An experimental water line list at 1950 K in the 6250 -- 6670 \cm\ region

An absorption spectrum of H$_2$$^{16}$O at 1950 K is recorded in a premixed methane/air flat flame using a cavity-enhanced optical frequency comb-based Fourier transform spectrometer. 2417 absorption lines are identified in the 6250 -- 6670 cm region with an accuracy of about 0.01 cm. Absolute line intensities are retrieved using temperature and concentration values obtained by tunable diode laser absorption spectroscopy. Line assignments are made using a combination of empirically known energy levels and predictions from the new POKAZATEL variational line list. 2030 of the observed lines are assigned to 2937 transitions, once blends are taken into account. 126 new energy levels of H$_2$$^{16}$O are identified. The assigned transitions belong to 136 bands and span rotational states up to $J=27$.


Introduction
Water is ubiquitous and its spectrum is important for a whole range of terrestrial and astronomical applications. Serious attempts have been made to characterize the spectrum of hot water both experimentally by observation of spectra [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17] and theoretically by the computation of extensive line lists [18,19,20,21,22,23,24]. These line lists are used to inform databases concerned with models of hot bodies such as HITEMP [25] and ExoMol [26,27]. A comprehensive assessment of water spectroscopy was undertaken by an IUPAC task group [28,29] whose work is currently being updated [30].
The ubiquity of water means that understanding its spectrum at all wavelengths and temperatures is always important. The spectrum of hot water is of particular interest in regions were absorption by room temperature water is weak. The present work concentrates on one such region as it probes the spectrum of hot water in the conventional telecom window (1.53 -1.565 µm) as well as the astronomers H-band (1.5 -1.8 µm). These regions are useful for remote sensing of hot water spectra due to the reduced atmospheric absorption. Previous high-temperature water spectra analyzed for this region [31,32,33,34,35,10,12,13] were recorded in emission in flames at atmospheric pressure at moderate spectral resolution; in addition, due to the lack of thermal stability, these spectra did not provide usable information on the line intensities. This paper presents a high temperature water absorption spectrum measured at Umeå University. The spectrum is measured in a premixed methane/air flat flame at atmospheric pressure using a cavity-enhanced optical frequency comb-based Fourier transform spectrometer (FTS) [36]. The combination of an FTS with a frequency comb allows the measurement of broadband and high resolution molecular spectra in short acquisition times and without visible influence of the instrumental line shape [37,38], while the cavity provides high sensitivity to absorption [39]. The ability to measure the present spectrum simultaneously over a broad bandwidth reduces systematic errors and the influence of fluctuations of the environmental conditions. The spectrum is recorded at high resolution (0.033 cm −1 ) in the near-infrared 6250 -6670 cm −1 region, and line positions are identified with an accuracy of 0.01 cm −1 . Knowledge of the temperature and water concentration, which have previously been measured for that specific burner by Qu et al. [40] using tunable diode laser absorption spectroscopy, as well as the thermally stable conditions, allow absolute line intensities to be determined.
The measured absorption spectrum is compared to the newly computed POKAZATEL hot line list [24] augmented by the inclusion of empirical energy levels [28]. This comparison allows us to assess both the contents of the measured spectrum and the reliability of the computed line list. The POKAZATEL line list is then used to make assignments to the spectrum resulting in a significant number of newly identified transitions and energy levels.
The following two sections of the paper describe the experimental set-up and results. Section 4 presents the experimental water line list. Comparisons with the computed line lists, particularly the most recent one [24], are given in section 5, followed by conclusions in section 6.

Experimental setup
The experimental setup is described in detail in references [36,41] and is therefore only briefly summarized here. The spectrometer consists of an Er:fiber femtosecond laser with a repetition rate of 250 MHz (0.0083 cm −1 ), a 60 cm long enhancement cavity with a finesse of around 150, and a fastscanning Fourier transform spectrometer (FTS). The comb is locked to the cavity using the two-point Pound-Drever-Hall method [39,42] with locking points at 6330 and 6450 cm −1 . The cavity is open to air, and a flat flame burner [43] is placed in its center. The burner is operated on premixed methane/air at stoichiometric ratio with a total flow rate of 10 L/min. The comb beam probes the line of sight in the flame (flame diameter of 3.8 cm) at atmospheric pressure and at a height above the burner (HAB) of 2.5 mm. At this HAB the temperature and species are rather homogeneously distributed along the line of sight [40,43], the average flame temperature is 1950 ± 50 K, the average water concentration is 17 ± 1% (both characterized using tunable diode laser absorption spectroscopy [40]), and the average hydroxide (OH) concentration is 0.28% [41].
The light transmitted through the cavity is coupled into an optical fiber 4 connected to the input of a fast-scanning FTS with an auto-balancing detector that acquires a spectrum with 0.033 cm −1 resolution in 0.4 s. The optical path difference is calibrated using a stabilized HeNe laser whose beam is co- Thus we estimate the frequency accuracy of the spectrum is 0.01 cm −1 . The high-temperature spectrum is averaged 20 times and normalized to a background spectrum measured when the flame is off. The baseline is additionally corrected for slowly varying etalons fringes.
We note that the influence of broadband flame emission can be neglected since the probablity of emission into the cavity mode is low and the cavity thus acts as an effective filter. Moreover, the collimator for coupling the cavity transmitted light into the fiber does not face the flame and is placed few tens of cm away from the flame, where the intensity of emission is already very low.

Cavity-enhanced absorption spectrum
The normalized transmission spectrum measured in the flame is shown in Fig. 1(a). To extract the absorption coefficient from this spectrum, we use the model for the transmission, I T , given by Foltynowicz et al. [42] where L is the interaction length between the light and the sample (i.e. the flame diameter), r is the frequency-dependent intensity reflection coefficient of the cavity mirrors, determined experimentally by cavity ringdown, α and φ are the molecular absorption and dispersion coefficients, respectively, and ϕ is the round-trip phase shift in the cavity. The round-trip intracavity phase shift is equal to a multiple of 2π for comb lines locked to the centers of the corresponding cavity modes. Because of the intracavity dispersion, caused by the cavity mirror coatings as well as the gas sample inside the cavity, the cavity modes are not equally spaced and only the comb lines around the locking points are exactly on resonance with their corresponding cavity modes [42]. However, because of the low cavity finesse, the relative comb-cavity offset is small in the entire spectral range of the comb, and the intracavity phase shift can be set to 2π, or zero. To extract the absorption coefficient from Eq. (1) we also neglect the molecular dispersion, since then the equation can be solved analytically. This approximation gives correct values for on-resonance absorption coefficients, since molecular dispersion is equal to zero at these frequencies.
The absorption spectrum obtained using the analytical solution to Eq.
(1) with molecular and cavity dispersion put to zero is plotted in Fig. 1 The noise on the baseline is 5 × 10 −7 cm −1 , which translates into a signal- locking points [42].

Experimental water line list
The center frequencies of absorption lines are found by taking the first derivative of the absorption spectrum [ Fig. 1 The experimental line intensities, S, are calculated from the value of absorption α max corresponding to each center frequency, using where χ max is the peak (on-resonance) value of the Voigt profile (in cm), and n T is water density at the temperature T (equal to 6.4×10 17 molecule/cm 3 for T = 1950 K and [H 2 O]=17%). Since no data exists for the pressure broadening parameter of water at these temperatures, we assume a Lorentzian half width of 0.027 cm −1 for all lines, as it matches relatively well to the data.
The Doppler half width varies from 0.0237 to 0.0253 cm −1 across the spectrum. The experimental line list contains 2417 lines; it is plotted in Fig. 2 and given in the supplementary information. The lowest line intensity that can be identified is 10 −25 cm/molecule, limited by the SNR in the spectrum.
The uncertainty in the intensity is 6% for the strongest lines, limited mainly by the uncertainty in the water concentration, and increases for weaker lines because of the lower SNR.
To illustrate the accuracy of the experimental line list, Fig. 3 The amplitude of the residual increases for higher wavenumbers since the comb-cavity offset increases away from the locking points.

Line assignment
The spectral analysis of the experimental line list was performed using the recently computed POKAZATEL hot line list [24] with energies replaced by empirical energy levels [28]. These empirical levels come from the recent IUPAC-sponsored study of water spectra [29] in which the MARVEL (measured active vibration-rotation energy levels) [45,46]  The second step in the spectral analysis was assignment of the remaining stronger lines that were not trivially using the POKAZATEL line list.
The trivially-assigned lines were also considered to be unassigned during this second step if their calculated intensity was less than half of the measured one. We only considered stronger theoretical lines with calculated intensities higher than 10 −23 cm/molecule. We concentrated on identifying those transi-  of 0.05 cm −1 ; these lines model essentially the whole intensity of this feature.
Single MARVEL assignment means that any other nearby lines are at least about an order-of-magnitude weaker.
The calculated line list contains many more weak lines than the experimental line list. These weak lines overlap with more intense water lines and therefore cannot be identified from the experimental spectrum. However, the contribution of these weak lines does not explain many apparent line strength discrepancies between the two line lists. The task of predicting line intensities for water using ab initio procedures is under constant review [48] and work is currently in progress at UCL to further improve the water dipole surface. Progress on this will be reported elsewhere.
A full list of the experimental lines with assignments are given in the supplementary data. This list specifies whether the line was trivially assigned using MARVEL or is associated with a new energy level. We note that the short spectral range and density of lines meant that these new energy levels 13 are not generally confirmed by combination differences.
The spectrum contains transitions from 136 bands, of which 45 contain only a single transition. Table 1 shows a summary of the main bands observed in this spectrum. Only about 20% of the observed lines involve transitions from the vibrational ground state with most corresponding to hot bands.
Transitions involve a large number of rotational states with J up to 27. Table 2 presents our newly determined energy levels. Differences between these and the values predicted by the POKAZATEL line list are also given.
The small value of these differences and their smooth behavior within a given vibrational state lends confidence to our new assignments. Note that these energy levels are derived from measurements made at atmosheric pressure and therefore will include small contributions due to the pressure shift. can be compated with 2937 here. This means that more than 70% of the line assignments given here are actually new.

Conclusion
A near-infrared absorption spectrum of water recorded in a flame at 1950 K using cavity-enhanced optical frequency comb-based Fourier transform spectrometer is shown to be a rich source of information on water transitions. About 85% of the lines observed in the spectral region 6250 -6670