2.1.2. Sampling by Liquid Condensation
In liquid condensation method, ambient atmospheric water vapor is
sampled by condensing the moisture from ambient air on an ice-cooled
conical surface at 0 °C. The aluminum cone (Diameter 15cm, Height 18cm)
is filled with ice cubes and covered with PVC lid so that its external
conical surface cools down to 0 °C and ambient water vapor condenses on
it. This condensation is faster compared to cryogenic trapping. The
duration of sampling period depends on the dew point. With an average Rh
of about 65 % and temperature of 27 °C, it typically took 45 minutes to
an hour to collect around 15 ml of liquid condensate.
The condensation in this method takes place at ≈ 0 °C throughout the
experiment and the liquid condensate is referred to as ‘liquid’
[representing fractionated isotopic composition] for the remainder
of this study. Detailed sampling procedure and sampling devices for
liquid condensation method is discussed by R. D. Deshpande et al.
(2013). As mentioned earlier, condensation method involves kinetic
fractionation due to preferential condensation of isotopically lighter
isotopic water molecule due to their higher diffusive velocities.
The samples from PRL, Ahmedabad were collected mostly during May to
September of 2005-2008 followed by from May of 2013 to October of 2014.
Few samples were collected in the years of 2009, 2010 and 2012 as well.
At NGRI, Hyderabad the samples were collected mostly from July, 2008 to
October, 2009. At NIH, Roorkee the collection was done mostly during May
to October, 2009 and then again in January, 2010.
The volume of samples collected in these experiments was very small
(~ 2ml for complete cryogenic trapping and <15
ml for liquid condensation). Adequate precautions were taken to ensure
that there is no evaporative isotopic enrichment of sample during
storage and transport. To ensure that any such sample doesn’t form part
of this study inadvertently, samples with d-excess values ≤-5 are not
included in this study.
Isotopic
Analysis
The oxygen and hydrogen isotopic analysis was carried out by standard
gas equilibration method using isotope ratio mass spectrometer (IRMS) in
continuous flow mode of gas bench (Maurya, Shah, Deshpande, & Gupta,
2009). Based on analyses of multiple aliquots of secondary laboratory
standards the precision of measurement was better than 0.1‰ for
δ18O and 1‰ for δD.
3.
Theory
In case of complete cryogenic trapping during unidirectional mass flow,
all the H2O molecules are converted from vapor to liquid
phase and hence isotopic composition of liquefied vapor is the same as
that of vapor. In ideal case of liquid condensation under equilibrium
condition (forward and backward rate of reaction same), liquid is
isotopically enriched in heavier isotopes (18O and
2H) compared to vapor from which it is condensed.
Isotopic enrichment in this case can be explained in terms of
equilibrium fractionation factor (Horita & Wesolowski, 1994; Majoube,
1970). In our experiments it is observed that compared to vapor from
which it is condensed, the liquid condensate is depleted in
18O and less enriched in 2H than
that expected under equilibrium condition. Consequently, the resultant
liquid condensate has high d-excess, due to kinetic isotope
fractionation involved in it (R. D. Deshpande et al., 2013).
Under the equilibrium condition ambient vapor pressure equals, the
saturation vapor pressure and rate of forward and backward reaction is
similar. But in liquid condensation method of this study, in which
condensation occurs on ice-cooled aluminium surface at 0°C, the actual
vapor pressure where condensation occurs is more than the saturated
vapor pressure (even though ambient air is undersaturated but at much
higher temperature than 0°C). Thus, on the ice-cooled metallic surface
there is a layer of air supersaturated with water vapor and hence
condensation of liquid from ambient air takes place under supersaturated
environment. The theory of kinetic effect associated with liquid
condensation under supersaturated environment is discussed in detail by
R. D. Deshpande et al. (2013), similar to the theory for the solid
condensation given by Jouzel and Merlivat (1984). It is noteworthy that
both these papers explain why condensate formed under supersaturated
environment has different isotopic composition compared to the ambient
vapor from which it is formed, but it is not possible to back calculate
true isotopic composition of vapor from the measured isotopic
composition of condensate. This is because the isotopic difference
between vapor and the condensate formed under supersaturated condition
strongly depend on the degree of supersaturation given by saturation
index (Si):
Si=\(\frac{\text{vapour\ pressure\ of\ water\ at\ ambient\ temperature\ and\ relative\ humidity}}{vapour\ pressure\ of\ water\ at\ condensation\ temperature\ (0)}\)(1)
During liquid condensation experiments the maximum degree of
supersaturation possible can be computed from measure ambient
temperature, Rh and condensation temperature (~0°C) but
the actual effective degree of supersaturation prevalent at the
condensing surface cannot be measured or estimated precisely because of
uncertainties in estimating condensation temperature. This is mainly
because the actual temperature at condensing surface would be slightly
more than the ice temperature (~0°C) because of latent
heat of condensation added to the condensation surface. Secondly, the
ice inside the cone also melts slowly during experiment period which
would slightly increase its temperature. Thus, temperature of
condensation is expected to be slightly more than 0°C. Further, at
molecular scale, removal of water molecules from vapor to liquid phase
due to condensation would reduce the effective degree of
supersaturation. Also, the effective diffusive velocities at prevalent
degree of supersaturation cannot be estimated accurately. These are the
reasons why it is not possible to theoretically back calculate the true
isotopic composition of ambient vapor from that of liquid condensate.
With these uncertainties in precisely estimating degree of
supersaturation, we observe that the δ18O values of
liquid condensate collected on different days have an inverse
relationship with degree of supersaturation Si. The
δ18O and δD
values of liquid condensate are found to progressively decrease with
increasing Si (Fig 1). This would suggest that a
microscopic layer supersaturated with water vapor governs
δ18O of liquid condensate by preferentially allowing
lighter isotopologues of water to pass through it from open atmosphere
to the condensation surface compared to heavier isotopolgues. This
discrimination against heavier isotopologues become stronger with
increasing degree of supersaturation and the resultant increase in
concentration gradient which drives the vapor from ambient air to
metallic cone.
To explain this, we define the saturation index Si as a
ratio of the prevalent partial pressure of the vapor
(ev) in ambient air to that of the saturation vapor
pressure (ei) over water at condensing surface in this
study.
For the sake of understanding the process, the immediate surrounding of
the conical cone can be divided into three discrete boxes (A), (B) and
(C). At time t=to, the ice-cubes were introduced into the cone hence
reducing condensation temperature of condensing surface to
~0°C which in turn reduces saturation vapor pressure
over water from ei to
ei’. The amount of reduction in
saturation vapor pressure (ei) after introducing
ice-cubes in the cone is large if the ambient temperature is higher i.e.
the difference between ambient and condensation temperature is greater.
When saturation vapor pressure (ei) drops below actual
vapor pressure (ev) the value of Si
increases to values greater than 1, which means that supersaturated
condition
(ev>ei’
ie. Si =
ev/ei’ >
1) is generated on the condensing surface (indicated by box S in the Fig
2). It is noteworthy that supersaturated condition generated at the
condensation surface doesn’t mean increase in the absolute humidity. It
only means that there are more water molecules present in the air than
it can hold at condensing temperature. Since the air cannot hold any
more water vapor, H2O molecules condense from vapor to
liquid and tend to reduce the degree of supersaturation in zone A.
Consequently, the actual water vapor content (absolute humidity) reduces
just on the condensing surface because H2O molecules
condense from vapor to liquid and are removed from the environment. To
compensate for this removal of water molecules from zone A, there is a
mass flow from zone B to A and zone C to B, such that actual vapor
pressure reduces from C to B to A
(ev2>ev1>ev).
Thus, we have a concentration gradient from (C) to (A) which drives
vapor to come and condense at the walls of the conical vessel. In this
process, isotopic water molecules
(H216O, HDO and
H218O) have to diffuse from zone C to
B to A to S. Lighter molecules have higher diffusivities and
consequently, lighter molecules reach faster at condensing surface and
get removed in liquid faster than heavier molecules. This
diffusivity-based discrimination of molecules in favour of lighter mass
becomes more prominent with increasing degree of supersaturation. This
explains our observation of progressively decreasing
δ18O with increasing Si (Fig 1(b)).
Jouzel and Merlivat (1984) have developed a model to explain the kinetic
isotope effect based on the diffusive velocities of the various isotopes
through air. This model relates kinetic fractionation factor with ratio
of diffusion coefficients:
αkin=\(\frac{S_{i}}{{[\alpha}_{\text{equil}}\times\frac{D}{D^{{}^{\prime}}}\times(S_{i}-1)]+1}\)(2)
where αequil is the equilibrium fractionation factor,
D/D’ represents the ratio of diffusivities for the
lighter to the heavier isotope of oxygen. For a given condensation
temperature, αequil and D/D’ are both
constants. Using this model, R. D. Deshpande et al. (2013) have
explained observed isotopic difference between vapor and liquid
condensate using extrapolated D/D’ values at 0°.
A similar model has been applied to present study aimed at estimating
true isotopic composition of vapor from that of liquid condensate. The
values of αequil were computed from the regression
equation given by Horita and Wesolowski (1994). It is to be noted that
αkin for supersaturated condition, obtained from eq. 2
above, is always less than unity, therefore, total fractionation (α =
Rl/Rv = αkin ×
αequil) involved in the liquid condensation works out to
be less than equilibrium fractionation. Consequently, liquid condensate
is less enriched in heavy isotopes compared to ambient vapor, than that
expected under equilibrium condition. In highly supersaturated
conditions when αkin <
1/αequil the liquid condensate is even isotopically
depleted in heavier isotopes compared to ambient vapor. In spite of
these theoretical facts, it is not possible to accurately compute
isotopic composition of vapor from the liquid condensate due to lack of
accuracy in estimating values of actual degree of supersaturation,
diffusive coefficients and condensation temperature (R. D. Deshpande et
al., 2013).
To overcome above problem a non-linear regression model is discussed in
the following which correlates the isotopic composition of liquid and
vapor such that true isotopic composition of ambient water vapor can be
more accurately estimated from measured values of liquid condensate.
Regression Equation and
Results
A non-linear regression equation is discussed in the following to relate
the experimental δ18O values of liquid condensate and
vapor which can be used to estimate the true isotopic composition of
vapor from measured values of liquid condensate. The variation of the
vapor isotopic values was modelled based on the equation provided by
Jouzel and Merlivat (1984) as follows.
\(1+\delta_{l}=\frac{D^{{}^{\prime}}\times(e_{v}\times\left(1+\delta_{v}\right)-e_{i}\times\frac{\left(1+\delta_{l}\right)}{\alpha_{\text{equil}}})}{D\times(e_{v}-e_{i})}\)(3a)
Where \(\delta_{l}\) and \(\delta_{v}\) stand for the liquid and vapor
δ18O values respectively, ev and
ei denote the partial vapor pressure and saturated vapor
pressure over water and D/D’ stands for the ratio of
diffusivities for the lighter to the heavier isotope of oxygen. This can
be further simplified to:
\({(10}^{-3}\times\delta_{l}+1)=\frac{S_{i}\times\alpha_{\text{equil}}\times(10^{-3}\times\delta_{v}+1)}{{[\alpha}_{\text{equil}}\times\frac{D}{D^{{}^{\prime}}}\times(S_{i}-1)]+1}\)(3b)
Where Si stands for the index of super-saturation and
D/D’ stands for the ratio of diffusivities for the
lighter to the heavier isotope of oxygen. This equation works on the
assumption that the kinetic effect is caused due to diffusion related
processes arising from super-saturated conditions. The saturation index
Si is defined as a ratio of the partial vapor pressure
of the vapor(ev) to that of the saturated vapor
pressure(ei) over water. This equation relates the
isotopic composition of liquid condensate and vapor in terms of
equilibrium fractionation, saturation index and ratio of diffusivities.
This equation also includes the terms which represent kinetic
fractionation as mentioned in Equation 2.
Therefore, Equation 3b is used as the basis to form our non-linear
regression model.
We intend to find \(\delta_{v}\) based on \(\delta_{l},\ S_{i}\) and
other parameters as discussed above. Hence, we simplify this equation to
express δv in terms of δl and
Si. The ratio of diffusivities D/D’ is
a constant. We can write:
Say,
δl/1000 = X and δv/1000 = Y;
D/D’=A,
Then equation (3b) reduces to
\begin{equation}
X+1=\frac{\alpha_{\text{equil}}\times S_{i}\times(Y+1)}{\alpha_{\text{equil}}\times A\times\left(S_{i}-1\right)+1}\nonumber \\
\end{equation}
Solving for Y we get:
\begin{equation}
Y=A\times X+\frac{X}{S_{i}}\times\left(\frac{1}{\alpha_{\text{equil}}}-A\right)+\frac{1}{S_{i}}\times\left(\frac{1}{\alpha_{\text{equil}}}-A\right)+A-1\nonumber \\
\end{equation}
In the above equation, A (=D/D’) and
αequil are both constants. The aim is to express Y
(=10-3 δv) in terms of X
(=10-3 δl) and Si only
and later solve for the coefficients using a non-linear regression
equation. Thus, our parameters X and Si take the form of
X, \(\frac{X}{S_{i}}\) and \(\frac{1}{S_{i}}\) multiplied by constants.
Since we are performing unconstrained optimization using regression
analysis, we can write
\(Y=A\times X+B\times\left(\frac{X}{S_{i}}\right)+C\times\left(\frac{1}{S_{i}}\right)+K\)(4)
Where A, B, C are terms made up of D/D’ and
αequil and can be replaced with constants and K is a
dimensionless constant.
Here A, B, C and K are to be obtained via our non-linear regression
equation. At a fixed temperature the diffusivity ratio
(D/D’) and equilibrium fractionation factor
(αequil) are constant. Hence, the vapor isotopic value
is a function of only the saturation index (Si) and the
liquid isotope values. Interpretative implications of this equation can
be evaluated for two extreme situations: one where there is just pure
equilibrium fractionation (i.e. Si =1); and the other
where there is a pure diffusional process with Si
tending to infinity.
In the case of the pure diffusion process, ev
>> ei, hence, plugging it into
equation (3a), we get:
\(1+\delta_{l}=\frac{D^{{}^{\prime}}\times(1+\delta_{v})}{D}\) (5)
Thus, the dependence on Si is expected to vanish
completely. Hence Si appears in the denominator of
equation (4) connecting δv and δl which
is expected. This means that the surrounding air is so super-saturated
that the diffusion effect far outweighs the contribution due to
equilibrium isotopic fractionation in this case.
In the case of the other extreme, we have equilibrium fractionation and
an absence of any kinetic isotope effect. Hence the Si
term disappears in this case. But in our experiment, we encounter a
hybrid of the two possible extremes with neither a pure equilibrium
process, nor a pure diffusional one. Hence, we encounter a cross term
δl/ Si which explains the cross-over
between an equilibrium and diffusion related underlying mechanism.
For the purpose of calibration, we used part of the data set obtained
from Physical Research Laboratory (PRL), Ahmedabad. We chose 75 samples
otherwise arbitrarily only making sure that the calibration data-set had
an equitable distribution over the range of Si values
(Table S1). The Si term is calculated using the local
relative humidity and temperature. Hence, the calibration set was chosen
to cover all possible range of Si values so that our
model is trained to work appropriately and robustly under all possible
weather conditions. We used the MATLAB Curve Fitting Toolbox for the
purpose of our regression analysis. The model was calibrated using this
dataset and equation (4) can now be written for δ18O:
\(\delta_{v}=0.9905\times\delta_{l}-0.6996\times\frac{\delta_{l}}{Si}-22.36\times\frac{1}{Si}+8.172\)(6)
Equation (6) is used to obtain the δ18O values of
ground level water vapor using the liquid isotopic values and saturation
index Si as input. The predicted δ18O
values for Ahmedabad site were plotted against the observed vapor values
(Fig 3) and the mean and standard deviation of their difference was
noted. The same was done for δD as well.
We can observe that the predicted results are in close agreement with
the observed values for Ahmedabad (Table S2) for both
δ18O and δD isotopes. To test the strength and
robustness of the model, we repeated this exercise for
δ18O for the two other sampling locations at Hyderabad
(Table S4) and Roorkee (Table S3) as shown in Fig 4. We also computed
the mean and standard deviation of the difference between the observed
and modelled values.
The mean and standard deviation of the difference between observed and
modelled δ18O is calculated (Table 1). It is observed
that predicted values based on above non-linear regression follow the
observed values with far better accuracy and precision than possible by
remote sensing. Significance of this method is that it can be
conveniently used for isotopic tagging of water vapor in any remote
areas like mountain, forest or desert to understand the vapor dynamics
in hydrologic and ecological systems.