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ArticleOn the Use of Mechanistic Soil−Plant Uptake Models: A
Comprehensive Experimental and Numerical Analysis on theTranslocation of Carbamazepine in Green Pea Plants
Giuseppe Brunetti,* Radka Kodešová, Helena Š vecová, Miroslav Fér, Antonín Nikodem, Aleš Klement,
Roman Grabic, and Jiří Š imůnek

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sı Supporting Information*

ABSTRACT: Food contamination is a major worldwide risk for human health.
Dynamic plant uptake of pollutants from contaminated environments is thepreferred pathway into the human and animal food chain. Mechanistic models
represent a fundamental tool for risk assessment and the development of
mitigation strategies. However, diﬃculty in obtaining comprehensive observationsin the soil−plant continuum hinders their calibration, undermining theirgeneralizability and raising doubts about their widespread applicability. To
address these issues, a Bayesian probabilistic framework is used, for the ﬁrst time,
to calibrate and assess the predictive uncertainty of a mechanistic soil−plantmodel against comprehensive observations from an experiment on thetranslocation of carbamazepine in green pea plants. Results demonstrate thatthe model can reproduce the dynamics of water ﬂow and solute reactive transport
in the soil−plant domain accurately and with limited uncertainty. The role ofdiﬀerent physicochemical processes in bioaccumulation of carbamazepine in fruits
is investigated through Global Sensitivity Analysis, which shows how soil hydraulic properties and soil solute sorption regulatetranspiration streams and bioavailability of carbamazepine. Overall, the analysis demonstrates the usefulness of mechanistic models
and proposes a comprehensive numerical framework for their assessment and use.

1. INTRODUCTION
Food contamination from polluted environments represents amajor risk for human health. Plants represent the most common
pathway into the human and animal food chain for environmental pollutants. Chemicals are taken up by plant roots andthen translocated toward the edible parts, where they arebioaccumulated1−6 or eventually metabolized in byproducts,7,8
which can be toxic.9,10 Soil is among the most important
pollution sources for plants.11 It has been shown that it can becontaminated by human and veterinary pharmaceuticals,12−14
uptake of which is controlled by plants, chemicals, and soil
properties.15−17
Carbamazepine (CBZ) is a widely prescribed anticonvulsant
pharmaceutical and antiepileptic drug. Once administered, it isdegraded by the liver in multiple metabolites, which are thenexcreted in both feces and urine. Due to its persistence, it isfrequently encountered in water bodies.18 CBZ is eﬃciently
taken up by many plants5,7,8,19,20 due to its chemical properties,
stability, and relative mobility in the soil.21−23 Despite its
stability in the soil, CBZ is translocated and metabolized inplants’ tissues (particularly in leaves) by plant cytochrome P450
enzymes.5,24,25 Root uptake and reactive transport are plant- andsoil-dependent,16,23,26 making it diﬃcult to generalize results.
Numerical models play an important role in better under© 2021 The Authors. Published byAmerican Chemical Society

standing of physicochemical processes involved in the dynamic
uptake of chemicals and risk assessment. To predict the behaviorof non-ionic organic compounds in the soil−plant continuum,
Brunetti et al.27 coupled the widely used Richards-based solver,
HYDRUS-1D,28 with a modiﬁed version of the multicompartment dynamic plant uptake model developed by Trapp.29 The
fully coupled soil−plant model is able to provide acomprehensive mechanistic description of transport andreaction processes in the soil−plant continuum. The model
was tested for three leaf vegetables (spinach, lamb’s lettuce, andarugula). The ﬁnal concentrations of CBZ and its two
metabolites in only two plant tissues (i.e., roots and leaves)
were measured and simulated. Despite promising results,
available observations were limited to draw conclusions about
the model’s applicability and generalizability.
Received: November 3, 2020
Revised: February 4, 2021
Accepted: February 7, 2021
Published: February 15, 2021

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ArticleTable 1. Model Parameters, Their Bounds, and Calculated 5%, 50%, and 95% Quantiles of the Parameters’ Posterior
Distributions from the Bayesian Analysisa
posterior distributions’ quantiles
parameterb

parameter description

parameter bounds

Soilθr1 [cm3cm−3]
θs1 [cm3cm−3]
α1 [cm−1]n1 [-]
Ks1 [cm day−1]θr2 [cm3cm−3]
θs2 [cm3cm−3]
α2 [cm−1]n2 [−]
Ks2 [cm day−1]
ρb [g cm−3]
λL [cm]Kf CBZ [cm3β μg1‑β g−1]

residual water content
saturated water content
VGM shape parameter
VGM shape parametersaturated hydraulic conductivity
residual water content
saturated water content
VGM shape parameter
VGM shape parametersaturated hydraulic conductivity
bulk density
dispersivitysoil−water partition coefficient

0.18
0.51
(0.001, 0.1)
(1.1, 3)
70
0.18
0.51
(0.001, 0.1)
(1.1, 3)70
1.1
1(1.1, 10)βCBZ [-]μLCBZ [day−1]

Freundlich exponent
CBZ degradation rate in the liquid phase

0.89
0.0068μSCBZ [day−1]

CBZ degradation rate in the solid phase

0.0068P0 [cm]POpt [cm]P2H [cm]
P2L [cm]
P3 [cm]CmaxCBZ [g cm−3]
CmaxEPX [g cm−3]
Roots
W [cm3gfw−1]
KRW [cm3gfw−1]
Mmax [gfw]M0 [gfw]
Kgr [day−1]τR [day−1]
Stem
W [cm3gfw−1]
KSW [cm3gfw−1]
Mmax [gfw]M0 [gfw]
Kgr [day−1]τS [day−1]
LeavesW [cm3gfw−1]
KLW [cm3gfw−1]
Mmax [gfw]M0 [gfw]
Kgr [day−1]τL [day−1]
SA [cm2gfw−1]
FruitsW [cm3gfw−1]
KFW [cm3gfw−1]
Mmax [gfw]M0 [gfw]
Kgr [day−1]τF [day−1]
SA [cm2gfw−1]
Compoundsm(CBZ) [g mol−1]m(EPX) [g mol−1]

Feddes’ parameter
Feddes’ parameter
Feddes’ parameter
Feddes’ parameter
Feddes’ parameter
maximum CBZ concentration taken up by roots
maximum EPX concentration taken up by roots

−15
−30
−300
−500
−8000
(1 × 10−9, 1 × 10−8)(0, 1.0 × 10−8)root water content
roots−water partition coefficientmaximum roots mass
minimum roots massroot growth rate
CBZ degradation rate in roots

0.88(1, 30)308
15
0.2(0, 0.55)

stem water content
stem−water partition coefficientmaximum stem mass
minimum stem massstem growth rate
CBZ degradation rate in stem

0.84
(1, 30)591
10
0.14(0, 0.55)

leaves water content
leaves−water partition coefficientmaximum leaves mass
minimum leaves mass
leaves growth rate
CBZ degradation rate in leaves
leaves specific area

0.84
(1, 30)757
14
0.13(0, 0.55)
70

fruit water content
fruit−water partition coefficient
Maximum fruit mass
Minimum fruit mass
fruit growth rate
CBZ degradation rate in fruit
fruit specific area

0.83
(1, 30)720
00.65(0, 0.55)
50

molar mass of CBZmolar mass of EPX

236.27252.28

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5%

50%

95%

S1 [-]

0.009
1.94

0.013
2.07

0.016
2.51

0.11
0.03

0.015
2.02

0.022
2.45

0.035
2.78

0
0

2.24

2.44

2.63

0.07

3.75 × 10−9
9.0 × 10−12

4.05 × 10−9
8.0 × 10−11

4.38 × 10−9
1.6 × 10−10

0.14
0

11.8

13.3

15.1

0.03

0.0

0.01

0.02

0.04

10.5

11.8

12.8

0.06

0.04

0.05

0.07

0.06

3.12

15.2

27.3

0

0.38

0.44

0.50

0

2.7

15.2

26.5

0

0.0

0.02

0.04

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ArticleTable 1. continued
The last column reports the ﬁrst-order sensitivity indices (S1) calculated using the RBD-FAST method to assess the inﬂuence of diﬀerent factors
on the accumulation of CBZ in the edible fruits. bThe subscripts 1 and 2 indicate the ﬁrst and second soil horizons, respectively.
acolumns during the entire experiment using ECH20 EC-5
sensors32 and microtensiometers Tensior 5,33 respectively. The
Freundlich sorption isotherm and the dissipation half-live of
CBZ in soil were evaluated using the batch sorption34 anddegradation35 experiments, respectively. The resulting parameters are presented in Table 1.
2.2. Analytical Methods. Concentrations of compounds insoils and plant tissues were analyzed using the methods
proposed and validated for CBZ and its four metabolites inour previous studies.16,17,21,23,36 Methods are also brieﬂy
described in the Supporting Information. Soils (four soil layers
per each column) and plant tissues were freeze-dried andgrounded. Compounds remaining in 2 g of soil samples wereextracted with 4 mL of extraction mixture 1 (acetonitrile/water,
1/1, v/v, acidiﬁed with 0.1% of formic acid) followed by 4 mL of
mixture 2 (acetonitrile/2-propanol/H2O, 3/3/4, v/v/v, acidiﬁed with 0.1% of formic acid) in an ultrasonic bath (DT 255,
Bandelin Electronic, Sonorex Digitec, Berlin, Germany) for 15
min. Compounds in 0.05 g of plant tissue samples were extractedwith 1 mL of extraction mixture 1 (acetonitrile/water, 1/1, 0.1%
of formic acid) by shaking at 1800 min−1 for 5 min (TissueLyser
II, Quiagen, Germany). A triple-stage quadrupole mass
spectrometer, Quantiva (Thermo Fisher Scientiﬁc, San Jose,
CA, USA), coupled with an Accela 1250 LC pump (Thermo
Fisher Scientiﬁc) and HTS XT-CTC autosampler (CTC
Analytics AG, Zwingen, Switzerland), was used for the analysis
of irrigation water. A hybrid quadrupole-orbital trap mass
spectrometer, Q Exactive HF Hybrid Quadrupole-Orbitrap
Mass Spectrometer (Thermo Fisher Scientiﬁc, USA), operated
in high-resolution product scan mode (HRPS), was used insteadof a triple quadrupole for more complex soil and plant extracts. A
Hypersil Gold aQ column (50 mm × 2.1 mm i.d., 5 μm particle
size, from Thermo Fisher Scientiﬁc San Jose, CA, USA) wasused for the chromatographic separation of these target
compounds. A detailed description of the instrument settings
can be found in ref 37. Recovery and LOQs of compounds indiﬀerent matrices are presented in Tables S4 and S5,
respectively.
2.3. Modeling Theory. 2.3.1. Model Description and
Setup. The numerical model developed by Brunetti et al.27 isused to simulate the translocation and transformation of CBZ inthe soil−plant continuum. The model combines the widely usedhydrological model, HYDRUS-1D,28 with a multicompartment
model of dynamic plant uptake.38 For a thorough description of
the model, please refer to ref 27.
The Richards equation describes the variably saturated waterﬂow in the soil:

To further test the model performance, a new, morecomprehensive experiment involving the exposure of green
pea plants (Pisum sativum L.) to CBZ was designed and carriedout in a controlled environment. The green pea plant is a
widespread edible vegetable, which was chosen due to its
eﬃciency in metabolizing CBZ23 and its relatively fast growthand fruit formation. Extensive measurements in the soil and theplants were used in this study to calibrate the soil−plant modeland assess, for the ﬁrst time, its predictive uncertainty in aprobabilistic Bayesian calibration framework. The calibrated
model was then coupled with Global Sensitivity Analysis to
identify the factors driving the accumulation of CBZ in theedible parts of the plant and shed light on the role of diﬀerent
physicochemical properties on the translocation of CBZ in thesoil−plant continuum.

2. MATERIALS AND METHODS
2.1. Case Study Description. Green pea plants (P. sativumL.) were planted in 24 soil columns (a height of 20 cm, adiameter of 15.4 cm) under greenhouse conditions. The soil was
taken from the surface horizon (0−25 cm) of a Haplic
Chernozem developed on loess (Table S1). Soil samples wereﬁrst air-dried under greenhouse conditions (up to a soil−watercontent of 0.15 g g−1), then carefully disintegrated into
aggregates with a diameter smaller than 5 mm, homogenized,
and packed into the plastic columns to obtain the same bulk
density (1.1 g cm−3) in all columns. Columns were then wetted
to a soil−water content of approximately 0.24 cm3cm−3. Threeplant seeds were sown directly into the columns in a triangularspacing. Plants (three per each column) were initially irrigatedwith fresh water for 16 days. Next, plants in 16 soil columns were
irrigated with a solution of CBZ and in eight columns with fresh
water. The columns were weighed before and after irrigation torecord the water balance and estimate evapotranspiration. An
evaporation pan (diameter = 19.7 cm) was used to estimate theevapotranspiration demand in the greenhouse. Irrigation doses(Table S2) depended on decreases in average soil column watercontents to keep plants’ optimal conditions. No outﬂow at thebottom was observed. The experiment was performed between
May 15 and July 2, 2018, under greenhouse conditions (naturallight, air humidity of 30%−40%, and air temperature of 20−24°C).
The columns were analyzed as follows. One column was
dissembled on the 16th day to examine fresh and dry masses ofstems, leaves, and roots. Next samplings were carried out on the
23rd, 30th, 41st, and 48th day. Four columns were always
analyzed to obtain information about a plant growth (i.e., themass of roots, stems, leaves, and fruits, Figure S1),
concentrations of CBZ and its metabolites in plant tissues,and concentrations of compounds in four soil layers. One
column irrigated with fresh water was similarly analyzed as acontrol. Plant leaves were scanned, and their area (Figure S3)
was evaluated using the ImageJ software, version 1.47.30 To
monitor changes in the soil hydraulic properties over time, three
undisturbed 100 cm3 soil samples were taken from one soilcolumn and analyzed using the multistep outﬂow experiment.31
Soil water contents, θ (at depths of 2.5 and 15 cm), and pressure
heads, h (at depths of 5 and 15 cm), were measured in four∂θ= ∇[K × ∇(h + z)] − S(h)∂t(1)

where t is time [T], z is the vertical coordinate [L], θ is thevolumetric water content [L3L−3], K is the unsaturated hydraulicconductivity [LT−1], h is the pressure head [L], and S is a sinkterm representing root water uptake [T−1]. The transport of theith solute in the soil is described using the advection-dispersionreaction equation, assuming that solutes can exist only in thesolid and liquid phases:
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∂θCi
∂ρsi
+
= ∇(θDiW × ∇Ci) − ∇(qCi) − ra , i − ϕi∂t∂tArticledue to the nonvolatile behavior of CBZ. Tissue-waterpartitioning (KRW, KSW, KLW, and KFW [L3M−1]) is assumed.
Since the only detectable CBZ’s metabolite in plants was EPX(Table S6), the analysis was restricted to these two compounds
using a ﬁrst-order degradation coeﬃcient, τ [T−1], in eachcompartment, which simulates the transformation of CBZ in
EPX. While input concentrations and sorption parameters areconverted to molar units before executing the model, output
concentrations are reported in ng/g for visualization purposes.
2.3.2. Bayesian Analysis. This study adopts a probabilistic
approach based on the Bayesian inference to calibrate thedynamic plant uptake model and assess its predictive
uncertainty. Model calibration is required to estimateparameters that are diﬃcult to measure in the laboratory (e.g.,degradation rates)3 and others (e.g., VGM parameters) thatneed to be adjusted to match the experimental conditions, which
can be diﬀerent from those encountered in the laboratory.42 To
this aim, the multimodal nested sampling (MULTINEST)43 iscombined with the soil−plant model and measured data toestimate the parameters’ posterior distribution. Multiple studies
have demonstrated the accuracy and computational eﬃciency ofthis algorithm,44−47 whose thorough description can be found inrefs 43 and 48. As in refs 44 and 45, a convergence analysis isused to assess the stability and accuracy of the MULTINEST
estimator.
If we assume that error residuals are uncorrelated andnormally distributed with a constant variance, σ2, the loglikelihood function S(Ω) for the jth set of measurements can be
written as(2)

where Ci is the concentration of the ith solute in the liquid phase[ML−3], si is the concentration of the ith solute in the solid phase[MM−1], ρ is the soil density [ML−3], DW
i is the dispersion
tensor for the ith solute in water [L2T−1], q is the water ﬂux[LT−1], ra,I is the root solute uptake term [ML−3 T−1], and ϕirepresents the reaction sink/source term [ML−3 T−1].
The soil column proﬁle (a depth of 20 cm) is discretized in
100 ﬁnite elements reﬁned at the top to accommodate gradients
induced by the atmospheric conditions. The soil domain isdivided into two horizons (0 ≤ z < −10 cm; −10 ≤ z ≤ −20 cm)
to account for the eﬀect of diﬀerent root densities (Figure S2) on
soil hydraulic properties, which are described by the unimodal
van Genuchten−Mualem (VGM) function39 (parameters: θr[L3L−3], θs [L3L−3], α [L−1], n [-], and Ks [LT−1]). The batch
experiment data, presented by Schmidtová et al.,34 indicates that
the Freundlich adsorption isotherm can describe the sorption of
CBZ to the solid phase (parameters: Kf CBZ [L3β M1‑β M−1] andβCBZ [-]). Measured data show that carbamazepine 10,11epoxide (EPX) is the only CBZ metabolite detected in the soil
during the experiment (Table S7). The CBZ degradation
process in the soil is thus simulated using a sequential decay
chain with ﬁrst-order rate coeﬃcients, μLCBZ and μSCBZ [T−1],
accounting for the transformation of CBZ in EPX in the liquidand solid phases, respectively.
The measured water content at the beginning of theexperiment is used as the initial condition. No solute waspresent in the soil before starting the experiment. An
atmospheric boundary condition is applied at the soil surface,
while a seepage face boundary condition (BC) is set at thebottom. The concentration ﬂux across the top boundary issimulated using the classic Cauchy-type BC, while a zeroconcentration gradient is imposed at the bottom.
The piecewise linear Feddes function parameterizes the root
water stress40 and regulates actual transpiration (parameters: P0,
POpt, P2H, P2L, and P3). Simultaneously, a root density
function modulates actual root water uptake depending on theroot growth. A logistic growth function was ﬁtted to themeasured wet masses of roots at diﬀerent depths (Figure S2) todetermine the average root growth rate, which was then used toestimate the root density during the numerical simulation. The
measured evapotranspiration demand is partitioned into
potential evaporation and transpiration using a time series ofleaf area indices, which were calculated by ﬁtting a logistic
function to the measured one-sided leaves area (Figure S3). The
diﬀerence between total evapotranspiration, measured byweighing the columns, and transpiration is used to estimate
evaporation from the soil surface (Figure S4). All compounds
dissolved in water are passively taken up by plant roots when
their concentrations are lower than maximum allowed solution
concentrations, Cmax [ML−3].41
Plants are conceptualized into four compartments: roots,
stem, leaves, and fruits. Each compartment is assumed to have alogistic growth38 (parameters: W [L3M−1], Mmax [M], M0 [M],Kgr [T−1], and SA [L2M−1]). The speciﬁc areas of fruits andleaves are used to partition transpiration ﬂuxes. The CBZ
solution was carefully applied on the soil surface to minimize its
dispersion in the surrounding environment. Therefore, the eﬀectof gaseous uptake and particle deposition could be neglected in
the model. Similarly, volatilization is excluded from modeling

k

k
k
1
S j(Ω) = − ln(2π ) − ln(σ 2) −∑ (Hi(Ω) − yi ̅ )22
2
2σ 2 i = 1(3)

where Hi(Ω) and y̅i are the ith model realization and its
corresponding measured value, respectively, and k is the numberof observations in the jth set of measurements. The measured
data used in the Bayesian analysis include the time series ofvolumetric water contents (θ) and pressured heads (h) at two
diﬀerent locations, CBZ (Csoil,CBZ) and EPX (CS,EPX) concentrations in the soil and CBZ and EPX concentrations in the roots(CR,CBZ, CR,EPX), stem (CS,CBZ, CS,EPX), leaves (CL,CBZ, CL,EPX), andfruits (CF,CBZ, CF,EPX). Therefore, the log-likelihood function
L(Ω) is the aggregated sum of single likelihoods. The mean andvariance of each measurement set used in the model calibration
are calculated from the column replicates (Tables S6 and S7).
12

L(Ω) = ∑ S j(Ω)
j=1

(4)

The dimensionality of the inverse problem is reduced by ﬁxing
speciﬁc model parameters (Table 1). In particular, the results ofmultistep outﬂow experiments are used to ﬁx the residual andsaturated water contents and saturated hydraulic conductivity.
This choice is motivated by the dynamics of the measured soil
moisture, which never approached nearly saturated conditions
during the experiment, thus providing negligible information
content in that range. Feddes’ parameters for green peas (i.e., P0,
POpt, P2H, P2L, and P3 in Table 1) are taken from theliterature.49 Results of batch and degradation experiments areused to ﬁx the Freundlich exponent and the ﬁrst-orderdegradation coeﬃcients for CBZ, respectively. The same
sorption parameters are assumed for EPX, whose further
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ArticleFigure 1. Comparison between the measured (black circles) CBZ (left column) and EPX (right column) concentrations in diﬀerent plant’s
compartments, CBZ concentration in soil (0 < z < −5 cm), pressure heads (z = −5 cm), and volumetric water contents (z = −2.5 and −15 cm), andcorresponding modeled values (blue lines) obtained by random sampling of 100 solutions from the posterior parameter distributions. The error bars
indicate the standard deviations of the measurements. The red line indicates the model predictions obtained by using the median solution reported inTable 1. The mean standard deviation used in the Bayesian analysis (σ) and the median root mean square error (RMSE) are reported in each subplot.

degradation in the soil is neglected.21 Water contents of plants’tissues are assumed constant and calculated from the averagemeasured fresh and dry weights during the experiment. Growthparameters of diﬀerent plant compartments are estimated byﬁtting logistic functions to the time series of measured plantmasses (Figures S1 and S2). Due to these prior assumptions, thedimensionality of the problem is reduced to 15 parameters.
Uniform prior distributions are used in the Bayesian analysis.
Parameter bounds are provided in Table 1.
2.3.3. Bioaccumulation of Carbamazepine in Edible Fruits:
Global Sensitivity Analysis. After the model calibration and theuncertainty assessment, a Global Sensitivity Analysis isperformed on the calibrated parameters to identify the mostimportant factors driving the bioaccumulation of CBZ in greenpeas’ fruits. The analysis provides a statistical basis to shed lighton the relative importance of diﬀerent physicochemical
processes on the translocation of CBZ toward the edible partsof the plant, which are directly linked to human and animals’
intake.

The Random Balance Designs Fourier Amplitude Sensitivity
Test (RBD-FAST)50,51 is applied. The method combines theaccuracy of the classic Fourier Amplitude Sensitivity Test52 withthe computational cheapness of Satterthwaite’s random balance
designs53 to estimate the ﬁrst-order eﬀect (S1) in a variancebased context.54 Higher S1 values are attributed to moreinﬂuential parameters. The main advantage of the RBD-FAST
method is that the total number of model runs is kept down to N
instead of d × N (like in Sobol’ or FAST methods), where d isthe number of factors investigated. In the present study, aconvergence analysis is used to determine N (Figure S5).

3. RESULTS AND DISCUSSION
3.1. Bayesian Analysis. Figure 1 shows a comparison
between the measured (black circles) CBZ concentrations in
diﬀerent plant’s compartments and soil (0 < z < −5 cm),pressure heads (z = −5 cm), and volumetric water contents at
two diﬀerent depths (z = −2.5 and 15 cm) and the model
predictive checks (blue lines) obtained by random sampling of2995

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ArticleFigure 2. Sensitivity analysis results. (A) and (B) Simulated CBZ concentrations in the fruits as a function of α and Kf, respectively. (C) and (D)Simulated root solute uptake as a function of α and Kf, respectively. (E) Simulated average pressure head (pF = log(|h|) in the root zone as a function ofα. (F) Simulated average CBZ concentrations in the liquid phase in the root zone as a function of Kf. The red dashed lines indicate the Feddes’
parameters (Table 1). The plots were obtained by performing numerical simulations with three diﬀerent values of α1 and Kf. In particular, the mediansolution reported in Table 1 was used as a reference, and only the values of α1 and Kf were alternatively changed to match the minimum and the
maximum listed in Table 1.

100 solutions from the posterior parameter distributions.
Posterior predictive checks are used to assess the eﬀect of theuncertainty on the model predictions and to “look for systematic
discrepancies between real and simulated data”,55 thus
representing a fundamental tool for model criticism. Results
demonstrate that the model can reproduce water ﬂow and soluteaccumulation in the soil as well as the dynamics of thetranslocation and metabolization of CBZ and EPX in all plantcompartments, with limited uncertainty and satisfactory
accuracy. The highest discrepancy is observed in the fruit andleaves compartments, for which the model overestimates thesolute concentrations, though the error magnitude is low. Thisdeviation can be attributed to dynamic variations in the plantwater content and the sorption coeﬃcient during the experiment, which are not considered in the model. The volumetricwater content is well described, while the model seems tounderestimate the variance in the measured pressure head.
However, this tendency might be partially related to a very small
measurement footprint of the tensiometers, which makes themextremely sensitive to heterogeneities in the soil’s hydraulicregime not represented in the model.
The calculated 5%, 50%, and 95% quantiles of the parameters’posterior distributions are reported in Table 1 and indicate awell-posed inverse problem characterized by low parameters’
uncertainty. The diﬀerence between the VGM shape parameters
for the two soil horizons is appreciable and conﬁrms the roots’
potential inﬂuence on water ﬂow. In particular, smaller values of
α and n calculated for the ﬁrst soil layer are compatible with anincreased pore heterogeneity caused by a higher root density inthat part of the soil column.56 The estimated soil−waterpartition coeﬃcient, Kf CBZ, is in line with the results of the batch
experiment (i.e., Kf CBZ ≈ 2.8 cm3β μg1‑β g−1) and with otherstudies,27,34 thus conﬁrming the overall reliability of the analysis.
The narrow conﬁdence intervals estimated for the soil hydraulicparameters suggest that the soil behavior inﬂuences the uptake
and translocation processes. This aspect is further investigated in
the following sensitivity analysis.
Interestingly, the Bayesian calibration framework reveals alimited solute uptake capacity of plants (Table 1). This is also
conﬁrmed by the measured data, which show a much higher
persistence of CBZ in the soil than in the plants (Figure S7). In
particular, the CBZ and EPX median maximum concentrations
taken up by plants are 4.45 and 0.1 ng cm−3, respectively. The
reduced uptake mechanism is potentially explained by thediﬀerence between root permeability to chemicals and water,
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Articlethe nonlinear sorption process (Figure S6). The solute
movement toward deeper soil horizons is restricted by low
water ﬂow velocities and solute dispersivity. Under suchconditions, the air-entry pressure parameter α1 partiallyregulates actual root CBZ uptake (Figure 2), the CBZconcentration in the fruit compartment, and the root zonepressure head and concentration, which increase with increasing
values of α1 and Kf, respectively. Root solute uptake is negatively
correlated with α1 [(C) in Figure 2], mainly due to the change inthe transpiration pattern induced by diﬀerent pressure head
distributions in the root zone [(E) in Figure 2]. In the simulated
scenarios, higher values of α1 lead to a lower (in absolute value)
simulated root zone pressure head, which drops below the
optimal pressure head value for transpiration (i.e., POpt in the
Feddes’ model), thus reducing actual root water and solute
uptake. This physical behavior is exacerbated after t = 30 days[(C) and (E) in Figure 2] and results in lower translocation of
CBZ toward the fruit compartment [(A) in Figure 2].
Conversely, for α1 = 0.001 (1/cm), the root zone pressure
head is shifted toward much higher values, where the actual
transpiration rate is also reduced, though the eﬀect is lesspronounced. For α1 = 0.013 (1/cm) (i.e., median value in Table1), the root zone pressure head oscillates in the optimaltranspiration range (i.e., P2H < h < POpt). Therefore, it can beconcluded that soil hydraulic properties aﬀect the accumulationof CBZ in fruits by simultaneously driving water ﬂow in theunsaturated domain and modulating the transpiration pattern.
These eﬀects then propagate nonlinearly into the plant.
However, it must be emphasized that these conclusions are
not general but restricted to the modeling scenario investigatedin the present study.
On the other hand, CBZ sorption in the soil aﬀects linearly
simulated CBZ concentrations in the fruit compartment.
Generally, higher sorption (which for CBZ increases withincreasing organic matter content in soils34) reduces the soluteavailability in the root zone [(F) in Figure 2], thus reducing theamount of solute entering the roots [(F) in Figure 2] and theconcentration in the fruits [(B) in Figure 2]. Klement et al.23
found positive correlations between Kf and normalized
concentration loads of the parent compound CBZ and its
metabolites. In particular, the correlation was signiﬁcant (95%level) for roots and stems but not signiﬁcant for leaves and fruits.
This suggests that organic-rich soils might reduce the translocation of CBZ and similar compounds to the edible parts of theplant.
3.3. Strengths and Limitations. We consider this study to
be innovative in two main aspects:

making the uptake of CBZ and EPX slower than that of water.
The use of a maximum uptake concentration used in HYDRUS1D shares some conceptual and mathematical similarities withthe retardation factor proposed by Gredelj et al.57 to simulate
the translocation of perﬂuoroalkyl acids in red chicory.
However, this model parameter lacks physical meaning andtheoretical background to generalize it for other modelingcircumstances. The diﬀerence between CmaxCBZ and CmaxEPX
suggests that CBZ is taken up to a greater extent than EPX,
whose occurrence in plant tissues results from in-plant
metabolism rather than plant uptake. This is also conﬁrmedby the negligible amount of EPX observed in the soil (Table S7).
Comparing the estimated ﬁrst-order degradation rates further
reveals that most of the CBZ metabolization occurs in the leaves.
This is further highlighted by the signiﬁcantly higher EPX
concentrations measured in the leaves compared to othercompartments. In contrast, roots and stem mainly act as
reservoirs for CBZ, which is either sorbed or translocatedupward. This behavior was observed in other studies aswell.2,16,17,20,23,25,27 Both the experiment and the model indicate
a low accumulation of a chemically active compound, such as
EPX, in the plant’s edible part. The lower accumulation of bothcompounds in fruits can be partially explained by thesigniﬁcantly shorter exposure to the contamination and lower
transpiration of fruits than leaves.23 In addition, the metabolization of CBZ in fruits has been proven to be generally lesseﬃcient.8,19,23
The comparison between the estimated partition coeﬃcients
conﬁrms that sorption occurs mainly in the roots and stem, while
the wide conﬁdence intervals for KLW and KFW imply the lack of
their statistical identiﬁability. The estimated median value forroots (i.e., KRW = 13.3 cm3gfw−1) agrees with Chuang et al.1 andis mainly related to the aﬃnity of CBZ to the plantcomposition58 and its hydrophobicity.59 In particular, diﬀerent
plant components such as lipids, carbohydrates, waxes, lignin,
and suberin can act as sorption sites for chemicals.60 Their
distribution is tissue-dependent,61 thus leading to diﬀerent
sorption coeﬃcients in diﬀerent plant compartments.
3.2. Global Sensitivity Analysis. The convergence analysis
indicated that 3000 model executions were suﬃcient to obtainstable estimations of the ﬁrst-order sensitivity indices (reported
in the last column of Table 1) for all investigated parameters(Figure S5). Nine factors out of 15 exhibit an appreciableinﬂuence on the translocation of CBZ toward fruits. The mostinﬂuential parameter is the maximum concentration taken up by
plants, which regulates the solute amount entering the roots.
Once the compound enters the plant, the sorption anddegradation processes in the roots and stem inﬂuence its
translocation into the fruits, as suggested by the calculatedsensitivity indices. Higher sorption in these compartments
retards the translocation of CBZ in the transpiration streams andprovides more time for the in-place enzymatic degradation. On
the other hand, the leaves’ role is insigniﬁcant as the phloem ﬂux
is neglected in the numerical simulations.
The role of soil hydraulic properties holds more interest. The
sensitivity analysis reveals that the VGM shape parameters of theﬁrst soil horizon and the soil−water partition coeﬃcient strongly
inﬂuence the accumulation of CBZ in the fruit compartment. In
contrast, the contribution of the second soil layer is insigniﬁcant.
The roots and solute distribution in the soil are bothcontributing factors to this behavior. Root water and solute
uptake occurs mainly in the upper part of the soil proﬁle, where
the root density is higher, and CBZ is more bioavailable due to

To our knowledge, this is the ﬁrst study involving
numerical simulations of dynamic plant uptake ofchemicals that includes extensive spatial and temporalmeasurements of soil- and plant-related quantities.
Indeed, compared to previous studies,62 the dataset
includes measured volumetric water contents and soilpressure heads at diﬀerent depths, providing further
information about the unsaturated soil domain. Thissigniﬁcant and variegated amount of data allows us tocharacterize water ﬂow and reactive solute transport in thesoil−plant continuum with low predictive uncertainty andsatisfactory accuracy.
Compared to other inverse modeling studies,44,63−66 thisstudy applies, for the ﬁrst time, a Bayesian calibration
framework to estimate both soil and plant parameters,
2997

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Environmental Science & Technology■

thus providing a statistical basis for the uncertainty
assessment in the soil−plant continuum. Furthermore,using the Nested Sampling algorithm allows us to estimate
the posterior parameter distribution and the marginal
likelihood simultaneously. While not being of immediate
interest to the present study, the latter can be used toassess model complexity, a valuable tool when dealing
with highly complex and parameterized models. Thismethodological feature represents an advantage against
other approaches focused on the use of Monte Carlo
Markov Chain algorithms.63−65

pubs.acs.org/est

ArticleASSOCIATED CONTENT

sı Supporting Information*

The Supporting Information is available free of charge athttps://pubs.acs.org/doi/10.1021/acs.est.0c07420.
Detailed description of the analytical methods, (Table S1)
basic soil characteristics of the Haplic Chernozem on
loess, (Table S2) irrigation doses and carbamazepine
concentrations, (Table S3) information about LC−MS/
MS parameters, (Table S4) compound recovery in 200 ng
per 2 g of soil and 50 ng per 0.05 g of plant tissues (%),
(Table S5) limits of compounds’ quantiﬁcation (ng g−1),(Table S6) concentrations of carbamazepine andcarbamazepine 10,11-epoxide in plant tissues, (TableS7) concentrations of carbamazepine and carbamazepine
10,11-epoxide in soils, (Figure S1) total wet and dry
masses and water ratios of plant tissues in each column,(Figure S2) wet and dry masses of roots at diﬀerent soil
depths, (Figure S3) total area of leaves in each column
evaluated on scanned fresh leaves using the ImageJsoftware, (Figure S4) measured transpiration, evaporation, and cumulative evapotranspiration, (Figure S5)
convergence analysis of ﬁrst-order sensitivity indices,(Figure S6) simulated root water uptake, pore water
concentration, and root solute uptake along the soil
proﬁle at diﬀerent times, and (Figure S7) measured
average fractions of the applied solute mass (the sum of
CBZ and EPX) in the soil and diﬀerent plant compartments at diﬀerent times (PDF)

However, these strengths are paired with several limitations.
First, for most practical risk assessment applications, it is notpossible to obtain comprehensive measurements due to time
constraints and budget limitations. This raises some questions
regarding the model’s applicability in a predictive setting in caseof limited observations. There is no clear and deﬁnite answer tothis. Still, we advocate the ubiquitous use of uncertainty analysis(e.g., Bayesian analysis) to identify the most justiﬁable model
complexity level in light of the information content of the data
available. Furthermore, a Global Sensitivity Analysis can, as
demonstrated in this study, be used in a prognostic way to target
the most important processes and focus the experimental andmodeling eﬀort on them. In such circumstances, a crossdisciplinary approach is of crucial importance.
Other model limitations include the macroscopic descriptionof root water uptake and the lack of the physical meaning of the
maximum uptake concentration. The former simpliﬁes the rootsystem hydraulics, which plays an important role in root waterand solute uptake.67 The latter hinders the generalization of theparticular modeling approach, which is appealing from acomputational point of view due to its simplicity, to otherconditions. Therefore, it is important to improve therepresentation of these processes in the model to increase its
generalizability and accuracy.
3.4. Implications and Future Outlook. This study’s main
aim was to evaluate further the performance of the coupled soil−
plant model developed by Brunetti et al.27 against measurementsfrom a comprehensive experiment on the translocation andtransformation of CBZ in green pea plants in a controlledenvironment. A probabilistic Bayesian framework was used tocalibrate the model and assess its predictive uncertainty. Results
conﬁrmed that the model could reproduce accurately and with
low uncertainty the transport of CBZ in the soil and its
translocation and transformation in diﬀerent plant tissues. The
following Global Sensitivity Analysis has further highlighted therole of soil in bioaccumulation of CBZ in the fruit compartment,
mainly by regulating actual transpiration streams and CBZbioavailability in the root zone.
Overall, the study conﬁrms that the model can be successfully
used for simulating the translocation of neutral compounds inthe soil−plant continuum in a partially mechanistic way. This
opens new possibilities for a more comprehensive assessment of
the contamination risk, allowing the development of reliable
mitigation strategies for environmental pollution problems inboth the soil and plant domains. On this basis, future studies
should explore the possibility of extending the model
applicability to ionic compounds frequently encountered incontaminated sites. However, this would require extensive
modiﬁcations to the plant model.68■

AUTHOR INFORMATION

Corresponding Author

Giuseppe Brunetti − Institute for Soil Physics and Rural Water
Management, University of Natural Resources and Life
Sciences, Vienna (BOKU), 1180 Vienna, Austria;
orcid.org/0000-0001-7943-8088;
Email: giuseppe.brunetti@boku.ac.at
Authors

Radka Kodešová − Faculty of Agrobiology, Food and Natural
Resources, Dept. of Soil Science and Soil Protection, Czech
University of Life Sciences Prague, CZ-16500 Prague 6, Czech
Republic
Helena Švecová − Faculty of Fisheries and Protection of Waters,
South Bohemian Research Center of Aquaculture andBiodiversity of Hydrocenoses, University of South Bohemia inČeské Budějovice, CZ-38925 Vodňany, Czech Republic
Miroslav Fér − Faculty of Agrobiology, Food and Natural
Resources, Dept. of Soil Science and Soil Protection, Czech
University of Life Sciences Prague, CZ-16500 Prague 6, Czech
Republic
Antonín Nikodem − Faculty of Agrobiology, Food and Natural
Resources, Dept. of Soil Science and Soil Protection, Czech
University of Life Sciences Prague, CZ-16500 Prague 6, Czech
Republic
Aleš Klement − Faculty of Agrobiology, Food and Natural
Resources, Dept. of Soil Science and Soil Protection, Czech
University of Life Sciences Prague, CZ-16500 Prague 6, Czech
Republic
Roman Grabic − Faculty of Fisheries and Protection of Waters,
South Bohemian Research Center of Aquaculture andBiodiversity of Hydrocenoses, University of South Bohemia in2998

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Environ. Sci. Technol. 2021, 55, 2991−3000

Environmental Science & Technology

pubs.acs.org/estČeské Budějovice, CZ-38925 Vodňany, Czech Republic;
orcid.org/0000-0002-0935-2075
Jiří Šimůnek − Department of Environmental Sciences,
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Notes

The authors declare no competing ﬁnancial interest.

■

ACKNOWLEDGMENTS
The authors acknowledge the Czech Science Foundation’s
ﬁnancial support, project Behavior of Pharmaceuticals in theSoil−Water−Plant system (no. 17-08937S). The work was also
supported by the European Structural and Investment Funds,
projects NutRisk (no. CZ.02.1.01/0.0/0.0/16_019/0000845).
Open access funding provided by University of Natural
Resources and Life Sciences Vienna (BOKU).

■

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https://dx.doi.org/10.1021/acs.est.0c07420
Environ. Sci. Technol. 2021, 55, 2991−3000