Received: 13 August 2022

Revised: 18 July 2023

Accepted: 18 August 2023

DOI: 10.1002/hyp.14982

RESEARCH ARTICLE

A virtual tracer experiment to assess the temporal origin ofroot water uptake, evaporation, and drainage
Paolo Nasta 1
Nunzio Romano| Jirka Šimůnek 2 |Tiantian Zhou 2| Christine Stumpp 3

|

1

1

Department of Agricultural Sciences, AFBE
Division, University of Naples Federico II,
Portici (Naples), Italy

Abstract
The temporal origin of drainage, evaporation, and root water uptake (RWU) are indi-2

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

Institute of Soil Physics and Rural Water
Management, University of Natural Resourcesand Life Sciences, Vienna, Austria
Correspondence
Paolo Nasta, Department of Agricultural
Sciences, AFBE Division, University of Naples
Federico II, Portici (Naples), Italy.
Email: paolo.nasta@unina.it
Funding information
MiUR-PRIN Project “WATer mixing in thecritical ZONe: observations and predictions
under environmental changes – WATZON”,
Grant/Award Number: 2017SL7ABC; 2018
Joint call of the Water Works 2017 ERA-NET
Cofund, Grant/Award Number:
ENWWW.2018.5

cators of ecosystem functioning that shed light on how natural and anthropogenic
disturbances affect plant resilience and aquifer vulnerability. A virtual tracer experiment was carried out in HYDRUS-1D using data from a soil lysimeter planted withwinter rye in Austria. The RWU (τR), evaporation (τE), and drainage (τD) transit times(τ) were determined by using the actual dispersivity optimized in a prior study. First,
τR and τD were compared to RWU (τPT,R) and drainage (τPT,D) advective transit times
estimated using the particle tracking algorithm. The τR values were in agreement with
τPT,R while large discrepancies were detected when estimating drainage transit times
using the two approaches. A sensitivity analysis revealed that dispersivity had a mild,
poor, and strong influence on τR, τE, and τD. The longitudinal dispersivity describes
how a tracer spreads along the flow paths. The longer the flow paths, the more dispersion affects the tracer transport. On average, water parcels originating from rainfall in the growing season took 18 and 201 days to reach the roots (with RWU being
21% of rainwater) and the soil profile bottom (with drainage being 36% of rainwater),respectively. In contrast, 10% of rainwater that fell in the dormant season became
RWU after 264 days, while 79% became drainage after 294 days. The temporal origin of water can be explored in other plots by using the guidelines proposed in thisstudy.
KEYWORDSHYDRUS-1D, lysimeter, particle tracking, tracer mass balance, transit time distribution (TTD),
water-stable isotopes

1|

I N T RO DU CT I O N

sustainable policies under rapid climate and land use changes. A critical component of hydrologic sensitivity to external forcings and plant

Optimal management of terrestrial (agricultural, urban, and forest)

characteristics arises from changes in the timing of water delivery to

ecosystems relies on water balance simulations using process-the soil–plant-atmosphere continuum (SPAC). Knowledge of the tem-oriented hydrological models. Such modelling tools require a large

poral origin of drainage (D), evaporation (E), and root water uptake

amount of environmental input data, which can only be retrieved from

(RWU) helps understand the impact of natural and anthropogenic dis-modern monitoring infrastructures and intensive sampling campaigns

turbances, such as drought and transport of contaminants to ground-(Romano et al., 2018; Vereecken et al., 2015; Yang et al., 2021). Still,water, on plant resilience and aquifer vulnerability (Sousa et al., 2013;

the hydrological processes need to be better understood to develop

Sprenger et al., 2019). An important variable for defining the water's

Hydrological Processes. 2023;37:e14982.
https://doi.org/10.1002/hyp.14982

wileyonlinelibrary.com/journal/hyp© 2023 John Wiley & Sons Ltd.

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NASTA ET AL.

temporal origin is the water transit time (τ), which is defined as thein the critical zone. Sprenger et al. (2016) used the virtual tracer experi-time a water parcel takes from entering the soil surface, as precipita-

ment to assess RWU and drainage transit time distribution over thirty-tion or irrigation, to exiting the soil as RWU (τR), evaporation (τE), or

five 200-cm-thick layered soil profiles and determined the rainfall con-drainage (τD). The transit time through the vadose zone integrates thetribution to RWU and drainage but neglected evaporation. The tempo-

information on rainwater partitioning into the main hydrological com-

ral origin of water taken up by Fagus sylvatica and Picea abies wasponents (drainage, evaporation, and transpiration), which is essential

determined by using 4-year-long isotope transport simulations in two

for a better understanding of the ecosystem hydrological functioning

70-cm-thick soil profiles (Brinkmann et al., 2018), combining RWU pat-

(Heidbüchel et al., 2012; Isch et al., 2022; Nasta et al., 2023).

terns with soil water residence time distributions at different soil

Field tracer experiments are used to assess the arrival time at thedepths to estimate age distributions of RWU. Brinkmann et al. (2018)

target position of a tracer injected at the entry position and trans-

missed to assess the drainage and evaporation transit time and rainfall

ported across the porous medium by advection and hydrodynamic

partitioning into evaporation, transpiration, and drainage.

dispersion. The arrival time is usually estimated at the peak tracer con-

The main research questions are:centration from the target point (Sprenger et al., 2016). Virtual tracer
experiments help track water pathways across the SPAC originatingi. What are the differences in RWU and drainage transit times

from a long sequence of rainfall events and are used to assess thewhen using the particle tracking approach (advective transport)

temporal origin of RWU and drainage. Yet the implementation of vir-

and the virtual tracer experiment (advective and dispersive
transport)?

tual tracer experiments is not straightforward, and clear guidelines arestill missing in the literature (Asadollahi et al., 2020; Brinkmannii.

tual tracer experiment?

et al., 2018; Haverd & Cuntz, 2010; Sprenger et al., 2016).
In this study, a special isotope-enabled module of HYDRUS-1D(Huang et al., 2015; Šimůnek et al., 2016; Sprenger et al., 2015;

What is the impact of dispersivity on tracer transport in the vir-iii.

How to assess the temporal origin of evaporation, transpiration,and drainage in the virtual tracer experiment?

Stumpp et al., 2012) was used for simulating water flow and tracer
transport for five years in a soil lysimeter planted with winter rye in

These research questions were addressed in three steps

Austria (Stumpp et al., 2012). This isotope-enabled module assumes(Figure 1). First, the advective RWU and drainage transit times (τPT,R

that the advection-dispersion equation governs the tracer transport inand τPT,D) were obtained from particle tracking and compared to thesoils and allows tracers to leave the soil profile with evaporation (con-advective-dispersive transit times (τR and τD) obtained from the virtual

trary to other types of solutes). Still, the tracer transport simulation istracer experiment (red box in Figure 1). Second, the sensitivity analysis

influenced by the hydrodynamic dispersion, λL (either measured, cali-

was carried out to evaluate the effect of dispersivity on the tracer

brated, or commonly assumed as 1/10th of soil profile depth), and thetransport simulations and estimations of RWU, evaporation, andtransit time is not given directly as a model output.
By contrast, particle tracking is a well-established approach to assess
advective transit time in many modelling applications over different spatial
and temporal scales (Baek & Lee, 1996; Bechtold et al., 2011; DaneshYazdi et al., 2018; de Rooij et al., 2013; Wilusz et al., 2020). The particle
tracking algorithm was recently implemented in version 5 of HYDRUS-1D
to trace water pathways in the soil profile from which RWU and drainagetransit times are estimated (Zhou et al., 2021; Zhou et al., 2022).
Few studies have attempted to assess the temporal origin of RWU,
evaporation, and drainage using HYDRUS-1D for experimental lysimeters or soil profiles (Asadollahi et al., 2020; Brinkmann et al., 2018;
Sprenger et al., 2016). To our knowledge, the virtual tracer experimenthas not yet been evaluated with a particle tracking algorithm, and theimpact of dispersivity on transit time is mostly unexplored. Asadollahi
et al. (2020) used a tracer tracking approach to estimate the age of
evapotranspiration and drainage for two experimental lysimeters containing 200 cm-thick layered soil columns. The above authors set evaporation to zero and assumed potential transpiration equal to potential
evapotranspiration. If water can leave the system only through root
water uptake by neglecting evaporation, the resulting water transit
times of evapotranspiration may be biased versus older ages (otherwise, younger water would be allowed to leave the soil via evaporation). Sprenger et al. (2016) and Brinkmann et al. (2018) used theisotope-enabled module of HYDRUS-1D to simulate isotope transportF I G U R E 1 Schematic overview of the three steps of this study:(1) comparison between advective RWU (τPT,R) and drainage (τPT,D)
transit times and advective-dispersive RWU (τR) and drainage (τD)
transit times (red box); (2) The impact of λL on the RWU (τR),
evaporation (τE), and drainage (τD) transit times was evaluated in thesensitivity analysis (green box); (3) the virtual tracer experiment was
carried out to assess the temporal origin of RWU, evaporation, anddrainage which was aggregated on a seasonal basis (blue box).

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drainage transit times (green box in Figure 1). Third, the tracer-based

The potential water flux across the soil surface (rTop), defined as thetransit times and contributions of rainwater to evaporation, transpira-difference between daily values of potential evaporation (Ep) and pre-tion, and drainage were calculated and aggregated at selected tempo-

cipitation (P), was used as the upper boundary condition for water flow.

ral resolutions (blue box in Figure 1).

The lower boundary condition was set to a seepage face by imposing azero pressure head (ψ = 0 cm) when the soil profile bottom was saturated and a zero water flux when it was unsaturated. The actual water

2

MATERIALS AND METHODS|

flux (drainage, D) across the soil profile bottom is referred to as vBot.
Crop-specific potential evapotranspiration (ETp) is partitioned into

2.1|

Site description and data availability

potential evaporation (Ep) and transpiration (Tp, which, when distributed over the root zone, gives potential RWU) using the following
empirical equation (Ritchie, 1972):

The datasets used in the present paper are taken from Stumpp et al.
(2012), who described a lysimeter experiment carried out at the experi-

Ep ¼ ET p ekLAI

mental site located at the research area of the HBLFA Raumberg-

ð1Þ

Gumpenstein, 190 km southwest of Vienna (Austria). This region is characterized by a temperate climate with a mean annual temperature ofwhere κ () is the dimensionless extinction coefficient for global solar

6.9 C and mean annual precipitation of 1035 mm. A total of five 150-cm-

radiation inside the canopy. The LAI was measured (Section 2.1), while

thick lysimeters (Lys1-Lys5) with a surface area of 1 m2 were installed inκ was assumed to be equal to 0.6 (Stumpp et al., 2012). The residual

agricultural fields that differed in their crop and fertilization methods. This

fraction of ETp was assumed to be equal to Tp. The root water extrac-

study considers the third lysimeter (Lys3) containing a layered soil mono-tion rate occurs through the roots distributed across the root zone

lith planted with winter rye (Secale cereale L.), sown each October, andaccording to a piece-wise function proposed by Hoffman and van Gen-

harvested by the end of August. Leaf area index (LAI) and rooting depthuchten (1983). The roots extend from the soil surface to the bottom ofwere determined daily, ranging between 0 and 2.9 m2 m2 and 0 andthe root zone with the maximum and minimum root density, respec-

100 cm, respectively; here, maximum values were provided by onsite

tively. The rooting depth is time-variant during the growing season, andoperators and from the literature (Allen, 2000; Bohner et al., 2007;

the maximum rooting depth is set to be equal to 100 cm. Actual RWU

Knisel & Davis, 2000) as given in detail in Stumpp et al. (2012). The soil

is obtained as a product of potential RWU (or Tp distributed over the

profile is made up of three soil layers (30 cm < z < 0 cm, 90 cm < z <root zone) and the stress response function, a piecewise linear reduc-30 cm, 150 cm < z < 90 cm). For the period between May 2002

tion function proposed by Feddes et al. (1978). The so-called Feddes

and February 2007, daily values of precipitation and crop-specific poten-

stress response function depends on prescribed pressure head values.

tial evapotranspiration (ETp) are available.

The default values in Hydrus-1D for wheat were used in our calculations. Crop uptake is reduced below ψ = 500 or 900 cm dependingon whether the potential transpiration rate is high or low, respectively.

2.2|

HYDRUS-1D model setup

The matric pressure head at the wilting point corresponds toψ = 16 000 cm. The actual surface flux (vTop) is given as the differ-

In this study, we used version 5 of HYDRUS-1D (Šimůnek

ence between actual evaporation (Ea) and precipitation (P) and depends

et al., 2016; Stumpp et al., 2012), and data available in the project

on limiting pressure heads on the soil surface. Details about the model

Lys3_Stumpp, which can be downloaded from the HYDRUS website

setup for water flow are reported in Table A1 and Data S1.

(https://www.pc-progress.com/en/Default.aspx?h1d-lib-Isotope).
The simulation period is 1736 days, from 3rd May 2002 to 1st

2.3 | Assessing RWU and drainage transit timewith particle tracking

February 2007 (corresponding to almost five years). The 150-cm-thicksoil profile is composed of three soil layers (30 cm < z < 0 cm,
90 cm < z < 30 cm, 150 cm < z < 90 cm). The van Genuchten(1980) parameters (θr, θs, α, n, Ks, l) of the soil water retention and hydrau-

The particle tracking algorithm, recently implemented in HYDRUS-1D

lic conductivity functions (Table 1) were calibrated by Stumpp et al.

(Zhou et al., 2021), requires the following two input parameters: wInit(2012) to provide physically-based descriptions of soil water content andand wPrec. The wInit parameter represents the initial water storage

pressure head values in each soil layer and drainage fluxes (Data S1).

between particles and determines the particle positions along the soil

T A B L E 1 Soil hydraulic parameters(θr, θs, α, n, Ks, and l) of the water
retention and hydraulic conductivity
functions of the three soil layers of theexperimental soil profile.

Profile interval
cm

θr

θs
3

cm cm

3

α
3

3

cm cm

n
1

cm

-

Ks

l
1

cm d

-

30 < z < 0

0.00

0.30

0.023

1.14

110

0.5

90 < z < 30

0.00

0.32

0.076

1.07

6000

0.5

150 < z < 90

0.00

0.32

0.016

1.90

110

0.5

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NASTA ET AL.

NASTA ET AL.

depth at the initial time, t0. The wPrec parameter is the amount of

tracking algorithm (Figure 2a). By selecting the third precipitationwater that passes through the soil surface before a new particle isevent (green bar in Figure 2a) at entry time (tin), the corresponding

released. This means that particles are released at the soil surface only

particle trajectory across the soil profile (extracted from the output

under humid conditions, that is, when infiltration exceeds actual evap-

text file “Particles.out”, which contains the z-coordinates of particle

oration. Under dry conditions, the surface flux is directed out of thepositions over time) is depicted by the black line (Figure 2b). The

soil profile; thus, new particles are not released. Instead, existing parti-

arrival time at the target point (tout) is identified as the time when thecles may exit from the soil surface due to evaporation. By setting

particle exits from the soil profile bottom (Figure 2b). The output file

wPrec = 1, a new particle is launched whenever the actual surface“Uptake.out” contains the root water uptake flux fed by the tracked

flux becomes negative (vTop <0), that is, when precipitation exceeds

water parcel. The arrival time of RWU is considered the time when

actual evaporation. The particle tracking algorithm considers only con-the cumulative actual RWU reaches its maximum value. A transit time

vective transport and neglects dispersion. See details in Data S1.

distribution is obtained by analysing the advective transit times of all

Figure 2 depicts an illustrative example for estimating drainage

particles released at the soil surface. An open-access Matlab script(τPT,D) and RWU (τPT,R) advective transit times using the particle(PT.m) is shared to read the output text files (more details are provided in Data S1).

2.4 | Assessing RWU, evaporation, and drainagetransit time and rainfall partitioning with the virtual
tracer experiment
The isotope-enabled module in HYDRUS-1D accounts for isotope
transport so that isotopes (or tracers) do not accumulate at the soil
surface and leave the soil profile with the evaporation flux (Stumpp
et al., 2012). Evaporation fractionation is not considered in the virtual
tracer experiment.
The initial tracer concentration was set to zero in the entire soil
profile. Roots can take up the tracer with unlimited passive root tracer
uptake by setting the cRootmax parameter to a large value. The actual
tracer flux across the soil surface and soil profile bottom are denotedas cvTop and cvBot, respectively, while the actual root tracer uptake inthe root zone is called cvRoot. Ten observation points were inserted at
the following soil depths: z = 5, 15, 30, 45, 60, 75, 90,
105, 120, and 135 cm.
The number of simulations in the virtual tracer experiment
depends on the total number of daily precipitation events (Nastaet al., 2023). In each ith simulation, a hypothetical tracer concentration is injected with the ith precipitation event by keeping the cTopvalues of the other rainfall events equal to zero. A zero concentration
gradient (free drainage) is used as the lower boundary condition.
Thirteen rainfall events are shown in the illustrative example of
Figure 3, and the tracer is injected with the third labelled rainfall event(cyan bar in Figure 3a). The main steps related to the tracer transport
simulation to obtain the drainage (τD) and RWU (τR) transit times andrainfall partitioning are:F I G U R E 2 Schematic representation of drainage (τPT,D) and RWU(τPT,R) advective transit time calculations using the particle tracking
algorithm. (a) A new particle is launched with the third precipitation
event (green bar) at entry time (tin); (b) the water parcel originatingfrom the third rainfall event (the z-coordinates of particle positions
are extracted from “Particles.out”) is tracked to identify the arrival
time at the bottom of the soil profile (tout); (c) RWU (extracted from
“Uptake.out”) fed by the water parcel originating from the third
rainfall event is used to identify the RWU arrival time (tout). Verticalgreen dashed lines depict tin and tout.

1. To fix an arbitrary tracer concentration (i.g., cTop = 100) in thelabelled rainfall event; for instance, the input tracer flux,
cvTop = 100 if vTop = 1.0 cm d1 (cyan bar in Figure 3a);2. To obtain the output tracer flux across the soil profile bottom, cvBot(Figure 3b), and the root system, cvRoot (Figure 3c); the arrival time
(tout) is defined as the time of median breakthrough curve (Ischet al., 2022; Nasta et al., 2023; Sprenger et al., 2016) and the rainfall contribution to water balance components is the ratio

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4 of 11(advection-dominated transport) results to minimize the impact of dispersivity on the estimated transit times in the virtual tracer experiment while maintaining the Peclet stability criterion. We calculated
the root mean square error (RMSE) between τD and τR and the corresponding τPT,D and τPT,R (Section 3.2).
Another set of rainfall events was used to carry out a sensitivity
analysis to evaluate the impact of λL on the tracer transport simulations and the estimation of RWU (τR), evaporation (τE), and drainage(τD) transit times (green box in Figure 1). The mean error (ME) was calculated between reference τR, τE, and τD obtained by using the original
dispersivity (λL = 4.7 cm) and τR, τE, and τD obtained by using a rangeof λL values between 0.5 cm and 20 cm (Section 3.3).
Finally, the virtual tracer experiment was carried out to assess
the rainfall contributions to RWU, evaporation, drainage, and associated transit times by keeping the actual dispersivity (blue box in
Figure 1). We selected only the effective rainfall events (P > Ep) toensure negative (downward) rTop values (Section 3.4). Transit times
and rainfall partitioning based on tracer transport simulations were
aggregated on a seasonal basis. Two seasons were identified in thisstudy: growing and dormant season. The growing season lasts from
May to August (when LAI and root depth values are above zero), andthe dormant season from September to April (when LAI and root
depth values are zero). This means that we tracked the precipitation
events from May to August (the growing season's precipitation) orfrom September to April (the dormant season's precipitation) to see
whether they were used during the vegetation period fortranspiration.
An open-access Matlab script (VTE.m) is shared to automate thevirtual tracer experiment simulations (more details are provided in
F I G U R E 3 Schematic representation of the application of thevirtual tracer experiment to estimate drainage (τD) and RWU (τR)
transit times: (a) the tracer (cTop = 100) is injected with the third
precipitation event (cyan bar) at entry time (tin); (b) the drainage arrival
time (tout) is identified when the cumulative bottom tracer flux
reached 50%; (c) the RWU arrival time (tout) is identified when the
cumulative root tracer flux reached 50%. Vertical cyan dashed lines
depict tin and tout.

Table A1 and Data S1).

3|

RE SU LT S

3.1 | Assessing RWU and drainage transit timewith particle tracking
A total of 803 precipitation events entering the soil surface (vTop < 0)(expressed in % of rain becoming Ea, Ta, and D) between the out-

were identified. The water parcels of 167 active rainfall events

put and the input tracer fluxes. The output tracer flux is associatedreached the bottom of the soil profile. The remaining water parcels

with actual evaporation, actual RWU (transpiration), or drainage,

returned to the atmosphere via evapotranspiration. Figure 4 showswhereas the input tracer flux is associated with the rainfall. Morethe particle trajectories (coloured lines in Figure 4b) originating fromdetails are reported in Data S1.

the 167 active rainfall events and actual fluxes at the upper (vTop,

The active precipitation events (the term “active” refers to thosearies. Note that the last 18 particle pathways were not included

events which were able to reach the bottom of the soil profile) identi-

among the 167 events because they did not reach the soil profile

blue line in Figure 4a) and lower (vBot, green line in Figure 4c) bound-

fied by the particle tracking algorithm (Section 3.1) were simulatedbottom within the simulation time. Estimating the drainage transit

using the virtual tracer approach (Section 3.2) to ensure a fair compar-

times associated with the 167 rainfall events was straightforward byison of results in the first subset of virtual tracer experiments (red box

tracking the particle positions in the soil profile. Several water par-in Figure 1). Two levels of dispersion were considered by using: (i) thecels were tracked within the root zone (black line in Figure 4b) for aoriginally calibrated dispersivity (λL = 4.7 cm) and (ii) the minimum dis-time period during the growing season. This range of time is defined

persivity (λL = 0.5 cm) not causing numerical instability problems. The

as the root zone soil water residence time, which refers to the age oflatter allowed a consistent comparison with particle tracking

a water parcel travelling within the root system. By contrast, the10991085, 2023, 9, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/hyp.14982 by University Of California, Wiley Online Library on [06/09/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License

5 of 11

NASTA ET AL.

NASTA ET AL.

F I G U R E 4 Daily values of (a) actual
surface fluxes, vTop (blue line), (b) particle
trajectories originating from the active
167 rainfall events (coloured lines) anddaily root depths (black line), and(c) drainage fluxes across the soil profile
bottom, vBot (green line).

RWU transit time was defined as the water age leaving the soil system through the roots across the soil profile.

3.2 | Comparing particle tracking and virtual tracer
experiment

Figure 5 shows the frequency distributions of drainage and
RWU advective transit times of the 167 rainfall events obtained

The active 167 precipitation events identified by the particle tracking

using particle tracking. Normality tests (Lilliefors and Kolmogorov–algorithm were simulated using the virtual tracer experiment.

Smirnov executed in Matlab) rejected the null hypothesis that the

Figure 6 shows the comparison between advective transit times

statistical distributions of the advective transit time values (drain-(τPT,R andτPT,D) obtained using particle tracking and those (τR and τD)

age transit time, τPT,D, in Figure 5a, and RWU transit time, τPT,R, in
Figure 5b) are normal at the 5% significance level. Therefore, themedian (309.9 days for τPT,D and 208.9 days for τPT,R) and mode
(334.5 days for τPT,D and 234.7 days for τPT,R) values were reported
instead of the mean values (296.1 days for τPT,D and 191.7 days for
τPT,R). A few events on the right tail of Figure 5a influenced thedrainage transit time distribution, while the RWU transit time distribution was skewed by low values (Figure 5b), indicating that roots
took up most rainfall water during the growing season. This waspartially caused by the rooting depth of winter rye being shallow
during early growing seasons, resulting in short RWU transit times(Figure 5b).

F I G U R E 5 Frequency distribution of (a) advective drainage transit
time, τPT,D (blue histograms), and (b) advective RWU transit time, τPT,R(green histograms), obtained using the particle tracking algorithm in
HYDRUS-1D. Vertical dashed lines indicate the mean (black), median(cyan), and mode (red).

F I G U R E 6 Comparison between (a) drainage transit times obtainedusing particle tracking (τPT,D) and tracer transport modelling (τD) with
λL = 4.7 cm (red circles), (b) RWU transit times obtained using particle
tracking (τPT,R) and tracer transport modelling (τR) with λL = 4.7 cm(green circles), (c) drainage transit times obtained using particle tracking(τPT,D) and tracer transport modelling (τD) with λL = 0.5 cm (magenta
circles), and (d) RWU transit times obtained using particle tracking (τPT,R)
and tracer transport modelling (τR) with λL = 0.5 cm (yellow circles).
The diagonal dashed line denotes the identity line. The root meansquare error (RMSE) values are reported in each subplot.

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6 of 11

using the virtual tracer experiment. The corresponding model perfor-

the original dispersivity (λL = 4.7 cm), the RWU and evaporation (redmance was evaluated in terms of RMSE values. The transit time based

and grey curves in Figure 7) transit times moderately decrease oron the virtual tracer experiment was identified by fixing dispersivity toincrease, respectively. Dispersivity has a higher impact on drainage

the original value (λL = 4.7 cm) calibrated in Stumpp et al. (2012) andtransit time, leading to a significant rise in inaccuracy as dispersivity

to the minimum value (λL = 0.5 cm). Figure 6a shows that many τDincreases (blue curve in Figure 7). If dispersivity is almost nullvalues based on λL = 4.7 cm are smaller than the corresponding(λL = 0.5 cm), ME of τR, τE, and τD is 0.90, 10.1, and 18.4 days,

advective drainage transit times (red circles) with a relatively large dif-

respectively. When dispersivity is unknown, several authors arbitrarily

ference (RMSE is about 50 days). The τR values based on λL = 4.7 cm

fix it at 1/10th of the travel distance as a rule of thumb (Gelhar

and the RWU advective transit time (green circles in Figure 6b) aligned

et al., 1992; Nasta et al., 2021; Sprenger, Tetzlaff, Buttle, Laudon, &fairly well, especially for values above 160 days, with an RMSE of

Soulsby, 2018; Vanderborght & Vereecken, 2007). This assumption

about 21 days. The lowest τR values were below the identity line.
By minimizing the impact of hydrodynamic dispersion (λL = 0.5 cm)(λL = 15.0 cm = 1/10th of the 150-cm-thick soil profile) led to ME of
τR, τE, and τD of 2.4, 7.9, and +32.4 days. The deviation from theon the tracer transport simulations, the drainage transit times (magenta

reference situation deteriorates substantially for the estimation of τD

circles in Figure 6c) aligned well on the 1:1 line with few exceptions due(ME = +43.1 days) and moderately for the estimation of τR

to numerical instabilities. The RMSE values decreased substantially to esti-(ME = 2.7 days) and τE (ME = 10.3 days), when λL = 20 cm.

mate drainage transit time when the longitudinal dispersivity was reduced
to λL = 0.5 cm. The RWU transit times (yellow circles in Figure 6d) did notchange much when setting λL = 0.5 cm. The longitudinal dispersivity
describes the spreading of a tracer along the flow paths. The longer the

3.4 | Assessing the temporal origin of RWU,
evaporation, and drainage

flow paths, the more affected by dispersion the tracer transport is; thus,
drainage transit times are very sensitive to λL. The root zone is denser

The subset 370 model simulations carried out in Section 3.3 was usednear the soil surface, that is, at the beginning of the flow paths, and there-

in this Section to assess the temporal origin of the main water balance

fore, the effect of dispersion on RWU is less pronounced.

components. Event-based transit times (and corresponding breakthrough curves) and rainfall contributions to actual evaporation, actual
transpiration, and drainage are illustrated in Figure 8. Drainage and3.3 | Sensitivity analysis to evaluate the impact ofdispersivity on tracer-based transit time

actual evaporation are the dominant hydrological fluxes in the study

Dispersivity is a transport parameter describing the spreading of a sol-tion time of the tracer between 115 and 454 days from the soil

ute or tracer. Dispersivity controls the shape of the breakthroughsurface to the soil profile bottom. Low drainage transit times are

curve and therefore influences the arrival time estimation. In a new

induced by frequent and intensive rainfall events following themodel simulation set, we considered 370 rainfall events in the virtual

selected labelled rainfall event, pushing the tracked water parcel

tracer experiment. Figure 7 shows the sensitivity analysis to evaluate

quickly downward towards the soil profile bottom. By contrast, a dry

the impact of λL on the transit times (τR, τE, and τD) in terms of theperiod after the selected rainfall event causes a slow migration of themean error (ME) between the transit time based on the actual λL andwater parcel across the soil profile. The vast majority of evaporationarea, as illustrated in Figure 8a,b (Figure S1 in Data S1). The cumulative tracer drainage fluxes (blue curves in Figure 8d) indicate a migra-

those based on λL ranging from 0.5 and 20 cm. As expected, λL influ-

fluxes are lost within the first ten days (Figure 8e), with a few cumula-ences transit times differently. If λL becomes smaller or greater thantive tracer evaporation fluxes (grey curves in Figure 8f) characterized
by a delay of 50–120 days. RWU transit times range from 2 to358 days (Figure 8g) resulting from the corresponding root tracer
fluxes (red curves in Figure 8h). High RWU ages are associated to low
RWU rates and viceversa. On the one hand, the old water parcels
travel for a few days within the deepest portion of the root zone,
where roots have the minimum density. On the other hand, the youngwater parcels reside in the uppermost portion of the root zone andare subject to the highest rates of RWU. The frequency distributionsof RWU, evaporation, and drainage transit times (not shown) are notnormal according to the normality tests (Lilliefors and Kolmogorov–
Smirnov executed in Matlab) mentioned in Section 3.1. The distributions of drainage and RWU transit times are multimodal, while theF I G U R E 7 Mean error (ME) between drainage (blue line),
evaporation (grey line), root water uptake (RWU, red line) transit timevalues obtained by using the original dispersivity λL = 4.7 cm and arange of λL values between 0.5 cm and 20 cm.

evaporation transit time distribution is exponential, with few values
surpassing ten days.
The 370 RWU, evaporation, and drainage transit time values weregrouped into precipitation sources from two seasons (growing and

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NASTA ET AL.

NASTA ET AL.

F I G U R E 8 (a) Rainfall contribution(in %) to actual evaporation, Ea (grey),actual transpiration, Ta (red), and drainage,
D (blue) for the 370 rainfall events, (b) apie chart of rainfall partitioning resulting
from the tracer mass balance, (c) drainagetransit times (τD) and (d) corresponding
cumulative bottom tracer fluxes (cvBot),(e) evaporation transit times (τE) and (f)the corresponding cumulative surface
tracer flux (cvTop), (g) RWU transit times(τR) and (h) the corresponding cumulativeroot tracer flux (cvRoot). The verticaldashed lines delimit the precipitation
events from growing (GS) and dormant(DS) seasons (subplots a, c, e, g).

dormant seasons). On average, it took 18, 3, and 201 days for rainfall

longest RWU transit times (>200 days) originated from waters infiltrat-water in the growing season to reach the roots (with actual RWU

ing at the beginning of the previous dormant season. The grouping of

being 21% of rainwater), the soil surface (with actual evaporation

evaporation and drainage transit time distributions did not provide

being 42% of rainwater), and the soil profile bottom (with drainage

two distinct sub-distributions (not shown).

being 36% of rainwater), respectively. In contrast, 10%, 10%, and 79%
of rainfall from the dormant season reached the roots, the soil surface,
and the soil profile bottom after 264, 6, and 294 days, respectively.

4|

DI SCU SSION

Most water parcels originating from the rainfall of the growing
season were quickly removed by dominant evapotranspiration fluxes.
Nevertheless, the cumulative root tracer fluxes were grouped into
two distinct sets for precipitation from the growing and dormant sea-

4.1 | The virtual tracer experiment for assessing
the temporal origin of RWU, evaporation, anddrainagesons (separation of RWU tracer breakthrough curves according toseasons is given in Figure S2 in Data S1). The histogram for precipita-

Several factors, including the depth and the soil hydraulic properties

tion from the growing season provides an exponential RWU transitof each layer, the time-variant crop characteristics, the seasonal pat-time distribution with the majority of arrival times below 15 days. The

tern of the atmospheric forcings, and the hydrodynamic dispersion,

RWU transit time multimodal distributions from the dormant season's

influence the assessment of the transit time through the vadose zone.

precipitation had two peaks at 81 and 298 days (Figure S2). The

Stumpp et al. (2012) measured or calibrated all these factors.

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8 of 11In this study, we assessed the age dynamics of water in ademographics (Sprenger et al., 2016). Indeed, a potential drought

150-cm-thick layered soil profile beneath winter rye. Importantly,

event in the growing season with a duration longer than the mean ofsetting the arrival time when the trace breakthrough is 50% reflects

the RWU transit time distribution could be detrimental to plant sur-the definition of median time provided by Benettin et al. (2015), whovival. Conversely, water falling during the dormant season could

envision the existence of a time distribution associated with the out-

buffer the lack of precipitation in the growing season within the age

put tracer flux originating from each rainfall event. The arrival times

distribution, which can range from a few days to several months

estimated using tracer transport simulations were compared to those(Brinkmann et al., 2018; Sprenger, Tetzlaff, Buttle, Laudon, Leistert,

estimated using the particle tracking algorithm. Both methods need to

et al., 2018).

be validated with field tracer experiments. The median (309.9 days),mode (334.5 days), and mean (296.1 days) of advective τPT,D arereported above in Section 3.1. The tracer-based approach resulted in5|

CONC LU SIONS

the median, mode, and mean of τD of 262.0, 308.5, and 260.5 days,
respectively. Stumpp et al. (2012) calculated the mean drainage transit

The temporal origin of root water uptake, evaporation, and drainage

time by considering the shift in the isotope peaks between input andwater represents a functional indicator to quantify ecosystem vulnera-

output on the soil surface and lysimeter bottom while correcting thebility and resilience to changes in climate and land use. For instance,

peak time by accounting for the given dispersivity. The mean drainage

the impact of seasonal rainfall anomalies on the resilience of forest

transit time in the third lysimeter (reported in table 3 in Stumpp

plantations is still uncertain. Plant reliance on past rainfall is importantet al., 2012) was 250 days. Anyway, we cannot fully interpret thein season-dry climates and even in humid climates punctuated bydifferences between the particle tracking algorithm and the virtual

drought. It is also essential to know how much rainwater percolates

tracer experiment. In this study, we tried to understand the role of dis-downward to the shallow aquifer and how much water is returned topersivity in tracer transport simulations.

the atmosphere through evapotranspiration to select the most cost-

Using the original (actual) dispersivity allows the tracer transporteffective crops to save irrigation water during the growing season andsimulation to be carried out under realistic conditions (Stumpp

simultaneously reduce groundwater pumping in cropland manage-

et al., 2012). The dispersivity is known to be a length-scale dependent

ment. The main advantage of using virtual tracer experiments is theparameter, and the impact of dispersivity on the advective-dispersive

possibility of generating scenario modelling approaches that enabletransit time still remains unclear. Therefore, we carried out a sensitiv-

the impacts of natural and anthropogenic disturbances on the tempo-

ity analysis to estimate τR, τE, and τD by changing λL (Figure 7). We

ral origin of the water balance components to be assessed based on

found that RWU and evaporation transit times are weakly or poorly

long-term (in the order of decades or centuries) simulations of water

sensitive to dispersivity because water parcels are removed by evapo-

flow and tracer transport.

transpiration fluxes near the surface (roots are mostly distributed nearIn this study, the temporal origin of water in the soil–plant-

the soil surface). By contrast, drainage transit time is positively corre-

atmosphere continuum system was estimated using a synthetic

lated with dispersivity. In this case, water parcels travel across theapproach based on tracer transport simulations carried out with aentire depth of the soil profile and are highly influenced by dispersiv-

process-oriented hydrological model. Our three main findings reflect

ity. The use of the original dispersivity in the virtual tracer experiment

the three research questions and associated goals and may be summa-

induced a faster downward movement of the tracer when compared

rized as follows:

to that of the particle (Figure 6a).
• Drainage and RWU water transit times obtained using the virtual
tracer experiment were compared to those obtained considering

4.2|

Future applications

advection-dominated transport. On the one hand, the RWU transit
times estimated by particle tracking and virtual tracer experiment

In this study, we set up a modelling protocol to carry out a virtual

agreed fairly well with relatively low errors. On the other hand, thetracer experiment which can be used to assess the temporal origin ofassessment of drainage transit times using the two methods is still

RWU, evaporation, and drainage in plot-scale applications (Benettin

affected by large errors. The large errors are due to different model

et al., 2021). The results for each daily event can be aggregated at any

setups of the two approaches and tracer transport simulations

desired temporal resolution to investigate the effects of climate sea-

being affected by dispersivity.

sonality on water balance and timing. We found that transpiration• The impact of dispersivity on tracer-based transit times was evalu-

timing is driven by seasonal dynamics characterizing plant growth andated by conducting a sensitivity analysis. Such analysis must be

dormancy. While it is well known that plants' water supply is replen-

considered, especially when dispersivities are unknown or assumed

ished by precipitation occurring in the dormant season under seasonalas 1/10th of the soil profile depth. While dispersivity strongly

climate regimes, the temporal origin of water used by roots underinfluences drainage transit times, its effect on evaporation andtemperate climates is still poorly understood (Brinkmann et al., 2018).

transpiration transit times is minimal. Large dispersivity values

Our results indicate that a key challenge in understanding hydrologicalmight exacerbate the differences between the particle tracking andprocesses in the critical zone is the determination of the water

virtual tracer experiment approaches. The actual dispersivity value

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NASTA ET AL.

NASTA ET AL.

calibrated in a previous study allows the implementation of thevirtual tracer experiment, even though its value influences drainagetransit times. We expect differences between the two methods tobecome larger when the investigated soil profile is deeper than150 cm and the actual dispersivity is greater than 4.7 cm.
• The virtual tracer experiment integrates the RWU, evaporation, anddrainage transit times with the corresponding rainfall partitioning
for each rainfall event. This information needs to be assessed insoil profiles over space, interpolated, and mapped to get vulnerability and resilience indicators. The seasonal aggregation of the RWU
temporal origin helped quantify two distinct frequency distributions, which can be used to assess the impact of climate variability
on water storage dynamics in the critical zone.
ACKNOWLEDGEMEN TS
The study reported in this paper was supported in part by MiUR-PRIN
Project “WATer mixing in the critical ZONe: observations andpredictions under environmental changes – WATZON” (Grant
2017SL7ABC), and in part by the “iAqueduct” project funded underthe 2018 Joint call of the Water Works 2017 ERA-NET Cofund that is
an integral part of the activities developed by the Water JPI (Project
number: ENWWW.2018.5).
DATA AVAI LAB ILITY S TATEMENT
Data can be downloaded from the HYDRUS website (https://www.
pc-progress.com/en/Default.aspx?h1d-lib-Isotope). Two open-source
Matlab scripts are available. The PT.m Matlab code determines thedrainage transit time based on the particle tracking algorithm, while
the VTE.m Matlab code determines the drainage and RWU transit
times and relative rainfall contributions to actual evaporation, actual
transpiration, and drainage using isotope transport simulations in
HYDRUS-1D (see details in Data S1).

ORCID
Paolo Nasta

https://orcid.org/0000-0001-9654-566X

Tiantian Zhou

https://orcid.org/0000-0002-6508-8694

Christine Stumpp

https://orcid.org/0000-0001-9041-2735

Nunzio Romano

https://orcid.org/0000-0001-7276-6994

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SUPPORTING INF ORMATION
Additional supporting information can be found online in the Supporting Information section at the end of this article.

How to cite this article: Nasta, P., Šimůnek, J., Zhou, T.,
Stumpp, C., & Romano, N. (2023). A virtual tracer experiment
to assess the temporal origin of root water uptake,evaporation, and drainage. Hydrological Processes, 37(9),e14982. https://doi.org/10.1002/hyp.14982

APPENDIX ATABLE A1HYDRUS-1D input and output variables and files.

Text file

AcronymDescription

ATMOSPH.IN

P

Precipitation

cTop

Soil surface tracer concentration

wPrec

Initial water storage between particles

wInit

Cumulative surface flux when a newparticle is launched

Ep

Potential evaporation rate

Tp

Potential transpiration rate

Options.in

T_Level.out

solute1.out

Particle.out

rTop

Potential surface flux (Ep-P)

Ea

Actual evaporation ratevTop

Actual surface flux (Ea-P)

Ta

Actual transpiration rate

vBot

Actual flux across the soil profile
bottom (drainage or lysimeter
discharge)

cvTop

Actual solute flux across the soil
surface

cvRootActual root solute uptake in the root
zone

cvBot

Actual solute flux across the soil profile
bottomNP

Number of particles at time tnTop

The number of particles added (+) or
removed () at the top boundarynBot

The number of particles added (+) or
removed () at the bottom boundary

Particle
depthParticle positions in the soil profile

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