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Geochimica et Cosmochimica Acta 73 (2009) 6697–6703
www.elsevier.com/locate/gca
Fractionation of oxygen and hydrogen isotopes
in evaporating water
Boaz Luz a,*, Eugeni Barkan a, Ruth Yam b, Aldo Shemesh b
b
a
The Institute of Earth Sciences, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
Department of Environmental Science and Energy Research, Weizmann Institute of Science, Rehovot 76100, Israel
Received 16 April 2009; accepted in revised form 10 August 2009; available online 19 August 2009
Abstract
Variations in oxygen and hydrogen isotope ratios of water and ice are powerful tools in hydrology and ice core studies.
These variations are controlled by both equilibrium and kinetic isotope effects during evaporation and precipitation, and
for quantitative interpretation it is necessary to understand how these processes affect the isotopic composition of water
and ice. Whereas the equilibrium isotope effects are reasonably well understood, there is controversy on the magnitude of
the kinetic isotope effects of both oxygen and hydrogen and the ratio between them. In order to resolve this disagreement,
we performed evaporation experiments into air, argon and helium over the temperature range from 10 to 70 °C. From these
measurements we derived the isotope effects for vapor diffusion in gas phase (ediffðHD16 OÞ for D/H and ediffðH2 18 OÞ for 18O/16O).
For air, the ratio ediffðHD16 OÞ /ediffðH2 18 OÞ at 20 °C is 0.84, in very good agreement with Merlivat (1978) (0.88), but in considerable
inconsistency with Cappa et al. (2003) (0.52). Our results support Merlivat’s conclusion that measured ediffðHD16 OÞ /ediffðH2 18 OÞ
ratios are significantly different than ratios calculated from simplified kinetic theory of gas diffusion. On the other hand,
our experiments with helium and argon suggest that this discrepancy is not due to isotope effects of molecular collision diameters. We also found, for the first time, that the ediffðHD16 OÞ /ediffðH2 18 OÞ ratio tends to increase with cooling. This new finding may
have important implications to interpretations of deuterium excess (d-excess = dD 8d18O) in ice core records, because as we
show, the effect of temperature on d-excess is of similar magnitude to glacial interglacial variations in the cores.
Ó 2009 Elsevier Ltd. All rights reserved.
1. INTRODUCTION
Variations of 18O/16O (or d18O) and 2H/1H (or dD) in
water and ice cores are important indicators of present
and past hydrologic processes and climate. The record of
these isotope variations in polar ice cores is certainly one
of the most detailed and important pieces of information
on climate conditions over glacials and interglacials. In particular, the combination of d18O and dD yields an additional
parameter, deuterium excess (d-excess = dD 8d18O). The
latter has been used as a proxy of past changes in atmospheric humidity and temperature in the source oceanic regions supplying moisture by evaporation to the polar ice
sheets. As it became clear from the pioneering works of
*
Corresponding author.
E-mail address: boaz.luz@huji.ac.il (B. Luz).
0016-7037/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved.
doi:10.1016/j.gca.2009.08.008
Craig (Craig, 1961; Craig et al., 1963), a major cause of
the d-excess is the different relations between the isotope
fractionation factors of oxygen (18a) and hydrogen (2a) in liquid/vapor equilibrium and in vapor diffusion in air. Later
on, Merlivat and Jouzel (1979) and Jouzel et al. (1982) proposed and used a method, based on variations in d-excess,
for estimating relative humidity of air over evaporation regions in the ocean. Johnsen and White (1989) realized that
temperature of the surface ocean region must play an important role affecting the magnitude of d-excess. Following
their logic, d-excess has been used as a proxy of temperature
variations in ice cores from Antarctica and Greenland (e.g.
Vimeux et al., 1999; Steffensen et al., 2008). Yet, for quantitative estimation of either humidity or temperature, it is necessary to know the fractionation factors of oxygen and
hydrogen isotopes for equilibrium and diffusion during
evaporation and precipitation.
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B. Luz et al. / Geochimica et Cosmochimica Acta 73 (2009) 6697–6703
In the case of the equilibrium fractionations there is
good agreement between various experimental studies
(Majoube, 1971; Horita and Wesolowski, 1994; Barkan
and Luz, 2005) as well as theory (e.g. Van Hook, 1968).
In contrast, as recently reviewed by Horita et al. (2008),
for the vapor-diffusion fractionation there is a considerable
scatter in the relationship between the diffusion fractionation effects of oxygen and hydrogen. Unfortunately, there
is no rigorous theory for calculating water diffusion coefficients in air and comparisons were made with simple models that are accurate only for monatomic gases. The
uncertainty in these parameters, in turn, raises questions
on the reliability of paleoclimatic and hydrologic interpretation of d-excess.
The goal of the present paper is to clarify the question
about the ratio between the diffusion fractionation factors
of oxygen and hydrogen isotopes in water. To this end we
partially evaporated water under carefully controlled conditions and determined the diffusion fractionation factors
from the enrichment of 18O over 16O and 2H over 1H in
the remaining water fraction.
Throughout this paper we present the fractionation factors (a’s) such that they are greater than 1. Thus, the isotopic
fractionation factor between an evaporating flux (e) and liquid water (w) is defined as: aevap = Rw/Re (and not Re/
Rw), where Rw and Re are the ratios between heavy and light
isotope species of water (1 H2 H16 O=1 H2 16 O or 1 H2 18
O=1 H2 16 O) in liquid and vapor, respectively. In the case of
vapor flux from an evaporating water reservoir at steady
state, this ratio can be expressed following Criss (1999)
and Cappa et al. (2003) as:
adiff aeq ð1 hÞ
1 aeq hðRa =Rw Þ
ð1Þ
where aeq is the liquid–vapor equilibrium fractionation factor; Ra is the isotopic ratio of air moisture; h is relative air
humidity; and adiff is the diffusion fractionation factor.
In our experimental setup the only source of water vapor
to the air column overlying the liquid is the flux of evaporating water vapor, hence Ra = Re and aevap = Rw/Ra. In
this case, Eq. (1) can be rewritten to express adiff as:
adiff ¼
aevap =aeq h
1h
udiff ¼
n
2
ediffðHD16 OÞ
adiff 1 ðDH2 16 O =DHD16 O Þ 1
¼ 18
¼
n
ediffðH2 18 OÞ
adiff 1 ðDH2 16 O =DH2 18 O Þ 1
ð3Þ
Merlivat (1978) obtained udiff of 0.88 (based on evaporation in laminar flow experiments), while Cappa et al. (2003)
obtained 0.52 (based on evaporation in turbulent flow
experiments). The discrepancy between the two studies cannot result from the different flow regimes because the effect
of turbulence (exponent n in Eq. (3)) on udiff is negligible. In
turn, Cappa et al. suggested that the difference between
their value and that of Merlivat was due to evaporative
cooling that was not taken properly into account by Merlivat. For that reason, in our experimental design we took
special care to minimize this effect, and below we show that
the high value obtained by Merlivat is unlikely a result of
overlooked evaporative cooling.
3. EXPERIMENTAL
3.1. Experimental setup
2. THEORETICAL BACKGROUND
aevap ¼ Rw =Re ¼
ies (e.g. Horita et al., 2008), we present the relationship between diffusion fractionations of hydrogen and oxygen by
using isotope effects e as:
ð2Þ
where all the parameters on the right are either known or
can be determined experimentally. aevap can be obtained
from Rayleigh fractionation experiments, and the relative
humidity (h) is calculated from the ratio of the evaporative
flux to the rate of dry gas flow. 18aeq and 2aeq are known
from previous experimental work (Majoube, 1971; Horita
and Wesolowski, 1994; Barkan and Luz, 2005).
Following Cappa et al. (2003), 18adiff and 2adiff can be
expressed as (DH2 16 O /DH2 18 O )n and (DH2 16 O /DHD16 O )n, where
DH2 16 O , DH2 18 O and DHD16 O are the molecular diffusivities of
1
H2 16 O;1 H2 18 O and 1 H2 H16 O, respectively. The exponent
n depends on the ratio of turbulent to molecular diffusion
and equals one for no turbulence. Then, as in previous stud-
The details of our experimental setup were given in Barkan and Luz (2007), where we measured the diffusion fractionation coefficients of 1 H2 17 O and 1 H2 18 O in air. An
important consideration in the design was minimization
of turbulence in the gas column above the liquid. To this
end, the flow of dry gas was directed away from the liquid
and was smoothed by passing it through glass wool. In
addition, the upper part of the evaporation tube was heated
(30 °C above the water temperature) such that a stabilizing temperature gradient was generated between the thermostatic lower part and the heated upper part. We
evaporated distilled water into nearly stagnant gas layer
(bath gas) the top of which was held at nearly zero humidity. The bottom of a glass tube with evaporating water was
held in thermostatic aluminum block. With the purpose to
minimize temperature differences between the evaporating
surface and the bulk of the liquid, the water was stirred.
In preliminary experiments we measured directly the differences between the temperatures of the block and the water,
as well as between the surface and bulk water, and in both
cases they were about 0.1 °C.
The d18O and dD of the remaining water after each
experimental run increased significantly due to fractionation effects of both equilibrium and molecular diffusivity.
Because turbulence in our setup was minimized, we obtained large isotope effects of molecular diffusivities. This,
together with the precise temperature control, allowed
increasing the accuracy of the derived ratios between the
diffusion coefficients.
3.2. Isotope analyses
Measurements of d18O were run at Hebrew University
using the method of Barkan and Luz (2005). In short,
2 ll of water are converted by fluorination into O2 gas using
CoF3 reagent. The produced O2 is transferred into a stain-
Author's personal copy
Oxygen and hydrogen isotopes in evaporating water
ln(δ18O + 1) (‰)
60
18α
evap = 1/(-34.026/1000+1) = 1.03522
40
20
y = -34.026Ln(x) - 5.194
0
2
R = 0.99998
-20
0
0.25
2α
120
ln(δD + 1) (‰)
less steel holding tube on a collection manifold immersed in
liquid helium. At the end of 10 sample processing, the manifold is warmed up to room temperature and connected to a
Thermo-Finnigan Deltaplus isotope ratio mass spectrometer
(Thermo Scientific, Bremen, Germany). The ratio 18O/16O
was measured in dual inlet mode by multi-collector mass
spectrometry. Each mass spectrometric measurement consisted of three separate runs during which the ratio of sample to reference is determined 30 times. The pressures of the
sample and reference gas were balanced before each of the
three runs. The reported d-values are averages of three runs.
The
mass spectrometer error (standard error of the mean (r
pffiffiffiffiffiffiffiffiffiffiffi
/ n 1; r = 0.02, n = 90) multiplied by Student’s t-factor
for a 95% confidence limits) in d18O was 0.004&.
The analyses of D/H ratios were done at the Weizmann
Institute using a Thermo-Finnigan H/D device connected
online to a Thermo-Finnigan MAT 252 mass spectrometer.
The sample is injected directly into a heated Cr oven
(850 °C), reduced, and the resulting hydrogen is admitted
to the dual inlet system for classical sample/standard isotope ratio measurements. The instrumental precision (statistics as for d18O measurements, r = 0.08, n = 6) was
0.09&.
6699
0.5
0.75
1
0.75
1
evap = 1/(-79.168/1000+1) = 1.08597
80
40
y = -79.168Ln(x) - 20.160
0
2
R = 0.99997
-40
0
0.25
0.5
Remaining fraction (f)
Fig. 1. An example of the regression analysis used for calculating
aevap. The change in isotopic ratios obeys a Rayleigh distillation
process. The data shown are for the experiment with air at 39.8 °C.
4. RESULTS
The experiments of water evaporation into air were conducted near 10, 20, 40 and 70 °C, and the duration of each
experiment was adjusted in order to obtain variations in the
remaining fraction of liquid water in the range 0.8–0.3. In
addition, similar experiments were done with He and Ar
as bath gases near 40 °C. The measurements of each sample
for both d18O and dD were run in triplicate and the results
are given in Table 1.
From the obtained data we first calculated the overall
fractionation coefficient of water evaporation (aevap) by
regression analysis (see Fig. 1 for an example). In a second
step, we used the derived aevap values together with known
liquid–vapor equilibrium fractionation factors and humidity to calculate 2adiff and 18adiff with Eq. (2) and then udiff
with Eq. (3). All the data are given in Table 2. The precision
is better than 0.0005 for 2adiff and better than 0.0003 for
18
adiff. At 10 °C the evaporation rate was much smaller than
at higher temperatures and the experiments took more than
one month for reaching f = 0.4. As a result, the precision of
the fractionation coefficients in this case was less – 0.001 for
both 2adiff and 18adiff.
In the case of 18adiff the results for diffusion in air are in
good agreement with those of Barkan and Luz (2007) except for the 69.5 °C experiment where 18adiff is considerably
smaller. As pointed out by O’Connell et al. (1969), the density of water vapor is smaller than that of air due to its lower molecular weight, and this may cause buoyancy
convection and thus turbulence in the gas column. Because
the evaporation rate at 69.5 °C was more than five times
Table 1
Remaining fraction (f), d18O and dD (& vs. VSMOW) of water during the evaporation experiments.
Bath gas
t (°C)
f
d18J
dD
Bath gas
t (°C)
f
d18J
dD
Air
69.5
1
0.637
0.419
0.194
5.10
7.01
18.09
38.72
20.10
4.36
27.90
73.17
Air
20.1
1
0.568
0.393
0.219
4.82
15.41
28.75
50.49
19.61
37.01
74.87
138.75
Air
39.8
1
0.559
0.377
0.261
5.10
14.58
28.35
41.43
20.10
26.50
58.70
89.90
Air
10.0
1
0.603
0.609
0.480
0.385
4.82
13.56
13.16
21.41
30.45
19.61
38.26
37.18
66.22
92.88
Ar
39.9
1
0.637
0.385
0.257
4.82
11.70
30.04
45.11
19.61
16.57
58.12
92.75
He
39.7
1
0.607
0.330
0.208
5.10
1.89
11.00
17.73
20.1
12.35
52.97
84.91
Note. Each data point represents an average of three determinations with a precision (absolute difference from the average) of 0.015& for
d18O and 0.25& for dD.
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B. Luz et al. / Geochimica et Cosmochimica Acta 73 (2009) 6697–6703
Table 2
Temperature, evaporation rate, relative humidity and fractionation factors for water vapor diffusion in air, argon and helium.
Bath gas
t (°C)
Evap. rate
(mmol m2 s1)
Humidity
2
Air
Air
Air
Air
Ar
He
10.0
20.1
39.8
69.5
39.9
39.7
0.11
0.37
1.30
6.79
1.23
3.70c
0.0195
0.0241
0.0274
0.0419
0.0274
0.0783
1.12864
1.10929
1.08597
1.05873
1.08675
1.06929
aevap
18
2
1.03758
1.03692
1.03522
1.02696
1.03734
1.01471
1.02876
1.02302
1.02060
1.01618
1.02144
1.00464
aevap
adiff
18
udiffa
1.02712
1.02753
1.02750
1.02130
1.02967
1.00694
1.06 ± 0.08b
0.84 ± 0.02
0.75 ± 0.03
0.76 ± 0.03
0.73 ± 0.02
0.67 ± 0.6
adiff
a
udiff = ediffðHD16 OÞ /ediffðH2 18 OÞ = ð2 adiff 1Þ=ð18 adiff 1Þ.
The errors are based on propagation of uncertainties of all the parameters used in the calculations.
c
The higher evaporation rate into helium is due to its lower resistance, than either air or argon, to vapor diffusion. An important factor
affecting the lower resistance of helium is its small atomic weight (see Eq. (4)).
b
faster than at lower temperatures, the air column was probably slightly destabilized by the higher buoyancy flux and
thus caused some turbulence.
In Fig. 2, we present the trends of diffusion coefficients
with temperature. As can be seen, the behavior of 2adiff
and 18adiff is different: while 18adiff remains about constant
(excluding the value at 69.5 °C), 2adiff keeps increasing as
the temperature goes down. This difference becomes clearer
in a plot of udiff vs. temperature (Fig. 3) because, as discussed above, the effect of turbulence is canceled out in such
plot. As can be seen, similar values were obtained at near 70
1.030
18α
diff
αdiff
1.025
2α
1.020
diff
1.015
0
20
40
Temperature
Fig. 2. Plots of
temperature.
60
80
( oC)
18
adiff (triangles) and
2
adiff (squares) vs.
1.20
1.10
ϕdiff
1.00
0.90
0.80
0.70
0.60
0
20
40
60
80
Temperature ( oC)
Fig. 3. udiff vs. temperature for water vapor diffusion in air (solid
squares), argon (open circle) and helium (open square). For clarity,
the errors for argon and helium (Table 2) are not shown.
and 40 °C, but udiff tends to increase at 20 and even more so
at 10 °C.
The results of the experiments with helium and argon at
40 °C (Table 2 and Fig. 3) show that within the experimental error there is no effect of bath gas on udiff.
5. DISCUSSION
5.1. Molecular diffusivities
The experiments of Merlivat (1978) and of Cappa et al.
(2003) were run at about 20 °C. At that temperature, our
value for 2ediff/18ediff (0.84) is in very good agreement with
Merlivat (0.88), but not with Cappa et al. (0.52). Cappa
et al. explained the discrepancy between their and Merlivat’s result by evaporative cooling that was not taken into
account by Merlivat in the calculation of aeq. Considering
that in Merlivat’s experiments the flow of gas was laminar,
evaporation rate must have been much smaller than in Cappa et al., while the isotope effects of molecular diffusivity
were large. Thus, the errors due to evaporative cooling
could not have significantly affected the reported udiff of
0.88. We also mention that in our experiments evaporative
cooling of the liquid surface was negligible, and we obtained a similar result as Merlivat. In contrast, Cappa
et al. did not measure the liquid surface temperature and
their calculations of cooling could be inaccurate. For example, Cappa et al. stated that evaporative heat loss can result
in water-surface cooling of up to 5 °C with respect to the
bulk temperature of the liquid. However, as we mentioned
previously (Barkan and Luz, 2007) direct measurements
(Paulson and Parker, 1972) of surface cooling at similar
experimental conditions as in Cappa et al. showed that
the surface-cooling effect could not be greater than 2 °C.
Importantly, Cappa et al. based their estimates on the
experimental work of Ward and Stanga (2001). These
experiments were conducted with distilled water at surface
temperatures below 4 °C and the temperature increased
with depth in the liquid. In such conditions, as is well
known, buoyancy-driven convection is not present and
strong temperature gradient may develop near the surface
of the evaporating water. In conclusion, the discrepancy
pointed out by Merlivat between the measured udiff and
the calculated value based on simplified kinetic theory is
real. Its origin, however, remains an open question.
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Oxygen and hydrogen isotopes in evaporating water
In the rigorous kinetic theory diffusion coefficients can,
in principle, be calculated from the nonlinear Boltzmann
integro-differential equation. However, the main problem
is solving this equation. Chapman and Enskog independently obtained a solution of the Boltzmann equation using
the following most important assumptions (for details, see
Hirschfelder et al., 1964): (1) there are only binary collisions; (2) the collisions are strictly elastic; (3) quantum effects are neglected; and (4) intermolecular forces react
only along the line connecting the centers of molecules. It
is clear that when using these assumptions the Chapman–
Enskog theory can be used only for monatomic gases at
low pressure and high temperature. Yet, in the absence of
other theoretical models, this theory is widely used for polyatomic gases (e.g. Poling et al., 2004).
In a general case, the solution for binary diffusion in the
Chapman–Enskog theory can, in the first approximation,
be expressed as:
DAB ¼ 1:858 103 T 3=2
ð1=M A þ 1=M B Þ1=2
P r2AB XAB
ð4Þ
where DAB is the diffusion coefficient of gas A in gas B;
cm2 s1; T is temperature in degrees Kelvin; MA and MB
are molecular masses; P is pressure, atm; X = f(kT/e) is
the so called collision integral; and e and r are characteristic
parameters of intermolecular forces – e is the maximum
depth of the potential energy well and r is an effective
molecular size for the selected intermolecular potential. Because high precision studies on gas binary diffusion are rare,
the values of e and r are mainly determined from viscosity
measurements or data on the second virial coefficients. We
note however, that in this way diffusion coefficients of polyatomic molecules are 10% lower than directly measured
values, and for polar molecules the difference should be
even greater (Barkan, 1988). Furthermore, both parameters
strongly depend on the chosen potential function and the
particular gas properties. Evidently, in most studies using
different intermolecular potentials for simple nonpolar
gases, the results obtained with Eq. (4) were satisfactory
(e.g. Barkan 1984a,b; Poling et al., 2004). In contrast, for
polyatomic gases, and especially for polar gases, the results
were poor (e.g. Poling et al., 2004). This confirms that a
priori Eq. (4) is not suitable for accurate determination of
the water diffusion coefficients.
Nevertheless, Merlivat (1978) compared her experimental values of adiff with ones based on simple theory by using
the following equation:
adiff ¼
DL
¼
DH
1=2 2
M H ðM L þ M G Þ
CH þ CG
CL þ CG
M L ðM H þ M G Þ
ð5Þ
where C is the corresponding molecular collision diameters,
and thus equals to r in Eq. (4); subscripts L and H stand for
any light and heavy isotope species, respectively; and subscript G refers to the bath gas in which water vapor diffuses
(air, argon and helium in our case). We point out that Eq. (5)
is based on a simplified form of Eq. (4) assuming that X values for heavy and light isotope species of water are equal.
For oxygen isotopes, the agreement between measured
(1.028, Merlivat, 1978; Barkan and Luz, 2007) and calcu-
6701
lated (1.0318, from Eq. (5) assuming equal collision diameters), adiff is reasonable. Moreover, Barkan and Luz (2007)
obtained nearly perfect agreement between measured and
calculated values for the ratio ln(17adiff)/ln(18adiff): 0.5185
and 0. 5184. However, in the case of deuterium substitution
of hydrogen, there is considerable difference between the
calculated 2adiff (1.0165) and the measured one (1.025).
Likewise, for udiff the calculated value is 0.52 and measured
values are 0.84 (the present study) and 0.88 (Merlivat,
1978).
The latter observation led Merlivat to suggest isotope effect of collision diameters. However, our experimental data
for water vapor diffusion in helium does not confirm this
explanation. Indeed, using the collision diameters for water
isotopes as in Merlivat, and taking C of helium as 2.55 Å
(Poling et al., 2004), we calculated udiff of 3.3. We note that
the obtained value of udiff is given only to indicate the order
of its magnitude because the figures used for collision diameters were only approximate. The calculated udiff is much
larger than the measured value (0.67 ± 0.06), while the latter value is similar within the experimental error to the corresponding figures determined for air and argon (Fig. 3).
We, therefore, conclude that whereas the measurements
of Merlivat are very reliable, her explanation for the deviation from the simplified theory of gas kinetics is inadequate.
The results in Table 2 and Fig. 3 show that diffusion of
water vapor in air deviates from simple theory of gas diffusion in yet another respect. As it follows from Eq. (4), binary
diffusion rates depend among other factors on temperature.
Yet, in the approach used by Merlivat (Eq. (5)) the temperature effect is cancelled out in the calculation of diffusivity
ratios (DL/DH = adiff) for any two heavy (H) and light (L)
isotope species. Likewise, udiff, which is calculated from
2
adiff and 18adiff, should also be temperature independent.
However, our results show temperature dependence of udiff,
and suggest that the assumption of equality of X values for
different isotope species is inaccurate.
In summary, the results of the present study give clear
evidence that a simplified kinetic theory is not suitable for
calculating accurate ratios of diffusion coefficients between
1 2 16
H H O and 1 H2 16 O. While a solution for this problem is
out of the scope of the present paper, our results, showing
the temperature dependence of udiff, may have important
implications for isotope hydrology and, therefore, for climatic interpretation of polar ice cores.
5.2. Implications for ice core records
Depending on the magnitude of udiff, shifts in d-excess
are interpreted to reflect larger or smaller effects of temperature and humidity in the oceanic source of vapor to polar
ice. Moreover, Jouzel and Merlivat (1984) showed that the
magnitude of d-excess depends not only on conditions in
the source evaporation region, but also on kinetic (diffusion) fractionation during ice condensation from atmospheric vapor. Given a certain d-excess in atmospheric
vapor, the effect of kinetic fractionation in ice condensation
is to lower the value of d-excess in snow. Our study shows
that udiff tends to increase as temperature decreases. At
present we do not know the udiff temperature dependence
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B. Luz et al. / Geochimica et Cosmochimica Acta 73 (2009) 6697–6703
below the freezing point, but in order to illustrate the possible importance of our observations we assume, as a first
approximation based on our data for 10 and 20 °C, that
it is linear: udiff = 1.25 0.02.t (t in °C).
For demonstration purpose we use a simple precipitation and fractionation simulation model similar to that of
Jouzel and Merlivat (1984). In their model, atmospheric vapor condenses to form ice due to progressive cooling of air
masses. As is well known, the heavier isotopes are preferentially removed to ice, and as a result, the remaining vapor
becomes depleted in heavy isotopes of oxygen and hydrogen. In the simple model we used, this isotope fractionation
is controlled by both solid–vapor equilibrium (asv) and kinetic fractionation due to vapor diffusion through air into
the precipitation site (akin):
Rs ¼ asv =akin Rv
ð6Þ
where R is H218O/H216O or 1H2H16O/H216O; and subscripts s and v stand for solid ice and atmospheric vapor,
respectively. Following Jouzel and Merlivat (1984), akin is
given by:
akin ¼
asv adiff ðS 1Þ þ 1
S
ð7Þ
where S is supersaturation and it is usually assumed to be
linearly related to cloud temperature (t) such that S = p
qt, where t is in °C. There are no direct observations
of S that are relevant to polar precipitation, and thus
parameters p and q are obtained from best fitting of snow
isotopic composition. In our calculations we used the
parameters of Landais et al. (2008): S = 1 0.0017t. 18adiff
was taken as 1.028 and 2adiff was calculated from 18adiff and
udiff using Eq. (3). We then simulated d18O and dD of precipitation with Eqs. (6) and (7) and used the derived numbers to calculate d-excess. Our simulation model differs
from Jouzel and Merlivat, and other similar but more
sophisticated models (e.g. mixed cloud isotope models of
Ciais and Jouzel (1994) and Kavanaugh and Cuffey
(2003)), in that udiff in Eq. (3) is temperature depended.
In Fig. 4, we plot simulated curves of d-excess vs. d18O
for temperature dependent udiff and also for constant udiff
value 0.88 (Merlivat, 1978) for the temperature range from
40 to 60 °C. The values derived with the new temperature dependent udiff differ considerably from the simulation
with the previous estimate of constant udiff. Admittedly, the
extrapolation from our data to very low temperature is not
satisfactory, and in future simulations it would be desirable
to have better estimates based on observations at sub freezing temperatures as well as on theory.
The magnitude of variations in d-excess in Antarctic ice
cores is about 2–4& (e.g. Vimeux et al., 1999; Uemura
et al. 2004), and they were interpreted to indicate humidity
and temperature shifts in the source oceanic region. Yet,
quantitative assessment of the records relies on models,
and they in turn, depend on observational constraints of
the major controlling mechanisms of evaporation and precipitation. The simple modeling based on our new results
indicates that depending on the input value of udiff, the simulated d-excess may change by several permil. These variations are of similar magnitude to those seen in the
VSMOW
6702
15
b
a
10
5
0
-60
-55
-50
-45
-40
-35
-30
-25
δ18O (‰ vs. VSMOW )
Fig. 4. Simulated d-excess vs. d18O for the temperature range from
40 to 60 °C. (a) Simulation with udiff = 0.88 (Merlivat, 1978).
(b) simulation with udiff = 1.25 0.02.T (T in °C). Note, that the
difference between curves (a) and (b) at d18O of about 55& is of
similar magnitude to variations seen in Antarctic ice core records
between glacials and interglacials.
Antarctic record, and thus previous interpretations in terms
of temperature and humidity changes may be in error. Of
course, our modeling is very simple and more sophisticated
modeling is necessary for better assessment of past humidity
and temperature. In addition, more experiments at low temperatures are needed in order to obtain better parameters for
such modeling. Nevertheless, it is clear that our new findings
must be considered in future evaluations of ice core records.
6. CONCLUSIONS
1. The ediffðHD16 OÞ /ediffðH2 18 OÞ value at 20 °C was estimated as
0.84, which is in very good agreement with measurements of Merlivat (1978), but not with Cappa et al.
(2003). Taking into account that the value of Cappa
et al. is based on estimated rather than on measured
water surface temperatures, we suggest that their value
is inaccurate.
2. Similar values of ediffðHD16 OÞ /ediffðH2 18 OÞ were derived from
evaporation into air, argon and helium. This shows that
different bath gases do not affect the diffusivity ratios.
Therefore, isotope effects of molecular collision diameters are not likely to be the cause for the discrepancy
between the measured values and calculated ones based
on the simplified kinetic theory.
3. It was experimentally observed, for the first time, that
ediffðHD16 OÞ /ediffðH2 18 OÞ depends on temperature – it tends
to increase with cooling. More experiments are needed
in order to obtain accurate ediffðHD16 OÞ /ediffðH2 18 OÞ values
at low temperatures. Yet it is clear, that the temperature
dependence of ediffðHD16 OÞ /ediffðH2 18 OÞ should be considered
in future model simulations and interpretation of d18O,
dD and d-excess in polar precipitation and ice cores.
This will allow improving our understanding of present
and past hydrologic processes and climate.
ACKNOWLEDGMENTS
We thank Martin Miller for careful reading of the manuscript
and for many valuable suggestions. The comments of Associate
Author's personal copy
Oxygen and hydrogen isotopes in evaporating water
Editor J. Horite and two anonymous reviewers were very helpful.
Discussions with Joel Gat and S.K. Bhattacharya were important
at the early stages of our study. B.L. thanks the Israel Science
Foundation for Grant 181/06 that supported this research.
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Associate editor: Juske Horita