domain: phys chim

text:
L Regalia

X Thomas

T Rennesson

S Mikhailenko

Line parameters of water vapor enriched by 18 O from 6525 to 8011 cm -1

Keywords: infrared spectroscopy, line intensity measurements, FTS spectra, water vapor, 18 O

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Introduction

The knowledge of spectroscopic parameters of atmospheric species is very important for the studies on the Earth atmosphere. Among these species, the water vapor plays a special role as it participates in the global radiative balance of the Earth atmosphere. Monitoring of water isotopologues in the atmosphere provides information about the water cycle. For planetary studies like Venus or Mars, the knowledge of the quantification of water vapor isotopologues is also essential, indeed this information is a tracer which can inform on the solar system evolution.

The aim of this work is to propose a new set of line intensities of water vapor enriched by 18 O in the spectral range between 6400 and 8000 cm -1 . However, to ensure the consistency of the whole dataset, line positions and self-broadening coefficients were analyzed simultaneously using a multispectrum fitting software. This present study is the continuation of a previous work performed in the same range from 6400 to 9400 cm -1 in natural abundance [START_REF] Régalia | Water vapor line parameters from 6450 to 9400 cm -1[END_REF] and this completes also the systemic review of the near infrared absorption of water vapor started since 1999 [START_REF] Régalia | Water vapor line parameters from 6450 to 9400 cm -1[END_REF][START_REF] Carleer | The near infrared, visible, and ultraviolet overtone spectrum of water[END_REF][START_REF] Mérienne | Water vapor line parameters in the 13 000 -9250 cm -1 region[END_REF][START_REF] Jenouvrier | Fourier transform measurements of water vapor line parameters in the 4200 -6600 cm -1 region[END_REF][START_REF] Oudot | Intensity measurements of H2 16 O lines in the spectral region 8000 -9350 cm -1[END_REF][START_REF] Mikhailenko | Inventory of data included in HITRAN2012 edition for water vapor between 6450 and 9400 cm -1[END_REF].

The paper is organized as follows, a short review of previous spectroscopic studies of H2 18 O absorption in the near infrared is presented in Section 1. The water line list contents of the spectroscopic databases are given in Section 2. Experimental conditions and the line parameters retrieval procedure are described in Section 3. Section 4 contains some details of vibration-rotation transition assignments and also intensity measurements results. Finally, Section 5 is devoted to a comparison with results obtained from previous studies and the conclusions are presented in Section 6.

Previous studies and spectroscopic databases

The study of H2 18 O absorption spectra in the region of interest have been done in several papers. The spectra of 18 O enriched water vapor were studied by Fourier transform spectroscopy (FTS) in Refs. [START_REF] Toth | Spectrum of H2 18 O and H2 17 O in the 6974 to 7387 cm -1 region[END_REF][START_REF] Chevillard | The first hexad[END_REF][START_REF] Toth | Transition frequencies and strengths of H2 17 O and H2 18 O: 6600 to 7640 cm -1[END_REF][START_REF] Liu | Fourier-transform absorption spectroscopy of H2 18 O in the first hexade region[END_REF]. Later Liu et al [START_REF] Liu | High sensitivity CW-CDRS of 18 O enriched water near 1.6 µm[END_REF] studied a spectrum of highly enriched by oxygen 18 O water vapor near 1.6 µm (between 5905 and 6726 cm -1 ) using high sensitivity continuous wave cavity ring down spectroscopy (cw-CRDS) technique. Additional H2 18 O absorption lines were obtained from the absorption spectrum studies of natural water vapor [START_REF] Régalia | Water vapor line parameters from 6450 to 9400 cm -1[END_REF][START_REF] Jenouvrier | Fourier transform measurements of water vapor line parameters in the 4200 -6600 cm -1 region[END_REF][START_REF] Macko | High sensitivity CW-cavity ring down spectroscopy of water in the region of the 1.5 µm atmospheric window[END_REF][START_REF] Tolchenov | Water line parameters for weak lines in the range 7400 -9600 cm -1[END_REF][START_REF] Mikhailenko | Weak water absorption lines around 1.455 and 1.66 μm by CW-CRDS[END_REF][START_REF] Mikhailenko | The absorption spectrum of water in the 1.25 µm transparency window (7408 -7920 cm -1 )[END_REF][START_REF] Leshchishina | CRDS of water vapor at 0.1 Torr between 6886 and 7406 cm -1[END_REF][START_REF] Leshchishina | An improved line list for water vapor in the 1.5 µm transparency window by highly sensitive CRDS between 5852 and 6607 cm -1[END_REF][START_REF] Campargue | The absorption spectrum of water vapor in the 1.25 µm atmospheric window (7911 -8337 cm -1 )[END_REF] and of deuterium [START_REF] Liu | CW-Cavity Ring Down Spectroscopy of deuterated water in the 1.58 µm atmospheric transparency window[END_REF] and 17 O [START_REF] Mikhailenko | CRDS of 17 O enriched water between 5850 and 6671 cm -1 : more than 1000 energy levels of H2 17 O and HD 17 O newly determined[END_REF] enriched water vapor. Line positions of Refs. [START_REF] Jenouvrier | Fourier transform measurements of water vapor line parameters in the 4200 -6600 cm -1 region[END_REF][START_REF] Toth | Spectrum of H2 18 O and H2 17 O in the 6974 to 7387 cm -1 region[END_REF][START_REF] Chevillard | The first hexad[END_REF][START_REF] Toth | Transition frequencies and strengths of H2 17 O and H2 18 O: 6600 to 7640 cm -1[END_REF][START_REF] Liu | Fourier-transform absorption spectroscopy of H2 18 O in the first hexade region[END_REF][START_REF] Liu | High sensitivity CW-CDRS of 18 O enriched water near 1.6 µm[END_REF][START_REF] Macko | High sensitivity CW-cavity ring down spectroscopy of water in the region of the 1.5 µm atmospheric window[END_REF][START_REF] Tolchenov | Water line parameters for weak lines in the range 7400 -9600 cm -1[END_REF][START_REF] Mikhailenko | Weak water absorption lines around 1.455 and 1.66 μm by CW-CRDS[END_REF] were used by an IUPAC task group (IUPAC-TG) [START_REF] Tennyson | IUPAC critical evaluation of the rotational-vibrational spectra of water vapor. Part I. Energy levels and transition wavenumbers for H2 17 O and H2 18 O[END_REF][START_REF] Tennyson | IUPAC critical evaluation of the rotational-vibrational spectra of water vapor. Part II. Energy levels and transition wavenumbers for HD 16 O, HD 17 O, and HD 18 O[END_REF] for the energy level determination of H2 18 O molecule. According to Refs. [START_REF] Tennyson | IUPAC critical evaluation of the rotational-vibrational spectra of water vapor. Part I. Energy levels and transition wavenumbers for H2 17 O and H2 18 O[END_REF][START_REF] Tennyson | IUPAC critical evaluation of the rotational-vibrational spectra of water vapor. Part II. Energy levels and transition wavenumbers for HD 16 O, HD 17 O, and HD 18 O[END_REF], about 3470 H2 18 O transitions have been reported in Refs. [START_REF] Jenouvrier | Fourier transform measurements of water vapor line parameters in the 4200 -6600 cm -1 region[END_REF][START_REF] Toth | Spectrum of H2 18 O and H2 17 O in the 6974 to 7387 cm -1 region[END_REF][START_REF] Chevillard | The first hexad[END_REF][START_REF] Toth | Transition frequencies and strengths of H2 17 O and H2 18 O: 6600 to 7640 cm -1[END_REF][START_REF] Liu | Fourier-transform absorption spectroscopy of H2 18 O in the first hexade region[END_REF][START_REF] Liu | High sensitivity CW-CDRS of 18 O enriched water near 1.6 µm[END_REF][START_REF] Macko | High sensitivity CW-cavity ring down spectroscopy of water in the region of the 1.5 µm atmospheric window[END_REF][START_REF] Tolchenov | Water line parameters for weak lines in the range 7400 -9600 cm -1[END_REF][START_REF] Mikhailenko | Weak water absorption lines around 1.455 and 1.66 μm by CW-CRDS[END_REF] between 6526 and 8011 cm -1 . On Figure 1 are shown the transition set used in Refs. [START_REF] Tennyson | IUPAC critical evaluation of the rotational-vibrational spectra of water vapor. Part I. Energy levels and transition wavenumbers for H2 17 O and H2 18 O[END_REF][START_REF] Tennyson | IUPAC critical evaluation of the rotational-vibrational spectra of water vapor. Part II. Energy levels and transition wavenumbers for HD 16 O, HD 17 O, and HD 18 O[END_REF] (red stars) and more than 220 transitions observed later in Refs. [START_REF] Mikhailenko | The absorption spectrum of water in the 1.25 µm transparency window (7408 -7920 cm -1 )[END_REF][START_REF] Leshchishina | CRDS of water vapor at 0.1 Torr between 6886 and 7406 cm -1[END_REF][START_REF] Leshchishina | An improved line list for water vapor in the 1.5 µm transparency window by highly sensitive CRDS between 5852 and 6607 cm -1[END_REF][START_REF] Campargue | The absorption spectrum of water vapor in the 1.25 µm atmospheric window (7911 -8337 cm -1 )[END_REF][START_REF] Liu | CW-Cavity Ring Down Spectroscopy of deuterated water in the 1.58 µm atmospheric transparency window[END_REF][START_REF] Mikhailenko | CRDS of 17 O enriched water between 5850 and 6671 cm -1 : more than 1000 energy levels of H2 17 O and HD 17 O newly determined[END_REF] (blue circles). Note, all transitions with an intensity below 1×10 -26 cm/molecule which are plotted on Figure 1, have been observed using CRDS measurements [START_REF] Liu | High sensitivity CW-CDRS of 18 O enriched water near 1.6 µm[END_REF][START_REF] Macko | High sensitivity CW-cavity ring down spectroscopy of water in the region of the 1.5 µm atmospheric window[END_REF][START_REF] Mikhailenko | Weak water absorption lines around 1.455 and 1.66 μm by CW-CRDS[END_REF][START_REF] Mikhailenko | The absorption spectrum of water in the 1.25 µm transparency window (7408 -7920 cm -1 )[END_REF][START_REF] Leshchishina | CRDS of water vapor at 0.1 Torr between 6886 and 7406 cm -1[END_REF][START_REF] Leshchishina | An improved line list for water vapor in the 1.5 µm transparency window by highly sensitive CRDS between 5852 and 6607 cm -1[END_REF][START_REF] Campargue | The absorption spectrum of water vapor in the 1.25 µm atmospheric window (7911 -8337 cm -1 )[END_REF][START_REF] Liu | CW-Cavity Ring Down Spectroscopy of deuterated water in the 1.58 µm atmospheric transparency window[END_REF][START_REF] Mikhailenko | CRDS of 17 O enriched water between 5850 and 6671 cm -1 : more than 1000 energy levels of H2 17 O and HD 17 O newly determined[END_REF].

Figure 1

The HITRAN2016 database [START_REF] Gordon | The HITRAN2016 molecular spectroscopic database[END_REF] contains 6368 H2 18 O transitions between 6525 and 8011 cm -1 . The minimum intensity corresponds to a cut-off of 5.5×10 -30 cm -1 / (molecule cm - 2 ) at T=296 K taking into account natural abundance of 0.199983%. Line intensities are partly from FTS [START_REF] Toth | Line list of water vapour parameters from 500 to 8000 cm -1[END_REF] and cw-CRDS [START_REF] Mikhailenko | The absorption spectrum of water in the 1.25 µm transparency window (7408 -7920 cm -1 )[END_REF][START_REF] Leshchishina | CRDS of water vapor at 0.1 Torr between 6886 and 7406 cm -1[END_REF][START_REF] Campargue | The absorption spectrum of water vapor in the 1.25 µm atmospheric window (7911 -8337 cm -1 )[END_REF][START_REF] Mikhailenko | A spectroscopic database for water vapor between 5850 and 8340 cm -1[END_REF] and partly from variational calculations [START_REF] Lodi | Line lists for H2 18 O and H2 17 O based on empirical line positions and ab initio intensities[END_REF]27] for this region. 5802 of 6368 line positions correspond to cw-CRDS results [START_REF] Mikhailenko | A spectroscopic database for water vapor between 5850 and 8340 cm -1[END_REF]. The line positions of thirteen transitions are observed values given by Toth [START_REF] Toth | Line list of water vapour parameters from 500 to 8000 cm -1[END_REF]. 262 line positions are calculated using empirical energy levels of IUPAC-TG [START_REF] Tennyson | IUPAC critical evaluation of the rotational-vibrational spectra of water vapor. Part I. Energy levels and transition wavenumbers for H2 17 O and H2 18 O[END_REF][START_REF] Tennyson | IUPAC critical evaluation of the rotational-vibrational spectra of water vapor. Part II. Energy levels and transition wavenumbers for HD 16 O, HD 17 O, and HD 18 O[END_REF]. In additional 291 weak transitions (SRV < 7.5×10 -28 cm/molecule) have variational line positions calculated by Bubukina et al. [START_REF] Bubukina | Optimized semiempirical potential energy surface for H2 16 O up to 26000 cm -1[END_REF].

Current version of the GEISA database [START_REF] Jacquinet-Husson | The 2015 edition of the GEISA spectroscopic database[END_REF] includes 6044 transitions in the 6525 -8011 cm -1 range. The intensity cut-off is 1×10 -29 cm/molecule. Six origins for line positions and line intensities are given in Table 1. The first reference of the second column shows the origin of the line position and the second one shows the origin of the line intensity. The experimental line parameters corresponding to M11, L12 and L13 origins are from CRDS studies of natural water vapor [START_REF] Mikhailenko | The absorption spectrum of water in the 1.25 µm transparency window (7408 -7920 cm -1 )[END_REF][START_REF] Leshchishina | CRDS of water vapor at 0.1 Torr between 6886 and 7406 cm -1[END_REF][START_REF] Leshchishina | An improved line list for water vapor in the 1.5 µm transparency window by highly sensitive CRDS between 5852 and 6607 cm -1[END_REF]. Line positions [START_REF] Lodi | Line lists for H2 18 O and H2 17 O based on empirical line positions and ab initio intensities[END_REF] were generated from empirical energy levels [START_REF] Tennyson | IUPAC critical evaluation of the rotational-vibrational spectra of water vapor. Part I. Energy levels and transition wavenumbers for H2 17 O and H2 18 O[END_REF]. Empirical values of the line intensities are coming from CRDS studies [START_REF] Mikhailenko | The absorption spectrum of water in the 1.25 µm transparency window (7408 -7920 cm -1 )[END_REF][START_REF] Leshchishina | CRDS of water vapor at 0.1 Torr between 6886 and 7406 cm -1[END_REF][START_REF] Leshchishina | An improved line list for water vapor in the 1.5 µm transparency window by highly sensitive CRDS between 5852 and 6607 cm -1[END_REF] or from FTS measurements of Toth [START_REF] Toth | Line list of water vapour parameters from 500 to 8000 cm -1[END_REF]. Calculated line intensities were taken either from web accessible information system SPECTRA [27] or were computed from ab initio dipole moment surface of Lodi et al [START_REF] Lodi | A global, high accuracy ab initio dipole moment surface for the electronic ground state of the water molecule[END_REF].

Table 1

Recently two empirical line lists of natural water were constructed by Mikhailenko et al in the 5850 -7920 cm -1 [START_REF] Mikhailenko | An accurate and complete empirical line list for water vapor between 5850 and 7920 cm -1[END_REF] and later in the 5850 -8340 cm -1 [START_REF] Mikhailenko | A spectroscopic database for water vapor between 5850 and 8340 cm -1[END_REF] spectral range. These lists are based on the results of CRDS studies of water vapor spectra [START_REF] Liu | High sensitivity CW-CDRS of 18 O enriched water near 1.6 µm[END_REF][START_REF] Macko | High sensitivity CW-cavity ring down spectroscopy of water in the region of the 1.5 µm atmospheric window[END_REF][START_REF] Mikhailenko | Weak water absorption lines around 1.455 and 1.66 μm by CW-CRDS[END_REF][START_REF] Mikhailenko | The absorption spectrum of water in the 1.25 µm transparency window (7408 -7920 cm -1 )[END_REF][START_REF] Leshchishina | CRDS of water vapor at 0.1 Torr between 6886 and 7406 cm -1[END_REF][START_REF] Leshchishina | An improved line list for water vapor in the 1.5 µm transparency window by highly sensitive CRDS between 5852 and 6607 cm -1[END_REF][START_REF] Campargue | The absorption spectrum of water vapor in the 1.25 µm atmospheric window (7911 -8337 cm -1 )[END_REF][START_REF] Liu | CW-Cavity Ring Down Spectroscopy of deuterated water in the 1.58 µm atmospheric transparency window[END_REF]. Both lists have an intensity cut-off of 1×10 -29 cm/molecule. The list [START_REF] Mikhailenko | An accurate and complete empirical line list for water vapor between 5850 and 7920 cm -1[END_REF] was adopted for current version of the GEISA database [START_REF] Jacquinet-Husson | The 2015 edition of the GEISA spectroscopic database[END_REF]. The list [START_REF] Mikhailenko | A spectroscopic database for water vapor between 5850 and 8340 cm -1[END_REF] contains about 6400 H2 18 O transitions between 6525 and 8011 cm -1 . Line positions were obtained by difference of empirical energy levels. These empirical energy values are mostly based on cw-CRDS studies of water vapor [START_REF] Liu | High sensitivity CW-CDRS of 18 O enriched water near 1.6 µm[END_REF][START_REF] Macko | High sensitivity CW-cavity ring down spectroscopy of water in the region of the 1.5 µm atmospheric window[END_REF][START_REF] Mikhailenko | Weak water absorption lines around 1.455 and 1.66 μm by CW-CRDS[END_REF][START_REF] Mikhailenko | The absorption spectrum of water in the 1.25 µm transparency window (7408 -7920 cm -1 )[END_REF][START_REF] Leshchishina | CRDS of water vapor at 0.1 Torr between 6886 and 7406 cm -1[END_REF][START_REF] Leshchishina | An improved line list for water vapor in the 1.5 µm transparency window by highly sensitive CRDS between 5852 and 6607 cm -1[END_REF][START_REF] Campargue | The absorption spectrum of water vapor in the 1.25 µm atmospheric window (7911 -8337 cm -1 )[END_REF][START_REF] Liu | CW-Cavity Ring Down Spectroscopy of deuterated water in the 1.58 µm atmospheric transparency window[END_REF] completed by literature data. Obtained energy levels are quite different compare to those of IUPAC-TG [START_REF] Tennyson | IUPAC critical evaluation of the rotational-vibrational spectra of water vapor. Part I. Energy levels and transition wavenumbers for H2 17 O and H2 18 O[END_REF]. The energy level differences are discussed in Ref. [START_REF] Mikhailenko | A spectroscopic database for water vapor between 5850 and 8340 cm -1[END_REF].

Experimental conditions and line parameter retrievals

Spectra recording

For this study of water vapor enriched by 18 O, a set of 36 spectra were recorded using the Connes' type FTS [START_REF] Connes | Astronomical Fourier spectrometer[END_REF] built in GSMA (Group of Molecular and Atmospheric Spectrometry) laboratory [START_REF] Plateaux | Reims high resolution Fourier transform spectrometer. Data reduction for ozone[END_REF][START_REF] Régalia | FTS improvements and connection with a long White cell. Application: H2 16 O intensity measurements around 1200 cm -1[END_REF]. These are among the last recorded spectra of this apparatus; indeed, it has since been demounted. This instrument had a 3-meter maximum path difference that corresponds to a non-apodized resolution of 0.0017 cm -1 . All the spectra were recorded with the following optical setup: a CaF2 beamsplitter, two InSb detectors and some lenses and windows in BaF2. During the recording time the whole absorption path was maintained under vacuum. For this study several absorption cells were used: a single-path cell with an optical path of 67 cm and two other White cells [START_REF] White | Long optical paths of large aperture[END_REF], a 2-meter and 50-meter cell to obtain the absorption lengths up to 88 and 1000 meters respectively. The samples used for these experiments were water vapor with an H2 18 O abundance enrichment of about 95%. The pressure and the temperature were continuously monitored during the whole recording time.

The pressure was measured with an uncertainty smaller than 0.3% using MKS Baratron manometers and the temperature was measured with platinum-resistance thermometers placed on the absorption cell, with an uncertainty smaller than 0.5 K.

The FTS's room was air-conditioned and any variation of temperature during the records was observed. To ensure stabilization of gas pressures and temperatures, the record was started several hours after the filling of the gas sample into the absorption cell.

To avoid possible problems due to the chromaticity of the beamsplitter that we have already observed with our step-by-step FTS, we chose to separate in two parts the whole recorded spectral range: the first spectral range named Region 1 from 6450 to 8150 cm -1 and the second named Region 2 from 8000 to 9400 cm -1 . For the moment we focus on the first region (Region 1), an example of spectra is given in Figure 2.

Figure 2

Experimental conditions of the nine spectra used for the line intensity determination in the Region 1 are summarized in Table 2. To avoid variations of isotopologues partial pressures, we introduced the water vapor sample only one time (about 12.8 Torr) for all recordings listed in the Table 2. So we had the same sample for different lengths of the cell and we only pumped on the gas sample to modify the total pressure. Before to pump on the gas cell, for each value of the cell length, we recorded also a spectrum in the second spectral window from 8000 to 9400 cm -1 , these spectra will be used in a further study. We also used a simple path cell with an optical path of 67 cm and our 50-meter White cell with an absorption path length of 1001 meter, to perform the determination of line positions but the knowledge of partial pressure values was not sufficient to obtain accurate intensity values for the strong and the weakest lines (see Figure 12 below).

Table 2

For the line profile, a Voigt profile was adopted in this study and no particular signature corresponding to a problem of profile was observed on the fit residuals. Spectra were analyzed using a software developed at GSMA (Reims) named "MultiFiT" (MFT) [START_REF] Plateaux | Multispectrum fitting technique for data recorded by Fourier transform spectrometer: application to N2O and CH3D[END_REF] in order to obtain simultaneously line parameters. Several pressures were selected for each absorption path length to obtain simultaneously the line position, the line intensity and the self-broadening coefficient with a multi-spectrum fitting procedure. The chosen absorption path lengths allowed us to measure line intensities distributed in an absorption range from 10 -27 to 10 -21 cm -1 / (molecule cm -2 ) at 296 K.

Determination of the partial pressure of water vapor isotopologues

The sample of water vapor used for the records came from the company Euriso-top and was enriched by 18 O of about 95%. To ensure the measurement of intensities with accuracy, before the measurement of line parameters, we took time to determine the partial pressure of each isotopologue, their abundances, except for H2 18 O, are estimated with the intensities of line referenced in the literature (see Table 3). The pressure parameter was fitted on isolated lines to determine the partial pressures using low pressure spectra (lower than 2 Torr), indeed, in these experimental conditions, the influence of the broadening parameters can be neglected.

Of course, to obtain the pressure parameter, the intensity parameter has to be fixed at the value found in several "reference" articles (Table 3).

Table 3

Then we determine the partial pressure of H2 18 O by using the following formula where Ptot is the total pressure of each used spectrum: P(H2 18 O) = Ptot -[ P(H2 16 O) + P(H2 17 O) + P(HD 16 O) + P(HD 18 O) + P(HD 17 O)].

For the determination of line intensities, only the spectra listed in Table 2 are used.

These spectra were recorded with the same cell where the water vapor sample was introduced only one time for the three series (as explained above). Indeed, we remark that the isotopic abundance is slightly different in other spectra after a new introduction of water vapor sample in the cell. We recorded at first the spectra with higher pressure with three different absorption path lengths, and then water vapor sample was pumped and new spectra were recorded with different absorption lengths, etc. The single introduction of water vapor ensures us to keep the same partial pressures. In Table 2, are listed the spectra in the order of their recording.

The abundance of the studied sample and the reference of the articles used to estimate the abundance of each isotopologue, except H2 18 O, are given in Table 3. The determined abundances are in good agreement with those reported in our previous study in the 1000 -2300 cm -1 region [START_REF] Oudot | Fourier transform measurements of H2 18 O and HD 18 O in the spectral range 1000 -2300 cm -1[END_REF] using the same sample enriched by 18 O.

Line parameters retrieval

First of all, we checked the real value of the iris radius of the aperture at the entry of the Michelson interferometer to minimize the effect of the apparatus function on the retrieval parameters. The nominal iris radius value was 2.5 mm and the iris radius parameter was fitted to obtain the effective value on the spectrum with the lowest pressure for each cell length. The fitted effective value was equal to 2.35 mm. This value was applied to each spectrum even for those with higher pressure, as the experimental conditions staying the same for all records.

The effective iris radius value is more realistic considering the optical effects at the input of the interferometer or variations of the signal during the displacement of the movable mirror.

Figure 3 shows the difference on the residual of a single spectrum fit at low pressure between the case using the nominal iris radius value and the case using the effective one. In addition, Figure 4 shows the same effect in multispectrum fitting procedure. The impact of this type of error on the line parameters retrieval is around 1% for the intensity determination and more for the collisional coefficients, around 5%.

Wavenumber calibration

As it was explained in section 3.2, we took care of the conditions for spectra recording especially to keep the same isotopic abundance. Unfortunately, these conditions are not suitable to the wavenumber calibration. In our optical configuration, the cell is placed before the interferometer so when we change the absorption path length we change also the way of the light beam arriving at the entry of the interferometer. So each time we change the absorption path length, the optical set-up is modified and it can induce a slight wavenumber shift.

Nevertheless we managed to calibrate spectra in wavenumber by using previous CRDS data of the region. The most accurate recent data [START_REF] Mikhailenko | CRDS of 17 O enriched water between 5850 and 6671 cm -1 : more than 1000 energy levels of H2 17 O and HD 17 O newly determined[END_REF][START_REF] Modelain | Combassisted cavity ring down spectroscopy of 17 O enriched water between 7443 and 7921 cm -1[END_REF][START_REF] Mikhailenko | Comb-assisted cavity ring down spectroscopy of 17 O enriched water between 6667 and 7443 cm -1[END_REF] were used for this purpose. The root mean square deviation (rmsd =

NT NT i CRDS i OBS i / ) ( 1 2 ∑ = -ν ν ) and mean deviation ( ∑ = - NT i CRDS i OBS i NT 1 / ) ( ν ν
) between our calibrated and CRDS data [START_REF] Mikhailenko | CRDS of 17 O enriched water between 5850 and 6671 cm -1 : more than 1000 energy levels of H2 17 O and HD 17 O newly determined[END_REF][START_REF] Modelain | Combassisted cavity ring down spectroscopy of 17 O enriched water between 7443 and 7921 cm -1[END_REF][START_REF] Mikhailenko | Comb-assisted cavity ring down spectroscopy of 17 O enriched water between 6667 and 7443 cm -1[END_REF] are 0.0013 cm -1 and 5×10 -5 cm -1 respectively for more than 5000 lines between 6526 and 7920 cm -1 .

Line list assignments and energy level determination

The nine spectra listed in Table 2 were used for determination of the line parameters.

As note in Section 3.1, all these spectra were recorded using 2-meter White cell. As mentioned above, two spectra with an optical path of 67 cm and 1001 m were used to precise line positions of some strongest (67 cm) and weakest (1001 m) lines. Overall 8092 lines were found in mentioned above spectra. 7993 lines were assigned to 8647 transitions of the six water isotopologues (H2 16 O, H2 18 O, H2 17 O, HD 16 O, HD 18 O, and HD 17 O). Finally 98 lines (1.2%) were left unassigned.

Like in our previous studies on the analysis of water spectra [START_REF] Régalia | Water vapor line parameters from 6450 to 9400 cm -1[END_REF][START_REF] Mikhailenko | Weak water absorption lines around 1.455 and 1.66 μm by CW-CRDS[END_REF][START_REF] Mikhailenko | The absorption spectrum of water in the 1.25 µm transparency window (7408 -7920 cm -1 )[END_REF][START_REF] Leshchishina | CRDS of water vapor at 0.1 Torr between 6886 and 7406 cm -1[END_REF][START_REF] Leshchishina | An improved line list for water vapor in the 1.5 µm transparency window by highly sensitive CRDS between 5852 and 6607 cm -1[END_REF][START_REF] Campargue | The absorption spectrum of water vapor in the 1.25 µm atmospheric window (7911 -8337 cm -1 )[END_REF][START_REF] Mikhailenko | CRDS of 17 O enriched water between 5850 and 6671 cm -1 : more than 1000 energy levels of H2 17 O and HD 17 O newly determined[END_REF], spectra line assignments were performed on the basis of available sets of (i) empirical line lists [START_REF] Toth | Line list of water vapour parameters from 500 to 8000 cm -1[END_REF][START_REF] Mikhailenko | A spectroscopic database for water vapor between 5850 and 8340 cm -1[END_REF][START_REF] Mikhailenko | An accurate and complete empirical line list for water vapor between 5850 and 7920 cm -1[END_REF], (ii) empirical energy levels [START_REF] Tennyson | IUPAC critical evaluation of the rotational-vibrational spectra of water vapor. Part I. Energy levels and transition wavenumbers for H2 17 O and H2 18 O[END_REF][START_REF] Tennyson | IUPAC critical evaluation of the rotational-vibrational spectra of water vapor. Part II. Energy levels and transition wavenumbers for HD 16 O, HD 17 O, and HD 18 O[END_REF][START_REF] Mikhailenko | A spectroscopic database for water vapor between 5850 and 8340 cm -1[END_REF][START_REF] Mikhailenko | Absorption spectrum of deuterated water vapor enriched by 18 O between 6000 and 9200 cm -1[END_REF] and (iii) calculated variational water spectra [27] based on the results of Partridge and Schwenke [START_REF] Partridge | The determination of an accurate isotope dependent potential energy surface for water from extensive ab initio calculations and experimental data[END_REF][START_REF] Schwenke | Convergence testing of the analytic representation of an ab initio dipole moment function for water: Improved fitting yields improved intensities[END_REF] (SP line lists). The summary of assigned transitions is shown in Table 4 for all six water isotopologues.

Table 4

The first step of water lines analysis is so-called "trivial assignment", i.e. a direct comparison of the experimental line list needs to be assigned against one of the empirical lists [START_REF] Toth | Line list of water vapour parameters from 500 to 8000 cm -1[END_REF][START_REF] Mikhailenko | A spectroscopic database for water vapor between 5850 and 8340 cm -1[END_REF][START_REF] Mikhailenko | An accurate and complete empirical line list for water vapor between 5850 and 7920 cm -1[END_REF]. We made assignment by comparison of our list against data of Ref. [START_REF] Mikhailenko | A spectroscopic database for water vapor between 5850 and 8340 cm -1[END_REF]. By this way we were able to assign all lines of H2 16 O, HD 16 O and HD 17 O species. All but two transitions of H2 17 O, 4106 of the 4236 transitions of H2 18 O and 745 of the 1267 transitions of HD 18 O isotopologues were also assigned using the list [START_REF] Mikhailenko | A spectroscopic database for water vapor between 5850 and 8340 cm -1[END_REF]. The second step of the assignment procedure is a comparison of the lines which left unassigned against one of variational lists. We used SP line lists [27] on this step. Our experience of the analysis of water absorption spectra [START_REF] Régalia | Water vapor line parameters from 6450 to 9400 cm -1[END_REF][START_REF] Jenouvrier | Fourier transform measurements of water vapor line parameters in the 4200 -6600 cm -1 region[END_REF][START_REF] Macko | High sensitivity CW-cavity ring down spectroscopy of water in the region of the 1.5 µm atmospheric window[END_REF][START_REF] Mikhailenko | Weak water absorption lines around 1.455 and 1.66 μm by CW-CRDS[END_REF][START_REF] Mikhailenko | The absorption spectrum of water in the 1.25 µm transparency window (7408 -7920 cm -1 )[END_REF][START_REF] Leshchishina | CRDS of water vapor at 0.1 Torr between 6886 and 7406 cm -1[END_REF][START_REF] Leshchishina | An improved line list for water vapor in the 1.5 µm transparency window by highly sensitive CRDS between 5852 and 6607 cm -1[END_REF][START_REF] Campargue | The absorption spectrum of water vapor in the 1.25 µm atmospheric window (7911 -8337 cm -1 )[END_REF][START_REF] Mikhailenko | CRDS of 17 O enriched water between 5850 and 6671 cm -1 : more than 1000 energy levels of H2 17 O and HD 17 O newly determined[END_REF] shows that the differences between observed (ν OBS ) and calculated (ν SP ) line positions are smooth series (ν OBSν SP ) for the same rotational number J or Ka with increasing of the number Ka or J respectively for a given band. The second criteria of the line assignment is a coincidence of observed ( OBS RV S ) and calculated ( SP RV S ) line intensities. Of course, the coincidence is limited by experimental accuracy of the line intensity determination (less than 2% when line parameter measurements are done on lines with an absorption depth from 20 to 60%) and by calculation inaccuracy. 16 O, HD 16 O, H2 17

H2

O, and HD 17 O

There are no new or corrected data for H2 16 O, HD 16 O and HD 17 O isotopologues compared to previous studies, observed line positions are in very good agreement with the positions of Ref. [START_REF] Mikhailenko | A spectroscopic database for water vapor between 5850 and 8340 cm -1[END_REF]. Corresponding root mean square deviations (rmsd =

NT NT i i OBS i / ) ( 1 2 ] 25 [ Ref. ∑ = -ν ν
, NT is the number of observed transitions) are 0.0021, 0.0024 and 0.0025 cm -1 respectively. The maximum deviation of observed line positions from those of Ref. [START_REF] Mikhailenko | A spectroscopic database for water vapor between 5850 and 8340 cm -1[END_REF] does not exceed 0.02 cm -1 . The biggest discrepancies correspond to very weak and blended lines.

Two of 1136 H2 17 O assigned transitions in recorded spectra were not observed in the CRDS studies summarized in Ref. [START_REF] Mikhailenko | A spectroscopic database for water vapor between 5850 and 8340 cm -1[END_REF]. Corresponding lines are due to the 2ν1 transitions 8 5 3 -9 4 6 at 7055.9516 cm -1 , SRV = 2.77×10 -26 cm/molecule and 11 2 9 -10 3 8 at 7376.7301 cm -1 , SRV = 2.7×10 -26 cm/molecule. These line positions give two previously unknown upper energy values 8393.4412 and 8819.7711 cm -1 of the (200) 8 5 3 and (200) 11 2 9 levels. Our assignments of these lines were later confirmed by the observation of others transitions associated with these upper levels from analysis of CRDS 17 O enriched water vapor spectrum [START_REF] Modelain | Combassisted cavity ring down spectroscopy of 17 O enriched water between 7443 and 7921 cm -1[END_REF]. The comparison of observed line positions against the line list [START_REF] Mikhailenko | A spectroscopic database for water vapor between 5850 and 8340 cm -1[END_REF] gives rmsd = 0.0024 cm -1 for 1134 transitions with maximum deviation of 0.013 cm -1 .

H2 18 O

Overall we assigned 4236 H2 18 O transitions in studied spectra (see Table 4). Table 5 shows band-by-band statistics of assigned transitions. Table 5 includes the number of transitions (NT), maximum values of the rotational numbers (J Ka) and the location for each of nine cold and five hot bands. Figure 5 demonstrates all assigned transitions (left panel) and 785 transitions reported for the first time (right panel). The minimum intensity of assigned transitions is about 1×10 -27 cm/molecule. Main part of the transitions (4106) was assigned by direct comparison of experimental line list against the list [START_REF] Mikhailenko | A spectroscopic database for water vapor between 5850 and 8340 cm -1[END_REF]. Thirty-nine assigned transitions are not included in the list [START_REF] Mikhailenko | A spectroscopic database for water vapor between 5850 and 8340 cm -1[END_REF] due to their weakness. Corresponding line positions were calculated using empirical energy levels. The transitions assigned for the first time allow us to determine 65 new vibration-rotation energies of seven vibrational states. Sixty-five new empirical energies as well as 12 corrected ones are listed in Table 6. Corrected term values differ from the literature data on the value bigger than 0.015 cm -1 . At least a part of firstly obtained and corrected energies are confirmed by the transition observation in recently reported CRDS studies [START_REF] Modelain | Combassisted cavity ring down spectroscopy of 17 O enriched water between 7443 and 7921 cm -1[END_REF][START_REF] Mikhailenko | Comb-assisted cavity ring down spectroscopy of 17 O enriched water between 6667 and 7443 cm -1[END_REF]. The comparison of 4124 observed line positions against the line list [START_REF] Mikhailenko | A spectroscopic database for water vapor between 5850 and 8340 cm -1[END_REF] gives rmsd = 0.0022 cm -1 with maximum deviation of 0.02 cm -1 .

Table 5

Figure 5 Table 6 4.3. HD 18

O

The most extended set of HD 18 O transitions in near infrared region was reported by Mikhailenko et al [START_REF] Mikhailenko | Absorption spectrum of deuterated water vapor enriched by 18 O between 6000 and 9200 cm -1[END_REF] from analysis of deuterated water vapor enriched by 18 abundance. First of all, it should be noted that the concentration of HD 18 O in the studied sample of Ref. [START_REF] Mikhailenko | Absorption spectrum of deuterated water vapor enriched by 18 O between 6000 and 9200 cm -1[END_REF] was estimated at more than 15.5% while in our samples it does not exceed the value of 0.5% (see Table 3). Despite this we observed the lines of twenty transitions which were not observed in Ref. [START_REF] Mikhailenko | Absorption spectrum of deuterated water vapor enriched by 18 O between 6000 and 9200 cm -1[END_REF]. The line at 7922.4333 cm -1 , SRV = 6.3×10 -27 cm/molecule is due to the 3ν2+ν3 8 2 6 -7 2 5 transition. This line position gives new empirical energy E Obs = 8439.2324 cm -1 of the upper level (031) 8 2 6.

Comparisons of observed line positions with two literature data sets give rmsd = 0.0019 cm -1 for 739 transitions with maximum deviation of 0.01 cm -1 for Ref. [START_REF] Gordon | The HITRAN2016 molecular spectroscopic database[END_REF] and rmsd = 0.0031 cm -1 for 1247 transitions with maximum deviation of 0.017 cm -1 for Ref. [START_REF] Mikhailenko | Absorption spectrum of deuterated water vapor enriched by 18 O between 6000 and 9200 cm -1[END_REF].

5.

Comparisons and discussions

Comparison with IUPAC-TG data for the line positions

We made comparisons of our line positions with those calculated from empirical energy levels recommended by an IUPAC task group [START_REF] Tennyson | IUPAC critical evaluation of the rotational-vibrational spectra of water vapor. Part I. Energy levels and transition wavenumbers for H2 17 O and H2 18 O[END_REF][START_REF] Tennyson | IUPAC critical evaluation of the rotational-vibrational spectra of water vapor. Part II. Energy levels and transition wavenumbers for HD 16 O, HD 17 O, and HD 18 O[END_REF][START_REF] Tennyson | IUPAC critical evaluation of the rotational-vibrational spectra of water vapor. Part III: Energy levels and transition wavenumbers for H2 16 O[END_REF]. It was possible for five isotopologues except HD 17 O because the corresponding energy set [START_REF] Tennyson | IUPAC critical evaluation of the rotational-vibrational spectra of water vapor. Part II. Energy levels and transition wavenumbers for HD 16 O, HD 17 O, and HD 18 O[END_REF] contains only energies for the ground and first excited states. General statistics of comparisons are shown in Table 7 for each isotopologue. Note, a part of observed frequencies cannot be calculated due to the lack of corresponding energy levels in the energy sets [START_REF] Tennyson | IUPAC critical evaluation of the rotational-vibrational spectra of water vapor. Part I. Energy levels and transition wavenumbers for H2 17 O and H2 18 O[END_REF][START_REF] Tennyson | IUPAC critical evaluation of the rotational-vibrational spectra of water vapor. Part II. Energy levels and transition wavenumbers for HD 16 O, HD 17 O, and HD 18 O[END_REF][START_REF] Tennyson | IUPAC critical evaluation of the rotational-vibrational spectra of water vapor. Part III: Energy levels and transition wavenumbers for H2 16 O[END_REF].

Table 7

As can be seen from Table 7, there are no significant differences between observed and calculated line positions for H2 16 O and HD 16 O species. The maximum deviation dmax = max |ν OBSν IUPAC | does not exceed 0.02 and 0.009 cm -1 for H2 16 O and HD 16 O respectively.

All fifteen H2 16 O transitions with the deviations bigger than 0.01 cm -1 associated with very weak or blended lines.

In general, a good agreement was found for H2 17 CRDS observations for these energy levels were discussed in Refs. [START_REF] Mikhailenko | The absorption spectrum of water in the 1.25 µm transparency window (7408 -7920 cm -1 )[END_REF][START_REF] Leshchishina | CRDS of water vapor at 0.1 Torr between 6886 and 7406 cm -1[END_REF]. 148 assigned transitions cannot be calculated using IUPAC energy levels due to the absence of corresponding upper levels in Ref. [START_REF] Tennyson | IUPAC critical evaluation of the rotational-vibrational spectra of water vapor. Part I. Energy levels and transition wavenumbers for H2 17 O and H2 18 O[END_REF]. All these line positions are in good agreement with calculated values using energy levels obtained from CRDS measurements [START_REF] Mikhailenko | CRDS of 17 O enriched water between 5850 and 6671 cm -1 : more than 1000 energy levels of H2 17 O and HD 17 O newly determined[END_REF].

The situation for H2 18 O is similar to those for H2 17 O. The rmsd = 0.0031 cm -1 for 4107 transitions with maximum deviation dmax ≈ 0.043 cm -1 for the line positions of the (002) 10 7 4

upper level. The deviations d1 are within the limit of 0.005 cm -1 for more than 95% transitions (see Table 7). All line positions but five, for which the deviations d1 are bigger than 0.015 cm -1 , are due to the difference in used upper energy levels. Seven corrected energies are given in Table 6. The differences between observed and calculated line positions using IUPAC energies [START_REF] Tennyson | IUPAC critical evaluation of the rotational-vibrational spectra of water vapor. Part I. Energy levels and transition wavenumbers for H2 17 O and H2 18 O[END_REF] of the (002) 11 7 4, (101) 11 9 2 and (120) 7 6 1 levels were recently discussed in

Refs. [START_REF] Mikhailenko | The absorption spectrum of water in the 1.25 µm transparency window (7408 -7920 cm -1 )[END_REF][START_REF] Leshchishina | CRDS of water vapor at 0.1 Torr between 6886 and 7406 cm -1[END_REF][START_REF] Leshchishina | An improved line list for water vapor in the 1.5 µm transparency window by highly sensitive CRDS between 5852 and 6607 cm -1[END_REF]. 128 assigned transitions cannot be calculated using IUPAC energy levels [START_REF] Tennyson | IUPAC critical evaluation of the rotational-vibrational spectra of water vapor. Part I. Energy levels and transition wavenumbers for H2 17 O and H2 18 O[END_REF].

Maximum deviation dmax for 1058 HD 18 O transitions is about 0.09 cm -1 (see Table 7).

The deviations d1 for thirty-five transitions are bigger than 0.01 cm -1 . The term values of all corresponding IUPAC energies [START_REF] Tennyson | IUPAC critical evaluation of the rotational-vibrational spectra of water vapor. Part II. Energy levels and transition wavenumbers for HD 16 O, HD 17 O, and HD 18 O[END_REF] were corrected by Mikhailenko et al [START_REF] Mikhailenko | Absorption spectrum of deuterated water vapor enriched by 18 O between 6000 and 9200 cm -1[END_REF]. Note maximum value of the deviations dmax = |ν OBSν Ref. [37] | is about 0.017 cm -1 with rmsd = 0.0031 cm -1 for 1247 transitions.

Line position comparison with the HITRAN2016 database

The HITRAN2016 database [START_REF] Gordon | The HITRAN2016 molecular spectroscopic database[END_REF] includes 38372 transitions of seven water isotopologues H2 16 O, H2 18 O, H2 17 O, HD 16 O, HD 18 O, HD 17 O, and D2 16 O between 6525 and 8011 cm -1 .

The line positions of H2 16 O are mainly from cw-CRDS empirical line list [START_REF] Mikhailenko | A spectroscopic database for water vapor between 5850 and 8340 cm -1[END_REF] or from Toth's water database [START_REF] Toth | Line list of water vapour parameters from 500 to 8000 cm -1[END_REF]. Only a small portion of transitions (1206 of 15792) are from empirical energy levels of Refs. [START_REF] Tennyson | IUPAC critical evaluation of the rotational-vibrational spectra of water vapor. Part III: Energy levels and transition wavenumbers for H2 16 O[END_REF][START_REF] Gordon | Private communication[END_REF] or from variational calculations [START_REF] Bubukina | Optimized semiempirical potential energy surface for H2 16 O up to 26000 cm -1[END_REF][START_REF] Barber | A high-accuracy computed water line list[END_REF]. The differences between 1875 observed line positions and those of the HITRAN2016 line list are within 0.019 cm -1 .

As well as for H2 16 O, 4332 positions of H2 17 O are from cw-CRDS empirical line list [START_REF] Mikhailenko | A spectroscopic database for water vapor between 5850 and 8340 cm -1[END_REF]. 318 line positions are from Lodi and Tennyson [START_REF] Lodi | Line lists for H2 18 O and H2 17 O based on empirical line positions and ab initio intensities[END_REF]. At least 277 of them are variationally calculated line positions. About 40 positions are from Toth's water database [START_REF] Toth | Line list of water vapour parameters from 500 to 8000 cm -1[END_REF] or calculated from IUPAC-TG energies [START_REF] Tennyson | IUPAC critical evaluation of the rotational-vibrational spectra of water vapor. Part I. Energy levels and transition wavenumbers for H2 17 O and H2 18 O[END_REF]. The differences between our observed H2 17 O line positions and those of the HITRAN2016 are up to 0.16 cm -1 . The greatest deviations come from the variational line positions given in Ref. [START_REF] Lodi | Line lists for H2 18 O and H2 17 O based on empirical line positions and ab initio intensities[END_REF].

161 positions of HD 16 O transitions are observed values from Toth's water database [START_REF] Toth | Line list of water vapour parameters from 500 to 8000 cm -1[END_REF]. 7607 of 8267 positions are empirical values obtained from energy levels of Refs. [START_REF] Tennyson | IUPAC critical evaluation of the rotational-vibrational spectra of water vapor. Part II. Energy levels and transition wavenumbers for HD 16 O, HD 17 O, and HD 18 O[END_REF][START_REF] Kyuberis | Room temperature line lists for deuterated water[END_REF] and about 500 positions are variationally calculated values by Kyuberis et al. [START_REF] Kyuberis | Room temperature line lists for deuterated water[END_REF]. The differences between 116 observed HD 16 O line positions from our spectra and the values found in the HITRAN2016 line list are within 0.009 cm -1 .

More than 1500 transitions of HD 17 O and HD 18 O [23] are coming from the line lists constructed by Kyuberis et al. [START_REF] Kyuberis | Room temperature line lists for deuterated water[END_REF]. The differences between 768 our observed HD 17 O and HD 18 O line positions and those coming from the HITRAN2016 line list are within 0.011 cm -1 .

More than 500 observed HD 18 O transitions are not included in the HITRAN2016 list due to a cut-off of 1.0×10 -29 cm/molecule [START_REF] Gordon | The HITRAN2016 molecular spectroscopic database[END_REF].

Empirical H2 18 O line positions [START_REF] Gordon | The HITRAN2016 molecular spectroscopic database[END_REF] are from IUPAC-TG energy levels [START_REF] Tennyson | IUPAC critical evaluation of the rotational-vibrational spectra of water vapor. Part II. Energy levels and transition wavenumbers for HD 16 O, HD 17 O, and HD 18 O[END_REF] (262 positions), Toth's water database [START_REF] Toth | Line list of water vapour parameters from 500 to 8000 cm -1[END_REF] (13 positions) and cw-CRDS empirical line list [START_REF] Mikhailenko | A spectroscopic database for water vapor between 5850 and 8340 cm -1[END_REF] (5802 positions). Twenty-nine assigned in our spectra transitions are not included in the HITRAN2016 line list due to a cut-off of 1.0×10 -29 cm/molecule [START_REF] Gordon | The HITRAN2016 molecular spectroscopic database[END_REF]. Maximum deviations between our observed H2 18 O line positions and those coming from the HITRAN2016 line list are up to 18.0 cm -1 . The biggest differences are for the line positions wrongly assigned in the line list [START_REF] Toth | Line list of water vapour parameters from 500 to 8000 cm -1[END_REF]. They are 2ν1 8 5 4 -8 4 5 at 7262.1077 cm -1 instead of 7270.3154 cm -1 [START_REF] Toth | Line list of water vapour parameters from 500 to 8000 cm -1[END_REF]; 2ν1 9 cm -1 instead of 7418.5935 cm -1 [START_REF] Toth | Line list of water vapour parameters from 500 to 8000 cm -1[END_REF]; ν1+ν3 11 3 8 -10 3 7 at 7446.9879 cm -1 instead of 7448.0820 cm -1 [START_REF] Toth | Line list of water vapour parameters from 500 to 8000 cm -1[END_REF].

In general, the HITRAN2016 line list gives a satisfactory quality of the spectrum modelization for our experimental conditions (see Table 2) below 8000 cm -1 . Nevertheless, we observed several significant disagreements between observed and calculated spectra due to incorrect H2 18 O line positions in the line list [START_REF] Gordon | The HITRAN2016 molecular spectroscopic database[END_REF]. Some examples of such disagreements are given between 7265 to 7415 cm -1 and 7418 to 7527 cm -1 respectively on Figures 7 and8.

Four transitions involving the (002) 6 1 6 upper level coming from the list [START_REF] Toth | Line list of water vapour parameters from 500 to 8000 cm -1[END_REF] have wrong positions in the HITRAN2016. Upper and lower panels of Figure 7 demonstrate an offset of 0.31 cm -1 for the 2ν3 6 1 6 -7 0 7 near 7266 cm -1 and 2ν3 6 1 6 -5 0 5 near 7525.7 cm -1 transitions respectively. In the same time, two correct line positions (6924.0189 and 7299.2679 cm -1 ) of the weak transitions 2ν3 6 1 6 -7 4 3 and 2ν3 6 1 6 -6 2 5 were calculated using empirical energy levels [START_REF] Tennyson | IUPAC critical evaluation of the rotational-vibrational spectra of water vapor. Part I. Energy levels and transition wavenumbers for H2 17 O and H2 18 O[END_REF].

Correct positions of seven weak transitions involving the (200) 9 4 6 upper level were calculated using empirical energy level [START_REF] Tennyson | IUPAC critical evaluation of the rotational-vibrational spectra of water vapor. Part I. Energy levels and transition wavenumbers for H2 17 O and H2 18 O[END_REF]. But the line position of the strongest transition 2ν1 9 4 6 -8 3 5 (7431.5260 cm -1 ) was taken from the list [START_REF] Toth | Line list of water vapour parameters from 500 to 8000 cm -1[END_REF]. The real position of corresponding line is at 7413.5221 cm -1 (see upper panel of Figure 8).

Figure 9

Finally, Figure 9 shows another missing line which is belonging to the 2ν1 band with the assignment 8 5 4 -8 4 5. Its position in the HITRAN2016 line list is 7270.315 cm -1 contrary to the observed position at 7262.1077 cm -1 .

Line intensity comparison with the HITRAN2016 database

We calculated a spectrum using the line parameters listed in the HITRAN2016 line list for a pressure of 13 Torr and a cell length of 88 meters, and we directly compared this spectrum with the observed one. The line intensity and broadening line parameters of the HITRAN2016 line list allow us to calculate a spectrum with a satisfactory quality compared to the observed one for the spectral region below 8000 cm -1 . Nevertheless, the following

Line intensity comparison with variational calculations

The observed line intensities of H2 18 O lines were compared to two variational calculations. The first one is SP line list [27] based on the results of Partridge and Schwenke [START_REF] Partridge | The determination of an accurate isotope dependent potential energy surface for water from extensive ab initio calculations and experimental data[END_REF][START_REF] Schwenke | Convergence testing of the analytic representation of an ab initio dipole moment function for water: Improved fitting yields improved intensities[END_REF]. As it was mentioned above, this line list was used for line assignments. The second one is new calculated Exomol line list provided by Polyansky et al [START_REF] Polyansky | ExoMol molecular line lists. XIX: high-accuracy computed hot line lists for H2 18 O and H2 17 O[END_REF]. An overview of the intensity ratios R = S OBS / S Ref is shown on Figure 12. The S Ref corresponds to SP line list and to ExoMol list on the left and right panel respectively. These two calculated line lists seem to be rather similar in the studied region (Figure 13) but if we look more in detail, we can observe some small differences. First we have to remind that the partial pressure of the spectrum (67 cm) was not sufficiently precise to determine accurate intensity values for the strong lines. This could explain why the ratio S OBS / S Ref in Figure 12 is smaller than 1 for the intensity range from 5×10 -22 to 2×10 -20 with the two calculated line lists. If we compare the intensity range from 10 -24 to 5×10 -22 , the ratio with the Ref. [START_REF] Polyansky | ExoMol molecular line lists. XIX: high-accuracy computed hot line lists for H2 18 O and H2 17 O[END_REF] seems to be slightly greater than 1, while the ratio with the Ref.

[27] shows a rather good agreement. For the intensity range from 10 -24 to 10 -26 , it seems to be different and the measures are in better agreement with the calculated Exomol line list [START_REF] Polyansky | ExoMol molecular line lists. XIX: high-accuracy computed hot line lists for H2 18 O and H2 17 O[END_REF].

Figure 12

Line intensity comparison with Ref. [1]

It is interesting to compare the line intensities of Ref. [START_REF] Régalia | Water vapor line parameters from 6450 to 9400 cm -1[END_REF] against those obtained in this study.

This comparison can give an estimation of intensity precision of reported data set. Next pictures (Figure 14) show the comparisons of line intensities reported in our previous studies using water vapor spectra in natural abundance [START_REF] Régalia | Water vapor line parameters from 6450 to 9400 cm -1[END_REF] against the data obtained in this study for the two principal observed isotopologues (H2 16 O and H2 18 O). Note the line intensities are for the natural abundance of the isotopologues on the X-axis. In Ref. [START_REF] Régalia | Water vapor line parameters from 6450 to 9400 cm -1[END_REF] with water vapor spectra in natural abundance, we observed H2 18 O lines in the intensity range from 3×10 -27 to 3×10 -23 .

Left panel of Figure 14 shows that the two data sets are consistent, except for the intensity range from 5×10 -24 to 3×10 -23 , where there is the same disagreement as observed in Figure 12. On the right panel of Figure 14, the situation is slightly different, it concerns the H2 16 O isotopologue, and we can observe that the values of the ratio between intensities determined on the spectra in natural abundance and those obtained on the spectra enriched in 18 O are different depending the intensity range. Indeed, within the range between 1×10 -21 to 5×10 -20 cm/molec, the ratio is slightly higher than 1 while between 1×10 -22 to 1×10 -21 it is smaller than 1. This type of problem is not observed on the left panel for the H2 18 O isotopologue. It is certainly due to the experimental conditions of the spectra in this work mainly dedicated to the study of H2 18 O. The line intensities for H2 16 O were not determined for all lines in the best conditions, meaning in an absorption range between from 20 to 60 %, as we did it with the spectra recorded in natural abundance [START_REF] Régalia | Water vapor line parameters from 6450 to 9400 cm -1[END_REF]. With this isotopic abundance (Table 3), it is also more difficult to find H2 16 O isolated lines and the determination of line intensity parameters is consequently more delicate.

Figure 14

Conclusion

New absorption spectra of enriched by 18 O water vapor were recorded between 6400 and 9500 cm -1 at room temperature with a resolution of 0.01 cm -1 using the Connes'type FTS built in the GSMA laboratory. The absorption path length was from 67 cm up to 1001 m with a pressure varying from 2 to 13 torr. The H2 18 O enrichment reached 95%.

In the spectral region between 6525 and 8010 cm -1 , the spectra were analyzed and assigned. About 8100 absorption lines were detected in this region. 7993 of them were assigned to about 8647 transitions of six water isotopologues (H2 16 O, H2 17 O, H2 18 O, HD 16 O, HD 17 O, and HD 18 O). Only 98 weak lines (SRV < 1.4×10 -25 cm/molecule) left unassigned. The lines of more than 800 transitions of H2 18 O, HD 18 O, H2 17 O, and HD 17 O were observed for the first time. Assigned transitions allow us to determine 76 new and 12 corrected vibrationrotation energies of H2 18 O and HD 18 O molecules.

Obtained data can be used to improve and complete existed sets of empirical energy levels [START_REF] Tennyson | IUPAC critical evaluation of the rotational-vibrational spectra of water vapor. Part I. Energy levels and transition wavenumbers for H2 17 O and H2 18 O[END_REF][START_REF] Tennyson | IUPAC critical evaluation of the rotational-vibrational spectra of water vapor. Part II. Energy levels and transition wavenumbers for HD 16 O, HD 17 O, and HD 18 O[END_REF][START_REF] Mikhailenko | A spectroscopic database for water vapor between 5850 and 8340 cm -1[END_REF][START_REF] Tennyson | IUPAC critical evaluation of the rotational-vibrational spectra of water vapor. Part III: Energy levels and transition wavenumbers for H2 16 O[END_REF] and created line lists such as HITRAN [START_REF] Gordon | The HITRAN2016 molecular spectroscopic database[END_REF] and GEISA [START_REF] Jacquinet-Husson | The 2015 edition of the GEISA spectroscopic database[END_REF].

Table captions

Table 1. List of the origins of the H2 18 O transitions between 6525 and 8011 cm -1 in the GEISA2015 line list [START_REF] Jacquinet-Husson | The 2015 edition of the GEISA spectroscopic database[END_REF] Table 2. Experimental conditions of recorded spectra (Region 1) Table 3. Isotopic abundance in the 18 O enriched sample and origins of the reference lines Table 4. Number of assigned transitions for each water isotopologues Table 5. Band-by-band statistics of H2 18 O assigned transitions Table 6. New and corrected empirical energies of H2 18 O Table 7. General statistics of the comparison of observed line positions against calculated values using empirical energy values [START_REF] Tennyson | IUPAC critical evaluation of the rotational-vibrational spectra of water vapor. Part I. Energy levels and transition wavenumbers for H2 17 O and H2 18 O[END_REF][START_REF] Tennyson | IUPAC critical evaluation of the rotational-vibrational spectra of water vapor. Part II. Energy levels and transition wavenumbers for HD 16 O, HD 17 O, and HD 18 O[END_REF]

Figure captions

Figure 1. Overview of previously reported H2 18 O transitions from FTS (red stars) and CRDS (blue circles). Transitions with red stars were used in Refs. [START_REF] Tennyson | IUPAC critical evaluation of the rotational-vibrational spectra of water vapor. Part I. Energy levels and transition wavenumbers for H2 17 O and H2 18 O[END_REF][START_REF] Tennyson | IUPAC critical evaluation of the rotational-vibrational spectra of water vapor. Part II. Energy levels and transition wavenumbers for HD 16 O, HD 17 O, and HD 18 O[END_REF] for the energy level determination.

Figure 2. Overview of recorded spectra for Region 1 and a zoom of three spectra between 6750 and 7100 cm -1 in lower panel Figure 3. Influence of the normal and effective iris radius value on the (Obs-Calc) difference in single spectrum fitting; H2 16 O line, 6917.3648 cm -1 , 4.504×10 -23 cm/molec (296 K), L = 48 m Figure 4. Influence of the normal and effective iris radius value on the (Obs-Calc) difference in multi spectrum fitting; H2 18 O line, 7239.59215 cm -1 , 1.172×10 -22 cm/molec (296 K), L = 8 m Figure 5. H2 18 O transitions observed in this study (left panel). The firstly observed transitions are given in open triangles (right panel) Figure 6. Overview comparison of the literature HD 18 O transitions [START_REF] Mikhailenko | Absorption spectrum of deuterated water vapor enriched by 18 O between 6000 and 9200 cm -1[END_REF] (blue circles) against those obtained in this study (green stars) vapor spectra in natural abundance [START_REF] Régalia | Water vapor line parameters from 6450 to 9400 cm -1[END_REF] against the data obtained in this study. In X-axis, are reported the line intensities in the natural abundance for both H2 16 O and H2 18 Intensity, cm/molecule

S

Ref. [47] , cm/molecule H2 16 O 1875 6530 -7920 H2 18 O 4236 6527 -8011 H2 17 O 1136 6531 -7801 HD 16 O 116 6528 -7966 HD 18 O 1267 6526 -7990 HD 17 O 17 7105 -7390 ---------------------------------Vib J Ka Kc E Obs dE a) ---------------------------------002 [START_REF] Liu | Fourier-transform absorption spectroscopy of H2 18 O in the first hexade region[END_REF] ------------------------------------------------------------------Vib J Ka Kc E Obs dE a) ---------------------------------101 11 [START_REF] Liu | High sensitivity CW-CDRS of 18 O enriched water near 1.6 µm[END_REF] HD 17 O 0 17 a) Number of transitions calculated using energy sets [START_REF] Tennyson | IUPAC critical evaluation of the rotational-vibrational spectra of water vapor. Part I. Energy levels and transition wavenumbers for H2 17 O and H2 18 O[END_REF][START_REF] Tennyson | IUPAC critical evaluation of the rotational-vibrational spectra of water vapor. Part II. Energy levels and transition wavenumbers for HD 16 O, HD 17 O, and HD 18 O[END_REF][START_REF] Tennyson | IUPAC critical evaluation of the rotational-vibrational spectra of water vapor. Part III: Energy levels and transition wavenumbers for H2 16 O[END_REF] b) Number of transitions which cannot be calculated using energy sets [START_REF] Tennyson | IUPAC critical evaluation of the rotational-vibrational spectra of water vapor. Part I. Energy levels and transition wavenumbers for H2 17 O and H2 18 O[END_REF][START_REF] Tennyson | IUPAC critical evaluation of the rotational-vibrational spectra of water vapor. Part II. Energy levels and transition wavenumbers for HD 16 O, HD 17 O, and HD 18 O[END_REF][START_REF] Tennyson | IUPAC critical evaluation of the rotational-vibrational spectra of water vapor. Part III: Energy levels and transition wavenumbers for H2 16 O[END_REF] c) Excluding the 2ν1 8 1 7 -9 2 8 transition with a deviation of 0.1474 cm -1 d) Excluding the 2ν1+ν2 9 2 7 -8 2 6 transition with a deviation of 0.0887 cm -1

6 .

 6 O. Now we are able to assign 1267 transitions of ten vibrational bands. The general comparison of two transition sets is shown on Figure Line intensities on Figure 6 are given for 100%

Figure 6

 6 Figure 6

  O. The deviations d1 = |ν OBSν IUPAC | which are bigger than 0.015 cm -1 correspond to upper energy levels (120) 4 weak blended lines in our spectrum. So, reported here observed line positions of these two transitions are not accurate enough. The observed line positions of the last three energies are in very good agreement with CRDS observations[START_REF] Mikhailenko | The absorption spectrum of water in the 1.25 µm transparency window (7408 -7920 cm -1 )[END_REF][START_REF] Leshchishina | CRDS of water vapor at 0.1 Torr between 6886 and 7406 cm -1[END_REF][START_REF] Modelain | Combassisted cavity ring down spectroscopy of 17 O enriched water between 7443 and 7921 cm -1[END_REF][START_REF] Mikhailenko | Comb-assisted cavity ring down spectroscopy of 17 O enriched water between 6667 and 7443 cm -1[END_REF] for the (200) 8 8 1, (200) 8 1 7 and (101) 11 0 11 levels. The differences of the IUPAC values from

Figure 7 Figure 8

 78 Figure 7

Figures

  Figures highlight several spectral windows with problems of overestimated or, in the contrary, underestimated line intensities.

Figure 10

 10 shows examples of overestimated line intensities on the upper and middle panel and on the contrary, the line intensity is underestimated in the HITRAN2016 line list for the 2ν3 4 0 4 -3 1 3 transition in the lower panel. The 2ν3 band is not the only one affected by the intensity problems.

Figure 11 gives

 11 similar examples for the 2ν1, 2ν2+ν3 and ν1+ν3 bands.

Figure 10 Figure 11

 1011 Figure 10

Figure 7 .Figure 8 .Figure 9 .

 789 Figure 7. Comparison of observed spectrum (P=13 torr, L=88 m, blue line) against simulation(orange line) using the HITRAN2016 line list[START_REF] Gordon | The HITRAN2016 molecular spectroscopic database[END_REF] around 7266 cm -1 (upper panel) and 7526 cm -1 (lower panel), see text

Figure 10 .Figure 11 .

 1011 Figure 10. Comparison of observed spectrum (P=13 torr, L=88 m, blue line) against simulation (red line) using the HITRAN2016 line list [23] around 7683 cm -1 (upper panel), 7495 cm -1 (middle panel) and 7492 cm -1 (lower panel), see text

Figure 12 .Figure 13 .Figure 14 .

 121314 Figure 12. Comparison of H2 18 O observed line intensities against variational SP (Ref. [27],left panel) and Exomol (Ref.[START_REF] Polyansky | ExoMol molecular line lists. XIX: high-accuracy computed hot line lists for H2 18 O and H2 17 O[END_REF], right panel) line listsFigure 13. Ratio between variational SP [27] and Exomol[START_REF] Polyansky | ExoMol molecular line lists. XIX: high-accuracy computed hot line lists for H2 18 O and H2 17 O[END_REF] intensity values for H218 O

Figure 4

 4 Figure 4

Figure 9

 9 Figure 9

Figure 10

 10 Figure 10

Figure 11

 11 Figure 11

  -------------------a) dE = E Obs (TW) -E Obs (Ref.[START_REF] Tennyson | IUPAC critical evaluation of the rotational-vibrational spectra of water vapor. Part I. Energy levels and transition wavenumbers for H2 17 O and H2 18 O[END_REF]) b) dE = E Obs (TW) -E Obs (Ref.[START_REF] Mikhailenko | The absorption spectrum of water in the 1.25 µm transparency window (7408 -7920 cm -1 )[END_REF])

  O species.

	1E-19
	1E-20
	1E-21
	1E-22
	1E-23
	1E-24
	1E-25
	1E-26
	1E-27
	1E-28
	6600	6800	7000	7200 Wavenumber, cm 7400	-1	7600	7800	8000

Table 2

 2

	Spectrum	Recording range	Cell length (cm)	Pressure (Torr)
	1	6450 -8100	8826.2	12.86
	2	6450 -8100	4826.2	12.85
	3	6450 -8100	826.2	12.85
	4	6450 -8100	826.2	5.41
	5	6450 -8100	4826.2	5.42
	6	6450 -8100	8826.2	5.42
	7	6450 -8100	8826.2	2.03
	8	6450 -8100	4826.2	2.03
	9	6450 -8100	826.2	2.03

Table 3

 3

			Abundance (%)
	Molecule	Reference lines	Sample enriched	Natural
			by 18 O
	H2 16 O	Régalia et al. [1]	4.05	99.73171
	H2 18 O		95.0106	0.199983
	H2 17 O	Régalia et al. [1]	0.587	0.0371884
	HD 16 O	Hitran2016 [23]	0.0167	0.0310693
	HD 18 O Mikhailenko et al. [37]	0.32	6.23003×10 -5
	HD 17 O Mikhailenko et al. [37]	0.0157	1.15853×10 -5

Table 4

 4

	Molecule	Number of transitions (NT)	Range, cm -1

Table 5

 5

	Band	NT	J Ka	Region, cm -1
	ν1+3ν2-ν2 ν1+2ν2	42 485	7 6 14 9	6527 -7206 6529 -7936
	2ν1	861	16 10	6530 -7917
	4ν2	59	14 7	6533 -7425
	2ν2+ν3 ν1+ν3	710 993	15 9 19 11	6533 -7804 6533 -7950
	3ν2+ν3-ν2	150	10 7	6547 -7311
	2ν3	657	14 10	6558 -7985
	2ν1+ν2-ν2 ν1+ν2+ν3-ν2 ν2+2ν3-ν2	72 154 16	10 4 12 5 7 5	6792 -7396 6803 -7577 7288 -7598
	5ν2 ν1+3ν2	18 11	11 3 12 3	7338 -7972 7912 -8011
	3ν2+ν3	8	8 3	7918 -8010

Table 6

 6

Table 7

 7

	Molec	NCT a)	NAT b)	Maximum deviation, 10 -3 cm -1		dmax, 10 -3 cm -	rmsd, 10 -3
	ule			d1 ≤ 1	1 < d1 ≤	5 < d1 ≤	d1 >	1	cm -1
					5	10	10
	H2 16 O	1875	0	1128	668	64	15	20.0	2.26
	H2 18 O	4107	128	2186	1717	158	46	43.5	3.12
	H2 17 O	988	148	496	419	55	18	147.4	2.95 c)
	HD 16 O	116	0	55	56	5		9.0	2.43
	HD 18 O	1058	209	466	474	83	35	88.7	5.23 d)

6 -8 3

at 7413.5221 cm -1 instead of 7431.5260 cm -1[START_REF] Toth | Line list of water vapour parameters from 500 to 8000 cm -1[END_REF]; ν1+ν3 11 4 8 -10 4 7 at 7420.4995

Acknowledgements

The authors would like to thank Prof. O. Polyansky and Dr. A. Kyuberis for providing their data for the comparisons. This work was partly done in the frame of the International Associated Laboratory SAMIA, supported by CNRS (France) and RFBR (Russia). SM activity was supported in the frame of the Russian Science Foundation, grant no. 18-11-00024.