We developed a method to measure in situ the isotopic composition of liquid water with minimal supervision and, most important, with a temporal resolution of less than a minute. For this purpose a microporous hydrophobic membrane contactor (Membrana) was combined with an isotope laser spectrometer (Picarro). The contactor, originally designed for degassing liquids, was used with N2 as a carrier gas in order to transform a small fraction of liquid water to water vapor. The generated water vapor was then analyzed continuously by the Picarro analyzer. To prove the membrane's applicability, we determined the specific isotope fractionation factor for the phase change through the contactor's membrane across an extended temperature range (8°C–21°C) and with different waters of known isotopic compositions. This fractionation factor is needed to subsequently derive the liquid water isotope ratio from the measured water vapor isotope ratios. The system was tested with a soil column experiment, where the isotope values derived with the new method corresponded well (R2 = 0.998 for δ18O and R2 = 0.997 for δ2H) with those of liquid water samples taken simultaneously and analyzed with a conventional method (cavity ring-down spectroscopy). The new method supersedes taking liquid samples and employs only relatively cheap and readily available components. This makes it a relatively inexpensive, fast, user-friendly, and easily reproducible method. It can be applied in both the field and laboratory wherever a water vapor isotope analyzer can be run and whenever real-time isotope data of liquid water are required at high temporal resolution.
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 Determination of the isotopic composition of liquid water by conventional methods like isotope ratio mass spectrometry (IRMS) is still very time-consuming and costly. With the development of laser-based isotope analyzers like off-axis integrated cavity output spectroscopy (OA-ICOS) or cavity ring-down spectroscopy (CRDS) the analysis of stable water isotopes became much faster, considerably less expensive, and the analyzers can be operated by less experienced users. Nonetheless, the conduction of isotope studies still is a trade-off between limited spatiotemporal resolution and extensive (and expensive) lab work. Therefore, it is virtually impossible to obtain stable isotope data at high temporal resolution (minute or below) as it is being common with in situ temperature or electrical conductivity measurements. However, recent attempts to deploy stable isotope analyzers into the field brought some relief on this issue [Berman et al., 2009]. They measured stable isotope ratios by high-frequency injections of liquid water and were able to reveal otherwise unnoticed fine-scale variations. Therefore, we believe that an in situ system to determine more or less continuously stable isotopes of water in the liquid phase would provide a very valuable tool for many studies in hydrology, soil science, and ecology.
 In conventional analysis, there is usually a significant lag between the time of sampling and the time of data acquisition. Again, the invention of laser-based instruments have the potential to bring some help, as they are capable of analyzing vapor directly and continuously instead of single injections of liquid water at preset time steps with no possibility to get any information in between. Thus, in order to be able to observe real-time processes in the liquid phase, one needs to continuously transfer the isotopic signal from liquid water to the vapor phase. Recent attempts used a marble-filled equilibrator and a minimodule device for this purpose [Koehler and Wassenaar, 2011]. However, their approach focused on the feasibility of converting liquid water to water vapor with different devices without stressing the potential of one method or relating to the temporal resolution in particular.
 In our study, we tested a microporous hydrophobic membrane contactor with the aim of developing a method that allows to achieve stable isotope sampling in liquid water with a temporal resolution of minutes and less and to significantly reduce the time lag between sampling and data acquisition.
2. Methods and Materials
2.1. Determination of the Fractionation Factors
 For the entire experimental setup a membrane contactor (Membrana, MicroModule 0.5 × 1 × 1 inches) originally designed for degassing liquids was selected (http://www.liquicel.com). Inside the contactor a microporous, hydrophobic, polypropylene-based membrane with a surface area of 100 cm2, divides the liquid from the gaseous phase. The producer's recommended liquid flow rate for complete degasification is from 5 to 30 mL min−1 and the maximum working pressure on the gas side at 25°C is 3.1 bars. Preliminary results indicated that there is no difference in obtained vapor concentration when flow rates of water and gas stay within these ranges. We used the MicroModule in the so-called “sweep mode” with N2 as the carrier gas to convert a fraction of liquid water to water vapor. The contactor's gas outlet is connected directly to a CRDS analyzer (Picarro, L2120-i) providing ppmv, δ18O and δ2H values. Since the instrument is capable of analyzing water vapor only, normally liquid water samples are being vaporized in an accessory vaporizer.
Figure 1 (including box a) shows how the liquid inlet of the membrane contactor was connected to water of known isotopic composition, pumped with a constant flow rate of 22 mL min−1. After passing along the membrane, the water at the liquid outlet is discarded (excess water). The gas inlet of the membrane contactor is connected to pure N2 with a constant flow of 200 mL min−1. At the surface of the membrane the initially completely dry nitrogen gets in contact with the liquid water diffusing through the membrane, and saturated vapor leaves the membrane contactor at the gas outlet side, which is connected to the sample inlet of the CRDS analyzer. Additionally, a gas excess line is installed because of a mismatch between the applied gas flow and the analyzer's demand (30 mL min−1). Also the temperature of the liquid water right before the contactor is being monitored and logged with a temperature logger (GMH 3750). Both, the contactor and the point of temperature determination are enclosed in a thermally isolated box to ensure measurement of relevant temperature to the greatest possible extent. Furthermore a three-port valve was custom installed at the analyzer's sample inlet port in order to switch between vapor from the membrane module and vapor from the vaporizer. This made it possible to calibrate with liquid standards before, during and after the experiment by conventionally injecting water into the vaporizer.
 In order to determine the relationship between the isotope fractionation factor and the liquid water temperature, we pumped water of known isotopic composition through a water bath that was gradually cooled down. After reaching a minimum temperature (∼8°C) at the contactor's water inlet port the basin was slowly heated to almost ambient room temperature (∼21°C) in order to avoid condensation of oversaturated vapor in the tubing using temperature around or above room temperature. This procedure was repeated several times and also repeated with water of isotopic compositions of −9.10‰ and −16.82‰ for δ18O and −62.5‰ and −126.5‰ for δ2H. Liquid water samples of isotopically appropriate in-house standards (−16.82‰ and −34.69‰ for δ18O and −126.5‰ and −270.8‰ for δ2H, all referenced to VSMOW-SLAP scale) were analyzed conventionally with the same analyzer before and after each run for calibration purposes.
 Since we conducted our experiment at varying temperatures, a wide range of vapor concentrations were encountered because of the different dew points. This made it necessary to perform a correction similar to the procedure described by Schmidt et al. . However, we did not distinct between “normal” and vaporizer-derived vapor. By injecting various amounts of three isotopically different lab standards we determined correction factors of 1.45 × 10−5 ‰/ppmv for δ18O and 3.05 × 10−4 ‰/ppmv for δ2H. No significant correlation between these slopes and the raw values of the isotopic composition (see Schmidt et al.  for details) could be observed.
 One important task was the determination of the time lag between measuring the isotopic composition of the vapor in the analyzer and the corresponding liquid water temperature. Such a time lag occurs since the temperature is being measured in situ while the vapor has to pass through the tubing into the analyzer's cavity. It was determined by shifting temperature and vapor concentration data against each other until no hysteresis could be observed in the respective scatterplot. Comparing the associated time data yielded a time lag of about 10 s (with the temperature being first, of course).
 For each run the isotopic composition values of the water vapor from the contactor were calibrated employing the raw values of the liquid standards measurements. Since the isotopic composition of the water running through the contactor was known, fractionation factors were calculated and assigned to the respective temperatures. The equilibrium fractionation of isotopes between different phases or chemical compounds depending on the temperature was expressed by a model of type 1 [Clark and Fritz, 1997]:
where α is the isotopic fractionation factor, TK is the temperature (in K), and a, b, and c are empirical parameters assigned to the isotopes (and chemical reaction) in question. By minimizing the sum of square errors (SSE), such a model was then fitted to the derived fractionation factor–temperature data for each run independently. Finally, averages of the obtained empirical parameters were calculated and used in the sequel of our experiment.
2.2. Application: Soil Column Experiment
 The above described setup was then applied to a column experiment with all settings i.e., flow of water and carrier gas kept constant. Two waters of significantly different isotopic compositions (−9.25‰ and −16.82‰ for δ18O, −63.7‰ and −126.5‰ for δ2H) were pumped alternatingly through a soil column with 10 cm diameter and 50 cm length filled with fine sand (Figure 1, box b). The flow rate through the column was 27 mL min−1. A portion of the water (22 mL min−1) from the column outlet was then divided to the contactor. Again, a water bath was used to intentionally cause highly unstable temperature conditions. Liquid water leaving the contactor at the excess port was sampled in vials in varying intervals (2 to 5 min) in order to verify the experimental results independently via conventional analysis with CRDS of liquid water samples. The water vapor was again sampled continuously by the CRDS analyzer. The liquid water isotopic compositions were then calculated using equation (1) including the derived mean empirical parameters a, b, and c and the continuously logged temperature at the contactor, shifted by 10 s.
 In the first part of our experiments, parameters were determined for the equation (1) describing the relationship between temperature and isotopic fractionation factor. For this purpose we used water of different isotopic compositions at changing temperatures (8°C–21°C). As described above, fractionation factors were calculated and equation (1) was fitted to the obtained data by minimizing the SSE. Figure 2 shows the experimentally determined fractionation factors depending on the water temperature for 18O and 2H for one experiment, where the dots represent the experimental values and the solid lines are the fitted model results.
 As stated before, the entire procedure was repeated four times. Figure 3 shows the final relationships between fractionation factor and temperature for each run (thin black lines). The thick solid black line represents the mean of all single experiments by averaging each parameter of equation (1) separately. The thick dashed line was derived similar to the thick solid black line, but here all respective data have been corrected for vapor concentration effects. In comparison, the thick gray line represents the relationship as presented by Majoube  for a free water surface. The parameters of all models according to equation (1) are summarized in Table 1. They deviate significantly from the Majoube  relationship and show a stronger dependence to temperature for 18O and 2H.
Table 1. Modeled Parameters According to Equation (1), Including the Standard Deviation
 In the second part of the study we used the contactor for a soil column experiment with varying water temperature (13.4°C to 19.6°C). Figure 4 (top) shows the derived time series of water temperatures and vapor concentrations. Corresponding to the temperature changes, they vary between 16,000 and 25,300 ppmv. We used the obtained averaged relationship between fractionation factor and temperature (Figure 3, thick solid black line) to calculate delta values for the liquid phase from the obtained vapor values and the respective temperatures, also shown in Figure 4 (middle) and Figure 4 (bottom). The light gray dots represent delta values calculated for each measurement time (time step of 1.8 s), the solid black line is the moving average with a window size of 120 s, whereas the black dots represent the delta values obtained by conventional analysis of liquid samples. The new method is capable of tracking the variation of isotope values very well even under abruptly varying water temperatures, which we introduced systematically. Even the fast changes of the isotope values during the transition from higher to lower values or vice versa are well captured. The relative short-term variations are larger for δ18O than for δ2H, which is also related to the relative higher standard deviation for water vapor measurements with the Picarro instrument.
 The scatterplot in Figure 5 shows the relationship of conventionally measured liquid water samples and the water vapor-derived values. The horizontal error bars of the liquid water samples show a constant value of 0.16‰ for δ18O and 0.6‰ for δ2H as observed in the lab with conventional analysis using the Picarro L2120-i. On the other hand, the vertical error bars of the vapor-derived values range from 0.12‰ to 0.64‰ for δ18O and 0.5‰ to 5.5‰ for δ2H. The standard error values have been calculated using the 60 individual data points representative of each individual dot. They are smaller in the case of an isotopic plateau (top right and bottom left in the scatterplot) under steady state conditions and higher in the case of transition from one plateau to another (central part of scatterplot). The errors for the vapor-derived observations during steady state conditions are in the same range as the errors of the liquid water observations. Regardless of the magnitude of the error bars, the values remain close to the 1:1 relationship.
 As can be seen in Figure 3, the differences in absolute values between the uppermost and the lowermost line representing the single experiments are very small. Within the temperature range of our study, standard deviations calculated from these values are below 0.00016 for α18O and below 0.0011 for α2H. Because of the relationship [Clark and Fritz, 1997]
these standard deviations result in analytical errors of about 0.16‰ and 1.1‰ for δ18O and δ2H, respectively. This happens to be in the order of magnitude of the error of the isotope analyzer for the case of δ18O and only slightly higher for δ2H. Further increase in the precision of our method is difficult to achieve. One can also see clearly that it was inevitable to determine new parameters for equation (1) that differ from the ones reported by Majoube  prior to application of the method (Figure 3, dashed line versus gray line). Obviously, isotope fractionation can be enhanced in the presence of the contactor's membrane. We found deviations from Majoube's  prediction ranging from 0.27‰ to 0.64‰ for δ18O and from 1.0‰ to 3.9‰ for the case of δ2H. This extends the results found by other researchers using a different membrane module [Koehler and Wassenaar, 2011]. They reported such deviations for only one isotope and only a limited temperature range without quantifying this effect.
 When applying our method to the soil column experiment, we refrained from correcting the measurements for vapor concentration effects separately as we had to determine new parameters for equation (1) anyway and were able to determine parameters that already include this correction (Figure 3, solid black line versus gray line). Figure 4 (top) shows that vapor concentration and temperature are highly correlated. Thus, a vapor concentration–temperature scatterplot yields a fine line (not shown here), making it easy to determine the response time of our system. The delta isotope values calculated are in excellent agreement (R2 = 0.998 for δ18O and R2 = 0.997 for δ2H) with the liquid reference samples, being analyzed conventionally with CRDS. There seems to be no dependency on absolute temperature or isotopic composition values or trends. Deviations between the two ways of data acquisition are predominantly less than one SD (error bars of values calculated from vapor versus liquid water samples in Figure 5). The magnitude of the error bars must be attributed to the fast change of isotopic composition but do not affect the precision (deviation from the 1:1 relationship in Figure 5). In the present form, our experiment is restricted to situations where water temperature does not exceed ambient air temperature, i.e., the temperature of the contactor itself and the tubing that transports the vapor from the membrane contactor to the analyzer. However, this limitation can be addressed by using any kind of tube heating or warm box housing of the entire setup.
 The new methodology presented in this study proved to be applicable for continuous, online analysis of liquid water stable isotope compositions under varying environmental conditions. Access to the isotope data is no longer restricted by time-consuming conventional analysis after the actual liquid water sampling, which can easily take several days or more depending on the number of samples. The precision achieved seems to be very promising compared to the precision for the liquid water sampling and during vapor sampling furthermore the entire setup requires only a minimum of supervision. Because of the size of the components in use, the respective volumes of water and vapor allow for a short response time of the entire system. Even great sudden shifts are easily followed indicating the potential of our method to decipher variations at small time scales. Further reduction of contactor housing and tubing could increase the temporal resolution even more. Limitations of the proposed method regarding possible exceedance of water temperature relative to air temperature can be easily solved.