Intensities and self-broadening coefficients of the strongest water vapour lines in the 2.7 and 6.25μm absorption bands self-broadening coefficients of the strongest water vapour lines in the 2.7 and

Intensities and self-broadening coef ﬁ cients are presented for about 460 of the strongest water vapour lines in the spectral regions 1400 – 1840 cm (cid:1) 1 and 3440 – 3970 cm (cid:1) 1 at room temperature, obtained from rather unique measurements using a 5-mm-path-length cell. The retrieved spectral line parameters are compared with those in the HITRAN database ver. 2008 and 2012 and with recent ab-initio calculations. Both the retrieved intensities and half-widths are on average in reasonable agreement with those in HITRAN-2012. Maximum systematic differences do not exceed 4% for intensities (1600 cm (cid:1) 1 band) and 7% for self-broadening coef ﬁ cients (3600 cm (cid:1) 1 band). For many lines however signi ﬁ cant disagreements were detected with the HITRAN-2012 data, exceeding the average uncer- tainty of the retrieval. In addition, water vapour line parameters for 5300 cm (cid:1) 1 (1.9 μ m) band reported by us in 2005 were also compared with HITRAN-2012, and show average differences of 4 – 5% for both intensities and half-widths.


Introduction
The HITRAN database [1] of spectral line parameters is an important resource for many atmospheric and spectroscopic applications. The latest version contains parameters of about 4.4 million spectral lines, and the database is regularly updated with line parameters derived from new measurements and theoretical calculations. Among different gases, water vapour plays one of the most important roles in the Earth's energy balance. Intensities and pressure broadening coefficients of water vapour lines are basic physical parameters required to calculate the Earth's radiation budget and also to interpret remotelysensed data.
There is also another related aspect for robust understanding of line parameters. During investigations of water vapour continuum absorption within three near-IR water vapour absorption bands [2][3][4] the authors identified a requirement for improved knowledge of the intensities and self-broadening coefficients of the strongest water vapour lines within these bands, to achieve a more confident retrieval of the continuum strength. As a result, at first, the parameters of about 450 of the strongest water vapour lines (intensity SZ2 Â 10 À 23 cm molec À 1 ) in the Laboratory (MSF RAL). Comparison of the retrieved in [5,6] self-broadening coefficients with those in the HITRAN-2004 and2008 [7,8] databases revealed strong (up to 20%) systematic differences for the group of "medium-intensity" lines (from 1 Â 10 À 21 to ca. 6 Â 10 À 21 cm molec À 1 ) with strong evidence in favour of the new data.
The problem with experimental determination of the self-broadening coefficients for the strongest spectral lines lies in saturation of their absorption even at small (a few cm) path-lengths. "Saturation" is considered here as optical depths exceeding 4-5, at which the output signal in FTS measurements becomes comparable with the noise level. Reducing the water vapour pressure can help if one is interested only in determining intensities of these strong lines, as intensity does not depend on line shape. However, it will not help in deriving their self-broadening coefficients, because at small (less than a few millibars) pressures the line shape of water vapour lines in near-IR region at room-temperatures approaches Gaussian with Doppler halfwidth. This would make retrieval of the self-broadening coefficient very uncertain. That is why a very short path length is required in order to keep the pressure not less than a few millibars and still avoid saturation in absorption of these strong water vapour lines.
In the measurements within the 1.9 μm band [5] an absorption cell with a path length of 29.13 cm was used. In the present paper we extend the spectral region to the much stronger water vapour absorption bands 2.7 and 6.25 μm (3600 and 1600 cm À 1 respectively). Only by reducing the path length to around 5 mm is it possible to reliably measure these lines.

Experimental setup
Because of the high absorption cross-section of water vapour lines within the bands under investigation, a special new single-pass cell was constructed at the Rutherford-Appleton Laboratory for these measurements. The cell had a 4.78 mm path length (measured with a micrometer) and was constructed of electropolished stainless steel with Parylene coated KBr windows, attached with low vapour pressure epoxy resin. A 1 litre spherical reservoir volume, attached to the cell, was used to increase the volume-to-surface ratio and stabilise the water vapour pressure (see Fig. 1).
The spectra were recorded using an IFS120 which has been upgraded to IFS125 specification (electronics, scan motor and optical layout), but retains the original analogue detectors. The unapodized spectral resolution was 0.002 cm À 1 (resolution is defined here as 0.9/maximumoptical-path-difference). The Bruker (FTS) was configured with a Globar source. Mertz phase correction [9] was applied to the measured interferograms. An optical filter was used for 6.25 μm band to limit the optical bandwidth to the spectral range of the measurement.
The cell was filled with water vapour to approximately the desired pressure and allowed to reach equilibrium over a period of several hours. The pressure was measured using 2 MKS Baratrons type 670 (1.3 and 13 mbar full scale) and the temperature measured using 4 PRTs attached to the cell. Measurement of spectra commenced when the pressure had stabilised which typically took 12 h in the mid-IR.
The measurements reported here were performed at a temperature about 294 K and at two pure water vapour pressures for the each band, ranging from 5.9 to 13.0 mbar (see the Table 1). Samples of water vapour were prepared using a clean stainless steel vacuum line from distilled liquid water (Analar grade, BDH Chemicals), which had previously been purified to remove dissolved air using at least three repeat 200 K freeze-pump-thaw cycles. During the measurements, pressure and temperature were recorded at 1-s intervals.
Background spectra with an evacuated cell were recorded before and after each filling of the cell. Prior to taking the background spectrum, high-resolution test measurements were performed to check that water vapour had been removed from the gas cell. In all cases, it was ascertained that the intensities of the strongest water vapour lines were reduced to the peak value of the spectral noise in the corresponding spectral region. Taking the ratio of the sample and averaged background spectra minimised errors in the transmittance or absorbance spectra arising from changes in baseline signal level, for example due to drifts in the intensity of the source. Typical background and sample spectra for two water vapour absorption bands investigated in this work are shown in Fig. 2.
The signal-to-noise ratio in each transmittance spectra exceeded 1000:1 across the entire spectral range considered here, giving an information-to-noise ratio in excess of 100:1 for absorbances between 0.2 and 3.5. For

Line fitting
The fitting procedure was similar to that described in detail in [5]. The observed laboratory transmittance spectra were compared with calculated spectra, generated for the measured laboratory conditions, using the HITRAN-2012 [1] water vapour line parameters and the line-by-line code of Mitsel et al. [10]. Information about the optical configuration of the FTS was used to calculate an instrument line shape (ILS) and convolute it with the calculated molecular spectrum. The initial ILS was determined from the ideal 'sinc'-function which was convolved with a boxcar field-of-view (FOV) function to account for the finite FOV of the spectrometer (i.e. the effect of off-axis rays passing through the aperture) [11]. This leads to the broadening of the final ILS function and a shift to lower wavenumber by an amount equal to the half-width of the FOV function.
During the fitting procedure only those parts of the spectrum with an optical depth of less than 4.0 were used, to minimise the impact of saturated spectral intervals. Unapodized FTS spectra were used for the fitting in this work. The undamped ringing (sidelobes) inherent in unapodized ILS functions necessitates the use of far ILS wings to convolve with the simulated spectrum which increases the time taken by the fitting procedure. The optimal distance at which the ILS can be truncated without significant loss in the accuracy of retrieved line parameters has been derived and checked carefully by fitting to synthetic spectra.
We used the Levenberg-Marquardt least squares algorithm to fit the parameters for about 460 of the strongest lines (S Z2 Â 10 À 21 cm molec À 1 ), 200 and 260 in the spectral regions 1400-1840 and 3450-3980 cm À 1 respectively. Four parameters: line centre position, intensity, selfbroadening halfwidth γ self and baseline, were fitted for each spectral line using the Voigt profile in the first stage (with the Doppler halfwidth calculated for each line). Then a fifth, the narrowing parameter β, was added to the fitting procedure to account for the collisional narrowing effect (Dicke-effect). The Rautian-Sobelman (R-S) profile describing a strong collision model [12] was used in a second stage of the fitting procedure. The average value of the pressure independent dimensionless collisional narrowing parameter β/γ self was found to be about 0.3 (with standard deviation 0.35) and 0.17 (standard deviation 0. 19) for the 1600 and 3600 cm À 1 band respectively. It weakly affected the retrieved line intensities and self-broadening coefficients of most lines. Not accounting for the collisional narrowing (i.e., fitting with the Voigt profile) led, on average, to underestimation of the fitted line intensities and self-broadening widths by about 0.5-1.5% and 2-4% respectively. This work was performed prior to the IUPAC recommendation [13] to use the Hartmann-Tran (H-T) profile [14] for atmospheric applications, and even before papers on this profile were published. It is known however [15] that in the case of dipole-dipole intermolecular interaction, which is dominant for H 2 O self-broadening, the relaxation constants should not depend on speed. This should significantly reduce the impact of speeddependence effect on water vapour lines. Indeed, according to Fig. 1 in [13] using just the Nelkin-Ghatak profile [16] (which accounts for collisional narrowing and is essentially equivalent to the R-S profile) is enough to reduce residuals by a factor of 5 compared to the Voigt profile and to bring deviations from the experimental profile to less than 0.2%. Using the more sophisticated H-T profile, which accounts also for speed-dependence of the relaxation rates and its correlation with velocity change due to collisions, reduces the deviations to below the 0.1% level.
Line-mixing has also rather little effect for H 2 O lines at such low pressures. It may slightly affect only particular pairs of water vapour lines, changing derived parameters by 2-4% [17]. Thus, one can expect that for majority of H 2 O lines the difference in retrieved intensities and selfbroadening coefficients between using the R-S and any more sophisticated line profile should be less than 1%. This is several times less than total experimental uncertainty of our data and thus can be neglected in this work.
The first guesses for each of the line parameters in the fitting procedure were taken from the HITRAN-2008 database. Spectral lines were fitted simultaneously in sets of 5-10 lines. The fitting procedure for the whole spectral region was repeated several times until the total residual between two consecutive iterations became negligible. Every line was fitted within 10γ v spectral interval from the line centre, where γ v is an average Voigt halfwidth at half-maximum of the spectral line for the measurement (γ v $ 0.006 cm -1 ). The impact of unfitted spectral lines (S o2 Â 10 À 21 cm molec À 1 ) was taken into account using parameters from HITRAN-2012.
The final parameters were defined as an average between values derived at two different pressures (see Table 1). Half of the difference between these values was included in the error estimation for the final parameter for every line. The retrieval error for each parameter also includes fitting error (produced by 'DRNLIN' and 'DRSTAT' MS Fortran Library) and uncertainty in the measured water vapour pressure. The latter was estimated in this work as E2%.
The HITRAN-2012-format files with the line parameters converted to the temperature T 2 ¼296 K is attached as Supplementary material. The parameters were converted according to the usual relations: where E″ is the lower state energy of the transition in cm À 1 ; n is the line width temperature dependence, T 1 is the temperature at which the experimental data were obtained. The S(T 1 ) and S(T 2 ) are both in cm molec À 1 here. Information about the intensity and self-broadening errors from this work has also been included in the HITRANformat file using the HITRAN uncertainty indices.

Fig. 3 compares intensities (a) and self-broadening coefficients (b) of the water vapour lines derived from
fitting to the experimental data in 1400-1840 cm À 1 spectral region (δ-band) with parameters from HITRAN-2008 [8], 2012 [1] and with the recent results of ab initio calculations by Polyansky et al. [18] (scaled by the isotopologue abundance). These calculations are based on the variational calculations using the DVR3D program suite [19]. As an input for this program the accurate dipole moment surface (DMS) and potential energy surface (PES) of water monomer is necessary. High accuracy ab initio calculation of the DMS is presented in [20], while semiempirical PES of high accuracy is given in [21]. The details of the calculation of the linelist with the line centres and line intensities used in this work will be presented in a forthcoming paper [18]. The line intensities calculated using Lody et al.'s DMS [20] have been compared with the experimental measurements of intensities of sub-percent accuracy made by Lisak et al. [22] in the spectral region of 7200 cm À 1 , and very recent comparison with the intensities [18] in the region of 3600 cm À 1 of water fundamental bands has been made by Pogany et al. [23]. In both cases the discrepancy within experimental error has been demonstrated: less than 1% for the data around 7200 cm À 1 [22] and about 2% for the fundamental bands in [23]. These comparisons suggest that we might expect the accuracy of the intensity calculations of water absorption lines [20] to be within about 2%. The preliminary results of Polyansky et al. [18] calculations for intensities of some strongest H 2 O lines are tabulated in the Supplementary file.
Comparison shows that intensities of the strongest H 2 O lines in HITRAN-2012 [1], originating from semi-empirical calculations by Coudert et al. [27,28], appear systematically underestimated (by 3.4%) compared to the result of our fitting. The situation is a little better than for the HITRAN-2008 (4.2% deviation). This deviation lies slightly beyond the error-bars of our experimental data. However, comparison with the calculations of Polyansky et al. [18] demonstrates a much better agreement with our values of intensities with systematic deviation of only 2.0%.
By contrast with the intensities, self-broadening coefficients (Fig. 3b) of the strongest (above 10 À 19 cm/molec) lines in HITRAN-2012 demonstrate markedly wider disagreement with our experimental values than, on average, those in the older (HITRAN-2008) version, reaching 15-20% for some lines. Analysis of the HITRAN reference indices presented in Fig. 3b, points to the reference index '72' as the source of self-broadening parameters in HITRAN-2012 having the largest deviation from our experimental data. The reference index '72' corresponds to the high-quality FTS measurements by Birk and Wagner [31]. It corresponds either to the values directly measured by Birk and Wagner [31] (for the lines with intensity less than $ 5 Á 10 À 21 cm/molec) 1   vibrational dependence in this region). Unfortunately it appears that in a few cases the data was not transferred from Birk and Wagner [31] paper to HITRAN correctly (Iouli Gordon, pers. comm.). For instance, self-broadening of the 1684.835 cm À 1 line in HITRAN ((010)-(000) (4,1,4)-(3,0,3) in the notation (V')-(V") (J',Ka',Kc')-(J",Ka",Kc"'); see also Fig. 3), was supposed to be taken from the corresponding measurement [31] of the line with same rotational quanta, but in a hot band ((020)-(010) (4,1,4)-(3,0,3)). However, the value for both transitions in HITRAN appears to be 0.416 cm À 1 /atm, while Table 5 of Ref. [31] gives 0.5167 cm À 1 /atm which is in excellent accord with the value of 0.511 cm À 1 /atm that we measured. Fig. 4 shows a few examples of comparison of experimental and simulated spectra for several lines having significant deviation from the HITRAN-2012 parameters in this band and highlighted in Fig. 3. It can be seen that fitting the procedure reproduces the experimental spectrum rather well. Visual verification of the fitting accuracy was performed for all lines for which parameters indicate a significant deviation from HITRAN-2012.  [30], averaged as a function of J" and asymptotic value of γ self (J" ¼50) ¼ 0.0400 cm À 1 atm À 1 (see [33] for details).
(ν-polyad In previous papers [5,6] we reported new line parameters in (ν þδ polyad) derived using a short-path (29.  [20]. These values are also in good agreement with the result of Polyansky et al. calculations [18], which is not surprising, taking into account that both calculations utilised the same dipole moment surface. It is interesting to note that our experimental data have, on average, a zero systematic deviation from intensity values in the HITRAN-2001 update (v. 11) [35] (see Fig. 8a and also [5]), where the main set of line intensities in this polyad was provided from the experimental data of Toth. It is important to mention that in [5] this fact was verified also by comparison with intensities derived from fitting to independently measured air-broadened water vapour spectrum. This makes us suggest that ab-initio calculations [18,20] may still systematically overestimate the intensities of the strongest lines in this spectral region by ca. 3-4%. Additional independent measurements are required to investigate this further.
The strong sawtooth-like deviation in self-broadening coefficients from our experimental data, that was reported earlier [5,6] for the HITRAN-2004 and 2008 versions, was corrected in HITRAN-2012 (Fig. 8b). However, the mean value of the remaining systematic deviation and the spread is still quite large, and the self-broadening coefficients of many lines in this spectral region require correction (see Figs. 8b and 9 Fig. 6. Comparison of the measured spectra with calculated ones using line parameters from HITRAN-2012 [1] and parameters derived in this work by fitting to the new experimental data. Four lines highlighted in Fig. 5a are shown. The measured spectra were obtained in pure water vapour at 13 mbar, path length 4.78 mm and at a temperature of 294.3 K.

Conclusion
We have presented intensities and self-broadening coefficients of about 460 of the strongest water vapour lines in the spectral regions 1400-1840 cm À 1 and 3440-3970 cm À 1 at room temperature, obtained from rather unique FTS measurements using a 5-mm-path-length cell, which avoids saturation of these strong lines and retains  Fig. 7. A similar comparison as in Fig. 6, but for lines highlighted in Fig. 5b as those having significant deviations from HITRAN-2012 in terms of the selfbroadening parameter.
information on the self-broadening. The retrieved spectral line parameters are compared with those in the HITRAN database ver. 2008 and 2012 and with recent ab-initio calculations. Both the retrieved intensities and half-widths are, on average, in reasonable agreement with those in HITRAN-2012. Maximum systematic differences do not exceed 4% for intensities (1600 cm À 1 band) and 7% for self-broadening coefficients (3600 cm À 1 band). For many lines, however, significant disagreements were detected with the HITRAN-2012 data, markedly exceeding the average uncertainty of the retrieval (on average 3% for line intensities and 5% for self-broadening coefficients of the strongest lines in the two investigated bands).
In addition, our earlier reported water vapour line parameters for 5300 cm À 1 (1.9 μm) band were also compared with those in HITRAN-2012. Again, although the systematic deviation lies within 4-5%, still, for many line parameters, especially for the self-broadening coefficients, deviations exceed the uncertainty in our experimental data. Systematic disagreement by 3-4% with the recent ab initio calculations [18,20] for line intensities in this spectral region indicates the need for independent experimental investigation. Table 2 [5] and Ptashnik and Smith [6] from fitting to experimental data in the spectral region 5040-5580 cm À 1 (ν þδ polyad), to corresponding parameters in HITRAN-2001 [35], HITRAN-2004 [7], HITRAN-2012 [1] and Polyansky et al. ab initio calculations [18]. Numbers in parentheses are the mean values and standard deviations. For one set of data the uncertainty in the retrieved parameters are shown by error-bars. The circled datapoints correspond to absorption lines shown in Fig. 9 with wavenumbers (cm À 1 ) stated nearby. The 'RI' refers to the Reference Indices used in HITRAN for particular sets of line parameters as following: 3 -Toth [25]; 18 -Toth [26]; 33 -Lodi et al. [20]; 50smoothed values from Toth [25]; 62 -Toth [34]; 66 -Gamache and Hartmann [27]; 71 -Polynomial fit of the values from [30], averaged as a function of J 0 and asymptotic value of γ self (J 0 ¼50) ¼ 0.0400 cm À 1 atm À 1 (see [33] for details); 73 - [6]. by more than the error in the derived parameters. The full list of the experimentally derived parameters as compared to the HITRAN-2012 is given in the Supplementary file 'Suppl_Tables'. This file also contains preliminary values of ab initio intensities from Polyansky et al. [18] shown in this work. In two additional supplementary files we also provide the same parameters (derived using both Voigt and Rautian-Sobelman line profile) in the HITRAN format.  Fig. 9. Comparison of the measured spectra with calculated ones using line parameters from HITRAN-2008, 2012 and parameters derived by fitting to experimental data [5,6] in the spectral region 5040-5580 cm À 1 (ν þ δ polyad). Lines highlighted in Fig. 8 are shown. The measured spectra were obtained in pure water vapour at 20 mbar, path length 29.13 cm and at a temperature of 298.8 K.

Table 2
Intensities S fit and self-broadening coefficients γ o fit of the strongest H 2 O lines n within two absorption bands in the 1500-1830 and 3447-3953 cm À 1 spectral regions, derived in this work by fitting Voigt profile to experimental FTS spectra. All parameters correspond to the temperature of 296 K. Also shown are estimated relative errors δ(%) and ratios of the derived values to those from HITRAN-2012 [1]. Quantum numbers (upper state vibrational index V 0 , and rotational indices J 0 , Ka 0 , Kc 0 , J 00 , Ka 00 , Kc 00 ) and line positions are taken from HITRAN-2012. The lower state vibrational index V 00 is 0 000 0 for all lines.