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SPECIAL SUBMISSIONS
Minimizing the Impact of Pesticides on the Riverine Environment in Australia

Endosulfan Transport

II. Modeling Airborne Dispersal and Deposition by Spray and Vapor

^a CSIRO Land and Water, Canberra, GPO Box 1666, Canberra, ACT 2601, Australia
^b Australian Water Technologies, Sydney, NSW, Australia
^c NSW Agriculture, Locked Bag 21, Orange, NSW 2800, Australia

Corresponding author (mike.raupach{at}cbr.clw.csiro.au)

Received for publication October 8, 1999.

	ABSTRACT

TOP ABSTRACT INTRODUCTION THEORY RESULTS CONCLUSIONS REFERENCES

 
Endosulfan (C₉H₆O₃Cl₆S; 6,7,8,9,10,10-hexachloro-1,5,5a,6,9,9a-hexahydro-6,9-methano-2,4,3-benzodioxathiepin 3-oxide) and other agricultural chemicals can be transported from farms to rivers by several airborne pathways including spray drift and vapor transport. This paper describes a modeling framework for quantifying both of these airborne pathways, consisting of components describing the source, dispersion, and deposition phases of each pathway. Throughout, the framework uses economical descriptions consistent with the need to capture the major physical processes. The dispersion of spray and vapor is described by similarity and mass-conservation principles approximated by Gaussian solutions. Deposition of particles to vegetation is described by a single-layer model incorporating contributions from settling, impaction, and Brownian diffusion. Vapor deposition to water surfaces is described by a simple kinetic formulation dependent on an exchange velocity. All model components are tested against available field and laboratory data. The models, and the measurements used for comparisons, both demonstrate that spray drift and vapor transport are significant pathways. The broader context, described in another paper, is an integrative assessment of all transport pathways (both airborne and waterborne) contributing to endosulfan transport from farms to rivers.

	INTRODUCTION

TOP ABSTRACT INTRODUCTION THEORY RESULTS CONCLUSIONS REFERENCES

 
IN the irrigated cotton (Gossypium hirsutum L.) industry in northern New South Wales, Australia, the insecticide endosulfan is widely applied by aerial spraying from November to January. A major water quality monitoring program (Cooper, 1996; Muschal, 1997, 1998) has shown that during and just after this spraying season, endosulfan concentrations in rivers near and downstream of cotton-growing areas are broadly in the range 0.02 to 0.2 µg L^-1, with occasional higher peaks. These values significantly exceed the present Australian environmental guideline for protection of ecosystems, currently 0.01 µg L^-1 (Australian and New Zealand Environment and Conservation Council, 1992). To manage and ameliorate such environmental contamination, it is vital to understand the pathways by which agricultural chemicals such as endosulfan move through the environment. Knowledge of the relative magnitudes and behavior patterns of these pathways is needed both for effective management of major pathways and also to avoid expensive efforts aimed at closing minor pathways.

This paper is the second of a pair, which have the overall aims of quantifying the magnitude, behavior, and relative importance of each of four major pathways (spray drift, vapor transport, dust transport, and runoff) by which endosulfan can move from farms to rivers, and elucidating management implications. The first paper (Raupach et al., 2001; henceforth Paper I) provides an overview, in which process models and data are combined to assess the contributions of each major transport pathway to riverine endosulfan concentrations. This paper provides modeling details for the airborne pathways. Parts of the work have appeared in several technical reports (Raupach et al., 1996; Raupach and Briggs, 1996, 1998; Briggs et al., 1998).

The present specific treatment of the major airborne pathways (spray and vapor) has several motivations. First, there is a need for a simple and robust framework for describing airborne pathways within the broader context of a complete integrative assessment of all transport pathways, undertaken in Paper I. Second, no adequate theoretical framework has hitherto existed for the vapor transport pathway. Third, many of the governing processes and conditions are common to both pathways, including turbulent dispersion and some aspects of source and deposition processes, so economy of description and proper comparisons between pathways are facilitated by using a single framework for these common processes.

Airborne transport pathways all involve three sequential processes, associated with (i) the source of the transported entity (spray droplets, contaminant vapor, or contaminant-bearing dust particles); (ii) the dispersion of the entity by wind and turbulence in the atmosphere; and (iii) the deposition of the entity to the water body. This paper assembles a suite of simple, compatible algebraic descriptions for the component processes, and tests these descriptions both separately and together with available experimental evidence. The major focus is on the spray and vapor pathways, since the dust pathway is not significant in the present context (Paper I).

The notation follows Paper I: subscripts "a" and "w" distinguish concentrations and other properties in air and water, and the , ß, and sulfate species are distinguished by superscripts , ß, or (where denotes the sulfate). Thus, the total endosulfan concentrations in air and water (in kg endosulfan m^-3) are respectively C_a = C_a + C^ß_a + C_a and C_w = C_w + C^ß_w + C_w. A superscript s denotes an arbitrary species.

	THEORY

TOP ABSTRACT INTRODUCTION THEORY RESULTS CONCLUSIONS REFERENCES

 
Dispersion of Particles and Vapor
To determine contaminant transport via any airborne pathway (spray drift, vapor transport, or dust transport), it is necessary to calculate deposition from a cloud of particles or gas dispersing in the air. Here we use a simple model based on mass conservation and a Gaussian-plume assumption. The starting point is the conservation equation for a scalar entity in the air:

[1]

where x, y, and z are along-wind, cross-wind, and vertical position coordinates (with z = 0 at the ground), t is time, C is the scalar concentration, _y and _z are the cross-wind and vertical flux densities, S is the source density, and u(z) is the wind velocity. In this section the subscript "a", denoting air concentrations, can be omitted without confusion. Fluxes in the air (_y and _z in Eq. [1]) are distinguished from fluxes entering water bodies (F_w(i) in Eq. [1] of Paper I) because _z is positive upward but F_w(i) is positive downward across the water surface for the spray, vapor, and dust pathways. All of the quantities C, S, _y, and _z are functions of x, y, z, and t in general, but the wind speed u is assumed to vary only with height z (that is, the wind field is steady in time and horizontally homogeneous).

We restrict attention to "puff" releases of scalar, defined as releases that are localized in time (but not necessarily instantaneous), so that C, S, _y, and _z have finite integrals of the form:

[2]

where a caret denotes integration over all time. Then, time integration of Eq. [1] yields:

[3]

The time-integrated downward flux at the ground is the deposition D(x,y) = -_z (x,y,0), with units (kg m^-2). This is specified by a deposition velocity W_d, which relates the downward flux of scalar at the surface to the concentration at a reference height z_r just above the surface:

[4]

Equation [4] is the lower boundary condition on Eq. [1] and [3]. The initial condition is that C is zero far upstream and as t -. We note the congruence between a time-integrated concentration field for a puff release and the concentration field for a steady plume release with the same source geometry; the former is described by Eq. [3] and the latter by Eq. [1] without the time derivative term, with similar boundary conditions in each case.

The deposition velocity W_d is a crucial parameter. In general, it is a conductance (a transfer coefficient with the dimension of velocity) specifying the air-to-surface flux of particles (-_z) through an equation of the form -_z = W_d(C_r - C_s) where C_s and C_r are the air concentrations at the surface and at a reference level z_r. For particles being deposited onto a surface it is generally assumed that C_s = 0, yielding Eq. [4]. The deposition velocity is controlled by different processes for particles and gases, leading to different models for the two cases as described below.

Suppose now that mass Q of scalar is released from a source in the yz plane at x = 0, not necessarily instantaneously or at a single point (y,z), but from a source sufficiently localized that S(x,y,z,t) has a finite integral over t, y, and z, and S is zero except at x = 0. Then an integral mass balance over the yz plane x = 0 shows that:

[5]

Physically, this means that Q equals the total mass of scalar (the time-integrated mass flux) crossing the yz plane just downwind of x = 0. However, as the scalar travels downwind it is removed by deposition to the surface. To describe this, we consider the mass fraction s(x):

[6]

which is the total mass of scalar crossing the yz plane at x, normalized by the original mass Q of scalar at x = 0. Clearly, s(0) = 1. An equation for the evolution of s(x) can be found by integrating Eq. [3] over the yz plane. Using Eq. [3] to [6], taking W_d as uniform over all x and y, and noting that fluxes vanish as y ± and z +, we obtain:

[7]

It is necessary to close this equation by relating the final concentration integral to s(x). This can be done generally by means of a similarity hypothesis about the concentration field (as will be shown in a later paper), but here it is sufficient to use the much more restricted assumption that the concentration field is Gaussian. In a Gaussian puff from a point release of mass Q at location x = 0, y = 0, and release height z = h_s, in a mean wind of speed u along the x axis, the time-integrated concentration is (Csanady, 1973; Hanna et al., 1982):

[8]

where _Y(x) is the plume width, _Z(x) is the plume depth, and z_s(x) is the height of the plume centroid. We can refer to _Y(x), _Z(x), and z_s(x) as "plume" characteristics because, as noted above, the time-integrated concentration field from a puff is congruent with the concentration in a steady plume. If the scalar is settling under gravitation with terminal velocity W_t, then the plume centroid can be assumed to obey z_s = max(h_s - xW_t/u, 0), while for a non-settling scalar material such as a gas, W_t = 0 and z_s = h_s. Empirical forms for _Y(x) and _Z(x) are often specified in terms of Pasquill stability classes, for example by Hanna et al. (1982) as summarized in Table 1. The relationship of these classes to more physical measures of stability, such as the dimensionless Richardson number, the Monin–Obhukov stability parameter, and the terrain roughness length, are given in Golder (1972) and Hanna et al. (1982). When the integral in Eq. [7] is evaluated using Eq. [8], we obtain:

[9]

which is an ordinary differential equation fully specifying s(x), given the starting condition s(0) = 1. This is similar to the result of the source-depletion method (Hanna et al., 1982), which calculates s(x) by using standard Gaussian formulae as if the source strength were Qs(x). The present derivation makes the assumptions easier to identify and generalize.

View this table: [in this window] [in a new window]   Table 1. Formulae recommended by Hanna et al. (1982) for the width Y(x) and depth Z(x) of a Gaussian plume from a point source near the ground, as a function of downwind distance x (km), valid for 0.1 < x < 10 km. A "super-unstable" class Z has been added.

[10]

which provides a useful check on numerical solutions. We use the numerical solution in practice, because it is not subject to the restrictions on Eq. [10].

Once s(x) is determined, the deposition D(x,y) from a point release of mass Q of scalar is given from Eq. [4] and [8] by:

[11]

where the exponentials involving z in Eq. [8] have been simplified to unity by assuming that both the reference height z_r and the source height z_s are small compared with _Z(x), which happens at sufficiently large x (in practice, quite quickly).

For line and plane sources, simpler expressions can be obtained by using mass conservation as expressed by the first equality in Eq. [7], which shows that for a unit source (a source of unit strength), the deposition is -ds/dx. This applies both to the laterally integrated deposition from a unit point source, and to the deposition D(x) from a laterally uniform unit line source (an extensive line source across the wind direction). Extending to area sources, the deposition from a laterally uniform unit plane source (extending over -x_p < x < 0 and - < y < ) is the integral of the unit line-source deposition, -ds/dx. Hence, if the actual plane source strength is D₀ and the deposition is D(x), then the deposition from a unit plane source is:

[12]

where the prime denotes differentiation, so that s'(x) = ds/dx. In a spraying operation, D₀ is the mass of spray released per unit area or the intended dose, and the ratio D(x)/D₀ is the drift deposition fraction f_drift(x) used in Paper I to quantify spray drift.

In practice, we are usually concerned with the dispersion of a cloud containing a distribution P(d) of particle sizes where d is the particle diameter. Particle size influences s(x) and thence the deposition D through the deposition velocity W_d, which is a strong function of d (discussed in the next subsection). Hence, the deposition is calculated by solving separately for each particle size and summing the results, weighted by P(d).

An experimental test of this model is presented later. The basic behavior of the model is shown in Fig. 1, by plotting the depleting mass fraction s(x) and the deposition -ds/dx = -s'(x) for a laterally uniform unit line source (both found from numerical solution of Eq. [9]), and the drift deposition fraction f_drift(x) for a plane source (from Eq. [12]). Results are shown for several particle size distributions, in typical conditions specified in the figure legend and defined below. The effect of particle size in limiting downwind drift is evident.

View larger version (25K): [in this window] [in a new window]   Fig. 1. Results from particle dispersion model for four different particle size distributions (log-normal with median particle diameter = 80, 160, 240, and 320 µm and standard deviation ln(1.8) throughout). Conditions assumed throughout: canopy height hc = 0.50 m; leaf dimension dc = 0.01 m; field length xp = 1000 m; spray release height hs = 2 m; initial plume height Z0 = 1 m; atmospheric stability is neutral (D); wind speed ur = 2 m s-1. Panels: (a) depleting mass fraction s(x); (b) deposition -ds/dx = -s'(x) for a laterally uniform unit line source; (c) drift deposition fraction fdrift(x) for a plane source from Eq. [12].

Particle Deposition
The deposition of particles to a vegetated surface occurs by three processes acting in parallel: direct gravitational settling to the surface, inertial impaction of particles on individual elements (leaves and stems), and Brownian diffusion of particles through the boundary layers of individual elements. The subject has been reviewed comprehensively by Davidson and Wu (1990). (Some authors, including Davidson and Wu, distinguish a fourth process, interception, which we treat as a form of impaction). All of these processes are strong functions of particle diameter (Fuchs, 1964; Chamberlain, 1967): gravitational settling dominates for large particles (>100 µm), impaction dominates in a middle size range centred around 10 µm, and Brownian diffusion dominates for very small particles (<<1 µm). Consequently, a plot of W_d against particle diameter exhibits a complex structure with a minimum at around 1 µm where none of the three processes is effective. Impaction and Brownian diffusion are also strong functions of the length scale of the canopy elements (such as a leaf width or stem diameter) and the local wind speed about the canopy elements, so W_d also depends on wind speed and canopy architecture. The first models used to describe this complex set of processes were single-layer models in which the vegetated surface was treated as a composite, bulk entity (Owen and Thomson, 1963; Chamberlain, 1967; Sehmel, 1980). Later work endeavored to resolve some of the complexities associated with the structure of the vegetation canopy through multilayer models that resolve the vertical variation of the wind field, particle concentration, and deposition processes inside the canopy (Bache, 1979a,b; Slinn, 1982; Davidson et al., 1982; Ferrandino and Aylor, 1985; Raupach, 1993). While many of these multilayer models provide good representations of data from specific experiments, they are too demanding on data and parameterizations to be useful in the present context. Therefore, we use a single-layer model here.

The model is based on antecedents for single-layer models of gas transfer to vegetation (Chamberlain, 1966; 1967; Shreffler, 1978; Hicks et al., 1985), but makes use of more recent understanding of leaf-scale processes as reviewed by Davidson and Wu (1990). The deposition velocity is treated as a bulk (single-layer) conductance made up of three component bulk conductances acting in parallel:

[13]

where W_t (the terminal velocity) accounts for gravitational settling, G_imp for impaction, and G_brow for Brownian diffusion. Of these three, W_t is a well-known function of particle diameter, particle-to-air density ratio, and air viscosity (Malcolm and Raupach, 1991). The bulk impaction conductance G_imp and Brownian conductance G_brow are both calculated by appealing to the analogy between particle transfer to the surface and momentum transfer.

The bulk aerodynamic conductance for momentum (G_aM =u²_*/u_r, where u_* is the friction velocity and u_r the mean wind speed at the reference level z_r) is a known property of the surface that can be specified in terms of the aerodynamic roughness length and thence the architecture of the canopy (Raupach, 1992, 1994). Two processes contribute to G_aM: form or pressure drag, and viscous or skin-friction drag (Thom, 1971), so we may write G_aM = G_aM(form) + G_aM(visc). For a typical canopy, Thom (1971) estimated the ratio of the contributions of form and viscous drag to the total drag to be about 3:1. If f_form is the fraction of the total canopy drag exerted as form drag, this implies that G_aM(form) = f_formG_aM and G_aM(visc) = (1 - f_form)G_aM, with f_form = 0.75.

Our hypothesis is that the Brownian conductance G_brow is proportional to G_aM(visc), and the impaction conductance G_imp is proportional to G_aM(form). For G_brow, the relationship is:

[14]

where Sc is the particle Schmidt number (Sc = _a/_p, where _a is the kinematic viscosity of air and _p the Brownian diffusivity for particles in air), and a_v is a factor of order 1 accounting for different effects of interelement sheltering on the molecular transfer of particles and momentum. The factor Sc^-2/3 accounts for the different molecular diffusivities of particles and momentum (Monteith, 1973). The Brownian diffusivity is given as a function of particle diameter d by the Stokes–Einstein formula (Fuchs, 1964): _p = (1 + 2.5_path/d)[kT/(3_aad)], where k is the Boltzmann constant, T the absolute temperature, _a the air density, and _path the mean free path of air molecules (about 2 x 10^-7 m at sea level).

For the particle impaction conductance G_imp, the hypothesis is:

[15]

where E_imp is the particle impaction efficiency (0 < E_imp < 1) and a_f is another factor of order 1 accounting for differential sheltering effects. The motivations for Eq. [15] are that a direct analogy between the conductances for particle impaction and form drag is only likely to be valid for particles with impaction efficiencies close to 1, and that the role of particle diameter in impaction can be quantified directly by the impaction efficiency. This can be specified as a function of the Stokes number St:

[16]

where _p is the particle density, d_c is the dimension of the canopy elements upon which impaction occurs, and U_c is the flow velocity about the canopy elements (which we characterize by the friction velocity u_*). The stokes number St is the ratio of the Stokes relaxation time _stoke to the radial traversal time d_c/(2U_c). Equation [16] uses a commonly assumed empirical form for the function E_imp(St), for which Bache (1981) and Peters and Eiden (1992) proposed p = 0.8 and q = 2 for several element shapes on the basis of fits to data.

Combining Eq. [13] to [15], the final form of the single-layer model for W_d is:

[17]

in which a_f and a_v are parameters to be determined empirically. Although this model is a great simplification of the real, multilayer physics, it has advantages for the present purpose: it includes enough physics to capture the dependence of the three major processes (settling, impaction, and Brownian diffusion) on particle diameter and wind speed; its two empirical coefficients are sufficient to permit matching to experimental reality but not enough to introduce parameterization problems; and it makes full use of information about bulk momentum transfer to characterize the aerodynamic properties of the canopy.

Figure 2 shows a test of Eq. [17] against the classical wind tunnel data set of Chamberlain (1967), for deposition of particles of various sizes to sticky (artificial) short grass of height 0.06 m. The coefficients a_f and a_v are treated as adjustable parameters and set at a_f = 2 and a_v = 8. The main observed features of the variation of W_d with d are reproduced quantitatively by the model, including the minimum in W_d(d) around d = 1 µm (where none of W_t, G_imp, or G_brow is effective), and the convergence of W_d to the settling velocity W_t for large particles. The model also satisfactorily reproduces the trend of the data with wind speed. Given the simplicity of the model, the agreement with measurements is satisfactory: it is better than some multilayer models (for instance Raupach [1993]) and is sufficient for the present purpose.

View larger version (22K): [in this window] [in a new window]   Fig. 2. Test of the single-layer model for the deposition velocity Wd, Eq. [15], against wind tunnel measurements of particle deposition to a sticky grass surface by Chamberlain (1967). Predictions are of Wd as a function of particle diameter d for vegetation of height 0.06 m and leaf area index 1, using the model of Raupach (1992)(1994) to calculate roughness length and other canopy aerodynamic properties. Data and predictions are for three wind speeds giving friction velocities of 0.35, 0.70, and 1.40 m s-1. The solid line is the predicted terminal velocity Wt as a function of d (Malcolm and Raupach, 1991).

View larger version (17K): [in this window] [in a new window]   Fig. 3. Contributions of the three terms Wt (settling), Gimp (impaction), and Gbrow (Brownian diffusion) to the deposition velocity Wd. Conditions as in Figure 1 with u* = 1.40 m s-1.

[18]

where V^s_d is a deposition velocity describing the (two-way) exchange of vapor between water and air, and A^s is the water–air partition coefficient, defined as the partition of the species s between water and air in a system at thermodynamic equilibrium:

[19]

Thus, A^s is the ratio of the water concentration C^s_w to the air concentration C^s_a when a vessel containing water, air, and the species s is allowed to come to equilibrium. Data reviewed in Paper I show that A^s is of order 10³ for -endosulfan, 10⁴ for ß-endosulfan, and 10⁵ for endosulfan sulfate, decreasing roughly by a factor of two for each 6°C increase in temperature.

Equation [18] shows that vapor deposition to water is driven by the difference between C_w and C_a (weighted by A^s) and is a bidirectional process: endosulfan moves from air to water when C_a is high and revolatilizes back to air when C_a is low. More precisely, if the water concentration C^s_w in a water body of depth H responds to the air concentration C^s_a only by air–water exchange, then C^s_w obeys the mass balance equation C^s_w/t = F^s_w/H (see Paper I). This can be written as C^s_w/t = /T^s, where T^s is the time scale A^sH/V^s_d. Hence, we have a first-order linear system in which C^s_w tends to track A^sC^s_a, with time averaging over a time of order T^s. For exposure to a steady air concentration C^s_a, the water concentration approaches the equilibrium value C^s_w = A^sC^s_a, which is at least 1000 times larger than the air concentration and is independent of water depth. This equilibrium is approached in a time scale T^s = A^sH/V^s_d, which depends on water depth, being about 1 d when H is 0.1 m and 10 d when H is 1 m (for A^s = 10³ and V^s_d = 1 mm s^-1).

The vapor deposition velocity V^s_d determines the air–water flux. According to the Deacon model (Deacon, 1977; Denmead and Freney, 1992), the inverse of V^s_d is a transfer resistance given by the series sum of contributions from three sequential parts of the water–air pathway: transfer through the water (R_w), the quasilaminar air sublayer occupying the lowest millimetre or so of the air (R_b), and the turbulent atmosphere (R_t). This contrasts with Eq. [13] for particle deposition velocity, which is a parallel sum of three conductances describing different, parallel processes operating over the entire pathway from air to surface. The model gives the vapor deposition velocity as:

[20]

where _a and _w are the densities of air and water, _a and _w are molecular diffusivities of endosulfan in air and water, _a and _w are the kinematic viscosities of air and water, u_* is the friction velocity, k_VK (= 0.4) is the von Karman constant, z_r is the reference height for the air concentration, and z_b is the thickness of the quasilaminar air sublayer (given by z_b = 50_a/u_*). The molecular diffusivities for endosulfan in air and water were estimated by multiplying the corresponding diffusivities for CO₂ by (M_c/M_e)^1/2 = (44/407)^1/2, where M_c and M_e are the molecular weights for CO₂ and endosulfan, respectively.

Figure 4 shows the behavior of the model by plotting V^s_d, R_t, R_b, and R_w/A^s against u_*· Typical values for V^s_d are about 2 mm s^-1 at u_* = 0.2 m s^-1, varying almost linearly with u_*. All of the resistance terms in Eq. [20] are significant.

View larger version (19K): [in this window] [in a new window]   Fig. 4. The deposition velocity of endosulfan vapor to water, from the Deacon model, Eq. [18]. Assumed parameters: a = 1.2 kg m-3, w = 1000 kg m-3, a = 1.5 x 10-5 m2 s-1, w = 1 x 10-6 m2 s-1, a = 4.8 x 10-6 m2 s-1, w = 5.3 x 10-10 m2 s-1.

Vapor Transport
Of the total endosulfan dose D₀ applied to the crop, a fraction f_vol is ultimately volatilized into the atmosphere (the rest ultimately degrading in situ or being transported away from the crop by waterborne pathways). Kennedy et al. (1998) found that f_vol is about 0.7. To specify the vapor source, we assume that the flux of endosulfan vapor into the air decays exponentially with time after spraying such that the total amount of endosulfan volatilized is f_volD₀ kg m^-2. This implies that:

[21]

where F^s_vol is the volatilized endosulfan (species s) flux from the crop into the air (kg m^-2 s^-1) at time t since spraying, and T^s_vol is a time constant for the volatilization of species s, which can be determined from measurements (Kennedy et al., 1998). The air concentration produced by this flux can be evaluated using a simple Gaussian dispersion model (see above), yielding:

[22]

where x and y are the downwind and crosswind coordinates of the receptor point relative to the source, and A is the area of the source (assumed to be a quasi–point source with dimensions small compared with x and y).

	RESULTS

TOP ABSTRACT INTRODUCTION THEORY RESULTS CONCLUSIONS REFERENCES

 
Comparison of Vapor Transport Model with Field Data
Experiments
Ahmad et al. (1995) and Edge et al. (1998) describe the field experiments used here for comparisons with the model. Two experimental sprays were carried out at Auscott Warren, NSW, at 0400 on 21 Dec. 1994 (Spray 1) and 1600 on 7 Jan. 1995 (Spray 2). In each spray, 3 L ha^-1 of ULV Thiodan (240 g L^-1 endosulfan) plus 0.5 L ha^-1 of a Bt formulation was applied aerially to 182 ha of cotton in Fields 4 and 5 (see Fig. 5). Sampling of endosulfan in the environment was maintained for 5 d after each spray, as follows:

View larger version (35K): [in this window] [in a new window]   Fig. 5. Layout of the field experiment at Auscott Warren, 1994–1995.

• Air samplers were placed within Field 4 and 200 m to its south at station S200m (Fig. 5). These yielded air concentrations of endosulfan species averaged over 4-h intervals for the first 24 h and then over 12-h intervals to 5 d. Unfortunately, no air concentration data were recovered from the S200m station for Spray 2.

• Water samplers consisted of water-filled galvanized iron trays, placed along four transects extending approximately south, north, east, and west of Fields 4 and 5, to distances up to 1000 m (Fig. 5). Each tray was 0.5 m² in surface area and 0.1 m deep, and was filled to depth 0.05 m with water. Tightly fitting lids were placed over the trays during spraying to prevent contamination of the water by direct spray drift. The lids were removed 1 h after spraying. Water samples were removed from the trays every 24 h, to 5 d, for analysis.

In addition to the above experiments, two additional experiments (Sprays 3 and 4) were carried out in the following season at Auscott Warren, on 18 and 27 Dec. 1995. In Spray 3, ULV Thiodan was applied aerially, in the same way as for Sprays 1 and 2, to 120 ha of cotton in Field 7 (adjacent to Fields 4 and 5, which were fallow). In Spray 4, Thiodan EC (350 g L^-1 endosulfan) was applied aerially to Field 7 at 2.1 L ha^-1 (together with Pix at 0.45 L ha^-1, with a total application rate of 20 L ha^-1). A major difference between Spray 4 and other sprays was in the droplet size distribution, which had a median of around 240 µm for the EC formulation (Spray 4) and around 80 µm for the ULV formulation (other sprays). The movement of volatilized endosulfan was determined after Sprays 3 and 4 using water-filled trays as described above. No air concentrations were measured. Site configuration prevented samples being taken more than 400 m from the edge of Field 7. The sampling periods were reduced from 5 d to 3 d (Spray 3) and 2 d (Spray 4), with sampling only every 24 h, because the results from Sprays 1 and 2 had shown that peak concentrations were achieved after 2 d. Because of these more restricted data sets we have not modeled Sprays 3 and 4 in detail, but we use them for qualitative comparisons.

Model Specifications
The vapor transport model was run for Sprays 1 and 2, using the parameters summarized in Table 2. These were assigned as follows:

The volatilization time scale in Eq. [21] was determined from the leaf samples, which showed that the endosulfan present on leaves decays approximately exponentially as implied by Eq. [21], with time constants of 0.5 d () and 1.5 d (ß) for Spray 1, and 1.0 d () and 5.0 d (ß) for Spray 2. The longer decay time for the ß isomer is caused by its lower vapor pressure (Paper I, Appendix A). The difference in decay times was caused by warmer conditions for Spray 1 than for Spray 2, and the strong dependence of the vapor pressure on temperature. The average maximum temperature for the 2 d after spraying was 40°C for Spray 1 and 29°C for Spray 2. These values for decay times are consistent with wind tunnel measurements by Hoechst Aktiengesellschaft (1993), who found values of less than 1 and about 3 d for the volatilization time scale of technical endosulfan from leaves and soil, respectively. Singh et al. (1991) found a much larger value, about 10 d, by exposing the liquid spray mixture in a petri dish on the roof of a laboratory, but this value is not applicable because of the unrealistic exposure technique.

• Meteorological parameters: Meteorological data including wind speed, wind direction, and air temperature were recorded at height 2 m during the months surrounding the trials by Dr. Nicholas Woods and colleagues, CPAS, Gatton College, University of Queensland. We used these data in half-hourly averaged form. Two gaps in the data (0830 to 1400 on 5 Jan. 1995, and 0700 on 8 January to 2230 on 9 January) were filled by copying data from periods of similar meteorological conditions, as judged from weather maps and data from nearby meteorological stations. Fortunately, the gaps occurred during periods of reasonably predictable wind and temperature. The missing 5.5 h on 5 January were filled using the same period on 11 January, and the missing 38.5 h on 8 and 9 January were filled with the same period on 3 and 4 January.

In the absence of direct information, stability classes were assigned according to time of day. Each 24-h period (0000–2400) was divided into eight 3-h blocks (0000–0300,..., 2100–2400). The stability classes for these eight blocks were prescribed by the sequence (E,E,B,A,A,A,E,E) on occasions of moderate wind (u > u_min = 2 m s^-1), and by the sequence (F,F,A,Z,Z,Z,F,F) for occasions of light wind (u < u_min). Sensitivity tests have confirmed that the model results are insensitive to the exact choice of stability classifications.

• Deposition and chemical parameters: The water depth in the trays was H = 0.05 m. The deposition velocity for vapor of species s to water, V^s_d, was determined by Eq. [20]. The chemical properties of endosulfan (Paper I, Appendix A) were evaluated by assuming that the temperature of the water in the trays was equal to the measured air temperature at the meteorological reference height. The friction velocity u_* was estimated from the mean wind speed (u) at the reference height (z_r = 2 m), since the ratio u_*/u is reasonably independent of wind speed. Over a rough surface such as an agricultural area, this ratio is about 0.1. However, the water in each experimental tray was nearly aerodynamically smooth and was significantly sheltered by additional mechanisms, mainly a tray side wall extending 50 mm above the water surface. To account for this we assume a shelter factor (the ratio of u_* within the tray to the ambient u_*) of 0.1. Thus, for the water in the trays, u_* = 0.01u. No stability corrections were applied. Sensitivity tests have shown that the model results are insensitive to assumptions about u_*. The reason is that u_* affects only the deposition velocity V^s_d, and therefore the rate at which the air–water equilibration proceeds (that is, the rate at which the flux in Eq. [18] approaches zero when C^s_a is steady). It does not affect the final equilibrium value of C^s_w, which is A^sC^s_a. The rate of equilibration is given by the time constant A^sH/V^s_d, which is fairly short (around 1.5 h for H = 0.05 m, A^s = 1000, V^s_d = 0.001 m s^-1). Therefore, over time scales of a day or so, the air and water concentrations are close to equilibrium and the rate of the exchange (influenced by u_*) is nearly immaterial.

Results of Comparisons
We first consider air concentrations. Measurements of air concentrations were made at stations within Field 4 and at the S200m station, 200 m to its south (Fig. 5). These are compared with predictions from the model in Fig. 6. There is a strong diurnal cycle in both the predicted and measured air concentrations, caused by the entrapment of air with high concentrations near the ground at night when atmospheric dispersion is much weaker than by day. The measured concentrations are similar within Field 4 and at S200m. Total measured endosulfan concentrations within Field 4 for Spray 1 are overpredicted by the model for the first 24 h after spraying, but tend to be underpredicted at later times. The comparisons between model and measurements are quite good at S200m for Spray 1, and also for Spray 2 (for which only within-field data are available). It is concluded that, despite major simplifications, the model is capable of reproducing the order of magnitude of measured air concentrations. This is sufficient for the purpose at hand.

View larger version (29K): [in this window] [in a new window]   Fig. 6. Predicted and measured endosulfan air concentrations (, ß, , total) at stations within Field 4 and at S200m outside Field 4.

View larger version (25K): [in this window] [in a new window]   Fig. 7. Predicted and measured endosulfan water concentrations (, ß, , total) at four westward receptor locations for Sprays 1 and 2.

View larger version (15K): [in this window] [in a new window]   Fig. 8. Time-averaged comparison (over 5 d) of measured and modeled total endosulfan concentrations at 13 receptor points, for Sprays 1 and 2.

View larger version (23K): [in this window] [in a new window]   Fig. 9. Time-averaged comparison (over 5 d) of measured and modeled endosulfan species concentrations (, ß, , total) at 13 receptor points, for (a) Spray 1; (b) Spray 2.

The water concentration data from Sprays 3 and 4 (1995–1996 season) were generally consistent with those from Sprays 1 and 2, though somewhat lower on average. Temperatures following spraying were also lower. The most significant aspect of these data was that there was no obvious difference between the EC and ULV formulations.

Given the difficulties involved in both measurements and modeling, the comparisons in Fig. 6 to 9 are generally encouraging. One reason for the disagreements is likely to be uncertainties in the chemical coefficients. The water–air partition coefficients A^s are the most important parameters determining the water concentrations of the and ß isomers, while the rate constants for oxidation to sulfate determine the sulfate concentrations at intermediate times of a few days. Both the values and the assumed temperature dependencies of these quantities are still uncertain.

Comparison of Spray Drift Model with Field Data
The spray drift model for the drift deposition fraction f_drift has been compared with field data from Bird et al. (1996). The model consists of Eq. [12] for f_drift, with the airborne particle fraction s(x) determined by the numerical (Runge–Kutta) solution of Eq. [9], using Eq. [17] to specify the deposition velocity W_d as a function of particle size d. The calculation of f_drift was carried out for 21 particle sizes determined by the particle size distribution P(d). The final f_drift for a spray with a broad particle size spectrum was calculated by integrating f_drift(x,d)P(d) over d, where f_drift(x,d) is the value appropriate at distance x downwind of the field for a single particle size d.

For the "standard case" of Bird et al. (1996), 36 experimental replicates are available for a single-swathe aerial boom spray with a median droplet diameter of close to 250 µm and an approximately log-normal particle size distribution P(d). We inferred mean measured values of f_drift(x) from plots at three different wind speeds corresponding to the 20th, 50th, and 80th percentiles of the wind speed range covered by their 36 replicates. Figure 10 compares these data with predictions for each wind speed, using model parameters (given in the figure caption) selected to match the experimental conditions. The predictions capture the magnitude and the streamwise trend of f_drift(x) well, slightly overestimating the magnitude of f_drift(x) at higher wind speeds. Given the major simplifications of the model, this is a satisfactory result that provides confidence that the values of f_drift being estimated by the model are reasonable.

View larger version (21K): [in this window] [in a new window]   Fig. 10. Comparison of particle dispersion (spray drift) model with data from Bird et al. (1996)(standard case) for three wind speeds u. Parameters: canopy height hc = 0.15 m; leaf dimension dc = 0.005 m; field length xp = 274 m; spray release height hs = 2.5 m; initial plume height Z0 = 1 m; median particle diameter = 250 µm; particle size distribution is log-normal with standard deviation ln(1.7); atmospheric stability is neutral (D) or slightly unstable (C).

	CONCLUSIONS

TOP ABSTRACT INTRODUCTION THEORY RESULTS CONCLUSIONS REFERENCES

Spray drift depends not only on dispersion but also on deposition to the underlying (usually vegetated) surface. A single-layer model for this deposition process has been formulated that is well supported by the laboratory data of Chamberlain (1967) and that shows that for spray droplets of around 100 µm or smaller, impaction and related processes dominate over gravitational settling in particle deposition. By combining this model with a simple dispersion model based on a settling Gaussian plume, a model for spray drift is obtained that agrees very well with field data from Bird et al. (1996).

For vapor transport, the model consists of a simple exponential-decay assumption for the post-spray volatilization of endosulfan from a sprayed crop, the same dispersion model used for spray drift, and a model for deposition of vapor to a water surface due to Deacon (1977) and Denmead and Freney (1992), based on a kinetic formulation for the air–water exchange and a deposition velocity. The dispersion model and field measurements (Edge et al., 1998) both show that volatilization and dispersion of endosulfan from sprayed crops produces air concentrations (C_a) in the range 1 to 5 µg m^-3 at sites within and adjacent to sprayed fields, immediately after spraying. Values are much higher at night than by day, because of entrapment of air with high concentrations near the ground at night. As volatilization proceeds, air concentrations decay with a time scale of 1 to 5 d, decreasing with increasing temperature.

The complete model of the vapor transport pathway (including volatilization, dispersion, deposition, and water chemistry) produces predicted endosulfan water concentrations (C_w) of order 0.1 to 0.5 µg L^-1 in a water body of depth 0.05 m within 1 km of a sprayed cotton crop, over the first few days after spraying. These predictions are in broad (though far from perfect) agreement with field observations by Edge et al. (1998). For experimental trays containing water of depth 0.05 m, they found water concentrations, averaged over the 5 d following spraying, ranging from 0.3 µg L^-1 (at a distance of 200 m from the crop) to 0.18 µg L^-1 (at 1 km) for Spray 1; the corresponding range for Spray 2 was 0.18 µg L^-1 (at 200 m) to 0.1 µg L^-1 (at 1 km). The highest observed concentrations in individual trays were around 0.5 µg L^-1, recorded around 48 h after spraying. Monitoring of two additional sprays (Sprays 3 and 4) in the following season gave similar (though somewhat lower) concentrations, but temperatures were also lower. No differences were observed between ULV and EC formulations, for which median spray droplet diameters are around 80 µm and 240 µm, respectively.

This level of agreement is sufficient for the purpose of establishing the overall significance of vapor transport relative to other possible transport pathways. However, modeling uncertainty remains in the physical and chemical properties of endosulfan species. It should also be noted that the water concentrations observed in the experimental trays cannot be directly scaled to infer the concentrations arising from vapor transport in a river, which has a quite different (generally much greater) depth and for which the exposure pattern is quite different. To make this conversion, one must consider the dynamical factors built into the model described in Part I.

	ACKNOWLEDGMENTS

 
We are grateful for many discussions with Nick Schofield, Dave Anthony, Phillip Ford, John Leys, Frank Larney, Ivan Kennedy, Brian Hearn, Monika Muschal, and Bruce Cooper. We likewise thank Nicholas Woods for both discussions and for access to the meteorological data recorded during the field experiments. We acknowledge with appreciation the support of the Land and Water Resources Research and Development Corporation (LWRRDC), the Cotton Research and Development Corporation (CRDC), and the Murray–Darling Basin Commission (MDBC), through the joint research program "Minimising the Impact of Pesticides on the Riverine Environment".

	REFERENCES

TOP ABSTRACT INTRODUCTION THEORY RESULTS CONCLUSIONS REFERENCES

 

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