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.