Original Research

L. Weihermüller*
R. Kasteel
J. Vanderborght
J. Šimůnek
H. Vereecken

Uncertainty in Pes cide Monitoring
Using Suc on Cups: Evidence from
Numerical Simula ons
Knowledge of the spatial and temporal distribution of pesticide concentrations is essential
for pesticide registration. In field experiments performed during the registration procedure,suctions cups are widely used to monitor the evolution of pesticide leaching over time andto calculate the mean concentration for a given drainage period. Until now, there has been
no detailed information regarding whether soil water sampling by suction cups is suitable
for accurately predicting the field-scale leaching of pesticides in heterogeneous soils. To
address this, we performed a numerical study to evaluate the uncertainties associatedwith suction cup sampling in heterogeneous soils under atmospheric boundary conditions
using two pesticides with contrasting sorption and degradation properties. To address thetwo main operation modes of suction cup sampling, continuous and weekly sampling wereanalyzed. First, the variability of pesticide breakthrough concentrations was analyzed fora single pesticide application in a physically heterogeneous soil profile. Second, a 10-yrtime series was used to analyze repeated pesticide applications, and estimate variability inthe leached mass fraction (LMF) and mean concentrations. In both cases, pesticide breakthrough was compared to the breakthrough of an inert tracer. The results indicate that fora single pesticide application, pore water velocities varied only slightly for all operation
sampling modes and compounds. On the other hand, the total extracted mass and LMF
varied greatly, suggesting that the acceleration of the breakthrough sampled by suction
cups plays an important role in terms of LMF and the mean concentration, especially for
degradable substances.
Abbreviations: BTC, breakthrough curves; CDE, convection–dispersion equation; LMF, leached mass fraction; PPP, plant protection product.

Numerical simulations in a heterogeneous media were used to estimate
the uncertainty of pesticide sampling by suction cups under transientboundary conditions. The results
indicate that the variability of thederived concentrations and leachedmass fractions highly depend on thephysico-chemical characteristics ofthe pesticides.

L. Weihermüller, R. Kasteel, J. Vanderborght,
and H. Vereecken, Agrosphere Inst. IBG 3,
Forschungszentrum Jülich GmbH, 52425
Jülich, Germany; J. Šimůnek, Dep. of Environmental Sciences, Univ. of California Riverside,
Riverside, CA 92521. *Corresponding author(l.weihermueller@fz-juelich.de).
Vadose Zone J. 10:1287–1298
doi:10.2136/vzj2011.0017
Received 15 Feb. 2011.
Posted online 31 Aug. 2011.
© Soil Science Society of America
5585 Guilford Rd., Madison, WI 53711 USA.

All rights reserved. No part of this periodical may
be reproduced or transmi ed in any form or by anymeans, electronic or mechanical, including photocopying, recording, or any information storage andretrieval system, without permission in writing fromthe publisher.

2011, Vol. 10

Risk assessments of pesticide leaching into the groundwater have become required
to a greater and greater extent in the recent past. In the European registration procedure
for plant protection products (PPP), a tiered approach, with respect to the estimation ofgroundwater contamination, has been established. In the third tier, evidence relevant toauthorization must be provided (in particular evidence using lysimeter studies or field
experiments) regarding the possibility and extent of groundwater contamination by a PPP
after its application while using good agricultural practice (Winkler et al., 1999).
Various methods are available to monitor the transport and leaching of PPPs in the vadosezone. The most common is the lysimeter concept (Führ et al., 1998). For experiments at thefield scale, soil coring or in situ sampling using capillary wicks, porous plates, and suction
cups is used. The advantage of in situ sampling systems is the high temporal resolution ofsolute extraction at different depths or horizons (Weihermüller et al., 2007). In particular,
suction cups play an important role in PPP monitoring due to their easy installation andlow cost and have therefore been used and studied widely. In general, most scientists havefocused on the alteration of the soil solution sampled by suction cups by chemical processes,
such as sorption and desorption of PPPs, as well as fi ltering effects (e.g., Grossmann andUdluft, 1991; Wessel-Bothe et al., 2000; Weihermüller et al., 2007). However, Dorrance
et al. (1991) have already stated that the chemical alteration of the sampled soil solution
may be less significant than variability in extracted soil water concentrations due to soil
physical heterogeneities, changes in the natural water flow field, and/or preferential flow.
During the last few years, various numerical approaches for characterizing and interpreting measured data from various sampling devices, including lysimeters, suction cups,
porous plates, and wick samplers, have been published (e.g., Tseng et al., 1995; Wu etal., 1995; Flury et al., 1999; Abdou and Flury, 2004; Köhne, 2005; Mertens et al., 2005,
2007; Weihermüller et al., 2005, 2006; Boesten, 2007; Kasteel et al., 2007). All of these

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approaches have clearly shown that numerical modeling is a
powerful tool for designing efficient experimental setups and for
obtaining better understanding of the effects of the sampling procedure on collected results in natural soils.
Vanderborght and Vereecken (2007) showed that the use ofdifferent sampling systems may greatly influence the apparent
spreading of reactive substances estimated from breakthroughcurves (BTC), compared to the theoretical dispersivities calculated from the flow rate and the actual water content. They also
stated that spreading can be related to the soil volume sampled
by the method. Weihermüller et al. (2005) presented the resultsof numerical experiments by analyzing water extraction using
a suction cup and found that these samplers only extract water
locally, so that only a small fraction of the total cross-sectional
area is sampled, even when a large number of samplers is used. As
a consequence, BTCs determined using local measurements may
deviate from the averaged BTC or average solute fluxes at thesame depth (Weihermüller et al., 2005, 2006). On the other hand,since suction cups also influence the natural flow field (Warrickand Amoozegar-Fard, 1977), natural pore water velocities anddispersivities may deviate from those calculated from suction-cupderived BTCs (Weihermüller et al., 2005, 2006).
One major disadvantage of the published work analyzing suction
cup samplers thus far (e.g., Tseng et al., 1995; Weihermüller et al.,2005, 2006), is that only steady-state flow conditions and nonreactive solutes have been considered. Therefore, we expanded thesesimulations to compounds with different physicochemical properties and more realistic transient upper boundary conditions to
examine the effect of soil heterogeneity on the BTCs measured
by suction cups. To be comparable to already published work (e.g.,
Boesten, 2007) and with already existing scenarios that are used
to assess pesticide leaching for registration of PPP in the EU, soil
parameters and meteorological data were taken from the FOCUS
Hamburg Scenario (FOCUS, 2000). This scenario is one of eighttest scenarios developed within the FOCUS working group to harmonize pesticide registration within the European Community.
So far, numerical studies have only focused on the effects that soil
solution sampling by suction cups, which were run in a continuous
suction mode, had on the measured breakthrough curves and estimated solute fluxes (Tseng et al., 1995; Weihermüller et al., 2005,
2006). Therefore, a second objective of our study was to investigate
the effects of the sampling mode. Results obtained using a continuous operation mode were compared with those obtained using a
discontinuous mode, whereby temporary suction is only applied
to the cup during the extraction of the soil solution. In practice, adiscontinuous sampling scheme is easier to accomplish. However,
the effects of a discontinuous sampling scheme on the transport
process cannot be compared directly with those using continuous
extraction. Finally, we analyzed how annually repeated applications of a chemical affect the variability of mass recovered, mean
concentration, and leached mass fraction.

For comparison, we used calculated effective transport variables,such as mean pore water velocity, as well as peak concentration, andmass recovery. Additionally, calculated mean solute concentrations
and leached mass fractions were used for an uncertainty assessment.
Note that preferential flow due to cracks, worm holes, and root
channels, which may be also important in naturally structured
soils, especially in fine clay soils, was neglected in our numericalexperiments. On the other hand, preferential or heterogeneous
flow processes were already accounted for by considering the heterogeneous distribution of the hydraulic properties, which are
typical for a coarse structured soil like that analyzed in this study.

6 Materials and Methods
For the simulation of water flow, the two-dimensional Richards
equation (Eq. [1]) was solved using the finite element code
HYDRUS-2D (Šimůnek et al., 1999, 2008; Šimůnek and van
Genuchten, 2008):⎛∂ψ ⎞⎤∂θ ∂ ⎡∂ψ ⎤ ∂ ⎡= ⎢K (ψ) ⎥ + ⎢K (ψ)⎜⎜⎜ − 1⎟⎟⎟⎥⎢⎝ ∂z ⎠⎥⎦⎢⎥∂t ∂x ⎣∂x ⎦ ∂z ⎣[1]

where θ is the volumetric water content [cm3 cm−3], ψ is the pressure head expressed in head units [cm], x and z are horizontal andvertical coordinates [cm] with z positive in the downward direction, and K(ψ) is the unsaturated hydraulic conductivity function[cm d−1]. The van Genuchten–Mualem functions were used todescribe the relations between K, ψ, and θ (van Genuchten, 1980),
where θ r [cm3 cm−3] and θ s [cm3 cm−3] are the residual and saturated volumetric water contents, respectively; α [cm−1], n [-], andm [-] (m = 1 − 1/n) are shape parameters; and Ks [cm d−1] is thesaturated hydraulic conductivity.
Solute transport for conservative (bromide) and reactive (pesticides) substances is described by a convection–dispersion equation(CDE) that includes degradation and sorption (Eq. [2]):∂θ Rc∂(v θ c ) ∂ ⎛⎜∂c ⎞⎟⎟⎜⎜ Dij θ=− i +⎟− μ cθ− μ ρ s∂t∂x i∂x i ⎜⎝∂x j ⎠⎟⎟[2]

where Dij are the components of the dispersion coefficient tensor[cm2 d−1], v is the mean pore water velocity [cm d−1], c and s are
the solute concentrations in the liquid phase [μg cm−3] and on
the solid phase [g g−1], μ [d−1] is the first-order rate coefficient for
degradation in the liquid phase and the solid phase, and R [-] isthe retardation factor. The components of the dispersion tensor
Dij describing the subscale dispersion are given byθ Dij = α1 q δ ij +(αl −αt )

qi

qj
q

+θ Dd τδ ij[3]where α l and α t are the longitudinal and transversal dispersivities [cm], respectively; qi and q j are the water flux densities in the

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x and z directions [cm d−1], |q| is the absolutevalue of the water flux density [cm d−1]; Dd isthe molecular diff usion coefficient of the substance in free water [cm2 d−1]; τ = θ 7/3/θ s2 is
the Millington and Quirk (1961) tortuosity
factor; and δ ij is the Kronecker delta, taking
values of 1 for i = j and 0 otherwise. The retardation factor R is defined by

R = 1+

ρ ds
θ dc

[4]

where ds/dc is the fi rst derivative of the relationship between concentrations in the solid(s) and liquid (c) phases, expressed by any
sorption isotherm. Finally, the first-orderdegradation coefficient μ equals ln(2)/DegT50,
where DegT50 is the half-life of a substance atreference conditions. For both pesticides studFig. 1. (a) Schematic overview of the simulation domain with boundary conditions, soil horizons, and a location of the suction cup and (b) dimensionless scaling factor for αh [-] associatedied (denoted A and D) linear sorption waswith the pressure head for realization run 1.
assumed. Additionally, degradation of thepesticides was assumed to be independent of
temperature; therefore, heat transfer was not simulated.
was considered (i.e., no plants), transpiration was assumed to
be zero. The lower boundary of the flow domain was defi ned as
For the simulations, a two-dimensional 100-cm-wide andfree drainage, which may be used when the groundwater table
150-cm-deep flow domain was defi ned, which was discretizedis far below the soil surface. No-flow boundary conditions were
nonequidistantly using smaller nodal distances in the vicinity
imposed along the remaining boundaries.
of the suction cup and at the upper boundary where larger gradients are to be expected (the total number of nodes was 23,351).
The boundary condition at the surface of the suction cup was specified
A suction cup with an outer radius of 2.0 cm was located 100
as a prescribed time-variable pressure head for the continuous mode or
cm below the soil surface in the horizontal center of the flow
as a constant pressure head during sampling and zero flux otherwise
domain. A sketch of the simulation domain is shown in Fig. 1.
for the discontinuous mode. A modification of the HYDRUS-2D
The boundary condition at the upper surface was set to atmocode was necessary to ensure that water and solute could leave acrossspheric conditions, using meteorological data from the Hamburg
this boundary, but not enter the simulation domain at times when
scenario of FOCUS (2000) to quantify the atmospheric inputs
the prescribed pressure head was higher than the soil pressure head(rainfall and potential evaporation, calculated using the Penmanin the direct vicinity of the suction cup. In all simulations, either aequation). Th is data set consists of 20 yr of weather data (1975–
prescribed pressure head of −600 cm was applied at the suction cup
1994), of which only the first 10 yr
were chosen for simulations (a total of3652 d). The initial conditions for thepressure heads were set to −150 cm at
the bottom and −100 cm at the top of
the domain, with linear interpolation
in between. The first 820 d, up until 31
March (in the third year), were used
as a “warming-up” period before theapplication of the test compounds was
begun (both for single and repeatedapplications) to ensure that the initial conditions did not influence themodeling results. An overview of theFig. 2. Climate data (rainfall and potential evaporation) for the Hamburg scenario (FOCUS, 2000).
meteorological data is plotted in Fig.
Cumulative values start at a time of compound application.
2. Note that since a bare soil system

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for 1 d a week starting from Day 820 (for a discontinuous mode), or a time-variable pressure head
was continuously applied at the suction cup (for acontinuous mode). The value of this time-variable
pressure head (Fig. 3) was calculated on a daily
basis as the horizontally averaged pressure head at
the installation depth (100 cm), using a reference
simulation for a 150- by 1000-cm flow domain
without any suction cups. An additional offset
of −30 cm was added to these pressure heads. The
technical limitations of the suction cup method (abubble point of most porous materials is smaller
than −1000 cm, and the limit of pressure pumps
Fig. 3. Simulated mean pressure heads at a depth of 100 cm for the 10-yr climate data of the
Hamburg scenario (FOCUS, 2000).
is approximately −1000 cm) were also taken into
account in the simulation exercise by fixing all
calculated pressure heads smaller than −1000 at Table 1. Hydraulic properties and the bulk density for soils of the soil profi le used in the simulations (taken from the Hamburg scenario of FOCUS 2000). Suction cup parameters were takena threshold value of −1000 cm.
from Weihermüller et al. (2006) with adapted Ks.

A sandy soil was chosen for the simulations.
The hydraulic properties and the bulk density of the soil were taken from the Hamburg
scenario of FOCUS (2000) (Table 1). The
hydraulic properties of the suction cup weretaken from Weihermüller et al. (2006),
whereby its saturated hydraulic conductivity
was modified to ensure that the conductanceof the suction cup would not limit the quantityof extracted water and solute.

Materialn

Ks

Bulk density

Corg

cm

θr
3
———cm cm−3 ———

cm−1

-

cm d−1g cm−3

%

0–30

0.391

0.014911.468

201.57

1.50

1.5

Depth

Horizon A

θs

0.036

α

Horizon B1

30–60

0.370

0.030

0.01255

1.565

273.631.60

1.0

Horizon B2

60–75

0.351

0.029

0.01808

1.598

244.77

1.56

0.2

Horizon C

75–150

0.310

0.015

0.028121.606

244.771.61

0.0

Suction cup

–

0.500

0.001

0.000502.800

280.001.50

0.0

Local-scale heterogeneity in hydraulic properties was generatedusing the Miller–Miller scaling theory (Miller and Miller, 1956).
The geostatistical parameters were chosen to be the same as thoseused by Weihermüller et al. (2006), with a variance, σ2f, of 0.25
and a correlation length, λ f, of 10 cm. The dimensionless scaling
factor for α h [-] associated with the pressure head is given exemplarily for the geostatistical realization of run 1 in Fig. 1b. Notethat the underlying heterogeneous structure, which was generated using the geostatistical parameters listed above, will increase
the effective dispersivity, λ eff. Even when the longitudinal andtransversal dispersivities were set to 3 and 1.5 cm, respectively, theresulting effective longitudinal dispersivity, λ eff, is about 7.6 cm
at the lower boundary for the conservative tracer with the given
heterogeneity of the underlying flow field and a simulation depthof 1 m. This value is still within the range of dispersivities that canbe expected for field-scale transport in natural soils (Vanderborght
and Vereecken 2007).
Ten realizations of the heterogeneous flow field of 150 by 100
cm were simulated. Simulating flow fields of this size, rather
than the entire ensemble of all realizations in a 150- by 1000cm flow field, greatly facilitated our numerical study. In general,
10 simulations represented an ensemble 150 cm deep and 1000
cm wide, containing a total of 10 suction cups installed at a

depth of 100 cm with a horizontal spacing of 100 cm. Since
no-f low boundary conditions were imposed at both sides ofthe flow domain, it was assumed that there was no lateral flow
between domains.
The two different pesticides, denoted A and D, with contrasting
sorption and degradation properties were chosen from FOCUS(2000). Parameter values chosen for substances A and D are used
to evaluate the pesticide leaching scenarios developed for pesticide registration procedures in Europe, but are not intended torepresent any specific compounds. For both pesticides, no further
reactions of the pesticide metabolites were assumed. For comparison, the nonreactive tracer (e.g., bromide) was simultaneously
applied with the pesticides. The transport and fate parameters,
Dd, Koc, and DegT50, are listed in Table 2 for all three chemicals.
Note that DeqT50 had to be recalculated to match the input ofthe degradation rate μ coefficient. Additionally, the degradation
rate μ was kept constant over the entire simulation depth and wasassumed to be independent of temperature and water content. In
correspondence with the FOCUS recommendations, 1 kg ha−1 ofthe substances A, D, and bromide were applied once per year on 31
March, beginning on Day 820. For the single application this was
only done once, on Day 820. In general, global water and solutenumerical mass balance errors were always less than 1 and 2.5% for
all time steps, respectively.

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Table 2. Properties of pesticides A and D (taken from the Hamburg
scenario of FOCUS, 2000) and of conservative tracer bromide.
Dd†

KOC

DegT50cm2 d−1

cm3 g−1

d

1.728

–

–

Pesticide A

0.430

103

60

Pesticide D

0.430

60

20

Substance

Bromide† Diff usion coefficient in water.

To compare with the one-dimensional simulations that are usually
performed in the FOCUS scenarios (FOCUS 2000), the results ofthe two-dimensional simulations in the heterogeneous flow fields
with suction cups were compared with one-dimensional simulations using the HYDRUS-1D code (Šimůnek et al., 2008). These
one-dimensional simulations were performed using the same setup
described above. These one-dimensional simulations were also used
as a reference case, whereby the one-dimensional simulations giveinformation about the complete mass recovery since no waterand solute can bypass the depth of measurement without being
sampled. Reference parameters used for scaling stochastic heterogeneity were used as the hydraulic parameters in one-dimensional
simulations (Table 1). The dispersivity was adjusted to match aneffective dispersivity, λ eff, of 7.6 cm, calculated from the bromide
breakthrough curve at a depth of 100 cm, obtained by the twodimensional simulation of a 150- by 1000-cm large heterogeneous
flow domain discussed above.
The BTCs of solute concentrations in water extracted by thesuction cup were used to evaluate the transport behavior of different compounds utilizing the moment analysis. Th is is a purely
statistical characterization of BTCs without any assumptions
regarding underlying processes. Because of the transient natureof the flow regime and for a better comparison with the onedimensional simulations, we used a transformed time coordinate,that is, a normalized cumulative amount of extracted water
depth, I [cm], in our analysis. However, suction cups extract
a volume of water. To convert this volume of water to a water
depth, the extracted volume needs to be divided by the area. In
general, the defi nition of this area is not trivial for suction cup
samplers. It could be either the area of the suction cup surface,through which water is extracted from the soil, or the area ofthe suction cup capture zone at the soil surface. To compare theextracted water depth directly with a cumulative infi ltration
depth or a cumulative depth of drainage for a flow field that is
not disturbed by a suction sampler, the surface area of the capturezone is more appropriate. The fraction of total infi ltration surface
corresponding to the suction cup sampling area (SCSA) can beapproximated by the ratio of the extracted water volume to thetotal infi ltrated water volume when differences in water storage
in the soil are neglected. Therefore, we fi rst calculated the SCSA
[cm 2] as defi ned by Weihermüller et al. (2005):

SCSA =

total_vol sampled
total_vol infiltrated

Infiltration surface[5]

where total_volsampled [cm3] is the cumulative amount of water
extracted by the suction cup during a certain time interval, total_
vol infi ltrated [cm3] is the cumulative amount of net infi ltration
during a time interval, and the Infi ltration surface is the lengthof the upper boundary multiplied by a unit length in a perpendicular direction (i.e., 100 cm2). SCSA, as defined above, can be
modified to provide information about the sampled mass fraction
by substituting water volume (sampled and infi ltrated) with mass
(sampled and applied), resulting in SCSA_solute. To calculate
total_volsampled and total_volinfi ltrated, we used the cumulative
quantity of water between the time of application (Day 820) anda chosen point in time (i.e., detection time), when only minimal
concentrations (below an assumed detection limit) appeared inwater captured by the suction cup. The detection time for bromide was set to 1933 d, and to 2157 d for pesticides A and D.
Note that total_volinfi ltrated was calculated for the 150- by 1000cm flow domain and was equal for all 10 realizations of smaller
flow domains, irrespective of any small variations that may occur
between realizations.
In the second step, the normalized cumulative amount of extracted
water depth, I [cm], was calculated asI=

vol sampled (t )

[6]

SCSA

where volsampled(t) [cm3] is the sampled water volume capturedby the suction cup at time t (day). Note that in the HYDRUS-2D
program, water volumes and surface areas are expressed per a unit
length in the direction perpendicular to the simulation domain.
For the moment analysis, we used the Nth normalized and transformed time moment, TN (cm N), as defined by Jury et al. (1991):∞

N f∫ I C wdIτ
TN = N = 0
τ0
τ0

[7]
∞

where the zeroth time moment, τ0 = ∫ C wf d I [μg cm−2], is0equal to the total mass of the substance recovered by the suction
cup, or for one-dimensional simulations to the total mass leaving
the bottom boundary of the simulation domain. Cw f is the flux
concentration [μg cm−3].
The fi rst normalized time moment, T1 (i.e., μ t), yields the quantity of water required for the center of mass to arrive at theobservation depth. The second central moment (variance σ t2 =T 2 − T12) describes the spreading of the solute pulse relative tothe quantity of water required for the center of mass to arrive at
the observation depth.

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Finally, travel time moments (Eq. [7]) can be used to derive transport parameters, such as pore water velocity, vs [cm cm−1], andeffective dispersivity, λ eff [cm]. As a consequence of the transformation of time into the cumulative extracted water depth, porewater velocity, vs, is expressed as the transport distance of soluteper a unit length of extracted water [cm cm−1]. The first and second
moments are related to effective CDE parameters by the following
equations (Jury and Roth, 1990) with
z
μt

[8]

v 2σ 2λeff = s t
2z

[9]

vs =
and

6 Results and Discussion
The BTCs calculated for a scenario when the suction cup was
sampled at a continuous variable pressure (an ambient pressure
head plus −30-cm offset, Fig. 3) and the three substances wereapplied on Day 820 are plotted in Fig. 4, whereby the run labels
indicate the different geostatistical realizations of the underlying
flow field. Cumulative water was set to zero at the day of application (820 d). As expected, the highest concentrations were
calculated for bromide (Fig. 4a) and the lowest for pesticide D,
which degrades the most quickly. Figure 4 clearly demonstrates
the influence of the underlying heterogeneous structure of the soil
and the actual location of the suction cup within the flow field.
As a result, BTCs vary between different realizations in terms ofpeak concentrations and the time (here expressed in units of thewhere z [cm] is the observation depth.
For a better comparison of the results from the two operation
modes of the suction sampler and to compare these findings with
one-dimensional simulations, we define a leached mass fraction(LMF) byLMF =mass_sampled infiltration surface
mass_applied
SCSA

[10]

where mass_applied [μg] is the total applied mass at the upperboundary and mass_sampled [μg] is the mass extracted by thesuction cup.
From Eq. [10] it becomes clear that for steady-state flow conditions, the LMF of an inert tracer is equal to 1. Note thatSCSA depends on the hydraulic conductivity of the soil, thehydraulic conductivity of the suction cup, the applied pressure
head at the cup, and the water pressure and flow rate in the soil
(Weihermüller et al., 2006). Under transient flow conditions andfor an operation mode of the suction sampler with a time-variable
pressure head, these variables change so that SCSA varies overtime as well. Since we defi ne SCSA as a ratio of sampled andinfi ltrated waters, which are collected over a certain period oftime, the SCSA represents an averaged value of the SCSA for thattime period. The time-averaged SCSA obtained may therefore
differ from the SCSA at each single time period between thesolute application and the full breakthrough of the solute plume.
To evaluate the effect of transient flow on the LMF as defi ned
in Eq. [10], LMFs for the inert tracer and different realizationsof the heterogeneous flow field were calculated. Therefore, thedeviation of LMF from that calculated for the inert tracer is ameasure of the uncertainty of the mass flux derived from suction
cup measurements.

Fig. 4. Breakthrough curves for (a) bromide, (b) pesticide A, and (c)pesticide D for 10 realizations of a heterogeneous flow field and acontinuously applied pressure head with a −30-cm offset. A reference
one-dimensional simulation with free drainage bottom breakthroughcurve. Note that axes do not have the same scale. Run 1 to 10 indicate
the different geostatistical realizations.

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normalized cumulative amount of extracted water according to Eq.
[6]) when breakthrough starts. Additionally, temporal variability
greatly increased for reactive substances, compared to the inert
tracer. Contrary to bromide, which leached primarily during thefirst winter, pesticide A showed double-peak BTCs, which were aresult of the annual water cycle, with high net infi ltration fluxes
during winter and low fluxes during summer. The fi rst peak is
associated with downward flow during the first winter after theapplication. During the following summer, the drainage flux ceases,
and due to evaporation, the substance plume moves upward in thesoil profi le. As this occurs, water from below the suction cup withlower pesticide concentrations is extracted. The subsequent risein concentrations corresponds with leaching during the second
winter period. Compared with pesticide A, the first arrival of pesticide D is much earlier due to weaker sorption of pesticide D, andis therefore not directly influenced by changes in flow direction as
discussed above. On the other hand, pesticide D also exhibited adouble-peak breakthrough, but to a much smaller degree, and at
earlier times.
Moment analysis was performed to quantitatively interpret particular BTCs. The results of the moment analysis, as well as thecalculated minimum (min) concentrations, maximum (max)concentrations, arithmetic means, percentages of variability[100(max/min)], and coefficients of variation calculated from the
10 realizations are listed in Table 3. In general, the mean dispersivity for bromide BTCs is slightly higher (mean = 10.2 cm, min.
= 9.6 and max. = 10.8 cm, with a standard deviation of 0.4 cm)
than that for the flow field undisturbed by the suction cup at thesame depth (7.6 cm). As was already shown by Weihermüller etal. (2005), sampling by a suction cup deforms streamlines toward
the sampler, leading to longer travel paths and a pronounced tailing of the breakthrough. The calculated mean pore water velocity
for the bromide BTC is 10.10 cm cm−1 (CV = 0.044), while theminimum and maximum velocities are 9.56 and 10.81 cm cm−1,
respectively. Due to sorption, mean transport velocities decrease
to 5.26 cm cm−1 (CV = 0.037) for pesticide D and 2.25 cm cm−1
(CV = 0.025) for pesticide A. In all cases, the variability between
minimum and maximum pore water velocities ranges between 110
and 113% (Table 3).
Looking at the total extracted solute mass calculated from thezero moment, the largest quantities can be recovered for bromide(mean = 463.3 μg, CV = 0.081), followed by pesticide A (mean= 0.0132 μg, CV = 0.167), and pesticide D (mean = 2.96 10−5
μg, CV = 0.266). Note that these relatively low values correspondwith low quantities of water extracted by the suction cups from thetwo-dimensional plane. Nevertheless, this pattern clearly reflects
the degradation characteristics of individual substances, with the
DegT50 value for pesticide D (20 d) one-third of that for pesticide A (60 d). Irrespective of the total sampled mass, variability
between the minimum and maximum total extracted mass (Table3) increased with decreasing DegT50 from 133% for bromide to 180
and 260% for pesticides A and D, respectively.
The BTCs for all three substances and a scenario with weekly sampling using a pressure head of −600 cm during 1 d per week aredepicted in Fig. 5. Comparable results of water depths [cm] forweekly and continuous sampling scenarios were obtained due tonormalization based on Eq. [6], even though only one-half thequantity of water was sampled during the weekly operation. In
comparison to the scenario with the continuous time-variable
pressure head (Fig. 4), fewer data points are available, due to lessfrequent sampling. Nevertheless, the same BTC patterns areobserved as for the continuous sampling scenario, except that theobserved peak concentrations are always lower for both pesticides(on average by 6 and 10% for pesticide A and D, respectively) for
the weekly sampling strategy. On the other hand, weekly sampling

Table 3. Calculated minimum, maximum, arithmetic mean, percentage of variability [100(max/min)], and coefficient of variation (CV) of the meanpore water velocity and the total mass of three substances for 10 realizations of heterogeneous flow fields. Continuous (continuous pressure head offset
by −30 cm), weekly (a pressure head of −600 cm applied for 1 d a week), and one-dimensional refer to operational modes.
Velocity
Substance

Min

Total mass
Max

Mean

%

CV

Min

Max

Mean

%

CV

————————————— cm cm−1 —————————————— ———————————————μg ———————————————
Continuous

WeeklyOne-dimensional

Bromide

9.56

10.81

10.10

113.1

0.044

406.9

Pesticide A

2.15

2.37

2.25

110.2

0.025

0.00995

Pesticide D

5.06

5.68

5.26

112.3

0.037

1.81E-5

Bromide

8.36

9.12

8.73

109.1

0.031

Pesticide A

2.07

2.25

2.16

108.7

0.024

0.00449

Pesticide D

4.70

5.05

4.86

107.4

0.022

0.82E-6

Bromide

–

–

7.55

–

–

–

–

Pesticide A

–

–

1.71

–

–

–

–

0.0238Pesticide D

–

–

3.96

–

–

–

–

203.9

www.VadoseZoneJournal.org | 1293

539.7

132.6

0.081

0.01784

0.01321 179.3

0.167

4.71E-5

2.96E-5 260.2

0.266

275.9

463.3

229.9

135.3

0.099

0.007620.00587 125.4

0.105

0.19E-5

1.31E-5 231.7

0.246

1000

–

–

–

–

3.67E-5 ––are extracted, especially during wetter periods (main drainage
events). Even if the total mass recovery is not the best comparative
indicator for the two operation modes, because the total amountof cumulative water will also be lower for weekly sampling, variability between individual realizations remains nearly unchanged(Table 3). Variability only decreased significantly for pesticide A.
If we look at the SCSA as defi ned in Eq. [5] for water (SCSA_
water), we can use it analogically for solutes after substituting
vol_ sampled and vol_infi ltrated with mass_ sampled and mass_applied
to get the SCSA_solute. For the bromide application (Table 4), we
can clearly see that while roughly 50% of the surface was sampled
in terms of SCSA_water (mean = 50.1 cm2) when the continuous sampling strategy was used, the SCSA_solute (mean = 46.3
cm2) was only slightly smaller. In the weekly sampling mode, themean SCSA_water and the SCSA_solute were only about one-halfthat (24.1 and 23.0 cm2 , respectively). For both cases, the ratio of
SCSA_water to SCSA_solute is close to 1, with ratios of 1.08 and1.05 for the continuous and weekly sampling modes, respectively.
Small differences between SCSA_water and SCSA_solute can be
attributed to small changes in soil water storage between the final
time selected for total_volsampled and total_volinfi ltrated, and thetime during which the breakthrough occurred. These differences
can also be attributed to mixing processes between those flow
channels bypassing the suction cup and those that are sampled.

Fig. 5. Breakthrough curves for (a) bromide, (b) pesticide A, and (c)pesticide D for 10 realizations of a heterogeneous flow field and a
weekly applied pressure head of −600 cm applied for 1 d. Note thataxes do not have the same scale. Run 1 to 10 indicate the different
geostatistical realizations.

produces slightly higher peak concentrations for bromide (on average by 3%).
In general, the calculated mean pore water velocities (Table 3) areonly slightly higher for the continuous sampling scenario, compared to the weekly extraction scenario for all substances. On theother hand, weekly sampling produced slightly lower coefficientsof variation (Table 3). At the same time, the total sampled mass
was roughly only one-half of the reference mass for continuous
sampling (Table 3), which corresponds to a smaller amount of
extracted water (also about two times lower). Nevertheless, thesefindings are at first sight rather surprising, considering that water
was extracted only during one-seventh of the total time. On theother hand, there is a simple explanation for this. Due to larger
pressure head gradients between the soil and the suction cup
during weekly sampling, considerably larger quantities of water

As a somewhat longer simulation time was used for pesticides A
and D, the SCSA_water is 55.8 cm2 and for the continuous sampling mode and 28.0 cm2 for the weekly sampling mode, resulting
in a ratio between continuous and weekly SCSA_solute of 2.0.
The corresponding SCSA_solute for pesticide A are 1.32 × 10−3
and 5.87 × 10 −4 and for pesticide D 2.96 × 10 −6 and 1.31 ×
10−6, for the continuous and weekly sampling modes, respectively.
The relatively low SCSA_solute for both pesticides and operation
modes is a direct consequence of the degradation process, whereby
the ratio of continuous to weekly SCSA_solute was also close to 2,
with 2.26 for pesticide A and 2.27 for pesticide D.
Finally, the LMF was calculated according to Eq. [10]. For bromide,
the mean LMF was 0.92 for the continuous sampling mode and0.95 for the weekly sampling strategy. For pesticides A and D, theLMF was 2.36 × 10−5 and 5.29 × 10−8 for continuous and 2 ×
10−5 and 4.68 × 10−8 for weekly sampling modes, respectively(Table 4).
To better understand the importance of these findings, we used
the results of a homogeneous one-dimensional simulation for comparison. As was already shown, the LMF was 1 for bromide for the
one-dimensional simulation. As a consequence of degradation, theLMF dropped to 2.4 × 10−5 for pesticide A and 3.7 × 10−8 forpesticide D. It is somewhat surprising that the LMF for pesticide
A for the one-dimensional simulation was similar to the LMF in aheterogeneous flow field with continuous sampling by the suction

www.VadoseZoneJournal.org | 1294

Table 4. Calculated arithmetic mean (mean), standard deviation (STD), and coefficient of variation (CV) for the SCSA_water, SCSA_solute, leachedmass fraction (LMF), and mean concentration [μg L−1] for one substance application, for 10 realizations of heterogeneous flow fields and for a onedimensional simulation.
SCSA_water
Substance

Mean

SD

SCSA_solute
CV

Mean

LMF

SD

CV

Mean

Mean concentration
SD

CV———————————— cm2 ————————————
Continuous

WeeklyOne-dimensional

Mean

SD

CV

——————μg L−1 —————

bromide

50.1

3.3

0.065

46.3

3.7

0.081

0.92

0.04

0.042

90.1

pesticide A

55.8

3.7

0.066

1.3E-32.0E-40.168

2.4E-5

3.2E-60.136

2.17E-3 2.94E-5

3.8

0.042
0.136

pesticide D

55.8

3.7

0.066

3.0E-6

7.9E-7

0.266

5.3E-8

1.2E-80.234

4.86E-6 1.14E-6

0.234

bromide

24.1

2.6

0.106

23.0

2.3

0.099

0.95

0.06

0.060

93.1

0.060

pesticide A

28.0

3.0

0.108

5.9E-4

9.9E-50.169

2.1E-5

2.9E-60.136

2.06E-3 2.81E-5

pesticide D

28.0

3.0

0.108

bromide---1.4E-6-

3.2E-7
-

5.7

0.136

0.246

4.7E-8

1.1E-80.229

4.59E-6 1.05E-6 0.239

-

1.0

-

-

87.0

-

-

pesticide A

-

-

-

-

-

-

2.4E-5--

1.81E-3 --pesticide D

-

-

-

-

-

-

3.7E-8--

2.78E-6 --cup. However, the LFM for pesticide D was somewhat lower
in the one-dimensional simulation (Table 4). As was shown by
Weihermüller et al. (2005), suction cup sampling increases waterflow toward the cup and therefore reduces breakthrough times.
This accelerated breakthrough is detectable for all substances
shown in Fig. 4. While bromide shows only a small delay in the
one-dimensional simulation, both pesticides produce much later
arrivals. Especially for substances with a small DegT50, the reduced
residence time in the soil can have important consequences for the
LMF by decreasing degradation.
Finally, the mean concentration was calculated (Table 4) using thetotal quantity of extracted water and solute mass since application. In general, there is no clear trend in systematically over- or
underestimating the mean concentration by one of the sampling
modes (continuous or weekly sampling) in the heterogeneous
flow field. For bromide, the mean concentration for each single
realization and the weekly sampling mode varied between 97.4
and 112.3% compared to the results for scenarios with continuouspressure head. Variations between 93.8 and 96.8% were obtainedfor pesticide A, and between 93.6 and 104.3% for pesticide D. The
overall differences between the weekly and continuous sampling
modes calculated by summing up all mass loads and extracted
water for all 10 realizations were 103 for bromide, 95.0 for pesticide A, and 94.5% pesticide D. This indicates that weekly sampling
may slightly underestimate the mean concentrations for reactive
substances. Compared to the mean concentration (87.0 μg L−1)
calculated by the one-dimensional simulation for homogeneous
undisturbed flow conditions, two-dimensional simulations forweekly and continuous sampling modes produced only slightly
higher mean bromide concentrations of 93.1 and 90.1 μg L−1,
respectively. For pesticide A, a slightly lower mean concentration
was observed for the one-dimensional simulation (1.81 × 10−3 μgL−1) in comparison to the two-dimensional simulations with thesuction cup sampling (continuous = 2.17 × 10−3 and weekly =2.06 × 10−3 μg L−1). For pesticide D on the other hand, the mean
concentration calculated from the one-dimensional breakthroughis only about one-half of values obtained by the two-dimensional
simulations with the suction cup sampling (Table 4). The explanation for these differences is the same as for the differences in LMF.
Additionally, we plotted breakthrough curves versus time for 10
two-dimensional realizations with continuous sampling with anapplied pressure head of −600 cm and three substances in Fig. 6.
For comparison, the BTC obtained from the reference one-dimensional simulation is also shown. In all cases, the timing (the firstarrival and tailing) of the one-dimensional breakthrough is nearly
the same as that for the heterogeneous flow field with suction cups.
On the other hand, as already discussed, pesticide concentrations
are much lower for the one-dimensional free drainage case.
To evaluate differences in leaching and sampling behavior over alonger observation time, a third set of simulations was performed.
As already stated, the solute application was repeated eight times,
with 1 yr between each application (all applications were done on
March 31). To reduce the computational effort, only the weekly
sampling for heterogeneous flow fields was analyzed. Solute concentration versus normalized cumulative flow captured by thesuction cups over the entire simulation period of 10 yr (eightrepeated annual applications) is plotted in Fig. 7. While the annual
peaks in bromide concentrations are clearly visible, the frequency
between peaks differs slightly between individual years as a resultof changing atmospheric boundary conditions. Additionally, peakconcentrations within each leaching period vary only slightly
between the model runs. Unlike the conservative tracer, pesticides A and D show a totally different breakthrough pattern withhigh concentrations over a certain period of time (?60–100 cm
cumulative water), and low concentrations during all other years(Fig. 7b and 7c). Three major peaks are detectable for pesticide D
at 48, 80, and 115 cm cumulative water. This pattern of unequal

www.VadoseZoneJournal.org | 1295

Fig. 6. Breakthrough curves versus time for (a) bromide, (b) pesticideA, and (c) pesticide D for 10 realizations of a heterogeneous flow field
and a continuously applied pressure head with a −30-cm offset. A
reference breakthrough curve for a one-dimensional simulation withfree drainage breakthrough curve. Note that axes do not have the same
scale. Run 1 to 10 indicate the different geostatistical realizations.

Fig. 7. Breakthrough curves for (a) bromide, (b) pesticide A, and (c)pesticide D for a weekly applied pressure head of −600 cm applied for
1 d and eight annually repeated application on 31 March. Note thataxes do not have the same scale. Run 1 to 10 indicate the different
geostatistical realizations.

concentrations during different years reflects actual water contents
at the time of solute application and subsequent atmospheric conditions during dry and wet seasons.

value of 1.10 × 10−3 μg, and the mean concentration varied between
1.88 × 10−4 and 2.61 × 10−4 μg L−1, with the mean value of 2.12
× 10−4 μμg L−1. The CV increased from bromide with a value of
0.097, to pesticide A with a value of 0.144, and 0.154 for pesticide
D. This pattern indicates increasing variability in the captured mass
for reactive substances compared to the conservative tracer. As stated
before, the quantity of sampled water varied between 4.64 and 6.31
L, resulting in a difference of 36%. Nevertheless, the mean concentration varied only by 9% for bromide. Much higher variations
were detected for pesticides A and D, with differences as high as 56
and 39% (see Table 5). Again, the mean LMF of 0.93 for bromide
was close to 1, reflecting the conservative behavior of the substance.
Reflecting the degradation of pesticides and the low sampled mass,
the LMF dropped to a mean of 7.17 × 10−5 and 5.15 × 10−7 forpesticides A and D, respectively.

The total mass of bromide sampled in different years varied between
1740 and 2383 μg, with a mean of 1977 μg (Table 5). At the sametime, the quantity of extracted water varied between 4.64 and 6.31
L, with a mean of 5.14 L. Mean bromide concentrations reflecteddifferences in the extracted quantity of water and total mass between
the model runs, and varied between 368 and 401 μg L−1, with themean value of 384.4 μg L−1. For pesticide A, the total extracted mass
varied between 0.130 and 0.189 μg (mean = 0.152 μg) and the mean
concentrations varied between 2.40 × 10−2 and 3.74 × 10−2 μg L−1(mean = 2.96 × 10−2 μg L−1). For pesticide D, the total sampled
mass varied between 8.94 × 10−4 and 1.40 × 10−3 μg with the mean

www.VadoseZoneJournal.org | 1296

Table 5. Minimum (min), maximum (max), arithmetic mean (mean), SCSA_water, SCSA_solute, leached mass fraction (LMF), and mean concentration for three substances, a simulation
period of 10 yr with eight annually repeated substance applications as plotted in Fig. 7.

Substance

BromidePesticide A

Pesticide D

Parameter

SCSA
Cumulative
water
Total mass Water

SoluteLMF—— cm2 ——Meanconcentration

L

μg

4.64

1740

Max

6.31

2383

Mean

5.14

1977

SD

0.51

192.6

2.64

2.41

0.024

9.75

CV

0.099

0.097

0.099

0.100

0.025

0.025

Min

4.64

0.129923.74

1.62e-3

5.80e-52.40e-2

Max

6.31

0.188932.64

2.36e-3

9.04e-5

3.74e-2

Mean

5.14

0.151526.59

1.89e-3

7.17e-5

2.96e-2SD

0.51

0.02142.64

2.67e-4

8.27e-6

3.42e-3

CV

0.099

0.144

0.099

0.141

0.115

0.115

Min

23.74

μg L−1

21.75

0.89

367.9

32.64

29.79

0.97

401.2

26.59

24.71

0.93

384.4

Min

4.64

8.94e-423.74

1.21e-5

4.54e-7

1.88e-4Max

6.31

1.40e-3

32.64

1.75e-56.30e-7

2.61e-4

Mean

5.14

1.10e-3

26.59

1.38e-55.15e-7

2.12e-4SD

0.51

1.70e-4

2.64

2.01e-6

4.96e-6

2.05e-5

The calculated LMF of the inert tracer, whichshould theoretically equal 1, was slightly underestimated (0.93) due to the fact that we had toapproximate the SCSA. In general, SCSA varies
over time for transient flow conditions. To convert the recovered solute mass to a fraction of
the solute mass that leaches below the sampling
depth for flow conditions that are not disturbed
by the suction sampler, an averaged value of the
SCSA must be used. One way to obtain suchan average value is to compare the sampled
water volume with the infi ltrated water volume.
Unfortunately, this averaging procedure may
not represent the average SCSA relevant for thesolute transport process. However, our simulations demonstrated that using an average SCSA
based on water volume measurements may leadto an error in the estimated total solute leachingof less than 13%.

Calculated mean concentrations were used for
direct comparisons of two operation modes. In
CV
0.099
0.154
0.099
0.146
0.096
0.096
general, the maximum differences in the mean
concentration for the same flow field were 12%
for bromide, 7% for pesticide A, and 11% for pes6
ticide D. Averaging over all flow fields led to a small overestimation in
The uncertainty in solute monitoring using suction cups induced by
the mean concentration for bromide (+3%), and a systematic underthe soil’s heterogeneity was assessed using numerical simulations
estimation for pesticides A (−5.0%) and D (−5.5%). Additionally,in a layered soil profi le with atmospheric boundary conditions. To
the normalized and time-dependent BTCs do not indicate large
account for reactive processes, two different pesticides were applieddifferences between the two operation modes. This suggests thattogether with an inert tracer. Additionally, two different operathe effect of the sampling strategy on mean concentrations, times
tion modes (sampling with a continuous pressure head and weeklyof breakthrough, and peak concentrations is negligible.
sampling) were used to evaluate the impact of the mode of appliedpressure head at the cup.
In the fi nal step, solute applications were repeated eight times
during a 10-yr simulation period, and water was extracted by sucFlow and transport were simulated in 10 realizations of a heterogetion cups on a weekly basis. Again, the results indicate that theneous flow field generated using the Miller–Miller scaling theory.
total amount of extracted water is less variable between different
First, all substances were applied a single time after a two year “conrealizations of the flow field compared to the total mass of sampled
ditioning” phase. The results indicated variability in pore water
pesticides. As a consequence, variability of calculated mean convelocities, sampled quantities, suction cup sampling areas for water
centrations is greater for pesticides than for bromide. Finally, the(SCSA_water) and solute (SCSA_solute), leached mass fractions
results in terms of absolute numbers are only representative for(LMF), and mean concentrations.
the particular heterogeneous structure and soil type used in thisstudy. Nevertheless, the overall findings of variable breakthroughIn general, the variability in calculated pore water velocities
and mean concentrations will also be valid, to some degree, forranged between 110.0 and 113.0% for the continuous tensiomother heterogeneous soils. Additionally, pesticide leaching, andeter-controlled sampling and 107.6 and 109.1% for the weekly
therefore, pesticide concentrations captured by the suction cups
sampling with a constant pressure head of −600 cm. The total
highly depend on the weather conditions during application andsampled mass showed larger variability for both pesticides in
the percolation period.
comparison to bromide. Overall, largest variability was foundfor pesticide D, with 260 and 230% for the continuous andIn comparison to the standard FOCUS scenarios (e.g., Boesten,
weekly sampling, respectively, while bromide varied only2007), root water uptake was neglected, and a constant DegT50
between 133 and 135%.
value was assumed over the entire simulated soil depth. The consequence of the fi rst assumption is faster drainage, resulting in

Summary and Conclusion

www.VadoseZoneJournal.org | 1297

reduced decomposition of the reactive substances. The second
assumption, on the other hand, will lead to greater decomposition at greater depths, reducing the total sampled mass, andconsequently the LMF and mean concentrations. However, theaim of this study was not an environmental risk assessment of thestudied substances, but an assessment of how suction cups can bias
the description of pesticide leaching. On the other hand, root water
uptake would likely increase differences in the captured solute
mass and, consequently, in mean concentrations.
In conclusion, soil heterogeneity can produce large variations in
the concentrations and leached mass fractions measured by suction
cups. The coefficient of variation of the leached mass fraction estimated from suction cup measurements in our study was found to
be up to 35%, and was the largest for the pesticide with the smallest
leached mass fraction. Second, suction cup samplers influence theflow regime and generally lead to a faster breakthrough than would
be otherwise observed under natural, undisturbed flow conditions.
This may lead to an overestimation of the leached solute mass by afactor 2 for the pesticide with the lowest LMF. Compared to thetwo previously mentioned effects, the impact of the suction sampler operation mode (a continuous tensiometer-controlled pressure
head versus a periodical sampling) on LMFs and mean concentration of the pesticides is negligible. Therefore, the additional effort
required to control the continuous pressure head by reference
tensiometers does not seem to be justified. Finally, uncertainty
in the leached mass fraction due to transient flow conditions andthe time-variable suction cup sampling area is negligible comparedwith the effects of soil heterogeneity and the bias caused by the
disturbance of the flow field.

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