RESEARCH ARTICLE
10.1029/2022WR034023
Key Points:• W hile factors in the Craig-Gordon
equation dominate evaporation
fractionation, soil tension effects
deplete isotopic composition of
surface soil water• Root water uptake origin interpretedby considering tension effects
is between no fractionation andCraig-Gordon fractionation scenarios• Using the Bayesian isotope mixing
model or the virtual tracer experimentis more demanding than water balanceor particle tracking methods
Supporting Information:

Supporting Information may be found in
the online version of this article.
Correspondence to:T. Zhou and V. Post,
tzhou035@ucr.edu;
vincent@edinsi.nl
Citation:Zhou, T., Šimůnek, J., Nasta, P., Brunetti,
G., Gaj, M., Neukum, C., & Post, V.
(2023). The impact of soil tension on
isotope fractionation, transport, andinterpretations of the root water uptake
origin. Water Resources Research,
59, e2022WR034023. https://doi.
org/10.1029/2022WR034023
Received 18 NOV 2022
Accepted 3 AUG 2023

The Impact of Soil Tension on Isotope Fractionation,
Transport, and Interpretations of the Root Water Uptake
OriginTiantian Zhou1 , Jiří Šimůnek1 , Paolo Nasta2
Christoph Neukum5, and Vincent Post6, Giuseppe Brunetti3, Marcel Gaj4,

1
Department of Environmental Sciences, University of California Riverside, Riverside, CA, USA, 2Department ofAgricultural Sciences, AFBE Division, University of Naples Federico II, Napoli, Italy, 3Department of Civil Engineering,
University of Calabria, Rende, Italy, 4Department of Hydrology, State Agency for Nature, Environment and Consumer
Protection, Minden, Germany, 5Federal Institute for Geosciences and Natural Resources (BGR), Hannover, Germany, 6Edinsi
Groundwater, Nederhorst den Berg, The Netherlands

Abstract The new isotope module in HYDRUS-1D can be used to infer the origin of root water uptake(RWU), a suitable dynamic indicator for agriculture and forest water management. However, evidence showsthat the equilibrium fractionation between liquid water and water vapor within the soil is affected not only bysoil temperature but also by soil tension. How soil tension affects isotope transport modeling and interpretationsof the RWU origin is still unknown. In this study, we evaluated three fractionation scenarios on model
performance for a field data set from Langeoog Island: (a) no fractionation (Non_Frac), (b) the soil temperature
control on equilibrium fractionation as described by the standard Craig-Gordon equation (CG_Frac), and(c) CG_Frac plus the soil tension control on equilibrium fractionation (CGT_Frac). The model simulations
showed that CGT_Frac led to more depleted isotopic compositions of surface soil water than CG_Frac. The
vertical origin of RWU was estimated using the water balance (WB) calculations and the Bayesian mixing
model (SIAR). While the former directly used water flow outputs, the latter used as input simulated isotopic
compositions (using different fractionation scenarios) of RWU and soil water. Both methods provided similarvariation trends with time and depth in different soil layers' contributions to RWU. The contributions of all soil
layers interpreted by the CGT_Frac scenario were always between Non_Frac and CG_Frac. The temporal origin
of RWU was deduced from particle tracking (PT, releasing one hypothetical particle for individual precipitation
event and tracking its movement based on the water balance between particles) and a virtual tracer experiment(VTE, assigning a known isotope composition to individual precipitation event and tracking its movement
based on the cumulative isotope flux). Both methods revealed similar variation trends with time in drainage
and root zone (RZ) travel times. The interpreted drainage and RZ travel times were generally ranked as Non_
Frac > CGT_Frac > CG_Frac. Overall, the factors considered in the standard CG equation dominated isotope
fractionation, transport, and interpretations of the RWU origin. Isotope transport-based methods (SIAR, VTE)
were more computationally demanding than water flow-based methods (WB, PT).
1. Introduction© 2023. The Authors.
This is an open access article under
the terms of the Creative Commons
Attribution-NonCommercial-NoDerivs
License, which permits use anddistribution in any medium, provided theoriginal work is properly cited, the use isnon-commercial and no modifications or
adaptations are made.

ZHOU ET AL.

Equilibrium and kinetic fractionation processes occur between soil water vapor and liquid water or within soil
water vapors and induce enrichment of stable isotopes of hydrogen ( 2H) and oxygen ( 18O) in the remaining
soil water during evaporation. Kinetic fractionation is influenced by transport resistances from the evaporating
surface to the atmosphere and isotope diffusivities. Equilibrium fractionation is usually determined as a functionof soil temperature (Majoube, 1971). However, recent research shows that soil tension can affect equilibrium
fractionation by influencing interactions between water films on soil particle surfaces and water vapor (Bowers
et al., 2020; Lin et al., 2018; Lin & Horita, 2016; Orlowski & Breuer, 2020). Soil tension represents the freeenergy required to remove water from the soil matrix and induces the water vapor pressure deficit within the soil.
At very high soil tensions (i.e., dry conditions), the surface of soil particles preferentially attracts lighter isotopes
due to limited surface free energy, and soil water vapor diffusion from the soil bottom toward the atmosphere
increases. As a result, tightly bound soil water (i.e., slow mobile water subject to capillary-driven flow) is thus
depleted of heavy isotope species, which induces the enrichment in isotopic signatures of surface soil water vapor(Gaj & McDonnell, 2019).

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Not considering this factor in the modeling analysis may have implications for interpreting the origin of water
fluxes in the soil-plant-atmosphere continuum. Considerable attention has been paid to the vertical and temporalorigin of root water uptake (RWU) because this information can guide when and how much to irrigate, maximize
RWU, and reduce deep percolation, thus improving agricultural water use efficiency.
The vertical origin of root water uptake (RWU) across the soil profile has been (a) determined graphically bycomparing the isotopic characteristics of xylem water and soil water at different depths in the dual-isotope
plots, (b) calculated by linear mixing models, or (c) estimated using statistical models such as the IsoSource
and Bayesian mixing models (SIAR, MixSIR, and MixSIAR). Multiple Bayesian models (i.e., SIAR, MixSIR,
and MixSIAR) were compared by Wang et al. (2019), who reported better performance of SIAR and MixSIAR
in identifying water sources. Compared with the IsoSource model, the Bayesian mixing models can accurately
estimate water sources for RWU while simultaneously considering their uncertainty (e.g., Zhang et al., 2022).
Compared with the vertical origin, research on the temporal origin of RWU (especially numerical modeling studies) has been limited to a few studies (Allen et al., 2019; Brinkmann et al., 2018; Luo et al., 2023; Miguez-Macho& Fan, 2021; Zhou et al., 2022). An important premise for inferring the temporal origin of RWU is an accurate estimate of travel times (TT) of irrigation/precipitation water to different depths in the soil profile (e.g.,
to the bottom of the soil profile as drainage or the root zone (RZ) as RWU, etc.). As summarized in Sprenger
et al. (2019), the three common methods to estimate travel times include (a) time-invariant TT distributions, (b)StorAge Selection (SAS) functions, and (c) flux tracking or particle tracking (PT) implemented in physically
based hydrological models. The first two methods require the optimization of isotope transport parameters inlumped models (Asadollahi et al., 2020; Benettin et al., 2015; Harman, 2015; Kim & Harman, 2022; Maloszewski
et al., 2006; Pangle et al., 2017; Rinaldo et al., 2015; Stumpp & Maloszewski, 2010; Tetzlaff et al., 2014, 2018;
Timbe et al., 2014). However, these lumped models oversimplify the isotope transport mechanisms (Sprenger
et al., 2016, 2019).
By contrast, physically based numerical models (e.g., the isotope-enabled module in HYDRUS-1D) have thepotential to continuously assess the spatio-temporal origin of RWU, by solving water flow and isotope transport using the Richards and the advection-dispersion equations, respectively (Stumpp et al., 2012; Zhou
et al., 2021, 2022). However, reliable model simulations are obtained only when the model setup accurately
describes water flow and isotope transport (Finkenbiner et al., 2022). Brinkmann et al. (2018) employed a flux
tracking approach (virtual tracer experiment) using the isotope-enabled module in HYDRUS-1D (neglecting
evaporation fractionation, Stumpp et al., 2012) to derive the residence time distribution of precipitation in the soil
and the temporal origin of RWU in a temperate forest. They found that 50% of water consumed by trees throughout the year came from precipitation during the growing season (May–October), while 40% of it originated fromprecipitation in the preceding winter (November–April) (Brinkmann et al., 2018).
A recent module implemented in HYDRUS-1D considers evaporation fractionation in isotope transport modeling(Zhou et al., 2021), in which equilibrium fractionation is controlled only by soil temperature. Post et al. (2022)
found that considering evaporation fractionation in the code of Zhou et al. (2021) could significantly improve
the isotope transport modeling on Langeoog Island. Zhou et al. (2022) used PT in HYDRUS-1D and found thatconsidering fractionation in the code of Zhou et al. (2021) resulted in longer residence times of precipitation insoil and older water ages of RWU for winter rye in a lysimeter. However, isotope transport modeling has often
ignored various factors influencing evaporation fractionation (e.g., soil tension). Although this does not affectwater flow, it affects the isotope mass balance and simulated isotopic signals. This may also introduce the riskof erroneously interpreting the origin of RWU when using isotope transport-based methods. Nevertheless, little
research has been carried out to compare the water flow-based (i.e., water balance and PT, which may act as abenchmark) and isotope transport-based (i.e., SIAR, virtual tracer experiment) methods in interpreting the origin
of RWU for different evaporation fractionation scenarios.
Therefore, we pose the following three scientific questions.
1. To what extent does the consideration of the soil tension control on equilibrium evaporation fractionation
affect the performance and isotope mass balance of the isotope transport model?
2. How will different modeling results (based on different fractionation scenarios) affect the interpretation of thespatio-temporal origin of RWU?
3. Is it better to use water-flow-based (water balance, PT) or isotope-transport-based (SIAR, virtual tracer experiment) methods to determine the spatio-temporal origin of RWU?
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Figure 1. Schematic outline of methods used. Model setup considered three fractionation scenarios (gray boxes), including
Non_Frac, CG_Frac, and CGT_Frac indicating no fractionation, fractionation described by the standard Craig-Gordon
equation with only soil temperature control on equilibrium fractionation, and fractionation according to the modified
Craig-Gordon equation with both soil temperature and tension controls on equilibrium fractionation, respectively. The originof root water uptake is based on either water-flow-based methods (blue boxes) or isotope-transport-based methods (green
boxes).

To answer these three scientific questions, we used isotope data collected across a 450-cm-thick soil profile
beneath grassland on Langeoog Island (Post et al., 2022) in combination with modified HYDRUS-1D (Zhouet al., 2021) to study the influence of soil tension effects on the isotope fractionation and transport modeling,
and to evaluate how different model setups and estimation methods affect the interpretation of isotopes signals in
determining the spatio-temporal origin of RWU (Figure 1). Since a one-dimensional model is used in this study,
any references to spatial distributions refer to vertical/depth distributions.

2. Materials and Methods
2.1. Study Area and Data Collection
Langeoog is a sandy barrier island off the coast of northern Germany. The annual precipitation rate on Langeoog
Island is 777 mm (Houben et al., 2014). The freshwater groundwater lens is the only water source on this islandthat helps balance water levels between island groundwater and seawater and prevents seawater intrusion.
However, this dynamic balance is fragile due to years of extensive groundwater pumping over the years resulting
from intensive tourism and seawater erosion of the island (Post et al., 2022).
Many natural or artificial dunes have been created to protect the coast from erosion (Post & Houben, 2017).
Over several years, these dunes have shifted from an almost unvegetated type to a vegetated kind, covered withZHOU ET AL.

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Figure 2. HYDRUS-1D model setup. W, H, and I represent water flow, heat transport, and isotope transport, respectively. Boundary condition (BC) denotes BC. Notethat the description of the variables in this figure is shown in Table S1 in Supporting Information S1.

mosses, grass, and low shrubs (Post et al., 2022). This vegetation change may bring about changes in groundwater
recharge processes due to increased RWU and transpiration. Many studies have been conducted on temporal variations of groundwater recharge in this dune area (Houben et al., 2014; Post et al., 2022). However, characterizing
travel times of precipitation to RWU and groundwater recharge is still lacking, while enhancing this understanding is critical for the sustainable development of groundwater resources on this island.
Additionally, the dune sands are very dry due to evaporation and RWU, and its surface soil water is enrichedwith heavy isotopes due to evaporation fractionation (Post et al., 2022). These conditions make it a good site forstudying the impacts of soil tension control on evaporation fractionation. The vegetated dune (Site LB01 in Post
et al. (2022), covered by grasses) was selected in this study to analyze the origin of its vegetation RWU.
The experiment was carried out between July 2012 and June 2019 in a 450-cm-thick soil profile. The meteorological data, including daily precipitation P, air humidity (ha), and mean/maximum/minimum air temperature (Ta),were measured at daily time resolution. Precipitation samples for isotopic compositions were collected fortnightly
or monthly. Soil samples were collected on 25 June 2019 (10–425 cm below the soil surface, about every 5 or
10 cm) to measure grain size, soil water contents, and soil water isotopic compositions. Soil hydraulic properties
were measured on soil cores collected at the nearby site (Figure 1 of Post et al., 2022) during an earlier project in2014 using the evaporation method carried out on the HYPROP semi-automatic device (METER Group, Munich,Germany) (Lipovetsky et al., 2020). The temporal distributions of relevant weather and vegetation growth variables are shown in Figures S1 and S2 in Supporting Information S1. More details about the study area and datacollection methods can be found in (Post et al., 2022).
2.2. HYDRUS-1D Model Setup
Water flow and isotope transport in the unsaturated zone were simulated using a modified version of the
HYDRUS-1D code that considers isotope evaporation fractionation (Zhou et al., 2021). Figure 2 shows a
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summary of the model setup. The simulation period is 2536 days long (corresponding to about 7 years), from 17
July 2012, to 25 June 2019. The 450-cm-thick soil profile is uniform with a single set of soil hydraulic (θr, θs, α,n, Ks) and isotope transport(𝐴𝐴𝑖𝑖𝑙𝑙0, λ, nk) parameters (Table S1 and Figure S8 in Supporting Information S1).
𝐴𝐴
The actual RWU rate of grass, S within the RZ depends on the rooting depth and the root density distribution(Figure S1 in Supporting Information S1). It is obtained from potential RWU and the stress response function
depending on the pressure head (Feddes et al., 1978).
The upper boundary condition (BC) is set to the potential water flux across the soil surface (i.e., the difference
between daily values of potential evapotranspiration, ETp, and precipitation, P), while the lower BC is set to freedrainage (a zero pressure head gradient). Temperature BC is used at upper and lower boundaries for heat transport. Daily isotope concentrations, δp, are assigned to their corresponding precipitation events to get the concentration flux for the upper BC, while a zero concentration gradient (i.e., free drainage) is set as the lower BC. The
initial soil water content (0.046 cm 3/cm 3), temperature (20°C) and isotopic composition (−110 ‰ for 2H and−10% for 18O) are used throughout the soil profile. Post et al. (2022) provide more details about the model setups.
In our analysis, three fractionation scenarios have been considered, including (a) no evaporation fractionation (theNon_Frac scenario), (b) evaporation fractionation described by the Craig-Gordon equation, which considers only
the soil temperature control on equilibrium fractionation (the CG_Frac scenario), and (c) evaporation fractionation according to the modified Craig-Gordon equation, which considers both the soil tension and soil temperature
controls on equilibrium fractionation (the CGT_Frac scenario).
2.2.1. Craig-Gordon Equation
Evaporation fractionation between the soil water and the free atmosphere includes both equilibrium and kinetic
fractionation processes (Craig, 1961). Craig and Gordon (1965) calculated the isotope evaporation flux at the soil
surface based on these two types of fractionations.
When the isotope concentration is expressed in kg m −3 (Eq. 1 in Zhou et al., 2021), the isotope evaporation flux
Ei (kg m −2 s −1) is:()′
𝐸𝐸𝑎𝑎 𝑀𝑀𝑖𝑖 RH𝑠𝑠 ⋅ 𝛼𝛼𝑣𝑣∕𝑤𝑤 ⋅ 𝑅𝑅𝐿𝐿 − RH𝑎𝑎 ⋅ 𝑅𝑅𝑎𝑎
outin
𝐸𝐸𝑖𝑖 = 𝐸𝐸𝑖𝑖 − 𝐸𝐸𝑖𝑖 = 𝑘𝑘
(1)RH𝑠𝑠 − RH𝑎𝑎 ′𝛼𝛼𝑖𝑖 𝑀𝑀𝑤𝑤
The isotope ratio of the evaporation flux RE [−] is expressed as:[] [()] 𝑀𝑀𝑖𝑖
𝑅𝑅𝐸𝐸 = 𝐸𝐸𝑖𝑖 ∕𝐸𝐸𝑎𝑎 = RH𝑠𝑠 ⋅ 𝛼𝛼𝑣𝑣∕𝑤𝑤 ⋅ 𝑅𝑅𝐿𝐿 − 𝑅𝑅𝑅𝑅𝑎𝑎 ′ ⋅ 𝑅𝑅𝑎𝑎 ∕ RH𝑠𝑠 − RH𝑎𝑎 ′ ⋅ 𝛼𝛼𝑖𝑖𝑘𝑘 ⋅
(2)
𝑀𝑀𝑤𝑤

where Ea (m/s) is the actual evaporation flux, Mi and Mw (kg/mol) are the molar masses of heavy water and ordinary water, respectively, RHs [−] is the relative humidity of the surface soil air phase,𝐴𝐴
𝐴𝐴𝐴𝐴𝑎𝑎 ′ [−] is the normalized
air relative humidity, RL [−] is the isotope ratio of the remaining surface liquid water, Ra [−] is the isotope ratioof the atmospheric water vapor, and αv/w
𝐴𝐴 and 𝐴𝐴𝑖𝑖𝑘𝑘 [−] are the equilibrium and kinetic fractionation factors, respectively. We only show the calculation of αv/w in the main manuscript. Calculations of other variables are shown in
Text S1 in Supporting Information S1.
2.2.2. Temperature Control on Equilibrium Fractionation
Majoube (1971) computed the equilibrium fractionation factor αv/w as a function of temperature T (K):)(
76.248 24.844 ⋅ 103
2
1
−3
−
𝛼𝛼
(
𝐻𝐻∕
𝐻𝐻)
=
exp
−52.612
⋅
10
+
(3)
𝑣𝑣∕𝑤𝑤
majoube𝑇𝑇𝑇𝑇)(
0.4156 1.137 ⋅ 103
18
16
−3
−
𝛼𝛼
(
𝑂𝑂∕
𝑂𝑂)
=
exp
2.0667
⋅
10
+
(4)
𝑣𝑣∕𝑤𝑤
majoube𝑇𝑇
𝑇𝑇 2

2.2.3. Tension Control on Equilibrium Fractionation
The equilibrium fractionation factor is affected not only by temperature but also by soil tension when it is above
1,260 hPa (about 1,284 cm) under dry conditions (Gaj & McDonnell, 2019). The empirical equations presented
by Gaj and McDonnell (2019) express the equilibrium fractionation factor αv/w as the contribution
𝐴𝐴 of 𝐴𝐴𝑣𝑣∕𝑤𝑤 majoube
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and the effect of soil tension, abs(h) (absolute values of soil matric potential h, cm), which is independent of soil
texture:𝛼𝛼𝑣𝑣∕𝑤𝑤 (2 𝐻𝐻∕1 𝐻𝐻) = 𝛼𝛼𝑣𝑣∕𝑤𝑤 (2 𝐻𝐻∕1 𝐻𝐻)majoube + 0.01498 𝑙𝑙𝑙𝑙𝑙𝑙 10 (𝑎𝑎𝑎𝑎𝑎𝑎(ℎ))
(5)𝛼𝛼𝑣𝑣∕𝑤𝑤 (18 𝑂𝑂∕16 𝑂𝑂) = 𝛼𝛼𝑣𝑣∕𝑤𝑤 (18 𝑂𝑂∕16 𝑂𝑂)majoube + 0.00607 𝑙𝑙𝑙𝑙𝑙𝑙 10 (𝑎𝑎𝑎𝑎𝑎𝑎(ℎ))
(6)The new isotope transport module used in this study is almost the same as in Zhou et al. (2021). Specifically, both
modules require the input of the atmospheric water vapor's relative humidity, temperature, and isotopic composition (Equation 1). The only difference is that the soil tension control on the equilibrium fractionation factor αv/w
can be optionally considered in the model. Note that the equilibrium fractionation factor αv/w is 1 in the Non_Fracscenario (Stumpp et al., 2012), smaller than 1 in the CG_Frac (Equations 3 and 4), but may be greater or smaller
than 1 in the CGT_Frac because of the tension control (Equations 5 and 6).
2.3. Interpreting the Origin of Root Water Uptake
The results of the three modeling scenarios were used to interpret the vertical and temporal origin of RWU using
both water flow- (water balance, PT) and isotope transport-based (SIAR, virtual tracer experiment) methods.
Note that all calculations were conducted on a daily interval.
2.3.1. Vertical Origin of Root Water Uptake
Soil water at different depths of the RZ represents the source of RWU. The 40-cm-thick RZ was divided into four
sub-layers (0–10, 10–20, 20–30, and 30–40 cm), considered separate water sources (Layer 1, Layer 2, Layer 3,
Layer 4, respectively). Capillary rise from groundwater was not considered because of a relatively shallow maximum rooting depth (40 cm) and deep water table (below 450 cm) in this study area. The contributions of different
soil layers to RWU were assessed using two methods.
The first method is the water balance calculation, in which RWU from different soil layers was directly retrieved
using information printed by HYDRUS-1D. The second method is the SIAR Bayesian isotope mixing model(Parnell et al., 2010) implemented in the R package. SIAR is widely used in estimating the contributions of different source tracers to a mixture tracer. In this model, each source tracer value and its standard error (because ofmeasurement errors, discrimination factors, etc.) are assumed to follow normal distributions. The mixture tracer
value is the sum of different source tracer values multiplied by their corresponding proportional contributions andthe residual error. More details can be found in Cao et al. (2022) and Stock et al. (2018).
In this study, different fractionation scenarios were first simulated using the HYDRUS-1D model to obtainisotopic compositions of RWU (root isotope uptake divided by RWU) and isotopic compositions of soil water at
different depths. Simulated δ 2H and δ 18O in RWU and soil water in different layers and corresponding standard
errors were then used as the mixture and source tracer values in the SIAR model. The discrimination values
were set to zero for both δ 2H and δ 18O because there is usually no isotope fractionation during RWU (Dawson& Ehleringer, 1991).
The Mann-Kendall trend test was used to determine whether there is a trend (indicated by τ values; positive
and negative τ values indicate increasing and decreasing trends, respectively) in the time series of contributionsof different water sources to RWU obtained by both methods. The null hypothesis is that the data has no trend(τ = 0). When the p-value of the test is below a certain significance level (p < 0.01 was used in this study), it canbe concluded that there is a statistically significant trend in the investigated time series.
2.3.2. Temporal Origin of Root Water Uptake
2.3.2.1. Particle Tracking (PT)The PT algorithm (Figure S3 and Text S2 in Supporting Information S1) requires two input parameters: wStandand wPrec (Zhou et al., 2021, 2022; Šimůnek, 1991). In this study, the input parameters wStand and wPrec were set
to 10 cm and a negative value, respectively. The former represents the water storage that separates adjacentparticles in the soil profile at the beginning of the simulation. The latter negative value causes the program torelease one particle for each precipitation event so that one can track the movement of each precipitation event
separately. The PT algorithm then calculates particle positions based on water mass balance calculations between
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Figure 3. Measured (blue circles) and simulated (a) δ 2H and (b) δ 18O profiles at the end of the simulation (25 June 2019) for
three fractionation scenarios (Non_Frac, CG_Frac, and CGT_Frac).

two neighboring particles (and the soil surface) during a specific time interval. Based on particle positions at
different times, one can deduce the residence times of each precipitation event for various soil depths. The difference between the times when a particle enters and leaves the soil profile (or the RZ) is defined as drainage (orRZ) travel time. The PT module also evaluates the contribution of each particle to RWU at different times, which
can be used to infer the temporal origin of RWU.
2.4. Virtual Tracer Experiment (VTE)
The virtual tracer experiment (VTE) method (Figure S4 in Supporting Information S1) was used to interpretdrainage and RZ travel times for different fractionation scenarios based on repeated simulations of isotope transport using HYDRUS-1D (Nasta et al., 2021). HYDRUS-1D is run n times (where n equals the number of precipitation events), assuming the initially isotope-free soil profile, assigning a known isotope composition to the ith
precipitation event, and keeping all remaining rainfall events isotope-free. This technique helps trace isotope
composition across the soil profile from every individual rainfall event. The arrival (or exit) time is calculated
when the cumulative isotope flux at the soil profile bottom reaches 50% of its final value. The travel time iscalculated as a difference between precipitation entry times and arrivals.

3. Results
To assess the possible impact of the soil tension control on equilibrium fractionation under various soil temperature and tension conditions, we carried out a preliminary sensitivity analysis of αv/w to soil temperature (from0 to 45°C, i.e., from 273.15 to 318.15 K) and tension (1,284, 2,500, 5,000, 10,000 cm) (Text S3 in Supporting
Information S1). The results show that the contribution of the soil tension control on αv/w (lower than 6.5% and2.5% for 2H and 18O, respectively) is always smaller than that of soil temperature control. Overall, the soil tension
control has a higher impact on αv/w of 2H than 18O. However, whether this small contribution results in a considerable difference in isotopic compositions, isotope mass balance components, and the interpretations of RWU
origin needs to be further explored.
3.1. Model Performance and Isotope Mass Balance
The model performance for the final isotopic composition profiles of each modeling scenario is shown in Figure 3,
and the corresponding root mean square errors (RMSE) are reported in Table 1. The model performance of the
CG_Frac and CGT_Frac scenarios were quite similar, although very different from the Non_Frac scenario. The
Non_Frac scenario produced lower isotopic compositions of surface soil water than the CG_Frac and CGT_Fracscenarios. On the other hand, the scenario that considered the soil tension control (CGT_Frac) predicted theisotopic composition of surface soil water to be more depleted (by −7.8‰ for δ 2H and −3.1‰ for δ 18O) in thisexample than the CG_Frac scenario.
The impact of isotope fractionation controlled by the standard Craig-Gordon (CG) equation and soil tension
on the model simulations was evaluated as a percentage of a contribution to the RMSE. As can be seen in
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Table 1
Root Mean Square Error (RMSE) Values (RMSE_δ 2H, RMSE_δ 18O, and RMSE_avg Refer to RMSEs for the δ 2H, δ 18O, andAverage, Respectively) for Different Fractionation Scenarios (Non_Frac, CG_Frac, and CGT_Frac)

CG_FracCGT_
Frac

CG_Fracrelative to
Non_Frac

CGT_Frac
relative to
CG_Frac

CGT_Frac
relative to
Non_Frac

Contribution of
the standard CG
equation (%)

Contributionof tension
control (%)

10.06

5.06

5.42

−5.00

0.35

−4.64

93

7

RMSE_δ O

1.66

0.56

0.79

−1.09

0.23

−0.87

83

17

RMSE_avg

5.86

2.81

3.10

−3.05

0.29

−2.75

91

9

RMSE (‰)

Non_
Frac

RMSE_δ H
18

2

Table 1, considering the standard CG equation (CG_Frac) almost halved RMSEs. Adding soil tension controls(CGT_Frac) also halved RMSEs, thus obtaining similar performance. In other words, adding tension control does
not provide substantial benefits and even slightly increased RMSEs in this example. The impact of considering
the CG model and tension controls on RMSE_avg was 91% and 9%, respectively. The factors considered in thestandard CG equations led the model performance.
Various isotope mass balance components were also evaluated to understand the reasons behind differences inmodel performance and subsequent practical applications of different fractionation scenarios (Text S4 and Table
S2 in Supporting Information S1). Overall, the isotope mass balance components in the CGT_Frac were almost
always between the Non_Frac and CG_Frac. The impact of considering the CG model on the isotope massbalance was 66% for 2H and 57% for 18O, while the impact of considering the soil tension control was 34% for 2H
and 43% for 18O. The factors considered in the standard CG equation dominated the isotope mass balance.
3.2. Vertical Origin of Root Water Uptake
The dynamics of contributions of the four soil layers to RWU obtained using the water balance method and the
SIAR model are shown in Figures 4 and 5 and Table 2 (note that their sum is one). Since the same set of soil
hydraulic parameters was used in all fractionation scenarios, the results of the vertical origin of RWU remained
the same when using the water balance method.
According to the Mann-Kendall trend tests (Text S5 in Supporting Information S1), the contribution of the
0–10 cm soil layer (i.e., Layer 1) showed a decreasing trend (characterized by negative τ values) with the largest
fluctuations. The contributions of the other soil layers showed increasing trends (suggested by positive τ values)
and were relatively stable. This is because the functioning of the top layer (0–10 cm) is different from the otherlayers as it is affected by evaporation fractionation during the dry season and mixing during precipitation (Barnes& Turner, 1998). The deeper soil layers gradually became more important water sources, probably due to thelack of rainfall (Figure S2 in Supporting Information S1), which increased the root water stress in the surface soil
and promoted uptake from deeper layers. The contributions decreased from Layer 1 to 4 because the root density
decreased as soil depths increased (Figure S1 in Supporting Information S1).
In general, considering fractionation (CG_Frac, CGT_Frac) interpreted a decrease in the simulated contribution of Layer 1 and an increase in contributions for the other soil layers (Table 2). Overall, the contributions inFigure 4. The contributions of different soil layers ((a) 0–10 cm, (b) 10–20 cm, (c) 20–30 cm, and (d) 30–40 cm) to root
water uptake for the last 250 days of the simulation (2018/10/18–2019/06/25) calculated using the water balance method.

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the CGT_Frac scenario were always between Non_Frac and CG_Frac for all soil layers. Table 2 (the last twocolumns) shows that the factors considered in the standard CG equation played a dominant role in interpretingthe contributions of all soil layers to RWU.
3.3. Temporal Origin of Root Water Uptake
3.3.1. Particle Tracking
Since the same set of parameters was used in all fractionation scenarios, the temporal origin of RWU remained thesame when using the PT method. The residence time distribution of precipitation in soil water and the temporalorigin of RWU showed seven cycles in the entire simulation period (Figures 6a and 6b). Only the last 250 days(2018/10/18–2019/06/25) of the relative frequency distributions of drainage and RZ travel times (Figures 6c
and 6d) are displayed to be consistent with the display of the results of the isotope transport-based methods. During
this period, the drainage travel times decreased with time (Figure 6a). RWU in each month except April and May
of 2019, mainly (more than 60%) originated from the current month's precipitation (Figure 6b). The corresponding
mean drainage and RZ travel times were about 230.96 and 12.64 days, respectively (Figures 6c and 6d, Table 3).
3.3.2. Virtual Tracer Experiment
Figures 7 and 8 show the dynamics of drainage and RZ travel times interpreted by different fractionation scenarios using the virtual tracer experiment. The drainage travel times generally decreased with time (Figure 7d)
because discharge increased overall with time (Figure 7c). There were always apparent differences in drainage
travel times between Non_Frac and fractionation scenarios (Gon_Frac or CGT_Frac), but the differences between
CG_Frac and CGT_Frac were noticeable almost only for precipitation events occurred during April to Augustof 2018 (Figure 7a) when surface soil tension remained around 10,000 cm (Figure 7b). This is because the soil
texture is sandy with a steep soil water retention curve (Figure S8 in Supporting Information S1), allowing rapid
recharge during high precipitation events, and draining during periods of high evaporation. Therefore, the tension
effect is like an on-off process (Figure 7b) that can only be detected during dry periods.
The dynamics of RZ travel times can be divided into three stages (Figure 8d). During the early stage (between
2018/10/18–2019/03/09), the RZ (0–40 cm) water storage remained, on average, relatively high, with a mean of
2.53 cm and large fluctuations reflecting individual precipitation events (Figure 8c). The RZ travel times wererelatively stable with time (2.83, 2.85, and 2.87 days on average, with a range of 0–9 days for all fractionation
scenarios) (Figure 8d).
During the middle stage (between about 2019/03/10–2019/05/18), the RZ was drier (with mean water storage of
2.15 cm), increasing the root uptake stress, as discussed in Section 3.2. Therefore, the RZ travel times increased
steeply with time (5.96, 5.72, and 6.04 days on average, with a range of 1–13, 0–12, and 0–13 days for the Non_
Frac, CG_Frac, and CGT_Frac scenarios, respectively) compared with the early stage. This stage corresponded
to April and May of 2019 when roots absorbed much more precipitation from the previous months than in othermonths (Figure 6b), probably due to the stimulus of increased RZ travel times during this period.
During the final stage (between 2019/05/19 and 2019/6/25), the RZ water storage increased with time (with amean of 2.11 cm), resulting in reduced RZ travel times (5.53, 4.80, and 5.50 days on average, with a range of
0–18, 0–17, and 0–18 days for the Non_Frac, CG_Frac, and CGT_Frac scenarios, respectively).
Overall, the dynamics of drainage and RZ travel times evaluated by the virtual tracer experiment were similar
to those obtained by PT. The mean drainage travel times were interpreted as 187.05, 185.18, and 185.40 days
(Figures 7e–7g, Table 3), while the mean RZ travel times were interpreted as 3.93, 3.73, and 3.98 days for the
Non_Frac, CG_Frac, and CGT_Frac scenarios, respectively (Figures 8e–8g, Table 3). The order of drainage andRZ travel times was in general: Non_Frac > CGT_Frac > CG_Frac. Table 3 (the last two columns) shows thatthe factors considered in the standard CG equation were in general more important than soil tension effects ininterpreting drainage and RZ travel times.

4. Discussion
4.1. Impacts of the Soil Tension Control Versus the Standard Craig-Gordon Equation
The isotopic composition profiles (Figure 3) and the statistical indicators (Table 1) show that the results of
the CG_Frac and CGT_Frac scenarios were quite similar and better than those of the Non_Frac scenario. ThisZHOU ET AL.

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Figure 5. The contributions of different soil layers ((a) 0–10 cm, (b) 10–20 cm, (c) 20–30 cm, and (d) 30–40 cm) to root water uptake for the last 250 days of thesimulation (2018/10/18–2019/06/25) interpreted by different fractionation scenarios (Non_Frac, CG_Frac, and CGT_Frac) using the SIAR model.

is because fractionation cannot be ignored in this example, as proved in the dual-isotope plot (Fig. 4 of Post
et al., 2022). The soil tension control on fractionation (the CGT_Frac scenario) always resulted in a more depleted
isotopic composition of soil water than the CG_Frac scenario, especially in the surface layer. This is because thetotal isotope flux across BCs off the model domain in the CGT_Frac is between Non_Frac and CG_Frac (Table
S2 in Supporting Information S1).
For the vertical origin of RWU, considering fractionation (CG_Frac, CGT_Frac) likely resulted in a decrease in
the contribution of Layer 1 and an increase in the contributions of the other soil layers (Figure 5 and Table 2).
Since the isotopic compositions of surface soil water and RWU was both higher in the fractionation scenarios(CG_Frac, CGT_Frac) than in the Non_Frac scenario (Figure S4 in Supporting Information S1), a decrease in thecontribution of Layer 1 may suggest that an increased isotopic composition of surface soil water exceeded thatof RWU in the fractionation scenarios. The contributions of all soil layers interpreted by the CGT_Frac scenario
were always between Non_Frac and CG_Frac. This is because the isotopic composition of soil water and RWU
within the RZ in the CGT_Frac scenario was always between Non_Frac and CG_Frac (Figure S6 in Supporting
Information S1).
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Table 2The Average Contributions of Different Soil Layers to Root Water Uptake Interpreted by Different Fractionation Scenarios(Non_Frac, CG_Frac, and CGT_Frac) Based on the Water Balance and SIAR Methods

MethodSource

Non_
Frac

WB

0–10 cm

0.603

10–20 cm0.240

20–30 cm

0.123

30–40 cm

0.035

0–10 cm

0.493

SIAR

CG_FracCGT_
Frac

CG_Fracrelative to
Non_Frac

CGT_Frac
relative to
CG_Frac

CGT_Frac
relative to
Non_Frac

Contribution of
the standard CG
equation (%)

Contributionof tension
control (%)

0.426

0.444

−0.0670.018−0.04979

21

10–20 cm

0.216

0.228

0.216

0.012

−0.012050

50

20–30 cm

0.150

0.165

0.161

0.015

−0.004

0.011

79

21

30–40 cm

0.140

0.180

0.179

0.04

−0.001

0.039

98

2

The order of drainage and RZ travel times obtained using the isotope transport-based method (VTE) was generally: Non_Frac > CGT_Frac > CG_Frac (Figures 7 and 8 and Table 3). This is because the removal of isotopes
by evapotranspiration makes it difficult for isotopes to move downwards to the RZ or soil profile bottom and thusincreases travel times. Since the isotope removal by evapotranspiration was largest in the Non_Frac scenario,
followed by CGT_Frac and CG_Frac (Table S2 in Supporting Information S1), the travel time order was thesame.
Overall, the model performance (Figure 3 and Table 1), isotope mass balance components (Table S2 in Supporting Information S1), contributions of different soil layers to RWU (Figure 5 and Table 2), and drainage and RZ
travel times (Figures 7 and 8, Table 3) interpreted by the CG_Frac and CGT_Frac scenarios were much moresimilar than in any combination of two other scenarios (i.e., Non_Frac and CG_Frac, Non_Frac and CGT_Frac).
This validates that the factors considered in the standard CG equation prevail over the soil tension control inisotope transport modeling.
4.2. Comparison of the Water Flow and Isotope Transport-Based Methods
Regarding the vertical origin, all methods reflected similar variation trends with time and depth in contributionsof different soil layers to RWU. However, absolute differences always existed among different methods. The
mean contributions of the middle layers (Layers 2 and 3) were similar using both methods, while those of theshallow and deep layers (Layers 1 and 4) were quite different (Table 2). This is because the SIAR model used thesimulated isotopic compositions of RWU and soil water as input, and considering different fractionation scenarios resulted in considerable changes in surface isotopic compositions (Figure 3 and S6 in Supporting Information S1). On the other hand, the isotopic compositions of water sources were assumed to be arithmetic averages
within the corresponding soil layers, which may not approximate reality. In addition, the vertical origin of RWU
can be reliably identified only when the isotopic composition profile gradient in the RZ is large and monotonic(Allen & Kirchner, 2022; Couvreur et al., 2020). However, the “monotonic” characteristic of the RZ (0–40 cm)
isotopic composition was clearly not fulfilled at least in the Non_Frac and CGT_Frac scenarios (Figure 3). This
indicates that the appropriate model setup plays a vital role in ensuring the accurate identification of the verticalwater origin when using the isotope transport-based methods.
Compared with the traditional in-situ isotopic measurements, the isotopic compositions of soil water and RWU
in this study were obtained directly from the model output, alleviating the measurement burden and achieving
higher vertical-temporal resolution (Stumpp et al., 2018). This is useful since several factors often compromise
the isotopic measurements, especially under arid conditions, such as sampling spatio-temporal representativeness, instrument deficiencies, etc. (Beyer & Penna, 2021). On the other hand, we used directly the isotope composition of RWU instead of xylem water. This can avoid the uncertainty of isotopic composition changes during thewater movement from the roots to the xylem (Allen & Kirchner, 2022; Barbeta et al., 2020; Chen et al., 2020).
Regarding the temporal origin, all methods revealed similar variation trends with time and relative differences
between the drainage and RZ travel times interpreted by different fractionation scenarios. However, absolute
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Figure 6. Residence times as a function of depth and time (a), the temporal origin of monthly root water uptake (b), and relative frequency distributions of drainage(c) and root zone (d) travel times. Note that only the travel times from the last 250 days are displayed in the graphs of relative frequency distributions. For the temporalorigin (b), the upper panel shows the monthly transpiration sums (in different colors), and the lower panel shows fractional contributions of water of a certain age/origin(by month) to the monthly transpiration sums.

differences always existed among different methods and were more significant for RZ than drainage travel times(Table 3). This is because the hydrodynamic dispersion may affect the virtual tracer experiment, which the PT
module neglects (Zhou et al., 2021). This may lead to apparent differences between the two methods. Larger
differences in the RZ travel times than the drainage travel times between the PT and virtual tracer experiment
methods were likely due to the shorter travel distance for the former. Therefore, outside factors make it easier to
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Table 3The Mean Drainage and Root Zone Travel Times (TT) Interpreted by Different Fractionation Scenarios (Non_Frac, CG_
Frac, and CGT_Frac) Based on Particle Tracking (PT) and Virtual Tracer Experiment Methods

Method
PT
VTE

Term

Non_
Frac

Drainage TT

230.96

RZ TT

12.64

Drainage TT
RZ TT

CG_Fracrelative to
Non_Frac

CGT_
Frac
relative to
CG_FracCGT_
Fracrelative to
Non_Frac

Contributionof thestandard CG
equation (%)

Contributionof tension
control (%)

CG_FracCGT_
Frac

187.05185.18185.40

−1.87

0.22

−1.65

89

11

3.93

3.73

3.98

−0.20

0.25

0.05

44

56

disturb the isotope mass balance between upward evapotranspiration, downward infiltration, and dispersion in the
RZ. This further resulted in the larger RZ travel times estimation errors by the virtual tracer experiment (relying
on the isotope mass balance).
In all, the influencing factors and applicable conditions (and corresponding model inputs) of isotope
transport-based methods (SIAR, virtual tracer experiment) are more complex and demanding than those considered in water flow-based (water balance, PT) methods. However, both are based (at least in this study) on numerical modeling results characterized by the equifinality problem (Beven, 2006). Therefore, it is hard to assess whichapproach is better. On the one hand, the simultaneous use of water flow and isotope transport-based methods may
be an excellent way to provide mutual validation. On the other hand, the accuracy of these two methods shouldbe verified by other benchmark methods, such as direct water balance measurements, artificial labeling tracers(Benettin et al., 2019; Seeger & Weiler, 2021), or tracer-based water balance analyses (Benettin et al., 2021).
4.3. Model Limitations and Future Work
Three isotope-enabled transport models are available in HYDRUS-1D: (a) the original one (Stumpp et al., 2012)is suitable when fractionation is negligible; (b) the module introduced by Zhou et al. (2021) considers the soil
temperature effect on equilibrium fractionation; (c) the new module presented in this study also considers thesoil tension effect on equilibrium fractionation. The soil tension effect on equilibrium fractionation is describedusing empirical equations (Equations 5 and 6). Replacing them with physically based equations may be possible
once identified in the future.
In this study, the surface soil tension often reached 10,000 cm (Figures 7b and 8b), the soil temperature was
between −7.5 and 33.5°C, and the equilibrium fractionation factor αv/w varied from 0.946 to 0.994 for 2H and1.007 to 1.016 for 18O in the CGT_Frac, while from 0.899 to 0.935 for 2H and 0.988 to 0.991 for 18O in the CG_
Frac (Figure S5 in Supporting Information S1). The isotopic composition of surface soil water in the CGT_Fracscenario changed by −7.8‰ (for 2H) and −3.1‰ (for 18O) compared to the CG_Frac scenario (Figure 3), while
the isotope mass balance components in the CGT_Frac changed up to 52% for 2H and 20% for 18O comparedto the CG_Frac (Table S2 in Supporting Information S1). This suggests that a small change in αv/w due tosoil tension may result in a considerable difference in isotopic compositions and isotope mass balance. In addition, as discussed in Section 4.1, these isotopic composition and isotope mass balance differences also propagate
into the interpretations of corresponding modeling results (with the SIAR model and virtual tracer experiments),
albeit only to a limited magnitude.
However, only the measured isotopic profiles on the final day of the experiment were available for this study,
while the impact of soil tension on equilibrium fractionation varied during the studied period (between wet anddry periods). It would thus be beneficial to have measurements available at finer time resolutions to investigate
the seasonal soil tension effects. On the other hand, the field data set in this study was collected in a humid region.
Changes in isotopic compositions and subsequent modeling results interpretations depend on specific experimental conditions and need further exploration, especially for arid regions (Allen & Kirchner, 2022; Finkenbiner
et al., 2022).
Additionally, kinetic fractionation may affect observed isotopic enrichment more than equilibrium fractionation especially under arid conditions. For example, we conducted Partial-Least Squared Regression analysis to
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Figure 7. Precipitation (contributing to drainage) (a), surface soil tension (b), discharge (c), drainage travel times (d), and their relative frequency distributions (e–g)
interpreted by different fractionation scenarios (Non_Frac, CG_Frac, and CGT_Frac) using the virtual tracer experiment.

quantify the contribution of different influencing factors of evaporation fractionation to δ 2H and δ 18O in the RZ(Text S6 and Table S3 in Supporting Information S1). Table S3 in Supporting Information S1 shows that thecontribution of soil (or air) temperature (very close) is always greater than that of soil tension. Again, this validates that soil tension effects are much less important than temperature effects on equilibrium fractionation as
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Figure 8. Precipitation (contributing to the root zone (RZ)) (a), surface soil tension (b), RZ water storage (c), RZ travel times (d), and their relative frequency
distributions (e–g) interpreted by different fractionation scenarios (Non_Frac, CG_Frac, and CGT_Frac) using the virtual tracer experiment. Note that the vertical red
dashed lines separate the early (between about 2018/10/18 and 2019/03/09), middle (between about 2019/03/10 and 2019/05/18), and final (between about 2019/05/19
and 2019/06/25) stages, respectively.

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shown in Text S3 in Supporting Information S1. Notably, the contribution of air humidity (an indirect reflectionof kinetic fractionation) is even larger than that of soil temperature for δ 18O (the dominant term of equilibrium
fractionation). However, the impact of soil tension on kinetic fractionation is not discussed in the current literature and needs further exploration.

5. Summary and Conclusions
In this study, we first quantified the soil tension effects on evaporation fractionation and model performance in
HYDRUS-1D. The results showed that additional consideration of the soil tension effect on equilibrium fractionation depletes the isotopic composition of surface soil water compared to when only the temperature effectis considered.
Regarding the vertical origin of RWU, all methods (water balance, SIAR) could reflect similar variation trendsof different soil layers' contributions. The contributions of all soil layers to RWU interpreted by additionallyconsidering soil tension effects were between the no fractionation and Craig-Gordon fractionation scenarios. The
average contributions of the middle soil layers to RWU were similar using both methods, while those of the top
and deep layers were quite different.
Regarding the temporal origin of RWU, all methods (PT, virtual tracer experiment) could reflect similar variation
trends in drainage and RZ travel times. The order of both drainage and RZ travel times was generally: No fractionation > Craig-Gordon fractionation plus soil tension effects > Craig-Gordon fractionation. Absolute differences
between different methods always existed and were more significant in RZ than drainage travel times.
Overall, considering the CG equation, rather than soil tension effects, is important for model performance, isotope
mass balance, and interpreting the vertical and temporal origin of RWU. The influencing factors and applicableconditions of isotope transport-based methods (SIAR, virtual tracer experiment) are more complex and demanding than water flow-based methods (water balance, PT).
This study emphasizes the necessity of selecting a suitable model setup and simultaneously employing the waterflow and isotope transport-based methods to secure reliable isotopic data interpretation. This study sheds lighton future experimental designs regarding the practical applications of isotope transport modeling. However, theimpacts of soil tension on isotope transport and corresponding practical applications should be further explored
under arid conditions where soil tension is higher, and thus the impact of soil tension is expected to be more
important.

Data Availability Statement
The software and data set used to produce the results of this study are available at Zhou, 2022
(https://doi.org/10.5281/zenodo.7336212).
Acknowledgments
This research was financially supportedby the Multistate W4188 program funded
by NIFA (Grant CA-R-ENS-5047-RR).
We also acknowledge the Editor Dr.
Simone Fatichi, and Dr. Matthias Beyer
and two other anonymous reviewers
for their constructive comments on thismanuscript.

ZHOU ET AL.

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