Deposition of 30–60 μm diameter droplets in winter wheat

Agricultural Meteorology, 28 (1983) 109--127 Elsevier Scientific Publishing Company, Amsterdam -- Printed in The Netherlands

109

DEPOSITION OF 3 0 - - 6 0 # m DIAMETER DROPLETS IN WINTER WHEAT B.A. CALLANDER* and M.H. UNSWORTH

Department of Physiology and Environmental Science, School of Agriculture, University of Nottingham, Sutton Bonington, Loughborough, Leicester (Gt. Britain) (Received August 26, 1982; accepted September 30, 1982)

ABSTRACT Callander, B.A. and Unsworth, M.H., 1983. Deposition of 3 0 - - 6 0 p m diameter droplets in winter wheat. Agric. Meteorol., 28: 109--127. Experiments in which droplets of a single size were released from a line source over periods of up to half-an-hour, were performed over wheat at different stages of development. The deposition observed on the soil and on all parts of the wheat, at distances up to 24 m downwind, was analysed in conjunction with measured profiles of wind-speed and droplet dose. The impaction efficiencies on the various parts of unsheltered plants agreed with wind tunnel studies. Within the stand, sedimentation and inertial impaction contributed in approximately equal proportions to total deposition on both young and mature crops, but the rate of deposition below the canopy was reduced by sheltering, quantified by the parameter p - 1. For soil below a canopy, p - 1 was related to leaf area by an exponential relationship analogous to Beer's Law. The deposition velocity had a significant turbulent deposition component that was consistent, in its relation to friction velocity, with published results for spores depositing on wet wheat. The average 'bluffbody' resistance to droplet transfer was 18 s m - 1,

INTRODUCTION

The deposition velocity, vg, defined as the ratio of deposition flux density to aerosol concentration at some reference height, is n o w a ubiquitous index of the efficiency with which a surface removes aerosol from the surface b o u n d a r y layer. Sehmel (1980) comprehensively reviewed the range of deposition velocities reported in the literature and chose the model of Sehmel and Hodgson (1976) as the best available predictor of vg. For short crops, however, this model predicts that the deposition of aerosols with particle sizes greater than a b o u t 1 0 p m is dominated by gravity, contrary to some experimental evidence cited b y Sehmel himself. Raynor (1976} found that deposition velocities of pollen grains, with diameters between 20 and 100pm, were typically three times the sedimentation velocity vs. The prediction is also less likely to be valid for cereal canopies, where the topmost elements encounter relatively high windspeeds that favour impaction. Among the few studies of the deposition of aerosols on such crops, that of Chamberlain and Chadwick (1972) showed that turbulent impaction could * Present address: Meteorological Office, London Road, Bracknell, Berkshire (Gt. Britain)

0002-1571/83/$03.00 © 1983 Elsevier Scientific Publishing Company

111 0

increase v~ significantly above v,. In addition, independent theoreticai approaches (see next section) have agreed in predicting that v~ should exceed v, because of turbulence. The magnitude and relative importance of turbulent deposition for particles in the 1 0 - - 1 0 0 # m size range remain, therefore, open questions. This paper presents the results of experiments carried out on wheat and aimed at answering these questions for that crop, The results are presented in the order of increasing scale, beginning with deposition on individual crop elements and ending with bulk deposition characteristics. The role of shelter and the sensitivity of vg to windspeed are analysed with reference to the detailed measurements. LITERATURE REVIEW

Bulk deposition on crops

Bache and Uk (1975) defined an aerosol attenuation coefficient ~ such that, if /3 is constant with height, aerosol concentration decreases with depth s in the canopy according to a Beer's Law-type equation, × = ×0 exp(--fls). For 4 0 p m droplets depositing in cotton, Bache and Uk concluded from the insensitivity of ~ to windspeed, that sedimentation was the dominant m o d e o f deposition for friction velocities up to at least 0.5 m s -1 . For the deposition of ragweed pollen (diameter 2 0 p m ) on maize, Aylor (1975) also concluded that sedimentation was the dominant mode of deposition in windspeeds up to 2 m s -1 . At windspeeds between 3 and 4 m s-1 some of Aytor's data pointed to a similar conclusion, but to accoun~ for the observation that the increased windspeed brought about a threefold increase in deposition at the t o p of the crop, Aylor inferred that impaction during gusts had contributed significantly to deposition. On the theoretical side, Bache (1979 and 1981) further developed the concept of the aerosol attenuation coefficient to produce theoretical curves of Vg as a function o f friction velocity u.. These curves were in reasonable agreement with the data of Chamberlain and Chadwick (1972). Generally it had been assumed that sedimentation alone could not produce an increase in vg with windspeed. However, Legg and Price (1980) demonstrated theoretically that sedimentation alone could still account for an increase in Vg with friction velocity u. commensurate with observations. Their argument was based on K-theory within the crop, in spite of doubts cast on this approach by Legg and Long (19751 and Legg and Monteith (1975). It allowed turbulence to increase the rate at which aerosol was transported to the lower leaf layers where it would be deposited b y sedimentation. Turbulent impaction on individual plant elements

The impaction efficiencies of plant elements have often been measured

111

in wind tunnels, where the evidence has suggested close similarity in droplet capture between leaves or stems and similarly dimensioned cylinders, e.g., Gregory and Stedman (1953). In contrast, similar measurements have rarely been performed in the field, where natural turbulence and plant movement may alter collection characteristics. Even if field measurements on isolated plants agreed with wind tunnel data, it would still be necessary to quantify the extent to which mutual sheltering between plants within a stand diminished aerosol capture. The importance of sheltering varies with crop structure. For wild oat grass, 65cm high and with a leaf area density of about 17m -1, Davidson and Friedlander (1978) obtained reasonable agreement between theory and experiment without taking any account of possible sheltering. In contrast, Rosinski and Nagamoto (1965) observed that particle deposition on coniferous trees was reduced by leaf shelter at high density. Belot et al. (1976) adjusted actual leaf area by a factor p - 1 to exclude that fraction of leaf area n o t accessible for deposition. (For example an array of n leaves, causing mutual shelter, would collect only n p - 1 times as much aerosol as a single leaf exposed to the same aerosol flux). For a forest, Belot et al. (1976) found p - 1 to be around 0.7. For the hypothetical wheat crop of Legg and Price (1980), with a leaf area density of 5.5 -1, Bache {1981) inferred that p - ~ would be around 0.2. As yet, there seems to be no simple theoretical framework that would allow prediction of p - 1 from a knowledge of crop structure. Analogy with m o m e n t u m transfer, where drag coefficients within the canopy are reduced in the wake of upwind elements (Seginer et al., 1976), may have little to offer, because the drag coefficient and the impaction efficiency of a cylinder exhibit different trends with windspeed (Chamberlain, 1975, Fig. 5). THEORY

Bulk deposition The deposition velocity v~ is defined by the equation vg -- D/×(z)

(1)

where D is the deposition rate per unit horizontal area and ×(z) is the concentration at z. The only assumption implicit in eq. 1 is that the vertical flux D is constant. Although this definition involves no assumptions regarding the mechanisms, either of transport or of deposition, it is convenient to introduce such assumptions by regarding vg as the algebraic sum of vs and the rate of turbulent deposition, yr. In order to meet the constant flux requirement of eq. 1, determinations of v~ should ideally be made at a distance x from the source large enough for the concentration profile to be fully developed up to at least z. For z = l m Doran (1977) suggested that x could be as much as l k m . However,

1 12 because the constant flux condition develops upwards from crop height, h, the deposition velocity at much smaller downwind distances can be estimated at z = h, then translated if necessary to the corresponding value at larger z, using the functional form of a fully developed profile. This translation also incorporates assumptions about the mechanism of aerosol transport. The correction formula of Chamberlain (1976, Eq. 10) assumed that aerosol flux is a combination of sedimentation, and of eddy diffusion governed by the same diffusion coefficients as m o m e n t u m exchange. (Bache, 1979, derived an equivalent equation containing similar assumptions). Chamberlain (1976) related the deposition velocity at z2 to that measured at z I by re(z2) = v , [ 1 - - A ( 1 .... C)] -1

where A = (z 1/z 2 )~, C = vs/v e (z 1) and a = v , / k u , , constant.

(2) k b e i n g v o n Karman's

D e p o s i t i o n on individual e l e m e n t s o f plants

The impaction efficiency El of an element, of length t and characteristic width w, is defined as the ratio of the number n of droplets impacted on the element, to the number that would have passed through the s a m e area in the absence of the element. That is, Ei = n / ( x u t l w )

(3)

where u is the mean windspeed and t is the averaging time. The product x u t is the area dose of droplets, assuming that there is no correlation be-

tween fluctuations of windspeed and of concentration. In the wind tunnel where the geometry of the target element with respect to the airstream can be precisely defined, and where concentration and windspeed are also precisely known, Ei can be accurately calculated. In the field there are two options. One is to expose individual plants so there is no interference from their neighbours, and make detailed measurements on and around those plants. This procedure produces precise values for an artificial situation. The second option is to leave plants within the stand, so that they encounter the mutual sheltering and airstream fluctuations caused b y their neighbours within the stand. By estimating area dose from the interpolation of profile data and using the physical, as opposed to the projected dimensions of the plant elements, values of E i are produced which require careful interpretation, b u t which relate to a 'real' situation. Both options were tried in t h e present experiments. E x p e r i m e n t a l discrimination b e t w e e n m e c h a n i s m s o f d e p o s i t i o n

The deposition due to sedimentation on a segment of leaf is given by ns = vs Xtlh Wh

113

where lh and wh are respectively the segment length and width projected onto a horizontal plane. The deposition due to inertial impaction is given by n~ = Eiuxtlvw~ where subscript v denotes dimensions projected onto a vertical plane perpendicular to u. If n8 and n; are divided by the total deposit on the leaf then the resultant fractions f8 and fi are independent of v~, X,u, and t. The relative importance of sedimentation will then be reflected b y the degree of correlation between f~ and the product lh wh, and that of impaction by the correlation between fi and the product Eilv wo. An objection might be raised against the assumption, implicit in the above approach, that deposition on horizontal surfaces occurs only by sedimentation, whereas the work of Gregory and Stedman (1953) showed that turbulence generated by the leading edge of horizontal surfaces could significantly affect the distribution and amount of deposit. However, such effects would be less pronounced in the low windspeeds within a dense canopy. Shelter factor

The shelter factor p - 1 has already been loosely defined in terms of area. A particular shelter factor p - 1 , applying to impaction alone, can be defined in terms of impaction efficiency. Suppose that a flux of droplets impinges on an array of rn similar targets each with a presentation area A. By assuming that the total presentation area of the array is mA, a mean effective impaction efficiency Ee for each target can be calculated by eq. 3. The impaction shelter factor is then given b y p

- 1

:

Ee/E

i

(4)

where E i is the impaetion efficiency of a single, isolated target exposed to the same flux. MATERIALS AND METHODS

Droplet production and release

In studies of deposition, droplets have the major advantage over spores or particles of not being subject to bounce-off. Droplets of a narrowlydefined size were released from a moving-point line source using a MiniULVA spinning disc atomiser (Micron Sprayers, Bromyard, Kent) over winter wheat (Triticum aestivum L. cv Flanders and cv Armada). The duration of release ranged between 142 s and 2115 s, and the system was fully described b y Callander (1982) and Callander and Unsworth (1982). The atomised liquid was ethanediol, labelled with a dispersed fluorescent p o w d e r (Saturn Yellow, Swada, London) added in the proportion 20 mg m1-1. The mixture was diluted with an equal volume of methanol, added in order

1],i to achieve a sufficiently small droplet size, but also having the additional benefit of narrowing the droplet size distribution around the mode. The methanol evaporated during and immediately after atomisation, and the remaining droplets remained substantially constant in size thereafter. For example, according to the formulae of Green and Lane (1957), a 5 0 g m drop of ethanediol would require 100s to diminish b y evaporation to 45pro, a time much longer than any flight encountered in these experiments. Actual measurements of droplet size at different distances showed no systematic variation. Droplet size was measured, usually at source, b y catching a sample of spray in a large box. The b o x was immediately closed and the drops allowed to settle onto magnesium oxide-coated slides. The slides were subsequently analysed under a microscope, allowing a spread factor of 0.86 between the image size and the original droplet diameter (May, 1945}. The airborne cloud of droplets was sampled by vertical rods, 12.5cm long, 6 . 3 m m diameter. A 4 c m segment towards the centre of each rod was painted black, and droplets were counted only on this part. The impacti0n efficiencies of the rods at each height were calculated from the curves of May and Clifford (1967), using windspeed from a 6-point profile measured by sensitive cup anemometers (Model A 100 S, Vector Instruments, Rhyl). 'Harp' collectors were constructed of square 'Perspex' frames strung with parallel 0.1 mm wire. By the results of May and Clifford (1967) the impaction efficiency of the wires exceeded 80% for all windspeeds down to about 0.1 m s- 1, so these samplers were used to estimate below-canopy dose. The o u t p u t from a lightweight windvane (Model W200/C, Vector Instruments) was logged every 7 s by a Solartron 'Compact' logger. From the mean and variance of the wind direction it was possible to determine whether the line source was effectively an 'infinite line' as far as the downwind measurements were concerned (Callander, 1982). The logger also recorded the instantaneous wind profile at the time intervals. UNCERTAINTIES

Deposition velocity vg is defined as D(x)/x(x,z), Errors in D and X from instrumental sources were much smaller than t h e scatter between values of vg for the same experiment b u t for different values o f x, so uncertainty in vg was taken to be equal to the statistical scatter.

Windspeed Individual measurements of windspeed above t h e c a n o p y were s u b j e c t to an absolute calibration uncertainty of -+ 5%. When the profile was extrapolated according to the ~ p o n e n t i a l law for windspeed-s within t h e c&-mpy, the uncertainty in u(5) was estimated to be less than 25% in the t o p third

115 of the canopy, increasing to 30--40% in the b o t t o m third. These latter uncertainties were based on the range of the attenuation coefficient observed in wheat by several workers (see for example, Pereira and Shaw, 1980).

Droplet dose, horizontal flux and concentration The estimation of airborne dose from the deposit observed on the 6 mm vertical rods was subject to uncertainty in the impaction efficiency Ei and to statistical variation in the number of droplets caught. For the range of droplet sizes and windspeeds encountered, the working relationship (1/Ei) (dEi/du) = 1.5 exp (--1.1u) was employed, where u is in m s -1 . The interception of droplets was assumed to follow Poisson statistics, so that a count of N droplets had an uncertainty of N 1/2. The error in averaging time was negligible, so the fractional errors in dose and horizontal flux were equal. Estimated mean concentration X was subject to the uncertainty in the product (Eiu). Using the working relationship above, it follows that ( l / x ) (dx/du) = 1.5 exp (-- 1.1u) + u -1 Typically, a 25% error in u produced a 30--35% error in X-

Sedimentation velocity Sedimentation velocity was estimated from published data for unit density spheres (Fuchs, 1964), with values increased by 10% to allow for the larger density of ethanediol (p = 1.1 × 10 a kg m -a ). It was particularly important for the interpretation of results that vs was not underestimated, and such underestimation could occur in three ways. First, droplet diameter ~bd could be underestimated, and the likely error was checked indirectly. The number of droplets that could be accounted for at any value of x was the sum of the airborne flux at x plus integrated deposition up to x, and this number could be compared with the number of droplets released, as calculated on the basis of measured droplet diameter and liquid flow rate. Discrepancy between the two figures that could be attributed to an error in ~bd was not more than 11%. It was concluded t h a t the error in ~b~, and hence in %, did not exceed 4%, because calculated droplet production rate was a function of the cube of ~ . The other two ways in which v~ could be underestimated are both due to potential effects of buoyancy. First, if a cloud of droplets increases the local density of the air parcel t h e y occupy by more than about 1% then that parcel will fall bodily, increasing the effective sedimentation velocity (A.C. Chamberlain, personal communication, 1982). When a source of strength Q (with dimensions, mass per unit time) and traversing crosswind at speed v, releases material of density Pa and velocity u, it can be shown that the local air density is increased by a fractional a m o u n t f l , given by

fz = Q ( P ~ I - P ~ I ) / ¢ b where q) = (v 2 + u 2 )1/2 do2, do being the initial dimension of the cloud seen

t16

across-wind. For the parameters of the present experiments, fl was never more than 0.2% and was usually around 0.01%. The second potential cause of changes in air density is the cooling effect of evaporation from the spray. If the spray contains a volatile diluent with a latent heat of vaporisation ~, and if that component evaporates at a rate Qe, then the m a x i m u m drop in temperature of the entrained air will be T = QeX/pacp¢ where cp is the specific heat of air. This will produce a fractional change in density f2 = A T / T where T, the absolute temperature, is assumed to be large compared to AT. In t h e present experiments f2 was always less than 0.1% and was typically around 0.01%. It was concluded, therefore, that density changes in the air entrained by the spray did not introduce any significant underestimation of vs, and consequently that total uncertainty in v~ did not exceed 4%. RESULTS

Mechanisms o f deposition Artificial " w h e a t plants" were constructed of vertical, 6 m m diameter rods to which 3 or 4 artificial leaves were attached at random orientations. The leaves consisted of a length of wire sandwiched between two long rectangles of black paper. The wire allowed the leaves to be f o r m e d into a succession of 3 or 4 segments, each at a different and well-defined angle, and the leaves were lightly waxed to simulate more closely the surface properties of real vegetation. By photographing t h e artificial plants from above and from the direction of t h e mean wind vector, both the vertically and horizontally projected dimensions of each segment could be measured directly. The artificial plants were placed within a mature wheat crop (h = 1.0 m) 11.5 m downwind of a line source which released droplets with modal diameter 58 (-+ 2) #m for period o f 37 min. The droplet count on each segment of leaf was expressed as the fraction f of the total count on that leaf (see page 000). The correlation between f and the 'sedimentation parameter', lh wh, and between f and the 'impaction parameter', l~ w~, are shown in Table I as a function of height within the canopy. It is clear that sedimentation was the more i m p o r t a n t mechanism on leaves at all levels. T h e friction velocity was 0 . 3 3 m s - 1 : windspeeds much in excess of this might m o d i f y the results in Table I, but the conclusion that sedimentation was the d o m i n a n t mode of deposition on leaves was unlikely to alter, and was assumed to apply to all t h e experiments described later. If the assumption is made t h a t all deposition on leaves is by sedimentation, and all deposition on stems and ears (vertical surfaces) is by impaction, then from the data of two experiments where deposition was measured on

117 TABLE I

Correlation coefficients (r) between observed leaf deposit and the parameters lhwh (sedimentation) and Eilvw v (impaction)lwith modal drop diameter = 58 # m and friction velocity (above the canopy) = 0.33 m s Sedimentation

Impaction

Height relative to crop height

r

Significance level (%)

r

Significance level (%)

0.67 (+ 0.05)

0.70

0.2

0.36 (+ 0.05)

0.52

5

0.02

n.s.

--0.21

n.s.

0.13 (+ 0.05)

0.83

0.2

--0.18

n.s.

Overall

0.67

0.2

--0.12

n.s.

all parts of the plant, a graph can be constructed of the relative contribution to deposition by the two mechanisms, as a function of height within the canopy (Fig. 1). In order to avoid an infinite deposition density at ground level, soil deposition was arbitrarily assumed to occur uniformly in the first 5cm above ground. The graph indicates that impaction is as important as sedimentation in deposition to the whole stand of wheat. Although the smaller sedimentation component of Fig. l b is in part due to a smaller leaf area index, it is also consistent with an enhanced impaction rate, compared to Fig. la, due to the higher windspeed and hence higher impaction efficiency of the ears and stems. Even for a very young crop with a leaf area index of 0.5, impaction on the short erect leaves contributed as much to total deposition as soil deposition. (a)

Ib)

0.8

o8

0.6

05

O.h

02

0.2 ~ / / / / / / J f H ~ 1

2

I

2

3

Fractional deposition per unit volume of crop (m-1)

Fig. 1. Relative contribution to total deposition by sedimentation ( ~ ) and inertial impaction (U::::/) as a function of height within the canopy of a mature wheat crop: (a) L A I = 5.5, u , = 0 . 3 7 m s -1 (b) L A I - - 2.5, u , = 0 . 5 6 m s -1

t :18

Sedimentation A deposition velocity for sedimentation alone, v~, was calculated as vgs = D,/X where D~ is the deposition flux to leaves and soil and therefore the sedimentation flux. Legg and Price (1980) suggested that vg~ should be a function of u . , but the present data did n o t demonstrate this, at least not at typical values of u . . Out of three experiments, two showed no significant difference between Vgs and v~ with u . = 0.56 m s - ' ; the third showed vgs to be significantly tess than v~ at the 5% level with u. = 0.37 ms -~ . Combining the three experiments, the mean value of vgs/vs was insignificantly different from unity.

Impaction Wind tunnel experiments designed to measure impaction efficiency Ei usually involve exposure of an isolated target to a precisely defined windspeed and droplet dose. Such an experiment was carried out in the field on wheat plants within a complete crop, but isolated from the surrounding plants. The crop was in the 'early b o o t ' stage of development, when all leaves are fully expanded, but just before the ear emerges from t h e leaf sheath. The characteristic dimensions of each plant were measured from photographs taken along the direction of the mean wind. The analysis assumed that there was no aerodynamic effect of leaf inclinations, i.e. that a surface, width d, inclined at angle 0 to the wind vector, collected droplets with the same efficiency as a surface, width d sin 0, at right angles to the wind vector. Such an assumption is justified by the experiments of Gregory and Stedman (1953): for impaction on 0.5cm wide glass strips, at windspeeds less than 2 m s -1 , collection efficiency was proportional to sin 0. Because of their definition of efficiency, this result was attributable to the sinusoidal change in presentation area of the target, plus a much smaller change in efficiency with the smaller effective diameter of the target. The wind profile down to flag leaf height was measured by cup anemometers, but the below-canopy profile was estimated by extrapolation to ground. Because a small upwind area of crop had been cleared in order to give an unimpeded airflow towards the target plants, the best form of extrapolation was not obvious. For simplicity, a linear relationship was used: comparison of this with the most extreme possible wind profile (a fully developed logarithmic profile from ground level} suggested that the calculated impaction efficiencies would be uncertain by no more than 10% at z = 0.2h. The profile of airborne droplet dose was estimated f r o m the deposit on successive 5cm lengths of 6 . 3 m m diameter rods stuck verticaUy in the ground. Modal drop diameter was 55ttm. Figure 2 shows the results of t h e experiment, with the data averaged over equal logarithmic intervals of Stokes number Stk. Strictly, only impaction efficiencies relative to the rods could be inferred and absolute

119

I

.s m 0

Ti

Leo~ i

~°°

,,i

i

i

i

!

3

10

Stokes

Number,

2sold

Fig. 2. Impaction efficiency of unsheltered wheat plants in the field. The curve corresponds to the wind tunnel results of May and Clifford (1967) for deposition of droplets on cylinders.

accuracy of the Ei values in Fig. 2 depends on the accuracy of the May and Clifford (1967) results for rods. Leaves have been included because in this experiment, unlike that of Table I, the leaves were exposed to much higher windspeeds than t h e y normally encounter within a stand. Consequently, the conclusion that sedimentation was the dominant mode of deposition on leaves did not necessarily apply in this case and, indeed, the concentration of deposit around the narrow parts of the leaves signified that inertial impaction was the d o m i n a n t mechanism. Figure 2 gives some evidence that stems are more efficient collectors than leaves, a feature to be expected in the field, because leaves will tend to streamline themselves in gusts which would otherwise contribute a relatively large a m o u n t to deposition. However, the overall conclusion to be drawn from Fig. 2 is that on unsheltered wheat leaves and stems in the natural turbulence of field conditions, drops have impaction efficiencies substantially as predicted by wind tunnel studies. Shelter Factors

An analysis analogous to that of Fig. 2 was carried out on the observed deposition of plants within an undisturbed canopy. Airborne droplet dose was estimated by extrapolation of above-canopy profiles, in conjunction with below-canopy data from harp collectors and 6.3 mm cylinders. These measurements were made at the same downwind distances as the sampled plants, but not necessarily in their immediate vicinity. No measurements were made of leaf area projected in the vertical and horizontal directions, and the characteristic dimensions used in the calculations were the actual dimensions of the elements. The wind profile below the canopy was assumed (in this case) to follow an exponential form down to z = h / 2 , with a decay

120

~6

•

~;~em

Y '-

g

02

03

I

3 Sfokes

10

30

Number

Fig. 3. Ratio of observed to theoretical impaction efficiency for vertical surfaces of sheltered wheat plants asa function of Stokes number,

constant derived from Pereira and Shaw (1980). In accordance with pui> lished findings, u(z) was assumed constant below h/2. Figure 3 summarises a large b o d y of data f r o m three experiments, t w o in a mature crop for which LAI was 4.5 and 5.5 and the third in a young crop ( h - 4.5cm) with erect leaves and LAI = 0.5. In contrast to Fig. 2, the data are presented as the ratio of observed to theoretical impaction efficiency. In accordance with the findings above regarding mechanisms of deposition, mature teaves were n o t included. The graph shows that, compared to Fig. 2, impaction efficiency, at a given value of 8tk, was reduced b y an average factor o f between six and seven for ears and y o u n g leaves, and of a b o u t ten for stems. Impaction on ears and stems is unaffected b y orientation vdth respect t o w i n d direction, because they are symmetzical. The erect leaves of the y o u n g crop, however, could b e aligned at any angle between 0 and 90 ° t o the wind vector. With reference again to the results of Gregory and Stedman (1953), m e u u r e d impaction efficiency, Era, is approximately related to Et, t h e (required) value o f the impaction efficiency at ~ = 90 ° b y E m = El sin 0. Use of the physical leaf dimensions, in~ead of the projected leaf dimensions, means that for randomly distributed 8, Em as plotted on Fig. 3 will on average underestimate Ei by a factor s ~ 0 = 2/~ -~ 0.6. That is, a factor o f a b o u t t w o in the r e d u c t i o n o f the impaction efficiency f o r y o u n g lemves can he a c c o u n t e d for b y g ~ n e t r i c effects. The effect of s h e l t e r i ~ within a c a n o p y is t o redtwe the ~ vatue of E~ b e y o n d that due to a n y geometrical effects. Before examining in detail the relationship b e t w e e n ~ and leaf area, it is necema.~y t o evaluate the equivalent sheL~r__ ~ t o r applicgdde to sedimentation. The deposition velocity due to sedimeatation alone is vg,. The reletive c o n ~ i b ~ t i o n to vg, b y each leaf layer q u m t i f ~ s the sedimentation sheltea • factor, p : z, appropriate to that layer. For example, if all sedimentation flux was deposited

121 Sedimentation [ ~ SoiL Leaves 10 • \ ' -

T c~

06

ImpQct on

O

r~ Ears and stems

Soil only:p-I= e×p(-036L z)

0¢

02 o

o

2

~

Total plant area index between z and

6 h,

Lz

Fig. 4. Shelter factor p - 1 (z) for b o t h s e d i m e n t a t i o n and impaction, as a f u n c t i o n of cumulative plant area index b e t w e e n z and crop height.

on the top leaf layer, then p~l would be unity for the top layer and zero for all lower layers. One problem remains: p[1 is related, through vg,, to concentration at canopy height, while p~ 1 is related, through the calculation of Ee, to concentration at the actual height of measurement. The below-canopy wind profile was assumed to follow an exponential form. Horizontal dose equals xut, so should also decrease exponentially, or faster, if × is not allowed to increase with decreasing height. Measurements, however, rarely showed the dose falling exponentially below the canopy. More c o m m o n l y the dose fell only slowly in the top half of the canopy. The probable reason is that droplets reach lower levels not by gradient diffusion, but by occasional eddies sweeping into the canopy, the same mechanism that is responsible for a large fraction of the m o m e n t u m transfer to crops such as wheat (Finnigan, 1979). To avoid interference from surrounding leaves, the samplers were placed in less dense areas of the stand, and the dose indicated at all heights was probably closely coupled to the dose at h. Thus p~l was, in effect, as closely linked to conditions at h as was p[1. In Fig. 4 p-l(z), whether for impaction or sedimentation, is plotted against Lz, the cumulative leaf area index between h and z. An exponential relationship would be analogous with Beer's Law for the attenuation of direct radiation within a crop, with a constant attenuation coefficient similar to Bache's coefficient /3. However, with one exception, the data do not exhibit a simple exponential curve. The exception is soil, the data for which fitted the relationship p~l (soil) = exp (-- 0.36 Lz) with a correlation coefficient of 0.94. All other data showed a very sharp decrease in p - 1 immediately below the canopy, thereafter remaining constant at values typically around 0.1. Figure 4 also shows no systematic difference between p[ 1 and PT 1 for all plant data.

1.22

Bulk deposition Deposition velocity In the present experiments vg (zz) was calculated at values of x between 3.0 and 24.0m. ×(z~ ) was interpolated f r om s m o o t h e d profile data recorded at each value of x. z 1 was equal to h when the crop was fully established, and equal to 0 . 2 5 m above the ground when t he soil was bare or only sparsely covered with crop, this being the lowest level at which c o n c e n t r a t i o n could be estimated with reasonable accuracy. For comparison with ot her measurements o f deposition velocity at different reference heights, the calculated values were am e nde d by eq. 2. Although x was never large enough for the vertical profile o f c o n c e n t r a t i o n up to 5m to be fully developed, v~ (zz) f o r the various experiments did n o t show any systematic trend with x, but there was m o r e scatter at small values o f x. T h e t u r b u l e n t deposition velocity, vt : vg ( z l ) vs was significantly greater than zero at t he 10% level or less f o r all but one of the experiments. T h e exception was bare soil, for which vg had been evaluated at only one value of x. There was no significant correlation bet w een vt and u , , but this was largely due to the small range of u, values. T he m a x i m u m u . , 0.56 m s- 1, c o r r e s p o n d e d t o winds in t he field t hat averaged up t o 6 m s- 1 at 2m . With gusts of perhaps 2 to 3 times the mean wind, these conditions represented th e limit in which experiments could be satisfactorily performed. In contrast, the wind tunnel experiments of Chamberlain and Chadwick (1972) which have indicated a correlation between vt and u . , have forced u, as high as 2 m s -~ , and it was only these e x t r e m e points which (apparently) made significant their correlation between t he two velocities. Nonetheless Fig. 5 demonstrates the consistency be t w een the present results, amended ols

,,,

010

0 /×

A%

(~0S

01~} Frtc~'~on

velocity,

015

0 20

uQ lrn S~ )

Fig. 5. Comparison o f data o f this author (o) with the 'wet-e~op' data of Chamberlain and Chadwick (1972) for wind tunnel studies on wheat heads (x), and for field stffdies on wheat and barley (4) and on grass (e). T h e line is that o f Chamberlain and Chadwick with slope o f 0.10.

123

to a reference height of 0.6m above the zero plane, and the field and wind tunnel data of Chamberlain and Chadwick. For the present data, the average value of vt ( 0 . 6 m ) / u . , on the basis of the mean values for the 7 experiments, was 0.09 (+ 0.02). Figure 1 indicated that impaction and sedimentation made comparable contributions to total deposition. With a reasonable assumption that most impaction takes place at the top of the crop, the response of deposition velocity to windspeed may be predicted from v~ = vs + Ee u(h)

(5)

The effective impaction efficiency (Ee) of the upper part of the crop, can be expressed as Ee = Ei ( J ) P - ' L ( j ) where L is leaf area index and j refers to the different plant elements important to impaction. This last relationship, involving the product of p - 1 and L (j), suggests that E e might have a similar value over a wide range of crops. From the data for three experiments, E e was typically 0.05. Differentiating (5) with respect to u(h) and using the working relationship, (1/Ei) (dEi/du) = 1.5 exp (-- 1.1u), shows that dvg/du(h) would typically be around 0.02. This is equivalent to d v g / d u . of 0.06, comparable with the observed ratio, v t / u . of 0.09. Resistance Analogues Comparison of vt(z ~) with the 'deposition velocity' for m o m e n t u m , v~ = u2./u(zl ) is more rationally done in terms of resistances, vm is the reciprocal of rm ( z l ) , the resistance to m o m e n t u m transfer between the height zz and the apparent sink of m o m e n t u m within the crop. The diffusive resistance to droplet transfer can be regarded as the sum of two resistances, r~op = rm + rb = v-[ 1 where rb, the 'bluff-body' resistance, takes account of the fact that m o m e n t u m transfer by pressure forces has no analogue in droplet transfer. The use of rm assumes that the turbulent transfer of droplets is similar to that of m o m e n t u m . Thus rb = v~l _ v ~ l

(6)

Table II summarizes the calculated exchange parameters for the seven experiments. For smooth surfaces, where m o m e n t u m transfer is mainly by skin friction, r b would be expected to be small and, indeed, for the two experiments with zero or very little ground cover, rb was not significantly different from zero. The predicted deposition velocities of Sehmel and Hodgson (1976) apply to this 'smooth surface' condition, and Fig. 4 of that paper states that vg = v s for D d - - 5 0 p m and u . = 0 . 5 m s - I . This, however, was not confirmed by experiment 2 for which vg(zl ) was significantly different from vs at the 5% level of significance. For the other 5 experiments with a mature crop, rb showed some variability, but the mean value 7 b = 18 s m- 1 (std. error 10 s m- 1 ) was significantly greater than zero at the 10% level. In comparison to other resistances, 7b was similar to the resistance to m o m e n t u m transfer between 2 m and the zero plane.

Bare soil

Young wheat

Matttre Wheat

Mature wheat

Mature wheat

Mature wheat

Mature wheat

1

2

3

4

5

6

7

1,00

1.00

1.00

0.80

0.80

0.08

0.00

0.105

0.105

0.066

0.049

0.049

0.070

0.073

vs

(m s- 1 )

h

(m)

t J f r b i s determined from measurements of vg, v m at zl •

tn is the numer of independent determinations of vg.

Surface

Expt. No.

T A B L E II Droplet exchange parameters u,

0.39

0.33

0.56

0.56

0.37

0.56

0.50

( m s -1 )

5

5

5

4

4

4

1

n¢

1.00

1.00

1.00

0.80

0.80

0.25

0.25

(m)

z{

0.21 (+ 0.05)

0.16 (2 0.03)

0.21 (± 0.05)

0.073 (+ 0.007)

0.068 (+ 0~09)

0.17 (+ 0.04)

0.20 (± 0.10)

--1

9

-1

35

46

--2

--13

rb CT

( s m -1)

vg (zl )

(ms-')

0.15 (± 0.03)

0.16 (± 0.03)

0.15 (+ 0.03)

0.068 (± 0.006)

0.059 (± 0.005)

0.12 (-+ 0.02)

0.14 (-+ 0.07)

vg (0.60m) ( m s -1 )

125 DISCUSSION AND CONCLUSIONS This paper has presented measurements from field experiments of droplet deposition. Such measurements are often characterised b y large variability, b u t three main aspects of the experimental technique made major contributions to the reproducibility of the results. The first was the use of a line, rather than a point source, which removed much of the data variability due to fluctuations of wind direction. The second was the use of averaging times of up to half-an-hour, thereby ensuring adequate sampling of the b o u n d a r y layer turbulence. The third was the replication of measurements, each estimate of vg being based on up to 270 measurements of deposition on individual plant segments. More detailed information on below-canopy windspeed would have improved the measurements, but, as suggested b y the studies of other workers (e.g. Legg and Long, 1975) and also b y the present measurements, information a b o u t gust would be as important as windspeed. Beer's Law, in the form applied to radiation within a canopy describes the mean radiant energy crossing layer z per unit horizontal area. The a t t e m p t to model the shelter factor p - ' at different levels within the stand according to Beer's Law worked only for soil below a canopy, probably because only for soil (a flat plane of unit area index) would the relationship between aerosol dose (analogous to radiation) and deposition be direct. For leaves, on the other hand, the relationship between aerosol dose and actual deposition depends on the additional factors of leaf orientation, area index and airflow. Beer's Law is based on straight line paths through a canopy. The fact that the attenuation coefficient for vegetation above soil, 0.36, should be similar to 'shape factors' governing the attenuation of direct radiation, typically in the range 0.2--1.1 (Monteith, 1973, p57) lends support to the hypothesis that much aerosol, travelling on large eddies follows a straight trajectory from entering the crop to point of deposition. In the spraying of pesticides, it has always been difficult to achieve penetration of a canopy. Two approaches are current. The first is to use very large droplets with diameters of a few hundred micrometres which fall through the canopy. The second is to use very large numbers of very small droplets, with diameters less than 100pro, which can still reach lower levels in large numbers. Unfortunately, at the t o p of the canopy, relatively high windspeeds favour impaction and large leaf areas favour sedimentation. These conditions always act to intercept a large fraction of the aerosol irrespective of droplet size. However, small droplets seem to have two distinct advantages: first they can 'ride' the large eddies that penetrate the crop, and second, they can be produced in far greater numbers from a given volume of liquid. The hypothesis that most droplet deposition within the canopy occurs in episodes of above average windspeed has some repercussions for Fig. 3, which was based on the assumption that windspeed decreased exponentially with depth within the canopy. If the windspeed effective for deposition was

126

u(h) at all depths, then the ratio of observed to theoretical impaction ef, ficiency would be reduced typically b y a factor of 0.7. Figure I showed that sedimentation and impaction are likely to be of equal importance to deposition of 3 0 - - 6 0 # m droplets in wheat. Combination of this finding with the detailed impaction efficiencies allowed a theoretical prediction of the windspeed dependence of Vg to be made, and this was found to agree with measurements. The concept of a deposition velocity remained valid even at such short range from the source as 4m, as long as X was measured very near the t o p of the crop. The results for deposition velocity may be summarised b y vg(0.60m) = v, + 0.1u. which is also consistent with Chamberlain and Chadwick (1972). Bluff-body resistance was found to have the realistic value of 18 s m -1 , larger than that normally found for, say, water vapour exchange; but of course this reflects a major difference between the transfer of the t w o properties. Molecules reach a surface ultimately b y Brownian diffusion, a mechanism that is negligible for droplets of the size used here. Indeed, a bluff-body formula based on vapour exchange (Chamberlain, 1968) predicted quite unrealistic values of rb • However, insofar as rb simply quantifies a difference in resistance between the turbulent transfer of droplets and m o m e n t u m , the concept remains valid for aerosols. ACKNOWLEDGEMENTS This work was funded b y the Natural Environment Research Council. The authors wish to thank D.E. Aylor for suggestions regarding experimental discrimination of deposition mechanisms.

REFERENCES Aylor, D.E., 1975. Deposition of particles in a plant canopy. J. Appl. Meteorol., 14: 52--57. Bache, D.H., 1979. Particle transport within plant canopies, If. Prediction of deposition velocities. Atmos. Environ., 13: 1681--1687. Bache, D.H., 1981. Analysing particulate deposition to plant canopies. Atmos. Environ., 15: 1759--1761. Bache, D.H. and UK, S., 1975. Transport of aerial spray, II. Transport within a crop canopy. Agric. Meteorol., 15: 371--377. Belot, Y., Baille, A and Delmas, J.L., 1976. Modele numerique de dispersion des polluants atmoapherique en p ~ n c e de couverts vegetaux. Atmoa. Environ., 10: 89-98. Callander, B.A., 1982. Simulation of a line source by a moving-point source of droplets, I. Theory. Atmos. Environ., 16: 1823--1827. Callander, B.A. and Unsworth, M,H., 1982. Simulation of a line source by a movingpoint source of droplets, IL Practice. A t r n ~ Envlron., 16: 1829-1833. Chamberlain, A.C., 1968. Transport o f g a ~ s to and from surfaces with bluff and wavelike roughness elements. Q.J.R. Meteorol. Soc., 94 : 318--332.

127 Chamberlain, A.C., 1975. The movement of particles in plant communities. In: J.L. Monteith (Editor), Vegetation and the Atmosphere, Vol. 1. Academic Press, London, pp 155--203. Chamberlain, A.C., 1976. Transport of Lycopodium spores and other small particles to rough surfaces. Proc. R. Soc. London, Ser. A: 296: 45--70. Chamberlain, A.C. and Chadwick, R.C., 1972. Deposition of spores and other particles on vegetation and soil. Ann. Appl. Biol., 71: 141--158. Davidson, C.I. and Friedlander, S.K., 1978. A filtration model for aerosol dry deposition: application to trace metal deposition from the atmoshpere. J. Geophys. Res., 83: 2343--2352. Doran, J.C., 1977. Limitations on the determination of deposition velocities. Boundary-Layer Meteorol., 12: 365--371. Finnigan, J.J., 1979. Turbulence in waving wheat, I. Mean statistics and honami. Boundary -Layer Meteorol., 16: 181--211. Fuchs, N.A., 1964. The mechanics of aerosols. Pergamon Press, London, 408 pp. Green, H.L. and Lane, W.R., 1957. Particulate Clouds: Dusts, Smokes and Mists. Spon, London, 425 pp. Gregory, P.H. and Stedman, O.J., 1953. Deposition of air-borne Lycopodium spores on plane surfaces. Ann. Appl. Biol., 40: 651--674. Legg, B.J. and Long, I.F., 1975. Turbulent diffusion within a wheat canopy, II. Results and interpretation. Q.J.R. Meteorol. Soc., 101: 611--628. Legg, B.J. and Monteith, J.L., 1975. Heat and mass transfer within plant canopies. In: D.A. de Vries and N.H. Afgan (Editors), Heat and Mass Transfer in the Biosphere, Part 1. Scripta Book Co., Washington, pp 167--186. Legg, B.J. and Price, R.I., 1980. The contribution of sedimentation to aerosol deposition to vegetation with a large leaf area index. Atmos. Environ., 14: 305--309. May, K.R., 1945. The cascade impactor: an instrument for sampling coarse aerosols. J. Sci. Instrum., 22: 187--195. May, K.R. and Clifford, R., 1967. The impaction of aerosol particles on cylinders, spheres, ribbons and discs. Ann. Occupational Hyg., 10: 83--95. Monteith, J.L., 1973. Principles of Environmental Physics. Arnold, London, 241 pp. Pereira, A.R. and Shaw, R.H., 1980. A numerical experiment on the mean wind structure inside canopies of vegetation. Agric. Meteorol., 22 : 303--318. Raynor, G.S., 1976. Experimental studies of pollen deposition to vegetated surfaces. In: G.A. Sehmel (Editor), Atmosphere--Surface Exchange of Particulate and Gaseous Pollutants. U.S. Atomic Energy Commission Syrup. Series, CONF--740921, NTIS: 265 279. Rosinski, J. and Nagamoto, C.T., 1965. Particle deposition on and reentrainment from coniferous forests, I. Experiments with trees. Kolloid Z., 204: 111--119. Seginer, I., Mulhearn, P.J., Bradley, E.F. and Finnigan, J.J., 1976. Turbulent flow in a model plant canopy. Boundary--Layer Meteorol., 10: 423--453. Sehmel, G.A., 1980. Particle and gas dry deposition: a review. Atmos. Environ., 14: 983--1011. Sehmel, G.A. and Hodgson, W.H., 1976. Predicted dry deposition velocities. In: G.A. Sehmel (Editor), Atmosphere--Surface Exchange of Particulate and Gaseous Pollutants. U.S. Atomic Energy Commission Symp. Series., CONF--740921, NTIS: 399--422.