Measurement of water vapor line strengths in the 1.4–2.7 µm range by tunable diode laser absorption spectroscopy

Journal of Quantitative Spectroscopy & Radiative Transfer 165 (2015) 108–122

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Measurement of water vapor line strengths in the 1.4–2.7 mm range by tunable diode laser absorption spectroscopy Andrea Pogány a, Alexander Klein a, Volker Ebert a,b,n a b

Physikalisch-Technische Bundesanstalt, Bundesallee 100, 38116 Braunschweig, Germany Center of Smart Interfaces, Technical University Darmstadt, Jovanka-Bontschits-Strasse 2, 64287 Darmstadt, Germany

a r t i c l e in f o

abstract

Article history: Received 18 May 2015 Received in revised form 20 June 2015 Accepted 28 June 2015 Available online 6 July 2015

Line strengths of nine water vapor absorption lines in the wavelength range between 1.37 and 2.71 mm with line strengths of 10–23–10–20 cm/molecule have been measured using direct tunable diode laser absorption spectroscopy (dTDLAS). Four different light sources were used: three distributed feedback (DFB) diode lasers with wavelengths of 1.37 mm, 2.55 mm and 2.71 mm for measuring one application-specifically selected absorption line with each laser, and a vertical-cavity surface-emitting laser (VCSEL) radiating around 1.39 mm for the measurement of six further absorption lines. Despite the different light sources and line strengths, a uniform measurement and data evaluation method was developed and applied to all lines, and the experimental set-up was kept as similar as possible. This allows a thorough and uniform uncertainty analysis and evaluation of the contributions of the individual experimental parameters to the uncertainty of the derived line strengths. A comprehensive and transparent uncertainty analysis is given for the measurements. Uncertainties of our measured line strengths are in the 1.1–2.5% range (k ¼ 2, 95% confidence level). Our measured line strength values agree well with line strengths in the HITRAN 2012 database and other literature sources, we realized lower uncertainties up to a factor of 5–10. & 2015 Elsevier Ltd. All rights reserved.

Keywords: Line strength Water vapor Tunable diode laser absorption spectroscopy Uncertainty, Metrology

1. Introduction Accurate and reliable spectral line parameters are inevitable in many scientific and technical applications. Water vapor is the most important greenhouse gas in the atmosphere; therefore it is extensively studied in in-situ [1,2] and remote sensing [3] measurements in the atmosphere and needs to be included in climate and radiative transfer models [4]. Furthermore, water vapor plays an important role in various industrial applications, i.e. the operation of combustion engines [5] or the processing of

n Corresponding author at: Physikalisch-Technische Bundesanstalt, Bundesallee 100, 38116 Braunschweig, Germany. Tel.: þ 49 531 5923201; fax: þ 49 531 5923209. E-mail addresses: [email protected], [email protected] (V. Ebert).

http://dx.doi.org/10.1016/j.jqsrt.2015.06.023 0022-4073/& 2015 Elsevier Ltd. All rights reserved.

natural gas [6]. Remote sensing and modeling applications directly rely on the quality of spectral line data, in particular the line strengths, which directly influence the uncertainty of the results. In the case of in-situ measurements, line data are indispensible for so-called absolute, self-calibrating spectroscopic measurements [7–9], where instead of calibrating the spectrometer with gas standards, the concentration of the analyte is deduced from the measured absorption spectrum and physical properties of the gas sample and the optical set-up according to the Beer–Lambert law. Absolute measurements are particularly valuable in the case of adsorptive and reactive analytes, where calibration gas mixtures have limited stability, accuracy and availability. Water vapor is one of these analytes. Reliable calibration gas mixtures, especially in the mmol/mol amount fraction range, require the use of carefully designed and validated generators, which are

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expensive and mostly not suitable to use for calibrations in harsh field environments (e.g. calibration of airborne spectrometers during the flight). As water vapor is one of the most often studied molecules, an unusually large amount of experimental and calculated line data is available in literature. The IUPAC Task Group on “A database of water transitions from experiment and theory” carried out a thorough analysis of available literature data [10]. They collected a large number of experimental line positions, analyzed them for consistency and combined them with computed line strengths [11] to obtain an extensive database. This database is particularly useful for obtaining highly accurate line positions. The commonly used source of line strengths, broadening coefficients and pressure shifts is the HITRAN [12] database, which is updated every 4 years. The 2012 edition of the database [13] contains data on more than 7.4 million absorption lines of 47 molecules, including 120 isotopologs, and thereby serves as an important source of spectral data for numerous applications. However, quality assurance in such an extensive database is not straightforward, and a uniform, well documented and transparent uncertainty assessment is not possible due to the high variety of data sources. The sources include experimental data obtained by different techniques by different research groups, as well as calculated line data using different models. The quality of the data is quantified by the authors in different ways – e.g. accuracy, precision, standard deviation, agreement with other literature data, standard or expanded uncertainty is given – and the conversion between these quantities is not straightforward. Consequently, the quality of the spectral data in HITRAN is only coarsely classified by uncertainty classes; moreover, uncertainties are often overestimated or not given at all. As an example, the uncertainty of the line strengths of 66% of the water vapor lines with line strengths above 10–23 cm/ molecule in the HITRAN 2012 database is 5–10%, which is critical for several practical applications. Our present publication aims to provide experimentally determined, highly accurate line strengths for a few application-specifically selected water vapor lines, and it concentrates on the metrological aspects of line strength measurements. Metrology attempts to improve reliability and comparability of measurement results. Traceability is a fundamental term in metrology; it refers to the “property of a measurement result, whereby the result can be related to a reference through a documented, unbroken chain of calibrations, each contributing to the measurement

109

uncertainty” [14]. General rules of uncertainty assessment are summarized in the ISO Guide 98-3 “Evaluation of Measurement Data – Guide to the Expression of Uncertainty in Measurement” (GUM) [15]. The study of these metrological aspects has already begun in the field of spectroscopy as well, and line strength measurements with the aim of traceability have been published by different research groups [16–19]. One main advantage provided by traceable measurements originates from the thorough, well-documented uncertainty analysis. This ensures comparability of the results and clearly indicates which experimental parameters contribute significantly to the measurement uncertainty. Based on the latter information it can also be deduced, which parts of the experiment need to be improved to further reduce the uncertainty. In the following, we present line strengths of nine water vapor lines measured by dTDLAS. The experimental section (Section 2) describes the spectrometer set-up and the measurement procedure, and also presents an overview of the studied lines and experimental conditions. In Section 3 (Results), first we discuss the two most critical parameters in our experiments (line area in Section 3.1 and gas handling in Section 3.2). Thereafter, we present the derived line strengths (Section 3.3) with a detailed uncertainty assessment (Section 3.4) and compare our results with literature data (Section 3.5). In the conclusions and outlook (Section 4) we discuss the further potentials and limitations of our experiments.

2. Experimental set-up 2.1. Selected lines The studied absorption lines, as well as the most important experimental conditions are listed in Table 1. All of these lines have been selected due to their suitability for certain practical applications. Several publications show that the line at 1.37 mm is one of the best suited near-infrared (NIR) absorption lines for highly accurate concentration measurements [5,20–22]. The line at 2.55 mm is one of the stronger water absorption lines in the 2.6 mm region [23] and is very well separated from CO, CO2 and other H2O lines, thus well suited for atmospheric monitoring, or high pressure engine measurements [24], while the line at 2.71 mm can be used for the simultaneous

Table 1 Summary of the studied absorption lines and experimental conditions. Wavenumber (cm–1)

Wavelength (nm)

Number of measurements

Pressure range (hPa)

Temperature range (K)

3684.528 3920.089 7180.400 7181.156 7182.209 7182.950 7185.394 7185.597 7299.431

2714.0 2551.0 1392.7 1392.5 1392.3 1392.2 1391.7 1391.7 1370.0

12 7 4 4 4 4 4 4 17

0.21–1.02 0.17–0.23 0.93–4.71 0.93–4.71 0.93–4.71 0.93–4.71 6.10–8.31 6.10–8.31 0.17–0.85

293.43–294.34 293.17–293.86 294.27–295.12 294.27–295.12 294.27–295.12 294.27–295.12 295.03–295.25 295.03–295.25 293.23–294.09

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detection of H2O and CO2 [9]. The lines around 1.39 mm show significantly different temperature dependence, which makes them suitable for spectroscopic thermometry [25]. Line strengths of the selected lines are in the range of 10–23–10–20 cm/molecule. 2.2. Spectrometer set-up The used experimental set-up was based on a single pass cell (stainless steel, 0.77 m path length, C in Fig. 1). Temperature sensors (three Pt100 sensors, TS2 in thermal connection with the cell wall, and TS1 and TS3 with the gas in the cell) and a pressure sensor (MKS Baratron, with 1 torr or 10 torr measurement range, PS) were connected to the cell. We used four different light sources: a telecommunication-type distributed feedback (DFB) diode laser in a butterfly package with 1.37 mm wavelength (NEL), two DFB diode lasers in a TO-5 package with 2.71 mm and 2.55 mm wavelengths (Nanoplus) and a vertical-cavity surface-emitting laser (VCSEL) in a TO-46 package with 1.39 mm wavelength (VERTILAS). The lasers (DL in Fig. 1) were installed one after the other in the measurement set-up to perform measurements at different wavelengths. Temperature and driving current of the lasers were controlled by laser drivers (Thorlabs, LD) and a wavelength scan was performed by means of a current ramp provided by a function generator (Agilent, FG). According to the wavelength range, the photodiode (D) was also exchanged; we used an InGaAS photodiode for the wavelength range 1.37–1.39 mm, and an InAs detector for 2.55–2.71 mm. The photodiode signal was amplified by a factor of 104–105 using a low-noise current amplifier (Femto, CA), digitized by an 18-bit data acquisition card (National Instruments, DAQ) and processed using a proprietary LabView-based fitting software running on a PC. Gas samples of 100% water vapor were prepared using a water reservoir filled with distilled water (H2O in Fig. 1), which was connected to the cell through a ball valve (V1). A turbomolecular pump (P) connected to the cell through a second ball valve (V2) was used to evacuate the cell and to adjust the pressure of the gas in the cell. 2.3. The measurement method The line strength measurements were performed in pure water vapor samples to reduce uncertainty in the water vapor mole fraction, as well as to ensure that adsorption– desorption processes on the cell walls do not change the chemical composition of the gas in the cell. Pressure in the gas cell was kept below 1 hPa during most measurements to minimize pressure broadening of the absorption lines. At such low pressures the Lorentzian width of the measured absorption lines is less than 4% of the Doppler width. In the case of the weaker lines, higher pressures up to 8.3 hPa were used to obtain a better signal-to-noise ratio, which resulted in Lorentzian widths up to 15% of the total line width. The measurements were performed at room temperature. The experimental conditions for all of our measurements are summarized in Table 1.

Fig. 1. Schematics of the measurement set-up. H2O: water reservoir, DL: light source (DFB diode laser at 1.37 mm, 2.55 mm, 2.71 mm or VCSEL at 1.39 mm), LD: laser driver, FG: function generator, C: gas cell, D: detector (InAs or InGaAs photodiode), CA: current amplifier, DAQ: data acquisition system, TS1, TS3: Pt100 temperature sensors in thermal connection to the gas in the cell, TS2: Pt100 temperature sensor in thermal connection to the cell wall, PS: pressure sensor, V1, V2: ball valves, P: turbomolecular pump, PC: computer, dashed line indicates a sealed housing to purge the optical part of the set-up with dry air (xH2 O o 3 mmol/mol).

A critical part of the experiment is the preparation of the pure water vapor samples. For this purpose we connected a reservoir filled with distilled water to the cell. After evacuation of the system, pure water vapor can be introduced into the measurement cell from the reservoir. We used two different methods to prepare the samples. Differences between line strengths obtained by measurements performed with the two sample preparation methods were found to be lower than the reproducibility of the measurements using either method, therefore negligible. Method (a) involved liquid water and consisted of four steps: 1. evacuating the cell by opening the valve to the pump (V2); 2. closing the valve to the pump and opening the valve to the water reservoir (V1) to fill the cell with water vapor up to the vapor pressure at room temperature (  23 hPa); 3. closing the valve to the reservoir and opening the valve to the pump to pump down the cell to the desired pressure of 0.1–8.3 hPa.

The procedure was repeated several times to evacuate the headspace above, as well as remove dissolved gases from the water in the reservoir. The water sample in the reservoir was o1 cm3 and the tube connecting it to the valve was as short as possible (  2 cm) to reduce headspace volume. Filling the gas cell with this method took approx. 3 min. Method (b) involved evacuation of the system after freezing the water in the reservoir and thereafter letting water vapor into the cell by warming up the ice in the reservoir. The procedure consisted of the following steps: 1. freezing the water in the reservoir using liquid nitrogen; 2. evacuating the system by opening both valves; 3. closing the valve to the pump (V2); 4. warming up the water in the reservoir to introduce water into the cell and closing the valve to the reservoir

A. Pogány et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 165 (2015) 108–122

(V1) when the desired pressure is achieved.

3. Results

This second method enabled a more effective evacuation of the headspace. However, the headspace in this case was also larger, the tube connecting the reservoir was  20 cm long to minimize cooling of the gas cell when freezing the water in the reservoir. Filling the gas cell using method (b) required 15 min, which is considerably longer than in the case of method (a), mainly due to the relatively long time required to evaporate the water from the cooled reservoir. After filling the cell we waited 10 min to let the system reach thermal equilibrium and, thereafter, recorded the spectra for another 10 min with a sampling rate of approx. 4 Hz, i.e. approx. 2400 spectra were recorded in one measurement sequence. Pressure and temperature values were recorded simultaneously with each individual spectrum. Line strengths were determined by fitting each spectrum individually and the obtained line strengths were averaged for the whole measurement sequence time of 10 min to obtain S0(i). The measurement procedure, including evacuating the cell, filling with water vapor and recording the spectra, was repeated 4–17 times. For each line, measurements on different days at different pressures were carried out to allow the determination of reproducibility and to identify possible bias caused by a wrong pressure measurement. Finally, the S0(i) values obtained from the individual measurement sequences were averaged to get the final line strength value (S0) for each absorption line. The spectra were fitted using the algorithm described in detail in Section 3.1 to obtain the integrated absorbance, i.e. line area (Aline). Line strengths were calculated from the line area using the Beer–Lambert law and the ideal gas law, according to ST ¼

kB U T UAline ; xH2 O UL Up U r iso

ð1Þ

where ST is the line strength at temperature T, kB is the Boltzmann constant, xH2 O is the amount fraction of water vapor in the sample, L is the optical path length, p is the pressure of the gas sample and riso is a correction factor for the isotopic composition of the gas sample. The temperature dependence of the line strength was taken into account, and the line strength at T0 ¼296 K was calculated using the polynomial correction suggested by Gamache et al. [26], as described by 
 Q h⋅c⋅E 1 1 kB ⋅T⋅Aline ⋅K T S0 ¼ ST ⋅ T exp ⋅ − ð2Þ ¼ ST ⋅K T ¼ kB T T0 Q T0 xH2 O ⋅L⋅p⋅r iso and Q T ¼ a0 þa1 UT þa2 UT 2 þ a3 U T 3 ;

111

ð3Þ

where S0 is the line strength at T0 ¼296 K, QT and Q T 0 are the partition sums at temperature T and T0 ¼296 K, respectively, h is the Planck constant, c is the speed of light in vacuum, E is the lower state energy of the transition and a0, a1, a2 and a3 are empirical coefficients suggested by Gamache et al. [26]. We summarized temperature dependence of the line strength in the correction factor KT. In the following, all given line strength values refer to T0 ¼ 296 K (S0).

3.1. Determination of the line area Due to the complexity of the fitting procedure, determining the line area is not straightforward. As has been shown in our previous publications [8,9,17], the line area has a significant contribution to the combined uncertainty of dTDLAS measurements; therefore, it is inevitable to discuss this parameter in detail. Ref. [24] explains the procedure of determining the line area. In the following, we concentrate on the uncertainties introduced by the individual steps of this procedure. Fig. 2 shows typical measured spectra with the DFB lasers, together with the fitted absorption line and the fit residuals. In the case of these light sources, the scanned spectral window was not more than 0.3 cm–1 and contained only one strong absorption line. The modulation frequency was 139.8 Hz, and the spectral window was sampled as 2000–3000 measurement points (sampling rate  600 kS/s), which resulted in a spectral resolution in the range of 1.10–2.35  10-4 cm–1. As can be seen in Fig. 2, the noise was the lowest in the case of the 1.37 mm laser. Residuals of all three spectra show higher deviations around the absorption lines, which is a typical indication of jitter, i.e. small fluctuations in the laser current. However, the well-structured residuals in Fig. 2e and f might also be caused by the hyperfine structure of the absorption lines. The VCSEL can be tuned over a much broader wavelength range than the DFB diode lasers; accordingly, much broader spectral windows can be covered. The six lines, which we investigated within the tuning range of the VCSEL, were recorded on two wavelength scans: one scanning over two lines from 7185.2 cm–1 to 7185.9 cm–1, and one over four lines from 7180.1 cm–1 to 7183.3 cm–1 (see Fig. 3). In the case of the VCSEL, a lower modulation frequency of 62.5 Hz was used in order to reach a higher spectral resolution with the same sampling rate ( 600 kS/s). The spectral resolution of the shorter scan in a spectral window of 0.73 cm–1 was 5.3  10–4 cm–1 (Fig. 3a), whereas that of the scan in the larger spectral window of 3.07 cm–1 was 1.2  10–3 cm–1 (Fig. 3b). The clearly visible uneven distribution of the measurement points in Fig. 3a and b, as well as the residuals (note the different scales), show that the jitter in the case of the VCSEL is considerably higher than in the case of the DFB lasers. The reason for this is the almost two orders of magnitude lower driving current (1–200 mA for DFB lasers and 0–5 mA for the VCSEL) and higher current tunability (typically 0.02 cm–1/mA for the DFB lasers and 0.5 cm–1/mA for the VCSEL), which makes accurate control and stabilization of the VCSEL current and, thus, the wavelength challenging. We note that in the case of fitting the spectra like on Fig. 3b in one spectral window of 3 cm–1 including all four lines, weak interference fringes were observed in the fit residuals. The fringes had a free spectral range of 1.2 cm–1 and an amplitude of 5  10–3. To suppress the effect of these fringes on the line area, all evaluations were done in much smaller spectral windows (typically 0.3 cm–1, as shown in Fig. 3d), in which case the fringes were fitted by the background polynomial.

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Absorbance

0.5 0.4 0.3

0.6

Measurement Voigt fit T = 294.1 K p = 42 Pa f = 139.8 Hz SNR = 1716

211-110

0.2

0.4 0.3

0.1

local 1σ = 1.4 x10

global 1σ = 2.07 x10

-4

-4

0.0 -5.0x10 7299.3

7299.4

0.0 5.0x10

Residual

Residual

817-716

T = 293.86 K p = 14 Pa f = 139.8 Hz SNR = 471

0.2

0.1 0.0 5.0x10

Measurement Voigt fit

0.5

Absorbance

0.6

global 1σ =1.16x10

0.0

local 1σ=5x10 -5.0x10 3920.0

7299.5

3920.1

-1

Wavenumber / cm

Absorbance

0.6

Measurement Voigt fit

0.5 0.4 0.3

3920.2

Wavenumber / cm

T = 293.4 K p = 55 Pa f = 62.5 Hz SNR = 440

303-322

0.2

Residual

0.1 0.0 5.0x10

global 1σ = 7.8 x10

-4

0.0

local 1σ = 6.5 x10

-5.0x10

3684.4

3684.5

-4

3684.6

Wavenumber / cm

-1

Fig. 2. Measured spectra with the DFB diode lasers at 1.37 mm (a), 2.55 mm (b) and 2.71 mm (c) together with the fitted absorption profile (red line) and fit residuals (d, e and f). Global σ indicates the standard deviation of the residuals in the whole spectral window, while local σ corresponds to the standard deviation of the residuals within the rectangle.

As can be seen in Figs. 2 and 3, the quality of the fit is significantly different for different lines. The expanded uncertainty originating from the fit (quantified by two times the standard error of the line area parameter in the Levenberg-Marquardt fit) ranged from 0.03% for the line at 7299.431 cm–1 measured with a DFB laser to 1.35% for the weakest line at 7185.394 cm–1 measured with the VCSEL. These differences can be explained by differences in the noise (see local σ in Figs. 2 and 3), jitter, as well as the spectral resolution of the light sources. Another difference stems from the peak absorbances of the spectra. In most cases, the pressure was adjusted so that the absorption line had an optimal peak absorbance of 0.4–0.6, which resulted in signal-to-noise ratios in the range of 400–1800 (see examples in Fig. 2). However, in the case of the weakest line measured with the VCSEL, peak absorbances of 0.025–0.035 were measured, giving signal-to-noise ratios down to 50. No temporal averaging was used; the spectra were fitted one by one, and the line area (Aline) was determined for each measured spectrum. The spectra were fitted with Voigt profiles. Higher order line shape models accounting for collisional narrowing and speed dependence of the absorption are being used in several studies; however, at the pressures used in our experiments these effects are rather insignificant. As has been shown by Goldenstein and Hanson

[27], the choice of the line shape function has a significant influence on the line width, but the influence on the line area was found to be well below 1% during their experiments conducted under similar conditions. Larcher et al. [28] observed up to 2% deviation between line areas obtained by the Voigt profile and the recently developed HartmannTran profile for CO2 lines around 1.6 mm. However, the difference was found to decrease toward lower pressures and was smaller than 0.3% in the 15–50 hPa range. Even though a residual structure was observed in several cases in our measurements (see Figs. 2e–f and 3c–d), which might also (partially) originate from line broadening or narrowing effects not included in the Voigt function, the integrated area under the residuals was found to be in the range of 0.001– 0.005% of the line area. This indicates that the effect of the residuals on the line area is negligible. Lorentzian and Doppler widths of the absorption lines were fitted as free parameters. The correctness of the fitted line widths was checked by comparing the fitted line widths to their calculated values. The calculations were based on Eqs. (4) and (5) using the self-broadening coefficients (γself) with their temperature exponents (n) and the line positions (ν0) from the HITRAN 2012 [13] database and molecular mass (m) from the NIST Chemistry WebBook [29]. As an example, Fig. 4 shows the fitted and calculated Lorentzian and Doppler widths for

A. Pogány et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 165 (2015) 108–122

5

0,6

Measurement Voigt fit

Measurement Voigt fit

4

T = 295.25 K p = 8.21 hPa f = 62.5 Hz

Absorbance

Absorbance

0,5 0,4

113

660-661 661-660

0,3 0,2

T = 295.06 K p = 4.69 hPa f = 62.5 Hz

3 2 1

0,1

523-660 0

Residuals

Residual

0,0 2,0x10

global 1σ = 1.49 x10 0,0

local 1σ = 3.9 x10

2x10

global 1σ = 5.1x10

0

local 1σ = 4.1x10

-2x10

-2,0x10 7185,2

7185,3

7185,4

7185,5

7185,6

7185,7

7185,8

7180.0

7185,9

7180.5

7181.0

7182.0

7182.5

7183.0

Wavenumber / cm

Wavenumber / cm –1

7181.5

–1

3684.528 cm

1.5x10

-1

-3

3684.528 cm

-1

-1

4 3

Measured wL / cm

from the calculated w G / %

Relative deviation of the fitted w G

Fig. 3. Measured spectra with the VCSEL at 7185 cm (a) and 7180–7183 cm (b) together with the fitted absorption profile (red line) and fit residuals (c and d). Global σ indicates the standard deviation of the residuals in the whole spectral window, while local σ corresponds to the standard deviation of the residuals within the rectangle. Fit residuals in (d) are shown in the used smaller spectral windows, each containing one measured absorption line.

2 1 0

1.0x10

-3

5.0x10

-4

-1 -4

2σ = 2.34%

-2 0

1

2

3

Y = -0.14(43)x10 +0.99(6) X

4

5

6

7

8

9 10 11 12 13

Measurement number

0.0 0.0

5.0x10

-4

1.0x10

Calculated w L / cm

-3

1.5x10

-3

-1

Fig. 4. Comparison of fitted and calculated line widths at 2.71 mm. (a) Relative deviation of the fitted Doppler width (wG) from the calculated value. Error bars indicate two times the standard deviation of the single-spectrum fitted Doppler widths during one measurement sequence, the horizontal line shows the average deviation, and 2σ represents two times the standard deviation of the average deviations. (b) Measured Lorentzian widths (wL) as a function of the calculated values together with a linear fit. Error bars indicate two times the standard deviation of the single-spectrum fitted widths during one measurement sequence.

the measurements performed at 2.71 mm. Error bars represent twice the standard deviation of the fitted widths within one measurement sequence. To check the effect of the difference in calculated and fitted line widths on the line area, we repeated fitting of the spectra with calculated Lorentzian and Doppler widths. The differences between the line areas obtained by the different evaluation methods were found to be well below the uncertainty of the line area. rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 U kB U T U ln 2 wG ¼ 2 U ν0 U ð4Þ m U c2
n T0 ð5Þ wL ¼ γ s Up U T The main uncertainty component of the line area is the determination of the dynamic tuning coefficient of the laser. The dynamic tuning coefficient was determined before the line strength measurements, using a 100 mm long silicon etalon in the spectral windows scanned with the DFB lasers and a 45 mm long ZnSe etalon for the larger spectral

windows scanned by the VCSEL. Proprietary semiautomated fringe fitting software was used for the evaluation [24]. The position of the fringes is determined by an Airy fit. The dynamic tuning coefficient (Δν/Δt) is calculated and plotted as a function of sample point or time (two examples are shown in Fig. 5a and b). Due to thermal effects, the tuning coefficient is not constant over the current ramp. This nonlinear behavior is approximated by an exponential function, which was fitted to the measurement points to obtain the dynamic tuning coefficient for the whole scan. The quality of this fit has been found to be significantly different for different light sources. Determination of the dynamic tuning coefficient could be performed with the highest accuracy for the DFB diode laser at 1.37 mm. The standard deviation of the residuals by fitting the dynamic tuning coefficient (Fig. 5c) was as low as 0.43%. In the case of the 2.71 mm laser, determination of the dynamic tuning coefficient was found to be significantly less accurate; standard deviation of the residuals (Fig. 5d) is 1.1%. As a first estimate, we took two times the standard deviation of the residuals as

-1

-1

0.14 0.13 0.12 0.11 0.10 3

Residuals / %

-1

Residuals / %

7299.431 cm

0.15

Dynamic tuning coefficient / cm /ms

A. Pogány et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 165 (2015) 108–122

Dynamic tuning coefficient / cm /ms

114

2 1 0 -1 -2

σ = 0.43%

-3 1.0

1.5

-1

0.055

0.050

0.045

0.040 3.0 1.5 0.0 -1.5 -3.0

2.0

2.5

3.0

3.5

3684.528 cm

0.060

σ = 1.1% 2

4.0

3

4

5

6

7

Time / ms

Time / ms

Fig. 5. Dynamic tuning coefficient of the (a) 1.37 mm laser and the (b) 2.71 mm DFB laser, with the corresponding residuals (c and d).

Table 2 Spectral characteristics of the applied light sources and light source specific uncertainty components. Laser type

Wave-number (cm–1)

Spectral window (cm–1)

Spectral resolution (cm–1)

Uncertainty of the line fitting (%)

Uncertainty of the laser tuning coefficient determined by Etalon fit residuals (%)

DFB DFB DFB VCSEL

a b

7299 3920 3684 7185 7180

0.32 0.22 0.27 0.73 3.07

–4

2.2  10 2.35  10–4 1.1  10–4 5.3  10–4a 1.2  10–3b

0.03 0.16 0.12 0.65–1.35a 0.55–1.13b

0.86 1.6 2.2 1.4a 1.6b

Spectr. comparison (%) wD

Δν

0.52 2.1 2.34 n/a

n/a n/a n/a 0.1a 0.7b

Shorter scans, as depicted in Fig. 4a. Longer scans, as depicted in Fig. 4b.

the expanded uncertainty of the dynamic tuning coefficient. The values for all lasers are listed in Table 2. A spectroscopic method to estimate the uncertainty of the dynamic tuning coefficient locally, at the position of the absorption line, is to compare the measured absorption line widths to their calculated values. In our previous publication [17] we compared the Doppler widths (wG) of the absorption lines calculated using Eq. (4) to the Doppler widths obtained from the fit. The average difference between the two values can be assigned to the laser line width, whereas the standard deviation of the differences obtained from repeated measurements gives the standard uncertainty of the tuning coefficient (two times the standard deviation yields the expanded uncertainty). This approach can be applied to the lines measured with the DFB lasers, where the pressure (see Table 1) was low enough to keep the influence of the uncertainty of the Lorentzian width (originating from the uncertainty of the self-broadening coefficient) on the total line width insignificant. The expanded uncertainty of the tuning coefficient was found to be in the range of 0.52–2.34%, which is in good agreement with uncertainties determined on the basis of the

fitting of the etalon fringes (see Table 2). We took the higher value as the uncertainty of the dynamic tuning coefficient. Measurements with the VCSEL were performed at significantly higher pressures (resulting in Lorentzian widths up to 15% of the total line width), which resulted in a higher uncertainty (up to 5%) in the fitted Doppler widths. Consequently, comparing the fitted Doppler widths to their calculated values could not be used for accurate validation of the dynamic tuning coefficient. Another spectroscopic method to check the correctness of the dynamic tuning coefficient is to compare the measured relative positions (Δν) of the absorption lines to the relative positions given in the HITRAN 2012 database. This method enables verification of the averaged dynamic tuning coefficient over the whole spectral window. We applied this to the spectra measured with the VCSEL, which contained at least two strong absorption lines, the positions of which are given with an accuracy of better than 0.0001 cm–1 (and better than 0.001 cm–1 for the doublet at 7185.597 cm–1) in the HITRAN 2012 database. The observed differences between reference and measured line separations were found to be  0.1% for

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the shorter scans (as in Fig. 3a) and  0.7% for the longer scans (as in Fig. 3b). This value is significantly lower than the uncertainties determined based on the fitting of the etalon fringes. The difference can be explained by the fact that looking at the relative position of the absorption lines with a separation of 0.2–2 cm–1 characterizes the average value of the dynamic tuning coefficient over this spectral range, whereas looking at the fit of the etalon fringes reveals local deviations as well. Since the width of the absorption lines is in the 10–2 cm–1 range, local deviations in the dynamic tuning coefficient might also affect the determined line area. Consequently, we took the higher value, the uncertainty determined from the fitting of the etalon fringes, as the uncertainty of the dynamic tuning coefficient of the VCSEL. As pointed out in our previous publication [17], amplified spontaneous emission and side modes are in the case of diode lasers a minor, but not negligible, problem. Our usual data evaluation method takes the signal measured when the laser is switched off as zero, which was found to be slightly lower than the signal measured in the case of total absorption. This introduces a systematic error in the line area. Previously [9,17], we accounted for this error in the uncertainty of the line area, while in this study we corrected this effect by taking the signal measured in the case of total absorption as zero. The difference between the line area calculated with optical zero as the signal measured during the laser off period or in the case of total absorption was found to be slightly different for the different light sources, i.e., 0.25% for the 1.37 mm laser, 0.35% for the 2.55 mm and the 2.71 mm lasers, and 0.15% for the VCSEL. The uncertainty of the optical zero determination is well below 0.1%, therefore negligible. Absorption outside the gas cell was minimized during the experiments by (a) minimizing the light path outside the cell and by (b) placing the laser, gas cell and detector in a sealed housing, which was continuously purged with dry air (xH2 O o3 mmol/mol). As was pointed out by Buchholz et al. [30], parasitic absorption might also occur inside the laser and detector housing, which cannot be suppressed by purging, and even though the optical path length in these

115

volumes is only a few mm, absorbances up to a few times 10–4 might occur in these closed volumes. In most of our experiments, absorbance of the measured line in the gas cell was in the range of 0.4–0.6 (i.e. three orders of magnitude higher than possible parasitic absorbance). Furthermore, the spectral windows used in our evaluations were comparable to the line width of a water vapor absorption line at atmospheric pressure; thus, parasitic absorption lines were corrected by the background polynomial fitting and did not influence the measured line area. As has been shown in our earlier publication [17], detector nonlinearity was negligible for the InAs detector. A publication in literature [31] as well as our measurements shows similarly good linearity for the InGaAs detector. Spectral characteristics of the light sources as well as uncertainty components discussed in this section are summarized in Table 2. Eq. (6) shows how the sources of errors listed above were taken into account to calculate the line area: Aline ¼ Afit line U ktuning ;

ð6Þ

Afit line

where is the determined line area with an uncertainty of 0.03–1.13% of the fitting, and ktuning is a correction factor with a value of 1 and expanded uncertainty of 0.82–2.2%. This correction factor was introduced to take into account the uncertainty of the tuning coefficient. 3.2. Correction introduced due to imperfections in the gas handling Despite attentive assembly of the set-up, a small leak caused a continuous increase in the gas cell pressure of 0.1 hPa/day. In the case of a pressure of 0.1 hPa, this leak dilutes the water vapor mole fraction in the cell from 100% to 99% in approximately 20 min (this is the reason why in most of our experiments the measurement time stated in Section 2.3 was kept below 20 min after filling the cell). This dilution effect is attenuated by water vapor desorbing from the cell walls during the measurement. As shown in Fig. 6a, the pressure increased significantly during the 1.0

32

-4

Δp - ΔAline= 1.075(4) 10 Δt - 0.002(3)

relative increase of the pressure ( Δp) relative increase of the line area ( Δ Aline)

0.8

Δp - Δ Aline / %

Relative increase since filling the cell / %

34

30 28 26

0.6 0.4

24

0.2

22

0.0

20 00:10

00:20

00:30

00:40

Time / hh:mm

00:50

01:00

00:10

00:20

00:30

00:40

00:50

01:00

Time / hh:mm

Fig. 6. (a) Relative increase in the pressure (black line) and in the line area (red line) during one measurement period, (b) difference in the relative increase of the line area and of the total gas pressure (black line) with a linear fit (red line). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.).

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measurement time. More than 95% of this increase is caused by desorption of water from the cell walls. Since the pressure was continuously monitored, this increase did not influence the accuracy of the measurements, only the pressure increase caused by the leak affected the water vapor mole fraction. To suppress the errors caused by the leak, a correction was introduced. Additionally, three further effects were taken into account, which might influence xH2 O : (a) the purity of the used water sample, (b) imperfect evacuation of the gas cell before the measurements, and (c) residual air in the headspace over the water surface in the reservoir. Eq. (7) was used to calculate xH2 O :   xH2 O ¼ x0 U kevac U khs U 1  qleak U Δt ¼ x0 Ukevac Ukhs Ukleak ð7Þ where x0 is the water concentration in the liquid water sample, kevac is a correction factor for imperfect evacuation of the cell before the measurement, khs is a correction factor for residual air in the headspace, qleak is the leak rate, Δt is the elapsed time since filling the cell with water vapor and kleak ¼ 1  qleak U Δt is a correction factor for the leak. The leak rate (qleak) was determined from the relative increase in the pressure and the line area as plotted in Fig. 6a. If only desorption occurred, these two quantities were equal. In our measurements, the relative increase in the pressure was slightly higher; the difference between the relative increase in the pressure and in the line area is caused by the leak. This difference (Δp–ΔAline, depicted in Fig. 6b) had a linear increase with time, with a slope of qleak ¼ 10–5–5  10–4 min–1, depending on the pressure, which agrees well with the leak rate calculated from the previously observed pressure increase of 0.1 hPa/day. The uncertainty of qleak was derived from the uncertainty of the slope of the fitted line and was found to be  0.4% relative. This results in an uncertainty of kleak in the range of 0.003–0.07%, depending on the pressure in the cell and the measurement time. The water reservoir was filled with double distilled water, the purity of which might be affected by gasses dissolved in it during storage. The solubility of common atmospheric gases in water is in the 10 mg/l range, which means a relative uncertainty in the water concentration in the 10–5 range. This value was used as the uncertainty of x0 (the value of x0, i.e. the expected amount fraction of H2O, is 1). During evacuation of the gas cell a pressure of  0.006 hPa was reached, after which the cell was filled with water up to the vapor pressure at room temperature, i.e.  23 hPa. The maximum error introduced by imperfect evacuation of the gas cell can be calculated as 0.006/ 23 ¼2.6  10–4. This was taken into account in kevac, i.e., the correction factor kevac has a value of 1 and a relative expanded uncertainty of 2.6  10–4. The effect of residual air in the headspace of the water reservoir is more difficult to estimate. As pointed out in Section 2.3, the headspace was evacuated several times prior to the measurement, to minimize this effect. The maximum error introduced by residual air in the headspace was estimated from the standard deviation of the measured S0(i) values. We took two times the standard deviation in the case of the best

reproducible measurements (0.4% for the measurements using the DFB laser at 7299.431 cm–1, see Fig. 8a) as the expanded uncertainty caused by residual air in the water reservoir. Since all measurements were performed using the same sample preparation procedures, the headspace effect is expected to be independent from the used light source. Higher standard deviations in the case of other light sources are attributed to laser-specific effects (e.g. stability of the lasers). Since several other effects might influence the standard deviation of S0(i), the error introduced by residual air is most probably even smaller than this number; however, the above-described method can be used as an estimate for the highest possible error. Note that most measurements were performed using the sample preparation method (a) (involving liquid water samples, see Section 2.3.). Uncertainty caused by the headspace is expected to be slightly lower for measurements performed by the sample preparation method (b). The correction factor khs has a value of 1 and an expanded uncertainty of 0.004. 3.3. The derived line strengths The line strengths were calculated from the determined line areas according to Eq. (2) taking into account the temperature dependence of the line strength and applying the correction described by Eq. (7) for dilution caused by a leak. Fig. 7a and b shows a series of measured line strengths for one measurement with the 1.37 mm and the 2.71 mm DFB laser, while Fig. 7c and d shows the corresponding histograms. The line strengths calculated for individual laser scans have been averaged to obtain S0(i) for a measurement sequence i. The statistical uncertainty of S0(i) is the standard deviation of the mean of the values shown in Fig. 7a and b, and was found to be well below 0.01% in all our measurements. This indicates that statistical uncertainty is negligible in our measurements. Fig. 8 shows the S0(i) values for the three DFB lasers, together with their expanded uncertainties (see Section 3.4 for the detailed uncertainty assessment). Reproducibility was determined as the standard deviation of the S0(i) values (2σ is indicated by the dashed lines in Fig. 8). The final S0 line strength figure for an absorption line is given by the mean of the S0(i) values for all repeated measurements (shown as “this work” on the right side of Fig. 8a–c). 3.4. Uncertainty assessment, traceability A model equation was set up based on Eq. (2) and the additional correction factors introduced in Eqs. (6) and (7). S0 ¼

kB U T UAfit line Uktuning Ukzero U K T x0 Ukevac Ukhs Ukleak UL U p U r iso

ð8Þ

Uncertainty of the obtained line strengths was determined by analyzing the uncertainty of each parameter of Eq. (8). A detailed description of the uncertainty evaluation of the optical path length (L), isotopic ratio (riso) and temperature dependence of the line strength (KT) is given in our previous publications [17,9]; an example for the

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117

Fig. 7. Measured line strengths and histograms during one measurement: 1.37 mm (a and c) and 2.71 mm (b and d).

estimated uncertainties for the present measurements is given in Table 3. Uncertainty of the pressure (p) and temperature (T) is also given in Refs. [17,9]; however, one improvement in our present work has to be mentioned. Previously, the long-term stability of the temperature and pressure sensors was estimated based on the specifications given by the manufacturer. The applied pressure and temperature sensors have been used for more than three years in traceable measurements in different experiments in our research group, which enables the investigation of longterm stability and its effect on the uncertainty of the pressure and temperature values in more detail. This is described in the following. The temperature sensors are calibrated annually at our institute, in a water bath using traceable reference thermometers. Three subsequent calibrations have been performed so far. All calibrations show a good overall accuracy of the sensors; their readings agree with the reference temperatures within 0.05 K. Long-term stability was found to be better than specified by the manufacturer; differences between the three calibrations were below 0.03 K. However, the uncertainty of 0.5 K (k¼2) given in Table 3 is still relatively high. This uncertainty originates predominantly from possible differences in the gas temperature and sensor temperature, as well as possible temperature inhomogeneities in the gas cell, and is based on the differences measured by the three sensors placed at three different positions in the experimental set-up (see Fig. 1). Temperature inhomogeneities might be caused by evaporation of liquid water in the gas handling system, as well

as cooling of the water reservoir during the sample preparation method (b). The pressure sensors are calibrated annually and in addition to a calibration by the manufacturer, three subsequent calibrations were performed at our institute with reference to a traceable pressure standard. The used pressure sensors showed an absolute accuracy of  0.5% (difference between sensor reading and reference pressure), which deviation has been accounted for by the calibrations. The differences between the individual calibrations are below 0.25%, which indicates a long-term stability better than 0.25%. This number agrees with the value given by the manufacturer. Due to the fact that the sensors with 1 torr measurement range are heated to 45 1C, as well as pressures down to 10 Pa had to be measured, the effect of thermal transpiration [9] was not negligible. For the correction we used the approach by Setina [32] and viscosity data from the NIST Chemistry WebBook [29]. The correction ranged from 0.3% (0.1 hPa and 20 1C) to 0.1% (a 1 hPa and 25 1C). The overall uncertainty of the pressure was dominated by the long-term stability of the sensors, the uncertainty of the calibration, and thermal transpiration effects (in the case of measurements below 1 hPa) and ranged from 0.34% to 0.24% in the pressure range of 0.1–9 hPa. The most critical parameter is the line area (Aline). As shown in Section 3.1, two main factors have been identified, which influence the uncertainty of the line area: uncertainty of the fitting and uncertainty of the dynamic tuning coefficient of the laser (as shown in Eq. (6)). From these two, the uncertainty of the dynamic tuning

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1.02x10

0 -20

-1

1.00x10

-2 -21

-3

9.80x10

2

4 6 8 10 12 14 16 Mearurement number

2 -21

3.9x10

1 0 -1

-21

3.8x10

-2 -3 -21

3.7x10

-4 18

0

2

Line strength / cm/molecule

Th

0

-20

3

4 6 8 10 Measurement number

12

14

Th is w HI ork TR AN

1

4

-1

3684.528 cm

-4 16

4

3920.089 cm-1

2.65x10

2 -20

2.60x10

0 -20

2.55x10

-2 -20

2.50x10

Deviation from the mean / %

2 -20

Line strength / cm/molecule

1.04x10

is w HI ork TR AN

Line strength / cm/molecule

3

-21

4.0x10

Deviation from the average / %

4

-1

7299.431 cm

-20

Deviation from the mean / %

118

-4 Measurement number

k

9

AN

8

or

7

R

6

w

5

IT

4

is

3

H

2

Th

1

Fig. 8. Line strengths obtained for repeated measurements (S0(i) at (a) 1370 nm, (b) 2714 nm and (c) 2550 nm. Error bars indicate the expanded uncertainty of the individual measurements; horizontal dash-dotted lines indicate two times the standard deviation of line strengths obtained from the individual measurements (2σ, 0.4% in (a), 1.2% in (b) and 0.4% in (c)). The right side of the figures show the averaged line strengths (S0) together with their uncertainties, as well as the line strength value in the HITRAN 2012 database (uncertainty is indicated by a dashed line due to the imprecise uncertainty figures).

Table 3 Uncertainty contributions from the different input parameters for one measurement at 7299.431 cm–1 (No. 8 in Fig. 8a). Quantity

Value

Relative expanded uncertainty (%)

Relative contribution to the uncertainty of the line strength (%)

p T L xH2 O

0.17 mbar 293.0 K 0.774 m 1 mol/mol 0.998 1 1 0.003378 cm  1

0.26 0.16 0.26 0.001 0.07 0.03 0.40 0.02

6.63 2.51 6.63 0.00 0.09 0.48 15.69 0.09

1 1.008 1 1.0123  10–20 cm/molecule

0.86 0.14 0.01 1.01

65.95 1.92 0.01

Aline KT riso S0

x0 kleak kevac khs Afit line ktuning

coefficient is the higher (0.8–2.4%). In case of the DFB lasers, this is the dominating uncertainty component of the line area, while the uncertainty of the fitting has a comparable contribution (up to 1.35%) in the case of weak absorption lines measured by the VCSEL. Water vapor amount fraction (xH2 O ) is the second most critical parameter. The water vapor amount fraction is different from 1, due to a small leak in the cell, which was

corrected using the method described by Eq. (7) in Section 3.2. The uncertainty of xH2 O was predominantly determined by residual air above the water sample in the reservoir, and was found to be in the range of 0.40–0.42%. Table 3 shows an example of the measured parameters and their uncertainties for one measurement with the 1.37 mm DFB laser. Note that the relative uncertainties given in Table 3 are valid for the S0(i) values obtained

Wavenumber / cm

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Laser type: DFB DFB VCSEL VCSEL VCSEL VCSEL VCSEL VCSEL DFB

3684.528 3920.089 7180.400 7181.156 7182.209 7182.950 7185.394 7185.597 7299.431 0

20

40

60

80

100

119

A

- tuning

A

- fit

x - headsp. x - leak x - evac. x - purity p T L K r

Relative contribution to the uncertainty / % Fig. 9. Relative contribution of the input parameters to the uncertainty of the obtained line strength.

from the individual measurements, as well as the final S0 line strength results. The reason for this is that the uncertainties listed in Table 3 are dominated by nonstatistical effects, which cannot be decreased by averaging results of repeated measurement sequences. Similar tables have been prepared for all lines. Fig. 9 shows an overview of the relative contribution of the input parameters to the combined uncertainty of the derived line strengths (last column in Table 3) for all measured absorption lines. Differences in the uncertainties for different experiments originate mainly from differences in the uncertainty of the line area. The dynamic tuning coefficient of the laser has the highest contribution (45–95%) to the combined uncertainty in all cases. The uncertainty of the spectral line fitting has a comparable contribution (10–45%) in the case of measurements with the VCSEL, whereas it is negligible (relative contribution o0.5%) in the case of the DFB lasers. The uncertainty caused by the headspace effect might be decreased by applying the sample preparation method (b); however, this would only cause a minor reduction of the uncertainty of the line strength. 3.5. Comparison to literature data and validation Table 4 summarizes all measured line strengths, together with their expanded uncertainties and the line strengths listed in the HITRAN 2012 database. (Note that the line at 7185.597 cm–1 is a doublet; the line strength value given in Table 4 is the sum of the line strengths of the two transitions.) The obtained line strength values were compared to literature data. Fig. 10 presents an overview of the comparison of our measured line strengths to various literature values. Relative line strength is plotted, which stands for the literature value divided by our measured line strength. Error bars indicate the expanded uncertainty (k ¼2, 95% confidence level) of the literature values. We note that the authors of the literature data describe the quality of their line strength values using different quantities, and conversion of these quantities to expanded uncertainty is not straightforward. In the following, we briefly discuss the agreement of the line strength data presented in the publications used in Fig. 10 with our measured results and explain how we interpreted the given uncertainties. The most commonly used source for line data is the HITRAN database [13]. We compared our line strength

values to the values in the HITRAN 2012 database (see Table 4) and found good agreement; relative deviations were found to be below 4% for all measured absorption lines. As pointed out in the Introduction, the HITRAN database lists only uncertainty classes instead of specific uncertainty values. The source of the line strength data of the studied lines in HITRAN 2012 is a database set up by Toth [33] (with the exception of the doublet at 7185.597 cm–1, the line strength of which is computed by Barber et al. [11]); however, these publications do not contain more specific information on the uncertainty assessment either. We took the upper limit of the uncertainty class given in HITRAN (10% in the case of the studied lines) and plotted it as expanded uncertainty in Fig. 10. Several further data can be found in the literature for the lines around 1.4 mm. Toth [34] measured line strengths of H2O in the 5750–7965 cm–1 region using FTIR spectroscopy. Seven of the lines measured in our study are included in his study as well, and their line strength values agree within 5% with the exception of the lines at 7182.209 cm–1 (11% deviation) and 7185.394 cm–1 (12% deviation). The uncertainties given by Toth are estimated from the variation of values obtained from different measurements and are in the range of 2–5% (with the exception of the weakest line at 7185.394 cm–1, which has 10% uncertainty). We take the uncertainties given by Toth as expanded uncertainties. Parvitte et al. [35] measured intensities of 23 lines in the 7165–7186 cm–1 region using TDLAS based on a DFB diode laser. Six of the measured lines were also included in our study, and our values differ by less than 3.5% from the values presented by Parvitte et al. We have to point out that Parvitte et al. gave no uncertainties for the measured line intensities. Lisak et al. [18] measured H2O line strengths near 7180 cm–1 including four lines that have also been measured in our study. They used a primary low frost-point humidity generator for preparing gas samples with known H2O amount fraction in N2, and a frequency-stabilized cavity ring-down spectrometer for the spectroscopic measurements. The line strengths obtained by Lisak et al. are 2.5–3.2% higher than the values derived from our study; however, three of the four lines agree within the uncertainties. Standard uncertainties given by Lisak et al. are in the range of 0.3–0.4% (we multiplied these uncertainties by a factor of k ¼2 to obtain expanded uncertainties). These uncertainties are lower than those estimated for

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Table 4 Summary of all measured line strengths and comparison to the values in the HITRAN 2012[13] database. Wavenumber (cm  1)

Measured line strength (cm/molecule)

Expanded uncertainty (%)

HITRAN line strength (cm/molecule)

HITRAN error code (%)

Deviation of the measured and HITRAN line strength (%)

7299.431 7185.597 7185.394 7182.950 7182.209 7181.156 7180.400 3920.089 3684.528

1.01E–20 7.89E–22 4.98E–23 3.69E–21 1.54E–21 1.47E–20 5.40E–22 2.58E–20 3.86E–21

1.1 1.7 2.1 1.9 2.1 1.8 2.0 2.2 2.5

1.01E–20 7.94E–22 5.16E–23 3.75E–21 1.54E–21 1.51E–20 5.61E–22 2.58E–20 3.93E–21

5–10 5–10 5–10 5–10 5–10 5–10 5–10 5–10 5–10

0.70  0.71  3.76  1.97  0.13  2.33  3.90  0.23  1.91

Fig. 10. Comparison of the measured line strengths to literature data. The square symbols (■) as well as the horizontal solid line represent our measured value, dashed lines indicate the expanded uncertainty (k ¼ 2, 95% confidence level). Uncertainties of the literature values are plotted as follows: for line strength given in the HITRAN 2012 database (◇) an uncertainty of 10% is plotted; standard uncertainties given by Lisak et al. [18] (△) are multiplied by a factor k ¼2 to obtain expanded uncertainty; the uncertainties given by Toth [34] (▲), Goldenstein et al. [23,36] (○) and Polyansky et al. [37] (●) are plotted as expanded uncertainties; Parvitte et al. [35] (★) gave no uncertainties in their publication.

our measurements, mainly due to the fact that frequency stabilization of the laser significantly decreases the uncertainty in the tuning coefficient (i.e. the most important uncertainty component in our measurements). There are significantly less literature data available in the 3600–4000 cm–1 region. Goldenstein et al. [23,36] measured line strengths of a few H2O transitions including the line at 3920.089 cm–1 that has been measured by us as well, and shows very good agreement, i.e. 0.4% deviation from our result. The uncertainty given by Goldenstein et al. (2.1%) is calculated by taking into account several factors (temperature, pressure, line fitting, line shape); however, it is not clear whether the given value is the standard or expanded uncertainty, and no detailed uncertainty analysis is provided. We plot the given uncertainty as expanded uncertainty in Fig. 10. We also compared our results to calculated line intensities. Polyansky et al. [37] calculated line strengths for water vapor transitions using the ab initio method. Their

calculated line strengths are generally a few percent higher than our measured values. Higher deviation, i.e. 7.5%, was observed for the line at 7185.394 cm–1, whereas the agreement was found to be better than 5% for the other eight lines. Polyansky et al. [37] gave an uncertainty of 5% for the lines in the ν3 and 2ν3 bands, and 1% for the rest of the data. We plot these uncertainties as expanded uncertainty in Fig. 10. The measured line strength for 2.71 mm has been used in another publication from our research group [9] to measure H2O mole fractions in the 5–600 ppm range with a spectrometer based on a Herriott cell with a 76 m path length. (Note that the uncertainty reported in Ref. [9] is a result of a preliminary analysis, thus slightly different from the value reported here.) Reference values for H2O amount fractions were provided by a traceable dew point mirror. Agreement better than 2% was found between the measured and the reference amount fractions in the 50– 600 mmol/mol range, which verifies our line strength value

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and demonstrates how it can be applied in calibration-free amount fraction measurements.

4. Conclusions and outlook We have measured the intensity of nine water vapor lines using the same experimental set-up and measurement procedure, based on direct tunable diode laser absorption spectroscopy (dTDLAS). The studied absorption lines are in the wavelength range between 1.37 and 2.71 mm (3680 and 7300 cm–1) and have line strengths of 10–23–10–20 cm/molecule. The measured line strengths and their uncertainties are summarized in Table 4. The obtained line strength values were found to agree well with data in the HITRAN 2012 database, as well as with further literature data. The combined expanded uncertainties of our measured line strengths are in the 1.1–2.5% range, which is a factor of 5–10 lower than the uncertainties listed in the HITRAN 2012 database. We have performed a detailed quantitative analysis of the sources of measurement uncertainty, as well as identified differences caused by the application of different light sources and experimental conditions. We have identified the line area as the most important source of uncertainty; differences between the uncertainties of the individual line strengths are mostly accounted to this parameter. Differences up to a factor of 2.5 have been found between the uncertainties of the dynamic tuning coefficients of the different lasers. Uncertainty of the fit was found to be up to one order of magnitude higher in the case of the VCSEL, due to the higher jitter observed with this light source. These two parameters explain the differences in the uncertainty of the line area. Our present publication proves the applicability of dTDLAS for accurate H2O line strength measurements using DFB diode lasers and a VCSEL for line strengths in the 5  10–23–2.6  10–20 cm/molecule range. In a previous publication, we have already demonstrated the applicability of dTDLAS in line strength measurements of CO2 [17] at 2.71 mm (line strengths of 1.5–2  10–20 cm/molecule). Expanded uncertainties of the measured CO2 and H2O absorption lines are in the 1.0–2.5% range. All measurements were performed using a very similar experimental set-up and measurement procedure, which can be easily applied in a wide wavelength range. The application of this method for further analytes with similar uncertainties is possible, provided that a suitable light source and gas cell with appropriate length are available. In a previous publication [9] dealing with traceability and uncertainties in amount fraction measurements using dTDLAS, we have already used the line strength value for the line at 3684.528 cm–1 presented here. As shown in Ref. [9], the line strength has the second largest uncertainty contribution in amount fraction measurements. Consequently, further reduction of the uncertainty is required to assist highly accurate, absolute amount fraction measurements. The reproducibility of our measurements (listed in Fig. 8) is a factor of 5–10 lower than the uncertainty, which suggests that the dominant sources of uncertainties are non-statistical. The largest uncertainty

121

contribution in our experiments was associated with the dynamic tuning coefficient of the lasers. This uncertainty could be decreased by stabilization of the laser, e.g. to a frequency comb [18], which would result in a significant decrease in the uncertainty of the line strength as well.

Acknowledgment The authors acknowledge financial support and collaboration in EMRP projects. The EMRP is jointly funded by the EMRP participating countries within EURAMET and the European Union. Part of the work was also integrated in and supported by the COORETEC-Turbo 2020 framework under project 03ET2013N. The authors are grateful to their colleagues Olav Werhahn, Steven Wagner, Steffen Scheppner and Karl Jousten for their contributions to the preparation of the manuscript, the data evaluation software and the pressure measurement. The authors also thank Oleg Polyansky for sharing his unpublished data.

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