BGBiogeosciencesBGBiogeosciences1726-4189Copernicus PublicationsGöttingen, Germany10.5194/bg-14-2199-2017Reviews and syntheses: Isotopic approaches to quantify root water uptake: a review and comparison
of methodsRothfussYouriy.rothfuss@fz-juelich.deJavauxMathieuhttps://orcid.org/0000-0002-6168-5467Institute of Bio- and Geosciences, IBG-3 Agrosphere,
Forschungszentrum Jülich GmbH, Jülich, 52425, GermanyEarth and Life Institute, Environmental Sciences (ELIE),
Université catholique de Louvain (UCL), Louvain-la-Neuve,
1348, BelgiumYouri Rothfuss (y.rothfuss@fz-juelich.de)2May20171482199222426September20165October201624March20174April2017This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://bg.copernicus.org/articles/14/2199/2017/bg-14-2199-2017.htmlThe full text article is available as a PDF file from https://bg.copernicus.org/articles/14/2199/2017/bg-14-2199-2017.pdf
Plant root water
uptake (RWU) has been documented for the past five decades from water stable isotopic analysis. By comparing
the (hydrogen or oxygen) stable isotopic compositions of plant xylem water to
those of potential contributive water sources (e.g., water from different
soil layers, groundwater, water from recent precipitation or from a nearby
stream), studies were able to determine the relative contributions of these
water sources to RWU.
In this paper, the different methods used for locating/quantifying relative
contributions of water sources to RWU (i.e., graphical inference, statistical
(e.g., Bayesian) multi-source linear mixing models) are reviewed with
emphasis on their respective advantages and drawbacks. The graphical and
statistical methods are tested against a physically based analytical RWU
model during a series of virtual experiments differing in the depth of the
groundwater table, the soil surface water status, and the plant transpiration
rate value. The benchmarking of these methods illustrates the limitations of
the graphical and statistical methods while it underlines the performance of
one Bayesian mixing model. The simplest two-end-member mixing model is also
successfully tested when all possible sources in the soil can be identified
to define the two end-members and compute their isotopic compositions.
Finally, the authors call for a development of approaches coupling physically
based RWU models with controlled condition experimental setups.
Introduction
Understanding how the distribution of soil water and root hydraulic
architecture impact root water uptake (RWU) location and magnitude is
important for better managing plant irrigation, developing new plant
genotypes more tolerant to drought or tackling ecological questions in
water-limited ecosystems, such as the competition for soil water by different
plants (Javaux et al., 2013).
Some examples of root water uptake sink term (S, in d-1)
profiles (blue lines) conceptualized as the sum of SuniH (green
lines), the root water uptake term proportional to root length density RLD
(dotted black line) and the compensatory root water uptake
(Scomp, red lines). (a)Scomp=0 (no root
compensation) leading to S=SuniH. (b)Scomp≠0 and becomes negative towards the surface but remains smaller (in
absolute terms) than SuniH. (c)Scomp≠0
and is negative at the surface, while it is greater than SuniH for
z>-0.08 m. In the last case, S is negative at the surface,
meaning hydraulic lift is observed.
RWU – defined as the amount of water abstracted by a root system from soil
over a certain period of time – is principally driven by transpiration flux
taking place in the leaves. Its magnitude depends on the atmospheric
evaporative demand and stomatal opening. The latter depends amongst others on
leaf water status and stress hormonal signals from the roots transported to
the leaves (e.g., Huber et al., 2015; Tardieu and Davies, 1993). Leaf water
status and stress hormonal signals are related to the soil water potential
distribution and to the plant hydraulic architecture (Huber et al., 2015).
The distribution of RWU is very variable in time and space, and depends on
the presence of roots and their ability to extract water. This ability is a
function of radial conductivity, but axial conductance may also limit water
flow in younger roots or when cavitation occurs. The flux of water depends
also on soil water availability, i.e., the ability of the soil to provide
water at the plant imposed rate (Couvreur et al., 2014): a highly conductive
root segment will not be able to extract water from a dry soil. Locally, this
is the difference of water potential between the root and the soil which
drives RWU, and its magnitude is controlled by the radial hydraulic
resistances in the rhizosphere, at the soil–root interface and in the root
system (Steudle and Peterson, 1998). The actual RWU profile is thus a
combination of different aspects: the root's ability to extract water
(characterized by the number of roots and their hydraulic properties), the
ability of the soil to fulfill the plant water demand, and the water
potential difference between soil and root (Couvreur et al., 2014).
Plants have numerous mechanisms to cope with heterogeneous soil water
distribution, e.g., adaptive root growth, adaptive root conductivity or
exudation (Carminati et al., 2016). A particular process, which has attracted
the attention of plant breeders and ecologists, is the ability of plants to
extract water from non or less water limited soil areas with potentially low
root length densities (RLD
(L L-3), usually expressed in cm root per cm3 soil), known as root
water uptake compensation (Heinen, 2014). To describe the RWU rate in soils,
we will use the root water uptake flow per volume of soil, defined as S
(L3 T-1 L-3), described as a sink term in the Richards
equation. According to Couvreur et al. (2012), root compensation is defined
as the process that decreases or increases RWU at a certain location compared
to the water uptake from that location when the soil water potential would be
uniform in the root zone. Thus, the distribution of the S(x,y,z) is a
sum of two spatially distributed components:
S(x,y,z)=SuniH(x,y,z)+Scomp(x,y,z),
where x, y and z are the three-dimensional (3-D) spatial coordinates,
SuniH is a term proportional to the root distribution and
Scomp is the compensatory part of the RWU distribution. The first
term on the right-hand side of Eq. (1) is always positive, while the second
one can be either positive or negative. Figure 1 illustrates how this
equation affects S distribution in a 1-D space. When there is no
compensation (Scomp(x,y,z)=0), the RWU distribution follows the
root distribution (i.e., highest at the surface and lowest in the deepest
layer, Fig. 1a). When Scomp(x,y,z)<0 but its absolute value is
lower than SuniH(x,y,z), then S(x,y,z) is positive and
different from the root vertical distribution. In case
SuniH(x,y,z) is small, as in Fig. 1c, Scomp(x,y,z)
can locally be higher in absolute value and S(x,y,z) can be locally
negative, which implies that there is a water efflux out of the root (called
“Hydraulic redistribution” or “Hydraulic lift” in this particular case,
Caldwell and Richards, 1989; Dawson, 1993; Kurz-Besson et al., 2006).
Despite its importance, datasets with measurements of RWU are lacking. This
is related to the difficulty of measuring root and soil water fluxes. Often
soil water content change is used as a proxy for RWU. Yet as change in soil
water content with time is not due to root extraction only (i.e., soil water
redistribution can also occur), the assessment of RWU based on water content
distribution alone is not possible in conductive soils (Musters and Bouten,
2000). Rather, the full soil water flow equation accounting for root uptake
and soil water redistribution must be solved in an inverse mode, and, with an
accurate knowledge of soil and root properties RWU distribution can be
inferred (Guderle and Hildebrandt, 2015; Hupet et al., 2002; Musters and
Bouten, 1999; Vandoorne et al., 2012). Nuclear magnetic resonance
imaging has been suggested as
an adequate technique to measure water flow velocity in xylem vessels, but no
application exists yet on living roots in soils (Scheenen et al., 2000). More
recently, Zarebanadkouki et al. (2012) were able to measure for the first
time RWU in porous media by combining a tracer experiment (i.e., deuterated
water) monitored by neutron tomography with inverse modeling of a transport
equation. Yet this was performed under controlled conditions, while there is
no standard method to monitor three-dimensional water uptake distribution of
growing roots in situ. In woody plants, in which roots are thick enough,
Nadezhdina et al. (2010, 2012, 2015) used sap flow measurements in roots to
quantify hydraulic redistribution.
Since the seminal work of Zimmermann et al. (1967) which reported that RWU of
Tradescantiafluminensis occurred in the absence of
fractionation against water oxygen stable isotopes, water stable
isotopologues (1H2H16O and 1H218O) have been
frequently used to identify and quantify RWU in soils through the
measurements of their natural (and artificial)
abundances. Methods include
simple graphical inference to more sophisticated statistical methods, i.e.,
two-end members and multi-source linear mixing models. While the former
attempts to locate the “mean root water uptake depth” in the soil, the latter category of methods provides
profiles of relative contributions to transpiration flux across a number of
defined soil layers.
This present paper has three objectives: (i) performing a literature review
on the use of water stable isotopes to assess RWU; (ii) presenting the
methods for translating the isotopic information into RWU profiles (i.e.,
graphical inference and statistical multi-source linear mixing models); and
(iii) comparing these methods with a series of virtual experiments differing
in the water and isotopic statuses in the soil and the plant. Prior to the
review and inter-comparison, the paper reports on the mechanisms at the
origin of the spatiotemporal dynamics of natural isotopic abundances in soil
and on the background knowledge of isotopic transfer of soil water to and
from roots. Finally, we evoke opportunities offered by novel isotopic
monitoring tools which provide unprecedented high-frequency isotopic
measurements, and call for a development of approaches making use of
physically based models for RWU determination.
(a) Simulated soil water isotopic composition
(δS) profiles for a water saturated (dark blue line) and
unsaturated (light blue dotted line) soil following Barnes and
Allison (1983). Indices “surf” and “EF” refer to soil surface and
evaporation front. “vapor” and “liquid” regions refer to soil regions
where water flow occurs predominantly in the liquid and vapor phases,
respectively. (b) Illustration of the graphical inference method for
determining the mean root water uptake depth (z¯). “Ti” stands for
the sap xylem water at the plant tiller. Case 1: one unique solution is
found; case 2: more than one solution is found. A smoothed profile is
designated by the symbols. The z¯ range is indicated by the gray
horizontal stripes.
Flow of isotopologues in the soil–plant system
In a study that laid the basis for future work in isotopic ecohydrology,
Zimmermann et al. (1967) provided a steady-state analytical solution for soil
water isotopic composition (δS, expressed in ‰
relative to the Vienna Standard Median Ocean Water international (VSMOW)
isotope reference scale, Gonfiantini, 1978) in a water-saturated isothermal
bare sand profile from which water evaporated at a constant rate. Under these
steady-state and isothermal conditions, the upward (convective) liquid flux
of isotopologues, triggered by evaporation (E) and rising from deeper layers,
equals the downward (diffusive) isotopic flux from the evaporating surface
which is enriched in the heavy stable isotopologues due to evaporation.
Furthermore, by conservation of mass, the isotopic composition of evaporation
equals that of its source (e.g., groundwater), i.e., δE=δsource. A profile is obtained (Fig. 2a, dark blue line)
whose exponential shape depends on boundary conditions, i.e., the source
water and surface water isotopic compositions (δsource and
δsurf), the diffusion coefficient of the isotopologues in
water and of a soil “tortuosity factor”, conceptually defined as the ratio
of the geometrical to actual water transport distance. Barnes and
Allison (1983) extended this formulation to a non-saturated sand column
evaporating at isotopic steady state. In this case, the evaporating surface
(i.e., the liquid–vapor interface) can be located below the soil surface and
splits the profile into two regions where isotopic transport predominantly
occurs either in the vapor phase above or in the liquid phase below it. In
the “vapor region”, relative humidity generally is still close to unity for
sand total water potential below 15 bars. At isotopic steady state, the
maximal isotopic enrichment is at the evaporation front (δEF at soil depth zEF) and can be simulated with the
Craig and Gordon (1965) model. The isotopic composition of the soil residual
adsorbed water in the “vapor region” above the evaporation front can be
obtained by assuming thermodynamic equilibrium conditions and by applying
Fick's law, and is shown to decrease linearly towards the value of the liquid
water at the soil surface which is at thermodynamic equilibrium with the
ambient atmospheric water vapor (Fig. 2a, light blue line). Finally, note
that Rothfuss et al. (2015) argued that, at transient state
(δE≠δsource), the maximal isotopic
enrichment in the soil profile might not point to the location of the
evaporation front. Instead, they proposed that the depth where the steepest
gradient in the isotopic profile is observed corresponds to the evaporation
front.
In a two-dimensional (δ18O, δ2H) space, liquid soil water
sampled below the evaporation front will plot on an “evaporation line” with
a slope typically greater than two and lower than six, depending on atmospheric and isotopic forcing, as a result
of kinetic processes during evaporation. Above the evaporation front and at
isotopic steady state, soil liquid water is in equilibrium with a mixture of
atmospheric water vapor (δ18O–δ2H slope ∼ 8) and
evaporated soil water vapor rising from the evaporation front
(2 <δ18O–δ2H slope < 6) (Sprenger et al.,
2016). As a result, an intermediate value for the slope is expected,
depending on the mixing ratio of atmospheric water vapor to evaporated soil
vapor at a given soil depth. Finally, under natural conditions, the
δS profile is not solely a result of isotopic fractionation,
but is also highly impacted both spatially and temporally by input
precipitation isotopic composition through modification of the upper boundary
condition (δsurf).
As opposed to the removal of water vapor by evaporation, RWU has been
described in a number of studies and over a wide variety of plant species not
to be associated with (kinetic) isotopic fractionation (Bariac et al., 1994;
Dawson and Ehleringer, 1993; Thorburn et al., 1993; Walker and Richardson,
1991; Washburn and Smith, 1934; White et al., 1985; Zimmermann et al., 1967).
Consequently, for plants growing in homogeneous external conditions, e.g., in
hydroponic solution, root xylem sap water and external water have the same
isotopic compositions. In natural soils where the liquid phase is not
homogeneous and a vertical gradient of isotopic composition due to
evaporation exists, the root system takes up water at different depths, thus
having different isotopic compositions.
Assuming that water transport time in roots is negligible, the isotopic
concentration of the xylem sap water at the root tiller (CTi
(M L-3)) can be modeled as the weighted average of the product of the
soil water isotopic concentration (CS (M L-3)) and S(x,y,z):
CTi=∫x,y,zCS(x,y,z)⋅S(x,y,z)⋅dx⋅dy⋅dz∫x,y,zS(x,y,z)⋅dx⋅dy⋅dz=∫x,y,zCS(x,y,z)⋅S(x,y,z)⋅dx⋅dy⋅dzJTi,
with JTi (L3 T-1) the xylem sap
flux at the root tiller. Following Braud et al. (2005),
C=ρ⋅RrefMiMwδ+1,
with ρ (M L-3) the volumetric mass of water, Rref
(–) the VSMOW hydrogen or oxygen isotopic ratio, Mw and Mi (M
L-3) the molar masses of 1H216O and isotopologues
(1H2H16O or 1H218O), respectively; the xylem
sap water isotopic composition at the root tiller δTi (–,
expressed in ‰) can be expressed as
δTi=∫x,y,zδS(x,y,z)⋅S(x,y,z)⋅dx⋅dy⋅dzJTi,
with δS(x,y,z) (–, expressed in ‰) the isotopic
compositions of soil water at coordinates (x,y,z). Mostly, a
one-dimensional description of RWU is used assuming that δS
and RWU do not vary in the horizontal direction and δS is
obtained for discrete soil layers of depths zj(j∈[1,n]) and
thickness Δzj=zj+1-zj. It is usually further
hypothesized that JTi equals the transpiration flux T
(L3 T-1) (low to no plant capacitance or phloem–xylem contact):
δTi=∑j=1,nδS(zj)⋅S(zj)⋅Δzj∑j=1,nS(zj)⋅Δzj=∑j=1,nδS(zj)⋅S(zj)⋅ΔzjqTi,
where qTi=JTi/(Δx.Δy)=T/(Δx.Δy) represents the sap flow rate in the root tiller per unit
surface area (L T-1).
δTi can be accessed at different locations in the plant
depending on the species, but the sampling location should not be affected by
evaporative enrichment in heavier isotopologues or back-diffusion of the
isotopic excess accumulated at the sites of transpiration (stomatal chambers)
in the leaf. For grasses and nonwoody plants, this is done by sampling the
root crown (e.g., Leroux et al., 1995), the aerial nodal roots (e.g.,
Asbjornsen et al., 2007), the meristematic petiole, or else the collars
(e.g., tillers) at the base of the plant (e.g., Dawson and Pate, 1996;
Sánchez-Perez et al., 2008). In the case of ligneous plants the fully
suberized stem (Asbjornsen et al., 2007) or sapwood (e.g., White et al.,
1985) is sampled. On the other hand, δS is usually measured by
sampling soil profiles destructively. Finally, water from plant and soil is
predominantly extracted by cryogenic vacuum distillation
(Araguás-Araguás et al., 1995; Ingraham and Shadel, 1992; Koeniger et
al., 2011; Orlowski et al., 2013; West et al., 2006).
Lin and Sternberg (1992) and Ellsworth and Williams (2007), amongst other
authors, reported however that for some xerophyte (plants adapted to arid
environments, e.g., Prosopis velutina Woot.) and halophytes species
(plants adapted to saline environments, e.g., Conocarpus erecta L.),
and mangrove species (e.g., Laguncularia racemosa Gaert.), RWU led
to fractionation of water hydrogen isotopologues. For mangrove species, it
was hypothesized that the highly developed Casparian strip of the root
endodermis would force water moving symplastically (i.e., inside the cells)
and therefore crossing cell membranes (Ellsworth and Williams, 2007). Water
aggregates are then dissociated into single molecules to move across these
membranes. This demands more energy for 1H2H16O than for
1H216O and 1H218O, thus preferentially affects
1H2H16O tranport and leads to a situation where xylem sap
water is depleted in this isotopologue with respect to source water.
Meanwhile, this affects to a much lesser extent 1H218O
transport, so that no detectable isotopic fractionation of water oxygen
isotopologues is observed. It can be concluded that, for the majority of the
studied plant species, either RWU does not lead to isotopic fractionation or
its magnitude is too low to be observable.
Results of the literature review when entering the search terms
((“root water uptake” or (“water source” and root) or “water uptake”)
and isotop*) into the ISI Web of Science search engine
(www.webofknowledge.com). (a) Evolution of the number of
citations per year and cumulative number of publications from 1985 to 2016;
(b) details are given on the plant cover; (c) the available
soil information; (d) the applied isotopic method and
(e) approach; and the type of experiment (f).
Finally, plant water samples will, similarly to soil water samples, fall onto
an “evaporation line” of a slope lower than eight in a two-dimensional
(δ18O, δ2H) space (Javaux et al., 2016).
Literature review
By entering the search terms ((“root water uptake” or (“water source” and
root) or “water uptake”) and isotop*) into the ISI Web of Science search
engine (www.webofknowledge.com), 159 studies published in the last
32 years were identified (see a listing of all studies in the Supplement).
Cumulative number of articles as a function of publication year follows an
exponential shape: on average over the period 1985–2014, number of
publications per year increased for about 0.3 and reached 8 (2014). In both
years 2015 and 2016, the isotopic method for locating or partitioning water
sources to RWU gained significantly more attention with 20 publications per
year (Fig. 3a).
When sorting plant species simply by their form and height, it appears that
trees are the most studied group of plants (present in about 60 % of the
studies), followed by annual and perennial grasses (21 %) and shrubs
(e.g., desert and mangrove species, 21 %) (Fig. 3b). Only 15 % of the
publications study RWU in agricultural systems (e.g., maize, wheat, millet,
rice), which is reflected by the small portion of peer-reviewed journals of
which the category is listed under “Agronomy and Crop Science” (8 %) by
Scimago Journal & Country Rank (www.scimagojr.com). This is a rather
surprising finding given the fact that drought stress is considered as a
major threat for crop yields and that RWU is a crucial mechanism to sustain
drought periods. “Soil Science” is a relatively underrepresented category
with 8 % as well. This is corroborated by the fact that 27 % of the
studies do not report any information about soils (e.g., texture, FAO class,
structure, particle size distribution, or physical properties) (Fig. 3c). In
comparison, the “Ecology” and “Ecology, Evolution, Behavior and
Systematics” categories are significantly more represented with 22 % of
the studies altogether.
Four classes of methods for RWU analysis on basis of isotopic information
emerged from our analysis (Fig. 3d). In a first one, representing 46 % of
the studies, RWU is either located in a specific soil layer using the method
of “direct inference” (Brunel et al., 1995) or in some water pool (or water
“source”, not to be mistaken with the concept of water source defined in
the previous section), e.g., groundwater, soil water, or rainwater (Andrade
et al., 2005; Beyer et al., 2016; Roupsard et al., 1999). In a second class
(32 % of the studies), relative contributions of at least three water
sources to RWU are determined using multi-source mixing models (e.g., IsoSource,
Phillips and Gregg, 2003, representing 21 % of the studies; SIAR, Parnell et al., 2013, 5 %; MixSir
and MixSIAR, Moore and Semmens, 2008, 2 %). In a third class (18 % of the studies),
relative contributions of two particular water sources (e.g., water in two
distinct soil layers, or groundwater versus recent precipitation) to RWU are
calculated “by hand” with a two-end-member linear mixing model (Araki and
Iijima, 2005; Dawson and Pate, 1996; Schwendenmann et al., 2015). Note that
classes two and three (representing 50 % of the studies) are both based
on end-member mixing analysis (EMMA) (Barthold et al., 2011; Christophersen
and Hooper, 1992) and will be further pooled into “statistical approach” in
Sect. 3.2 of this study.
In a fourth class, only accounting for 4 % of the studies, assessments
are provided using physically based analytical (Boujamlaoui et al., 2005;
Ogle et al., 2014, 2004) or numerical (i.e., SiSPAT-Isotope,
Rothfuss et al., 2012; HYDRUS-1D, Stumpp et al., 2012; Sutanto et al., 2012)
models, therefore leading to an estimation of a RWU profile variable in time.
Note that all methods have in common the use of an inverse modeling approach:
the RWU distribution is obtained by optimizing model input parameters until
the simulated δTi and/or the simulated δS
profiles fit to the isotopic measurements. One important feature of the three
first classes of methods is that they consider soil water isotopic transport
flow to be negligible for the duration of the experiment. Numerical models
such as HYDRUS-1D and SiSPAT-Isotope on the other hand take this into account
in the computation of RWU profiles. The first three methods also differ from the last one by
the fact that they only give fractions of RWU instead of absolute RWU rates
changing in time and space.
Sixty-one percent
of the studies based their estimation of location or quantification of
relative contributions on measurement of either δ2H or
δ18O, i.e., in a single isotope framework, while 25 % used both
δ2H and δ18O (i.e., in a dual isotope framework). In the
remaining studies, both isotopic compositions were measured and used to
provide two separate estimates of relative contribution distributions even
though δ2H or δ18O distributions were strongly linked
(see Sect. 2). This last approach is in the present study referred as
“double single” (see the Supplement). The vast majority of the studies
(82 %) took advantage of natural isotopic abundances, while the rest
(18 %) applied labeling pulses to the soil (either in the profile or at
the soil boundaries, e.g., the soil surface and groundwater) to infer RWU
from uptake of labeled water.
To summarize, we observe that isotopic analyses have mainly been used up to
now to assess water sources under natural ecosystems mainly using statistical
approaches. On the opposite, these techniques have not been used much to
investigate RWU of crops. It is also observed that the use of water isotope
composition datasets combined with explicit physical models is lacking. In
the next sections, we analyze the main methods currently use to retrieve RWU
with water isotopic compositions and
compare the different methods. Table 1 summarizes 21 particular isotopic
studies that use either one of the first three classes of methods (i.e.,
accounting for about 96 % of the published studies), while class four
(physically based RWU models) will be treated separately in Sect. 4 of this
study. These 21 studies were chosen according to either the number of
citations and contribution importance (for studies published before 2015) or
to the novelty of the publications (publication year ≥ 2015).
Summary of the reviewed studies that use one of either the three
methods (graphical inference), two-end-member mixing model, and multi-source
mixing models) for plant water source partitioning.
MethodAuthorsExperimentalconditions(field: F/laboratory: L)Plant speciesRoots profile (soil depth: SD (m)/increment: I (m)/number of profiles: NprSAMPLES FOR ISOTOPIC MEASUREMENTS Soil profile (soil depth: SD (m)/increment: I (m)/number of profiles: Nps/Replicates)SAMPLES FOR ISOTOPIC MEASUREMENTS Plant (organ: O/number of samples: Ns/replicates: R/temporal resolution: TR (h))Water extraction method (cryogenic vacuum distillation: Cr/azeotropic distillation Az/direct equilibration: GI/mild vacuum distillation: Mi)Natural abundance: Nab/labelling Experiment: LESingle: S/Dual: D/“Double Single”: DS isotope approachMain results (RWU depth: zRWU (m)/soil depth z (m)/fraction of transpiration: x/Source: So)Graphical inference Leroux et al. (1995)F (tropical)Hyparrhenia diplandra, Andropogon schirensis, Imperata cylindrica (grasses), Cussonia barteri, Crossopteryx febrifuga, BrideIia ferruginea (shrubs)SD = 1.80/I = 0.10/R = 160.10 < SD < 2.00/0.01 < I < 0.10/ R = 3O: sapwood trunks (shrub), Crown (grasses)/8 < Ns < 24/0.5 < TR < 1CrNabS (δ18O)0.00 <zRWU< 0.05 (grasses, early morning)/0.05 <zRWU< 0.10 (grasses, midday)/zRWU= 0.30 or zRWU> 1.50 (shrubs, no unique solution)Thorburn and Ehleringer (1995)F (semi-arid; cold desert, subhumid)Eucalyptus largiflorens, camaldulensis, Acer negundo and grandidentatum, Atriplex canescens, Chrysothamnus, nauseosus, Vanclevea stylosaNo profiles, but single roots sampled after excavationNo profiles, but soil directly surrounding roots are sampledO: non-green, suberised stems/Ns = 3Cr/AzNabS (δ2H)Dominant source: groundwater (Mountain and floodplain)/0.3 <zRWU< 0.4 (cold desert)Weltzin and McPherson (1997)F (temperate semi-arid savanna)Quercus emoryi Torr., Trachypogon montufari (H.B.K.) Nees.noneSD = 1.50/I = 0.05/3 < R < 4O: stem with phloem tissue/R = 4 (tree and sapling)/O: stem without green tissue/R = 4 (seedling)/O: culm base with sheaths removed/3 < R < 4CrNabDzRWU> 0.50 (trees and sapling)/zRWU< 0.15 (2-months-old seedling)/0.20 <zRWU< 0.35 (1- and 2-year-old seedlings and grasses)Jackson et al. (1999)F (tropical forest/savanna)Cerrado woody species: 5 deciduous (Qualea grandiflora Mart., Q. parviflora Mart., Kielmeyera coriacea (Spr.) Mart., Pterodon pubescens Benth., and Dalbergia myscolobium Benth.)/5 evergreen (Didymopanax macrocarpum, Sclerolobium paniculatum, Miconia ferruginata, and Roupala montana)noneSD = 5.00 (depending on the site) R = 2/0.05 < I < 0.20O: wood or suberized, mature, stem segments (outer bark and phloem are removed)/R = 2CrNabS (δ2H)zRWU< 2.00 (four evergreen and one deciduous species)/zRWU> 2.00 (three deciduous and one evergreen species)Moreira et al. (2000)F (eastern Amazon)(invasive) Solanum crinitum Lamb. (native) Panicum maximum Jacq.SD = 4/0.25 < I < 0.50/R = 34 < SD < 6/0.05 < I < 2.00O: well suberized stems (trees)/thick fleshy culms covered with dry leaves (grass)/3 < R < 5CrLES (δ2H)Fraction of root water uptake from the labeled region x= 0.20 (Solanum crinitum Lamb.) zRWU< 1.00 (P. maximum Jacq.)Chimner and Cooper (2004)F (desert)Sarcobatus vermiculatus, Chrysothamnus nauseosus, and Chrysothamnus greeneinone (reference made to Cooper and Chimner, unpublished data)(1st campaign) SD = 0.6/I = 0.10/R = 2 at each site/4 < Nps (per site) < 6/(2nd campaign) SD = 2.1/0.2 < I < 0.30/Nps = 10O: fully suberized stem sections from the base of plants/(1st campaign, S. Vermiculatus) 4 < Ns (per site) < 8/R = 3/(1st campaign, C. nauseosus) 5 < Ns (per site) < 6/R = 3/(2nd campaign) 3 < Ns < 5 (depending on the species)CrNabS (δ18O)0.00 <zRWU< 0.50 (C. nauseosus, pre-monsoon and monsoon periods)/(S. vermiculatus and C. nauseosus) dominant source: groundwater (pre-monsoon period) and switched to precipitation recharged water (0.30 <zRWU< 0.40, during mansoon).Kulmatiski et al. (2006)F (shrub-steppe)(invasive) Centaurea diffusa, (native) Pseudoroegneria spicata; Bromus tectorum L.1.20 < SD < 2.20/I = 0.151.05 < SD < 2.20/0.10 < I < 0.60O: stemCrNabDSzRWU= 0.15 (Bromus tectorum L., early season)/zRWU= 1.20 (Centaurea diffusa Lam, late season)Li et al. (2007)F (cold continental-semiarid)Larix sibiricanoneSD = 1.00/0.05 < I < 0.30O: stem/Ns (per sampling date) = 5CrNabDS0.10 <zRWU< 0.40 from δ18O meas/0 <zRWU< 0.80 from δ2H measWang et al. (2010)F (warm temperate/monsoon climate)Summer corn and cotton (species not specified)noneSD = 1.50/0.05 < I < 0.30/Nps = 7O: stems (epidermis contacted with air was removed)/Ns = 7/TR = 1 per vegetation stageCrNabDSzRWU= 0.10 (Corn, jointing stage)/zRWU= 0.50 (Corn, flowering stage)/zRWU= 0.10 (Corn, full ripe stage)/zRWU= 0.40 (Cotton, seedling stage)/zRWU= 0.50 (Cotton, bud stage)/zRWU= 1.10 (Cotton, bolls open stage)Stahl et al. (2013)F (tropical)tropical rainforest treesnone (reference made to other literature)SD = 2.00/0.20 < I < 0.30/R = 6O: branch (length = 0.07 m; diameter = 0.1–0.3 m). Bark tissue is immediately removedCrLEDzRWU> 1.00 (dry periods, tall trees)/More diffuse zRWU for shorter treesTwo-end members mixing model White et al. (1985)F (temperate)Taxodium distichum/Pinus strobusnonenoneO: wood samples taken at breast heightnone (Sap flow water)Nab(δ2H)Groundwater: 0.46 <x< 0.64 wet site)/0.16 <x< 0.25 (intermediate site)Dawson and Ehleringer (1991)F (riparian zone)Acer grandidentatum Nutt., A negundo L., Quercus gambelii Nutt.noneSD = 0.50O: mature suberized stemsCrNabS (δ2H)So: Groundwater (streamside mature trees)/So: stream water (younger streamside trees)/So: Precipitation (younger non-streamside trees)Brunel et al. (1995)F (aeolian sand dune)“Mallee Tree” (Eucalyptus sp.)none50 < SD < 4.2/0.10 < I < 0.25O: twigs (bark is removed)/R = 2AzNabD0 <zRWU< 0.4 with 0.7 <x< 0.9 (1st site)/0 <zRWU< 1.5 with x= 0.07 (2nd site)Dawson and Pate (1996)F (mediterranean)Banksia prionotes, Dryandra sessilis, Grevillea (species unknown)none (qualitative observation)none (sand around the root system)O: roots, trunks, stem baseMiNabS (δ2H)So: deeper soil layers (dry season)/So: shallow soil layers (wet season)McCole and Stern (2007)Field conditions (subtropical)Juniperus asheinone (reference made to other literature)SD = 0.30/0.05 < I < 0.10/4 < Nps (per site) < 5O: stemCrNabS (δ18O)zRWU> 0.30 m (hot, dry summer)/0.10 <zRWU< 0.30Goebel et al. (2015)F (semi-arid)Gossypium hirsutum L.noneSD = 0.3/I ∼ 0.02/Nps = 4 per irrigation treatmentO: meristematic petiole reduced in size to 5 mm./14 < Ns < 17 (depending on the irrigation treatment)/R = 2/TR = 1CrNabS (δ18O)Evidence for shifting to rainwater predominantly
Continued.
MethodAuthorsExperimentalconditions(field: F/laboratory: L)Plant speciesRoots profile (soil depth: SD (m)/increment: I (m)/number of profiles: Npr)SAMPLES FOR ISOTOPIC MEASUREMENTS Soil profile (soil depth: SD (m)/increment: I (m)/number of profiles: Nps/Replicates)SAMPLES FOR ISOTOPIC MEASUREMENTS Plant (organ: O/number of samples: Ns/replicates: R/temporal resolution: TR (h))Water extraction method (cryogenic vacuum distillation: Cr/azeotropic distillation Az/direct equilibration: GI/mild vacuum distillation: Mi)Natural Abundance: Nab/labelling Experiment: LESingle: S/Dual: D/“Double Single”: DS isotope approachMain results (RWU depth: zRWU (m)/soil depth z (m)/fraction of transpiration: x/Source: So)Multi-source mixing model Asbjornsen et al. (2007)F (cornfield, prairie, oak savanna, and woodland)Quercus macrocarpa, Umus americana L. (trees), Zea mays L. (crop), and Andropogon gerardii (grass)none1.40 < SD < 2.00/0.05 < I < 0.20/ R = 2 per siteO: stem (trees); aerial nodal roots just above the soil surface (Zea mays L.); stem (grass)/Ns = 2 per speciesDiNabS (δ18O)0.0 <zRWU< 0.20 m with x< 45 % and x< 36 % (crop and grass, resp.)/0.00 <zRWU< 0.20 m with x< 40 % and x< 20 % and zRWU> 0.60 m with x< 60 % and x< 80 % (Q. macrocarpa and U. americana L., resp.)Wang et al. (2010)F (warm temperate/monsoon climate)Summer corn and cotton (species not specified)noneSD = 1.50/0.05 < I < 0.30/Nps = 7O: stems (epidermis contacted with air was removed)/Ns = 7/TR = 1 per vegetation stageCrNabDS0 <zRWU< 0.20 with 96 <x< 99 (Corn, jointing stage)/0.20 <zRWU< 0.50 cm with 58 <x< 85 (Corn, flowering stage), 0.00 <zRWU< 0.20 with 69 <x< 76 (Corn, full ripe stage)//0.00 <zRWU< 0.20 with 27 <x< 49 (Cotton, seedling stage), 0.20 <zRWU< 0.50 cm with 79 <x< 84 (Cotton, bud stage)/0.50 <zRWU< 0.90 with 30 <x< 92 (Cotton, blooming stage)/zRWU> 90 cm with 69 <x< 92 (Cotton, boll open stage)Huang and Zhang (2015)F (desert)Caragana korshinskii and Artemisia ordosicanoneSD = 2.00/0.05 < I < 0.50O: twigs (1–2 cm of stem with bark immediately removed)/R = 3CrNabDS0.1 <zRWU< 1.0 (wet seasons)/zRWU not affected by small rainfall events/zRWU> 1.00 with x observed to increase from 2 (±0.7) to 10 (±1.4) % for both plants after large rainfall event.Prechsl et al. (2015)F (temperate)Phleum pratense, Lolium multiflorum, Poa pratensis, Taraxacum officinale, Trifolium repens, Rumex obtusifolius, Trisetum flavescens, Phleum rhaeticum, Carum carvi, and Achillea millefolium, Rumex alpestris, Taraxacum officinale and Trifolium, pratense.SD = 0.30/0.075 < I < 0.125/ 6 < Npr < 70.30 < SD < 0.40/0.04 < I < 0.10/ R = 3O: root crown/2 < Ns < 10CrNabDS<zRWU< 0.10 with 0.43 <x< 0.68 (Drought treatment)/0 <zRWU< 0.10 with 0.04 <x< 0.37 and 0.20 <zRWU< 0.35 with 0.29 <x< 0.48 (control treatment)Volkmann et al. (2016b)F (temperate)Quercus petraea and Fagus sylvaticaSD = 0.60/0.05 < I < 0.10/R = 4SD = 0.60/0.05 < I < 0.10/Nps > 17none (measurement of transpiration isotopic composition)noneLES (δ2H)Constant RWU depth profile with 0.15 <x< 0.18 (beech)/x< 0.15 for z< 0.20 and 0.15 <x< 0.25 for z> 0.30 (beech/oak mixture and oak monoculture)Graphical inference (GI)
This straightforward approach first proposed by Brunel et al. (1995) and
applied by, e.g., Leroux et al. (1995), Weltzin and McPherson (1997)
(Table 1) and elsewhere by Midwood et al. (1998), Armas et al. (2012), and
Isaac et al. (2014) (see the Supplement) defines the “mean root water uptake
depth” z¯ as the depth where δS=δTi. z¯ conceptually indicates the soil depth where
the plant root system, represented as one unique root, would extract water
from.
There are cases where z¯ cannot be unambiguously identified (e.g.,
z¯1 and z¯2 of case 2, Fig. 2b) due to the
non-monotonic character of the δS profile (shown in black
dashed line, case 2 of Fig. 2b). In order to define a mean RWU depth for such
a case one can derive a monotonously decreasing δS profile
by smoothing the profile (shown as symbols in Fig. 2b), e.g., by averaging
δS in a number of layers using the following mass balance,
δS,J=∑j≤JδS(zj)⋅θ(zj)⋅Δzj∑j≤Jθ(zj)⋅Δzj
where J represents the set of depths that belong to the Jth soil layer,
with θ (L3 L-3) and Δzj (L) the soil
volumetric water content and thickness of the soil layer centered around
depth zj. Due to this smoothing, the vertical resolution may be
drastically reduced. In the example presented in Fig. 2b where a uniform
θ profile is assumed, the δS,J profile intersects
with the vertical line of value δTi deeper than for the
initially non-monotonic δS profile, i.e., z¯
(case 2, integrated δS profile) <z¯2<z¯1. Some authors rule out solutions in the case of multiple mean
RWU depths, e.g., by excluding the z¯ solutions where soil water
content is low and/or soil water
potential is high in absolute value
(e.g., Li et al., 2007; see Table 1).
Note that while Eq. (5) provides a representative value for the isotopic
composition that would be measured in soil layer J as a function of those
of the water in the set of depths, δS,J is equivalent to the
isotopic composition “sensed by the plant” only if the root profile is
homogeneous, i.e., when RLD is constant over depth in that particular soil
layer J.
The graphical inference method may not only provide z¯ but also its
uncertainty caused by the uncertainty in measuring δTi (e.g.,
based on the precision of the isotopic analysis and/or sampling natural
variability, shown as gray stripe in Fig. 2b). The steeper the soil water
isotopic profile, the larger the uncertainty in determining z¯ is.
Figure 2b illustrates this with estimated minimum and maximum z¯ for
the monotonic δS profile and for the vertically averaged
profile. In the latter case, the possible range of z¯ is the
largest. These ranges give first quantitative indication of variance around
z¯. Finally, for a complete “graphical assessment” of the variance
of z¯, one should consider the uncertainty associated with
measurements of the δS profile as well (not shown here; for
a complete assessment of errors associated with determination of
δS, see Sprenger et al., 2015).
Statistical approachesTwo-end-member (TM) mixing model
The TM method is a particular case of end-member mixing analysis (EMMA) and
is based on the concept that (i) a plant extracts water from two predominant
water sources A and B (e.g., water in distinct upper and lower soil layers,
or groundwater and recent precipitation water) in given proportions,
(ii) there is no isotopic fractionation during water uptake, and (iii) there
is a complete mixing inside the plant of the contributing water sources A and
B to RWU. The mass conservation for isotopologues gives
JTii=JAi+JBi,CTi⋅JTi=CA⋅JA+CB⋅JB,
with JA, JB, and JTi (L3 T-1)
(respectively, JAi, JBi, and
JTii (M T-1)), and the fluxes of water (or
isotopologues) originating from water sources A and B, and at the plant
tiller. CA, CB, and CTi (M L-3) are water
sources A and B, and xylem sap water measured isotopic concentrations. By
introducing x=JA/JTi and following Eq. (3),
Eq. (6b) becomes
δTi=x⋅δA+(1-x)⋅δB.
In this approach, δTi is therefore defined as the mean value
of the isotopic compositions of water sources A and B (δA and
δB) weighted by the proportions to JTi of water
volume extracted by the plant from water sources A and B, i.e., x and (1-x), respectively. The error associated with the estimation of x
(σx (–, expressed in ‰)) can be calculated following
Phillips and Gregg (2001):
σx2=∂x∂δA2⋅σδA2+∂x∂δB2⋅σδB2+∂x∂δTi2⋅σδTi2,σx=σx2=1(δA-δB)σδTi2+x2⋅σδA2+(1-x)2⋅σδB2,
with σδA, σδB, and
σδTi the standard errors associated with the
measurements of δA, δB, and δTi,
respectively. The sensitivity of Eq. (8b) to different values of
σδA, σδB, and
σδTi can be tested by considering either minimal
possible errors, i.e., the analytical precision of the isotopic analyzer
(e.g., isotope ratio mass spectrometer, laser-based spectrometer), or by
taking additional errors involved with sampling procedure and vacuum
distillation technique (see, e.g., Rothfuss et al., 2010) into account.
Equation (8b) also shows that, independently of the values considered for
σδA, σδB, or
σδTi, σx is inversely proportional to
1/(δA-δB), indicating that the two end-members
should have the greatest possible isotopic dissimilarities for a low standard
error of x. Therefore, it is especially important, e.g., for partitioning
between water from an upper and lower portion of the soil profile, to
properly define the thickness of these layers, so that they have distinct
isotopic compositions, and that the difference is considerably larger than
the precision of the isotopic measurements. Figure 4 shows for example that
when (i) x is evaluated at 10 % and (ii) σδA,
σδB, and σδTi are
estimated as equal to 0.02 ‰ (dark blue solid line),
(δA-δB) should be greater than 0.75 ‰
(in absolute terms) in order to reach a σx value lower than
5 %, i.e., more than 37 times the error made in δA,
δB, and δTi. To obtain the same standard error
for x in the case of a higher standard error in the estimation of
δA, δB, and δTi (e.g.,
σδA, σδB, and
σδTi=0.1 ‰), (δA-δB) should be greater than 3.00 ‰ (in absolute terms).
This difference becomes much greater for σδA,
σδB, and σδTi=1.00 ‰ and reaches 42 ‰ (not shown in Fig. 4). This
certainly highlights the advantage of artificially labeling soil water with
water enriched (or depleted) in heavy isotopologues for a more precise
assessment of the relative contribution of soil water sources to RWU, as
mentioned by Moreira et al. (2000). In another study, Bachmann et al. (2015)
labeled the upper and lower portions of the soil profile in a natural
temperate grassland with 18O-enriched and 2H-enriched water,
respectively. They defined two distinct (upper and lower) soil water sources,
for which they calculated the corresponding δ2H or δ18O
on the basis of measured soil water isotopic profiles and using Eq. (5). They
were able to find evidence against the hypothesis of “niche complementarity” regarding plant
water use, which states that RWU of competitive plant species is spatially
and temporally distinct, and that this distinction is stronger at high
species richness. Figure 4 also illustrates that for given (δA-δB), σδA, σδB, and σδTi values, the “optimal x
value” for a low σx is 50 % (shown by the orange lines).
Standard error (σx) associated with the estimation of the
relative contribution (x) of source A water to root water uptake in the
case of two distinct sources (A and B of isotopic compositions
δA and δB). Three x values (0.1, dark blue
color; 1/3, light blue; 1/2, orange) and three values of standard errors
associated with sampling and measurement of δA,
δB, and of the isotopic composition of the tiller sap water
(δTi) (0.02, solid line; 0.10 and 1.00, dashed lines) are
tested.
Table 1 displays a sample of studies that used the two-end-member mixing
approach. Authors were able to distinguish between uptake of irrigation and
precipitation water (Goebel et al., 2015), precipitation and groundwater
(White et al., 1985), soil water and groundwater (McCole and Stern, 2007), or
else between stream water and soil water (Dawson and Ehleringer, 1991;
McDonnell, 2014). Thorburn and Ehleringer (1995) were for instance able to
locate the dominant source for RWU, i.e., groundwater for their mountain and
a floodplain test site and water from the soil between 0.3 and 0.4 m depths
for their cold desert test site. Other authors (e.g., Brunel et al., 1995)
combined two mixing equations, i.e., one for each isotopologue, into a single
one, or else calculated the ratio of geometrical distances between
δTi and δA and between δTi and
δB in dual isotope (δ18O and δ2H) space
(Bijoor et al., 2012; Feikema et al., 2010; Gaines et al., 2016). As infrared
laser-based spectrometry now enables simultaneous measurements of
δ18O and δ2H at lower cost, we believe that this
dual isotope approach (referred to
as “D” in Table 1) will or should gain in importance in isotopic studies.
This is especially useful when (i) under natural conditions the
δ18O–δ2H slope is not constant over depth (Sprenger et
al., 2016) or (ii) in the context of pulse labeling experiments, which can
artificially change the value of the δ18O–δ2H slope at
given locations in the soil profile. In these cases, two independent mixing
equations are obtained, one for each isotopologue.
Multi-source (MS) mixing models
When there are more than two identified plant water sources contributing to
RWU, e.g., water from different layers j(j∈[1,N]) in the
soil profile, Eq. (7) becomes
δTi=∑j=1Nxj⋅δS,j,
with N the number of plant water sources (e.g., soil layers) and
∑j=1Nxj=1. As there are more water sources than
(number of mixing equations +1), there is not a unique solution but an
infinite range of possible solutions. However, based on background
information or knowledge, some of these solutions are not likely or possible.
A range of solutions that is most likely based on prior information can be
obtained using Bayesian methods. In the method proposed by Phillips and
Gregg (2003), the isotopic composition calculated for each considered xj
combination (δTi) is compared with the measured value
(δTi,m). The number of combinations depends on the value of
the contributing increment (i, %, typically 5 or 10 %) and the
combinations for which δTi meets the following requirement are
selected:
δTi≤δTi,m±τ,
where τ (–, expressed in ‰), standing for “tolerance”,
usually accounts for the precision of the isotopic measurements or possible
errors during sampling and vacuum distillation steps. This multi-source
mixing model approach strongly depends on τ and i, which therefore
should be carefully chosen by the user; e.g., a smaller i refines the
analysis. For this, the IsoSource program
(https://www.epa.gov/sites/production/files/2015-11/isosourcev1_3_1.zip)
is available (Phillips et al., 2005). Wang et al. (2010) compared the outcome
of the GI and MS approaches and came to the conclusion that even though the
latter did not solve the non-uniqueness problem and provided diffuse patterns
of frequency that were difficult to interpret in some cases (e.g., in the
case of a non-monotonic isotopic profile), it had the advantage over the
former method of providing a systematic and quantitative assessment of ranges
of relative contributions. Romero-Saltos et al. (2005) extended the model of
Phillips and Gregg (2003) by constraining RWU to follow a normal distribution
within a delimited 50 cm soil vertical segment of 1 cm vertical resolution
and centered around z¯, the mean RWU depth. The location of this
section and thus z¯ is also obtained by mass balance from inverse
modeling similarly to IsoSource (see applications of Grossiord et al., 2014;
Rossatto et al., 2013; Stahl et al., 2013).
Parnell et al. (2010) proposed to overcome two limitations of the approach of
Phillips and Gregg (2003), i.e., its inability to (i) account for uncertainty
in the estimations of δTi and of the water sources isotopic
compositions δS,j, and to (ii) provide a optimal solution rather
than ranges of feasible solutions. For doing this, they use a Bayesian
framework (for details see Erhardt and Bedrick, 2013; Moore and Semmens,
2008; Parnell et al., 2013), which allows uncertainty in the xj
proportions and incorporates a residual error term εj
(normally distributed with mean equal to zero and variance σ2):
δTi=∑j=1Nxj⋅δS,j+εj.(9′)
Note that the terms of (i) trophic enrichment factor (TEF (–, expressed in ‰); see, e.g., the
meta-analysis of Vanderklift and Ponsard, 2003) and (ii) isotope
concentration dependency (Koch and Phillips, 2002; Phillips and Koch, 2002)
originally incorporated into the formulation of Parnell et al. (2010) for
other applications are not present in Eq. (9′) since (i) no isotopic
fractionation during RWU is assumed and (ii) isotope concentration dependency
applies only for situations where isotopic compositions of different elements
are measured and available.
Parnell et al. (2010) developed the program “Stable Isotope Analysis in R”
(SIAR, https://cran.r-project.org/src/contrib/siar_4.2.tar.gz) in which
the initial (a priori) xj distribution is by default the Dirichlet
distribution, of which information can be partly specified by the user. A
posteriori xj distribution is obtained by fitting the linear model to
data via a Metropolis–Hastings (Hastings, 1970; Metropolis et al., 1953)
Markov chain Monte Carlo algorithm.
Prechsl et al. (2015) apply both graphical and Bayesian approaches to
evaluate the shift in z¯ and change in the RWU profile following
drought treatments (approx. 20 to 40 % precipitation reduction with
transparent rainout shelters) in both extensively and intensively managed
grasslands. From both approaches it appeared that a shift in z¯ was
non-existent or not observable from isotopic analyses. Another recent
application of the Bayesian approach was performed by Volkmann et
al. (2016b), who took advantage of a newly developed soil isotopic monitoring
method to confront high-frequency δS profile time series
with
time series of δTi (indirectly obtained from the isotopic
measurement of the transpired water and assuming isotopic steady state, i.e.,
δTi=δT) following a labeling pulse (see Table 1 for
details on the study).
Inter-comparison of methods
We tested and compared the different methods (GI, TM, MS) during a series of
virtual experiments in a single isotope framework (δ18O) and at
natural isotopic abundance. Mean RWU depths (provided by the GI method) and
xj distribution (provided by the two-end-member and multi-source mixing
models) were determined from the δS profile and the δTi value. For each virtual experiment the δS
profile was prescribed to the different methods, while δTi was
calculated with the physically based analytical RWU model (referred to as
“Couv”) of Couvreur et al. (2012).
It has been proved (Couvreur et al., 2012) that this model gives similar
results to a 3-D physically based model with detailed descriptions of the
root architecture and of the water flow in soil and roots. In that sense,
this is the best current model existing nowadays to simulate water fluxes in
a soil–plant system (based on biophysical considerations). Other current
models make assumptions or use empirical relations to predict RWU, which are
not based on bio-physical considerations only (Jarvis, 2011; Simunek and
Hopmans, 2009). Obviously, we do not mean that the model of Couvreur et
al. (2012) gives the reality, but rather the best estimate of the water flow
based on our physical knowledge.
The inter-comparison of models was performed using a single isotope
(18O) approach as the focus here was the differences of outcomes rather
than the impact of the input isotopic data on these results. The reader is
referred to Appendix B1 for a description of the model of Couvreur et
al. (2012) and to Appendix B2 on how it was implemented for the
inter-comparison.
Soil, plant, and isotopic synthetic input data for the different
modeling approaches (depth (z) profiles of soil water content θ,
total soil water potential HS, soil water oxygen isotopic
composition δS, root length density RLD, transpiration rate
T, and leaf water potential HL) “collected” during eight
virtual experiments differing in the depth of the groundwater table (Shallow
– Sh/Deep – De) and the water status at the soil surface (Dry – Dr/Wet –
We).
We developed eight virtual plausible scenarios of soil–plant systems under
different environmental conditions. For each scenario, we set one total soil
water potential (HS) profile and one soil water oxygen isotopic
composition (δS) profile. These profiles resulted from the
combination of a lower boundary condition, i.e., the depth of the groundwater
table, and an upper boundary condition, i.e., the soil surface water status.
The groundwater table (of water isotopic composition equal to
-7 ‰) was either shallow at -1.25 m depth (prefix “Sh”) or
deep at -6 m depth (prefix “De”). The soil water potential was
considered to be at static equilibrium below the groundwater level. The soil
surface was either dry under evaporative conditions (suffix “Dr”) or wet,
e.g., shortly after a rain event (suffix “We”). For instance, for scenario
“ShDr”, we set the δS profile to be maximal at the
surface, due to evaporation, and minimal from -0.5 m downward, due to the
shallow groundwater table location. For scenario “DeWe”, on the other hand,
the increase in δS towards the surface was not monotonic due
to a recent precipitation event (of water isotopic composition equal to
-7 ‰). Finally, we tested two different values of plant
transpiration rate (T) and leaf water potential (HL) with each of
these four combinations (i.e., ShDr, ShWe, DeDr, and DeWe). The transpiration
rate was either low (e.g., relevant at night, T=0.01 mm h-1,
suffix “_lT”) or high (T=0.30 mm h-1, suffix “_hT”). All
eight scenarios relied on a common measured root length density vertical
distribution of Festuca arundinacea. Table 2 reports the input data.
Note that, as hypothesized in Eq. (4b), transpiration and sap flow rates
(i.e., per unit of surface area (L T-1)) were considered equal.
The objective was not to use an advanced numerical model such as, e.g.,
SiSPAT-Isotope or Soil-litter-iso, to produce these scenarios, but rather use
synthetic information based on (i) experimental data and
(ii) expert-knowledge which would ideally illustrate the performances or
limitations of the different methods.
Setup of the models
The two-end-member mixing approach (TM) was tested against the isotopic data
for two different cases: (i) two conjoint soil layers spreading from 0 to
0.225 and from 0.225 to 2.00 m and (ii) two disjoint soil layers spreading
from 0 to 0.225 and from 1.75 to 2.00 m. The latter case was designed to
evaluate the impact of lacunar soil isotopic information on the calculation
of x, i.e., when not all potential water sources are properly identified.
Representative values of water oxygen isotopic compositions for these soil
layers (δS,J, J∈[I,II]) were
obtained from the mass balance (Eq. 5) after interpolation of the measured
soil water content and δS profiles at a 0.01 m vertical
resolution.
Simulated depth (z, in m) profiles of xCouv (%)
(solid colored lines), the
simulated relative contributions to transpiration provided by the model of
Couvreur et al. (2012) for experiments “ShDr” (soil with a shallow
groundwater table and a relatively dry soil surface), “ShWe” (soil with a
shallow groundwater table after a rainfall event), “DeDr” (soil with a deep
groundwater table with a relatively dry soil surface), and “DeWe” (soil
with a deep groundwater table and a wet soil surface). Suffices “lT” and
“hT” refer to “low” and “high” transpiration rate simulations. The
color-shaded areas depict the uncertainty of the model estimates on account
of the precision of the measurements. The horizontal gray-shaded areas
delimit the mean root water uptake layer(s) obtained by the graphical
inference method. At the bottom right corner of each plot is a detail
presented for z≥-0.10 m. Finally, results from the first term of the
model of Couvreur et al. (2012) which considers uptake proportional to root
length density are plotted as a dashed brown line for comparison. Note that
negative xCouv means hydraulic redistribution by the roots.
For the multi-source mixing models of Phillips and Gregg (2003) (IsoSource)
and Parnell et al. (2010) (SIAR), the number of potential water sources was
initially fixed to three, i.e., water from the soil layers I
(0.000–0.050 m), II (0.050–0.225 m), and III (0.225–2.000 m). Upper and
lower boundaries of these layers were defined to reflect the exponentially
shaped (monotonic) δS profiles (experiments ShDr and DeDr) or to
smooth the non-monotonic δS profiles observed during experiments
ShWe and DeWe. IsoSource and SIAR were tested for eight soil layers (i.e., as
many layers as measurement points, I: 0.000–0.020, II: 0.020–0.050, III:
0.050–0.110, IV: 0.110–0.225, V: 0.225–0.400; VI: 0.400–0.750, VII:
0.750–1.500, and VIII: 1.500–2.000 m) as well. Increment and tolerance in
IsoSource were fixed to 10 % and 0.25 ‰, respectively. Similarly
to the TM approach, profiles of δS,J (J∈[I,III] or [I,VIII]) were obtained
from the mass balance (Eq. 5) after interpolation of the measured soil water
content and δS profiles at a 0.01 m vertical resolution.
Finally, for the SIAR model, uncertainty associated with δS
measurements was set to 0.2 ‰ and the number of iterations was fixed
to 500 000 and number of iterations to be discarded to 50 000.
For a detailed description of the inter-comparison methodology, the reader is
referred to Appendix C.
Results and discussion
Figure 5 displays xCouv, the S(z)dzT/(Δx⋅Δy) ratios (solid colored lines) simulated by the analytical model of
Couvreur et al. (2012) for the eight scenarios together with uncertainty
(shaded areas) and the corresponding δTi_Couv
(±1 SD) (for a description on how uncertainty was assessed, refer to
Appendix C). In general, at high T the compensation was negligible and the
S profile was mainly proportional to the RLD profile (Fig. 5b, d, f, and
h). The only exception was a soil with a deep groundwater table and a dry
surface, where this dry layer limited RWU (DeDr_hT). At lower
transpiration demand, the S profile predicted by the Couvreur et al. (2012)
model generally differed from the RLD profile (Fig. 5a, c, e, and g). This is
due to the fact that the second term of Eq. (1) (i.e., Scomp; see
Eqs. B4 and B4′ in Appendix B) was proportionally larger. Water uptake from
the upper layer was always more than proportional to the RLD, when this layer
was wetter, and vice versa. Water release to the soil (i.e.,
hydraulic redistribution) was observed only for the soil
with the deep groundwater table and dry upper layer (DeDr_hT, Fig. 5e).
From the graphical method GI, either a single or two distinct solutions for
z¯ (displayed as gray-shaded horizontal stripes) were retrieved,
depending on the monotonic/non-monotonic character of the δS
profile, and ranged between -0.02 and -0.95 m.
Figure 6a displays the relative contribution to T of the uppermost layer
0–0.225 m in the case of two conjoint soil layers as computed with the TM
approach and a comparison with the results of the analytical model. Except
for the very last two virtual experiments with the deep groundwater table and
wet upper layer at both low and high transpiration rates (i.e., DeWe_lT
and DeWe_hT), there was a very good agreement between the analytical model
and the two-end-member mixing model: the absolute difference between
xCouv and xTM ranged between 1.5 % (ShDr_lT) and
6.3 % (ShDr_hT). For the experiment with the deep groundwater table
and dry upper layer at a low transpiration rate (DeDr_lT), the TM approach
estimated that x was equal to 12.3 %, while the analytical model
simulated hydraulic redistribution, i.e., excluded the 0–0.225 m layer as a
potential source. The significant difference between results of the two
models during experiments DeWe_lT and DeWe_hT and the higher standard
error associated with xTM (σx, displayed in the form of
error bars in Fig. 6) were due to the small difference between the isotopic
compositions of the defined soil water sources δS,I
(-6.0 ‰) and δS,II (-5.3 ‰)
as illustrated in Sect. 3.2.1. Figure 6b gives the relative contribution to
T of the 1.75–2.00 m layer in the case of two disjoint soil layers, i.e.,
when not all potential water sources are accounted for in the calculation of
δS,I and δS,II. In this
case there were important disparities between xTM and
xCouv. The mean absolute difference between these two estimates was
equal to 43.5 (±17.8) %. Omitting some of the potential water sources
contributing to T had in this second case the consequence of artificially
overestimating the contribution of the lowest layer. We therefore suggest to
always attempt to fully characterize the soil isotopic profile before
aggregating the isotopic information when defining the two water sources.
Comparison between relative contributions to transpiration (x, in
%) simulated by the analytical RWU model of Couvreur et al. (2012) and the
two-end-member mixing model in the case of two defined soil layers.
Panel (a) displays x from the topmost soil layer (0–0.225 m) in
the case of two conjoint soil layers (0–0.225 and 0.225–2.00 m), whereas
(b) displays x from the lowest soil layer (1.75–2.00 m) in the
case of two disjoint soil layers (0–0.225 and 0.225–2.00 m); i.e.,
information on soil water isotopic composition is lacking between 0.225 and
1.75 m. “Sh” (“De”) stands for the virtual experiments where the soil
has a shallow (deep) groundwater table, while “Dr” and “We” stand for
when the soil is dry or wet at the surface. Suffixes “lT” and “hT” refer
to “low” and “high” transpiration rate simulations. “*” refers to
when hydraulic redistribution is simulated by the analytical model, leading
to a negative x. Error bars are either 1 standard deviation (for the RWU
analytical model) or 1 standard error (for the TM approach).
Simulated ranges of possible relative contributions to transpiration
from three defined soil layers (I: 0.00–0.05 m; II: 0.050–0.225 m; and
III: 0.225–2.000) provided by the IsoSource multi-source mixing model
(Phillips and Gregg, 2003) (displayed in the form of gray histograms).
Density distribution functions following the SIAR Bayesian model (Parnell et
al., 2010) (gray lines). “Sh” (“De”) stands for the virtual experiments
where the soil has a shallow (deep) groundwater table, while “Dr” and
“We” stand for when the soil is dry or wet at the surface. Suffices “lT”
and “hT” refer to “low” and “high” transpiration rate simulations. The
colored vertical lines give xI_Couv,
xII_Couv, and xIII_Couv, the
relative contributions to transpiration from layers I, II, and III simulated
by the analytical model of Couvreur et al. (2012). The color-shaded areas
associated with xI_Couv,
xII_Couv, and xIII_Couv refer to
their uncertainty associated with input data uncertainty.
Figure 7 gives the relative contributions from soil layers I, II, and III
(upper, middle, and lower panels, respectively) to T provided by IsoSource,
the multi-source mixing model of Phillips and Gregg (2003) (xIsoS,
in %, displayed in the form of gray histograms), and by SIAR, the Bayesian
method of Parnell et al. (2010) (xSIAR, in %, gray probability
density curves). The colored vertical lines are
xI_Couv, xII_Couv, and
xIII_Couv, the simulated
S(z)dzT/(Δx⋅Δy) ratios from layers I, II,
and III. The color-shaded areas associated with
xI_Couv, xII_Couv, and
xIII_Couv refer to their uncertainty by accounting for
the uncertainty of the input data. As for Fig. 5, δTi_Couv is reported above each plot along with its
standard deviation. The xJ_IsoS probability distribution was
observed to be either narrow (e.g., for the experiment with the deep
groundwater table and the dry upper layer at a low transpiration rate –
DeDr_lT/layer I, Fig. 7m) or broad (e.g., for the experiment with the deep
groundwater table and the wet upper layer at a high transpiration rate –
DeWe_hT/layer I); i.e., the range of possible solutions for
xJ_IsoS was relatively small or large (10 and 100 %,
respectively, for these two examples). In general, both IsoSource and SIAR
results were in good agreement: the xSIAR's most frequent value
(MFV, at the peak of the density distribution curve) was in most cases either
located near the median value of the xIsoS probability range (e.g.,
for the experiment with the shallow groundwater table and wet upper layer at
a low transpiration rate – ShWe_lT/layer I, Fig. 7g) or matched exactly
the xIsoS unique value (i.e., for the experiment with the deep
groundwater table and dry upper layer at a low transpiration rate –
DeDr_lT/layer I, Fig. 7m). In contrast, the statistical methods succeeded
best in providing x estimates similar to those of the model of Couvreur et
al. (2012) in the case of a shallow groundwater table and at low T only
(Fig. 7a–c and g–i), i.e., when water availability was high and root
compensation was low. In these cases, xI_Couv was
included in the estimated xI_IsoS range and the mean
absolute difference (MD) between xJ_Couv and xSIAR
MFV was equal to 8.6 %. This difference was greatest (129.2 %) for
experiment DeDr_lT, when hydraulic redistribution by the roots was
simulated by the analytical model (Fig. 7m–o).
Most frequent value (mfv) and range of the density distribution
curve of the relative contribution to transpiration across eight defined soil
layers as determined by the Bayesian method of Parnell et al. (2010)
(xSIAR, %) and the mean relative contribution (with standard
deviation) provided by the analytical model of Couvreur et al. (2012)
(xCouv, %). Profiles of relative contribution were computed for
eight soil–plant virtual experiments differing in the depth of the
groundwater table (shallow – Sh/deep – De), the soil surface water status
(dry – Dr/wet – We), and the plant transpiration rate (low – lT/high –
hT).
Soil layer (m)Shallow groundwater table (Sh) Dry surface conditions (ShDr) Wet surface conditions (ShWe) Low T (ShDr_lT) High T (ShDr_hT) Low T (ShWe_lT) High T (ShWe_hT) xSIARxCouv (1SD)xSIARxCouv (1SD)xSIARxCouv (1SD)xSIARxCouv (1SD)mfv(range)(%)mfv(range)(%)mfv(range)(%)mfv(range)(%)(%)(%)(%)(%)0–0.021(0–35)5(1)6(0–37)11(1)18(0–48)13(1)16(0–53)11(1)0.02–0.051(0–35)7(1)5(0–38)9(1)13(0–42)10(1)7(0–43)9(1)0.05–0.113(0–41)11(1)10(0–48)11(1)11(0–41)13(1)7(0–41)11(1)0.11–0.22515(0–57)10(1)14(0–47)10(1)11(0–46)10(1)3(0–43)10(1)0.225–0.419(0–57)11(0)16(0–55)10(0)16(0–53)9(0)16(0–49)10(0)0.4–0.7516(0–55)16(0)17(0–48)14(0)18(0–44)13(1)15(0–48)14(0)0.75–1.517(0–52)27(2)18(0–46)23(2)16(0–48)21(2)16(0–53)23(2)1.5–217(0–59)14(2)17(0–47)12(2)15(0–52)11(2)16(0–51)12(2)Soil layer (m)Deep groundwater table (De) Dry surface conditions (DeDr) Wet surface conditions (DeWe) Low T (DeDr_lT) High T (DeDr_hT) Low T (DeWe_lT) High T (DeWe_hT) xSIARxCouv (1SD)xSIARxCouv (1SD)xSIARxCouv (1SD)xSIARxCouv (1SD)mfv(range)(%)mfv(range)(%)mfv(range)(%)mfv(range)(%)(%)(%)(%)(%)0–0.021(0–42)-170(16)1(0–41)5(1)2(0–49)24(2)10(0–52)12(1)0.02–0.051(0–42)-17(1)2(0–45)8(1)17(0–55)18(2)13(0–54)9(1)0.05–0.111(0–44)19(6)5(0–47)12(1)16(0–58)21(2)16(0–51)12(1)0.11–0.2253(0–55)28(5)11(0–51)10(1)1(0–39)3(0)12(0–43)9(1)0.225–0.47(0–75)33(4)17(0–51)11(0)0,8(0–38)1(0)9(0–38)10(0)0.4–0.7515(0–68)57(3)17(0–56)16(0)5(0–46)7(1)15(0–53)14(0)0.75–1.516(0–74)98(1)16(0–54)26(2)16(0–51)17(2)16(0–45)23(2)1.5–217(0–76)51(4)18(0–53)13(2)18(0–53)9(2)16(0–46)12(2)
When considering eight soil layers instead of three, uncertainties in the
assessment of the relative contributions to T as determined by IsoSource
increased. The estimated probability ranges increased in most of the cases
(results not shown). However, it considerably improved the results of the
Bayesian model: the mean absolute difference between xJ_Couv
and the most frequent xSIAR value was equal to 4.7 % for the
scenarios with a shallow groundwater table and low transpiration rate and
equal to 52.1 % in the case of hydraulic redistribution by the roots
(Table 3).
Independent of the number of defined soil layers, lowering the value of
increment to 5 % in IsoSource refined the analysis where the probability
distribution was already narrow (i.e., in the case of a well-identified
xIsoS value, e.g., Fig. 7m), while it produced distributions that
were flatter and contained fewer gaps when no clear solutions had emerged
before (results not shown). Artificially increasing the value of tolerance
had the consequence that more solutions to Eq. (10) were found for each
experiment–transpiration value–layer combination and vice versa
(results not shown). An increase or decrease of a factor 2 in the number of
runs as well as the number of runs to be discarded from the analysis had only
a marginal impact on the density distribution curves obtained with the SIAR
model in the case of three or four soil layers.
The modeling exercise illustrated the disparities of outcome between the
graphical method on the one hand and the statistical and mechanistic methods
on the other: there simply cannot be single or multiple “root water uptake
depths”, but rather a continuous RWU profile or statistical solutions of
contributions to transpiration (provided by IsoSource and SIAR). Significant
changes in δTi do not necessarily mean important changes in
the depth of RWU, but rather a slight (but nevertheless significant)
modification of the RWU profile. The authors believe that the relatively
novel statistical tools presented in this review should therefore be
preferred over the graphical inference method, especially since the two
former are available as user-friendly programs and packages and do not
require significant computing time, and therefore can be run locally on a
personal computer. As highlighted in this series of virtual experiments, the
Bayesian method showed for the case of two and three soil layers much more
convincing results than the method of Phillips and Gregg (2003). The Bayesian
method was particularly efficient in the case of eight soil layers,
illustrating the interest of reaching the best vertical resolution and
maximizing the number of identified potential sources (Table 3). Note that no
prior information on the relative contributions to T from the different
soil layers was used when running the SIAR program; i.e., the authors opted
for flat priors. This can be changed by the user, based on additional
collected data such as, for instance, information on root architecture and
function across the soil profile or information on soil hydraulic properties
and water status.
One can show from this inter-comparison of methods that labeling of soil
water in either 18O or 2H has potentials for improving the
different methods presented here theoretically if water is taken up by the
roots from the labeled region predominantly. However, this was never the case
when considering the results of the analytical model. A dual isotope
(18O or 2H) labeling pulse experiment that would artificially
disconnect the strong link between δ18O and δ2H would on
the other hand much more constrain the inverse problem and provide more
accurate estimates.
Challenges and progressOffline destructive versus online nondestructive isotopic
measurements in plant and soil waters
For determination of δS, soil profiles are usually
destructively sampled, typically with an auger down to a depth of a few
centimeters (Rothfuss et al., 2010) to a few meters (Moreira et al., 2000)
(see Table 1), depending on the depths of the root system and of the water
table. The sampling depth resolution should, when possible, match the
exponential decrease in isotopic composition (Wang et al., 2010), and it
should capture sudden variations with time at the soil surface due to
precipitation, i.e., be maximal at the surface and minimal deeper in the soil
profile where isotopic dynamics are less pronounced. Not doing this can lead
to a situation where source partitioning is not feasible from isotopic
measurements. Under field conditions (i.e., ∼ 95 % of the studies
reviewed in this work, summarized in Table 1) soil material is generally not
a limiting factor, and thus can be sampled twice or thrice to average out or
characterize lateral heterogeneity without significant disturbance of the
soil.
Water from plant and soil materials is predominantly extracted by cryogenic
vacuum distillation (Araguás-Araguás et al., 1995; Ingraham and
Shadel, 1992; Koeniger et al., 2011; Orlowski et al., 2013; West et al.,
2006). Accuracy of this extraction method was shown to be maximal at higher
water content and for sandy soils and lower for soils with high clay content
(e.g., Koeniger et al., 2011; West et al., 2006). In the latter case,
extraction times should be longer and temperatures higher to mobilize water
strongly bound to clay particles, which has a distinct isotopic composition
from that of pore “bulk” water (Araguás-Araguás et al., 1995;
Ingraham and Shadel, 1992; Oerter et al., 2014; Sofer and Gat, 1972).
Certainly one of the main limitations of all isotopic approaches for
quantifying RWU is the destructive character of isotopic sampling (see
Sect. 3.1) and associated offline analyses (Sect. 2.2 and 2.3). This usually
leads to poor spatial (maximum a few cm2) as well as temporal (minimum
hourly) resolution of the inferred results, when comparing with measuring
frequency of other soil and plant state variables, e.g., soil water content
and potential, and leaf water potential (Sect. 3.2.2). In addition, one may
question the representativeness of plant samples, in which tissues and thus
water with very different water
residence time is mixed.
Recently developed methods take advantage of laser-based spectroscopy which
allows in situ, online, and continuous
isotopic measurements in the gas phase at high frequency. These methods rely
on coupling a laser spectrometer (e.g., wavelength-scanned cavity ring-down
spectroscopy – WS-CRDS, Picarro Inc., Santa Clara, CA, USA; cavity-ring-down
laser absorption spectroscopy – CRLAS; and off-axis integrated cavity output
spectroscopy – ICOS, Los Gatos Research, Los Gatos, USA) with specific soil
gas sampling probes consisting of gas-permeable microporous polypropylene
membranes or tubing. These membranes or tubing exhibit strong hydrophobic
properties, while their microporous structures allow the intrusion and
collection of soil water vapor. Several authors (Gaj et al., 2016; Gangi et
al., 2015; Herbstritt et al., 2012; Oerter et al., 2016; Rothfuss et al.,
2013; Sprenger et al., 2015; Volkmann and Weiler, 2014) were able to
determine the soil liquid water isotopic composition in a nondestructive (yet
invasive) manner from that measured in the collected soil water vapor
considering thermodynamic equilibrium between vapor and liquid phases in the
soil. In contrast to “traditional” isotopic methods, these novel isotopic
monitoring methods also have the distinct advantage of determining soil
liquid water isotopic composition at very low water content, since water
vapor, in contrast to soil liquid water, is not limited for analysis. These
novel methods allow a vertical resolution down to 1 cm and an approximately
hourly time resolution. However, they do not allow horizontal resolution
along the tube, and the laser spectrometers could be, as pointed out by
Gralher et al. (2016) for the specific case of a Picarro WS-CRDS,
significantly sensitive to the carrier gas used. In their opinion papers,
McDonnell (2014) and Orlowski et al. (2016a) urged a comparison between
methods, which was addressed by Orlowski et al. (2016b) and Pratt et
al. (2016) (for vapor measurements only).
In the coming years, effort should be made towards developing novel methods
for a direct and nondestructive determination of δTi based on
the use of gas-permeable membranes, which was recently initiated for trees
(Volkmann et al., 2016a). This should be further tested for other (non-woody)
plant species. This will imply the major challenge of not disrupting the
water columns in the active xylem vessels when installing such a
membrane-based system. Another potential issue to be investigated is the
species-specific extent of water exchange between xylem and phloem conductive
tissues which might lead to isotopic “contamination” of the xylem sap water
(Farquhar et al., 2007).
Call for a coupled experiment–modeling approach for
determination of plant water sources on the basis of isotopic data
In order to fully benefit from the potential of water stable isotopic
analysis as a tool for partitioning
transpiration flux, the authors call for the development of approaches making
use of physically based models for RWU and isotopic fractionation to analyze
experimental data, especially since several soil–vegetation–atmosphere
transfer (SVAT) models are available that can simulate flow of isotopologues
in the soil and the plant (i.e., SiSPAT-Isotope, Braud et al., 2005;
Soil-litter-iso, Haverd and Cuntz, 2010; R-SWMS, Meunier et al., 2017;
TOUGHREACT, Singleton et al., 2004; HYDRUS, Sutanto et al., 2012).
To the authors' knowledge, there are only a few studies which attempted to do
so. Rothfuss et al. (2012) ran an experiment under controlled laboratory
conditions where they measured on four dates (corresponding to four different
stages of vegetation and therefore root development) soil water potential and
isotopic composition profiles, and root length density distribution profiles.
In their experiment, the isotopic composition of transpiration was known. The
authors used a global optimization algorithm to obtain the set of parameters
of SiSPAT-Isotope that best reflected the experimental dataset. Distributions
of RWU could be determined on
these four dates. Also, in the study of Mazzacavallo and Kulmatiski (2015),
the RWU model of HYDRUS could
be parameterized during a labeling (heavy water 2H2O) pulse
experiment on the basis of measurements of xylem water hydrogen and oxygen
isotopic compositions. This provided insights into the existence of niche
complementarity between tree (mopane) and grass species. Note, however, that
this HYDRUS version did not incorporate isotopic transport through the soil
and the roots.
Another example is the work of Ogle et al. (2004), who were able to
reconstruct active root area and RWU profiles from isotopic measurements
using the 1-D analytical macroscopic model of Campbell (1991) in a Bayesian
framework (root area profile and deconvolution algorithm – RAPID). By
assuming normal a priori distributions for the xylem water oxygen and
hydrogen isotopic compositions and considering prior knowledge on RWU
distribution (i.e., synthetic information based on measurements of other
studies), Ogle et al. (2004) obtained a posteriori distributions of x of a
desert shrub (Larrea tridentate).
Simple analytical models, such as the formulation of Couvreur et al. (2012),
can be applied and confronted with isotopic data. In comparison with
statistical tools, such physical models provide profiles with high spatial
resolution and lower uncertainty, on the condition that all required
(isotopic) data are
available. We recognize that in comparison with the statistical and
conceptual methodologies presented in this review, using a physical
(analytical or numerical) model implies the measurements of additional state
variables to be fed as input to the model, and of one parameter
(Kplant) (when considering the assumption Kplant=Kcomp valid; see Appendix B). Some of these variables are
laborious to obtain (e.g., RLD) or not straightforward to measure
(HS, HL, and T) – especially in the field – but are
mandatory to be able to determine contributions to T across a set of
identified water sources. In addition, they are necessary to gain insights
into soil–plant interactions, e.g., dynamics of the root function (active
versus non-active roots in the soil profile) in water uptake and, thus,
quantify the disconnection between measured RLD and the prognostic variable
SSF (see Appendix B1). To do this, controlled conditions in state-of-the-art
climatic chambers are ideal, as they allow for a reduction of the inherent
spatial heterogeneity present under natural conditions and, thus, the
deconvolution of environmental effects on RWU. Experimental facilities that
not only control atmospheric forcing (soil upper boundary conditions for
latent and heat flow), but also impose lower boundaries for the soil
compartment (e.g., drainage and capillary rise dynamics) and provide the
means to close the hydrological balance are required. Moreover, macrocosm
experiments (∼ m3 scale) should be favored over mesocosm
(∼ dm3 scale) experiments to avoid or reduce inherent side effects
that would ultimately hamper the mimicking of natural conditions.
Conclusion
Root water uptake is a key process in the global water cycle. More than
50 % of total terrestrial evapotranspiration crosses plant roots to go
back to the atmosphere (Jasechko et al., 2013). Despite its importance,
quantification of RWU remains difficult due to the opaque nature of the soil
and the spatial and temporal variability of the uptake process.
Water stable isotopic analysis is a powerful and valuable tool for the
assessment of plant water sources. In an inverse modeling framework,
water isotopic analysis of plant tissues
and soil also allows for obtaining of species-specific parametrization of
physically based analytical and numerical RWU models. They provide a unique
way to tackle the difficulty of disentangling actual RWU profiles with root
traits and characteristics. Yet our literature review revealed that isotopic
data have been up to now mainly used to assess water sources under natural
ecosystems using statistical approaches. Only 4 % of current scientific
publications demonstrate the use of a physically based model for analyzing
isotopic data.
Three methods (representing 90 % of the studies) have been used for
partitioning water sources: the “direct inference” method, the
two-end-member mixing model and two examples of multi-source mixing models.
We performed a comparison between these methods. We were able to quantify the
impact of the definition of the plant water sources (i.e., whether they are
spatially disjoint or not and whether their isotopic composition values are
significantly different or not) on the outcome of the two-end-member mixing
model. We highlighted the importance of systematically reporting
uncertainties along with estimates of contribution to T of given plant
water sources. The inter-comparison also illustrated the limitations of the
graphical inference method and the multi-source mixing model of Phillips and
Gregg (2003), whereas it underlined the good performance of the Bayesian
approach of Parnell et al. (2010), which uses a more rigorous statistical
framework, if the number of considered water sources matches the number of
isotopic measurements in the soil profile. However, in contrast to the
analytical model, none of the graphical and statistical methods was able to
locate and quantify hydraulic redistribution of water.
Finally, the authors call for a generalization of coupled approaches relying
on the confrontation between labeling experiments under controlled conditions
and three-dimensional RWU numerical modeling. This type of approach could be
used in agronomy to quantify RWU as a function of plant genotype and soil
structure. It also has great potential for quantifying RWU in seminatural and
natural ecosystems for understanding the mechanisms underlying the vegetation
feedbacks to the atmosphere in the contexts of land cover and climate
changes.
Data used by the authors are available in Table 2.
List of symbols.
SymbolDescriptionDimensionEquationMeasured (m)/numbersimulated (s)/prescribed (p)C, CS, CA, CB, CTiWater stable isotopic concentration, soil water stable isotopic concentration, sources A and B water stable isotopic concentrations, xylem sap water isotopic concentration, root water uptake isotopic concentrationM L-32, 3, 6a, 6bmE, EiEvaporation rate for 1H216O isotopologue, Evaporation rate for 1H2H16O or 1H218O isotopologueL3 T-1B1–B4m/shMatric headLmHeq, HL, HSSoil water equivalent and leaf water potentials, total soil water potentialPmJA, JB, JTiFluxes of water originating from water sources A and B, and at the plan tillerL3 T-16bmJAi, JBi, and JTiiFluxes of isotopologues originating from water sources A and B, and at the plan tillerM T-16amKplant, KcompPlant and compensatory conductances to water flowL3 P-1 T-1B1–B4m/pMw, MiMolar masses of water and isotopologue (1H2H16O or 1H218O)M L-33mRLDRoot length densityL L-3B3m/pRLD1DRoot length density per unit of surface areaL L-1m/pRrefVSMOW hydrogen or oxygen stable isotopic ratio–3mS, SuniH, ScompTotal root water uptake sink term as simulated by the analytical model of Couvreur et al. (2012), Root water uptake sink term under uniform soil water potential distribution, compensatory root water uptake sink term.L3 L-3 T-11–4, B4, B5sSSFStandard sink fraction–B2, B4, B4′m/pt, ΔtTime, time stepT11mTTranspiration fluxL3 T-12, 4a, 4b, B1, B3, B4mx, xj, xCouv, xJ_Couv, xJ_IsoS, xJ_SIARRelative contribution to transpiration, source j relative contribution to transpiration, continuous and integrated (layer J) relative contributions to transpiration as simulated by the analytical model of Couvreur et al. (2012), integrated (layer J) relative contributions to transpiration as determined by the IsoSource and SIAR models of Phillips and Gregg (2003) and Parnell et al. (2010). Relative contribution to transpiration under conditions of uniform soil water potential–7, 8b, 9, 9′sz, zj, zj+1, Δzj, zmax, zRWUSoil depth, soil depth of layers j and j+1, thickness of soil layer j, depth of the root system, “mean root water uptake depth”L4b, 5, B2–B4′m/pδ, δ2H, δ18O, δsource, δsurf, δS, δS,j, δS,J, δA, δB, δTi, δTi,m, δTi_Couv, δEWater stable isotopic composition, water hydrogen and oxygen stable isotopic compositions, source, soil surface, soil water, soil layer j and J water isotopic composition, sources A and B water stable isotopic compositions, isotopic composition of xylem sap water at the plant tiller, isotopic composition of xylem sap water measured at the plant tiller, isotopic composition of xylem sap water at the plant tiller as simulated by the model of Couvreur et al. (2012)– (expressed in ‰)3–5, 7–9, 11m/sεjResidual error term– (expressed in ‰)9′sθSoil volumetric water contentL3 L-35, 11mρVolumetric mass of waterM L-33mσx, σδA, σδB, σδTi, σδTi_Couv, σxStandard errors associated with the measurements of x, δA, δB, and δTi and estimated uncertainty of δTi_Couv as simulated by the analytical model of Couvreur et al. (2012), error associated with the estimation of the relative contribution to T of water source A in the case of two distinct sources– (expressed in ‰)8a, 8bsτIsotopic tolerance– (expressed in ‰)10pThe macroscopic RWU model of Couvreur et al. (2012)Presentation of the model
In the approach of Couvreur et al. (2012), RWU is based on
physical equations describing the water flow processes but without the need
of the full knowledge of the root system architecture and local hydraulic
parameters. Instead, three macroscopic parameters are needed. The first
equation defines plant transpiration:
JTi=Kplant⋅Heq-HL,
where JTi (L3 T-1) is the sap flow rate in the root tiller
and is considered to be equal to the transpiration rate, and Kplant
(L3 P-1 T-1) is the plant conductance to water flow (the
first macroscopic parameter of Couvreur et al., 2012's model). HL
(P) is the leaf water potential and Heq (P) the “plant averaged
soil water potential” defined as the mean soil water potential “sensed” by
the plant root system in the one-dimensional (vertical) space:
Heq=∫zSSF(z)⋅HS(z),
where z is the soil depth, HS (P) is the total soil water
potential, and SSF (–) is the standard sink term fraction (the second
macroscopic parameter of the model of Couvreur et al., 2012). SSF is defined
as the RWU fraction under the condition of totally uniform soil water
potential (i.e., when HS(x,y,z)=HS=cst). Under
such conditions, if all the root segments had the same radial conductivity
(and the xylem conductance would not be limiting), the RWU distribution in a
uniform soil water potential profile would be exactly the same as the root
length density per unit of the surface area (RLD1D of dimension
(L L-1)) profile. SSF could be defined as
SSF(z)=SuniH(z)dzqTi≈RLD1D(z)⋅dz∫zRLD1D(z)⋅dz,
where qTi=JTi/(Δx.Δy) represents the sap
flow rate in the root tiller per unit surface area (L T-1), and
SuniH (T-1) is the RWU sink term under a uniform soil water
potential profile. The RWU under conditions of heterogeneous soil water
potential is described with the following equation:
S(z)=SuniH(z)+Scomp(z)=qTi⋅SSF(z)+Kcomp⋅Hs(z)-Heq⋅SSF(z)V(z),
where Kcomp (L3 P-1 T-1) is the compensatory
conductance, Scomp (L3 T-1) is the compensatory RWU
accounting for the non-uniform distribution of the soil water potential and
V(z) is the volume of soil considered. If the soil water potential is
uniform, this term vanishes from the equation, as HS=Heq
for any z, and water is extracted from the soil proportionally to RLD. When
the water potential at a certain location is smaller (more negative, which
means drier) than Heq, less water is extracted from this location.
On the other hand, when the soil is wetter (HS less negative), a
larger amount of water can be taken up from the same location as compared.
Note that if HS<Heq and if the compensatory term is
higher than the first one, S can become positive, and water is released to
the soil (i.e., hydraulic redistribution). From Eq. (B4), it can be concluded
that hydraulic redistribution will preferably occur when qTi is
small and when large soil water potential gradients exist. Plant root
hydraulic characteristics will control compensation through the
Kcomp term. The importance of the compensatory RWU term has been
discussed in the literature for a long time (e.g., Jarvis, 1989). Except if
plants activate specific mechanisms to avoid it, compensation always takes
place under natural conditions due to the spatially heterogeneous
distribution of soil water potential (Javaux et al., 2013).
A simplifying hypothesis that can be made (Couvreur et al., 2014, 2012) is to
consider that Kplant and Kcomp are equal, which
substituted in Eq. (B4) leads to
S(z)=SSF(z)⋅Kplant⋅Hs(z)-HL/V(z).(B4′)
Finally, the uptake of water stable isotopologues, i.e., the “isotopic sink
term” (Si (M T-1)), is defined as
Si(z)=S(z)⋅C(z),
where C (M L-3) is the water isotopic concentration.
Running the model for the inter-comparison
The root water uptake (S) depth profiles and corresponding δTi_Couv were simulated using the model of Couvreur et
al. (2012) (Eq. B4′) for all eight scenarios. For this, HS,
δS, and RLD input data were interpolated at a 0.01 m
vertical resolution and the resistance of the xylem vessels was assumed to be
negligible, so that HTi=HL. A Kplant value of
2.47 × 10-6 h-1 was taken and was determined based on
concomitant T, Heq and HL data measured for
Festuca arundinacea. δTi_Couv was then
calculated from Eq. (4b) (Sect. 2.3). From these simulations, the depth
profiles of xCouv (%), the ratio S(z)dzT/(Δx⋅Δy) at each interpolated depth z was determined, and
xJ_Couv, the ratio SJ⋅dzJ(T/(Δx⋅Δy)) from each of the integrated soil layers J (J≤ III or J≤ VIII) were calculated. In order to account for
uncertainty of the input data (i.e., total soil water potential and oxygen
isotopic composition HS and δS, and root length
density RLD), the model was run a 1000 times where a single offset randomly
selected between -5 and +5 cm, -0.2 and +0.2 ‰, and -0.1
and +0.1 cm cm-3 was added to the initial values (reported Table 2)
of HS, δS, and RLD, respectively. By doing this we
obtained a posteriori distributions of S and corresponding
δTi_Couv standard deviations
(σδTi_Couv).
Inter-comparison methodology
The graphical inference method (GI), the two-end-member mixing model (TM),
and multi-source mixing models IsoSource (Phillips and Gregg, 2003) and SIAR
(Parnell et al., 2010) were compared to each other in the following manner
for each of the eight virtual experiments.
Single (or multiple) mean RWU depth(s) (z¯) were graphically
identified following the GI method as the depth(s) where δTi_Couv=δS. The uncertainty of method
GI was determined on the basis of the δTi_Couv a
posteriori distribution: by taking into account
σδTi_Couv, z¯ results were
translated into “RWU layers”.
relative contribution of RWU to transpiration (xTM, %) to two
defined soil layers (either conjoint: 0–0.225 and 0.225–2.00 m or
disjoint: 0–0.225 and 1.75–2.00 m) were determined using the TM approach.
For this, representative values for the water oxygen isotopic compositions of
these soil layers were computed using Eq. (5) which uses soil volumetric
water content (θ, in m3 m-3) as input data. θ
distribution was obtained from HS distribution and the van
Genuchten (1980) closed-form equation. Values for its different parameters,
i.e., the soil residual and saturated water contents (θres and
θsat), and the shape parameters related to air entry potential
and pore-size distribution (α and n) were equal to 0.040 and
0.372 m3 m-3, 0.003 cm-1, and 3.3, respectively.
Possible range of xJ_IsoS: the relative
contribution of RWU to transpiration for each of the integrated soil layers
following the IsoSource model was computed based on the smoothed
δS,J profile and δTi_Couv by
solving the following equation:∑JxJ_IsoS⋅δS,J≤δTi_Couv±t,with τ=σδTi_Couv.
δS,J was computed similarly to the TM method.
Density distribution of xJ_SIAR, the relative
contribution of RWU to transpiration for each of the three (or eight) soil
layers following the SIAR model was determined based on smoothed δS,J profile and δTi_Couv data as well.
To compare with the IsoSource model (i) the number of δTi
replicates was fixed to three and equal to δTi_Couv-σδTi_Couv, δTi_Couv, and δTi_Couv+σδRWU_Couv, and
(ii) xJ_SIAR was computed at a 10 % increment (i). No
prior information on the relative contributions to T was used to run the
model; i.e., we opted for flat priors;
Results obtained at steps (i)–(iv) were compared to each other.
Sensitivity of IsoSource to the values of i and τ, and of SIAR to
values of arguments iterations and burnin, were finally
briefly tested.
The Supplement related to this article is available online at doi:10.5194/bg-14-2199-2017-supplement.
Youri Rothfuss reviewed the published literature. Youri Rothfuss and Mathieu Javaux
designed the virtual experiments, analyzed, and discussed the obtained
results.
The authors declare that they have no conflict of
interest.
Acknowledgements
This study was conducted in the framework of and with means from the
Bioeconomy Portfolio Theme of the Helmholtz Association of German Research
Centers. The authors would like to thank their colleagues Harry Vereecken,
Jan Vanderborght, and Nicolas Brüggemann for their comments on the
initial draft. We are grateful to Matthias Sprenger, two anonymous reviewers,
and associate editor Michael Bahn for their ideas and suggestions along the
discussion/review process. The article
processing charges for this open-access publication were
covered by a Research Centre of the Helmholtz
Association. Edited by: M. Bahn
Reviewed by: M. Sprenger and two anonymous referees
ReferencesAndrade, J. L., Meinzer, F. C., Goldstein, G., and Schnitzer, S. A.: Water
uptake and transport in lianas and co-occurring trees of a seasonally dry
tropical forest, Trees-Struct. Funct., 19, 282–289,
10.1007/s00468-004-0388-x, 2005.Araguás-Araguás, L., Rozanski, K., Gonfiantini, R., and Louvat, D.:
Isotope effects accompanying vacuum extraction of soil-water for
stable-isotope analyses, J. Hydrol., 168, 159–171,
10.1016/0022-1694(94)02636-P, 1995.Araki, H. and Iijima, M.: Stable isotope analysis of water extraction from
subsoil in upland rice (Oryza sativa L.) as affected by drought and
soil compaction, Plant Soil, 270, 147–157, 10.1007/s11104-004-1304-2,
2005.Armas, C., Kim, J. H., Bleby, T. M., and Jackson, R. B.: The effect of
hydraulic lift on organic matter decomposition, soil nitrogen cycling, and
nitrogen acquisition by a grass species, Oecologia, 168, 11–22,
10.1007/s00442-011-2065-2, 2012.Asbjornsen, H., Mora, G., and Helmers, M. J.: Variation in water uptake
dynamics among contrasting agricultural and native plant communities in the
Midwestern US, Agr. Ecosyst. Environ., 121, 343–356,
10.1016/j.agee.2006.11.009, 2007.Bachmann, D., Gockele, A., Ravenek, J. M., Roscher, C., Strecker, T.,
Weigelt, A., and Buchmann, N.: No evidence of complementary water use along a
plant species richness gradient in temperate experimental grasslands, PLoS
ONE, 10, e0116367, 10.1371/journal.pone.0116367, 2015.Bariac, T., Gonzalezdunia, J., Tardieu, F., Tessier, D., and Mariotti, A.:
Spatial variation of the isotopic composition of water (O-18, H-2) in organs
of aerophytic plants .1. Assessment under Laboratory Conditions, Chem. Geol.,
115, 307–315, 10.1016/0009-2541(94)90194-5, 1994.Barnes, C. J. and Allison, G. B.: The distribution of deuterium and O-18 in
dry Soils. 1. Theory, J. Hydrol., 60, 141–156,
10.1016/0022-1694(83)90018-5, 1983.Barthold, F. K., Tyralla, C., Schneider, K., Vache, K. B., Frede, H. G., and
Breuer, L.: How many tracers do we need for end member mixing analysis
(EMMA)? A sensitivity analysis, Water Resour. Res., 47, W08519,
10.1029/2011wr010604, 2011.Beyer, M., Koeniger, P., Gaj, M., Hamutoko, J. T., Wanke, H., and
Himmelsbach, T.: A deuterium-based labeling technique for the investigation
of rooting depths, water uptake dynamics and unsaturated zone water transport
in semiarid environments, J. Hydrol., 533, 627–643,
10.1016/j.jhydrol.2015.12.037, 2016.Bijoor, N. S., McCarthy, H. R., Zhang, D. C., and Pataki, D. E.: Water
sources of urban trees in the Los Angeles metropolitan area, Urban Ecosyst.,
15, 195–214, 10.1007/s11252-011-0196-1, 2012.Boujamlaoui, Z., Bariac, T., Biron, P., Canale, L., and Richard, P.:
Profondeur d'extraction racinaire et signature isotopique de l'eau
prélevée par les racines des couverts végétaux, C. R.
Geosci/, 337, 589–598, 10.1016/j.crte.2005.02.003, 2005.Braud, I., Bariac, T., Gaudet, J. P., and Vauclin, M.: SiSPAT-Isotope, a
coupled heat, water and stable isotope (HDO and H218O) transport
model for bare soil. Part I. Model description and first verifications, J.
Hydrol., 309, 277–300, 10.1016/j.jhydrol.2004.12.013, 2005.Brunel, J. P., Walker, G. R., and Kennettsmith, A. K.: Field validation of
isotopic procedures for determining sources of water used by plants in a
semiarid environment, J. Hydrol., 167, 351–368,
10.1016/0022-1694(94)02575-V, 1995.Caldwell, M. M. and Richards, J. H.: Hydraulic Lift – Water efflux from
upper roots improves effectiveness of water-uptake by deep roots, Oecologia,
79, 1–5, 10.1007/Bf00378231, 1989.
Campbell, G. S.: Simulation of water uptake by plant roots, in: Modeling
Plant and Soil Systems, edited by: Hanks, J. and Ritchie, J. T., American
Society of Agronomy, Madison, WI, 1991.Carminati, A., Kroener, E., and Ahmed, M. A.: Excudation of mucilage (Water
for Carbon, Carbon for Water), Vadose Zone J., 15,
10.2136/vzj2015.04.0060, 2016.Chimner, R. A. and Cooper, D. J.: Using stable oxygen isotopes to quantify
the water source used for transpiration by native shrubs in the San Luis
Valley, Colorado USA, Plant Soil, 260, 225–236,
10.1023/B:Plso.0000030190.70085.E9, 2004.Christophersen, N. and Hooper, R. P.: Multivariate-analysis of stream water
chemical-data – the use of principal components-analysis for the end-member
mixing problem, Water Resour. Res., 28, 99–107, 10.1029/91wr02518, 1992.Couvreur, V., Vanderborght, J., and Javaux, M.: A simple three-dimensional
macroscopic root water uptake model based on the hydraulic architecture
approach, Hydrol. Earth Syst. Sci., 16, 2957–2971,
10.5194/hess-16-2957-2012, 2012.Couvreur, V., Vanderborght, J., Draye, X., and Javaux, M.: Dynamic aspects of
soil water availability for isohydric plants: Focus on root hydraulic
resistances, Water Resour. Res., 50, 8891–8906, 10.1002/2014WR015608,
2014.
Craig, H. and Gordon, L. I.: Deuterium and oxygen-18 variations in the ocean
and marine atmosphere, in: Stable isotopes in oceanographic studies and
paleotemperatures, edited by: Tongiorgi, E., Proceedings, Spoleto, Italy,
Consiglio Nazionale delle Ricerche, Lab. de Geologia Nucleare, Pisa, Italy,
9–130, 1965.Dawson, T. E.: Hydraulic lift and water-use by plants – implications for
water-balance, performance and plant-plant interactions, Oecologia, 95,
565–574, 10.1007/BF00317442, 1993.Dawson, T. E. and Ehleringer, J. R.: Streamside trees that do not use stream
water, Nature, 350, 335–337, 10.1038/350335a0, 1991.Dawson, T. E. and Ehleringer, J. R.: Isotopic enrichment of water in the
woody tissues of plants – Implications for plant water source, water-uptake,
and other studies which use the stable isotopic composition of cellulose,
Geochim. Cosmochim. Ac., 57, 3487–3492, 10.1016/0016-7037(93)90554-A,
1993.Dawson, T. E. and Pate, J. S.: Seasonal water uptake and movement in root
systems of Australian phraeatophytic plants of dimorphic root morphology: A
stable isotope investigation, Oecologia, 107, 13–20, 10.1007/Bf00582230,
1996.Ellsworth, P. Z. and Williams, D. G.: Hydrogen isotope fractionation during
water uptake by woody xerophytes, Plant Soil, 291, 93–107,
10.1007/s11104-006-9177-1, 2007.Erhardt, E. B. and Bedrick, E. J.: A Bayesian framework for stable isotope
mixing models, Environ. Ecol. Stat., 20, 377–397,
10.1007/s10651-012-0224-1, 2013.
Farquhar, G. D., Cernusak, L. A., and Barnes, B.: Heavy water fractionation
during transpiration, Plant Physiol., 143, 11–18, 2007.Feikema, P. M., Morris, J. D., and Connell, L. D.: The water balance and
water sources of a Eucalyptus plantation over shallow saline groundwater,
Plant Soil, 332, 429–449, 10.1007/s11104-010-0309-2, 2010.Gaines, K. P., Stanley, J. W., Meinzer, F. C., McCulloh, K. A., Woodruff, D.
R., Chen, W., Adams, T. S., Lin, H., and Eissenstat, D. M.: Reliance on
shallow soil water in a mixed-hardwood forest in central Pennsylvania, Tree
Physiol., 36, 444–458, 10.1093/treephys/tpv113, 2016.Gaj, M., Beyer, M., Koeniger, P., Wanke, H., Hamutoko, J., and Himmelsbach,
T.: In situ unsaturated zone water stable isotope (2H and 18O)
measurements in semi-arid environments: a soil water balance, Hydrol. Earth
Syst. Sci., 20, 715–731, 10.5194/hess-20-715-2016, 2016.Gangi, L., Rothfuss, Y., Ogée, J., Wingate, L., Vereecken, H., and
Brüggemann, N.: A new method for in situ measurements of oxygen
isotopologues of soil water and carbon dioxide with high time resolution
Vadose Zone J., 14, 10.2136/vzj2014.11.0169, 2015.Goebel, T. S., Lascano, R. J., Paxton, P. R., and Mahan, J. R.: Rainwater use
by irrigated cotton measured with stable isotopes of water, Agr. Water
Manage., 158, 17–25, 10.1016/j.agwat.2015.04.005, 2015.Gonfiantini, R.: Standards for stable isotope measurements in natural
compounds, Nature, 271, 534–536, 10.1038/271534a0, 1978.Gralher, B., Herbstritt, B., Weiler, M., Wassenaar, L. I., and Stumpp, C.:
Correcting Laser-Based Water Stable Isotope Readings Biased by Carrier Gas
Changes, Environ. Sci. Technol., 50, 7074–7081, 10.1021/acs.est.6b01124,
2016.Grossiord, C., Gessler, A., Granier, A., Berger, S., Brechet, C., Hentschel,
R., Hommel, R., Scherer-Lorenzen, M., and Bonal, D.: Impact of interspecific
interactions on the soil water uptake depth in a young temperate mixed
species plantation, J. Hydrol., 519, 3511–3519,
10.1016/j.jhydrol.2014.11.011, 2014.Guderle, M. and Hildebrandt, A.: Using measured soil water contents to
estimate evapotranspiration and root water uptake profiles – a comparative
study, Hydrol. Earth Syst. Sci., 19, 409–425, 10.5194/hess-19-409-2015,
2015.Hastings, W. K.: Monte-carlo sampling methods using markov chains and their
applications, Biometrika, 57, 97–109, 10.2307/2334940, 1970.Haverd, V. and Cuntz, M.: Soil-Litter-Iso: A one-dimensional model for
coupled transport of heat, water and stable isotopes in soil with a litter
layer and root extraction, J. Hydrol., 388, 438–455,
10.1016/j.jhydrol.2010.05.029, 2010.Heinen, M.: Compensation in Root Water Uptake Models Combined with
Three-Dimensional Root Length Density Distribution, Vadose Zone J., 13,
10.2136/vzj2013.08.0149, 2014.Herbstritt, B., Gralher, B., and Weiler, M.: Continuous in situ measurements
of stable isotopes in liquid water, Water Resour. Res., 48, W03601,
10.1029/2011wr011369, 2012.Huang, L. and Zhang, Z. S.: Stable Isotopic Analysis on Water Utilization of
Two Xerophytic Shrubs in a Revegetated Desert Area: Tengger Desert, China,
Water, 7, 1030–1045, 10.3390/w7031030, 2015.Huber, K., Vanderborght, J., Javaux, M., and Vereecken, H.: Simulating
transpiration and leaf water relations in response to heterogeneous soil
moisture and different stomatal control mechanisms, Plant Soil, 394,
109–126, 10.1007/s11104-015-2502-9, 2015.Hupet, F., Lambot, S., Javaux, M., and Vanclooster, M.: On the identification
of macroscopic root water uptake parameters from soil water content
observations, Water Resour. Res., 38, 1300, 10.1029/2002wr001556, 2002.Ingraham, N. L. and Shadel, C.: A comparison of the toluene distillation and
vacuum heat methods for extracting soil-water or stable isotopic analysis, J.
Hydrol., 140, 371–387, 10.1016/0022-1694(92)90249-U, 1992.Isaac, M. E., Anglaaere, L. C. N., Borden, K., and Adu-Bredu, S.:
Intraspecific root plasticity in agroforestry systems across edaphic
conditions, Agr. Ecosyst. Environ., 185, 16–23,
10.1016/j.agee.2013.12.004, 2014.Jackson, P. C., Meinzer, F. C., Bustamante, M., Goldstein, G., Franco, A.,
Rundel, P. W., Caldas, L., Igler, E., and Causin, F.: Partitioning of soil
water among tree species in a Brazilian Cerrado ecosystem, Tree Physiol., 19,
717–724, 10.1093/treephys/19.11.717, 1999.Jarvis, N. J.: A simple empirical model of root water uptake, J. Hydrol.,
107, 57–72, 10.1016/0022-1694(89)90050-4, 1989.Jarvis, N. J.: Simple physics-based models of compensatory plant water
uptake: concepts and eco-hydrological consequences, Hydrol. Earth Syst. Sci.,
15, 3431–3446, 10.5194/hess-15-3431-2011, 2011.Jasechko, S., Sharp, Z. D., Gibson, J. J., Birks, S. J., Yi, Y., and Fawcett,
P. J.: Terrestrial water fluxes dominated by transpiration, Nature, 496,
347–350, 10.1038/Nature11983, 2013.Javaux, M., Couvreur, V., Vander Borght, J., and Vereecken, H.: Root Water
Uptake: From Three-Dimensional Biophysical Processes to Macroscopic Modeling
Approaches, Vadose Zone J., 12, 10.2136/vzj2013.02.0042, 2013.Javaux, M., Rothfuss, Y., Vanderborght, J., Vereecken, H., and
Brüggemann, N.: Isotopic composition of plant water sources, Nature, 536,
E1–E3, 10.1038/nature18946, 2016.Koch, P. L. and Phillips, D. L.: Incorporating concentration dependence in
stable isotope mixing models: a reply to Robbins, Hilderbrand and Farley
(2002), Oecologia, 133, 14–18, 10.1007/s00442-002-0977-6, 2002.Koeniger, P., Marshall, J. D., Link, T., and Mulch, A.: An inexpensive, fast,
and reliable method for vacuum extraction of soil and plant water for stable
isotope analyses by mass spectrometry, Rapid Commun. Mass Sp., 25,
3041–3048, 10.1002/Rcm.5198, 2011.Kulmatiski, A., Beard, K. H., and Stark, J. M.: Exotic plant communities
shift water-use timing in a shrub-steppe ecosystem, Plant Soil, 288,
271–284, 10.1007/s11104-006-9115-2, 2006.Kurz-Besson, C., Otieno, D., do Vale, R. L., Siegwolf, R., Schmidt, M., Herd,
A., Nogueira, C., David, T. S., David, J. S., Tenhunen, J., Pereira, J. S.,
and Chaves, M.: Hydraulic lift in cork oak trees in a savannah-type
Mediterranean ecosystem and its contribution to the local water balance,
Plant Soil, 282, 361–378, 10.1007/s11104-006-0005-4, 2006.Leroux, X., Bariac, T., and Mariotti, A.: Spatial partitioning of the
soil-water resource between grass and shrub components in a west-African
humid savanna, Oecologia, 104, 147–155, 10.1007/BF00328579, 1995.Li, S. G., Romero-Saltos, H., Tsujimura, M., Sugimoto, A., Sasaki, L., Davaa,
G., and Oyunbaatar, D.: Plant water sources in the cold semiarid ecosystem of
the upper Kherlen River catchment in Mongolia: A stable isotope approach, J.
Hydrol., 333, 109–117, 10.1016/j.jhydrol.2006.07.020, 2007.Lin, G. H. and Sternberg, L. D. L.: Comparative-study of water-Uptake and
photosynthetic gas-exchange between scrub and fringe red mangroves,
Rhizophora-Mangle L, Oecologia, 90, 399–403, 10.1007/Bf00317697, 1992.Mazzacavallo, M. G. and Kulmatiski, A.: Modelling water uptake provides a new
perspective on grass and tree coexistence, PLoS ONE, 10, e0144300,
10.1371/journal.pone.0144300, 2015.McCole, A. A. and Stern, L. A.: Seasonal water use patterns of Juniperus
ashei on the Edwards Plateau, Texas, based on stable isotopes in water, J.
Hydrol., 342, 238–248, 10.1016/j.jhydrol.2007.05.024, 2007.McDonnell, J. J.: The two water worlds hypothesis: ecohydrological separation
of water between streams and trees?, WIREs Water, 1, 323–329,
10.1002/wat2.1027, 2014.Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H., and
Teller, E.: Equation of state calculations by fast computing machines, J.
Chem. Phys., 21, 1087–1092, 10.1063/1.1699114, 1953.Meunier, F., Rothfuss, Y., Bariac, T., Biron, P., Durand, J.-L., Richard, P.,
Couvreur, V., Vanderborght, J., and Javaux, M.: Measuring and modeling
Hydraulic Lift of Lolium multiflorum using stable water isotopes,
Vadose Zone J., accepted, 2017.Midwood, A. J., Boutton, T. W., Archer, S. R., and Watts, S. E.: Water use by
woody plants on contrasting soils in a savanna parkland: assessment with
δ2H and δ18O, Plant Soil, 205, 13–24,
10.1023/A:1004355423241, 1998.Moore, J. W. and Semmens, B. X.: Incorporating uncertainty and prior
information into stable isotope mixing models, Ecol. Lett., 11, 470–480,
10.1111/j.1461-0248.2008.01163.x, 2008.Moreira, M. Z., Sternberg, L. D. L., and Nepstad, D. C.: Vertical patterns of
soil water uptake by plants in a primary forest and an abandoned pasture in
the eastern Amazon: an isotopic approach, Plant Soil, 222, 95–107,
10.1023/A:1004773217189, 2000.Musters, P. A. D. and Bouten, W.: Assessing rooting depths of an Austrian
pine stand by inverse modeling soil water content maps, Water Resour. Res.,
35, 3041–3048, 10.1029/1999wr900173, 1999.Musters, P. A. D. and Bouten, W.: A method for identifying optimum strategies
of measuring soil water contents for calibrating a root water uptake model,
J. Hydrol., 227, 273–286, 10.1016/S0022-1694(99)00187-0, 2000.Nadezhdina, N., David, T. S., David, J. S., Ferreira, M. I., Dohnal, M.,
Tesar, M., Gartner, K., Leitgeb, E., Nadezhdin, V., Cermak, J., Jimenez, M.
S., and Morales, D.: Trees never rest: the multiple facets of hydraulic
redistribution, Ecohydrology, 3, 431–444, 10.1002/eco.148, 2010.Nadezhdina, N., David, T. S., David, J. S., Nadezhdin, V., Cermak, J.,
Gebauer, R., Ferreira, M. I., Conceicao, N., Dohnal, M., Tesar, M., Gartner,
K., and Ceulemans, R.: Root Function: In Situ Studies Through Sap Flow
Research, Measuring Roots: An Updated Approach, 14, 267–290,
10.1007/978-3-642-22067-8_14, 2012.Nadezhdina, N., Ferreira, M. I., Conceicao, N., Pacheco, C. A., Hausler, M.,
and David, T. S.: Water uptake and hydraulic redistribution under a seasonal
climate: long-term study in a rainfed olive orchard, Ecohydrology, 8,
387–397, 10.1002/eco.1545, 2015.Oerter, E., Finstad, K., Schaefer, J., Goldsmith, G. R., Dawson, T., and
Amundson, R.: Oxygen isotope fractionation effects in soil water via
interaction with cations (Mg, Ca, K, Na) adsorbed to phyllosilicate clay
minerals, J. Hydrol., 515, 1–9, 10.1016/j.jhydrol.2014.04.029, 2014.Oerter, E. J., Perelet, A., Pardyjak, E., and Bowen, G.: Membrane inlet laser
spectroscopy to measure H and O stable isotope compositions of soil and
sediment pore water with high sample throughput, Rapid Commun. Mass Sp., 31,
75–84, 10.1002/rcm.7768, 2016.Ogle, K., Wolpert, R. L., and Reynolds, J. F.: Reconstructing plant root area
and water uptake profiles, Ecology, 85, 1967–1978, 10.1890/03-0346,
2004.Ogle, K., Tucker, C., and Cable, J. M.: Beyond simple linear mixing models:
process-based isotope partitioning of ecological processes, Ecol. Appl., 24,
181–195, 10.1890/1051-0761-24.1.181, 2014.Orlowski, N., Frede, H.-G., Brüggemann, N., and Breuer, L.: Validation
and application of a cryogenic vacuum extraction system for soil and plant
water extraction for isotope analysis, J. Sens. Sens. Syst., 2, 179–193,
10.5194/jsss-2-179-2013, 2013.Orlowski, N., Breuer, L., and McDonnell, J. J.: Critical issues with
cryogenic extraction of soil water for stable isotope analysis, Ecohydrology,
9, 3–10, 10.1002/eco.1722, 2016a.Orlowski, N., Pratt, D. L., and McDonnell, J. J.: Intercomparison of soil
pore water extraction methods for stable isotope analysis, Hydrol. Process.,
30, 3434–3449, 10.1002/hyp.10870, 2016b.Parnell, A. C., Inger, R., Bearhop, S., and Jackson, A. L.: Source
partitioning using stable isotopes: coping with too much variation, PLoS ONE,
5, e9672, 10.1371/journal.pone.0009672, 2010.Parnell, A. C., Phillips, D. L., Bearhop, S., Semmens, B. X., Ward, E. J.,
Moore, J. W., Jackson, A. L., Grey, J., Kelly, D. J., and Inger, R.: Bayesian
stable isotope mixing models, Environmetrics, 24, 387–399,
10.1002/env.2221, 2013.Phillips, D. L. and Gregg, J. W.: Uncertainty in source partitioning using
stable isotopes, Oecologia, 127, 171–179, 10.1007/s004420000578, 2001.Phillips, D. L. and Gregg, J. W.: Source partitioning using stable isotopes:
Coping with too many sources, Oecologia, 136, 261–269,
10.1007/s00442-003-1218-3, 2003.Phillips, D. L. and Koch, P. L.: Incorporating concentration dependence in
stable isotope mixing models, Oecologia, 130, 114–125,
10.1007/s004420100786, 2002.Phillips, D. L., Newsome, S. D., and Gregg, J. W.: Combining sources in
stable isotope mixing models: alternative methods, Oecologia, 144, 520–527,
10.1007/s00442-004-1816-8, 2005.Pratt, D. L., Lu, M., Barbour, S. L., and Hendry, M. J.: An evaluation of
materials and methods for vapour measurement of the isotopic composition of
pore water in deep, unsaturated zones, Isotopes Environ. Health Stud., 52,
529–543, 10.1080/10256016.2016.1151423, 2016.Prechsl, U. E., Burri, S., Gilgen, A. K., Kahmen, A., and Buchmann, N.: No
shift to a deeper water uptake depth in response to summer drought of two
lowland and sub-alpine C3-grasslands in Switzerland, Oecologia, 177,
97–111, 10.1007/s00442-014-3092-6, 2015.Romero-Saltos, H., Sternberg Lda, S., Moreira, M. Z., and Nepstad, D. C.:
Rainfall exclusion in an eastern Amazonian forest alters soil water movement
and depth of water uptake, Am. J. Bot., 92, 443–455,
10.3732/ajb.92.3.443, 2005.Rossatto, D. R., Sternberg, L. D. L., and Franco, A. C.: The partitioning of
water uptake between growth forms in a Neotropical savanna: do herbs exploit
a third water source niche?, Plant Biol., 15, 84–92,
10.1111/j.1438-8677.2012.00618.x, 2013.Rothfuss, Y., Biron, P., Braud, I., Canale, L., Durand, J. L., Gaudet, J. P.,
Richard, P., Vauclin, M., and Bariac, T.: Partitioning evapotranspiration
fluxes into soil evaporation and plant transpiration using water stable
isotopes under controlled conditions, Hydrol. Process., 24, 3177–3194,
10.1002/Hyp.7743, 2010.Rothfuss, Y., Braud, I., Le Moine, N., Biron, P., Durand, J. L., Vauclin, M.,
and Bariac, T.: Factors controlling the isotopic partitioning between soil
evaporation and plant transpiration: Assessment using a multi-objective
calibration of SiSPAT-Isotope under controlled conditions, J. Hydrol., 442,
75–88, 10.1016/j.jhydrol.2012.03.041, 2012.Rothfuss, Y., Vereecken, H., and Brüggemann, N.: Monitoring water stable
isotopic composition in soils using gas-permeable tubing and infrared laser
absorption spectroscopy, Water Resour. Res., 49, 1–9,
10.1002/wrcr.20311, 2013.Rothfuss, Y., Merz, S., Vanderborght, J., Hermes, N., Weuthen, A., Pohlmeier,
A., Vereecken, H., and Brüggemann, N.: Long-term and high-frequency
non-destructive monitoring of water stable isotope profiles in an evaporating
soil column, Hydrol. Earth Syst. Sci., 19, 4067–4080,
10.5194/hess-19-4067-2015, 2015.Roupsard, O., Ferhi, A., Granier, A., Pallo, F., Depommier, D., Mallet, B.,
Joly, H. I., and Dreyer, E.: Reverse phenology and dry-season water uptake by
Faidherbia albida (Del.) A. Chev. in an agroforestry parkland of Sudanese
west Africa, Funct. Ecol., 13, 460–472,
10.1046/j.1365-2435.1999.00345.x, 1999.Sánchez-Perez, J. M., Lucot, E., Bariac, T., and Tremolieres, M.: Water
uptake by trees in a riparian hardwood forest (Rhine floodplain, France),
Hydrol. Process., 22, 366–375, 10.1002/hyp.6604, 2008.Scheenen, T. W. J., van Dusschoten, D., de Jager, P. A., and Van As, H.:
Quantification of water transport in plants with NMR imaging, J. Exp. Bot.,
51, 1751–1759, 10.1093/jexbot/51.351.1751, 2000.Schwendenmann, L., Pendall, E., Sanchez-Bragado, R., Kunert, N., and
Holscher, D.: Tree water uptake in a tropical plantation varying in tree
diversity: interspecific differences, seasonal shifts and complementarity,
Ecohydrology, 8, 1–12, 10.1002/eco.1479, 2015.Simunek, J. and Hopmans, J. W.: Modeling compensated root water and nutrient
uptake, Ecol. Model., 220, 505–521, 10.1016/j.ecolmodel.2008.11.004,
2009.Singleton, M. J., Sonnenthal, E. L., Conrad, M. E., DePaolo, D. J., and Gee,
G. W.: Multiphase reactive transport modeling of seasonal infiltration events
and stable isotope fractionation in unsaturated zone pore water and vapor at
the Hanford site, Vadose Zone J., 3, 775–785, 10.2136/vzj2004.0775,
2004.Sofer, Z. and Gat, J. R.: Activities and concentrations of oxygen-18 in
concentrated aqueous salt solutions – analytical and geophysical
implications, Earth Planet. Sc. Lett., 15, 232–238,
10.1016/0012-821x(72)90168-9, 1972.Sprenger, M., Herbstritt, B., and Weiler, M.: Established methods and new
opportunities for pore water stable isotope analysis, Hydrol. Process., 29,
5174–5192, 10.1002/hyp.10643, 2015.Sprenger, M., Leistert, H., Gimbel, K., and Weiler, M.: Illuminating
hydrological processes at the soil-vegetation-atmosphere interface with water
stable isotopes, Rev. Geophys., 54, 674–704, 10.1002/2015RG000515, 2016.Stahl, C., Herault, B., Rossi, V., Burban, B., Brechet, C., and Bonal, D.:
Depth of soil water uptake by tropical rainforest trees during dry periods:
does tree dimension matter?, Oecologia, 173, 1191–1201,
10.1007/s00442-013-2724-6, 2013.Steudle, E. and Peterson, C. A.: How does water get through roots?, J. Exp.
Bot., 49, 775–788, 10.1093/jxb/49.322.775, 1998.Stumpp, C., Stichler, W., Kandolf, M., and Simunek, J.: Effects of Land Cover
and Fertilization Method on Water Flow and Solute Transport in Five
Lysimeters: A Long-Term Study Using Stable Water Isotopes, Vadose Zone J.,
11, 10.2136/vzj2011.0075, 2012.Sutanto, S. J., Wenninger, J., Coenders-Gerrits, A. M. J., and Uhlenbrook,
S.: Partitioning of evaporation into transpiration, soil evaporation and
interception: a comparison between isotope measurements and a HYDRUS-1D
model, Hydrol. Earth Syst. Sci., 16, 2605–2616,
10.5194/hess-16-2605-2012, 2012.Tardieu, F. and Davies, W. J.: Integration of Hydraulic and Chemical
Signaling in the Control of Stomatal Conductance and Water Status of
Droughted Plants, Plant Cell Environ, 16, 341–349,
10.1111/j.1365-3040.1993.tb00880.x, 1993.Thorburn, P. J. and Ehleringer, J. R.: Root water uptake of field-growing
plants indicated by measurements of natural-abundance deuterium, Plant Soil,
177, 225–233, 10.1007/Bf00010129, 1995.Thorburn, P. J., Walker, G. R., and Brunel, J. P.: Extraction of water from
eucalyptus trees for analysis of deuterium and O-18 – laboratory and field
techniques, Plant Cell Environ., 16, 269–277,
10.1111/j.1365-3040.1993.tb00869.x, 1993.van Genuchten, M. T.: A closed-form equation for predicting the hydraulic
conductivity of unsaturated soils, Soil Sci. Soc. Am. J., 44, 892–898,
10.2136/sssaj1980.03615995004400050002x, 1980.Vanderklift, M. A. and Ponsard, S.: Sources of variation in consumer-diet
δ15N enrichment: a meta-analysis, Oecologia, 136, 169–182,
10.1007/s00442-003-1270-z, 2003.Vandoorne, B., Beff, L., Lutts, S., and Javaux, M.: Root water uptake
dynamics of Cichorium intybus var. sativum under water-limited conditions,
Vadose Zone J., 11, 10.2136/vzj2012.0005, 2012.Volkmann, T. H. M. and Weiler, M.: Continual in situ monitoring of pore water
stable isotopes in the subsurface, Hydrol. Earth Syst. Sci., 18, 1819–1833,
10.5194/hess-18-1819-2014, 2014.Volkmann, T. H., Kühnhammer, K., Herbstritt, B., Gessler, A., and Weiler,
M.: A method for in situ monitoring of the isotope composition of tree xylem
water using laser spectroscopy, Plant Cell Environ., 39, 2055–2063,
10.1111/pce.12725, 2016a.Volkmann, T. H. M., Haberer, K., Gessler, A., and Weiler, M.: High-resolution
isotope measurements resolve rapid ecohydrological dynamics at the
soil–plant interface, New Phytol., 210, 839–849, 10.1111/nph.13868,
2016b.Walker, C. D. and Richardson, S. B.: The use of stable isotopes of water in
characterizing the source of water in vegetation, Chem. Geol., 94, 145–158,
10.1016/0168-9622(91)90007-J, 1991.
Wang, P., Song, X. F., Han, D. M., Zhang, Y. H., and Liu, X.: A study of root
water uptake of crops indicated by hydrogen and oxygen stable isotopes: A
case in Shanxi Province, China, Agr. Water Manage., 97, 475–482,
10.1016/j.agwat.2009.11.008, 2010.Washburn, E. W. and Smith, E. R.: The isotopic fractionation of water by
physiological processes, Science, 79, 188–189,
10.1126/science.79.2043.188, 1934.Weltzin, J. F. and McPherson, G. R.: Spatial and temporal soil moisture
resource partitioning by trees and grasses in a temperate savanna, Arizona,
USA, Oecologia, 112, 156–164, 10.1007/s004420050295, 1997.West, A. G., Patrickson, S. J., and Ehleringer, J. R.: Water extraction times
for plant and soil materials used in stable isotope analysis, Rapid Commun.
Mass Sp., 20, 1317–1321, 10.1002/rcm.2456, 2006.White, J. W. C., Cook, E. R., Lawrence, J. R., and Broecker, W. S.: The D/H
ratios of sap in trees – implications for water sources and tree-Ring D/H
ratios, Geochim. Cosmochim. Ac., 49, 237–246,
10.1016/0016-7037(85)90207-8, 1985.Zarebanadkouki, M., Kim, Y. X., Moradi, A. B., Vogel, H. J., Kaestner, A.,
and Carminati, A.: Quantification and modeling of local root water uptake
using neutron radiography and deuterated water, Vadose Zone J., 11,
10.2136/vzj2011.0196, 2012.
Zimmermann, U., Ehhalt, D., and Münnich, K. O.: Soil water movement and
evapotranspiration: changes in the isotopic composition of the water,
International Atomic Energy Agency, Vienna,
567–584, 1967.