a certain maximum value. This means for Danish conditions that after 1 hour with dry deposition 13% of the compound is removed from the air in the case of cropland and 25% in the case of forests. This indicates that there exists a general potential for long-range transport for all released compounds in the atmosphere as long as there is no precipitation. In the case of a low source the concentration near the surface can be very high and the removal rate close to the source can for that reason be much higher until the compound is fully mixed over the whole mixing layer. But even in this case there is a certain limit to the removal rate by dry deposition and a substantial part of the released compound will also be transported over long distances (see section 1.12).

1.6 Emission

The purpose of this report is only to describe the atmospheric processes related to pesticides. As we have seen in section 1.4, surface exchange (emission, dry deposition) of pesticides is also influenced by processes in or on the surface (soil, crops), which fall beyond the scope of this report. It was, nevertheless, decided to give some general information here on emission of pesticides after application to the soil and crops that include some processes in the soil and on the crops.

1.6.1 Emission of pesticides from fallow soil

After application of pesticides volatilisation from the soil starts. In the initial phase it is rather important to know the initial penetration depth of the pesticide as this determines the gaseous pesticides concentration in the upper layer of the soil, which drives the volatilisation (16). About this initial penetration depth not much is known. Moreover, if the soil is rather dry, drops with dissolved pesticide can just lay on the surface in stead of being adsorbed in the upper soil layer. Due to the uncertainty in these initial processes, it is difficult to model the emission of pesticides in this initial phase of the emission.

To model the emission of pesticides from fallow soil requires a description of all soil and atmospheric processes involved. In section 1.4 the exchange between the soil and the atmosphere was already discussed. So we will focus here on the description of the processes in the soil that are of importance.

Pesticides are transported in the soil together with the solvent they are dis solved in. Moreover, transport occurs by diffusion in the soil water and in the gas phase in the soil. It should be noted that although the concentration of the pesticide in the gas phase in the soil is small, the transport by diffusion in the gas phase can nevertheless be as important as the diffusive transport in the water phase because the diffusivity of the pesticide in the gas phase is several thousand times larger than that in the water phase. The transport of pesticides in the soil is reduced by the fact that pesticides can be adsorbed onto soil particles. Pesticides compete with water for the adsorption onto soil particles. If more water is present a substantial fraction of non-polar pesticides can desorb from the soil. For that reason it is important to know the soil water content and the water transport that determines this content. The vapour pressure over an aqueous solution of pesticides is highly temperature dependent (see section 1.2.3). Due to the fact that the transport and adsorption of pesticides is influenced by water and by the temperature, volatilisation of pesticides can only be modelled if the water transport (including precipitation and evaporation) and the heat transport in the soil is modelled. When the heat transport is modelled, the temperature of the soil is known, which is not only essential to modelling of the volatilisation of the pesticide, but also to modelling of the evaporation of water from the soil. As a result a model for volatilisation of a pesticide contain a description of the following processes:

1. Transport of the pesticide dissolved in soil water including diffusion in the water phase.
2. Transport of the pesticide in gas phase in the soil by diffusion.
3. Adsorption of the pesticide to the soil particles.
4. Transformation of the pesticide in the soil.
5. Equilibrium between the pesticide in the gas phase and the water phase (Henry’s law coefficient).
6. Transport of water in the soil.
7. Transport of heat in the soil.
8. Transport of pesticide from the soil across the laminar boundary layer into the atmosphere.
9. Transport of water (water vapour, rain) across the laminar boundary layer to/from the atmosphere.

Jury et al. (1983, 1984) were among the first to model the volatilisation of pesticides from the soil. Jury et al. (1984) and Spencer et al. (1988) distinguish between three categories of pesticides with regard to volatilisation from fallow soil: highly volatile pesticides, slightly volatile pesticides and moderately volatile pesticides. To which category a pesticide belongs depends on the Henry’s law coefficient K_H.

Highly volatile pesticides

The volatilisation for this category of pesticides (K_H > 2.65´ 10^-5) is controlled by diffusion in the gas phase in the soil. The volatilisation decreases with time, independent of the evaporation of water vapour. The pesticide is not concentrated at the soil surface.

Slightly volatile pesticides

The volatilisation of this category of pesticides (K_H < 2.65´ 10^-5) is controlled  by the rate at which the pesticide can diffuse through the laminar boundary layer in the atmosphere just above the soil surface. Evaporation of water causes concentration of the pesticide at the soil surface, because the pesticides are less volatile than water. The volatilisation can increase with time if evaporation of water continues. It can be expected that the emission of this category of pesticides depends rather much on the meteorological conditions, because they determine the thickness of the laminar boundary layer.

Moderately volatile pesticides

The volatilisation of this category of pesticides (K_H » 2.65´ 10^-5) is controlled by diffusion in the gas phase in the soil if the soil humidity is low and by diffusion through the laminar boundary layer in the atmosphere just above the soil surface.

Emission of freshly applied pesticides from soil surfaces

Woodrow et al. (1997) were interested in the worst case fluxes of pesticides, that often occur within a few hours after application. They were especially interested in these high values because they can be used to estimate the maximum concentrations and effects. They used published studies to derive a relation between the flux and physical and chemical properties of the compounds. They used compounds with vapour pressures that differed up to 10⁷. They found the following relation (Figure 11):

It should be noted here, that VP, S_w and Henry’s law coefficient K_H are related (see section 1.2.3)

Figure 11
Correlation of pesticide flux from soil with chemical properties. Reprinted with permission from Woodrow et al., (1997). Copyright 1997 American Chemical Society.

Korrelation af pesticidfluxen fra jord med kemiske egenskaber.

For most experiments data were available on the application rate of the compound. So they tried to correlate the measured flux for those experiments with the properties of the compounds, but now also taking the application rate into account because it is logical to expect that the flux increases with the application rate. They found the following relation:

where AR is the application rate (kg ha^-1)

It should be noted here that the uncertainty in the flux is still considerable (presumably a factor 2-3). They did not take any possible relationship with meteorological conditions (temperature, wind speed) into account as they would expect that these conditions were similar for the different studies used. This does not mean that meteorological conditions do not play an important role, it illustrates just that the flux is highly correlated e.g. the vapour pressure, because the compounds have such an extreme wide range of vapour pressures. Nevertheless, this approach can be useful to get a first estimate of a possible maximum flux.

Cumulative emission of pesticides from the soil

Smit et al. (1997) were interested in the cumulative emission from the soil after most of the pesticide had been volatilised and not in the worst case situation as Woodrow et al. (1997). They used also published experimental results to correlate the emission with physical and chemical properties. They found the following relations:

where:

CV = cumulative volatilisation (% of dosage active ingredient).
FP_gas = faction of the pesticide in the gas phase in the soil.

FP_gas can be found from the concentration of pesticide in the soil, the volume fraction of gas in the soil, the volume fraction of moisture in the soil and the dry bulk density of the soil (see Smit et al., 1997 for further details).

1.6.2 Emission of pesticides from plants

This is a more complicated case. One reason is that the pesticide is not only deposited onto the plants, but also onto the underlying soil. Other reasons are that different plants have different surfaces (wax layer, hairs, structure), that there are leaves on various heights of the plants and that they actively can take up the pesticide. Moreover, pesticides can be washed off by rain. As a result there are no real mechanistic models to calculate the emission of pesticides from plants as do exist for emission from soils.

Emission of freshly applied pesticides from plants

Woodrow et al. (1997) studied also the maximum volatilisation of pesticides from inert surfaces (glass, plastic) and from plant surfaces. It appeared that  the flux from plant surfaces during this initial phase of volatilisation correlated in the same fashion with the vapour pressure as the fluxes from the inert surfaces. It was therefore concluded that plants were non-interactive, at least during the initial phase of volatilisation. This meant that they also could use the experimental data of volatilisation from inert surfaces to estimate volatilisation from plants, so that a greater data set could be used in the correlation studies. Figure 12 shows the correlation found:

It should be noted here, just as in the case of volatilisation from the soil, that they find such a good correlation because they use compounds with a very wide range of vapour pressure. It does not mean that meteorological conditions do not play a role, but that the variation in the flux due to variations in meteorological conditions is much less than the variation in the flux due to variations in the vapour pressures.

Figure 12
Correlation of pesticide flux from inert surfaces (plants, glass, plastic) with vapour pressure. Reprinted with permission from Woodrow et al., (1997). Copyright 1997 American Chemical Society.

Cumulative emission of pesticides from plants

Smit et al. (1998) studied the cumulative volatilisation of pesticides at 7 days after application. They found the following relation:

In this equation is VP the vapour pressure in mPa.

They also found that the volatilisation was only to a minor extent influence by sorption processes in and on the leaves that are commonly represented by the K_ow. The volatilisation was also not very well correlated with the K_H, which indicates that the water in the pesticides drops evaporates relatively quickly and that the pure compound is left on the plant surfaces.

1.6.3 Improvement in the modelling of the emission of pesticides

Although it could be satisfactory for many purposes to estimate the initial volatilisation rate or the cumulative volatilisation by the statistical relations found by Woodrow et al. (1997), Smit et al. (1997) and Smit et al. (1998), mechanistic models are needed to better understand the underlying processes related to volatilisation. Only in this way it would be possible to get models to study the effects of a strategies to reduce the evaporation of pesticides, to study the influence of meteorological conditions on the volatilisation and to generalise the results. Measurements are needed for compounds with a wide range of properties to test these mechanistic models, because the number of experiments currently available is limited.

1.7 Removal of material by precipitation

Airborne material can be removed from the atmosphere by precipitation processes. This is called "precipitation scavenging". It is an overall term, which covers the result of many different processes. Some of these processes will be discussed here.

1.7.1 Cloud physical processes

Cloud formation

The atmosphere contains aerosol particles, each of which consists of a variety of compounds, that can vary with particle size. Most aerosol particles contain hygroscopic substances. When the relative humidity is more than 40%, aerosols contain at least 30% water by weight. When the relative humidity increases, more water vapour condenses onto the aerosols and cloud droplets are formed. In this way aerosols act as "condensation nuclei" and as a result the compounds originating from the aerosols can be found in the cloud droplets. Cloud droplets are so small that they have small fall velocities compared to the vertical wind speed in the cloud. As a result many of them remain airborne. If they come outside a cloud, where the relative humidity is less than 100% they will evaporate in a few seconds. Cloud droplets can also take up gases. Table 2 gives some characteristic properties associated with different cloud types (Cotton and Anthes, 1989). It should be noted that the values can vary much within a cloud type and that there are not only droplet of one size in a cloud, but droplets of a whole range of sizes.

Table 2
Some characteristic properties of different cloud types.

Nogle karakteristiske egenskaber for forskellige skytyper.

Clouds as reactors

Most clouds will never give any precipitation. Their droplets will evaporate and the compounds present in the drops will remain as aerosols and gases. It is estimated that this cycle is repeated on the average about ten times before the content of the drops reaches the earth’s surface in the form of precipitation. Compounds present in the cloud droplets can react with each other. In that sense are clouds chemical reactors.

Precipitation formation

Cloud droplets are very small, they have radii of 1-100 m m. Raindrops have a radii of 100-2500 m m. This means that about a million cloud droplets need to find each other to form one raindrop. Precipitation can already be formed relatively shortly (0.3-1 hours) after the first cloud has been formed. So there must be a very effective process leading to precipitation formation.

Warm clouds

Cloud droplets of different sizes, have different inertia and may collide due to turbulence in the cloud to form a larger droplet. In the tropics this process can lead to precipitation, because the number of droplets is larger in these areas is larger than in the midlatitudes. This process is, however, not so effective that it can explain formation of precipitation in the midlatitudes. It can maybe lead to some drizzle, but not to significant amounts of precipitation.

Cold clouds

Most clouds that give precipitation in the midlatitudes extend to heights where the temperature is below 0° C. At these heights water is "undercooled", i.e. it is still liquid and not frozen. This occurs at temperatures > - 15 ° C. It is apparently difficult to start formation of ice crystals in the very clean water in the clouds. Some types of aerosols consisting of unsoluble material (soil particles or particles that originate from plants) can act as "ice nucleii", i.e. that the formation of ice crystals starts on this material. This because they contain molecules or crystals with a similar structure as ice crystals. At the same temperature the water vapour pressure over ice is lower than the water vapour pressure over liquid water. As a result the water from the undercooled cloud droplets will evaporate and be deposited on the ice crystals. In this way ice crystals will become so large that they fall fast enough to pick up other crystals and/or undercooled cloud droplets which will then freeze. In this way snowflakes are formed which are transformed into raindrops if they during their fall pass through a part of the atmosphere with a temperature above 0° C. This chain of processes is much more effective than collision of cloud droplets and can explain the formation of precipitation within a relative short time. As a result almost all rain in the midlatitudes has once been snow.

In-cloud scavenging

The precipitation formation process leads to the removal of the compounds dissolved in the cloud water. This is the way compounds associated with condensation nucleii and gases dissolved in cloud and raindrops are removed from the part of the atmosphere where clouds are. Removal from this part of the atmosphere is called in-cloud scavenging.

Uptake by snowflakes and sleet

Not much is known about removal by snowflakes and sleet under the cloud. Snowflakes and sleet can maybe take up aerosols more efficiently than raindrops because they have a large surface area combined with a relatively low fall velocity. Sleet consists of melting snowflakes which are covered by a layer of water and can take up gasses more efficiently than raindrops for the same reasons why it is a more efficient scavenger of aerosols. About 10% of the precipitation in Denmark arrives in the form of snow and sleet at the earth’s surface, but a somewhat larger fraction of the precipitation has been scavenging the below-cloud part of the atmosphere partly in the form of snowflakes and sleet. Due to its relative unimportance and the fact that not much is known, uptake of airborne material by snowflakes and sleet is not treated in this report.

Precipitation in Denmark

The average annual amount of precipitation in Denmark is about 700 mm and varies from about 550 to 900 mm. The variation from year to year can be high.

Fall velocity of cloud and raindrops

When a drop starts to fall it will take a few seconds to accelerate to their terminal velocity. At this velocity the friction forces exerted by the surrounding are equals the gravitation forces (Pruppacher and Klett, 1997). Figure 13 shows the terminal velocity of water drops as a function of their size. (Rain)drops with a radius greater than about 3500 m m (3.5 mm) are unstable and break up into smaller droplets. Figure 13 shows that the terminal velocity is about 0.01 m s^-1 for cloud droplets, about 1 m s^-1 for the smallest raindrops and about 9 m s^-1 for the largest ones. The terminal velocity influences the residence time of raindrops under the cloud. It influences the rate at which water evaporates from drops or the rate at which gases can be taken up. The smallest raindrops will evaporate before they reach the ground and will not give a contribution to precipitation. The larger ones fall so fast that they will only be able take up a very small amount of gas before they reach the ground. Droplets of different sizes can unite during their fall, because they have different terminal velocities. In the discussions in this report we will not take this process into account because we will illustrate the principles of the uptake of gases and particles by drops, rather than to give a complete description.

Figure 13
Terminal velocity of raindrops as a function of their radius.

Size distribution of raindrops

There is a relation between the rainfall rate and the size distribution of   raindrops. At higher rainfall rates the average radius of the drops is larger, as everybody knows by experience. Figure 14 shows number of raindrops as a function of their size for two common rainfall rates using an equation given by Marshall and Palmer (1948). Figure 15 shows the distribution of the liquid water content of air belonging to these size distributions. Both Figure 14 and Figure 15 are given for an arbitrary raindrop radius interval. This radius interval is not important here. What is important to note is the relative difference between Figure 14 and 15. This difference reflects the fact that the smallest drops are most abundant, but that their contribution to the liquid water content of the cloud is not large. The liquid water content of the cloud a maximum about a drop radius of 0.5-1 mm. Such raindrop distributions as show in Figure 14 are more representative for an average situation. The size distributions during events may deviate from the equation given by Marshall and Palmer. Moreover, different authors use different types of equations, which give somewhat different results. Most distributions of the raindrop size have been measured to relate the radar reflection of precipitation drops to measured size distributions at ground level. They give a good description of the larger raindrops, which are reflect the radar waves most and contribute most to the amount of precipitation, but the description of the smaller drops in the distribution, that are more important for the uptake of gases, is somewhat more uncertain. The resulting uncertainty in the removal rate of gases by raindrops will be discussed later. It should be noted that the liquid water volume of raindrops/snowflakes in cloud is much less than the liquid water volume of cloud water.

Figure 14
Number of raindrops per volume of air as a function of their radius for a drop radius interval of 1.25´ 10^-5 m.

Antallet af regndråber per luftvolumen som funktion af deres radius med et dråberadiusinterval på 1,25´ 10^-5 m.

Figure 15
Liquid water volume of raindrops per volume of air as a function of their radius for a drop radius interval of 1.25´ 10^-5 m.

Cloud base height

During unstable conditions (convection) an air parcel which is unsaturated with water vapour can from near the earth’s surface will be transported upward and will be cooled down with -0.01° C m^-1. As the saturation pressure (Pa) over liquid water decreases with temperature, the air parcel will become more and more saturated with height due to cooling and if the saturation pressure is reached, a substantial condensation of water vapour on aerosols will occur and a cloud is formed. The cloud base is in this case at the height, where the first cloud droplets form. During these unstable conditions, there is a relation between the relative humidity and the temperature at the ground and the cloud base height. During neutral and stable conditions there is no such relation. The layer with the clouds may have a totally different origin than the air at ground level. This is especially the case near warm and cold fronts, where warm and cold air meet. It is important to know the cloud base height, because airborne material is removed by precipitation by different processes in and below the cloud and what is even more important material is removed at different rates.

Estimated cloud base height

The cloud base height is either measured (usual at large airports) or estimated   by meteorological observers. Figure 16 shows the frequency distribution of the cloud base height during precipitation in Denmark for 5 stations (Asman and Jensen, 1993). The cloud base height is given as a code, which refers to height intervals (Table 3). It should be noted here that the height intervals are not the same for all codes. On the basis of the frequency distribution an average cloud base height was calculated for each of the five stations (Table 4). The uncertainty in these values is rather large due to the procedure and because the estimated cloud base height depends also to some extent on the observer.

Figure 16
Frequency distribution of the cloud base height during precipitation for 1979-1988. Data from the Danish Meteorological Institute (DMI).
Station code: Kas = Kastrup, Kar = Karup, Skr = Skrydstrup, Bel = Beldringe, Aal = Aalborg. The cloud base height classes are explained in Table 3.

Table 3
Explanation of the cloud base height code and the height interval used in Figure 16.

Forklaring af koden for skybasehøjde og højdeinterval anvendt i Figur 16.

Table 4
Average cloud base height during precipitation for five Danish meteorological stations.

Gennemsnitlige skybasehøjde under nedbørsperioder for fem danske meteorologiske stationer.

1.7.2 Exchange of gases between drops and the air

The uptake of gases by cloud and rain drops can be described by a sequence of steps that must be taken (Seinfeld, 1986):

1. Diffusion of the gas from some distance of the drop to the drop surface.
2. Transfer of gas across the gas-water interface.
3. Extremely fast reactions in the water phase near the surface of the drop. This reaction should be so fast, that it is completed before the diffusing gas has been mixed throughout the whole drop. This is usually only the case for ionisation reactions. If this occurs, not the dissolved gas will diffuse into the water phase, but the reaction products
4. Diffusion of the dissolved gas or extremely rapidly formed reaction products in the water phase throughout the drop.
5. Other, not extremely fast reactions in the water phase.

In this report we will only focus on uptake of gases where no reaction occurs, as this seems to be more relevant for pesticides.

After less than 0.1 seconds a steady state situation is achieved for cloud and raindrops that are exposed to a gas. The steady state situation is defined as the situation where the flux in the gas phase from some distance to the drop equals the flux through the gas-water interface, which equals the flux into the water phase. The overall rate at which a gas can be taken up depends on the resistance to transport in the gas phase, across the interface and in the water phase. Although it cannot be excluded that in some cases the resistance in the water phase is considerable, this seems not to be the case in general. One of the reasons is that drops with a radius > 100 m m develop during their fall an internal circulation leading to mixing within the drops and as a result the resistance in the water phase is small compared to the resistance in the water phase.

Flux in the gas phase

The transport of the gas in the gas phase and transfer across the gas-water interface is given by (Pruppacher and Klett, 1997):

The ventilation coefficient is approximately given by:

where Re is the Reynolds number: Re =2rv_t/n (dimensionless), where r = radius of the drop (m), v_t = terminal velocity of the drop (m s^-1) , n = kinematic viscosity of the air (m² s^-1) and Sc is the Schmidt number (dimensionless). The Schmidt number is n /D_g, where D_g is the diffusivity of the gas in the gas phase (m² s^-1).

The ventilation coefficient f_g is 1 for small, almost not moving cloud droplets to up to about 20-30 for the largest falling raindrop and gases with molecular weights varying from 200-400. It depends mainly the radius of the drop (which also determines the terminal velocity) and the diffusivity of the gas.

F_g is the flux, i.e. kg of the gas that passes through 1 m² of drop surface per second. It is more useful to have a change in concentration per second in the drop in stead. This can be done by multiplying the flux with the surface of the drop (4p r²) and dividing by the volume of the drop ((4/3)p r³):

It is interesting to note that c_wH is just equal to the gas phase concentration that would be in equilibrium with the concentration in the bulk water phase in the drop. This equation is, in fact, much alike the equation for the dry deposition flux (16), which also depends on a concentration difference.

If we integrate (31) and assume that c_w = 0 at t = 0, the following equation is obtained:

The characteristic time constant of absorption is t _abs = 1/k₁. If t = t _abs about 63% of the gas that can potentially be absorbed has been absorbed. The value of t _abs for drops of different size can be calculated from Table A2-1 in Appendix 2.

For raindrops, which have a noticeable terminal velocity it is more convenient to express the concentration in the drop as a function of the fall distance. Realising that the fall distance (m) is z_f = v_t*t the following is found from (32):

If we integrate (35) and assume that c_w = 0 at z_f = 0, the following equation is obtained:

The characteristic distance of absorption is D _abs = 1/k₂. If the drop has fallen a distance z_f = D _abs about 63% of the gas that can potentially be absorbed has been absorbed. The value of D _abs for drops of different size can be calculated from Table A2-1 in Appendix 2.

It can be seen from (36) that the concentration approaches the equilibrium concentration c_g/H (saturation) if t is relatively large. It can also be seen from k₁ and k₂ that if H is larger (the gas is more volatile, i.e. less soluble) it takes less time/fall distance to get saturation of the drop. The ventilation coefficient f_g in (33) increases with r, but much less than with r², so k₁ decreases with the drop radius. This means, that it takes more time for larger drops to get saturated. The value of k₂ decreases even faster with the drop radius, because here v_t is in the denominator and v_t increases with the drop radius (see Figure 13).

1.7.3 Scavenging of gases

General situation

Figure 17 illustrates the differences between uptake of highly and slightly soluble gases in clouds (in-cloud scavenging) and below-clouds (below-cloud scavenging). In each "comic" three situations are shown:

1. The situation before formation of the cloud.
2. Effect of in-cloud scavenging.
3. Effect of below-cloud scavenging.

Figure 17
Differences in in-cloud and below-cloud scavenging of highly (upper figures) and slightly soluble gases (lower figures).

Forskelle mellem in-cloud scavenging og below-cloud scavenging af letopløselige (øverste figurer) og tungtopløselige gasser (nederste figurer).

1. Before the formation of the cloud

Before the formation of the cloud the concentrations in the air are the same   everywhere for both gases in this example (situation 1).

2. Uptake of gases in the cloud water after cloud formation

After formation of the cloud (situation 2) equilibrium is reached between   concentrations in the gas and water phase in the cloud droplets. This holds for both the highly and the slightly soluble gas. Most of the highly soluble gas can be found in the droplets (one droplet is shown) and the concentration in the air within the cloud is very low, i.e. much lower than the concentration in the air outside the cloud. It will take somewhat more time to reach equilibrium for highly soluble gases than for slightly soluble gases, because a larger amount of gas has to be transported into the droplets. But even then it will take less than a minute before these small cloud droplets have reached equilibrium. Their lifetime is much more than a minute (see Table A2-1 in Appendix 2), so equilibrium is reached rather fast compared to their lifetime. The situation for the slightly soluble gas is somewhat different. The concentration in the cloud droplets is rather low and as a result the concentration in the air within the cloud has not changed much due to the uptake of the gas and is almost equal to the concentration of the gas in the air outside the cloud.

3. Uptake of gases below the cloud

After some time precipitation is formed and the raindrops that contain about  the same concentration as the cloud droplets, they will start to fall and take up gas on their way (situation 3). In the case of a highly soluble gas the drops are not saturated at all compared to the surrounding air and they will take up a additional gas. Due to the relatively short time drops are under the cloud base (1-6 minutes for a cloud base of 400 m; see Table A2-1 in Appendix 2) the drops do not get saturated as there is a physical limit as to how much gas can be taken up in this relatively short time. Drops may get more and more saturated after they have been collected in a precipitation sampler if they still are in contact with the surrounding air. The situation for slightly soluble gases is quite different. The raindrops are almost saturated when they leave the cloud and if the concentration in the air under the cloud is not much different from the concentration in the air in the cloud, they will almost be saturated when they reach the surface. So for those drops it is reasonable to adopt equilibrium. For both highly and slightly soluble gases holds that if the concentration in the air is the same at ground-level and higher up in the atmosphere where clouds are formed, the contribution from in-cloud scavenging is larger than the contribution from below-cloud scavenging. Near relatively strong sources, the concentration in the air below the cloud can become much higher than the background concentration in the atmosphere. Only in this situation the contribution from below-cloud scavenging can become larger than that from in-cloud scavenging.

The over-all effect of in- and below-cloud scavenging can be described empirically by a an overall scavenging ratio:

c_pr = concentration of the compound in precipitation (kg m^-3)

c_g = concentration of the compound in the air (kg m^-3)

The philosophy behind this empirical approach is that it is logical to adopt a linear relation between the concentration in precipitation and the concentration in air. S_overall is usually found from measured concentrations in precipitation and air at ground-level. As can be see from Figure 17 this is a reasonable assumption for slightly soluble gases if the concentration in air at ground-level is about the same as in air at cloud height. In that case equilibrium can be assumed to exist between the gas and the rain and S_overall can be found from the Henry’s law coefficient:

For highly soluble gases this approach is more tricky. Usually there is no equilibrium between the concentration in the air and precipitation at ground-level, or between the concentration in the air outside the cloud at cloud height and the concentration in precipitation. For highly soluble gases the S_overall is often set to about 1´ 10⁶, an upper limit, which depends more on the removal rate of precipitation itself than on the Henry’s law coefficient of the gas. Sometimes S_overall is also made slightly dependent on the rainfall rate. The rate at which a compound is removed from the atmosphere by scavenging is called scavenging coefficient and is defined by:

L _overall = scavenging coefficient (s^-1)
I = rainfall rate (m s^-1)
z_mix = mixing height (m)

For highly soluble gases and adopting a mixing height of 1000 m this gives removal rates of 2.8´ 10^-4 s^-1 at 1 mm hr^-1 to 2.8´ 10^-3 s^-1 at 10 mm hr^-1. This means that at a precipitation rate of 1 mm hr^-1 64% of the gas is removed from the air after 1 hour with precipitation. At a precipitation rate of 10 mm hr^-1 more than 99.9% is removed from the air. (This can be calculated with (43)).

Scavenging close to important sources

The situation close to important low-level sources is different form the general situation in that the plume coming from the field on which the pesticide has been applied usually reaches the cloud base height at a distance between 2-10 km from the source. In that case all scavenging is below-cloud scavenging which is not so effective for highly and slightly soluble gases as in-cloud scavenging. Usually no equilibrium will be reached, neither for the highly nor for the slightly soluble gas. There is a limitation to the uptake of a gas: no more gas can be taken up than is transported to the raindrop. This sets an upper limit to the below-cloud scavenging which is reached for highly soluble gases. For slightly soluble gases the below-cloud scavenging is less than this value. The upper limit for convective conditions is given by (Asman, 1995):

In this equation a and b depend on the relative humidity and temperature at ground level and the diffusivity of the gas at 25° C (see Appendix 3). In this case I is the rainfall rate in mm hr^-1. If the diffusivity of the gas is not known it can be estimated from (15). For non-convective conditions one could e.g. calculate a scavenging coefficient by assuming a temperature of 10° C and a relative humidity of 85%. Figure 18 shows this maximum below-cloud scavenging coefficient of a gaseous pesticide with a molecular weight of 300 as a function of the rainfall rate. Due to the uncertainty in the drop size distribution the uncertainty in the scavenging coefficient is at least a factor of two. For highly soluble gases this gives removal rates of 3.8´ 10^-5 s^-1 at 1 mm hr^-1 to 1.6´ 10^-4 s^-1 at 10 mm hr^-1. After one hour with precipitation 13 and 44% will be removed at a precipitation rate of 1 and 10 mm hr^-1 respectively. (see (43)). These rates that are about a factor of 10 lower than for in-cloud scavenging. The fact that the drops that reach the ground are not in equilibrium with the concentration in the air for highly soluble gases can lead to artefacts during sampling of precipitation, because the collected drops on the funnel or in the bottle will still be able to take up gas after the precipitation has stopped.

Figure 18
Below-cloud scavenging coefficient for a highly soluble gas with molecular weight of 300 as a function of the rainfall rate at ground level. At ground-level the temperature is 10° C and the relative humidity is 85%.

Below-cloud scavengingkoefficienten for letopløselig gas med en molekylemasse på 300 som funktion af regnintensiteten i jordniveau. Temperaturen og relativ fugtigheden i jordniveau er henholdsvis 10° C og 85%.

1.7.4 Scavenging of particles

Particles containing pesticides will usually be removed rather efficiently by in-cloud scavenging. Below-cloud scavenging of particles is less efficient and depends on the size distributions of the raindrops and the particles (Slinn, 1983). A scavenging ratio of 1´ 10⁶ can be adopted for an overall-scavenging of particles because scavenging is in general dominated by in-cloud scavenging. Close to sources only below-cloud scavenging is important, the scavenging ratio will often be considerably less and has to be calculated with the appropriate size distributions of raindrops and particles. Rain contains also particles that are only partly dissolved. Pesticides with a low solubility may therefore not only exist in rain as a dissolved gas but also as be part of particles.

Change in concentration in the air due to wet deposition

The concentration left in the air after a precipitation period with length t (s) can be found from:

where L can be the in-cloud scavenging coefficient, below-cloud scavenging coefficient or the overall scavenging coefficient.

Measurements of the wet deposition rate

The wet deposition of pesticides can be measured. It is in principle also   possible to derive an overall scavenging coefficient for pesticides from measured concentrations in air and precipitation using (39) and (41). In this case the measured air concentration should be representative for the whole air column, i.e. it should not be measured close to sources.

1.8 Intermezzo: Main conclusions on wet deposition and a comparison with dry deposition

In-cloud scavenging properties of the compound

Highly soluble and reactive gases are removed by in-cloud scavenging at a and high rate. Almost all gas will be dissolved in the cloud droplet and the concentration in the interstitial air in the cloud will be low. For that reason the scavenging rate does not depend on the Henry’s law coefficient, but on the rainfall rate, as almost all gas is dissolved in the cloud drops.

For slightly soluble gases the situation is different: a substantial fraction of the compound is found in the interstitial air in the cloud. The removal rate for these gases will be a function of the Henry’s law coefficient and the precipitation rate.

Most particles act as condensation nucleii and will for that reason be removed at a high rate that is determined by the precipitation rate. The removal rate will not depends much on the size of the particles as long as they are hygroscopic.

Below-cloud scavenging and properties the compound

Highly soluble and reactive gases are removed by below-cloud scavenging of at a higher rate than slightly soluble gases, but the removal rate by below cloud scavenging is less than by in-cloud scavenging (see below). The removal rate for highly soluble gases does in general not depend on the Henry’s law coefficient but on the speed at which the gas can diffuse into the drop, which is e.g. a function of the diffusivity of the gas and the raindrop size, which in turn is a function of the precipitation rate. For slightly soluble gases the raindrop is almost saturated with the gas by in-cloud scavenging when the drop reached the air below the cloud. If the air below the cloud has the same concentration no more gas will be taken up. If the air below the cloud has a higher concentration more gas can be taken up. If the air below the cloud has a lower concentration that in the cloud the drops will degas, i.e. dissolved gas will evaporate into the atmosphere.

Particles will in general also be removed by below-cloud scavenging at a lower rate than by in-cloud scavenging. Their removal rate will be a function of their size and the size of the raindrops which is a function of the precipitation rate.

In-cloud scavenging vs. below-cloud scavenging

In case of in-cloud scavenging at a precipitation rate of 1 mm hr^-1 64% of a   highly soluble gas is removed after 1 hour with precipitation. At a precipitation rate of 10 mm hr^-1 more than 99.9% is removed from the air after 1 hour.

For highly soluble gases the removal rate by below-cloud scavenging is highest. This gives removal rates of 3.8´ 10^-5 s^-1 at 1 mm hr^-1 to 1.6´ 10^-4 s^-1 at 10 mm hr^-1. After one hour with precipitation 13% and 33% are removed from the air at a precipitation rate of 1 and 10 mm hr^-1 respectively. In case only below-cloud scavenging is occurring, e.g. close to a low level source, still a considerable fraction of the highly soluble gas remains airborne. The removal rate for slightly soluble gases will be less than for highly soluble gases.

The wet removal rate for particles will also be dominated by in-cloud scavenging and will be the same as for highly soluble gases, at least if the concentration at cloud level is about the same as below the cloud.

Origin of pesticide in precipitation close to an important source

Close to low sources, like fields after application of pesticides, the plume has not yet reached the cloud and for that reason only below-cloud scavenging occurs. As a result the wet deposition near a low source will only be a relatively small fraction of the amount of pesticide volatilised, even in the case of a highly soluble pesticide. It should be noted that in general a background concentration of pesticides will be present in the atmosphere. This background concentration will also exist at cloud level. As in-cloud scavenging is much more efficient than below-cloud scavenging, a larger fraction of the background will be scavenged near the low source than of the released compound from the low source. Only in the case where the low source emits at a relatively high rate or the precipitation period last for a long time, the concentration in precipitation can be dominated by a nearby low source.

Non-soluble particles

Rain contains also particles that are only partly dissolved. Pesticides with a low solubility may therefore not only exist in rain as a dissolved gas but also as be part of particles.

Wet deposition vs. deposition

The dry deposition velocity of gases increases in general with the solubility dry of the gas. The same is the case for removal rates of gases by in-cloud and below-cloud scavenging. For particles the situation is different. Particles with a radius between 0.1 and 1 µm are not removed well from the atmosphere by dry deposition, but are removed well by in-cloud scavenging because they can act as condensation nucleii. As it does not rain that often, their atmospheric lifetime is rather long, of the order of 5 days or longer.

The maximum removal rate by dry deposition is much lower than the maximum removal rate by wet deposition. After 1 hour under Danish conditions only 13% of the a highly soluble gas is removed in the case of cropland and 25% in the case of forests.

The maximum removal rate by precipitation is determined by in-cloud scavenging, if the concentration of the compound in the air at cloud level and below the cloud are the same. It is then 64% hr^-1 at a precipitation rate of 1 mm hr^-1 or more than 99.9% hr^-1 at a precipitation rate of 10 mm hr^-1.

So it looks as if wet deposition will be the dominating removal process. This is, however, not necessarily true. The reason for this is that dry deposition occurs all the time, even during precipitation, whereas wet deposition only occurs during precipitation, i.e. during 5-10% of the time. Consequently the average amount dry deposited over a longer period can be of the same order of magnitude as the amount wet deposited, despite the fact that the process is less efficient than dry deposition.

It is very difficult to measure the dry deposition rate and even in the case it can be measured like for highly soluble gases, it is not likely that it will be done continuously. On the contrary it is possible to measure the wet deposition rate.

1.9 Conversion from the gaseous to the particulate phase

As we have seen in section 1.4, dry deposition of particles proceeds at another speed than dry deposition of gases. Pesticides released as gases can be converted to particles and as a result the pesticide will be removed from the atmosphere at another rate than if it were in the gas phase. This process can potentially be important for slightly soluble gases that are not well removed by dry deposition or precipitation scavenging.

It is therefore crucial to know if a pesticide exists in the gas phase or in the particulate phase. Moreover, it is necessary to know at which rate a gaseous pesticide can be converted to its particulate form, so that we e.g. whether the gaseous pesticide is already converted to the particle phase to a substantial extent during the transport over the first 2 km discussed in this report

Ratio particle-gas for pesticides

If gaseous pesticides are transformed to particles, they do not form pure   pesticide particles. For thermodynamical reasons it is favourable for gases to condense on existing particles. Junge (1977) found the following relation for the ratio R_pg of the concentration of a compound in the particulate phase over the total concentration of the compound in the particulate and gaseous phase:

The typical average background value for j is 1.5´ 10^-4 m² m^-3 (Whitby, 1978). This means that if P⁰_L > 2´ 10^-4 Pa, over 90% of the compound is in the gaseous phase, whilst at P⁰_L < 2´ 10^-6 Pa, over 90% of the compound is in the particulate phase (van Pul et al., 1998).

1.10 Photochemical reaction

Gaseous pesticides can be transformed in the atmosphere by photolysis (degradation under influence of sunlight) or by reaction with the following photochemically formed reactive compounds: OH-radical, NO₃-radical and O₃. The rate at which a gaseous pesticide is transformed by the reactive compounds depends on the concentrations of these reactive compounds and the reaction rate of the pesticides with these compounds. The reaction rate of pesticides depends on their chemical structure and will be different for different pesticides. For many pesticides the reaction rates will not be known, but sometimes they can be estimated using some empirical relationships between the structure of the pesticide and its reactivity (Atkinson, 1987, 1988; Winer and Atkinson, 1990). It should be noted here that if a pesticide reacts, reaction products are formed. These reaction products can also be toxic and are in some cases even more toxic than the pesticides themselves. One should in fact also investigate the fate of these reaction products in the atmosphere. This can be rather complicated because usually more than one reaction product is formed. The reaction products can be removed from the atmosphere at different rates than their precursors, because they have different properties.

1.11 Spray drift and other forms of deposition

Different forms of deposition

Pesticide application can lead to different forms for deposition:

1. Deposition of the larger sprayed drops due to sedimentation caused by gravitation. This form of deposition is mainly influenced by the physical properties of the drops (e.g. inertia, which is a function of the size of the droplets) and not by the chemical properties of the pesticide. Moreover, it is influenced by other factors like wind speed, boom height and other meteorological factors.
2. Deposition of sprayed droplets that are so tiny that their movement is not influenced by gravitation, but only by atmospheric turbulence. This is a form of dry deposition. The deposition mechanism is different than for the larger drops previously mentioned, that deposit due to sedimentation. However, in both cases the physical properties of the drops and not the chemical properties of the drops determine the deposition flux to a substantial extent. This form of deposition can be more important than the deposition of sprayed drops due to sedimentation (Peter Kryger Jensen, Danish Institute of Agricultural Sciences, Flakkebjerg, Slagelse, personal communication). For more information on this process see under dry deposition.
3. During spraying, part of the pesticide can evaporate from the droplets before they reach the ground. How much evaporates will depend on the size of the droplets (physical factor), the Henry’s law coefficient of the pesticide, properties of the solvent and other related chemical properties. Moreover, it will be influence by meteorological factors like temperature, wind speed and by the height of the boom sprayer over the surface and the type of surface. The evaporated pesticide can later reach the surface in the form of dry and wet deposition.
4. After the spray drops have hit the surface, pesticide can evaporate, and the gaseous pesticide can then later be deposited in the form of dry or wet deposition.
5. Dry deposition. This is deposition of pesticides in gaseous form, or after conversion to particles in particulate form to the surface under influence of atmospheric turbulence. For gases the chemical properties, the meteorological conditions, the concentration in and properties of the surface they deposit onto that determine the deposition flux. For particles (solid or liquid, i.e. also including tiny spray droplets) physical properties, properties of the surface where they deposit on and meteorological processes determine the dry deposition flux.
6. Wet deposition. This is deposition of pesticides that are removed from the atmosphere in gaseous or particulate form by precipitation. For pesticides in gaseous form the chemical properties (Henry’s law coefficient) can have a large influence on the wet deposition flux. For pesticides in particulate form the physical properties (which is a function of the size of the particles) has a large influence on the wet deposition flux.

Deposition of sprayed drops due to sedimentation occurs only on the field where the pesticide is applied or up to about 20 m outside this area. All other forms of deposition occur also at longer distances from the field (0 to greater than 500 km). Pesticides are either deposited on the field where they are applied or outside the field. The physical and chemical processes are the same whether they are deposited on the field or not, but for other reasons (agricultural, environmental, political) differentiation between deposition on the field and outside the field is required.

Different definitions of spray drift

There exist apparently different (implicit) definitions of spray drift. One definition of spray drift is that all pesticide deposited outside the target area is spray drift. This is not a very useful definition because it includes the results of many different processes operating on various scales. In the following only spray drift due to sedimentation will be discussed, but it should be kept in mind that this is not the only form of deposition of drops.

Spray drift due to sedimentation: boom sprayers

In this report we will only compare the dry and wet deposition of pesticides  as a function of distance to the field onto which pesticides are applied with the  spray drift due to sedimentation. Table 5 gives an impression of the deposition caused by spray drift due to sedimentation onto crops caused by conventional boom sprayers (Ganzelmeier, 1995). This results were based on experiments where the fluorescence on crops was measured of a dye that was added to the sprayed drops.

Table 5
Deposition caused by spray drift due to sedimentation as a function of distance to the downward wind edge of a field onto which pesticides are applied (Ganzelmeier, 1995).

Deposition forårsaget af afdrift på grund af sedimentation som funktion af afstanden til kanten af en mark nedstrøms, hvor pesticider er sprøjtet (Ganzelmeier, 1995).