Agricultural Water Management 292 (2024) 108668

Contents lists available at ScienceDirect

Agricultural Water Management
journal homepage: www.elsevier.com/locate/agwat

Water uptake by plants under nonuniform soil moisture conditions: A
comprehensive numerical and experimental analysis
Anooja Thomas a, Brijesh Kumar Yadav b, Jiří Šimůnek c, *a

Department of Agricultural & Biological Engineering, University of Florida, Gainesville, FL 32603, USA
Department of Hydrology, Indian Institute of Technology Roorkee, Roorkee 247667, Indiac
Department of Environmental Sciences, University of California Riverside, Riverside, CA 92521, USAb

A R T I C L E I N F O

A B S T R A C T

Handling Editor: Dr R Thompson

The spatiotemporal pattern of root water uptake (RWU) depends on multiple factors, such as plant root biomass,soil water availability, and prevailing weather conditions at the site. The water uptake reduction due to thenonuniformity in soil water contents is often mitigated through compensated root water uptake (CRWU) andhydraulic redistribution (HR). Although previous studies have often considered these two processes indepen­dently due to the simplicity and feasibility of analyzing them separately, CRWU and HR can coexist in field
conditions. Therefore, this work demonstrates the importance of considering CRWU and HR simultaneously inestimating daily transpiration and RWU distribution for nonuniform soil moisture conditions. For that, we have
implemented the mechanistic RWU models developed by de Jong van Lier et al. (denoted below as the DJmodel), Couvreur (CR), and Nimah and Hanks (NH) (see the references in the main text) into the widely-used
HYDRUS-1D model, in addition to the previously available Jarvis (JF) and Feddes (FD) models. The perfor­
mance of these models was then compared for varying soil water contents and boundary conditions using
experimental data and hypothetical modeling scenarios. Our analysis has shown that these models are beneficial
in estimating RWU with varying degrees of accuracy. The DJ and CR models are effective in simultaneously
simulating CRWU and HR. NH and JF models can simulate CRWU but cannot simulate HR satisfactorily.
Implementing these models into the HYDRUS platform for simultaneously considering CRWU and HR will
significantly improve the accuracy of RWU predictions.

Keywords:
HYDRUS
Root water uptake
Mechanistic RWU models
Compensated root water uptake
Hydraulic redistribution

1. Introduction
Water uptake by plants constitutes a major component of the ecohydrological cycle. It is a vital factor affecting various hydrologicaland environmental processes such as solute transport and groundwater
recharge (Yadav et al., 2009a). Root water uptake (RWU) is also adecisive factor in irrigation planning and management and a major
component of various ecosystem models. Therefore, the adequate rep­resentation of RWU in these models is essential. RWU is a dynamic
process associated with various exogenous and endogenous factors,
including soil water status, soil hydraulic properties, plant physiology,
and meteorological conditions (Albasha et al., 2015; Thomas et al.,2020). Under non-limiting soil water conditions, plants transpire at thepotential demand, and RWU is usually proportional to the root mass
distribution and root system properties (Feddes et al., 1978). However,this linear relationship between the root distribution and soil water

extraction cannot always be maintained as the soil water content can beheterogeneously distributed in the vadose zone. In such cases, plants
rely on strategies to minimize the impact of water stress, with RWU
shifting from a plant-atmosphere demand-driven process to a soil water
availability-dependent process (Carminati and Vetterlein, 2013). In
addition, plants can initiate adaptive water uptake processes such ascompensated root water uptake and root-mediated hydraulic redistri­bution to maintain transpiration at the potential demand (Dawson,
1993; Amenu and Kumar, 2008; Albasha et al., 2015; Dara et al., 2015).
Compensated root water uptake (hereafter CRWU) represents theability of plants to preferentially extract water from the moist zone tooffset a reduction of RWU from the water-stressed zone (Yadav et al.,2009a; Šimůnek and Hopmans, 2009; Verma et al., 2014). Thereby,
CRWU allows plants to transpire at or closer to the potential transpira­tion demand, even though some parts of the root system may experiencewater stress (Thomas et al., 2020). On the other hand, hydraulic* Corresponding author.
E-mail address: jiri.simunek@ucr.edu (J. Šimůnek).
https://doi.org/10.1016/j.agwat.2024.108668
Received 25 August 2023; Received in revised form 29 December 2023; Accepted 2 January 2024
0378-3774/© 2024 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

A. Thomas et al.

Agricultural Water Management 292 (2024) 108668

redistribution (HR) refers to the passive transfer of soil water (following
the pressure head gradient) through the root system from a relatively
wetter soil zone to drier soil layers under reduced transpiration demandor after rainfall/irrigation (Kitajima et al., 2013; Oliveira et al., 2005;
Prieto et al., 2010a,b). HR significantly modulates transpiration, en­hances nutrient uptake, and also prevents xylem embolism (Caldwell
et al., 1998; Domec et al., 2006; Neumann and Cardon, 2012; Prieto
et al., 2012, 2014; Prieto and Ryel, 2014; Thomas et al., 2020). CRWU
and HR thus delay the onset of transpiration reduction and allow theplant to survive during prolonged dry periods (Smithwick et al., 2014).
In addition, plants develop a highly conducting root system (deep roots)that facilitates CRWU and HR under dry conditions (Da Rocha et al.,
2004; Yan and Dickinson, 2014; Baker et al., 2008). Therefore, on an
ecosystem scale, the presence of deep roots and these adaptive RWU
processes strongly influence various eco-hydrological processes, such as
the increased global evapotranspiration rate (Lee et al., 2005; Wang andDickinson, 2012), declining groundwater tables (Fan andMiguez-Macho, 2010), elevating carbon sequestration (Baker et al.,2008; Scott et al., 2008; Domec et al., 2010, 2012), and reduced rainfall
runoff and altered energy partitioning (Zheng and Wang, 2007; Baker
et al., 2008). Consequently, the combined effects of CRWU and HR playa crucial role in optimal resource utilization. Hence, it is vital to consider
the coexistence and combined impacts of CRWU and HR in various
eco-hydrological applications (Šimůnek and Hopmans, 2009; Yadav
et al., 2009a).
Over the last few decades, several modeling studies have been per­formed to improve our understanding of water acquisition by plantsfrom drying soil (e.g., Feddes et al., 1978; Ojha and Rai, 1996; Li et al.,
1999; Jackson et al., 2000; Lai and Katul, 2000; Heinen, 2001; Vrugt
et al., 2001; Arnold et al., 2012; Šimůnek et al., 2013, 2016). Most of thevadose zone models, including the HYDRUS models, use the Richards
equation to describe the soil water dynamics, while RWU is accounted
for by adding a source/sink term to it (Richards, 1931; Šimůnek et al.,2013, 2016, 2022; Šimůnek and Hopmans, 2009). Over the years,
various models have been developed for estimating RWU, considering
different assumptions, theoretical bases, and dimensionality. Based on
the hydrological perspective, these models can be classified as macro­scopic or microscopic (Šimůnek and Hopmans, 2009; Yadav et al.,2009b; Peters et al., 2017). In empirical macroscopic approaches, RWU
is represented as a function of potential transpiration, root density, andsoil water contents or soil matric pressure heads (van Dam, 2000; Feddes
et al., 2001; Homaee et al., 2002; Skaggs et al., 2006). Few of thesemodels are capable of simulating CRWU and HR, even though theseprocesses may sometimes be considered separately (Ryel et al., 2002;
Šimůnek and Hopmans, 2009; Yadav et al., 2009a), and their integrated
role on RWU is largely ignored. The conventional way of expressing
empirical CRWU is to use in the definition of RWU an empirical stressresponse function term that ranges from zero to one (e.g., Lai and Katul,
2000; Jarvis, 1989; Li et al., 2001; Yadav et al., 2009a). On the other
hand, empirical representations of HR usually consider an approach ofinterconnected rhizosphere layers, which allow the soil water to flow
between the soil layers based on the average root hydraulic conductivity
and water potential gradients (e.g., Ryel et al., 2002; Kitajima et al.,2013). However, the concept and parameters used in these RWU models
are empirical and, therefore, they cannot be linked to root systemproperties.
In contrast, microscopic models consider the root system architec­
ture that explicitly reflects their hydraulic properties to simulate root
water uptake (de Jong van Lier et al., 2006; Vereecken et al., 2016; Kochet al., 2018; Schnepf et al., 2023). Models such as RootTyp (Pagès et al.,2004), RootBox (Leitner et al., 2010), R-SWMS (Javaux et al., 2008), andSPACSYS (Bingham and Wu, 2011) represent a few examples of thesemodels, which significantly improved our understanding of soil-root
interactions and plants responses in heterogeneous environments.
While these models can account for the concepts of CRWU and HR,
estimating the root hydraulic parameters in real-time under field

conditions remains challenging (Lobet and Draye, 2013; Cai et al.,2018a). Moreover, these models require extensive parameterization andcomplex geometrical and functional operations and demand substantial
computational resources (Dunbabin et al., 2013).
Some of these microscopic models have been upscaled to simplified
mechanistic macroscopic models, which require reduced data input andcomputational time (e.g., Amenu and Kumar, 2008; de Jong van Lieret al., 2008, 2013; Couvreur et al., 2012, 2014; Vanderborght et al.,2021, 2023). The description of flow through the root systems in the
RWU models of Amenu and Kumar (2008) and de Jong van Lier et al.,(2008, 2013) is simplified, and an empirical factor or resistance repre­
sents root hydraulic properties. In contrast to these models, the modelsof Couvreur et al. (2012, 2014) and, more recently, Vanderborght et al.
(2021) focused on the root hydraulic properties and derived upscaled orsimplified approaches to represent root hydraulics. Finally, Vander­borght et al. (2023) presented an approach that combined the soil androot hydraulic approaches. The semi-empirical models, in empiricalforms with added physical parameters, have also gained increased
attention (e.g., Jarvis, 2011; Santos et al., 2017). These models arederived from the existing mechanistic models and are simplified to theclassical empirical approach while retaining the dynamic functionalityof the RWU process.
The availability of various RWU models that can simulate CRWU andHR with different complexities and parameter requirements is poten­
tially confusing when selecting the appropriate model for a given
problem. Moreover, the lack of understanding of various models adds
uncertainty to interpreting predicted RWU processes, especially whensimulated under distinct climates or simulation conditions. Therefore,
this study aims to investigate the possibility of simultaneous estimationof CRWU and HR by different types of empirical, semi-empirical, andprocess-based RWU models and to discuss their advantages and draw­
backs. This study also aims to understand how the modeling of soil water
dynamics in HYDRUS-1D can be improved while considering CRWU and
HR in the RWU term.
To achieve these aims, we revisited the processed-based RWU model
proposed by de Jong van Lier et al. (2008, 2013), Couvreur et al. (2012),
and Nimah and Hanks (1973), and compared their results with the re­sults of two other (standard HYDRUS) RWU models suggested by Feddes
et al. (1978) and Jarvis (1989) (hereafter called DJ, CR, NH, FD, and JF,
respectively). We compared these models in terms of their ability to
predict drought survival, assess the contributions of CRWU and HR to­wards the transpiration demand, and estimate soil water distributions
and RWU dynamics in maize (Zea mays L). This is achieved by inte­
grating the DJ, CR, and NH models into the HYDRUS-1D platform as a
submodule. To validate the performance of these models, we conducteda column lysimeter experiment and compared the soil water dynamics
under dry-down conditions with the simulation result. Additionally, we
compared the RWU estimates for various scenarios with and without
considering CRWU and HR to understand the importance of considering
these processes while modeling agricultural, environmental, andeco-hydrological processes.
2. Material and methods
2.1. Model description
The HYDRUS-1D platform, a widely used software package forsimulating soil water movement in the vadose zone (Šimůnek et al.,2013, 2016), is used in this study to conduct a comparative analysis ofvarious RWU models. The standard version of the HYDRUS-1D code
numerically solves the Richards equation to simulate the soil water
dynamics. The Richards equation includes a macroscopic sink term,
which accounts for RWU and lumps all RWU processes into a single termof the governing mass balance equation. An empirical, macroscopic
formulations of Feddes (the FD model; Feddes et al., 1978) and Jarvis(the JF model; Jarvis, 1989) are used in HYDRUS-1D to represent RWU.
2

A. Thomas et al.

Agricultural Water Management 292 (2024) 108668

The empirical Feddes (FD) model (see the mathematical description
below) distributes potential transpiration across the root zone based on
the roots’ spatial distribution and then reduces it locally due to various
environmental (e.g., saturation or salinity) stresses. This reduction isrepresented using empirical stress response functions. The standard
Feddes model does not account for CRWU or HR. Jarvis (1989) modified
the FD model by introducing a critical value of the water stress index, aso-called root adaptability factor, representing a threshold value above
which root water uptake reduced in stressed parts of the root zone isfully compensated by increased uptake from other parts. Thus, the JF
model can account for CRWU but cannot account for HR.
While simple and potentially efficient, these models are often subject
to criticism (Couvreur et al., 2012). First, most of the macroscopic pa­
rameters require calibration since they cannot be directly measured.
Second, these models neglect the effect of root hydraulic properties andarchitecture (Draye et al., 2010). Third, RWU stops when Tp is equal tozero, preventing the simulation of HR, which may occur during lowtranspiration rate periods (Dawson, 1993; Song et al., 2000).
HYDRUS-1D is written in a modular form so that it allows for
replacing empirical descriptions of the sink term with different
processed-based descriptions of RWU, enabling us to incorporate thepreviously reported RWU models of de Jong van Lier et al. (2013),
Couvreur et al. (2012), and Nimah and Hanks (1973). Since all threemodels are processed-based, they can help us overcome some of thedisadvantages of the RWU models currently available in HYDRUS-1D
and potentially account for both CRWU and HR.
de Jong van Lier et al., (2008, 2013) (the DJ model) derived amacroscopic RWU model from an approximate analytical solution of adetailed RWU model for the 1D radially symmetric Richards equation
for water flow around a single root. The final formulation of themacroscopic RWU sink term is the product of the matrix flux potential
gradient between the soil and roots and the root function, which ac­
counts for spatial root distribution but does not account for root
conductance and, thus, the root system hydraulic architecture, contrary
to the model of Couvreur et al. (2012). However, similarly to the NH
model driven by the pressure head gradients, the DJ model driven by thematrix flux potential gradients allows for HR and CRWU.
Couvreur et al. (2012, 2014) (the CR model) developed a macro­scopic RWU model based on analytical water flow solutions in a simple
root system hydraulic architecture and then validated it for more com­plex hydraulic architectures. In contrast to current RWU models, the CR
model decouples water stress and compensatory RWU processes, making
it more appropriate for HR simulations. The model is based on upscaling
the Doussan model of water flow inside a 3D root system (Doussan et al.,1998a, 1998b) for a given root architecture and root hydraulic proper­
ties (i.e., root radial and axial conductances), from which it identifies
macroscopic parameters (spatially distributed root parameters, andstress and compensatory RWU functions) controlling the macroscopic
uptake process. The CR model thus accounts for water flow from the soil
through the 3D root architecture into the atmosphere along potential
gradients while considering individual resistances along the path.
CRWU and HR naturally arise from this model description since waterexchange between soil and roots occurs according to potential gradients,
with water entering or leaving the roots according to the sign of thepotential gradient.
Finally, Nimah and Hanks (1973) proposed a simple RWU model (theNH model) based on the concept of Gardner (1960), in which theroot-sink term is computed as the product of the bulk soil hydraulicconductivity, the normalized root length density, and the difference
between the effective water potential in the root at the soil surface (H0)and the soil (Nimah and Hanks, 1973) (see the mathematical descriptionof the NH model below). The value of H0 is obtained by making RWUover the entire soil profile equal to potential transpiration provided thevalue of H0 is higher than the wilting point (hw). Since the integration of
RWU is done over the soil profile regardless of its sign, the model allows
for HR and CRWU.

In the following, we describe the five RWU models currently avail­able in the HYDRUS-1D software, including the new numerical imple­
mentation of the three processes-based models (the DJ, CR, and NH
models) into HYDRUS-1D. The readers are referred to the originalliterature for the detailed derivation of these models.
2.1.1. The DJ model
In the de Jong van Lier et al. (2013) model (or DJ), the soil water
movement between soil and root is represented by the radial soil waterflow equation considering plant roots as a series of cylinders of radius r0[L], distributed over the root zone, z [L], as represented below (de Jongvan Lier et al., 2006):

∂θ
q ∂q
= − −
r ∂r
∂t

(1)

The analytical solution of Eq. (1) can be obtained by relating the soil
water flux, q [LT− 1], with the matric flux potential, M [L2T− 1], asfollows:(2)

q = − ∂M/∂rwhere the matric flux potential is an integral of the water potential, h,and hydraulic conductivity, K(h), and can be represented as:∫hM=K(h)dh(3)
hw

When K(h) is known, M(h), can be determined either analytically or
numerically depending on the complexity of the K(h) function (de Jongvan Lier et al., 2009). Thus, the sink term obtained by solving Eq. (1) as afunction of M for prevailing boundary conditions at the root-soil inter­face (de Jong van Lier et al., 2008) can be expressed as:4(Ms − M0 )⃒ ⃒ = ρ(Ms − M0 )) ⃒ m⃒( 2⃒
Rm + R20 ln⃒⃒a.R
R0 ⃒

S=
2

R0 −

(4)

a2 R2m + 2

with ρ [ L− 2] is defined by:

ρ=
2

R0 −

4
(

a2 R2m + 2 R2m + R20⃒ ⃒) ⃒a.Rm ⃒ln⃒⃒ R0 ⃒⃒(5)

where Rm [L] is the half mean distance between roots or the rhizosphereradius, a [L] is the distance from the root axis relative to half the mean
distance between roots at which the mean (bulk) soil water content
occurs (R/Rm), and Ta [LT− 1] is the actual transpiration obtained byintegrating the sink term over the root zone as follows:∫∫
Ta = S(z)dz = ρ(Ms − M0 )dz(6)
where Ms is the soil matric flux potential [L2T− 1], M0 is the matric flux
potential at the root-soil interface [L2T− 1], and ρ [L− 2] is defined in Eq.
(5). M0 is also a function of h0 (the pressure head at the soil root inter­face), which is unknown. h0 can be obtained by solving the continuity
equation representing soil water movement within the xylem vessels,
assuming a constant water content within the root tissues (de Jong vanLier et al., 2013), i.e.:h0 + φM0 = hl +

Ta
+ φMs
L1

(7)

where
φ=

ρR2m ln RR0x
2Kroot(8)and hl is the leaf water potential [L], L1 is the conductance over the rootto-leaf pathway [T− 1], and Kroot is the root conductivity [LT− 1] for radial3

A. Thomas et al.

Agricultural Water Management 292 (2024) 108668

movement of water from an outer radius to a xylem radius, Rx [L1]. Eq.
(7) contains three unknown parameters: Ta, hl, and h0.
The steps to solve the equation are briefly described here (de Jongvan Lier et al., 2008). First, calculate the maximum possible transpira­tion (Tm) assuming M0 = 0 in Eq. (6). If Tm < Tp, the plant is under water
stress, and actual transpiration equals the maximum possible transpi­
ration (Ta = Tm). Therefore, the sink term can be obtained bysubstituting M0 = 0 in Eq. (7), i.e., Si = ρi (Ms,i – 0). If Tm > Tp, the planttranspires at the potential demand and Ta = Tp. In this case, to solve M0,
we assume a value for hl, find h0 and M0 (a function of h0) using thebracketing (bisection) method, and calculate Ta using Eq. (6). If Ta issmaller (or larger) than Tp, we decrease (or increase) the value of hl, andrepeat this until Ta becomes equal to Tp. The sink term can be estimatedby substituting M0 obtained from Eq. (6).

β * [L− 2] is the root distribution function (defined as a ratio of RDF(z)and Δx), Rr is the root resistance, which is equal to 1 +Rc, and Rc is theflow coefficient in the root system assumed to be 0.05. Note that theβ * function [L− 2] in the NH model has different units than β [L− 1] in the
CR and FD models. H0 is an effective water potential in the root at thesoil surface where z is considered zero, and it can range anywhere be­
tween zero and the permanent wilting point (hw). The value of H0 is
calculated assuming plant transpiration is at its potential rate, Tp, and
thus:
{∫
}
K(z)β∗ (z)[h(z) + Rr z]dz − Tp∫
H0 = max(16),hw
K(z)β∗ (z)dz
If calculated H0 is greater than hw, the above assumption is valid, andH0 can be estimated from Eq. (16). Otherwise, the transpiration rate is
below the potential value and H0 is equal to hw. The final sink term canbe calculated from Eq. (15) by substituting the value of H0.

2.1.2. The CR model
Couvreur et al. (2012, 2014) divided RWU into two components: 1)
water uptake under uniform soil conditions or the standard RWU term
(Sstd), and 2) compensatory root water uptake under nonuniform con­ditions (Scomp). Sstd is a function of space and time and is defined as a
product of the normalized root length density β [L− 1] and actual tran­
spiration (Ta):
Sstd (z) = β(z)Taand the compensated water uptake term, Scomp, is expressed as:)(
Scomp (z) = Kcomp (z)β(z) H(z) − Heq

2.1.4. The FD model
In the Feddes et al. (1978) model (FD), potential root water uptake(Sp) is estimated as a function of potential transpiration Tp and thenormalized root density distribution (β) [L− 1]. Actual root water uptake
can then be obtained by multiplying Sp by a water stress response
function, α[-], that accounts for water/salinity/oxygen stresses (e.g.,
Feddes et al., 1978; van Genuchten, 1987):(9)

S(z) = α(z)Sp (z) = α(z)β(z)Tp(10)

The stress response function, α[-], was defined by Feddes et al. (1978)
as a piece-wise linear function of the pressure head and the potential
transpiration rate (see also Šimůnek and Hopmans, 2009; or the HYD­
RUS manual).

where H is the hydraulic head, Heq is the average or effective hydraulichead at the soil-root interface along the rooting depth [L] that can be
expressed as:∫
Heq = β(z)H(z)dz(11)

2.1.5. The JF model
To account for CRWU in the FD model, Jarvis (1989) integrated a
stress index function, ω[-], into the sink term as follows:∫Tω = a = α(h, z)β(z)dzTp(18)α(h, z)S(z) = Sp (z)max[ω, ωc ]Thus, the RWU term proposed by Couvreur et al. (2012) can becalculated as:
S(z) = Sstd (z) + Scomp (z)(12)

Ta in Eq. (9) is calculated as a function of the collar water potential(Hcollar) [L] and the root system conductance (Krs) as represented below:()(13)
Ta = Krs Heq − Hcollar/
Hcollar = Heq − Tp Krs

where ωc is the critical stress index, a threshold value of ω, above whichfull compensation for localized water stress occurs (Jarvis, 1989;
Šimůnek and Hopmans, 2009). Note that ω is defined using the actual
non-compensated transpiration Ta rather than the final actual compen­sated transpiration, which is obtained by integrating the second equa­tion in (18) over the entire rooting depth. This integrated approach isalready incorporated into the HYDRUS model and has often been used toestimate CRWU.

(14)

The collar water potential, Hcollar, is calculated using Eq. (13),assuming the plant is transpiring at the potential rate (Tp). This
assumption is valid only if the estimated value of Hcollar reaches (orexceeds) a critical leaf hydraulic head Hcrit, otherwise Hcollar = Hcrit. For
any location with H>Heq, Scomp is positive and leads to CRWU. Whenh<heq, Scomp becomes negative and S smaller than Sstd. When Scomp is
negative, and its absolute value is smaller than Sstd, then negative S
represents HR. Thus, HR can be considered a special case of CWRU
(Couvreur et al., 2012).

2.2. Lysimeter experiment and model validation
We evaluated and validated the performance of the selected RWU
models by analyzing data collected in a column lysimeter experiment(Thomas et al., 2020). The experimental setup followed the same pro­
tocol described by Thomas et al. (2020). The lysimeter had a diameter of
15.24 cm and a height of 55 cm and was planted with fully grown Zea
mays (Fig. S1A). The soil water data were collected at four different
locations of varying depths, 5 cm (S1), 15 cm (S2), 25 cm (S3), and35 cm (S4), at 30-minute intervals (Fig. S1B). A control lysimeter
experiment was conducted in parallel to estimate actual and potential
transpiration at the predefined time intervals (Fig. S1C). Evaporationfrom the lysimeter was prevented to ensure that any change in soil watercontent was solely due to RWU. The experiment began with irrigating
the lysimeter to its field capacity, followed by nine days of dry-down
conditions to attain the wilting point. At the end of the experiment,
the lysimeter was segmented into five parts, and roots from each section

2.1.3. The NH model
Following the concept of Gardner (1960), Nimah and Hanks (1973)
proposed RWU as a function of the soil water potential as follows:
S(z) = − K(z)RDF(z)[H0 − Rr z − h(z)] = − K(z)β∗ (z)[H0 − Rr z − h(z)]
Δx

(17)

(15)

where K(z) is the soil hydraulic conductivity [LT− 1], RDF(z) is thefunction proportional to the total active roots in depth z [− 1], Δx is the
distance between the plant roots at the point in the soil where h(z, t) ismeasured (arbitrarily assumed to be one by Nimah and Hanks, 1973),
4

Agricultural Water Management 292 (2024) 108668

A. Thomas et al.

were isolated and measured for root length using image analysis(Fig. S1D). The data was then converted into a root length per volume, orroot density (RD) (Fig. S1E), as shown in Figure S1F. RWU and soil water
dynamics in the column lysimeter were estimated using five different
RWU models described in Supplementary Information 1.

considered. This simulation also adopted three different levels of RLD:
high (1.2 cm/cm3), medium (0.8 cm/cm3), and low (0.4 cm/cm3).
Additionally, in the DJ model, different combinations of Rx, R0, and Kroot
were considered to assess the influence of root properties on plant
physiological activities (Supplementary Information 2). Different pa­
rameters used to simulate RWU using these models are listed in Table 1.

2.3. Model performance

Case 2. This case should explore the possible co-occurrences of CRWU
and HR. A constant transpiration demand of 1 cm/day for 18 days wasconsidered, while all other parameters were kept the same as in Case 1.
Additionally, a 1 cm/hour rainfall event for 6 h was considered on day
12.

To assess the performance of these RWU models, a comparative
analysis was conducted by comparing modeling results with the exper­
imentally observed soil water contents (Brocca et al., 2010). Threeevaluation metrics were used for this analysis: (i) correlation coefficient(r), (ii) index of agreement (I), and (iii) root mean square error (RMSE).
These metrics were used to quantitatively measure the agreement be­
tween the results simulated by the RWU models and the observed soil
water dynamics.
)()θsim,i − θsim θobs,i − θobs̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅
r = √[
][ n
]̅
n (
)2 ∑
(
)2
∑
θsim,i − θsim
θobs,i − θobs

Case 3. While HR is prominent during low transpiration demand pe­
riods, i.e., during nighttime, CRWU occurs under high transpiration
demand conditions (Šimůnek and Hopmans, 2009; Prieto et al., 2012).
To mimic such conditions, the transpiration demand was set to
1 cm/day for 18 days with a sinusoidal diurnal variation of 0.9 cm/day
and a constant nighttime value (10% of daytime transpiration),assuming equal halves of the day-night distribution.

n (
∑
i=1

i=1

⎡

Case 4. Deep-rooted plants/shrubs in arid and semiarid regions mainly
survive due to RWU from a deeper root zone in a capillary fringe (Hanet al., 2015). Thus, this test was performed to investigate the response of
RWU near a groundwater table during meteorological droughts. A
no-flux boundary condition was specified at the soil surface, and azero-pressure head boundary condition was considered at a depth of
130 cm to represent saturated conditions. As in Case 3, the daily tran­
spiration demand followed a sinusoidal variation with a mean value of
1 cm/day.

i=1
n (
∑

⎢
I = 1− ⎢
n (⃒
⎣∑
⃒

(19)

θsim,i − θobs,i

)2

⎤

⎥
⎥
⃒ ⃒
⃒)2 ⎦
θsim,i − θsim ⃒ + ⃒θobs,i − θobs ⃒
i=1

(20)

i=1

√̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅
√∑
)2
√n (
√
θ
− θobs,i√i=1 sim,i
RMSE =
n(21)

3. Results

where θsim is the simulated soil water content, θobs is the observed soil
water content, θsim and θobs are the mean absolute values of θsim and θobs ,respectively, and n is the number of data points.

To investigate the possible coexistence of CRWU and HR and theircontribution towards meeting the daily transpiration demand, we usedfour different RWU models (DJ, CR, NH, and JF) with a potential tosimulate either CRWU or HR or both, while the FD model was chosen asa baseline. All models were first validated against the soil water content
data obtained from the column lysimeter experiment. Soil water content
distributions and RWU dynamics simulated by the five models for dry-

2.4. RWU scenarios
Since the column lysimeter experiment limits the representation of
extreme climatic conditions and diverse soil properties, we used various
additional numerical simulation experiments to evaluate the coexistenceof CRWU and HR. The RWU patterns and soil water dynamics were
simulated using five RWU models (i.e., DJ, CR, NH, JF, and FD) for
heterogeneous root zone parameters. The exponential root distribution
by Gale and Grigal (1987) was used as the root density distributionfunction with a maximum root density of 1.2 cm/cm3. The rooting depth
and simulation domain were 100 cm and 130 cm, respectively. The
initial soil water potential was set at a constant value of − 100 cm. A
no-flux boundary condition was specified at the top, which means that
evaporation from the soil surface was assumed to be zero.
Reference RWU under simulated soil water conditions was estimatedusing the FD model. Any increase in RWU above this rate is considered
CRWU, while any negative RWU is considered HR. Transpiration due to
CRWU (Tcomp) is the sum of CRWU over the rooting depth at a particulartime interval, and the hydraulically redistributed water (THR) is the total
HR over the rooting depth during a time period. The degree of CRWU
(Tcomp/Ta) is used to assess the contribution of CRWU in meeting thetranspiration demand. A sensitivity analysis for different parameters
involved in the DJ model was also performed.
The following simulation scenarios were considered to investigate
the coexistence of CRWU and HR:

Table 1
Soil hydraulic and root parameters used in simulations of RWU with different
RWU models (de Jong van Lier et al., 2013; Couvreur et al., 2012).

Case 1. A drying-out simulation, assuming no irrigation/rainfall
throughout the simulation time, representing a summer drought. Threelevels of the transpiration demand (Tp) of 0.75 cm/day, 1.0 cm/day, and1.5 cm/day (low, medium, and high, respectively), evenly distributed
throughout the day for 24, 18, and 12 days, respectively, were
5

Parameters

Value

Unit

Root hydraulic conductivity, Kroot (DJ model)

2.00e-04

Root-to-leaf pathway conductance, L1 (DJmodel)
Root radius, R0 (DJ model) (de Jong van Lieret al., 2013)
Xylem radius, Rx (DJ model) (de Jong van Lieret al., 2013)
Root hydraulic conductance, Krs (CR model)
Compensatory RWU conductance, Kcomp (CRmodel)
Critical stress index (JF model)
Wilting point, hw, h4 (Feddes et al., 1978)
The pressure head threshold values h1, h2, h3,
and h4 (Feddes et al., 1978)
Saturated soil water content for loam, θs (Carsel
and Parrish, 1988)
Residual soil water content for loam, θr (Carsel
and Parrish, 1988)
Saturated hydraulic conductivity for loam, Ksat (Carsel and Parrish, 1988)
van Genuchten’s alpha for loam, α (Carsel andParrish, 1988)
Pore-connectivity parameter, lvan Genuchten’s n for loam (Carsel and Parrish,
1988)

0.5000[cm
day− 1][day− 1]

0.05

[cm]

0.02

[cm]

2.00e-04
2.00e-3[day− 1][day− 1]0.6
-15000-25, − 300,
− 1000, − 1500
0.43

[-]
[cm]
[cm]

0.036

[cm3
cm− 3][cm3
cm− 3][cm
day− 1][cm− 1]

0.5
1.56

[-]
[-]

0.078
24.96

A. Thomas et al.

Agricultural Water Management 292 (2024) 108668

down conditions were then compared using four hypothetical scenarios
described above.
In the column lysimeter experiment, it was observed that under the
optimal soil water conditions, RWU was prominent in the high-density
root regions, indicated by the largest drop in the soil water content inthese regions (Fig. S1B). Meanwhile, RWU from other regions showed asteady but slow decrease in the soil water content over time. When thehighest RLD zone dried up, the roots from the lower compartments were
found to facilitate the RWU demand through CRWU (Figs. S1BC), as
reported previously (Thomas et al., 2020). This is indicated by a sig­
nificant reduction in the soil water content in the lower compartment
towards the end of the experiment. On the other hand, an increase in thesoil water content was not observed, indicating that there was no HR,
which is consistent with the findings of Thomas et al. (2020).
The soil water dynamics in the column lysimeter were simulatedusing the DJ, CR, and JF models. The simulated results were comparedwith the measured values in Fig. 1. The comparative analysis showed agood correlation between the simulated and experimentally measured
values at 5, 15, and 25 cm depths till day 6 (Fig. 1ABC). In contrast, theperformance declined in larger soil depths (Fig. 1D). The average r
values for observed and simulated soil water contents at four different
depths were 0.969, 0.984, and 0.972 for DJ, CR, and JF, respectively,
indicating that all RWU models performed considerably well. Similarly,
the I values were found to be 0.957, 0.977, and 0.97, while the RMSE
values (expressed in %) were 3.7218, 2.972, and 2.788 for the DJ, CR,
and JF models, respectively. The detailed comparison of the selectedmodels with the column lysimeter experiment data is summarised in
Supplementary Information 1.

3.1. RWU under constant transpiration demand
The simulations performed for Case 1 suggest that accounting for
CRWU in RWU models improves the prediction of Ta (De Willigen et al.,2012; Cai et al., 2018b). In the DJ model, RWU was found to be pro­portional to RDL during the early days of the simulation, with a corre­
lation coefficient of 0.989 and 0.933 on days 1 and 2, respectively(Fig. 2A). Continued RWU from the topsoil resulted in water stress and asubsequent reduction in water uptake (Figs. S2BC). However, this wascompensated by increased uptake from deeper layers with sufficient soil
water contents (Fig. 2A, S2BC). Between days 2 and 6, Tcomp continued toincrease (Fig. 2B), maintaining the transpiration rate close to its po­
tential rate (Fig. S2A). For given conditions, plants transpired at thepotential demand till day 6.5, followed by a rapid reduction in tran­
spiration (Fig. 2B, S2A). On day 6, 75% of total transpiration occurredfrom the lower half of the root zone, indicating the important role of
CRWU in maintaining the transpiration demand. The analysis of RWU
using the DJ model for different root densities indicates that the degreeof CRWU is positively correlated with RDL and that an increase in RDL
delayed the onset of water stress by increasing Ta through increased
Tcomp (Supplementary information 2). Similarly, an increase in Rx and R0
also improved Ta and Tcomp, indicating that the plants with deep, highdensity, and large radii roots have a higher potential to survive underwater stress conditions due to CRWU (Cai et al., 2018). In contrast, Ta
and Tcomp are independent of Kroot, while the emergence and degree ofcompensation are highly related to Kroot (Supplementary information 2).
In the CR model, RWU was directly proportional to the root density
distribution during the initial days of simulation (days 0 to 3) (Fig. 2C).
CRWU emerged when the plant experienced soil water stress and a

Fig. 1. Soil water content (%) measured (Lysimeter) and simulated by different RWU models (CR, DJ, and JF) at different depths: (A) S1 (5 cm), (B) S2 (15 cm), (C)S3 (25 cm), and (D) S4 (35 cm).
6

A. Thomas et al.

Agricultural Water Management 292 (2024) 108668

Fig. 2. Root water uptake profiles simulated by the DJ (A, B), CR (C, D), NH (E, F), and JF (G, H) RWU models for dry-down conditions (Case 1) withpotential transpiration of 1.5 cm/day: A, C, E, and G represent the root water uptake distribution profiles, and B, D, F, and H represent potential transpiration (Tp),
actual transpiration (Ta), transpiration due to CRWU (TComp), and transpiration due to HR (THR). TComp is the sum of CRWU over the rooting depth, and THR is the total
HR over the rooting depth.

subsequent water uptake reduction occurred in the top soil layer(Fig. 2D, S2EF). As water stress along the rooting depth increased, anabrupt increase in Tcomp was observed on day 3 (Fig. 2D). In contrast to
the other models, the NH model showed CRWU from day 0, even before
the emergence of water stress, and remained high for an extended period(Fig. 2EF). This resulted in the overestimation of CRWU compared to theother models during the early days of simulation and a nearly uniform
soil water distribution over the root zone (Figs. S2HI). Similar to the DJ
and CR models, the RWU pattern in the JF model was proportional to
RDL during the early simulation days (Fig. 2G). CRWU occurred whenRWU in the top layer was affected by water stress (Fig. 2H, S2JK).
A comparison of the degree of CRWU, the emergence of water stress,and cumulative Tcomp and Ta between the five models (with Tp = 1.5 cm/day) reveals that CRWU improved the resilience of plants towards water
stress by increasing total transpiration (Fig. 3C). The FD model, which
could not simulate CRWU and HR, recorded the lowest cumulative Ta of
10.12 cm (Fig. 3C) and water stress emerged earliest among all models(Fig. 3A). On the other hand, the cumulative Ta simulated using the DJ
and CR models was 12. 1 and 14.24 cm, respectively, which is 21% and40.6% higher than when simulated using the FD model without CRWU
(Table S1 a). The DJ and CR models also showed a 3-day delay in theonset of water stress compared to the FD model. In addition, the degreeof CRWU varied among these models, with the CR model predicting thehighest value of 88.4% and the JF model the lowest value of 34.8%(Fig. 3B). Detailed comparisons of the performance of the models fordifferent transpiration demands are summarised in Supplementary In­formation 2.

maintained for a few days after the rainfall (Fig. 4BFJN). Notably, in the
DJ and CR models, RWU from the top layer increased 3-fold and 2.5fold, respectively, after the rainfall (Fig. 4AE). The process of HR was
also initiated in these models by redistributing the soil water from thewetter top zone to the water-stressed lower zone (Fig. 4CDGH). In the DJ
and CR models, 30.9% and 33.5% of the total water extracted from thewet soil layer was released back to the water-stressed zone through HR.
Such reverse HR is reported in various studies (e.g., Cai et al., 2018a).
Although RWU from the top root zone increased due to CRWU after therainfall in the NH and JF models (Fig. 4IM), no HR was detected in thesemodels despite a high water potential gradient (Fig. 4KLOP).
3.3. Combined effects of CRWU and HR under sinusoidal transpiration
demandIn the DJ model, Tcomp was negligible during the initial four simu­
lation days, followed by a gradual increase until day 9, when it peaked,
and a reduction after that (Fig. 5. C). This model also predicted HR as
indicated by negative values of RWU, triggered during the night by
nonuniform soil water conditions and a low transpiration demand(Fig. 5. A, D). It was observed that under reduced transpiration andwater stress, the contribution of CRWU and HR during the daytime
decreased significantly after day 10. However, nighttime transpiration
was unaffected until day 18, although CRWU and HR were negligible(Fig. 5B).
Similarly, in the CR model, both CRWU and HR were significant
when the soil was subjected to localized water stress beginning on day 5(Fig. 5EGH). This was followed by a gradual increase in CRWU and HR,
which peaked on day 11 and declined after that (Fig. 5G). However,CRWU and HR in the CR model were consistently high during the earlydays of water stress (days 9–12), unlike in the DJ model (Fig. 5G). Also,in the CR model, from day 11 onwards, more than 60% of nighttime
RWU contributed to HR (Fig. 5G). As a consequence of higher HR
simulated by the CR model compared to the DJ model, the CR model
predicted longer drought survival of plants than the DJ model.
Similar to Case 1, in the NH model, CRWU was observed from theearly simulation days, then it gradually increased until it peaked on day

3.2. Profiling CRWU and HR after rainfall
In Case 2, the RWU profiles simulated by all models were similar toCase 1 until the occurrence of rainfall (Fig. 4AEIM). After the rainfall
event, the surface soil water content increased to near-optimum levels(Fig. S3). In response, root water uptake from the wetter top zone
increased to compensate for the RWU reduction from the lower waterstressed zone through CRWU, except in the FD model(Fig. 4ADEHILMP). As a result, the transpiration demand was7

A. Thomas et al.

Agricultural Water Management 292 (2024) 108668

In the CR model, the RWU pattern in Case 4 was comparable to Case
3 till day 12 (Fig. 6FG). Likewise, CRWU and HR were relatively low or
negligible during the first six simulation days (Fig. 6FG). However,CRWU and HR became predominant when the topsoil experienced water
stress. From day 12 to day 18, CRWU and HR contributed to Ta mainly
from the lower root zone and groundwater (Fig. 6FG). Similarly, in the
NH model, groundwater played a significant role in daily transpiration
through CRWU (Fig. 6IKL). However, similar to Case 3, HR was not
visible in the results of the NH model despite having groundwater as thebottom boundary condition (Fig. 6IKL). For the JF model, the contri­
bution of CRWU to daily transpiration was relatively low compared to
the DJ and NH models, while HR remained zero.
Comparing Cases 3 and 4 (with groundwater), total Ta in Case 4 withgroundwater as a bottom boundary condition was 17.10, 16.34,
17.47 cm, and 11.69 cm in the CR, DJ, NH, and JF models, respectively,
which is 38.3%, 13.7%, 54.5%, and 3.7% more than in Case 3(Figs. S4AB). This increase in Ta was due to increased CRWU and HR
facilitated by groundwater. Among these models, the DJ and NH models
showed a notable increase in cumulative Tcomp, which was as high as
117% and 167%, respectively, helping to increase the transpiration rate
in Case 4 compared to Case 3 (Fig. 5BJ, 6BJ). However, a significant
difference in HR was not observed in the DJ model between these twocases. On the other hand, in the CR model, both CRWU and HR increasedin the presence of the groundwater table (20.75% and 61.53%, respec­tively). Compared to the other three models (DJ, CR, and NH), theresponse of the JF model to the presence of the groundwater table wasnegligible. Since the JF and FD models do not simulate HR, its contri­
bution to Ta was zero.
4. Discussion
The present study describes computational modifications andincorporation of previously proposed RWU models, namely DJ, CR, andNH, into the HYDRUS-1D model, in addition to the JF and FD models, toimprove the estimation of RWU under varying soil water conditions.
Since these five models differ in their input requirements and mathe­
matical formulations, a comparative analysis was conducted to provide
a comprehensive outlook. The DJ model was improved by incorporating
an efficient iteration step before integrating it as a submodule into
HYDRUS-1D. The performance of each RWU model was first evaluated,followed by their experimental validation using the soil water content
profile obtained from a column lysimeter. All five models selected forthis study have been previously used in the literature for estimating
RWU (e.g., De Willigen et al., 2012; Cai et al., 2018a; Brunetti et al.,2019; Lei et al., 2019; Nguyen et al., 2020; De Melo and de Jong vanLier, 2021). The FD model was used as a "negative" control as it does notaccount for CRWU or HR. The JF model is an empirical model thatconsiders only CRWU and ignores HR. In contrast, mechanistic models,
including DJ, CR, and NH, can simulate CRWU and HR simultaneously.
Despite this, these models have primarily been used for estimating
CRWU while disregarding HR. However, HR can play a significant rolein the RWU process and coexist with CRWU (Orellana et al., 2012; Gouet al., 2018). Therefore, this study addresses the simultaneous estima­tion of CRWU and HR under nonuniform soil water conditions.
The reliability and significance of each model were further studied
by considering four hypothetical simulation scenarios that cover a broad
spectrum of soil water nonuniformities, which plants may encounter indifferent geographical habitats. The differences in computational re­quirements among the CR, NH, JF, and FD models are minimal, as
evaluating the sink term in the Richards equation represents only a small
fraction of the overall required computational time for solving the
Richards equation. In contrast, the DJ model requires significantly morecomputational time as the model requires two levels of iterations tosolve the RWU term. This is further aggravated by the need to evaluate
the matrix flux potential for each node, time step, and iteration. How­ever, this step can be significantly speeded up by using the internal

Fig. 3. Comparison of five RWU models (DJ, CR, NH, JF, and DF for Case 1) inthe simulation of (A) transpiration reduction function (Ta/Tp), (B) transpiration
ratio due to CRWU (TComp/Ta, %), and (C) cumulative actual transpiration (Ta,cm) and cumulative transpiration due to CRWU (TComp, cm). The solid line
indicates Ta, and the dashed line indicates TComp.

8 (Fig. 5I-L). Also, the higher CRWU in the NH model resulted in a
uniform distribution of soil water content and constant RWU throughout
the soil profile, irrespective of the root density (Fig. 5I-L). In the JF
model, Tcomp was observed from day 4, peaked on day 6, followed by areduction in both Ta and Tcomp (Fig. 5M-P). As expected, HR was notobserved in the JF model.
3.4. Impact of groundwater table on daily transpiration
A comparative analysis of the results produced by five RWU models
for Case 4 with a groundwater table at the bottom boundary revealed
that the pattern of RWU was highly influenced by the presence of agroundwater table when considering CRWU and HR, which is inagreement with previous studies (e.g., Shouse et al., 2011; Orellana
et al., 2012; Karimov et al., 2014; Han et al., 2015; Gou et al., 2018; Xueet al., 2018) (Fig. 6). In the DJ model, when the soil water content in the
topsoil decreased below 0.11 cm3/cm3 on day 4, the transpiration de­mand was achieved by CRWU from the capillary-fringe water (Fig. 6BC).
Here, CRWU helped plants to maintain actual transpiration closer to its
potential demand throughout the simulation period (Fig. 6A). Towards
the end of the simulation, RWU mostly relied on CRWU from ground­water, which contributed 80% of Ta. Also, groundwater contributed
significantly to Ta through HR (Fig. 6C). Compared to Case 3, in Case 4
with the groundwater table, the daily CRWU and HR were also high inthe DJ model.
8A. Thomas et al.

Agricultural Water Management 292 (2024) 108668

Fig. 4. Root water uptake simulated using the DJ (A-D), CR (E-H), NH (I-L), and JF (M-P) models for a rainfall event on day 12 and the transpiration
demand of 1.0 cm/day (Case 2). A, E, I, and M show RWU distributions over the root zone on different days. B, F, J, and N display the transpiration reduction
function (Ta/Tp). The transpiration demand (Tp), actual transpiration (Ta), transpiration due to CRWU (TComp), and hydraulically redistributed water (THR) arepresented in C, G, K, and O. The RWU profiles for the DJ, CR, NH, and JF models are presented in D, H, L, and P, respectively.

Fig. 5. : Root water uptake simulated using the DJ (A-D), CR (E-H), NH (I-L), and JF (M-P) models for a sinusoidal transpiration demand of 1.0 cm/day(Case 3): A, E, I and M show RWU distributions over the root zone on different days. The soil line indicates RWU during mid-day, and solid dotted lines indicate
nighttime transpiration. B, F, J, and N show the transpiration reduction function (Ta/Tp). The transpiration demand (Tp), actual transpiration (Ta), transpiration due
to CRWU (TComp), and hydraulically redistributed water (THR) are presented in C, G, K, and O. The RWU profiles for the DJ, CR, NH, and JF models are presented in D,
H, L, and P, respectively.

9A. Thomas et al.

Agricultural Water Management 292 (2024) 108668

Fig. 6. : Root water uptake simulated using the DJ (A-D), CR (E-H), NH (I-L), and JF (M-P) models for a sinusoidal transpiration demand of 1.0 cm/day andwater table as the bottom boundary (Case 4): (A, E, I, and M show RWU distributions over the root zone. RWU during mid-day is indicated by a solid line, and solid
dotted lines indicate nighttime transpiration. B, F, J, and N show the transpiration reduction function (Ta/Tp). The transpiration demand (Tp), actual transpiration(Ta), transpiration due to CRWU (TComp) and hydraulically redistributed water (THR), are presented in C, G, K, and O. The RWU profiles for the DJ, CR, NH, and JF
models are presented in D, H, L, and P, respectively.

interpolation tables, similarly as done for other soil hydraulic properties.
Since the selected RWU models use different sink term formulations
and root hydraulic parameters, they tend to generate different RWU
dynamics and soil water distribution profiles. Despite its complex
formulation and numerical implementation, the DJ model demonstrated
more consistent predictions of CRWU and HR under low transpiration
demand conditions. This model incorporates important root parameterssuch as RDL, Rx, R0, and Kroot, which play a crucial role in determining
CRWU and HR for the accurate estimation of RWU (Bechmann et al.,2014). This contrasts the CR, and JF models, which generated compa­
rable RWU profiles but with varying degrees of CRWU and HR. The
differential behavior of RWU models also influenced the soil watercontent distributions in the root zone under water-stressed conditions.
In the DJ and NH models, the soil water content profile did not approach
the wilting point (θr), likely because CRWU occurred before the soil
water in the water-stressed zone reached this point.
The simulation of CRWU in the CR model depends on an add-on
function, Scomp, which depends on Kcomp and the water potential
gradient between the soil and the root surface. On the other hand, CRWU
in the JF model is based on a stress index function, ω, having a value
between 1 and the root adaptability factor, ωc. Although the formulationand nature of parameters in the mechanistic CR and empirical FJ models
differ, they predict comparable RWU dynamics under optimal soil
moisture conditions. Therefore, it is possible to find a similarity between
the CR and JF models. For instance, in Case 1, ωc corresponding to the
CR model (Kcomp of 4.0000e-04 cm/day) was found to be 0.148. Thismeans that RWU simulated by the JF model with the ωc value of 0.148
showed a high correlation with RWU simulated by the CR model(Pearson correlation coefficient of 0.98). Therefore, in Case 1, theemergence of CRWU was comparable between these models., eventhough the degree of compensation depended on different input pa­
rameters (i.e., Kcomp in the CR model and ωc in the JF model). Never­theless, the CR and JF models predicted different RWU under asinusoidal transpiration demand, as the CR model predicted HR into thedry soil layers during the night. This hydraulically redistributed water
was then absorbed during the following day, resulting in non-zero RWU
from all layers, unlike in the JF model.
The RWU profile simulated by the NH model deviated from RDL
under optimal conditions due to the early emergence of CRWU. More­over, compared to the other models, the NH model has limitations in its
applicability under optimal or near-saturated soil moisture conditions,as well as concerning HR. This is because the NH model estimates RWU
based on the water potential gradient between the soil and the root-soil
interface and the soil hydraulic conductivity, which is highly influenced
by root zone soil conditions. For example, in loam soil, the soil hydraulicconductivity (K) can vary from 25 cm/day to 1.7e-09 cm/day between
saturation and the wilting point, making the RWU profile highly sensi­
tive to soil properties. This may lead to either over-representation orunder-representation of water-stress-coping strategies based on the rootzone environment. For instance, when the soil water content in the rootzone approaches saturation, the RWU profile becomes unrealistic, with ahigh rate of HR, even with a slight variation in soil water contents. In
contrast, in the region with a low water potential, the hydraulic con­ductivity is at its lowest, restricting the release of water into this region.
This limits the applicability of the NH model for the HR simulation andthe RWU estimation when the root zone is near saturation. However,under moderate soil moisture conditions, the NH model behaves simi­
larly to the DJ model.
The comparison of transpiration fluxes simulated using the fivemodels in four cases indicates the significance of CRWU and HR inmaintaining transpiration. In all four cases, the cumulative actual
transpiration simulated using the DJ, CR, NH, and JF models signifi­
cantly increased compared to the FD model, indicating that ignoring
CRWU and HR may cause a significant error in ecological and agricul­
tural models simulating RWU (Deb et al., 2013). Interestingly, whencomparing Case 3 and Case 1 with and without HR, significant
10

A. Thomas et al.

Agricultural Water Management 292 (2024) 108668

differences in cumulative Ta were not observed. This suggests that theeffect of HR is negligible under dry-down conditions (as simulated by the
DJ and CR models). In contrast, the RWU pattern showed a significant
difference in Case 4, which considers HR with a groundwater table. This
indicates that the role of HR becomes more pronounced when an
external water source, such as groundwater or rainfall/irrigation, isavailable in the root zone. This may also be prominent for plants withdeep roots that can extract water from the deep vadose zone, as applies
to CRWU to some extent. This synergy effect can be justified whencomparing total transpiration in Cases 3 and 4. In Case 4, total tran­
spiration increased by 13.7% in the CR model, and the plant transpired
at its potential demand in the DJ model. CRWU and HR also increased
considerably in Case 4 due to the contribution from the deeper
water-saturated zone. Thus, in plants with access to groundwater orplants with deep roots, the CRWU and HR play a major role in main­taining the transpiration demand, which is in agreement with previous
studies (Zhu et al., 2009; Miller et al., 2010; Barbeta and Peñuelas, 2017;
Gou et al., 2018; Zhao et al., 2020). Thus, for sites without external
water sources to the root zone in the form of irrigation/rainfall or
groundwater, the CRWU can delay the onset of transpiration reduction(Thomas et al., 2020). However, a significant impact on Ta cannot be
expected in the long run, as substantiated by comparing Case 1 vs Case 2
and Case 3 vs Case 4. Likewise, CRWU and HR are predominant underheterogeneous soil water conditions, and therefore, under irrigatedagriculture and humid conditions, CRWU and HR are likely lessimportant (Albasha et al., 2015). Moreover, deep-rooted plants withhigher axial hydraulic conductance favor CRWU and HR from deeper
soil layers compared to plants with finer, shallower roots (Zwieniecki
et al., 2002; Šimůnek and Hopmans, 2009). Thus, when modeling RWU
and total transpiration of shallow-rooted agricultural crops such asmaize, the impact of CRWU and HR can be neglected unless ground­water is shallow or the site is partially irrigated. Under such conditions,empirical RWU models like JF and FD may perform sufficiently well.
The current study provides a comparative analysis of five wellaccepted RWU models and offers insights into their significance infield applications. This study also contributes to the selection ofcommonly used RWU models with respect to parameter availability,
accuracy, and root zone properties.

Writing – review & editing, Writing – original draft, Supervision,
Methodology, Conceptualization.
Declaration of Competing Interest
The authors declare the following financial interests/personal re­lationships which may be considered as potential competing interests:
Anooja Thomas reports financial support was provided by United StatesIndia Educational Foundation (USIEF)- Fulbright-Nehru Doctoral
Fellowship (FNDR). Anooja Thomas reports financial support was pro­vided by Ministry of Human Resource Development (MHRD), Govt. ofIndia.
Data availability
Data will be made available on request.
Acknowledgments
Anooja Thomas (AT) is supported by SRF from the Ministry of
Human Resource Development (MHRD), Govt. of India. AT is also
thankful to the United States-India Educational Foundation (USIEF),
India, for the Fulbright-Nehru Doctoral Fellowship (FNDR). We arethankful to Prof. Quirijn de Jong van Lier (Center for Nuclear Energy inAgriculture, University of São Paulo, Brazil) for insightful discussions on
this paper. We sincerely thank Jees Sebastian for editing and proof­
reading the manuscript. We also acknowledge the Editor, AE, and threeanonymous reviewers for their very constructive comments.
Appendix A. Supporting information
Supplementary data associated with this article can be found in the
online version at doi:10.1016/j.agwat.2024.108668.
References
Albasha, R., Mailhol, J.C., Cheviron, B., 2015. Compensatory uptake functions in
empirical macroscopic root water uptake models–experimental and numericalanalysis. Agric. Water Manag. 155, 22–39. https://doi.org/10.1016/j.
agwat.2015.03.010.
Amenu, G.G., Kumar, P., 2008. A model for hydraulic redistribution incorporating
coupled soil-root moisture transport. Hydrol. Earth Syst. Sci. 12, 55–74. https://doi.
org/10.5194/hess-12-55-2008.
Arnold, J.G., Moriasi, D.N., Gassman, P.W., Abbaspour, K.C., White, M.J., Srinivasan, R.,
Santhi, C., Harmel, R.D., Van Griensven, A., Van Liew, M.W., Kannan, N., 2012.
SWAT: model use, calibration, and validation. Trans. ASABE 55, 1491–1508.
https://doi.org/10.13031/2013.42256.
Baker, I.T., Prihodko, L., Denning, A.S., Goulden, M., Miller, S., Da Rocha, H.R., 2008.
Seasonal drought stress in the Amazon: reconciling models and observations.
J. Geophys. Res. Biogeosci 113, G00B01. https://doi.org/10.1029/2007JG000644.
Barbeta, A., Peñuelas, J., 2017. Relative contribution of groundwater to planttranspiration estimated with stable isotopes. Sci. Rep. 7, 10580 https://doi.org/
10.1038/s41598-017-09643-x.
Bechmann, M., Schneider, C., Carminati, A., Vetterlein, D., Attinger, S., Hildebrandt, A.,
2014. Effect of parameter choice in root water uptake models–the arrangement ofroot hydraulic properties within the root architecture affects dynamics andefficiency of root water uptake. Hydrol. Earth Syst. Sci. 18 (10), 4189–4206. https://doi.org/10.5194/hess-18-4189-2014.
Bingham, I.J., Wu, L., 2011. Simulation of wheat growth using the 3D root architecture
model SPACSYS: validation and sensitivity analysis. Eur. J. Agron. 34, 181–189.
https://doi.org/10.1016/j.eja.2011.01.003.
Brocca, L., Melone, F., Moramarco, T., Morbidelli, R., 2010. Spatial-temporal variabilityof soil moisture and its estimation across scales. Water Resour. Res. 46 (2) https://doi.org/10.1029/2009WR008016.
Brunetti, G., Kodešová, R., Šimůnek, J., 2019. Modeling the translocation andtransformation of chemicals in the soil-plant continuum: A dynamic plant uptake
module for the HYDRUS model. Water Resour. Res. 55 (11), 8967–8989. https://doi.
org/10.1029/2019WR025432.
Cai, G., Vanderborght, J., Couvreur, V., Mboh, C.M., Vereecken, H., 2018a.
Parameterization of root water uptake models considering dynamic root
distributions and water uptake compensation. Vadose Zone J. 17, 170125 https://doi.org/10.2136/vzj2016.12.0125.
Cai, G.C., Vanderborght, J., Langensiepen, M., Schnepf, A., Huging, H., Vereecken, H.,
2018b. Root growth, water uptake, and sap flow of winter wheat in response to

5. Conclusions
We assessed the performance of five RWU models while considering
the combined effect of CRWU and HR. We implemented three additional
RWU models (DJ, CR, and NH) in the HYDRUS-1D model. Our finding
revealed that the DJ and CR models provided the most realistic pre­dictions of RWU under nonuniform soil water conditions, with the po­tential to capture both CRWU and HR. Despite differences in theformulation and parameterizations of the sink term in the CR and JF
models, these models predicted similar distributions of RWU. However,
the NH model was found inadequate to simulate RWU accurately whilesoil water was near saturation.
In conclusion, the DJ and CR models were found to be effective inquantifying the combined effects of CRWU and HR and better represent
the soil water dynamics in the vadose zone than the FD, JF, and NH
models. Implementing these models into the HYDRUS platform tosimultaneously consider CRWU and HR and making them available to
the HYDRUS users will improve RWU predictions by the model andundoubtedly facilitate and encourage future research on water uptake
by plant roots using mechanistic models.
CRediT authorship contribution statement
Simunek Jiri: Writing – review & editing, Writing – original draft,
Software, Methodology, Conceptualization. Thomas Anooja: Writing –review & editing, Writing – original draft, Visualization, Validation,
Software, Methodology, Conceptualization. Yadav Brijesh Kumar:
11

A. Thomas et al.

Agricultural Water Management 292 (2024) 108668

different soil water conditions. Hydrol. Earth Syst. Sci. 22 (4), 2449–2470. https://doi.org/10.5194/hess-22-2449-2018.
Caldwell, M.M., Dawson, T.E., Richards, J.H., 1998. Hydraulic lift: consequences ofwater efflux from the roots of plants. Oecologia 113, 151–161. https://doi.org/
10.1007/s004420050363.
Carminati, A., Vetterlein, D., 2013. Plasticity of rhizosphere hydraulic properties as a key
for efficient utilization of scarce resources. Ann. Bot. 112, 277–290. https://doi.org/
10.1093/aob/mcs262.
Carsel, R.F., Parrish, R.S., 1988. Developing joint probability distributions of soil water
retention characteristics. Water Resour. Res. 24, 755–769. https://doi.org/10.1029/
WR024i005p00755.
Couvreur, V., Vanderborght, J., Javaux, M., 2012. A simple three-dimensional
macroscopic root water uptake model based on the hydraulic architecture approach.
Hydrol. Earth Syst. Sci. 16, 2957–2971. https://doi.org/10.5194/hess-16-29572012.
Couvreur, V., Vanderborght, J., Beff, L., Javaux, M., 2014. Horizontal soil water potential
heterogeneity: simplifying approaches for crop water dynamics models. Hydrol.
Earth Syst. Sci. Discuss. 18 (5), 1723–1743. https://doi.org/10.5194/hess-18-17232014.
Da Rocha, H.R., Goulden, M.L., Miller, S.D., Menton, M.C., Pinto, L.D., de Freitas, H.C., e
Silva Figueira, A.M., 2004. Seasonality of water and heat fluxes over a tropical forest
in eastern Amazonia. Ecol. Appl. 14 (sp4), S22–S32. https://doi.org/10.1890/026001.
Dara, A., Moradi, B.A., Vontobel, P., Oswald, S.E., 2015. Mapping compensating root
water uptake in heterogeneous soil conditions via neutron radiography. Plant Soil
397, 273–287. https://doi.org/10.1007/s11104-015-2613-3.
Dawson, T.E., 1993. Hydraulic lift and water-use by plants—implications for waterbalance, performance and plant–plant interactions. Oecologia 95, 565–574. https://doi.org/10.1007/BF00317442.
de Jong van Lier, Q., Metselaar, K., van Dam, J.C., 2006. Root water extraction andlimiting soil hydraulic conditions estimated by numerical simulation. Vadose Zone J.
5, 1264–1277. https://doi.org/10.2136/vzj2006.0056.
de Jong van Lier, Q., van Dam, J.C., Metselaar, K., De Jong, R., Duijnisveld, W.H.M.,
2008. Macroscopic root water uptake distribution using a matric flux potential
approach. Vadose Zone J. 7, 1065–1078. https://doi.org/10.2136/vzj2007.0083.
de Jong van Lier, Q., van Dam, J.C., Durigon, A., dos Santos, M.A., Metselaar, K., 2013.
Modeling water potentials and flows in the soil-plant system comparing hydraulicresistances and transpiration reduction functions. Vadose Zone J. 12, 1–20. https://doi.org/10.2136/vzj2013.02.0039.
De Melo, M.L.A., de Jong van Lier, Q., 2021. Revisiting the Feddes reduction function formodeling root water uptake and crop transpiration. J. Hydrol. 603, 126952 https://doi.org/10.1016/j.jhydrol.2021.126952.
De Willigen, P., van Dam, J.C., Javaux, M., Heinen, M., 2012. Root water uptake assimulated by three soil water flow models. Vadose Zone J. 11 (3) https://doi.org/
10.2136/vzj2012.0018.
Deb, S.K., Shukla, M.K., Šimůnek, J., Mexal, J.G., 2013. Evaluation of spatial andtemporal root water uptake patterns of a flood-irrigated pecan tree using the
HYDRUS (2D/3D) model. J. Irrig. Drain. Eng. 139 (8), 599–611. https://doi.org/
10.1061/(ASCE)IR.1943-4774.000061.
Domec, J.C., Scholz, F.G., Bucci, S.J., Meinzer, F.C., Goldstein, G., Villalobos-Vega, R.,
2006. Diurnal and seasonal variation in root xylem embolism in neotropical savanna
woody species: impact on stomatal control of plant water status. Plant Cell Environ.
29 (1), 26–35. https://doi.org/10.1111/j.1365-3040.2005.01397.x.
Domec, J.C., King, J.S., Noormets, A., Treasure, E., Gavazzi, M.J., Sun, G., McNulty, S.G.,
2010. Hydraulic redistribution of soil water by roots affects whole-standevapotranspiration and net ecosystem carbon exchange. N. Phytol. 187, 171–183.
https://doi.org/10.1111/j.1469-8137.2010.03245.x.
Domec, J.C., Ogée, J., Noormets, A., Jouangy, J., Gavazzi, M., Treasure, E., Sun, G.,
McNulty, S.G., King, J.S., 2012. Interactive effects of nocturnal transpiration andclimate change on the root hydraulic redistribution and carbon and water budgets ofSouthern US pine plantations. Tree Physiol. 32, 707–723. https://doi.org/10.1093/
treephys/tps018.
Doussan, C., Pages, L., Vercambre, G., 1998a. Modelling of the hydraulic architecture ofroot systems: an integrated approach to water absorption – Model description. Ann.
Bot. 81, 213–223. https://doi.org/10.1006/anbo.1997.0540.
Doussan, C., Vercambre, G., Pages, L., 1998b. Modelling of the hydraulic architecture ofroot systems: an integrated approach to water absorption – Distribution of axial andradial conductances in maize. Ann. Bot. 81, 225–232. https://doi.org/10.1006/
anbo.1997.0541.
Draye, X., Kim, Y., Lobet, G., Javaux, M., 2010. Model-assisted integration ofphysiological and environmental constraints affecting the dynamic and spatial
patterns of root water uptake from soils. J. Exp. Bot. 61, 2145–2155. https://doi.
org/10.1093/jxb/erq077.
Dunbabin, V.M., Postma, J.A., Schnepf, A., Pagès, L., Javaux, M., Wu, L., Leitner, D.,
Chen, Y.L., Rengel, Z., Diggle, A.J., 2013. Modelling root–soil interactions using
three–dimensional models of root growth, architecture and function. Plant Soil 372,
93–124. https://doi.org/10.1007/s11104-013-1769-y.
Fan, Y., Miguez-Macho, G., 2010. Potential groundwater contribution to Amazon
evapotranspiration. Hydrol. Earth Syst. Sci. Discuss. 14 (10), 2039–2056. https://doi.org/10.5194/hess-14-2039-2010.
Feddes, R.A., Kowalik, P.J., Zaradny, H., 1978. Simulation of Field Water Use and Crop
Yield. John Wiley & Sons, New York, NY.
Feddes, R.A., Hoff, H., Bruen, M., Dawson, T., de Rosnay, P., Dirmeyer, P., Jackson, R.B.,
Kabat, P., Kleidon, Lilly, A, Pitman, A.J., 2001. Modeling root water uptake inhydrological and climate models. B. Am. Meteorol. Soc. 82 (12), 2797–2809.

Gale, M.R., Grigal, D.F., 1987. Vertical root distributions of northern tree species inrelation to successional status. Can. J. . Res. 17 (8), 829–834. https://doi.org/
10.1139/x87-131.
Gardner, W.R., 1960. Dynamic aspects of water availability to plants. Soil Sci. 89 (2),63–73.
Gou, S., Miller, G.R., Saville, C., Maxwell, R.M., Ferguson, I.M., 2018. Simulating
groundwater uptake and hydraulic redistribution by phreatophytes in a highresolution, coupled subsurface-land surface model. Adv. Water Resour. 121,
245–262. https://doi.org/10.1016/j.advwatres.2018.08.008.
Han, M., Zhao, C., Šimůnek, J., Feng, G., 2015. Evaluating the impact of groundwater on
cotton growth and root zone water balance using Hydrus-1D coupled with a crop
growth model. Agric. Water Manag. 160, 64–75. https://doi.org/10.1016/j.
agwat.2015.06.028.
Heinen, M., 2001. FUSSIM2: Brief description of the simulation model and application to
fertigation scenarios. Agronomie 21, 285–296. https://doi.org/10.1051/agro:
2001124.
Homaee, M., Feddes, R.A., Dirksen, C., 2002. Simulation of root water uptake. II. Nonuniform transient water stress using different reduction functions. Agric. Water
Manag. 57, 111–126. https://doi.org/10.1016/S0378-3774(02)00071-9.
Jackson, R.B., Sperry, J.S., Dawson, T.E., 2000. Root water uptake and transport: using
physiological processes in global predictions. Trends Plant Sci. 5, 482–488. https://doi.org/10.1016/S1360-1385(00)01766-0.
Jarvis, N., 1989. A simple empirical model of root water uptake. J. Hydrol. 107, 57–72.
https://doi.org/10.1016/0022-1694(89)90050-4.
Jarvis, N., 2011. Simple physics-based models of compensatory plant water uptake:
Concepts and eco-hydrological consequences. Hydrol. Earth Syst. Sci. 15,
3431–3446. https://doi.org/10.5194/hess-15-3431-2011.
Javaux, M., Schröder, T., Vanderborght, J., Vereecken, H., 2008. Use of a threedimensional detailed modeling approach for predicting root water uptake. Vadose
Zone J. 7 (3), 1079–1088. https://doi.org/10.2136/vzj2007.0115.
Karimov, A.K., Šimůnek, J., Hanjra, M.A., Avliyakulov, M., Forkutsa, I., 2014. Effects ofthe shallow water table on water use of winter wheat and ecosystem health:Implications for unlocking the potential of groundwater in the Fergana Valley(Central Asia). Agric. Water Manag. 131, 57–69. https://doi.org/10.1016/j.
agwat.2013.09.010.
Kitajima, K., Allen, M.F., Goulden, M.L., 2013. Contribution of hydraulically lifted deep
moisture to the water budget in a Southern California mixed forest. J. Geophys. Res.
Biogeosci. 118, 1561–1572. https://doi.org/10.1002/2012JG002255.
Koch, T., Heck, K., Schröder, N., Class, H., Helmig, R., 2018. A New Simulation
Framework for Soil-Root Interaction, Evaporation, Root Growth, and Solute
Transport. Vadose Zone J. 17 (1), 170210 https://doi.org/10.2136/
vzj2017.12.0210.
Lai, C.T., Katul, G., 2000. The dynamic role of root-water uptake in coupling potential toactual transpiration. Adv. Water Resour. 23, 427–439. https://doi.org/10.1016/
S0309-1708(99)00023-8.
Lee, J.E., Oliveira, R.S., Dawson, T.E., Fung, I., 2005. Root functioning modifies seasonal
climate. Proc. Natl. Acad. Sci. U. S. A. 102, 17576–17581. https://doi.org/10.1073/
pnas.0508785102.
Lei, G., Zeng, W., Zhu, J., Zha, Y., Fang, Y., Song, Y., Chen, M., Qian, Y., Wu, J.,
Huang, J., 2019. Quantification of leaf growth, height increase, and compensatoryroot water uptake of sunflower in heterogeneous saline soils. J. Agron. 111 (3),1010–1027. https://doi.org/10.2134/agronj2018.06.0418.
Leitner, D., Klepsch, S., Knieß, A., Schnepf, A., 2010. The algorithmic beauty of plantroots - an L-system model for dynamic root growth simulation. Math. Comput. Model
Dyn. 16, 575–587. https://doi.org/10.1080/13873954.2010.491360.
Li, K.Y., Boisvert, J.B., De Jong, R., 1999. An exponential root water uptake model. Can.
J. Soil Sci. 79, 333–343. https://doi.org/10.4141/S98-032.
Li, K.Y., De Jong, R., Boisvert, J.B., 2001. An exponential root-water-uptake model withwater stress compensation. J. Hydrol. 252, 189–204. https://doi.org/10.1016/
S0022-1694(01)00456-5.
Lobet, G., Draye, X., 2013. Novel scanning procedure enabling the vectorization of entire
rhizotron-grown root systems. Plant Methods 9 (1). https://doi.org/10.1186/17464811-9-1.
Neumann, R.B., Cardon, Z.G., 2012. The magnitude of hydraulic redistribution by plantroots: a review and synthesis of empirical and modeling studies. N. Phytol. 194,
337–352. https://doi.org/10.1111/j.1469-8137.2012.04088.x.
Nguyen, T.H., Langensiepen, M., Vanderborght, J., Hüging, H., Mboh, C.M., Ewert, F.,
2020. Comparison of root water uptake models in simulating CO 2 and H 2 O fluxes
and growth of wheat. Hydrol. Earth Syst. Sci. 24 (10), 4943–4969. https://doi.org/
10.5194/hess-24-4943-2020.
Nimah, M.N., Hanks, R.J., 1973. Model for estimating soil water, plant, and atmosphericinterrelations: I. Description and sensitivity. Soil Sci. Soc. Am. J. 37 (4), 522–527.
https://doi.org/10.2136/sssaj1973.03615995003700040018x.
Ojha, C.S.P., Rai, A.K., 1996. Nonlinear root water uptake model. J. Irrig. Drain. Eng.
122, 198–202. https://doi.org/10.1061/(ASCE)0733-9437(1996)122:4(198).
Oliveira, R.S., Dawson, T.E., Burgess, S.S., Nepstad, D.C., 2005. Hydraulic redistribution
in three Amazonian trees. Oecologia 145, 354–363. https://doi.org/10.1007/
s00442-005-0108-2.
Orellana, F., Verma, P., Loheide, S.P., Daly, E., 2012. Monitoring and modeling watervegetation interactions in groundwater-dependent ecosystems. Rev. Geophys. 50 (3)https://doi.org/10.1029/2011RG000383.
Pagès, L., Vercambre, G., Drouet, J.L., Lecompte, F., Collet, C., Le Bot, J., 2004. Root Typ:a generic model to depict and analyse the root system architecture. Plant Soil 258(1), 103–119. https://doi.org/10.1023/B:PLSO.0000016540.47134.03.
Peters, A., Durner, W., Iden, S.C., 2017. Modified Feddes type stress reduction function
for modeling root water uptake: Accounting for limited aeration and low water12

A. Thomas et al.

Agricultural Water Management 292 (2024) 108668
uptake and hydraulic redistribution. Plant Soil 457 (1), 421–435. https://doi.org/
10.1007/s11104-020-04738-3.
Van Dam, J.C. (2000). Field-scale water flow and solute transport. SWAP model
concepts, parameter estimation, and case studies. PhD-thesis, Wageningen
University, Wageningen, The Netherlands, 167 p., ISBN 90-5808-256-3, English andDutch summaries. (https://library.wur.nl/WebQuery/wurpubs/fulltext/121243).
van Genuchten, M.T., 1987. A numerical model for water and solute movement in andbelow the root zone. Tech. Rep. 121. U.S. Salinity Laboratory, USDA, ARS, Riverside,CA.
Vanderborght, J., Leitner, D., Schnepf, A., Couvreur, V., Vereecken, H., Javaux, M., 2023.
Combining root and soil hydraulics in macroscopic representations of root water
uptake. Vadose Zone J., e20273 https://doi.org/10.1002/vzj2.20273.
Vanderborght, J., Couvreur, V., Meunier, F., Schnepf, A., Vereecken, H., Bouda, M.,
Javaux, M., 2021. From hydraulic root architecture models to macroscopic
representations of root hydraulics in soil water flow and land surface models.
Hydrol. Earth Syst. Sci. 25 (9), 4835–4860. https://doi.org/10.5194/hess-25-48352021.
Vereecken, H., Schnepf, A., Hopmans, J.W., Javaux, M., Or, D., Roose, T.,
Vanderborght, J., Young, M.H., Amelung, W., Aitkenhead, M., Allison, S.D., 2016.
Modeling soil processes: Review, key challenges, and new perspectives. Vadose Zone
J. 15 (5) https://doi.org/10.3929/ethz-b-000116746.
Verma, P., Loheide, S.P., Eamus, D., Daly, E., 2014. Root water compensation sustains
transpiration rates in an Australian woodland. Adv. Water Resour. 74, 91–101.
https://doi.org/10.1016/j.advwatres.2014.08.013.
Vrugt, J.A., van Wijk, M.T., Hopmans, J.W., Šimunek, J., 2001. One-, two-, and threedimensional root water uptake functions for transient modeling. Water Resour. Res.
37 (10), 2457–2470. https://doi.org/10.1029/2000WR000027.
Wang, K., Dickinson, R.E., 2012. A review of global terrestrial evapotranspiration:
Observation, modeling, climatology, and climatic variability. Rev. Geophys. 50 (2),
RG2005. https://doi.org/10.1029/2011RG000373.
Xue, J., Huo, Z., Wang, F., Kang, S., Huang, G., 2018. Untangling the effects of shallow
groundwater and deficit irrigation on irrigation water productivity in arid region:
New conceptual model. Sci. Total Environ. 619, 1170–1182. https://doi.org/
10.1002/2015WR017522.
Yadav, B.K., Mathur, S., Siebel, M.A., 2009a. Soil moisture dynamics modelingconsidering the root compensation mechanism for water uptake by plants. J. Hydrol.
Eng. 14, 913–922. https://doi.org/10.1061/(ASCE)HE.1943-5584.0000066.
Yadav, B.K., Shashi, M.M., Siebel, A., 2009b. Soil moisture flow modelling with water
uptake by plants (wheat) under varying soil and moisture conditions. J. Hydrol. Eng.
135 (3), 375–381. https://doi.org/10.1061/(ASCE)IR.1943-4774.0000068.
Yan, B.Y., Dickinson, R.E., 2014. Modeling hydraulic redistribution and ecosystem
response to droughts over the Amazon basin using Community Land Model 4.0(CLM4). J. Geophys. Res. 119, 2130–2143. https://doi.org/10.1002/
2014JG002694.
Zhao, M., Wang, W., Wang, Z., Chen, L., Ma, Z., Wang, Q., 2020. Water use of Salix in thevariably unsaturated zone of a semiarid desert region based on in-situ observation.
J. Hydrol. 591, 125579 https://doi.org/10.1016/j.jhydrol.2020.125579.
Zheng, Z., Wang, G., 2007. Modeling the dynamic root water uptake and its hydrologicalimpact at the Reserva Jaru site in Amazonia. J. Geophys. Res. 112, G04012. https://doi.org/10.1029/2007JG000413.
Zhu, Y., Ren, L., Skaggs, T.H., Lü, H., Yu, Z., Wu, Y., Fang, X., 2009. Simulation ofPopulus euphratica root uptake of groundwater in an arid woodland of the Ejina
Basin, China. Hydrol. Process. 23 (17), 2460–2469. https://doi.org/10.1002/
hyp.7353.
Zwieniecki, M.A., Thompson, M.V., Holbrook, N.M., 2002. Understanding the hydraulicsof porous pipes: tradeoffs between water uptake and root length utilization. J. Plant
Growth Regul. 21, 315–323. https://doi.org/10.1007/s00344-003-0008-9.

potential. Agric. Water Manag. 185, 126–136. https://doi.org/10.1016/j.
agwat.2017.02.010.
Prieto, I., Ryel, R.J., 2014. Internal hydraulic redistribution prevents the loss of root
conductivity during drought. Tree Physiol. 34 (1), 39–48. https://doi.org/10.1093/
treephys/tpt115.
Prieto, I., Kikvidze, Z., Pugnaire, F.I., 2010a. Hydraulic lift: soil processes andtranspiration in the Mediterranean leguminous shrub Retama sphaerocarpa (L.)
Boiss. Plant Soil 329, 447–456. https://doi.org/10.1007/s11104-009-0170-3.
Prieto, I., Armas, C., Pugnaire, F.I., 2012. Water release through plant roots: new insights
into its consequences at the plant and ecosystem level. N. Phytol. 193, 830–841.
https://doi.org/10.1111/j.1469-8137.2011.04039.x.
Prieto, I., Martínez-Tillería, K., Martínez-Manchego, L., Montecinos, S., Pugnaire, F.I.,
Squeo, F.A., 2010b. Hydraulic lift through transpiration suppression in shrubs from
two arid ecosystems: patterns and control mechanisms. Oecologia 163, 855–865.
https://doi.org/10.1007/s00442-010-1615-3.
Richards, L.A., 1931. Capillary conduction of liquids through porous mediums. Physics 1,
318–333. https://doi.org/10.1063/1.1745010.
Ryel, R.J., Caldwell, M.M., Yoder, C.K., Or, D., Leffler, A.J., 2002. Hydraulicredistribution in a stand of Artemisia tridentata: evaluation of benefits totranspiration assessed with a simulation model. Oecologia 130, 173–184. https://doi.org/10.1007/s004420100794.
Santos, M.A., Jong van Lier, Q.D., Dam, J.V.C., Freire Bezerra, A.H., 2017. Benchmarking
test of empirical root water uptake models. Hydrol. Earth Syst. Sci. 21, 473–493.
https://doi.org/10.5194/hess-21-473-2017.
Schnepf, A., Black, C.K., Couvreur, V., Delory, B.M., Doussan, C., Heymans, A.,
Javaux, M., Khare, D., Koch, A., Koch, T., Kuppe, C.W., Landl, M., Leitner, D.,
Lobet, G., Meunier, F., Postma, J.A., Schäfer, E.D., Selzner, T., Vanderborght, J.,
Vereecken, H., 2023. Collaborative benchmarking of functional-structural rootarchitecture models: Quantitative comparison of simulated root water uptake. silico
Plants 5 (1). https://doi.org/10.1093/insilicoplants/diad005.
Scott, R.L., Cable, W.L., Hultine, K.R., 2008. The ecohydrologic significance of hydraulicredistribution in a semiarid savanna. Water Resour. Res. 44, W02440. https://doi.
org/10.1029/2007WR006149.
Shouse, P.J., Ayars, J.E., Šimůnek, J., 2011. Simulating root water uptake from a shallow
saline groundwater resource. Agric. Water Manag. 98 (5), 784–790. https://doi.org/
10.1016/j.agwat.2010.08.016.
Šimůnek, J., Hopmans, J.W., 2009. Modeling compensated root water and nutrient
uptake. Ecol. Model. 220 (4), 505–521. https://doi.org/10.1016/j.
ecolmodel.2008.11.004.
Šimůnek, J., van Genuchten, M.Th, Šejna, M., 2016. Recent developments andapplications of the HYDRUS computer software packages. Vadose Zone J. 15 (7), 25.
https://doi.org/10.2136/vzj2016.04.0033.
Šimůnek, J., Šejna, M., Saito, H., Sakai, M., van Genuchten, M.T., 2013. The HYDRUS-1D
Software package for simulating the one-dimensional movement of water, heat, andmultiple solutes in variably-saturated media, Version 4.16. Department ofEnvironmental Sciences. University of California Riverside, Riverside, California.
Skaggs, T.H., van Genuchten, M.T., Shouse, P.J., Poss, J.A., 2006. Macroscopic
approaches to root water uptake as a function of water and salinity stress. Agric.
Water Manag. 86 (1–2), 140–149. https://doi.org/10.1016/j.agwat.2006.06.005.
Smithwick, E.A., Lucash, M.S., McCormack, M.L., Sivandran, G., 2014. Improving therepresentation of roots in terrestrial models. Ecol. Model. 291, 193–204. https://doi.
org/10.1016/j.ecolmodel.2014.07.023.
Song, Y., Kirkham, M.B., Ham, J.M., Kluitenberg, G.J., 2000. Root-zone hydraulic lift
evaluated with the dual-probe heat-pulse technique. Aust. J. Soil Res 38, 927–935.
https://doi.org/10.1071/Sr99096.
Thomas, A., Yadav, B.K., Šimůnek, J., 2020. Root water uptake under heterogeneous soil
moisture conditions: an experimental study for unraveling compensatory root water

13