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^{1}, Elena S. F. Berman

^{1}, Lindsay Liebson

^{2}and Manish Gupta

^{1,a)}

### Abstract

Developments in cavity-enhanced absorption spectrometry have made it possible to measure water isotopes using faster, more cost-effective field-deployable instrumentation. Several groups have attempted to extend this technology to measure water extracted from plants and found that other extracted organics absorb light at frequencies similar to that absorbed by the water isotopomers, leading to δ^{2}H and δ^{18}O measurement errors (Δδ^{2}H and Δδ^{18}O). In this note, the off-axis integrated cavity output spectroscopy (ICOS) spectra of stable isotopes in liquid water is analyzed to determine the presence of interfering absorbers that lead to erroneous isotopemeasurements. The baseline offset of the spectra is used to calculate a broadband spectral metric, *m* _{ BB }, and the mean subtracted fit residuals in two regions of interest are used to determine a narrowband metric, *m* _{ NB }. These metrics are used to correct for Δδ^{2}H and Δδ^{18}O. The method was tested on 14 instruments and Δδ^{18}O was found to scale linearly with contaminant concentration for both narrowband (e.g., methanol) and broadband (e.g., ethanol) absorbers, while Δδ^{2}H scaled linearly with narrowband and as a polynomial with broadband absorbers. Additionally, the isotope errors scaled logarithmically with *m* _{ NB }. Using the isotope error versus *m* _{ NB } and *m* _{ BB } curves, Δδ^{2}H and Δδ^{18}O resulting from methanol contamination were corrected to a maximum mean absolute error of 0.93 ‰ and 0.25 ‰ respectively, while Δδ^{2}H and Δδ^{18}O from ethanol contamination were corrected to a maximum mean absolute error of 1.22 ‰ and 0.22 ‰. Large variation between instruments indicates that the sensitivities must be calibrated for each individual isotopeanalyzer. These results suggest that the properly calibrated interference metrics can be used to correct for polluted samples and extend off-axis ICOS measurements of liquid water to include plant waters, soil extracts, wastewater, and alcoholic beverages. The general technique may also be extended to other laser-based analyzers including methane and carbon dioxide isotope sensors.

### Key Topics

- Isotopes
- 24.0
- Ethanol
- 17.0
- Absorption spectra
- 9.0
- Spectrum analysis
- 6.0
- Contaminants
- 5.0

##### G01V

## Figures

Measured off-axis ICOS transmission spectra of an uncontaminated water standard, a 100 ppm_{v} methanol-in-water mixture (blue), and a 1% ethanol-in-water mixture (green). Insets show the non-linear, least-squares fits to the measured water standard and methanol mixture in red with residuals shown in grey. The methanol adds discrete, narrowband absorptions that can be clearly identified in the marked regions of interest. Ethanol (and larger organics) acts as a broadband absorber, which shifts the baseline offset coefficient, b_{0}.

Measured off-axis ICOS transmission spectra of an uncontaminated water standard, a 100 ppm_{v} methanol-in-water mixture (blue), and a 1% ethanol-in-water mixture (green). Insets show the non-linear, least-squares fits to the measured water standard and methanol mixture in red with residuals shown in grey. The methanol adds discrete, narrowband absorptions that can be clearly identified in the marked regions of interest. Ethanol (and larger organics) acts as a broadband absorber, which shifts the baseline offset coefficient, b_{0}.

Δ*δ* ^{18}O scales linearly with *m* _{ BB }, whereas Δ*δ* ^{2}H follows a 3rd order polynomial. Standard #1 and Standard #2 were measured twice for each ethanol concentration (total of four points at each doping level). Data points are an average of 4 injections and error bars show the standard error of the average. Note that the data are plotted versus (*m* _{ BB } − 1) such that isotope measurement error is zero at *m* _{ BB } = 1. Fits are forced through (0,0). The approximate ethanol concentration is shown on the upper x axis. Data plotted are from instrument #4.

Δ*δ* ^{18}O scales linearly with *m* _{ BB }, whereas Δ*δ* ^{2}H follows a 3rd order polynomial. Standard #1 and Standard #2 were measured twice for each ethanol concentration (total of four points at each doping level). Data points are an average of 4 injections and error bars show the standard error of the average. Note that the data are plotted versus (*m* _{ BB } − 1) such that isotope measurement error is zero at *m* _{ BB } = 1. Fits are forced through (0,0). The approximate ethanol concentration is shown on the upper x axis. Data plotted are from instrument #4.

Δ*δ* ^{18}O and Δ*δ* ^{2}H scale linearly with log(*m* _{ NB }). Standard #1 and Standard #2 were measured twice for each methanol concentration (total of four points at each doping level). Data points are an average of 4 injections and error bars show the standard error of the average. Note that the x axis zero is defined by the average log(m_{NB}) value of uncontaminated water standards. Fits are forced through (0,0). For larger values of *m* _{ NB }, a small deviation from linear behavior is visible; other groups have used a piecewise function to describe this relationship but observed a similar logarithmic trend.^{10} Approximate methanol concentration is shown on the upper x axis. Data plotted are from instrument #7.

Δ*δ* ^{18}O and Δ*δ* ^{2}H scale linearly with log(*m* _{ NB }). Standard #1 and Standard #2 were measured twice for each methanol concentration (total of four points at each doping level). Data points are an average of 4 injections and error bars show the standard error of the average. Note that the x axis zero is defined by the average log(m_{NB}) value of uncontaminated water standards. Fits are forced through (0,0). For larger values of *m* _{ NB }, a small deviation from linear behavior is visible; other groups have used a piecewise function to describe this relationship but observed a similar logarithmic trend.^{10} Approximate methanol concentration is shown on the upper x axis. Data plotted are from instrument #7.

Isotope error vs. metric fits for all 14 instruments: (a) 3rd order polynomial fits to Δ*δ* ^{2}H vs. *m* _{ BB }-1 showing a wide variety of responses to contamination with ethanol. Poor fits (i.e., low R^{2}) typically have a small total deviation, indicating minimal error dependence on *m* _{ BB } and thus ethanol contamination. (b) Linear fits to Δ*δ* ^{18}O vs. *m* _{ BB }−1. The terminal markers in (a) and (b) correspond to 2% ethanol. (c) Linear fits to Δ*δ* ^{2}H vs. log(*m* _{ NB }). (d) Linear fits to Δ*δ* ^{18}O vs. log(*m* _{ NB }). The terminal markers in (c) and (d) correspond to 100 ppm_{v} methanol. R^{2} values for each fit are shown in the legend.

Isotope error vs. metric fits for all 14 instruments: (a) 3rd order polynomial fits to Δ*δ* ^{2}H vs. *m* _{ BB }-1 showing a wide variety of responses to contamination with ethanol. Poor fits (i.e., low R^{2}) typically have a small total deviation, indicating minimal error dependence on *m* _{ BB } and thus ethanol contamination. (b) Linear fits to Δ*δ* ^{18}O vs. *m* _{ BB }−1. The terminal markers in (a) and (b) correspond to 2% ethanol. (c) Linear fits to Δ*δ* ^{2}H vs. log(*m* _{ NB }). (d) Linear fits to Δ*δ* ^{18}O vs. log(*m* _{ NB }). The terminal markers in (c) and (d) correspond to 100 ppm_{v} methanol. R^{2} values for each fit are shown in the legend.

Average absolute deviation after correction using the metrics described in this note. Black points were contaminated with a maximum of 100 ppm_{v} methanol, red points with a maximum 2% ethanol.

Average absolute deviation after correction using the metrics described in this note. Black points were contaminated with a maximum of 100 ppm_{v} methanol, red points with a maximum 2% ethanol.

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