Introduction
Stable isotopologues of water, namely, 1H2H16O and
1H218O, are powerful tools used in a wide range of research
disciplines at different and complementary temporal and spatial scales. They
provide ways of assessing the origin of water vapor (e.g., Craig, 1961; Liu
et al., 2010), solving water balances of lakes (Jasechko et al., 2013) and
studying groundwater recharge (Blasch and Bryson, 2007; Peng et al., 2014).
Analysis of the isotope compositions (δ2H and δ18O)
of soil surface and leaf waters allows for partitioning
evapotranspiration into evaporation and transpiration (e.g., Yepez et al.,
2005; Rothfuss et al., 2012; Dubbert et al., 2013; Hu et al., 2014).
Moreover, from soil water δ2H and δ18O profiles,
it is also possible to derive quantitative information, such as soil
evaporation flux, locate evaporation fronts, and root water uptake depths
(Rothfuss et al., 2010; Wang et al., 2010). Zimmermann et al. (1967) and
later Barnes and Allison (1983, 1984) and Barnes and Walker (1989) first
analytically described soil 1H2H16O and 1H218O
movement at steady/non-steady state and in isothermal/non-isothermal
soil profiles. Between precipitation events, the soil water δ2H
and δ18O profiles depend on flux boundary conditions,
i.e., fractionating evaporation and non-fractionating capillary rise as well as on
soil properties (e.g., soil tortuosity). In a saturated soil, the excess of
heavy isotopologues at the surface due to evaporation diffuses back
downwards, leading to typical and well-documented exponential-shaped
δ2H and δ18O profiles. For an unsaturated soil,
assuming in a first approximation that isotope movement occurs in the vapor
phase above the soil evaporation front (EF) and strictly in the liquid phase
below it, the maximal soil water δ2H and δ18O values are no
longer observed at the surface but at the depth of the EF. Above the EF in
the so-called “vapor region”, according to Fick's law, soil water
δ2H and δ18O decrease towards the isotopically
depleted ambient atmospheric water vapor δ2H and
δ18O. Braud et al. (2005), Haverd and Cuntz (2010), Rothfuss et al. (2012),
Singleton et al. (2004) and Sutanto et al. (2012) implemented the
description of the transport of 1H2H16O and
1H218O in physically based soil–vegetation–atmosphere
transfer (SVAT) models (HYDRUS 1D, SiSPAT-Isotope, soil–litter–iso,
TOUGHREACT). In these models, movement of soil 1H2H16O and
1H218O occurs in both phases below and above the EF, and heat
and water transports are properly coupled.
However, these tools suffer from the comparison with other “traditional”
methods developed to observe and derive soil water state and transport. In
contrast with soil water content and tension measured by, e.g., time-domain
reflectometry and tensiometry, isotope compositions of soil water are
determined either by following
destructive sampling, or non-destructively (i.e., with suction cups in
combination with lysimeters for soil water tension higher than -600 hPa;
e.g., Litaor, 1988; Goldsmith et al., 2011) but
with poor spatial and temporal resolution. This greatly limits their
informative value. Only since recently, non-destructive methodologies based
on gas-permeable membrane and laser spectroscopy can be found in the
literature (Herbstritt et al., 2012; Rothfuss et al., 2013; Volkmann and
Weiler, 2014; Gaj et al., 2015).
The central objective of this study was to demonstrate that a direct
application of the method of Rothfuss et al. (2013) to a soil column would
allow for monitoring soil water δ2H and δ18O profiles
in the laboratory with high temporal resolution and over a long time period.
We will demonstrate that the obtained isotope data can be used to locate the
EF as it recedes into the soil during the experiment. Finally, the data will
be also used to test the expression proposed by Gat (1971) and based on the
Craig and Gordon (1965) model, for the determination of the slopes of
evaporation lines.
Material and methods
Isotopic analyses
Isotopic analysis of liquid water and water vapor was performed using a
cavity ring-down spectrometer (L1102-i, Picarro, Inc., Santa Clara, CA,
USA), calibrated against the international primary water isotope standards VSMOW2 (Vienna Standard Mean Ocean Water),
GISP (Greenland Ice Sheet Precipitation), and SLAP (Standard Light Antartic Precipitation) by liquid water injection into the vaporizer of the
analyzer. The isotope compositions of primary and working standards were
measured at 17 000 ppmv water vapor mixing ratio (number of replicates = 4,
number of injections per replicate = 8). Mean values and standard
deviations were calculated omitting the first three values of the first
replicate to account for a potential memory effect of the laser
spectrometer. The laser spectrometer's dependence on water vapor mixing
ratio was also investigated according to the method of Schmidt et al. (2010).
Hydrogen and oxygen isotope ratios of water are expressed in per mil (‰)
on the international delta scale as defined by
Gonfiantini (1978) and referred to as δ2H and δ18O, respectively.
Soil column and measurements
The experiment was conducted in a 0.0057 m3 acrylic glass column
(0.11 m inside diameter, 0.60 m height; Fig. 1a). The bottom of the column
consisted of a porous glass plate (10 × 10-6 m < pore size
diameter < 16 × 10-6 m (4th class), Robu®
GmbH, Hattert, Germany) connected to a two-way manual valve (VHK2-01S-06F,
SMC Pneumatik GmbH, Germany).
Three ports were available at each of eight different depths (-0.01,
-0.03, -0.05, -0.07, -0.10, -0.20, -0.40, and -0.60 m): one inlet for
the carrier gas, i.e., synthetic dry air (20.5 % O2 in N2, with
approx. 20–30 ppmv water vapor; Air Liquide, Germany), one sample air
outlet, and one duct for a soil temperature (TS) sensor (type K
thermocouple, Greisinger electronic GmbH, Regenstauf, Germany; precision:
0.1 ∘C). An additional fourth port at depths -0.01, -0.03,
-0.05, -0.10, -0.20, and -0.60 m was used for the measurement of soil
volumetric water content (θ) (EC-5, Decagon Devices, USA; precision:
0.02 m3 m-3).
(a) Scheme of the acrylic glass column used in the
experiment; (b) experimental setup for sampling water vapor at the different
soil depths of the soil column: from the ambient air, and from the two soil
water standards (standard 1 and 2).
At each depth inside the column a 0.15 m long piece of microporous
polypropylene tubing (Accurel® PP V8/2HF, Membrana GmbH,
Germany; 1.55 × 10-3 m wall thickness, 5.5 × 10-3 m inside
diameter, 8.6 × 10-3 m outside diameter) was connected to the gas
inlet and outlet port. The tubing offers the two advantages of being
gas-permeable (pore size of 0.2 × 10-6 m) and exhibiting strong
hydrophobic properties to prevent liquid water from intruding into the
tubing. It allows for sampling of soil water vapor and, hence, the determination
of the isotope composition of soil liquid water (δSliq) in a
non-destructive manner considering thermodynamic equilibrium between liquid
and vapor phases as detailed by Rothfuss et al. (2013).
Internal isotope standards
Two internal standards (“st1” and “st2”) were prepared using the same
procedure as described by Rothfuss et al. (2013). Two closed acrylic glass
vessels (0.12 m i.d., 0.22 m height), in each of which a 0.15 m long
piece of tubing as well as a type K thermocouple were installed, were filled
with FH31 sand (porosity = 0.34 m3 m-3, dry bulk density = 1.69 × 103 kg m-3, particle size distribution: 10 %
(> 0.5 × 10-3 m), 72 % (0.25–0.5 × 10-3 m), and
18 % (< 0.25 × 10-3 m)) (Merz et al., 2014; Stingaciu et al.,
2009). Each vessel was saturated with water of two different isotope
compositions: δ2Hst1 = -53.51 (±0.10) ‰,
δ18Ost1 = -8.18 (±0.06) ‰ and
δ2Hst2 = +15.56 (±0.12) ‰,
δ18Ost2 = +8.37 (±0.04) ‰.
Soil water vapor from each vessel was sampled 8 times per day for 30 min
during the whole experiment.
Atmospheric measurements
Laboratory air was sampled passively with a 1/8′′ 3 m long stainless
steel tubing at 2 m above the sand surface for isotope analysis of water
vapor (δa). Air relative humidity (RH) and temperature (Ta)
were monitored at the same height with a combined RH and Ta
sensor (RFT-2, UMS GmbH, Germany; precision for RH and Ta were 2 % and
0.1 ∘C, respectively). Vapor pressure deficit (vpd) was calculated
from RH and Ta data using the Magnus–Tetens formula (Murray, 1967) for
saturated vapor pressure. The laboratory was air conditioned and ventilated
with seven axial fans (ETRI 148VK0281, 117 L s-1 airflow,
ETRI/Rosenberg, USA) positioned at 1.80 m height above the sand surface.
Sampling protocol and applied isotopic calibrations
The column was filled in a single step with FH31 sand and carefully shaken
in order to reach a dry bulk density close to in situ field conditions. The sand
was then slowly saturated from the bottom from an external water tank filled
with st1 water on 2 December 2013. After saturation, the column was
disconnected and sealed at the bottom using the two-way manual valve. It was
finally installed on a balance (Miras 2 – 60EDL, Sartorius, USA), and let
to evaporate for a period of 290 days in a ventilated laboratory.
δSliq was determined in a sequential manner at each available
depth once a day following the method developed by Rothfuss et al. (2013)
(Fig. 1b). Dry synthetic air at a rate of 50 mL min-1 from a mass flow
controller (EL-FLOW Analog, Bronkhorst High Tech, Ruurlo, the Netherlands)
was directed to the permeable tubing for 30 min at each depth. The
sampled soil water vapor was diluted with dry synthetic air provided by a
second mass flow controller of the same type. This allowed for the following: (i) reaching a
water vapor mixing ratio ranging between 17 000 and 23 000 ppmv (where
L1102-i isotope measurements are most precise) and (ii) generating an excess
flow downstream of the laser analyzer. By doing this, any contamination of
sample air with ambient air would be avoided. The excess flow was measured
with a digital flow meter (ADM3000, Agilent Technologies, Santa Clara, CA,
USA). The last 100 observations (corresponding to approx. 10 min) at
steady state (standard deviations < 0.70 ‰ and
< 0.20 ‰ for δ2H and δ18O, respectively)
were used to calculate the raw isotope compositions
of soil water vapor (δSvap). The latter was corrected for the
water vapor mixing ratio dependence of the laser analyzer readings with
17 000 ppmv as reference level. Measurements that did not fulfill the abovementioned conditions for δ2H and δ18O standard
deviations were not taken into account. Finally, these corrected values were
used to infer the corresponding δSliq at the measured TS
(Eqs. 1 and 2; taken from Rothfuss et al., 2013):
δ2HSliq=104.96-1.0342⋅TS+1.0724⋅δ2HSvap,δ18OSliq=11.45-0.0795⋅TS+1.0012⋅δ18OSvap.
The isotope composition of laboratory water vapor (δa) was
measured 8 times a day. δa, δSvap and
δSliq values were finally corrected for laser instrument drift
with time, using the isotope compositions of the two water standards,
δst1 and δst2.
Water vapor of the ambient air, of both standards, and from the different
tubing sections in the soil column were sampled sequentially in the
following order: soil (0.60 m) – soil (0.40 m) – atmosphere – st1 – st2 – soil
(0.20 m) – soil (0.10 m) – atmosphere – st1 – st2 – soil (0.07 m) – soil
(0.05 m) – atmosphere – st1 – st2 – soil (0.03 m) – soil (0.01 m).
Atmosphere water vapor was sampled twice as long (i.e., 1 h)
as soil water vapor from the column/standards, so that each sequence lasted
exactly 10 h and started each day at the same time. The remaining 14 h
were used for additional standard and atmosphere water vapor
measurements (i.e., on five occasions each).
Irrigation event
On day of experiment (DoE) 290 at 09:30 LT the sand surface was irrigated with
70 mm of st1 water. This was achieved over 1 h in order to avoid
oversaturation of the sand and avoid preferential pathways that would have
affected the evaporation rate. For this, a 2 L polyethylene bottle was used.
Its bottom was perforated with a set of 17 holes of 5 mm diameter and its
cap with a single hole through which a PTFE bulkhead union tube fitting
(Swagelok, USA) was installed. The bulkhead fitting was connected to a
two-way needle valve (Swagelok, USA). Opening/closing the valve controlled
the flow rate at which air entered the bottle headspace, which in turn
controlled the irrigation flow rate.
To better observe the dynamics directly following the irrigation event,
water vapor was sampled at a higher rate, i.e., 1, 3, 4, 5, 6, 9, 11, and
11 times per day at -0.60, -0.40, -0.20, -0.10, -0.07, -0.05, -0.03, and
-0.01 m, respectively. Water vapor from both standards was sampled twice a
day. The experiment was terminated after 299 days on 26 September 2014.
Evaporation lines
Gat (1971) proposed an expression based on the model of Craig and
Gordon (1965) for the slope of the so-called “evaporation line”
(SEv, [–]) which quantifies the relative change in
δ2HSliq and δ18OSliq in a water body undergoing
evaporation:
SEv=Δδ2HSliqΔδ18OSliq=RH⋅δa-δSliq_ini+εeq+Δε2HRH⋅δa-δSliq_ini+εeq+Δε18O,
where δSliq_ini is the initial soil water (hydrogen
or oxygen) liquid isotope composition, i.e., prior to removal of water vapor
by fractionating evaporation. εeq [–, expressed in
‰] is the equilibrium enrichment in either
1H2H16O or 1H218O. It is defined by the
deviation from unity of the ratio between water and isotopologue saturated
vapor pressures and can be calculated using the empirical closed-form
equations proposed by, e.g., Majoube (1971). Δε [–,
expressed in ‰] is the so-called “kinetic isotope
effect” associated with 1H2H16O and 1H218O
vapor transports. Assuming that (i) turbulent transport is a
non-fractionating process and considering that (ii) the ratio of molecular
diffusion resistance to total resistance equals one, it follows that (Gat, 2000)
Δε=(1-RH)⋅DvDiv-1⋅n.
In Eq. (4), the product (DvDiv - 1) ⋅ n
is the kinetic isotope enrichment (εK [–,
expressed in ‰]). In the present study, values for
ratios of diffusivities (Dv/Div) were taken from Merlivat (1978):
DvD2Hv=0.9755DvD18Ov=0.9723.
The term n accounts for the aerodynamics in the air boundary layer and
ranges from na = 0.5 (turbulent diffusion, i.e.,
atmosphere-controlled conditions) to nS = 1 (molecular diffusion,
i.e., soil-controlled conditions) with a value of two-thirds corresponding to laminar
flow conditions (Dongmann et al., 1974; Brutsaert, 1975). We tested the
formulation proposed by Mathieu and Bariac (1996) where n is considered as a
function of soil water content:
n=θsurf-θres⋅na+θsat-θres⋅nSθsat-θres,
where θres, θsat and θsurf are the
residual, saturated and surface soil water contents [m3 m-3], respectively.
Note that Eq. (3) contrasts with the expression for the slope
characterizing equilibrium processes (e.g., precipitation formation) and
therefore is strictly temperature dependent (i.e., Seq = εeq2H/εeq18O). While Seq might
range for instance from 7.99 to 8.94 (for temperatures between 5 and
30 ∘C), a much wider spread in SEv values is possible and has
been measured between 2 and 6 (Barnes and Allison, 1988; Brunel et al.,
1995; DePaolo et al., 2004).
Water vapor mixing ratio (WVMR) and isotope composition
(δ18O and δ2H; [‰ VSMOW]) of
the water vapor sampled on day of experiment 150 from the ambient air
(“atm”), both standards (“st1” and “st2”), and from the tubing
sections at soil depths 1, 3, 5, 7, 10, 20, 40, and 60 cm.
Time series of the laboratory ambient air temperature (Ta),
relative humidity (RH), and water vapor isotope
compositions (δ18Oa and δ2Ha
[‰ VSMOW]) over the course of the experiment.
Time series of water content (θ),
evaporation flux (Ev), evaporation flux normalized to vapor pressure deficit (Ev/vpd), and water vapor isotope compositions
(δ18OSvap and δ2HSvap
[‰ VSMOW]) during the course of the experiment.
Results
Example of a measuring sequence
Figure 2 shows exemplarily the measuring sequence for DoE 150. Soil and
standard water vapor mixing ratios were stable and ranged from 17 200 to
18 200 ppmv during the last 10 min of each sampling period (Fig. 2a).
δSvap was within the range spanned by δst1vap and
δst2vap for both 2H and 18O (Fig. 2b). On DoE 150,
the soil surface was sufficiently dry so that atmospheric invasion of water
vapor had started to significantly influence the δSvap of the
upper soil layers. Therefore, δSvap measured at -0.01 m was
lower than at -0.03 m for both 2H and 18O, but less pronounced
for 2H.
Time courses of air temperature, relative humidity and atmospheric δ2H and δ18O
During the experiment, the laboratory air temperature ranged from 15.6 to
22.5 ∘C (average: 18.7 ± 1.5 ∘C, Fig. 3a) and
the relative humidity from 19 to 69 % (average: 40 % ± 0.08 %,
Fig. 3a). Lower values of δa were observed from DoE 0 to 125
at lower air temperatures, whereas higher values occurred after DoE 125
at higher air temperatures (Fig. 3b).
Evolution of soil water content, temperature, evaporation flux and δSvap from DoE 0–290
The soil temperature ranged from 16.2 to 22.3 ∘C (average:
18.6 ± 1.3 ∘C, data not shown) and closely followed that in the
air, i.e., differences between daily mean soil and air temperatures ranged
from -0.2 to 0.2 ∘C during the experiment. Following the
saturation of the column, a strong decrease in water content was observed in
the upper 10 cm, whereas after 287 days the sand was still saturated at
-0.60 m (Fig. 4a). Figure 4b shows the time series of evaporation flux
normalized by the vapor pressure deficit in the laboratory air (Ev / vpd, expressed
in mm day-1 kPa-1). Ev / vpd ratio was high at the beginning of the
experiment, i.e., ranged from 2.44 to 3.22 mm day-1 kPa-1 during the
first two experimental days. After DoE 180 and until the soil was irrigated,
Ev / vpd stabilized around a mean value of 0.03 (±0.02) mm day-1 kPa-1.
Due to fractionating evaporation flux, the δSvap of the topmost
layer (-0.01 m) increased instantaneously (i.e., from DoE 0 onward) from
the equilibrium δSvap value with the input water (-17.3 and
-132.3 ‰ for 18O and 2H, respectively, at 16.5 ∘C, Fig. 4c and d). Through
back diffusion of the excess heavy stable isotopologues from the evaporation
front, δSvap measured at depths -0.03, -0.05, -0.07, -0.10,
and -0.20 m departed from that same equilibrium value after 2, 3, 10, 25,
and 92 days of experiment, respectively. On the other hand,
δSvap of the layers -0.40 and -0.60 m were constant over the entire
duration of the experiment. Until DoE 65, the δSvap of the
first 10 cm increased. From DoE 65 to 113, δSvap reached an
overall stable value in the top layers -0.01 m (δ2HSvap = 4.82 ± 2.06 ‰;
δ18OSvap = 11.72 ± 67 ‰) and -0.03 m
(δ2HSvap = 5.61 ± 3.14 ‰;
δ18OSvap = 10.41 ± 0.81 ‰), whereas
δSvap measured at depths -0.05, -0.07, and -0.10 m still
progressively increased; from DoE 72 onward, δSvap at -0.20 m
started to increase. δ2HSvap and δ18OSvap
values started to decrease after about DoE 113 and DoE 155, respectively.
δ2HSvap at -0.01, -0.03, and -0.07 m
on the one hand and δ18OSvap at -0.01, -0.03, and -0.07 m
on the other followed similar trends with maximum values measured below
the surface down to -0.05 m.
Soil temperature (TS), water content
(θ), and liquid water isotope compositions
(δ18OSliq and δ2HSliq
[‰ VSMOW]) profiles from day of experiment (DoE) 0–100
(top panel), from DoE 101–287 (middle panel), and from DoE 288–299 (bottom panel).
Linear regressions (gray dotted line) between laboratory
atmosphere water vapor δ18O and δ2H
[‰ VSMOW] and between soil water δ18O and
δ2H (solid black line). Each plot represents data from 50 consecutive
days of experiment (DoE). Global meteoric water line (GMWL;
defined by δ2H = 8 × δ18O + 10, in blue dotted
line) is shown on each sub-plot for comparison. Coefficient of determination
(R2) as well as the slope of the linear regressions (LRS) are reported.
Evolution of soil water content, temperature, evaporation flux and δSvap from DoE 290 to 299
The layers -0.01, -0.03, -0.05, -0.10, and -0.20 m showed increases in
θ of 0.31, 0.22, 0.30, 0.23, and 0.16 m3 m-3 following
irrigation, whereas θ at -0.60 m remained constant (Fig. 4e).
θ-0.01m and θ-0.03m rapidly decreased down to
values of 0.12 and 0.13 m3 m-3. Note that when θ-0.01m and θ-0.03m reached these values prior to
irrigation, the evaporation rate was similar
(i.e., Ev / vpd = 0.65 (±0.12) mm day-1; Fig. 4f).
Immediately after irrigation and for both isotopologues, δSvap
at -0.01, -0.03, and -0.05 m was reset to a value close to that in
equilibrium with st1 water (i.e., -17.8 and -132.0 ‰ for 18O and 2H, respectively, at
21.8 ∘C soil temperature; Fig. 4g and h). At -0.07 m,
δSvap reached the abovementioned equilibrium values after about
3.5 days. δSvap at -0.20 m evolved in a similar way, whereas at
-0.10 m the equilibrium values were reached after 6 h. Finally,
δSvap at -0.40 and -0.60 m and for both isotopologues were
not affected by the water addition, which was consistent with the observed
θ changes.
Evolution of soil temperature, water content and δSliq profiles
In Fig. 5, TS, θ and δSliq profiles for both
isotopologues are plotted in three different panels, from DoE 0 to 100
(Fig. 5a–d, top panels), from DoE 101 to 287 (Fig. 5e–h, center panels) and from
DoE 288 to 299 (Fig. 5i–l, bottom panels). The represented profiles were
obtained from a linear interpolation of the times series of each variable.
Thus, since the measuring sequence started each day at 08:00 LT and ended at
18:00 LT, the depicted profiles are centered on 13:00 LT.
Even if the soil temperature fluctuated during the course of the experiment,
quasi-isothermal conditions were fulfilled at a given date, as the column
was not isolated from its surroundings. On average, TS only varied by
0.2 ∘C around the profile mean temperature at a given date. The
δSliq profiles showed a typical exponential shape from DoE 0 to
approx. 100. Around DoE 100, when θ at -0.01 m reached a value of
0.090 m3 m-3 (i.e., significantly greater than the sand residual
water content θ = 0.035 m3 m-3, determined by Merz et
al., 2014), the maximal δSliq values were no longer observed
at the surface and atmosphere water vapor started invading the first
centimeter of soil. Note that this happened slightly faster for
1H2H16O than for 1H218O. On DoE 290, when the
column was irrigated, the isotope profiles were partly reset to their
initial state, i.e., constant over depth and close to -53.5 and
-8.2 ‰ for 1H2H16O and 1H218O,
respectively, with the exception of still higher values at -0.07 m.
δ2H–δ18O relationships in soil water and atmosphere water vapor
Each plot of Fig. 6 represents data of 50 consecutive days of
experiment. Laboratory atmosphere water vapor δ2H and
δ18O (gray symbols) were linearly correlated (linear regression
relationships in gray dotted lines) during the entire experiment (R2
ranging between 0.74 and 0.90, F-statistic p value < 0.01), with the
exception of the period DoE 125–155 (R2 = 0.31, p < 0.001),
when atmospheric water vapor δ2H was remarkably high in the
laboratory (Fig. 6c and d).
The linear regression slopes (LRS) between δ2Ha and
δ18Oa ranged from 6.20 (DoE 50–100, p < 0.01) to 8.29
(DoE 0–50, gray dotted line, p < 0.001). These values were
significantly lower than Seq, the calculated ratio between the
liquid-vapor equilibrium fractionations of 1H2H16O and
1H218O (Majoube, 1971) that characterizes meteoric water
bodies, which should have ranged from 8.41 to 8.92 at the measured monthly
mean atmosphere temperatures (Forschungszentrum Jülich weather station,
6∘24′34′′ E, 50∘54′36′′ N; 91 m a.s.l.). Therefore, it
can be deduced that the laboratory air moisture was partly resulting from
column evaporation, typically leading to a δ2H–δ18O
regression slope of lower than eight. This also highlights the
particular experimental conditions in the laboratory, where other sources of
water vapor (e.g., by opening the laboratory door) might have influenced the
isotope compositions of the air.
Considering all soil depths, the δ2HSliq–δ18OSliq
LRS increased from 2.96 to 4.86 over the course of the
experiment (with R2 > 0.89, p < 0.001). These values
were much lower than that of the slope of the global meteoric water line
(GMWL; i.e., slope = 8) also represented in Fig. 6. However, Fig. 6
highlights the fact that in the upper three layers (-0.01, -0.03 and
-0.05 m) δ2HSliq–δ18OSliq LRS followed
a significantly different evolution as the soil dried out. Figure 7 shows
average δ2H–δ18O LRS calculated for time intervals
of 10 consecutive days for the atmosphere (gray line), the three upper
layers (colored solid lines), and the remaining deeper layers (-0.07,
-0.10, -0.20, -0.40 and -0.60 m, black dotted line). While both
δ2H–δ18O LRS in the atmosphere and in the first
three depths fluctuated during the experiment, the combined LRS of the
remaining deeper layers varied only little between 3.07 and 4.49
(average = 3.78 ± 0.54). From DoE 150, δ2H–δ18O LRS
of the atmosphere and at -0.01, -0.03 and -0.05 m in the soil were linearly
correlated (R2 = 0.73, 0.48 and 0.42, with p < 0.001,
p < 0.01 and p < 0.05, respectively), whereas they were not
correlated before DoE 125, demonstrating again the increasing influence of
the atmosphere (atmospheric invasion) on the soil surface layer as the EF
receded in the soil. Note the negative δ2Ha–δ18Oa
LRS (R2 = 0.26, p < 0.001) observed between
DoE 125 and 150, due to remarkably high atmosphere vapor δ2H
measured in the laboratory.
Discussion
Long-term reliability of the method
The method proved to be reliable in the long term as the tubing sections
positioned at -0.60 and -0.40 m (i.e., where the sand was saturated or
close to saturation during the entire experiment) remained watertight even
after 299 days. As demonstrated by Rothfuss et al. (2013), (i) the length of
the gas-permeable tubing, (ii) the low synthetic dry air flow rate, and
(iii) the daily measurement frequency allowed for removing soil water vapor
which remained under thermodynamic equilibrium with the soil moisture.
Moreover, this was also true for the upper soil layers even at low soil
water content; steady values for water vapor mixing ratio and isotope
compositions were always reached during sampling throughout the experiment.
Finally, our method enabled inferring the isotope composition of tightly
bound water at the surface. This would be observable by the traditional
vacuum distillation method with certainly a lower vertical resolution due to
low moisture content. As also pointed out by Rothfuss et al. (2013), it can
be assumed that the sand properties did not cause any fractionation of pore
water 2H and 18O. In contrast, this could not be the case in
certain soils with high cation exchange capacity (CEC) as originally
described by Sofer and Gat (1972) and recently investigated by Oerter et al. (2014).
Time course of the slopes of the δ18O–δ2H
linear regressions (LRS) for time intervals of 10 consecutive days
of atmosphere data (gray solid line), soil data from the upper three layers
(1, 3, and 5 cm, colored solid lines), and combined soil data from the
remaining bottom layers (from 7 to 60 cm, black dotted line). Mean standard
errors are represented by the error bars in the bottom left corner.
Locating the evaporation front depth from soil water δ2H and δ18O profiles
From Fig. 4b no distinct characteristic evaporation stages, i.e., stages I
and II referring to atmosphere-controlled and soil-controlled evaporation
phases, respectively, could be identified. The opposite was observed by Merz
et al. (2014), who conducted an evaporation study using the same sand. This
indicates greater wind velocity in the air layer above the soil column due
to the laboratory ventilation. For higher wind velocities, the boundary
layer above the drying medium is thinner and the transfer resistance for
vapor transfer lower than for lower wind velocities. But for thinner
boundary layers, the evaporation rates depend more strongly on the spatial
configuration of the vapor field above the partially wet evaporating
surface. This makes the evaporation rate decrease and the transfer
resistance in the boundary layer increase more in relative terms with
decreasing water content of the evaporation surface for higher than for
lower wind velocities (Shahraeeni et al., 2012).
Locating the EF in the soil is of importance for evapotranspiration
partitioning purposes; from the soil water isotope composition at the EF, it
is possible to calculate the evaporation flux isotope composition using the
Craig and Gordon formula (Craig and Gordon, 1965). For a uniform isotope
diffusion coefficient distribution in the liquid phase, an exponential
decrease of the isotope composition gradient with depth is expected.
However, when evaporation and thus accumulation of isotopologues occur in a
soil layer between two given observation points, then the isotope gradient
between these two points is smaller than the gradient deeper in the profile.
Therefore, we can consider the time when the isotope composition gradient is
no longer the largest between these two upper observation depths as the time
when the EF moves into the soil layer below.
(a) and (b) 1H218O and 1H2H16O
composition gradients calculated between consecutive observation points in
the soil. (c) Evolution of the evaporation front depths z18OEF [m] (red
solid line) and z2HEF [m] (black solid line) inferred from the
1H218O and 1H2H16O composition gradients.
(a) Comparison between soil liquid water
δ18O–δ2H linear regressions slopes (LRS, solid black line)
calculated for time intervals of 10 consecutive days and simulated time
series of evaporation line slope (SEv, dotted gray line) obtained from
Eqs. (3)–(6) (Gat, 1971; Merlivat, 1978; Mathieu and Bariac,
1996). Black error bars give the standard errors of the estimated
δ18O–δ2H LRS. Gray error bars are the standard errors
associated with calculation of SEv following Phillips and Gregg (2001).
Coefficient of determination (R2), root mean square error (RMSE) and
Nash and Sutcliffe efficiency (NSE) between model and data are reported.
(b) Time series of n parameter (Eq. 6) and soil relative humidity at the
evaporation front (RHEF) that provided the best model-to-data fit.
(c) εK2H and εK18O time series obtained from fitted n
values (“fitted”) and calculated following Mathieu and Bariac (1996) (“MB96”).
Figure 8a and b display the evolutions of the isotope compositions gradients
d(δ18OS)/dz and d(δ2HS)/dz calculated between two consecutive
observation points in the soil (between -0.01 and -0.03 m in brown
solid line, between -0.03 and -0.05 m in red solid line, etc.). Figure 8c
translates these isotope gradients in terms of EF depths (z18OEF
and z2HEF). Each day, the maximum
d(δ18OS)/dz and
d(δ2HS)/dz define the layer where evaporation occurs,
e.g., when d(δ18OS)/dz is maximal between -0.01 and -0.03 m on a
given DoE, z18OEF is estimated to be greater than –0.01 m and is
assigned the value of 0 m. When d(δ18OS)/dz is maximal between -0.03 and
-0.05 m on a given DoE, z18OEF is estimated to range between -0.01 and
-0.03 m and is assigned the value -0.02 m. From both d(δ18OS)/dz
and d(δ2HS)/dz, a similar evolution of the depth of the EF
was derived despite the fact that δ2HSliq and
δ18OSliq time courses were different and showed maxima at
different times. It was inferred that after 290 days under the prevailing
laboratory air temperature, moisture and aerodynamic conditions, and given
the specific hydraulic properties of the sand, the EF had moved down to an
approximate depth of -0.06 m.
Kinetic isotope effects during soil evaporation
For each period of 10 consecutive days, the minimum measured
δ2HSliq and δ18OSliq provided
δ2HSliq_ini and δ18OSliq_ini in Eq. (3).
δ2Ha and δ18Oa were obtained from the mean
values of their respective times series. Mean soil surface water content
(θsurf) measured in the layer above the EF (as identified in
Sect. 4.2) provided the n parameter in Eq. (5) and ultimately
εK2H and εK18O (Eq. 5).
εeq2H and εeq18O
were calculated from Majoube (1971) at
the mean soil temperature measured at zEF. Relative humidity was
normalized to the soil temperature measured at the EF. Finally, standard
error for SEv was obtained using an extension of the formula proposed by
Phillips and Gregg (2001) and detailed by Rothfuss et al. (2010). For this,
standard errors associated with the determination of the variables in
Eq. (3) were taken equal to their measured standard deviations for each
time period. Standard errors for the parameters θres and
θsat were set to 0.01 m3 m-3 (i.e., comparable to the
precision of the soil water content probes) and for the diffusivity ratios
D/D2H and D/D18O to zero (i.e., no
uncertainty about their value was taken into account, although debatable;
e.g., Cappa et al., 2003).
Figure 9a shows the comparison between time courses of SEv and
δ2HSliq–δ18OSliq LRS computed with data below
the EF. Both ranged between 2.9 and 4.8, i.e., within the range of reported
values (e.g., Barnes and Allison, 1988; Brunel et al., 1995; DePaolo et al.,
2004). Note that values of both observed and simulated slopes increased over
time, even though the air layer above the EF gradually increased as the soil
dried out. The opposite was observed by, e.g., Barnes and Allison (1983),
who simulated isotopic profiles at steady state with constant relative
humidity. In the present study, however, the relative humidity of the
atmosphere gradually increased, which in turn decreased the kinetic effects
associated with 1H2H16O and 1H218O vapor
transport and thus increased slopes over time. The general observed trend
was very well reproduced by the model between DoE 30 and 150 (NSE = 0.92;
Nash and Sutcliffe, 1970), whereas SEv departed from data from DoE 150
onwards (NSE < 0). Overall, the Craig and Gordon (1965) model could
explain about 62 % of the data variability with a root mean square error (RMSE)
of 0.58 (and 76 % when data from the period DoE 0–10 are left out,
p value < 0.001, RMSE = 0.52). At the beginning of the experiment
(DoE 0–20), simulated values were greater than computed
δ2H–δ18O LRS, even when taking into account the high
SEv standard errors due to fast changing θsurf (Phillips
and Gregg, 2001). Although SEv was equal to 3.8 for the period DoE 0–10,
δ2H–δ18O LRS had already reached (down) a value of 2.9,
meaning that the EF should have been no longer at the surface
(i.e., between the surface and 0.01 m depth) leading to greater n, therefore lower slope value.
After DoE 150 and until DoE 290, when evaporation flux was lower than 0.40 mm day-1,
the difference between model and data progressively increased.
For a better model-to-data fit, the 1H2H16O and
1H218O kinetic effects should decrease, through either
(i) decrease of n, which from a theoretical point of view contradicts, e.g., the
formulation of Mathieu and Bariac (1996), or (ii) decrease of term (1 – RH),
or else (iii) a combination of (i) and (ii). In another laboratory study
where δ18O of water in bare soil columns was measured
destructively, and δ18O of evaporation was estimated from
cryogenic trapping of water vapor at the outlet of the columns' headspaces,
Braud et al. (2009a, b) could capture εK18O dynamics by inverse modeling. In their
case, εK18O generally reached
values close to εK18O = 18.9 ‰ corresponding to laminar conditions above the
liquid-vapor interface (n = 2/3). However, they found values lower than
reported in the literature (i.e., εK18O < 14.1 ‰) at the end
of their experiments, when the dry soil surface layer had increased in
thickness and soil surface relative humidity was significantly lower than
100 %. These results were partly explained by the particular experimental
conditions leading to uncertainties in characterizing the isotope
compositions of evaporation when the dry soil surface layer was developed
the most. Nevertheless, the same observation was made in the present study
despite a different soil texture (silt loam versus quartz sand) and
noticeably
different atmospheric conditions (“free” laboratory atmosphere versus sealed
headspace circulated with dry air). Figure 9c displays the evolution of
εK2H (resp. εK18O) that provided the best fit with the
data (NSE = 0.99) by fitting the n parameter (shown in Fig. 9b) instead
of calculating it with Eq. (5). In this scenario, n decreased from one
to 0.59, with a mean value of 0.96 ± 0.03 during the period DoE 0–150.
Instead of changing the value of n over time (and therefore those
of εK2H and εK18O), another possibility is to consider
that after some time the relative humidity at the EF (RHEF) was different
from 100 %, although the EF was still at thermodynamic equilibrium. In
that case kinetic effects would have depended on the difference (RHEF–RH)
instead of (1–RH). Figure 9b shows the RHEF time course that
provided the best model-to-data fit (NSE = 0.92), when
εK2H and εK18O
were calculated (Eqs. 5 and 6). In
this second scenario, RHEF decreased from 100 to 81 % with a mean
value of 99.5 ± 0.03 % for the period DoE 0–150, i.e., in a similar
fashion than fitted n values obtained in the first scenario. These values
were significantly lower than those calculated with Kelvin's equation
linking RHEF with soil water tension at the EF in the case of
liquid-vapor equilibrium, which for the given soil retention properties
(Merz et al., 2014) would range between 100 and 99.6 %. In a third
scenario one could consider a combined decrease of n and RHEF to a
smaller extent, for which there are no unique solutions at each time step.
In a fourth scenario, the ratio of turbulent diffusion resistance to
molecular diffusion resistance is no more negligible, leading to n′ values
ranging between 0 and n (Merlivat and Jouzel, 1979). This last scenario was,
however, not verifiable. In any case, only decreasing kinetic effects could
provide a better model-to-data fit. Note that the formulation of kinetic
enrichments proposed by Merlivat and Coantic (1975) and based on the
evaporation model of Brutsaert (1982) was not tested due to lack of
appropriate data (i.e., unknown wind distribution profile over the soil
column). The formulations of Melayah et al. (1996) (n = 0) and Barnes and
Allison (1983) (n = 1) were also not tested as they give kinetic
enrichments constant over time and cannot explain a change of SEv value
through change of n. Finally, SEv calculations using diffusivity ratios
determined by Cappa et al. (2003) lead to lower values of SEv and a less
good model-to-data fit.
In the present study, information on δ2H and δ18O
of the evaporation flux was missing to address uncertainties in the
determination of εK2H
and εK18O. The experimental
setup would also have benefited from the addition of appropriate sensors
(e.g., micro-psychrometers) to measure the soil surface relative humidity
and especially RHEF, although the dimensions of the column would
certainly be a limiting factor. A more in-depth investigation of the
behavior of SEv (and isotope composition gradients with depth for that
matter) with time could be carried out with detailed numerical simulations
using an isotope-enabled SVAT model such as SiSPAT-Isotope.