Figure 3. A typical QMS spectrum of2H2O m/z 1 to 40. The small inserts show the logarithmic plots of m/z 0 to 10 (top) and 14 to 24 (bottom).
In analogy to the mixing of enriched 18O water and the replicate for SLAP, we added the amount of2H2O that was calculated to achieve a δ2H ≈ 0‰ to SLAP-rep-O.2H2O was weighed in a glass vial on an analytical balance (approximately 75 mg was weighed), SLAP-rep-O was weighed on a precision balance (1 L) in a 1 L brown Duran bottle. This vial was submerged in the 1 L flask with SLAP-rep-O. The resulting mixture VSMOW-rep-D was stirred for at least 48 hrs. All weights were corrected for the buoyancy effect.
In this second approach, the product VSMOW-rep-D (δ2H ≈ 0‰, δ18O, still SLAP-like, ≈ -55.5‰) was the basis of the mixing process with highly enriched 18O water.
The adding of highly enriched 18O water needed to arrive at δ18O ≈ 0‰ and the mixing of those two fluids was the same as described before.
Characterization of the isotopic delta values of VSMOW-rep-D was performed by the LGR-LWIA by direct comparison with SLAP for δ18O analysis and by direct comparison with VSMOW for δ2H analysis (on the VSMOW-SLAP scale). Subsequently, the produced VSMOW-rep-OD was measured by direct comparison with original VSMOW water, for both isotopes.
For the calculation of the best δ18O value for SLAP with the help of a validated spreadsheet (Faghihi16, the 17O and 18O abundances of the enriched 2H2O water had to be characterized as well. In analogy to the determination of2H and 17O abundances in enriched18O water, 2H2O was diluted first with demineralized Groningen tap water (1:7). Carbon dioxide with a known isotopic signature was equilibrated with this diluted 2H2O at 25 ºC for 48 hours (procedure described in Meijer17. CO2was extracted and δ 18O was measured on a dual inlet IRMS Mass spectrometer (a VG (now Isoprime) SIRA10). IAEA607 with approximately the same δ 18O signal as the diluted 2H2O water and some other local CIO references were identically treated and were used for normalization. δ 17O was determined via a method described in Elsig and Leuenberger18. Theδ 13C from the initial equilibration gas is known, and deduced from the deviation in δ 13C of the CO2 gas after equilibration and before equilibration with the known δ 13C,δ 17O could be determined. IAEA607 and the same local CIO references as for δ 18O analysis, were used for normalization. The 17O and18O abundances of the2H2O water are presented in the results section, along with their standard deviations of three repetitions.
The difference in stable isotopes measurements and the calculated stable isotope values by the validated spreadsheet (Faghini16) translates directly into a bestδ 18O value for SLAP with respect to VSMOW. In addition, the second approach has the beneficial side-effect that additionally a best δ 2H for SLAP could be determined. δ 2HVSMOW-rep-D was initially calculated from the actually added (buoyancy-corrected) weight and isotopic abundances of the 2H2O water and the weight and isotopic delta values of SLAP-rep-O (on the VSMOW-SLAP scale). Subsequentlyδ 2HVSMOW-rep-D was measured alongside VSMOW. The difference between this measurement and the calculated value translates directly into a bestδ 2H value for SLAP with respect to VSMOW.
We took care that the differences between the replicates and the genuine VSMOW and SLAP were small, so the δ18O and δ2H difference between the officially δ18O and δ 2H values (VMSOW-SLAP scale) and the ’true’ isotopic difference, or in other words, possible scale contractions, did not play a role.
2.4 Final uncertainty calculation.
To calculate the combined uncertainty for each single experiment, a Monte Carlo simulation was performed for the full experimental process. For all different sources in the total process, from weighing waters, to18O abundance measurements by QMS, until isotopic measurements with the LGR-LWIA, the uncertainties were determined or estimated.
To ascertain the contribution of uncertainties in the weighing process, a flask was weighed multiple times in order to determine the reproducibility of weighing. This procedure revealed that the spread in the weighing of the same flask multiple times, was within 5 times the uncertainty specified by the manufacturers, and thus multiplied by a factor of 5. So, for weights measured on the precision balance the accuracy was estimated at ± 0.05 g and for the analytical balance the accuracy was estimated at ± 0.05 mg. As a part of the quality control measures we have adopted in our laboratory, all balances, including the ones used in this work, are frequently calibrated.
As a cautious estimate, the uncertainties for the QMS18O abundances of the enriched 18O waters were chosen to be the standard deviations of the repetitional measurements. In Table 3 this is displayed for every enriched18O water. The 2H and17O abundances are determined via dilution. The isotopic measurements of the diluted 18O waters were performed on two different measurement days, and performed nine times per measurement day. From the weighted average of the total number of analyses and twice the standard error of the mean, the2H and 17O abundances were deduced with their 2σ uncertainty.
The isotopic measurements for SLAP, VSMOW and their replicates were measured on the LGR-LWIA. Per measurement day every replicate was injected 60 times, and VSMOW and SLAP were injected 90 times. The difference in δ18O (Δ δ18O) between the replicate and its “parent” (so SLAP for SLAP-replicate, and VSMOW for VSMOW-replicate) was averaged per measurement day. The error in the mean in the parent-replicate Δ δ18O was calculated (typically better than 0.03‰) and was the basis for the weights for calculating the weighted average for every Δ δ18O parent-replicate on multiple (typically 3) measurement days.
For the Monte Carlo simulation, a calculation was programmed in R. All calculations steps were performed 10,000 times with all the parameters and their uncertainties (assumed to belong to a normal distribution) as described above. This Monte Carlo simulation gives the uncertainty for product VSMOW-rep-O. A quadratic sum from the Monte Carlo uncertainty and the standard error in the mean of the isotopic measurements for product VSMOW-rep-O yielded the combined uncertainty per experiment. The Monte Carlo simulation was performed for the full calculation process for each experiment. The combined uncertainties per experiment are shown in the supplementary material, Table 4, and in the graph, Figure 6.
The three main uncertainty components in this combined uncertainty are the weight and 18O concentration determination of the enriched 18O water and theδ 18O measurement of SLAP-rep-O.
Despite one extra step in the second approach, the uncertainty in the final result is the same. In the first approach the Δδ 18O between SLAP-rep-O and SLAP and VSMOW-rep-O and VSMOW leads to a best δ 18O value for SLAP with respect to VSMOW. In the second approach Δδ 18O between VSMOW-rep-D and SLAP and VSMOW-rep-OD and VSMOW leads to a best δ 18O value for SLAP with respect to VSMOW.
All uncertainty sources are considered to be random errors, only causing variability in the end result. In addition, there are two sources of systematic error. The first would be a biased QMS 18O measurement method. It is unlikely, but still possible, that we systematically measure an 18O abundance that is too low. If this would be the case, the final end result for δ 18O value for SLAP would be more negative. In the next section, we describe a number of tests we performed to scrutinize our QMS-based abundance measurements.
The other source of systematic uncertainty is the 18R value for (V)SMOW and its uncertainty as reported by Baertschi718R = (2005.20 ± 0.45) x 10-6. Changing this value by one standard deviation up would lead to a 0.013‰ less negative delta value for SLAP.
As the total number of experiments is rather small (seven), the standard error in the mean of the averaged results forδ 18O value for SLAP for seven experiments, is increased by multiplying with a Student’s T-distribution factor.