Probabilistic calculation of aquatic exposure via spray drift
3 Probabilistic
exposure calculation
3.2.5 Concentration
of the pesticide in the ditch
3.3 Summary of assumptions and sources of uncertainty and variability
Exposure is calculated for instantaneous concentrations arising from spray drift impacting on agricultural ditches. The exposure distribution expresses the variation in concentrations of the pesticide in the water column of agricultural ditches resulting from variability in individual spray events and variability in the morphology of individual ditches. Uncertainty in the calculation is expressed using confidence intervals around the median distribution of exposure concentrations.
The assessment is based on the conceptual model depicted below. Exposure of individual ditches is calculated for single spray events with a model describing the influence of landscape features.
Conversion of the conceptual model into mathematical form is described in Section 3.2. A summary of the sources of variability and uncertainty included and excluded in the assessment is given below.

Considered 
Not considered 
Variability 
Measured drift generation and deposition
under reference conditions 
Deviations from reference spray drift
conditions (e.g. wind speed and direction, boom height, nozzle type, speed of
tractor) 

Distance from edge of sprayed area to water 
Variation in deposition across the water
surface 

Dimensions of the water body 
Volume of water in the ditch at application 
Uncertainty 
Sampling uncertainty in drift experiments Interception of spray drift by bankside
vegetation depending on type, height and density of vegetation, crop and boom
height, width of vegetated strip etc. 
Measurement bias in drift experiments Deviation of deposition on a surface below
ground level from measured deposition at the same level as the treated area 

Errors in application rate (e.g. tank
filling, machine calibration) 
Interception by riparian vegetation or
aquatic plants 


Reduction in initial exposure concentration
due to sorption to sediment or macrophytes Errors in measuring ditch and bankside
properties Bias in sampling of ditches 


Uncertainty in vertical distribution of
pesticide within the water column Uncertainty in sprayed area relative to
edge of crop 


Uncertainty in extrapolating the results to
a broader landscape 


Model error for exposure model 


Uncertainties in MonteCarlo sampling 
Probabilistic risk assessment aims to show the effects of variability and uncertainty on the assessment. Variability is an inherent property of natural systems and cannot be reduced by further measurement. Uncertainty is, crudely, the sum of what we do not know; it includes, for example, sampling bias, measurement error, inadequate descriptions of processes in a model, phenomena which remain unknown and/or unquantified etc.
Methods for propagating uncertainty
Exposure concentrations are calculated
using using a model coded in MATLAB v8. Selected sources of uncertainty and
variability are accounted for in the modelling of exposure. Uncertainty and
variability are separated out by 2D
Some of the factors considered in the exposure model are both variable and uncertain (e.g. interception of spray drift by each type of bankside vegetation). It is, however impossible to separate uncertainty and variability due a lack of information. In this case, all variation is classified as uncertainty and considered in the outer loop.
Advantages of 2D
Disadvantages:
Methods for representing dependencies
and model uncertainty
In this study, uncertainty in the calculation is expressed using confidence intervals around the median distribution of exposure concentrations. The confidence interval(s) to be reported is a user input. The 95%^{ }confidence interval has often been used in communicating results from uncertainty analyses. However, other percentiles can be derived and reported as required.
Predicted environmental concentrations from spray drift are usually calculated for ditches because they have limited potential for dilution of residues and calculations are based on several worstcase assumptions. The standard exposure assessment method in Europe for a single application without any nospray buffer restrictions assumes: (i) a treated area 1 m away from a static ditch with vertical sides in which the water column is 1 m wide and 30 cm deep; (ii) wind blowing towards the ditch and at right angles to it at a constant 2‑5 m/s; (iii) 90^{th} percentile drift deposition (Rautmann et al., 2000) over the entire width of the ditch; and (iv) no vegetation in the strip between the treated crop and the edge of the water. This scenario probably represents a reasonable worstcase in that such situations may be found in agricultural landscapes. However, there are also many circumstances under which such conditions do not occur, and where exposure is much less.
The probabilistic assessment of exposure concentrations in natural agricultural landscapes is designed to account for the uncertainty and variability in ditch geometry and pesticide deposition. Uncertainty and variability in the measurement of spray drift are separated by analysing the distribution of replicate results within experiments (taken as uncertainty) and between experiments (taken as variability). Additionally, uncertainty associated with application rate (e.g. error in tank filling or in machine calibration) and interception by the bankside vegetation are characterised using available data and expert judgment.
The methodology is exemplified for clay landscapes, based on data from the vicinity of Coleshill in Oxfordshire. This is one of four landscapes implemented into the WEBFRAM software. General data inputs are the same for the other three landscapes, though specific values differ and are available by viewing the relevant distribution data within the software.
A probabilistic
assessment of concentrations of the pesticide is carried out for ditches within
the Coleshill catchment in
The uncertainty
considered in the exposure assessment for the Coleshill landscape includes (1)
errors in the application rate of the pesticide, (2) uncertainty in the amount
of pesticide intercepted by the bankside vegetation and (3) uncertainty in
measured drift generation and deposition. The variability considered includes
(1) variations between ditches in distance to treated fields, and in morphology
and (2) variation in drift deposition.
Figure 1. Conceptualisation
of the field surroundings and receiving ditch
a_{l} = left bank width to
freeboard a_{r}
= right bank width to freeboard
b_{l} = left bank height from
freeboard b_{r}
= right bank height from freeboard
c = freeboard width d
= freeboard height (includes water)
e = water width f = water depth
h = top width (total width from lowest
bank) i = bottom width
k = distance from top of bank to edge
of water l = length of water body
l and r subscripts refer to left
and right bank
m =
distance from edge of field to top of bank
The conceptualisation of the water body receiving the drift input and the surrounding field is shown in Figure 1. Detailed field measurements of the geometry of water bodies in the Coleshill catchment have been made for 25 ditches for DEFRA project PS2304. These measurements included bank width and height, water width and depth, freeboard width and height, top and bottom width. The length of the water body (l) is adjusted such that the surface area at water level corresponds to 1 m^{2}. The remaining model input variables are calculated from:
Distance from top of bank to edge of water (k) = 0.5 (c – e) + a
Distance from edge of field to near edge of water (z1) = k + m
Distance from edge of field to far edge of water (z2) = z1 + e
Water volume = [i × f + ((ei) × f)
/ 2] x l
Ditches which contained no or very small volumes of water (depth £ 1 cm) just after a significant rainfall event are excluded from the analysis (6 ditches). The width of the left bank of the remaining 19 ditches differed from the dimensions of the right bank. Each side is considered a separate measurement giving a total of 38 sets of data. One of the 38 ditch sides is sampled randomly in each of the model iterations (all values are given equal weight). The measured and calculated variables describing the geometry of the sampled ditch are used in the drift calculations.
Data on the distance from the edge of the field to the top of the bank of the ditch are available from a GIS analysis of aerial photographs within the Coleshill catchment. Where a field is located on both sides of the ditch, each side is considered separately. This results in a total of 156 data records. Each ditch is sampled with a frequency weighted according to its length. The distance from the field to the top of the bank for this ditch is then used in the calculations.
Mean (integrated) drift deposition across the width of the water body is calculated according to the algorithm presented by FOCUS (2001):
_{}
where z1 and z2 are the distance from the edge of the treated field to the near and far edge of the water body, respectively, and A and B are regression constants.
The distances z1 and z2 are derived from measured data and GIS analysis as described above. The calculation of the regression constants A and B is based on measured drift data provided by Rautmann et al. (2001). The authors measured deposition in a number of experiments at different distances from the edge of a field cultivated with arable crops. Each experiment consisted of 510 replicates. A lognormal distribution is fitted to the mean values for all experiments at each individual distance. The means of these lognormal distributions are then plotted against distance. A power law function is fitted to the data (Figure 2). This results in values for A and B of 1.246 and ‑0.938, respectively.
Figure 2. Power
law function (▬) fitted to the mean values of the lognormal distributions
of measured drift losses at each distance (p)
Initial values for drift at z1 and z2
The percentage drift at the closest edge of the water D(z1) _{initial} and at the far edge of the water D(z2) _{initial} are calculated from the power law function.
Uncertainty in
drift deposition at each distance
Drift deposition is considered to be both variable and uncertain. The difference between replicate measurements for each trial is considered to represent uncertainty (e.g. from measurement error) whereas differences between the experiments are considered to reflect variability (e.g. from differences in wind speed or in nozzle performance). A subset of data is analysed to characterise the uncertainty in the lognormal distributions fitted to the average values for each experiment at each distance (see above). Drift at 5 m distance has been measured in a total of 50 experiments. Between 5 and 10 replicate measurements were made for each trial. One of these replicates is randomly sampled from each study using the Crystal Ball software. This procedure is repeated to give 50 combinations of 50 randomly sampled values. Lognormal distributions are fitted to each of the 50 sets of data. The mean and coefficient of variation (CV) of each distribution are recorded and basic statistics calculated:

Mean of lognormal distribution at 5 m distance 
CV of lognormal distribution at 5 m distance 
n 
50 
50 
Min 
0.2600 
57.6 
Max 
0.3961 
119.0 
Average 
0.3062 
82.0 
Stdev 
0.0236 
9.1 
CV (%) 
7.71 
11.1 
It is assumed that the uncertainty in the mean and the CV of the lognormal distributions at all distances is the same as at 5 m distance.
The uncertainty of the mean of the lognormal distribution at each distance is taken into account by sampling from a normal distribution in the outer loop. The standard deviation of this distribution is set to 7.71% of the mean drift loss at each distance. This resulted in a new sampled mean at each distance.
The uncertainty of the coefficient of variation of the lognormal distribution at each distance is also considered by sampling from a normal distribution in the outer loop. The mean of this distribution is set to 11.1% of the mean coefficient of variation at each distance. A new standard deviation is calculated from the sampled mean and the sampled coefficient of variation at each distance.
Individual mean values and standard deviations are sampled in each iteration of the outer loop, giving x lognormal distributions at each distance.
Final values
for drift at z1 and z2
A value for drift loss is sampled from the updated lognormal distribution in the inner loop (a userspecified number of runs for each of the x iterations in the outer loop) to express uncertainty in the drift curve. The new drift loss at each distance is compared with the initial value. The percentage drift at distance z1 is then scaled using the ratio for the distance closest to z1.
D(z1) final = D(z1)_{ initial} x [D(closest distance) _{final} / D(closest distance) _{initial]}
Drift at z2 is scaled using the same ratio as for z1.
The parameters of the power law equation are then recalculated from the new values for D(z1) and D(z2). Drift deposition over the total width of the water column is integrated using the updated parameters.
The percentage of applied pesticide that is
discharged into the ditch is multiplied by the application rate and corrected
for interception by the bankside vegetation (see Section 3.2.4).
The target application rate of the pesticide is a user input. The actual application rate is, however, uncertain. Possible sources of uncertainty include: errors in the concentration of active substance within the formulated herbicide product, errors in measuring the product and filling the tank, and uncertainties related to application technology (e.g. mixing in tank, pressure at nozzle, speed of the tractor, machine calibration). The rate of pesticide actually applied is assumed to be normally distributed with a mean set to the target rate . The 2.5^{th} percentile and the 97.5^{th} percentile of the distribution are assumed to correspond to the mean application rate ± 5% (e.g. for a target rate of 1500 g a.s./ha, the 2.5^{th} and 97.5^{th} percentile are 1425 and 1575 g a.s./ha, respectively).
Interception of spray drift by bankside vegetation
is a significant process which is also very difficult to quantify. The amount
intercepted depends on a large number of factors including the height of the
vegetation in relation to the height of the spray boom, the type and density of
the vegetation, the width of the vegetated strip and its distance from the
field and from the edge of the ditch. Only limited data are available in the
literature on the influence of these factors on interception. Interception
within the Coleshill catchment is, thus, considered to be highly uncertain.
This uncertainty is included in the outer loop of the 2D
The ditches in the Coleshill catchment have
been categorised for Defra project PS2304 according to the type of features
present in the zone between the field and the ditch (Table 2).
Table
2. Description
of features present in the zone between the field and the ditch
Feature 
Code 
Description 
Buffer strip 
B 
Bare, grassy or low scrub area: default
area assumed to surround other certain features or to exist on its own 
Track 
T 
An unsurfaced track suitable for farm
vehicles: effectively a low buffer 
Hedge 
H 
Hedge 
Setaside 
S 
An area at least 5 metres wide left as a
strip of deliberately uncultivated land, either due to agricultural practice
or due to the land being unsuitable for agriculture: low vegetation 
Wooded strip 
W 
Shrubby or tree area: does not include
widely spaced planted trees 
Fence 
F 
A fence, probably wooden, creating a
reasonably large obstruction to drift: simple wire fences not included 
Bank 
K 
A bank where the top is significantly
raised with respect to both the ditch and the field 
Seven combinations of the above features
have been identified as specific drift zone types for the Coleshill catchment
(Table 3). Each ‘type’ represents a single side of the ditch. The approximate length of each
ditch is estimated using GIS analysis of aerial photographs.
Table 3. Categorisation
of drift zones present in the Coleshill catchment and total length of ditches in each category estimated by GIS
analysis
Zone

Feature 
Length
(m) 
type 
combination 

I 
B 
16739 
II 
BTB 
1823 
III 
BHB 
7588 
IV 
BHTB 
1991 
V 
BSB 
314 
VI 
BHSB 
343 
VIII 
WB 
2671 
Io 
overgrown* 
462 
Total 

31931 
* an overgrown buffer is where the ditch is
not distinguishable from the surroundings on the aerial photograph due to
complete cover by dense woody vegetation (e.g. bramble / sallow)
Each
ditch category is sampled with a relative frequency that corresponds to the
ratio of the length of ditches in that category and the total length of all
ditches. Interception is then sampled from distributions assigned to each drift
zone category (Table 4). The presence of hedges or wooded strips is considered
to increase interception relative to grassed buffer strips on their own. Hedges
are also assumed to reduce pesticide losses to a larger extent than wooded
strips due to their larger density. Tracks or setaside land with no or very
short vegetation are assumed not to have any additional effect on interception.
Table 4. Distributions
describing the uncertainty in interception by features present in the zone between the field
and the ditch

Category^{a} 
Featurespresent^{a} 
Type
of distribution^{b} 
Minimum Reduction (%) 
Median
/ likeliest value (%) 
Standard
deviation 
Maximum Reduction (%) 
Buffer
strip (on its
own or in combination with a track or setaside land) 
I II V 
B BT BS 
Lognormal 
0 
30 
13.1 
85.00 
Hedge (in
combination with a buffer and either a track or setaside land) 
III IV VI 
BH BHTB BHSB 
Inverse
lognormal 
20 
90 
11.4 
99.99 
Buffer +
Wooded strip 
VIII 
WB 
Inverse
triangular 
15 
70 

99.99 
Overgrown
ditch 
Io 

Inverse
lognormal 
20 
80 
12.8 
99.99 
^{a}
For definition of features and categories see Tables 2 and 3
^{b} A distribution is assigned to the percentage NOT intercepted and interception calculated thereafter as 100 minus sampled value
The amount of pesticide discharged into the water body is calculated from the percentage drift loss, the application rate and interception. The load is then divided by the volume of the water column (1 m^{2} surface area) to give the concentration of the pesticide in the ditch.
Results from the probabilistic calculation should be considered in the light of the simplifying assumptions made:
·
Exposure of
surface waters via spray drift is calculated for a single 100 km^{2}
area in the
· The assessment refers to fields sown with the target crop and assumes that every field is treated at the maximum target rate and has ditches adjacent (and is therefore an overestimate). The assessment also assumes that treated ditches are a random selection of all ditches. Ditches not adjacent to the target crop will have different exposure (other crops treated with the pesticide at different rates) or no exposure (no treated crops). Wind is blowing in one direction such that deposition of spray drift only occurs from a single side of the ditch at any one time.
· The amount of pesticide applied is assumed to be uncertain (errors in tank mixing, machine calibration etc.) and to follow a normal distribution with 95% of the values being within ± 5% of the target application rate. This range is defined using expert judgement.
· Variability and uncertainty in the calculation of exposure via spray drift are differentiated using 2D Monte Carlo simulation. Drift generation and deposition are calculated on the basis of experiments by Rautmann et al. (2001). The authors measured deposition in a number of experiments at different distances from the edge of a field cultivated with arable crops. Each experiment consisted of 510 replicates. Differences between the replicates are considered to represent uncertainty due to measurement error and smallscale spatial variability in drift deposition. Differences between the experiments are considered to reflect the variability in measured drift generation and deposition under reference conditions. Uncertainty and variability are separated by analysing data for 5 m drift distance (for details see Section 3.2.2). It is assumed that the uncertainty is the same at all distances. Differences between the variability at different distances are considered.
· The effect of deviations of drift conditions at the time of application from reference spray drift conditions (e.g. wind speed and direction, boom height, nozzle type, pressure at nozzle, speed of tractor) on relative drift losses is not factored into the assessment. However, the uncertainty in the application rate arising from these factors is considered.
· The experiments by Rautmann et al. (2001) measured drift deposition onto a flat surface at the same level as the cropped area. Deposition on a water surface that is below ground level may differ from that in the experiments. This source of uncertainty is not considered.
· The variability in the measured depth of water present in the ditch is taken into account. However, differences between water depth at the time of the field survey and the time of application are not considered.
· Interception of spray drift by bankside vegetation is highly variable and uncertain. Little information exists of the influence of vegetation type, height, density, spray boom height relative to crop height and the width of the vegetated strip on interception. In this study, interception is sampled from distributions which are defined by expert judgement (with regard to the available literature). The presence of hedges or wooded strips is considered to increase interception relative to grassed buffer strips on their own. Hedges are also assumed to reduce pesticide losses to a larger extent than wooded strips due to their greater density. Tracks or setaside land with no or very short vegetation is assumed not to have any additional effect on interception.
·
The exposure assessment considers the instantaneous
concentration of pesticide in the ditch arising from drift deposition. The
pesticide is assumed to be completely mixed with the
entire volume of the ditch. However, the deposition of pesticide decreases with
increasing distance from the treated area and is thus smaller at the far side
of the ditch than at the near side. The chemical is deposited at the water
surface leading to higher initial concentrations in a thin layer of water. In
stagnant water bodies, the time required for a complete mixing may be
relatively long and concentrations at certain points within the ditch may
differ from those calculated here for considerable periods of time. Any
sorption of the pesticide to sediment or macrophytes is ignored in the
calculation of initial PEC values. This introduces errors into the assessment
and leads to a conservative estimate of exposure concentrations.
The main sources of variability and uncertainty included and excluded in the calculation of exposure are summarised in Section 2.1.