The Dynamic Plant Uptake Modulefor HYDRUS (2D/3D)
Simulating the Translocation and Transformation of
Neutral Compounds in the Soil-Plant Continuum
Version 1.0

Giuseppe Brunetti1, Jirka Šimůnek2, Radka Kodešova, and Miroslav Šejna3
April 2021
1

Institute for Soil Physics and Rural Water Management,
University of Natural Resources and Life Sciences, Vienna, Austria
2

Department of Environmental Sciences
University of California Riverside, Riverside, CA, 92521, USA
3

PC Progress, Ltd., Prague, Czech Republic© 2021 J. Šimůnek and M. Šejna. All rights reserved.

Table of Contents
TABLE OF CONTENTS .................................................................................................... 2
LIST OF FIGURES ............................................................................................................. 3
LIST OF TABLES ............................................................................................................... 4
ABSTRACT .......................................................................................................................... 5
1. INTRODUCTION............................................................................................................ 7
2. CONCEPTUAL MODEL ............................................................................................... 8
3. DYNAMIC PLANT UPTAKE........................................................................................ 93.1. Mass Balance ............................................................................................................ 93.2. Plant Growth ........................................................................................................... 10
3.3. Chemical Equilibrium and Partitioning .................................................................. 10
3.4. Translocation........................................................................................................... 11
3.5. Exchange Plant-Air: Plant Permeability ................................................................. 11
3.6. Volatilization........................................................................................................... 13
3.7. Gaseous Uptake and Particle Deposition ................................................................ 13
3.8 Metabolization of Neutral Compounds .................................................................... 14
4. NUMERICAL IMPLEMENTATION ......................................................................... 16
5. PREPROCESSING AND INPUT DATA .................................................................... 175.1. Main Processes ........................................................................................................ 175.2. DPU Parameters ...................................................................................................... 17
6. POST-PROCESSING .................................................................................................... 20
6.1. Results – Profile Information .................................................................................. 20
7. EXAMPLE PROBLEMS .............................................................................................. 21
7.1. Example 1. Translocation and Tranformation of Carbamazepine in Green Pea
Plants ...................................................................................................................... 21
7.2. Example 2. Uptake of Benzene from Air................................................................ 26
8. REFERENCES ............................................................................................................... 29

2

List of Figures
Figure 1. Schematic of the physicochemical processes in the (A) soil-plant continuum andtheir theoretical conceptualization in the (B) coupled soil-plant model. .................................. 8
Figure 2. Examples of (A) double, (B) sequential, and (C) closed metabolization chains of
three compounds in the jth compartment (in this case, j = 1, i.e., in the roots). Black circles
indicate an incomplete conversion of the reactant in by-products. ......................................... 15
Figure 3. The Main Processes dialog window (left) and the Navigator Bar with the displayed
Dynamic Plant Uptake command (right). ............................................................................... 17
Figure 4. The Dynamic Plant Uptake Module Parameters dialog window. ........................... 18
Figure 5. The metabolization information. ............................................................................. 18
Figure 6. The DPU-related results displayed on the Navigator Bar. ...................................... 20
Figure 7. The DPU Parameters dialog window for example problem 1. ................................ 22
Figure 8. CBZ concentrations in different plant compartments versus time. ......................... 22
Figure 9. CBZ metabolization fluxes in different plant compartments versus time. .............. 23
Figure 10. EPX concentrations in different plant compartments versus time. ....................... 23
Figure 11. EPX inflow fluxes in different plant compartments versus time. ......................... 24
Figure 12. Masses of plant compartments in fresh weight versus time. ................................. 24
Figure 13. CBZ mass balance error in different plant compartments versus time. ................ 25
Figure 14. The DPU Parameters dialog window for example problem 2. .............................. 26
Figure 15. Benzene concentrations in different plant compartments versus time. ................. 27
Figure 16. Gaseous uptake of benzene in different plant compartments. ............................... 27
Figure 17. Volatilization flux of benzene in different plant compartments. ........................... 28

3

List of Tables
Table 1. The list of output files created by the DPU module. ................................................ 20

4

Abstract
Brunetti, G., J. Šimůnek, and M. Šejna, The Dynamic Plant Uptake Module for HYDRUS(2D/3D) Simulating the Translocation and Transformation of Neutral Compounds in the soilplant continuum, Version 1.0, PC Progress, Prague, Czech Republic, 30 pp., 2022.
This manual presents the implementation of the Dynamic Plant Uptake (DPU) model
developed by Brunetti et al. (2019a) to describe the translocation and transformation ofneutral compounds in the soil-plant domain. The numerical approach combines a mechanistic
description of water flow and solute transport in the soil with a multi-compartment
conceptualization of transport and reaction processes in the plant. In particular, the model cansimulate translocation of compounds from the roots to the stem, and from the stem to leaves
and fruits with the transpiration stream; volatilization of compounds in the stem, leaves, andfruits; gaseous and particle deposition from air to the stem, leaves, and fruits, compounds
dilution by plant growth in all compartments, and compounds metabolization in allcompartments. The model was successfully applied by Brunetti et al. (2021) to predict theuptake and metabolization of Carbamazepine in green pea plants.
The purpose of this report is to document the DPU module for the HYDRUS (2D/3D)
software package (Šimůnek et al., 2018). The module, as well as the description of the modulein this report, is largely based on the theoretical development of Brunetti et al. (2019a). The
report serves as both a Technical Manual and a User Manual, as well as a reference documentof the Graphical User Interface of DPU-related parts of the HYDRUS software package.

5

DISCLAIMER
The DPU module was developed as a supplemental module of the HYDRUS (2D/3D software
package to simulate the translocation and transformation of neutral compounds in the soilplant continuum. The software has been verified against selected test cases. However, nowarranty is given that the program is entirely error-free. If you do encounter problems with thecode, find errors, or have suggestions for improvement, please contact the senior author at
Giuseppe Brunetti
Email: giuseppe.brunetti@boku.ac.at

6

1. Introduction
Food contamination is a direct consequence of environmental pollution and represents amajor risk for human health. Recently, the Food and Agricultural Organization of the United
Nations (FAO, 2019) reported that food contaminated natural toxins or chemicals are
responsible for more than 339,000 people falling ill and 20,000 dying worldwide every year.
Plants represent the most common pathway into the human and animal food chain forenvironmental contaminants. Chemicals from polluted environments are taken up by plants,
where they are bioaccumulated, and eventually metabolized in active by-products (e.g.,
Mattina et al., 2003; Sabourin et al., 2012; Zhang et al., 2009), some of which can be
dangerous for human health (e.g., Kodešová et al., 2019a; Malchi et al., 2014; So et al., 1994;
Warner et al., 1992). Thus, widespread pollution forces the scientific community to better
understand physicochemical processes within the soil-plant-atmosphere continuum in orderto develop reliable mitigation strategies for food risk assessment and food safety.
Numerical models certainly play a crucial role in reaching this goal. Several plant uptake
models have been developed and tested in the past, ranging from empirical to mechanistic
models. Trapp (2007) and Rein et al. (2011) developed a mechanistic multi-compartment
model encompassing all major physicochemical processes occurring during the Dynamic
Plant Uptake (DPU) process. The model, initially developed for neutral compounds, waslater extended to ionic chemicals and tested successfully against measured data under
different operating conditions (Trapp, 2009). Despite acceptable results, existing DPU
models generally lack an accurate description of physicochemical processes in soils, which
are among the most important sources of pollution for plants (Eugenio et al., 2018). To
overcome this limitation, Brunetti et al. (2019a) coupled HYDRUS and a modified versionof the multi-compartment dynamic plant uptake model proposed by Trapp (2007), which
accounts for differentiated multiple metabolization pathways in plant’s tissues. The
developed model was successfully applied to predict the translocation and transformation of
Carbamazepine in green pea plants (Brunetti et al., 2021).
The main aim of this report is to document the implementation of the Dynamic Plant Uptake(DPU) module in the HYDRUS software suite. The model simulates translocation andtransformation of neutral compounds in the soil-plant continuum and calculates soluteconcentrations in different plant’s compartments. The general conceptual basis of the module
is discussed in detail in Brunetti et al. (2019a). Here, we provide the theoretical background,the implementation details, and some examples.
The documentation in this report focuses mainly on the dynamic plant uptake. All processes
related to variably-saturated water flow and solute transport in the soil are described in detail inthe HYDRUS (2D/3D) documentation (Šimůnek et al., 2018) and will not be repeated here.

72. Conceptual Model
The numerical model is based on the multi-compartmental approach proposed by Trapp(2007) and further developed by Rein et al. (2011) and Legind et al. (2011). The model
simulates translocation and biodegradation of N neutral compounds in plants, which areconceptualized in four compartments: roots, stem, leaves, and fruits. Transport processes
consist of advection (with xylem flow) and diffusive losses or gains, while reaction processes
mainly represent the enzymatic biodegradation in plant’s tissue. More specifically, thefollowing processes are considered in the DPU model:- Translocation of compounds from the roots to the stem, and from the stem toleaves and fruits with the transpiration stream. The phloem flux is neglected.
- Volatilization of compounds in the stem, leaves, and fruits.
- Gaseous and particle deposition from air to the stem, leaves, and fruits.
- Compounds dilution by plant growth in all compartments.
- Compounds metabolization in all compartments.

Figure 1. Schematic of the physicochemical processes in the (A) soil-plant continuum andtheir theoretical conceptualization in the (B) coupled soil-plant model.

83. Dynamic Plant Uptake
3.1. Mass Balance
The concentration matrix C has N rows (for each compound, represented below by asubscript i) and four columns (for each compartment, i.e., 1=roots, 2=stem, 3=leaves, and
4=fruits, represented below by a subscript j), and contains concentrations expressed as massof each compound per fresh weight in different plants’ compartments [MsMfw-1; wheresubscript s refers to solutes and fw to fresh weight].
Transport and reaction processes depend on the physical and chemical properties of the plantand compounds, respectively. In particular, the characteristics of four plant tissues are
summarized in seven vectors:
 M 10 
 M 1max  K1gr  S1A W1 
 L1 
 1 
 0
 max  gr 
 A
W 
L 
 
 2
 2
M 2 
M 2 
K2 
 S2 
 2 
W    ; L    ; M 0   0  ; M max   max  ; Κ gr   gr  ; S A   A  ; ρ   
W3  L3 
M 3 
M 3 
 K3 
 S3 
 3 
0max
gr
AW4 
 L4  M 4 
 M 4 
 K 4  S4   4 (1)

where W is the water content of the plant [L3Mfw-1], L is the lipid content of the plant[MlMfw-1; where subscript l refers to the lipid content], M0 is the initial plant mass [Mfw],
Mmax is the maximum plant mass [Mfw], Kgr is the growth rate coefficient [T-1], SA is theplant’s specific area [L2Mfw-1], and ρ is the plant’s density [MfwL-3]. On the other hand,compounds’ properties are described by four vectors:

 log KOW1  K AW1  C A1  m1 






 
 log KOW2  K AW2  C A2  m2 
K OW   ; K AW  ; CA  
;m   
:


 : 
 : 
 : 
log K K 
C m N OWN  AWN  AN 

(2)where KOW is the n-octanol-water partition coefficient [-], KAW is the air-water partition
coefficient [L3L-3], CA is the compound concentration in the air [MsL-3], and m is the molar
mass [M]. Other required inputs are the air temperature T [K] and the relative humidity ϕ [-].
The mass balance of N compounds in the four plant’s compartments is mathematicallydescribed using a system of ordinary differential equations that is written in a compact formas:dC
 Q IN  Q DEP  QGAS  QTR  QVOL  Ω
dt(3)

where QIN is the inflow flux [MsMfw-1T-1] (for each compound and each compartment), QDEPis the deposition of a chemical from particle deposition, QGAS is chemical gaseous uptake

9

from the air, QTR is the translocation flux between compartments, QVOL is the volatilization
flux, and Ω represents reactions.
In the numerical model, Eq. 3 is solved implicitly in time using the backward Euler method(Butcher, 2016) to increase the stability of the numerical solution:

Ct t  Ct
t
t t
t t
t t
 QtINt  QtDEP QGAS
 QTR
 QVOL Ωt tt(4)

Eq. 4 is expressed as a linear equation system, which is solved using the iterative quasiNewton Broyden’s method (Broyden, 1969) at each time step.
3.2. Plant Growth
Many annual crops exhibit a logistic growth characterized by an exponential growth at the
beginning and an asymptotic behavior towards ripening. Accordingly, the change of the plantmass in each compartment M [Mfw] as a function of time t [T] is expressed as:
dMM  K gr M 1 dt
 M max (5)The plant mass in each compartment can be calculated by integrating the logistic growth
function as follows:

M(t ) 

M max
M

K t
1   max  1 exp gr
 M0


(6)

The plant surface area A [L2] is related to the plant mass M through the specific surface area
SA [L2Mfw-1]:

Aj (t )  S jA M j (t )(7)where index j refers to four plant compartments. The model can alternatively use measured
plant growth data and interpolate between measured data points.
3.3. Chemical Equilibrium and Partitioning
The typical timescale for chemical diffusion of neutral compounds through a cell membrane
is negligible compared to the timescale of soil-plant processes. Under such circumstances,
the rate of the sorption process is fast enough to consider instantaneous equilibrium, and thecapacity of a chemical to diffuse across membranes can be described by the equilibrium
partition coefficient. In particular, the equilibrium partitioning between a hydrophobic phase(lipids, oils, etc.) and water is described by the n-octanol-water partition coefficient KOW [-].

10

Measured values are available for many compounds, and they are usually expressed using alogarithmic scale. Similarly, the coefficient KAW [-] describes the partitioning between liquidand air.
Briggs et al. (1982) defined a plant-water partition coefficient KPW [L3Mfw-1], which isexpressed in its matrix form as:b
K PWij  W j  L j aK OWii  1, N and j  1, 4

(8)

where Wj and Lj are the water [L3Mfw-1] and lipid contents of the plant compartments [MlMfw1], respectively, a is a coefficient [L3Ml-1] usually assumed 0.00122 m3kgl-1 (Trapp, 2007),and b is an exponent equal to 0.77 and 0.95 for roots and plant shoots, respectively. Indices iand j refer to matrix columns (to N compounds) and rows (4 compartments), respectively.
3.4. Translocation
Xylem is responsible for water translocation from the roots to other plant compartments
induced by plant transpiration. The effect of the plant water storage is neglected (e.g., Javaux
et al., 2013; Manoli et al., 2014). Such assumption, which is valid only for small crops(Hartzell et al., 2017; Vogel et al., 2017), implies that the xylem flow QXYL [L3T-1] is equal to
the transpiration stream through the roots and stem, QTP, while it is partitioned in fruits andleaves using corresponding surface areas (Trapp, 2007):Q XYL  QTP


QTP

QTP 

A4QTP
A4  A3

A4QTP 
A4  A3 (9)The solute translocation flux QTR [MsMfw-1T-1] is expressed as:

QTRij QXYLij Cij(10)

M j K PWij

Leaves and fruits are the ends of the xylem system, and thus no further translocation isassumed in these compartments. Such an assumption implies that to facilitate the model
implementation, we can similarly define for each compartment the solute inflow QIN [MsMfw1 -1
T ], which contains the compounds. In particular, solute inflow into the root compartment isrepresented by actual solute uptake calculated by HYDRUS for a soil surface area, which isthe product of the “length of the surface associated with transpiration“ multiplied by a one
length unit in the penpendicular direction, divided by the roots mass [MsMfw-1T-1], while thetranslocation flux from the roots is the inflow for the stem. Finally, the xylem flow from thestem is divided into two streams that enter leaves and fruits.
3.5. Exchange Plant-Air: Plant Permeability

11

The plant-air exchange is regulated by the permeability of the plant’s components (Trapp,
2007). A chemical in the air has to overcome only the air boundary layer between the leaf
surface and the turbulent atmosphere. It can then adsorb on the leaf surface, which is a waxy
layer known as the cuticle. On the other hand, a chemical transported by the transpiration
stream into the leaf can be exchanged with air through cuticles or stomata. Thus, threedifferent phases provide resistance (aqueous phase, lipid phase, and gas phase), and two
pathways are in parallel (stomatal and cuticular pathways). The more lipophilic a compound,the higher its permeability across the cuticle barrier:PCi  100.704log K OWi 11.2(11)where PC is the cuticle conductance [LT-1]. The next resistance is provided by the airboundary layer surrounding the plant, Pair [LT-1]. Resistance of 200 sm-1 was estimated as
typical for a chemical with molar weight m=300 g mol-1 (Thompson, 1983). The conductanceof the air boundary layer, Pair, for a chemical with a molar mass m is thus:
Pairi K AWi 300

(12)

200 miwhere m is the molar mass of the chemical. However, water does need to cross the aqueous
layer in the apoplast. The permeability of this layer Paqua [LT-1] is:Paquai 

DO2 32

mi

(13)

z

where z is the thickness of the aqueous layer assumed 0.0005 m, and DO2 is the diffusion
coefficient of oxygen in water (2x10-9 m2s-1). Thus, the total cuticle permeability PC,tot [LT-1]
is:

PC ,tot 

1
1
1
1


PC Pair Paqua(14)

The role of the stomata is gas exchange. While the stomata are open, carbon dioxide is taken
up and water vapor is lost. Details on the calculation of transpiration are provided in thefollowing sections. The conductance of the stomata, PS [LT-1], can thus be calculated fromthe xylem flow QXYL as:
PSij 

QXYL j  water

Aj  CH 2O ,sat  CH 2O ,sat 

18
K AWi
mi

(15)

12

where ϕ is the relative air humidity [-], ρwater is the water density [ML-3], and CH2O,sat is thewater concentration inside plant’s shoots [ML-3], which can be calculated as:

CH 2O , sat 

pH 2 O
461.9T(16)

where pH2O is the saturation vapor pressure [ML-1T-2] at a given temperature T [K], calculatedusing the empirical Magnus equation:
7.5(T  273.15)(17)

pH 2O , sat  610.7 10 237  (T  273.15)

The exchange of the chemical through cuticle and stomata occurs in parallel, and thus
permeabilities are added to derive the total permeability for the exchange between the plant
and air, PP [LT-1]:
PP  PS  PC ,tot

(18)

3.6. Volatilization
Chemicals can leave or enter the plant in several ways. This exchange process is regulated by
the plant-air partition vector KPA [L3L-3], which is expressed as:
K PAij 

K PWij  j

(19)

K AWi

No volatilization is assumed in the roots since they are generally not exposed to air. The
volatilization rate depends on the permeability of plant’s compartments, PP. In the developedmodel, only the cuticular pathway is used for the stem, while for fruits and leaves, exchangesof the chemical occur through the cuticle and stomata in parallel (Rein et al., 2011). The
volatilization flux vector QVOL [MsMfw-1T-1] is expressed as:

QVOLij 

Aj PP ,ij  j Cij(20)

M j K PAij

3.7. Gaseous Uptake and Particle Deposition
The gaseous uptake flux of chemicals from the air, QGAS [MsMfw-1T-1], is defined as:

QGASij 

Aj PP ,ij (1  f p )C Ai

(21)

Mj

13

where fp is the fraction of a chemical adsorbed on the particles (-). The uptake of chemicalfrom particle deposition, QDEP [MsMfw-1T-1], is:

QDEPij 

Aj vdep f p C Ai

(22)

Mj

where vdep [LT-1] is the particle deposition velocity (Trapp and Matthies, 1998).
3.8 Metabolization of Neutral Compounds
Plant compounds’ metabolism is divided into three stages: transformation (I), conjugation(II), and compartmentation and storage processes (III), although plants have no excretion
systems. Cellular storage sites are the vacuole and the cell wall (Sandermann, 1992). Plants
thus can metabolize chemicals by exploiting the enzyme degradation. Furthermore, it is wellknown that millions of bacteria live on, but also inside of, plants. Most of these bacteria areheterotrophic and use chemicals as a substrate to grow. Compounds can be used as anelectron acceptor, an electron donor, an energy source, or a precursor for other molecules.
Nevertheless, traditional modeling approaches are based on using a single first-order rate
coefficient to describe compound’s biodegradation (e.g., Legind et al., 2011; Rein et al.,2011; Trapp, 2007). Such an approach completely neglects the transformation chain in theplant’s tissues, which leads to the formation of new chemical by-products. These metabolites,
which can be chemically active, are important for risk assessment (e.g., So et al., 1994;
Warner et al., 1992) and must be considered in the analysis. In addition to that, recent studies
have shown differentiated biodegradation rates in different plant’s compartments (e.g.,
Fantke & Juraske, 2013; Kodešová et al., 2019), suggesting the need to use a more flexible
mathematical description. To overcome such limitations in the present model, plant
metabolization is modeled using multiple metabolization matrices Γj. These matrices consistof multiple first-order rate coefficients, which provide connections between parent anddaughter species. The matrix Γj is a square matrix of a dimension N (i.e., a number of
metabolites considered):  11 ..  1' N NΓj   ::  with  ij  0
i 1
 '

 N 1 ..  NN 

(23)

where τ are first-order rate constants for the compound [T-1], while τ’ are similar first-order
rate constants providing connections between individual chain species [T-1]. The
metabolization rate vector for the jth compartment, Ωj [MsMfw-1T-1], is thus defined as the dot
product of the metabolization and concentration matrices:14  11 ..  1' N   C1 j   
Ω j  Γ j C j   ::    : 
 '
  
 N 1 ..  NN  CNj (24)

The proposed approach guarantees high modeling flexibility for handling multiple nonsequential degradation chains and simulating the effect of reaction yields. Figure 2 shows aschematic of three metabolization chains in the jth compartment with their respective model
implementations.

Figure 2. Examples of (A) double, (B) sequential, and (C) closed metabolization chains of
three compounds in the jth compartment (in this case, j = 1, i.e., in the roots). Black circles
indicate an incomplete conversion of the reactant in by-products.

15

4. Numerical Implementation
Neutral compounds are generally passively taken up by plants with the transpiration flux.
Under such conditions, the plant uptake process is considered purely advective. This ismathematically expressed as a one-way coupled system, in which the soil and plant domains
are sequentially coupled, and no feedback mechanism exists between the two domains.
Briefly, HYDRUS calculates actual root water and solute uptake, which are then used as
input for the roots compartment where the dynamic plant uptake starts.
The standard HYDRUS code has been modified to include the DPU component. In particular,
all subroutines related to the DPU model have been collected in a separate FORTRAN file.
This file contains reading and writing subroutines, as well as the solver for eq. (4), which arecalled by the main code at each time step during model execution. The implementation canbe summarized in a few steps:
1. Initialization: The HYDRUS model is set up in the usual way by defining all
simulated processes, domain properties, and input parameters. A separate dialog isused to define general information, plant physical characteristics (eq. 1),
compounds’ chemical properties (eq. 2), and metabolization matrices for eachcompartment (eq. 24). In this step, DPU output files are created.
2. Coupled model execution: the HYDRUS main code initializes variables, reads the
input, and starts the calculation. At each time step, water flow and heat and solutetransport are solved first. Simulated actual root water and solute uptakes are thenpassed to the DPU solver, which in turn calculates the compounds’ distribution inplant’s tissues. The time step is dictated by the main HYDRUS solver.
3. Output: If the simulation is convergent, pre-initialized output files are populatedwith results of the numerical simulation, which continues until the simulation
period ends.

16

5. Preprocessing and Input Data
5.1. Main Processes
The DPU module is activated in the Main Processes window (Error! Reference source notfound.) by selecting the Dynamic Plant Uptake check box, which is active only when both
Solute Transport and Root Water Uptake are simulated. Once selected, the “Dynamic
Plant Uptake Module Parameters" command is displayed in the Project Navigator under“Root Water and Solute Uptake” (Error! Reference source not found.):Figure 3. The Main Processes dialog window (left) and the Navigator Bar with the displayed
Dynamic Plant Uptake command (right).
5.2. DPU Parameters
Input parameters (in addition to those required by the standard HYDRUS (2D/3D) program)required by the DPU module are specified in the "Dynamic Plant Uptake Module
Parameters" dialog window.

17

Figure 4. The Dynamic Plant Uptake Module Parameters dialog window.

In the "Dynamic Plant Uptake Module Parameters" dialog window, users specify
parameters required by the DPU Module to describe the environmental conditions, thesettings for the numerical solver, the plant characteristics, and the solute information. By
pressing the Next button in the Solute Information and Metabolization Matrices section (after
entering Solute Information), users are asked to input the metabolization rates for eachcompartment (e.g., roots, stem, leaves, and fruits) (Error! Reference source not found.),which are required to build the Metabolization Matrices described in eq. (24).

Figure 5. The metabolization information.
18

General Information
fp
Fraction of a chemical adsorbed on the particles [-]vdep
Particles’ deposition velocity [m/s]phiAverage relative air humidity during the simulation period [-]T
Average air temperature during the simulation period [°C]
MaxiterMaximum number of iterations for the Broyden nonlinear solver [-]AbsTolAbsolute tolerance for the Broyden solver [M/kg]
Plant Information
W
Water content of plant’s compartments [L3/kg]
L
Lipid content of plant’s compartments [-]Mmax
Final mass of plant’s compartments [kg/L]
M0
Lipid content of plant’s compartments [kg/L]
kgr
Growth rate of plant’s compartments [1/T]
SpASpecific surface area of plant’s compartments [L2/kg]
roDensity of plant’s compartments [kg/L3]
Solute Information
Kaw
Air-water partition coefficients for each solute [-]log Kow
Octanol-water partition coefficient for each solute [-]Ca
Solutes’ concentration in the air [M/L3]
mol
Molar mass of solutes [g/mol]
Metabolization Matrices
tau
Metabolization rate for each solute [1/T]19

6. Post-processing
6.1. Results – Profile Information
The DPU module generates multiple output files that are listed in Table 1.
Table 1. The list of output files created by the DPU module.
Output File Name
Output File Description
DPU_PlMasses.out

Masses [M/kg] of roots, stem, leaves, and fruits, versus time.

DPU_PlSolutej.out

Concentrations [M/kg] of the jth solute in roots, stem, leaves, andfruits, versus time.

DPU_PlFluxesj.out

Fluxes [M/kg] of the jth solute in roots, stem, leaves, and fruits,
versus time.

DPU_PlMasBalj.out

Mass Balance Error [M/kg] of the jth solute in roots, stem, leaves,and fruits, versus time.

Results of the DPU module are reported in the Results - Other Information section (Figure6). The first set of graphs (DPU - Concentrations) displays the solutes concentrations inroots, stem, leaves, and fruits versus time. The second set of graphs (DPU – Plant Masses)
displays the mass of roots, stem, leaves, and fruits versus time. Finally, the last graph (DPU –Solute Fluxes) displays the solute fluxes in the roots, stem, leaves, and fruits versus time.
Examples of these graphs can be seen in the following Section.

Figure 6. The DPU-related results displayed on the Navigator Bar.

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7. Example Problems
7.1. Example 1. Translocation and Tranformation of Carbamazepine in Green Pea Plants
The first example is taken from Brunetti et al. (2021), who analyzed the uptake andmetabolization of Carbamazepine (CBZ) in green pea plants by coupling HYDRUS-1D andthe DPU module. The main aim of the analysis was to predict translocation and redistributionof CBZ and its metabolite, carbamazepine-10,11–epoxide (EPX), in different plant’s tissues.
For all modeling details, the reader is referred to Brunetti et al. (2021). This manual mainly
reports an overview of how to set up the DPU parameters and visualize results using thegraphical user interface in HYDRUS (2D/3D).
The soil domain consists of a layered soil profile 1 cm wide and 20 cm deep. An atmosphericboundary condition and a seepage face are set at the top and bottom of the domain,
respectively, while zero-flux is imposed at the sides. The problem considers sorption,translocation, and metabolization of CBZ and EPX in the soil-plant domain. Gaseous uptake
and particle deposition are neglected, as well as the phloem flux. Therefore, the particle
deposition velocity and fraction, vdep and fp, are set to their default values. The relative air
humidity and temperature, ϕ and T, are set to 0.5 and 20 °C, respectively, while themaximum number of iterations is fixed to 200. An absolute tolerance of 0.001 ng/kg is
considered sufficient for this problem. To consider sorption to other plant components, eq.
(8) is simplified by setting the lipid content L to 0 in all plant compartments. By doing so, it
is possible to input directly the partition coefficients calibrated by Brunetti et al. (2021) incolumn W. In HYDRUS, plant masses are specified per unit length. The air-water partition
coefficients, KAW, are 4.5e-06 for both CBZ and EPX, which will lead to negligible
volatilization fluxes. Finally, metabolization rates in different plant compartments are set
according to Brunetti et al. (2021).

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Figure 7. The DPU Parameters dialog window for example problem 1.
Figure 8 shows the simulated CBZ concentration in fresh weight in different plantcompartments versus time. While CBZ accumulates mainly in roots, it is simultaneouslytranslocated with transpiration streams into leaves and fruits. CBZ metabolization occurs
mostly in leaves and stem, and to a lower extent in fruits and roots (Figure 9).

Figure 8. CBZ concentrations in different plant compartments versus time.

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Figure 9. CBZ metabolization fluxes in different plant compartments versus time.
Consequently, most of the EPX bioaccumulates in leaves (Figure 10), while its concentration
remains relatively low in the edible part of the plant (i.e., fruits). The model indicates that the
EPX bioaccumulation is mainly due to in-plant metabolization, while its uptake andtranslocation from the soil are limited (Figure 11).

Figure 10. EPX concentrations in different plant compartments versus time.

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Figure 11. EPX inflow fluxes in different plant compartments versus time.
Finally, the model also calculates the time series of plant masses (Figure 12) and massbalance errors [eq. (4)] in each compartment and for each solute. The latter is not displayedin the GUI but can be easily imported and visualized in other softwares. As shown in Figure
13, the mass balance errors remain under the prescribed tolerance (i.e., AbsTol = 0.001 M/kg)
during the entire numerical simulation.

Figure 12. Masses of plant compartments in fresh weight versus time.

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Figure 13. CBZ mass balance error in different plant compartments versus time.

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7.2. Example 2. Uptake of Benzene from Air
The second example focuses on the numerical analysis of benzene uptake from the air ingreen pea plants. Benzene is a highly volatile neutral compound present outdoor and indoor
in significant concentrations. Its air and n-octanol-water partition coefficients, KAW and log
KOW, are 0.23 and 2.12, respectively, making it suited for gaseous uptake from plant leaves
and fruits. The benzene concentration in the air is 0.0044 ng/cm3. Uptake from roots andstem is neglected in this example (i.e., SpA=0). The water content is constant and equal to
900 cm3/kg in all compartments, while the lipid content is 0.05 in roots, stem, and leaves, and0.01 in fruits (Figure 14). This difference has an impact on the sorption properties defined ineq. (8). The degradation rate is set to -0.2 1/day in all compartments, and metabolites are notconsidered.
For this example, we use morphological settings similar to Example 1 (geometry, soil
hydraulic properties, root growth, irrigation doses), except for the transport of benzene in thesoil, which is neglected. This is accomplished by setting all inflow concentrations in
HYDRUS to zero. It is not possible to deactivate the solute transport since the DPU
module implicitly assumes that the transport happens in the soil-plant continuum.

Figure 14. The DPU Parameters dialog window for example problem 2.
Figure 15 shows the benzene concentrations in different plant compartments versus time. As
expected, roots and stem don’t bioaccumulate benzene since the phloem flux is not simulated,and gaseous uptake has been excluded for these compartments. Conversely, there is a strong
accumulation in leaves and fruits, mainly due to particle deposition, which, however,declines with time due to dilution induced by plant growth.

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Figure 15. Benzene concentrations in different plant compartments versus time.
Gaseous uptake increases with time as it is regulated by the plant permeability (Figure 16),
which depends on the transpiration streams [eqs. (21) and (15)]. Lower values are observed
for fruits due to their lower specific surface area. Conversely, particle deposition remains
constant since it is not influenced by plant properties. The benzene is then metabolized or lostby volatilization. The latter process is reduced in fruits due to a higher lipid content (Figure17), which increases the benzene sorption. Highly volatile compounds undergo a significant
exchange with plant shoots and are generally not bioaccumulated.

Figure 16. Gaseous uptake of benzene in different plant compartments.

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Figure 17. Volatilization flux of benzene in different plant compartments.

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