D Mondelain
email: didier.mondelain@univ-grenoble-alpes.fr

S Vasilchenko

S Kassi

A Campargue

The water vapor foreign-continuum in the 1.6 µm window by CRDS at room temperature

Keywords: Water vapor, foreign-continuum, MT_CKD model, CRDS, transparency window, atmosphere

Water vapour foreign-continuum absorption cross-sections, CF, are measured for the first time at room temperature in the 1.6 µm transparency window, of importance for atmospheric applications. The measurements are performed by cavity ring down spectroscopy (CRDS) at 15 selected spectral data points. These data, covering the 5700-6640 cm -1 spectral range, are derived from the variation of the absorption signal during pressure ramps of humidified air up to 1 atm with a typical 1% humidity rate. The foreign-continuum absorption was obtained as the excess of the measured loss rate compared to the sum of the loss rate measured with dry air, the local water monomer contribution and the self-continuum absorption. CF values were derived from the linear dependence of the foreign-continuum absorption with the product of the partial pressures of water vapour and air. The semi-empirical MT_CKD CF values are found significantly underestimated in the centre of the window. The temperature dependence is discussed using high temperature measurements available in the literature.

Introduction

Water vapour is known to strongly absorb the infrared radiations in the Earth's atmosphere and thus to play a key role in its radiative budget [START_REF] Cubasch | Introduction[END_REF]. In addition to the usual absorption by water rovibrational lines, water vapour is responsible for an absorption slowly varying with wavenumber, the so-called water vapour continuum. Paynter and Ramaswamy studied the impact of this continuum in the atmospheric radiative transfer using their own empirical continuum model (BPS continuum) [START_REF] Paynter | Variations in water vapor continuum radiative transfer with atmospheric conditions[END_REF] and the semi-empirical MT_CKD model [START_REF] Clough | Line shape and the water vapor continuum[END_REF][START_REF] Mlawer | Development and recent evaluation of the MT_CKD model of continuum absorption[END_REF]. These models exhibit differences which can be particularly important in the mid-and shortwave IR regions leading to significant changes (up to 1 Wm -2 ) of the atmospheric absorption. It is thus important to produce accurate experimental absorption cross-sections to test and validate these empirical models, in particular in the transparency windows where the relative impact of the continuum is the largest. Since now one decade, large experimental efforts have been performed to complete the pioneer works of Burch [START_REF] Burch | Continuum absorption by H2O[END_REF][START_REF] Burch | Continuum absorption by H2O in the 700 -1200 cm -1 and[END_REF][START_REF] Burch | Absorption by H2O in narrow windows between 3000 and 4200 cm -1[END_REF], using different techniques: Fourier transform spectroscopy (FTS) [START_REF] Paynter | Laboratory measurements of the water vapor continuum in the 1200-8000 cm -1 region between 293 K and 351 K[END_REF][START_REF] Ptashnik | Water vapor self-continuum absorption in near-infrared windows derived from laboratory measurements[END_REF][START_REF] Ptashnik | Near-infrared water vapour self-continuum at close to room temperature[END_REF][START_REF] Ptashnik | Water vapor continuum absorption in near-IR atmospheric windows[END_REF], cavity enhanced absorption spectroscopy (CEAS) [START_REF] Cormier | Cavity ringdown spectroscopy measurements of the infrared water vapor continuum[END_REF][START_REF] Cormier | Infrared water vapor continuum absorption at atmospheric temperatures[END_REF][START_REF] Mondelain | The water vapour self-continuum by CRDS at room temperature in the 1.6 μm transparency window[END_REF][START_REF] Mondelain | Temperature de-pendence of the water vapor self-continuum by cavity ring-down spectroscopy in the 1.6 μm transparency window[END_REF][START_REF] Campargue | Accurate laboratory determination of the near infrared water vapor self-continuum: A test of the MT_CKD model[END_REF][START_REF] Richard | Water vapor self-continuum absorption measurements in the 4.0 and 2.1 μm transparency windows[END_REF][START_REF] Lechevallier | The water vapour self-continuum absorption in the infrared atmospheric windows: new laser measurements near 3.3 and 2.0 μm[END_REF][START_REF] Mondelain | The self-and foreign-absorption continua of water vapor by cavity ring-down spectroscopy near 2.35 µm[END_REF][START_REF] Vasilchenko | The water vapour self-and foreigncontinua in the 1.6 μm and 2.3 μm windows by CRDS at room temperature[END_REF][START_REF] Ventrillard | Accurate measurements and temperature dependence of the water vapor self-continuum absorption in the 2.1 μm atmospheric window[END_REF], calorimetric interferometry [START_REF] Bicknell | Search for low-absorption regions in the 1.6-and 2.1-µm atmospheric windows[END_REF][START_REF] Fulghum | Interferometric calorimeter for the measurement of water-vapor absorption[END_REF] and photo-acoustic spectroscopy [START_REF] Kapitanov | Photoacoustic measurements of the water vapor continuum absorption in the 1.6 µm window[END_REF]. This is particularly true for the self-continuum absorption due to the interaction between two water molecules. As a result, the latest version (3.2) of the MT_CKD self-continuum has been recently constrained in the 4.0, 2.1, 1.6 and 1.25 µm windows [25],

taking into account most of the CEAS cross-sections of Refs. [16 ,17,18,19,21].

In the case of the foreign-continuum arising from interactions between water molecules and molecular oxygen and nitrogen, scarce experimental data are available [START_REF] Hartmann | Recent advances in collisional effects on spectra of molecular gases and their practical consequences[END_REF], in particular at room temperature. This includes in-band continuum measurements in the 3500-4000 cm -1 spectral range by direct absorption spectroscopy [START_REF] Burch | Absorption by H2O in narrow windows between 3000 and 4200 cm -1[END_REF] and between 1300 and 7500 cm -1 by FTS [START_REF] Paynter | Laboratory measurements of the water vapour continuum in the 1200-8000 cm -1 region between 293K and[END_REF]. As concerned the transparency windows, cross-sections provided by FTS [START_REF] Baranov | The continuum absorption in H2O+N2 mixtures in the 2000-3250 cm -1 spectral region at temperatures from 326 to[END_REF][START_REF] Baranov | H2O-N2 collisioninduced absorption band intensity in the region of the N2 fundamental: ab initio investigation of its temperature dependence and comparison with laboratory data[END_REF][START_REF] Baranov | The water vapour self-and water-nitrogen continuum absorption in the 1000 and 2500 cm -1 atmospheric windows[END_REF] in the mid-IR windows and by cavity ring down spectroscopy (CRDS) in the 2.1 µm window [START_REF] Mondelain | The self-and foreign-absorption continua of water vapor by cavity ring-down spectroscopy near 2.35 µm[END_REF] have led to a significant increase of the MT_CKD foreign-continuum since the 2.8 version [25]. Note that FTS data were reported by the CAVIAR consortium at high temperature (350-430 K) over the wide 1.1 -5.0 µm spectral range thus including the 1.6 µm window of present interest [START_REF] Ptashnik | Water vapour foreign-continuum absorption in near-infrared windows from laboratory measurements[END_REF]. Additional measurements by CRDS are available at 10.6 µm [START_REF] Cormier | Infrared water vapor continuum absorption at atmospheric temperatures[END_REF], in the 0.94 µm absorption band [START_REF] Reichert | First CRDS-measurements of water vapour continuum in the 940 nm absorption band[END_REF] and, very recently, in the 2.1 µm window by our group [START_REF] Vasilchenko | The water vapour self-and foreigncontinua in the 1.6 μm and 2.3 μm windows by CRDS at room temperature[END_REF]. This latter work compared with [START_REF] Ptashnik | Water vapour foreign-continuum absorption in near-infrared windows from laboratory measurements[END_REF] at high temperature shows a weak positive temperature dependence of the foreign continuum also reported in the infrared in the 296-363 K range [START_REF] Baranov | The continuum absorption in H2O+N2 mixtures in the 2000-3250 cm -1 spectral region at temperatures from 326 to[END_REF][START_REF] Baranov | H2O-N2 collisioninduced absorption band intensity in the region of the N2 fundamental: ab initio investigation of its temperature dependence and comparison with laboratory data[END_REF] and in the 260-360 K range near 183 GHz [START_REF] Brogniez | A review of sources of systematic errors and uncertainties in observations and simulations at 183 GHz[END_REF]. provide insights on the origin of the continuum which can be due to different processes like the far wings of the rovibrational lines, water dimers (in the case of the self-continuum) and collision-induced absorption (CIA) [START_REF] Serov | On the origin of the water vapour continuum absorption within rotational and fundamental vibrational bands[END_REF][START_REF] Shine | The Water Vapour Continuum: Brief History and Recent Developments[END_REF].

The present work is part of an extensive study that we conduct since several years to better characterize the water vapour continuum absorption in the short-wave and mid-infrared transparency windows [START_REF] Mondelain | The water vapour self-continuum by CRDS at room temperature in the 1.6 μm transparency window[END_REF][START_REF] Mondelain | Temperature de-pendence of the water vapor self-continuum by cavity ring-down spectroscopy in the 1.6 μm transparency window[END_REF][START_REF] Campargue | Accurate laboratory determination of the near infrared water vapor self-continuum: A test of the MT_CKD model[END_REF][START_REF] Richard | Water vapor self-continuum absorption measurements in the 4.0 and 2.1 μm transparency windows[END_REF][START_REF] Lechevallier | The water vapour self-continuum absorption in the infrared atmospheric windows: new laser measurements near 3.3 and 2.0 μm[END_REF][START_REF] Mondelain | The self-and foreign-absorption continua of water vapor by cavity ring-down spectroscopy near 2.35 µm[END_REF][START_REF] Vasilchenko | The water vapour self-and foreigncontinua in the 1.6 μm and 2.3 μm windows by CRDS at room temperature[END_REF][START_REF] Ventrillard | Accurate measurements and temperature dependence of the water vapor self-continuum absorption in the 2.1 μm atmospheric window[END_REF]. The self-continuum including its temperature dependence was investigated by CRDS in these references. Because of the weakness of the signal to be measured, the experiment is particular challenging in the 1.6 µm window. This applies in particular for the foreign-continuum measurements which require relatively large changes in the gas pressure which may affect the optical alignment. In the following part 2, we will present the experimental procedure adopted for the determination of the foreign-continuum cross-sections at room temperature at 15 selected spectral points of the 1.6 µm window. Data acquisition by CRDS and data treatment as well as the error budget will be discussed in part 3 and the resulting data will be compared to experimental data available in the literature and to the MT_CKD model in part 4.

Experimental

The CRDS setups

Measurements were performed using two cavity ring down spectrometers. As described in [START_REF] Kassi | Cavity ring down spectroscopy with 5×10 -13 cm -1 sensitivity[END_REF], a distributed feedback (DFB) laser diode (either from Eblana Photonics or NEL) is coupled into a high finesse cavity fitted by two mirrors with highly reflective coatings. Our two spectrometers used mirrors optimized for the 1500-1700 nm and the 1730-1840 nm spectral regions The output mirror of the cavity is mounted on a piezoelectric transducer to periodically change the cell length allowing covering one free spectral range (FSR) of the cavity and thus achieving resonance between the laser light and one longitudinal mode of the cavity. After a build-up time necessary to fill the cavity with photons at resonance, the injection of laser light is stopped thanks to an acousto-optic modulator and the purely exponential decay time of photons leaking from the cavity (i.e. the ring down (RD) time, τ) is measured with a photodiode. The fitted RD time is directly related to the absorption coefficient of the absorbing gas, α(ν), through equation [START_REF] Cubasch | Introduction[END_REF].

𝛼(𝜐) = 1 𝑐𝜏(𝜐) - 1 𝑐𝜏 0 (𝜐) (1)
With c the speed of light, ν the laser frequency and 𝜏 0 the ring down time with the optical cavity empty or filled with a non-absorbing gas.

To measure the laser frequency, a part of the laser light was directed via a fibre either to an optical interferometer-based wavelength meter (model 621-A IR from Bristol, ±1.5×10 -3 cm -1 accuracy or model WA-1650 from Burleigh, ±1.1×10 -3 cm -1 accuracy) or to a Fizeau wavelength meter (High Finesse WS-U-30 IR, 6.6×10 -4 cm -1 accuracy) depending on the selected data point and on the availability of the instrument.

A 1000 mbar pressure gauge (model 622AB from MKS instruments) was installed on the cavity to continuously measure the total pressure with an accuracy of 0.15% between 100 and 1000 mbar. A temperature sensor (TSic 501 from IST, ±0.1 K accuracy) was fixed on the external wall of the cavity and enveloped by thermal insulation foam to continuously record the temperature.

Data acquisition

Foreign continuum cross-sections were determined for 15 spectral points between 5700 cm -1 and 6640 cm -1 (see Table 1). Each spectral point corresponds to the frequency of the radiation delivered by a distributed feedback (DFB) laser diode. Some measurements were repeated several times to check the repeatability The spectral points were selected because they are located in spectral intervals mostly free of absorption lines and thus correspond to weak local monomer contribution. The following procedure was adopted to derive the foreign crosssection value at each selected spectral point.

The high finesse cavity was first flushed with dry air (Alphagaz 2 from Air Liquide, purity > 99.9999%) at a total pressure of 700 Torr, regulated with a solenoid valve and a proportional integral software based loop acting on the gas flow. A spectrum, including at least one isolated water line reported in HITRAN2016 [START_REF] Gordon | The HITRAN2016 Molecular Spectroscopic Database[END_REF] with an accuracy between 1% and 2% (called the reference line, hereafter), was recorded to check the low residual water vapour concentration (typically on the order of 100 ppmv). The loss rate,

1 𝑐𝜏 0 (𝜐)
, at the laser frequency fixed to one of the selected spectral points was measured during pressure ramp of dry air decreasing from 700 Torr to 350 Torr (Figure 1). The typical duration of the pressure ramp was a few minutes.

As mentioned above a major difficulty of the experiment is that the amplitude of the pressure variation required to measure the foreign-continuum induces significant changes in the optical alignment of the CRDS cavity. As illustrated in the dry air recordings of Fig. 1, the pressure induced variation of the loss rate is mostly negligible on the edges of the window but, in the centre of the window, reaches values on the order of the additional losses due to water in the humidified air recordings. This would prevent foreign-continuum determination if the observed pressure induced variation were not repeatable. In fact, as illustrated in the superimposed traces of the dry air recordings presented in Fig. 1, the pressure effect on the optical alignment was checked to be highly repeatable allowing to use dry air pressure ramps as zero absorption baseline of the humidified air pressure ramps.

After the dry air recording, the cell was evacuated and filled with humidified air up to 700 Torr using a home-made humidifier [START_REF] Vasilchenko | The water vapour self-and foreigncontinua in the 1.6 μm and 2.3 μm windows by CRDS at room temperature[END_REF]. Humidified air was flushed until a constant water vapour concentration of typically 1% was achieved (Above this value, the water concentration was not stable enough. In order to check the stability of the water partial pressure, a series of consecutive CRDS spectra, including the reference water line, was recorded. For each spectrum, the concentration was deduced from a fit to the water absorption line using a Voigt profile. Once the water relative concentration in the cell was stabilized within better than 1% (typically after 60 min), the injection of humidified air was stopped and the loss rates were measured at the selected spectral point, during pressure ramp decreasing from 700 to 350 Torr (Figure 1). An additional spectrum around the reference line was recorded at 350 Torr to check that the water vapour concentration has remained unchanged during the ramp.

For this type of measurements, the stability of the ramp is essential. This is why we checked carefully both the short-term and long-term stability of our set-up by recording several decreasing and increasing dry air ramps consecutively and comparing dry air ramps recorded at several hours of distance and/or at different days for a given spectral point. We observed a very good repeatability with no detectable changes on the short term scale (Figure 1) and changes of 5×10 -10 cm -1 (offset) at maximum on the long term scale (over days) which represents between 2% and 50% of the maximum measured absorption of the foreigncontinuum, depending on the considered spectral point. Let us mention that pressure ramps were restricted to the 350 -700 Torr range as a small hysteresis, probably caused by changes in the mirror alignment, was observed when the cell was fully evacuated. Note that the procedure described here based on pressure ramps at fixed frequency was adopted because it is less time consuming than that applied in reference [START_REF] Vasilchenko | The water vapour self-and foreigncontinua in the 1.6 μm and 2.3 μm windows by CRDS at room temperature[END_REF], where spectra of air with different water vapour concentrations were recorded. -1 ) and near the center (6022 cm -1 ) of the 1.6 µm window. Note the variation of the loss rate of the dry air recordings with pressure due to a change of the mirrors alignment. This variation is checked to be repeatable by the superposed results obtained here for three dry air pressure ramps at 6022 cm -1 (lower panel). Note the different amplitude of the losses due to water vapor (green) at 5752 cm -1 and 6022 cm -1

Figure 1. Variation of the CRDS loss rate for humidified and dry air pressure ramps on the low energy edge (5752 cm

Analysis and resulting CF cross-sections

Data analysis and CF cross-sections retrieval

In a mixture of water vapor in air, the total absorption coefficient can be expressed as the sum of four terms:

𝛼 𝑡𝑜𝑡 (𝜈, 𝑇) = 𝛼 𝑐𝑎𝑣𝑖𝑡𝑦 + 𝛼 𝑊𝑀𝐿 + 𝛼 𝑊𝐶𝑆 + 𝛼 𝑊𝐶𝐹 = 𝛼 𝑐𝑎𝑣𝑖𝑡𝑦 + 𝛼 𝑊𝑀𝐿 + 1 𝑘𝑇 𝐶 𝑆 (𝜈, 𝑇)𝑃 𝐻 2 𝑂 2 + 1 𝑘𝑇 𝐶 𝐹 (𝜈, 𝑇)𝑃 𝐻 2 𝑂 𝑃 𝑎𝑖𝑟 (2)
where cavity, WML, WCS and WCF are the contributions due to the cavity, water vapor "monomer local lines" (WML), water vapor self-continuum (WCS) and foreign-continuum (WCF), respectively. CS and CF cross-sections are expressed in cm 2 molecule -1 atm -1 .

From Equation (2), the foreign continuum absorption for a total pressure P= Pair+𝑃 𝐻 2 𝑂 , is thus obtained by subtracting three contributions from the measured humidified air absorption (𝛼 𝑡𝑜𝑡 ): the dry air signal (𝛼 𝑐𝑎𝑣𝑖𝑡𝑦 ) for the same total pressure, P, corresponding to the losses of the cavity in absence of water vapor, the contribution of the air-broadened rovibrational lines, 𝛼 𝑊𝑀𝐿 , and the water vapor self-continuum absorption at the 𝑃 𝐻 2 𝑂 partial pressure. Note that at a total pressure of 700 Torr, losses due to Rayleigh scattering in dry air and in air humidified with 1% water concentration differ by a negligible quantity of 2×10 -11 cm -1 calculated from [START_REF] Thalman | Rayleigh scattering cross-section measurements of nitrogen, argon, oxygen and air[END_REF]. After subtraction of the baseline, the quantity 𝛼 𝑡𝑜𝑡 -𝛼 𝑐𝑎𝑣𝑖𝑡𝑦 = 𝛼 𝑊𝑀𝐿 + 𝛼 𝑊𝐶𝑆 + 𝛼 𝑊𝐶𝐹 shows a linear dependence with 𝑃 𝐻 2 𝑂 Pair as illustrated in Figure 2. In particular, note the linearity of 𝛼 𝑡𝑜𝑡 -𝛼 𝑐𝑎𝑣𝑖𝑡𝑦 achieved at 6022.1 cm -1 confirming that the pressure effects on the mirror alignment, although important (see lower panel of Figure 1), is corrected by using the dry air measurements. The lines contribution was simulated at the selected spectral points, for total pressures of 350, 500, 600 and 700 Torr and the 𝑃 𝐻 2 𝑂 partial pressure fixed to its measured value (corresponding to about 1% concentration). Simulations were performed using the HITRAN2016 line list [START_REF] Gordon | The HITRAN2016 Molecular Spectroscopic Database[END_REF], using a Voigt profile and the standard [-25 cm -1 , +25 cm -1 ] convention cut-off for the line wings [START_REF] Ptashnik | Water vapor self-continuum absorption in near-infrared windows derived from laboratory measurements[END_REF]. The selected spectral points, νi, being located at frequency values far from line centers, the pressure dependence of 𝛼 𝑊𝑀𝐿 is proportional to 𝑃 𝐻 2 𝑂 𝑃 𝑎𝑖𝑟 . The pressure dependence of the simulated WML values were thus fitted with a second order polynomial which was used to subtract the local line contribution over the pressure ramp (Figure 2). The self-continuum contribution was calculated using the selfcontinuum cross-sections from [START_REF] Vasilchenko | The water vapour self-and foreigncontinua in the 1.6 μm and 2.3 μm windows by CRDS at room temperature[END_REF]. As the pressure ramps were performed at constant humidity rate (𝑃 𝐻 2 𝑂 /𝑃 𝑎𝑖𝑟 ≈ 1%), 𝛼 𝑊𝐶𝑆 is also proportional to 𝑃 𝐻 2 𝑂 𝑃 𝑎𝑖𝑟 . The relative contributions of the local monomer and of the self-and foreign-continuum, to the total absorption are provided in Table 1.

Figure 3 shows the achieved linear dependence of 𝛼 𝑊𝐶𝐹 versus 𝑃 𝐻 2 𝑂 𝑃 𝑎𝑖𝑟 r for different selected spectral points. The change of the slope illustrates the frequency dependence of the foreign-continuum cross-sections which were derived from a linear fit (Eq.2). A small positive offset is observed at null pressure. The origin of this offset is not clear. After several tests, we only observed that the slope seems not being affected by a change of the offset value. No offset of this sort was observed in our previous measurements in the 2.3 µm window [START_REF] Vasilchenko | The water vapour self-and foreigncontinua in the 1.6 μm and 2.3 μm windows by CRDS at room temperature[END_REF]. The CF values derived from the procedure described above are listed in Table 1 and presented in Figure 4. A 5 th order polynomial fit of the CF cross-sections (weighted by their uncertainties) is also shown in Figure 4 and was used to provide CF cross-sections every 10 cm -1 between 5700 cm -1 and 6640 cm -1 as Supplementary Material.

Table 1. Foreign-continuum cross-sections in the 1.6 µm window and their 1σ estimated uncertainties in units of the last digit (in parenthesis). The relative contributions of the "local line monomer", selfand foreign continuum to the total absorption are also given in the three last columns. During the whole period of measurements temperature varied between 296 K and 298.5 K. a Due to the large estimated uncertainty, only an upper limit value can be given at 6369 cm -1 .

 cm -1 CF cm 2 molecule -1 atm -1

Error budget

Uncertainties on the derived CF values have been calculated with the error propagation approach using Eq. 2 and assuming uncorrelated variables. As discussed earlier, the baseline stability was evaluated to be below 5×10 -10 cm -1 . Temperature and total pressure are measured with accuracies of 0.1K and 0.15%, respectively. Their contributions are almost negligible.

The uncertainties on CS values used here are reported in [START_REF] Vasilchenko | The water vapour self-and foreigncontinua in the 1.6 μm and 2.3 μm windows by CRDS at room temperature[END_REF].

The knowledge on the water vapour partial pressure is the main contributor to the error budget through the monomer contribution which is proportional to 𝑃 𝐻 2 𝑂 and the self-continuum contribution proportional to 𝑃 𝐻 2 𝑂 2 . The partial pressure is derived from the fitted area of wellisolated H2O lines with intensities reported in HITRAN2016 with uncertainties better than 2% [START_REF] Gordon | The HITRAN2016 Molecular Spectroscopic Database[END_REF]. This value is adopted as the uncertainty on 𝑃 𝐻 2 𝑂 considering that the quality figure of the fits, defined as the ratio between peak signal and rms fit residuals, of several hundred, limits the error on the fitted area below 1%.

The monomer contribution uncertainties were determined by taking into account the error bars on the line intensities, self-broadening, air-broadening coefficients and water vapour pressure. Four simulations, 𝛿 𝑖 (𝜈), were performed, each of them with either, the intensities, self, air coefficients or 𝑃 𝐻 2 𝑂 values increased by their error bar. The uncertainty on αWML was obtained from: 𝛿𝛼 𝑊𝑀𝐿 (𝜈) = [∑ 𝛿 𝑖 (𝜈) 2 4 𝑖=1

] 1/2 .

The uncertainties detailed above are of type-B. To quantify statistical (type-A) uncertainties we recorded consecutively six decreasing pressure ramps of humidified air at the selected spectral point of 5933.75 cm -1 chosen because of a limited impact of the uncertainty on 𝑃 𝐻 2 𝑂 .

Between each ramp, the cell was filled again with humidified air from 350 Torr to 700 Torr and two CRDS spectra were recorded to check the stability of the water concentration and determine this concentration. All the ramps were base line corrected using the same dry air ramp recorded just before. Nevertheless, a dry air ramp recorded just after exactly superposed to the ramp used. A relative standard deviation of 2.1% was obtained on the derived CF values showing the very good short term repeatability. Two months before a CF value 13% lower than the averaged value on the 6 ramps was measured for the same spectral point with the other CRDS spectrometer used in this work showing that largest statistical uncertainties have to be considered. We also achieved measurements at 5842.24 cm -1 , 5905.72 cm -1 and 6369.00 cm -1 done each time at three different days. From these data we extended to each spectral point a statistical uncertainty that we chosen inversely proportional to the ratio between the value of 𝛼 𝑊𝐶𝐹 at 0.08 atm 2 (i.e. the maximum of the pressure ramps) and the minimum detectable absorption coefficient αmin for the pressure ramp.

Combining the type-A and type-B uncertainties, we obtained the final uncertainties reported in Table 1 for each spectral point.

Comparison to literature data

To our knowledge, the only previous determinations of foreign-continuum cross-sections available in the 1.6 µm window have been reported in [START_REF] Ptashnik | Water vapour foreign-continuum absorption in near-infrared windows from laboratory measurements[END_REF] by the CAVIAR consortium at high temperature. In this work, CF values were derived from spectra recorded at a single pressure value, with a Fourier transform spectrometer coupled to a White cell providing a 17.7 m optical path length. To increase the absorption continuum signal, the cell was heated between 350 K and 430 K allowing for water vapour partial pressure to be increased up to 266 mbar and 600 mbar, depending on the cell temperature. No temperature dependence of the foreign-continuum could be evidenced in the 350-430 K temperature interval of the FTS measurements. The spectrally smoothed CAVIAR CF values reported at 400 K [START_REF] Ptashnik | Water vapour foreign-continuum absorption in near-infrared windows from laboratory measurements[END_REF] are plotted in Figure 4 with their corresponding error bars ranging between about 25% and 120% on the edges and near the centre of the window, respectively. Overall, the CAVIAR CF values (density normalized) at 400 K are larger than our cross-sections by factors between ~3 and ~8, on the edges and near the centre of the window, respectively. Such important increase between 296 K and 400 K is significantly larger than the FTS error bars [START_REF] Ptashnik | Water vapour foreign-continuum absorption in near-infrared windows from laboratory measurements[END_REF] (see Figure 4).

Nevertheless, the fact that no clear temperature dependence was evidenced between the CAVIAR measurements at 350 K and 430 K questioned the correctness and amplitude of the positive temperature dependence between 296 K and 400 K. Note that in the 2.3 µm window [START_REF] Vasilchenko | The water vapour self-and foreigncontinua in the 1.6 μm and 2.3 μm windows by CRDS at room temperature[END_REF], a constant CF ratio of ~3 was observed over most of the window between the CAVIAR and CRDS cross-sections (density normalized). Again, the significance of this variation close to the 1 error bar of the FTS CF values, remains to be confirmed.

Finally, let us recall that the foreign-continuum temperature dependence in the windows is by no means similar to that of the self-continuum which exhibits a clear negative temperature dependence (see for example [START_REF] Ptashnik | Water vapor self-continuum absorption in near-infrared windows derived from laboratory measurements[END_REF][START_REF] Richard | Water vapor self-continuum absorption measurements in the 4.0 and 2.1 μm transparency windows[END_REF]). Finally, let us consider the humidified measurements by calorimetric interferometry reported by Bicknell [START_REF] Bicknell | Search for low-absorption regions in the 1.6-and 2.1-µm atmospheric windows[END_REF]. In the 2.3 µm window where the continuum is larger, we could calculate the self-contribution to Bicknell's continuum using our determination of the CF values and obtained a good agreement with our CS value [START_REF] Vasilchenko | The water vapour self-and foreigncontinua in the 1.6 μm and 2.3 μm windows by CRDS at room temperature[END_REF]. In the considered 1.6 µm window, Bicknell reported a total (self+foreign) continuum absorption coefficient of 3.2×10 -8 cm -1 at 6150 cm -1 for a mixture of 18.75 Torr of H2O in N2 with a total pressure of 760 Torr (see [START_REF] Ptashnik | Near-infrared water vapour self-continuum at close to room temperature[END_REF] for details). For the same experimental conditions, we calculate an absorption coefficient of ~1×10 -8 cm -1 when using our present CF determination of 5.4(9)×10 -27 cm 2 molec -1 atm -1 and a CS value of 4.9(7)×10 -25 cm 2 molec -1 atm -1 from Ref. [START_REF] Vasilchenko | The water vapour self-and foreigncontinua in the 1.6 μm and 2.3 μm windows by CRDS at room temperature[END_REF]. This difference by a factor of 3 is outside the combined error bars and difficult to interpret on the basis of the scarce experimental information provided in Ref. [START_REF] Bicknell | Search for low-absorption regions in the 1.6-and 2.1-µm atmospheric windows[END_REF] (see [START_REF] Shine | The water vapour continuum in near-infrared windows -Current understanding and prospects for its inclusion in spectroscopic databases[END_REF] for discussion). Note that our CF determinations rely on careful study of the pressure dependence of the continuum signal while Bicknell's measurements were performed at a single pressure [START_REF] Bicknell | Search for low-absorption regions in the 1.6-and 2.1-µm atmospheric windows[END_REF].

Conclusion

Water vapor foreign-continuum cross-sections have been obtained at room temperature in the 1.6 µm window. The corresponding small cross-sections were derived from CRDS measurements during pressure ramps recorded at fixed spectral points between 5700 cm -1 and 6640 cm -1 . Fifteen spectral points were selected to sample the window at frequencies corresponding to small contribution of the water monomer lines. The CAVIAR measurements at high temperature in the same window are larger in amplitude but show a similar wavelength dependence.

The foreign-continuum absorption is very weak at room temperature, in particular, in the very centre of the window. For instance, the absorption coefficient to be measured is on the order of 10 -9 cm -1 for 1 atm of humidified air with 1 % of water vapor (≈ 7 Torr). Measurements in this central region were made possible thanks to the very good repeatability of the loss rates of our CRDS set up. Although the dry air CRDS loss rates were found to be sensitive to the pressure variation during the pressure ramp, their dependence was found highly repeatable allowing us to use dry air recordings as baseline of the humidified air recordings.

Two factors could help to decrease the CF relative uncertainties which range between 10% and 100%. Firstly, our home-made humidifier provides humidified air with stable water vapor relative concentration limited to 1% at most, corresponding to a relative humidity of 33% at 296 K. The increase by a factor of two of the water vapor partial pressure could help to decrease the relative uncertainties. Secondly, the uncertainty on the water vapor partial pressure (or concentration) is the main contributor to the final uncertainties through the selfcontinuum and the water monomer subtracted contributions. At the moment, a 2% uncertainty is achieved on the knowledge of the water concentration in the used humidified air, mainly due to the uncertainty on the intensity reported in HITRAN2016 for the water reference line used to derive the water partial pressure. Alternative techniques as dew point mirror hygrometers are considered to improve the determination of the water vapor partial pressure by at least a factor of two and thus the accuracy of the reported CF values, in particular near the centre of the window.

Figure 2 .

 2 Figure 2. Humidified air pressure ramp recorded at 5715.30 cm -1 (left panel) and 6022.06 cm -1 (right panel) after subtraction of the dry air ramp (black solid line). The water monomer local contribution (αWML), the self-(αWCS) and the foreign-continuum contributions (αWCF) are also plotted. The water relative concentration, 𝑷 𝑯 𝟐 𝑶 /𝑷 𝒂𝒊𝒓 , on the order of 1% was maintained constant during the pressure ramp.

Figure 3 .

 3 Figure 3. Absorption coefficient of the foreign-continuum for pressure ramps obtained for different selected spectral points. Two linear fit are also added to show the small observed offsets.

Figure 4 .

 4 Figure 4. Overview of the foreign-continuum cross-sections, CF, in the 1.6 µm window obtained in this work and found in the literature. The red solid line corresponds to the fit of our data with a 5 th order polynomial. Note that for comparison purposes, the CF values are density normalized and are given in cm 2 molecule -1 .

Foreign-continuum provided

  by the latest version of the MT_CKD model (MT_CKD3.2) is included in Figure 4 for comparison purposes. No temperature dependence is provided for the MT_CKD foreign cross-sections. For the low energy edge of the window, the MT_CKD CF values are significantly larger than our measurements in contrast with the values in the centre of the window which are smaller by a factor of ~9. Nevertheless, near the centre of the window, the foreign continuum is very weak and the experimental uncertainty reaches almost 100%. More accurate measurements are thus required to be conclusive in the very centre of the window, near 6300 cm -1 .

Acknowledgments

This project is supported by the Labex OSUG@2020 (ANR10 LABX56) and the LEFE-ChAt program from CNRS-INSU.


A Campargue
email: alain.campargue@univ-grenoble-alpes.fr

E V Karlovets

E Starikova

A Sidorenko

D Mondelain

The absorption spectrum of 13 CH 4 in the 1.58 µm transparency window (6147-6653 cm -1 )

Keywords: methane, 13 CH4, absorption spectroscopy, HITRAN, Empirical lower state energy

The room temperature absorption spectrum of 13 CH4 is recorded by high sensitivity cavity ring down spectroscopy (CRDS) near 1.58 µm. The investigated region (6147-6653 cm -1 ) corresponds to a spectral region of weak absorption located between the strong bands of the tetradecad and icosad. The sensitivity of the recordings allowed for the measurement of more than 13000 lines for which line centers and line intensities are derived using a multiline fitting program. The obtained list is the first extensive list of 13 C enriched methane in the region. It is believed to include a significant number of lines of 13 CH3D.

In addition, 185 lines were measured at 80 K by direct absorption spectroscopy (DAS) near 6600 cm -1 . The line intensity detectivity threshold is on the order of a few 10 -29 cm/molecule for the CRDS recordings at 296 K and 10 -26 cm/molecule for the DAS recordings at 80 K. From the intensity ratio of the lines in common in the 296 K and 80 K empirical line lists near 6600 cm -1 , 438 empirical values of the lower state energy level (Eemp) were derived. An additional set of 200 Eemp values were obtained by combining the present CRDS line intensities to DAS literature data near 6150 cm -1 . The comparison to the TheoReTS ab initio line list shows an overall very good agreement on the line intensity. Significant deviations on the order of 0.1 cm -1 are noted for line positions. The obtained experimental data will be valuable to tune ab initio line positions to empirical values in future versions of the theoretical line lists. Finally, a first set of 900 lines belonging to the 5ν4 and ν 2+4ν4 bands of the icosad are rovibrationally assigned on the basis of an effective Hamiltonian model. The energy values of the involved vibrational sublevels are determined.

INTRODUCTION

The present work aims at extending the knowledge of the absorption spectrum of the 13 CH4 minor isotopologue of methane in a spectral region of weak absorption (or transparency window) of importance for planetary applications, in particular for Titan. As a rule, the general appearance of the absorption spectra of 12 CH4 and 13 CH4 is very similar because the isotopic substitution of the central carbon atom leads to global shifts of the different variational bands limited to a few tens wavenumbers in the near infrared. (This not the case for CH3D -see below)

The 1.58 µm window is located between strong bands of the tetradecad and of the icosad at low and high energies, respectively (see Fig. 1). The tetradecad (14 vibrational levels and 60 sub-levels) and the icosad (20 vibrational levels and 134 sub-levels) are polyads of vibrational levels in strong rovibrational interaction. The number of levels involved and the strength of the interactions lead to a highly congested spectrum with no apparent regular structure except for the strong 23 and the 2+23 bands at 6000 and 7500 cm -1 , respectively.

Fig. 1

Overview of the 13 CH4 line list between 5600 and 7700 cm -1 . Upper panel: Line list provided by the HITRAN2016 database (line intensities correspond to the pure 13 CH4 species) Lower panel: Empirical line lists obtained by direct absorption spectroscopy (DAS) in the tetradecad and icosad and by CRDS in the present work (red and black, respectively).

Direct absorption laser spectroscopy (DAS) and Fourier transform spectroscopy (FTS) do not provide sufficient sensitivity to characterize the 1.58 µm window of methane. The only previous study in the region was performed by cavity ring down spectroscopy (CRDS) with a sample with natural isotopic abundance. Recordings performed at room temperature and with a CRDS cell cooled at liquid nitrogen temperature allowed for the elaboration of two empirical line lists for methane in natural isotopic abundance, at 296 K and 80 K. The corresponding empirical values of the lower state energy level, Eemp, were determined using the two-temperature method (see below). Being located at the low energy edge of the icosad and thus less affected by interactions, the 12 CH4 lines of the 54, 2+44, 1+34 bands could be rovibrationnally assigned at 80 K. Their line positions could be modelled by an effective Hamiltonian obtained by reduction of the full Hamiltonian of methane nuclear motion based on an ab initio potential energy surface.

The assignment of the 12 CH4 room temperature spectrum has not been reported so far. In its present version, the HITRAN database reproduces the CRDS line list at 296 K as part of the WKLMC line list and includes a limited number of rovibrational assignments (from Ref. []). It is worth mentioning that, in spite of its low isotopic relative abundance (about 5×10 -4 ), CH3D has a large relative contribution to the absorption in the 1.58 m methane transparency window. As a consequence of the strong isotopic shift of the CD stretching frequency (2) compared to CH, the 32 band near 6430 cm -1 falls in the region of weakest CH4 absorption. As a result, CH3D in natural abundance (about 5×10 -4 ) represents between 10 and 20% of the methane absorption at 296 K in the 6300-6500 cm -1 interval [papier CH3D]. At low temperature (80K), this percentage increases up to 75 % near 6300 cm -1 . Due to the importance of the 1.58 µm window for planetary application (the D/H isotopic ratio is strongly dependent on the considered planet), a spectroscopic study was devoted to CH3D in the region. The spectrum of high purity CH3D was recorded both at room temperature and at 81 K. As CH3D transitions in the region are strong (line intensities up to 10 -22 cm/molecule), the DAS technique provided sufficient sensitivity (min  5×10 -8 cm -1 ). On the basis of this work, the lines of CH3D present in the spectrum of "natural" methane could be systematically identified in the 1.58 µm window.

A similar work remains to be done for the 13 CH4 species. As illustrated in Fig. 1, only the strongest 13 CH4 lines (intensity larger than about 4×10 -26 cm/molecule for pure 13 CH4) were detected and could be identified in the spectrum of "natural" methane. The DAS technique applied to 13 CH4 in the tetradecad below 6200 cm -1 and in the icosad above 6600 cm -1 does not provide sufficient sensitivity in the 1.58 µm window. In the present work, we report the first high sensitivity study of the 13 CH4 spectrum in the region. The spectra of methane highly enriched in 13 C were recorded by CRDS at room temperature. The CRDS recordings and the line list construction are detailed in the next paragraph. In the discussion (Section 4), we present a comparison to ab initio calculations and to the 13 CH4 HITRAN list in the region.

EXPERIMENT AND CONSTRUCTION OF THE LINE LIST

The CRDS spectrum of 13 CH4 at room temperature was recorded from 6147 to 6653 cm -1 with a fibered CRDS spectrometer using distributed feed-back (DFB) diode lasers as light sources. The stainless steel high finesse cell (HFC) (l= 1.42 m, in= 11.7 mm) is fitted by a pair of super mirrors (~99.998% reflectivity) giving rise to ring down times on the order of 200 s. The whole spectral region was continuously covered with the help of twenty-four fibered DFB lasers. The DFB lasers driven at a constant current of 140 mA have a tuning range of about 40 cm -1 for a temperature scan from -10 to 60°C. About 40 ring down events were averaged for each spectral data point separated by approximately 2×10 -3 cm -1 . A complete DFB temperature scan was achieved within 65 minutes. Ring down (RD) events were obtained by switching off the laser beam with the acousto-optic modulator (AOM) used on its order +1, each time a longitudinal mode of the HFC falls in coincidence with the laser frequency. Resonances were achieved by modulating the HFC length over one free spectral range thanks to a piezo tube supporting the output mirror [Romanini1997]. Ring down times, , were measured by fitting with a purely decreasing exponential function the signal measured with an InGaAs photodiode. The obtained loss rate, 1/c, is the sum of the loss rate with the cell evacuated, 1/c0, and of the extinction coefficient, (), due to the gas:

              0 1 1 c c (1)
where c is the speed of light.

The CRDS cell was filled with pure 13 CH4 (ISOTEC 13 C enrichment > 99%). Series of recordings were performed for two pressure values. A pressure of 7.5 Torr was adopted in the center and high energy range of the window (6254-6653 cm -1 ) while recordings were performed at 1.0 Torr in the low and high frequency edges (6147-6283 cm -1 ) and 6520-6653 cm -1 ). The pressure value given by a capacitance gauge (Baratron) was continuously monitored during the recordings as well as the cell temperature (296±1 K).

Fig. 2

Overview of the 13 CH4 CRDS recordings between 6150 and 6650 cm -1 . The successive enlargements reveal the high spectral congestion of the spectrum. The sample pressure was 7.5 Torr. The alternate colors correspond to recordings performed with different distributed feed-back diode lasers

The line list construction was particularly laborious. First, as illustrated in Fig. 2, the spectral congestion is considerable. The CRDS sensitivity allows for the detection of very weak lines down to a detectivity threshold on the order of 10 -29 cm/molecule while the strongest lines have intensity four orders of magnitude larger. As a result, the density of detected transitions is high, on the order of 25 lines/ cm -1 . The line centers and line intensities were obtained by using a homemade interactive least squares multi-lines fitting written in LabVIEW. The line parameter derivation consisted in delimitating narrow spectral intervals corresponding to groups of (overlapping) lines which could be fitted independently. For each interval, line centers, integrated absorption coefficients, the Lorentzian contribution of each line and a baseline (assumed to be a linear function of the wavenumber) were provided by the fitting procedure. The line intensity, 0 S  (cm/molecule), of a rovibrational transition centered at 0, was obtained from the integrated absorption coefficient,

0 A  (cm -2 /molecule): 0 0 ( ) ( ) line A T d S T N        (2)
where is the wavenumber in cm -1 ,  is the absorption coefficient in cm -1 obtained from the cavity ring down time (Eq. 2) and N is the molecular concentration in molecule/cm 3 obtained from the measured pressure and temperature values: P= NkT. The agreement between the spectral simulation and the CRDS spectrum is illustrated in Fig. 3. Additional difficulties were due to the fact that the absorption of some lines were too strong for CRDS, making the light intensity transmitted by the cell insufficient for accurate measurement of the RD times. This issue concerns lines on the low and high energy edges of the studied interval. In the 6147-6200 cm -1 interval which includes lines with intensity as large as 10 -23 cm/molecule, line parameters obtained by DAS in Ref. were adopted for the strong lines. At high energy (6520-6653 cm - The complete line list provided as Supplementary Material was obtained by gathering the line lists corresponding to the different DFB laser diodes. It includes a total of 13032 lines with intensity at 296 K ranging between about 10 -29 and 1.8×10 -23 cm/molecule.

ANALYSIS AND DISCUSSION

3.a. Empirical determination of the lower state energy

The two temperature-method uses the temperature dependence of the line intensity to derive the empirical value of the lower state energy of the considered transition. The 2T-method was successfully applied to DAS spectra of 13 CH4 recorded at 296 K and 80 K in the tetradecad (up to 6200 cm -1 ) and in the icosad (from 6600 cm -1 ). In the present work, CRDS recordings were not performed at low temperature but the DAS recordings in the icosad were extended down to 6543 cm -1 . The spectra were recorded at a pressure of 6.0 Torr with an absorption pathlength of 282 cm. The reader is referred to A set of about 200 lines were measured and gathered with the 80 K DAS list of Ref. . As a result, 2T-method could be applied in the 6147-6200 cm -1 and 6547-6653 cm -1 intervals which are in common between the DAS lists at 80 K and the present CRDS list at room temperature (see Fig. 4).

The lower state energy (Eemp) of the transitions in common in the two datasets was determined from the ratio of line intensities measured at 80 and 296 K ( [7,15]:

                 0 1 1 0 0 1 1 1 exp ) ( ) ( ) ( ) ( 0 0 kT kT E T Z T Z T S T S emp v v , (3)
where 0 v S and Z are the intensity and partition function, respectively (T0 = 296 K, T1= 80 K).. The above derivation of Jemp, assumes that the measured lines belong to 13 CH4 and not to 13 CH3D while we mentioned in the introduction that 13 CH3D is expected to contribute to the spectrum in the region. As illustrated in Fig. 6 of Ref. [], the strongest bands of 13 CH3D are not located in the two intervals where we apply the 2T-method but in the center of the window. For instance, taking into account an estimated isotopic shift of 20 cm -1 , compared to 12 CH3D, the 32 band of 13 CH3D is predicted to be centred near 6410 cm -1 The list at 80 K in the 6147-6200 and 6547-6653 cm -1 intervals is provided as Supplementary Material and includes the position and intensity of the coincident lines at 296 K used to derive the Eemp and Jemp values. Similarly, in the 296 K list, we provide the position and intensity of the coincident lines at 80 K. A sample of the 80 K list is reproduced in Table 1 Table 1 Wavenumbers and intensities of 13 CH4 absorption lines recorded by DAS at 80 K and CRDS at 296 K near 6610 cm -1 . The empirical values of the lower state energy, Eemp and corresponding Jemp values were obtained by the 2T-method for the transitions whose centers at 296 K and 80 K coincide within0.003 cm -1 . This Table is a section of the list attached as Supplementary Material. A similar list is also provided for T= 296 K.

3.b. Comparison to the HITRAN and TheoReTs databases

The overview included in Fig. 1 shows that the HITRAN2016 list of 13 CH4 is largely incomplete in the 1.58 µm transparency window and in the icosad. Indeed, while in the 23 region of the tetradecad around 6000 cm -1 , HITRAN list reproduces the results of a DAS study of pure 13 CH4, in the region above 6200 cm -1 , the 13 CH4 line parameters of the HITRAN list were obtained from studies of natural methane. The natural relative abundance of 13 CH4 being about 1.1 % many 13 CH4 lines were obscured by stronger 12 CH4 lines or poorly measured. The present measurements in the transparency window together with the recent DAS study of pure 13 CH4 in the icosad will be valuable to complete the HITRAN.

The TheoReTS ab initio line list computed by the Reims-Tomsk collaboration [12,14,15] is accessible via the TheoReTS information system [START_REF] Rey | Theoretical hot methane line lists up to T=2000 K for astrophysical applications[END_REF] (http://theorets.univ-reims.fr, http://theorets.tsu.ru). The TheoReTS list was computed by variational method [11,46,47] using recent ab initio potential and dipole moment surfaces [31,48,49] conducting to RNT (Rey-Nikitin-Tyuterev) line lists as described in [12,42]. This is illustrated on Fig. 6: while the overview comparison of the CRDS spectra with the TheoReTS list at room temperature shows an excellent agreement. The enlargement around 6433 cm -1 shows a good coincidence between the experimental and ab initio intensities but some ab initio line positions show deviations on the order of 0.1 cm -1 or more. The Upper panels: Overview between 6150 and 6650 cm -1 . The alternate colors correspond to recordings performed with different distributed feed-back diode lasers Lower panels: Enlargement around 6433 cm -1 showing the good agreement for the line intensities and significant deviations of the line positions TheoReTS list (blue sticks). On the lowest panel, the red symbols correspond to the CRDS line list.

Table 2

Statistics for the empirical line lists of 13 CH4 in the 5695.3-5850.4 cm -1 region.

The intensity cut off of the TheoReTS lists is fixed to 1×10 -29 cm/molecule. Experimentally, this detection limit was achieved only in the most transparent region around 6400 cm -1 (see Fig. 1) and thus a considerable number of very weak calculated 13 intensities measured by CRDS between 6147 and 6653 cm -1 is 1.068×10 -21 cm/molecule while the sum of the ab initio intensities in the same spectral interval is 1.076×10 -21 cm/molecule. Such a good agreement within the experimental uncertainty on the intensity measurements might be fortuitous but it indicates that the missing lines have a very small contribution.

3.c. Rovibrational assignments

The TheoReTS line list does not provide full rovibrational assignment but only the J value, symmetry, ??? please complete Eugenia. In the 296K line list provided as Supplementary Material, we give a first set of 900 rovibrational assignments in the center of the window between 6284 and 6543 cm -1 . The assigned lines are highlighted on Fig. 4. The assignments were limited to cold band transitions of the icosad with line intensities larger than 2×10 -27 cm/molecule. They were obtained on the basis of the effective Hamiltonian (EH) model obtained in our previous analyses of cold spectra of 13 CH4 methane [1][2][3]. The initial non-empirical EH for the methane polyads was constricted? from the potential energy surface (PES) [4] and dipole moment surfaces (DMS) [5] via high order Contact Transformation (CT) procedure [6,7]. Then some diagonal EH and resonance coupling parameters were empirically optimized as the assignment and experimental data treatment progressed. Finally, the EH model describes 7077 observed and assigned lines transitions of the 13 CH4 tetradecad with rms deviation of 1.35×10 -3 cm -1 . Using this model a list of predicted ro-vibrational transitions for the range under investigation was created allowing us to assign 901 lines of the 5ν4 and ν 2+4ν4 bands of the icosad. The statistics of the assigned transitions is presented in Table 2 together with the predicted (quel genre de predictions?? Qd tu as P1, c'est une valeur experimentale?? ) values for band centers.

In the future, the assignments will be extended to the entire icosad for which a large set of Eemp values has been derived by the 2T-method []. Eugenya qqs phrases d'ouverture pour les attributions??

CONCLUDING REMARKS 975 lines in hitran

In this work, empirical line lists for 13 CH4 at 80 K and 296 K have been elaborated in the very congested center of the tetradecad (5695.32-5850.49 cm -1 excluding the 5718.82-5724.25 and 5792.75-5812.11 cm -1 intervals). The constructed lists include 3300 and 2070 lines at room temperature and liquid nitrogen temperature, respectively, allowing for the derivation of 1530 empirical values of the lower state energy level using the 2T-method. These results will be used together with the results of a similar study performed recently with natural methane in the same region [START_REF] Ghysels | The methane absorption spectrum near 1.73 μm (5695-5850 cm -1 ): Empirical line lists at 80 K and 296 K and rovibrational assignments[END_REF], to extend to lower energy the WKLMC list covering the 5852-7919 cm -1 range [17,23]. Note that the present DAS recordings were used in Ref. [START_REF] Ghysels | The methane absorption spectrum near 1.73 μm (5695-5850 cm -1 ): Empirical line lists at 80 K and 296 K and rovibrational assignments[END_REF] to identify the 13 CH4 lines present in the DAS spectra of natural methane (1.1 % relative concentration abundance).

The obtained experimental data will be valuable for extending theoretical studies of the isotopic effects [START_REF] Nikitin | Isotopic substitution shifts in methane and vibrational band assignment in the 5560-6200 cm -1 region[END_REF] in highly excited vibrational states of methane. In Ref. [START_REF] Ghysels | The methane absorption spectrum near 1.73 μm (5695-5850 cm -1 ): Empirical line lists at 80 K and 296 K and rovibrational assignments[END_REF], an important part of the 12 CH4 lines in the region were rovibrationnally assigned using an effective Hamiltonian model developed in Refs. [20][21][START_REF] Nikitin | Analysis of the absorption spectrum of 12 CH4 in the region 5855-6250 cm -1 of the 2ν3 band[END_REF]. The assignment of the experimental 13 CH4 lines reported in the present paper will benefit from ab initio predictions of the 12 C → 13 C isotopic shifts in vibrational band centers. These shifts (up to a few tens cm -1 , depending on the excited vibrational state) are predicted with an accuracy much higher than that of the absolute value of the band centers [START_REF] Nikitin | Isotopic substitution shifts in methane and vibrational band assignment in the 5560-6200 cm -1 region[END_REF]. As they are mostly constant for a given vibrational band, the calculated isotopic shifts allow finding one-to-one correspondence between 12 CH4 and 13 CH4 lines. Thus, the next step of the present project will be to transfer the 12 CH4 assignments of Ref. [START_REF] Ghysels | The methane absorption spectrum near 1.73 μm (5695-5850 cm -1 ): Empirical line lists at 80 K and 296 K and rovibrational assignments[END_REF] to the present 13 CH4 line lists on the basis of the predicted values of the vibrational isotopic shifts. The agreement between the obtained assignments and the Eemp values presently obtained will be used as validation tests.

The 13 CH4 HITRAN2016 line list in the region has GOSAT2009 origin [3] and consists of less than 400 lines from which only about 50 have associated lower state energy values (the rest are left with a 333.33 cm -1 default value). About one third of the HITRAN2016 assignments are found in contradiction with the observed temperature dependence of the intensity of the corresponding line. The comparison of the DAS spectra of 13 CH4 to the TheoReTS ab initio line list [12] indicates that the line lists constructed in this work will be valuable to adjust the ab initio positions to their empirical counterparts.

Fig. 3 .

 3 Fig. 3. Line parameter retrieval Upper panel: CRDS spectrum of 13 CH4 near 6213 cm -1 (P= 1.0 Torr, T= 297 K) Medium panel: fitted spectrum using a Voigt profile for each line and corresponding stick spectrum, Lower panel: Residuals between the simulated and experimental spectra. Each 40 cm -1 wide spectrum corresponding to one DFB recording was calibrated independently on the basis of the wavenumber values provided by a Fizeau type wavemeter (WSU-30 Highfinesse, 5 MHz resolution and 20 MHz accuracy). The calibration was refined using reference line positions of H2O (present as an impurity) from the HITRAN database [Gordon2017]. We estimate the uncertainty on the position of well isolated lines to be 1×10 -3 cm -1 .

Fig. 4

 4 Fig. 4 Overview of the 13 CH4 line list in the 1.58 µm transparency window. Upper panel: Lists at 296 K obtained in this work by CRDS (red), in Ref. [] and Ref. [] for the tetradecad and icosad regions (grey circles). Lines with full rovibrational assignment are highlighted in green. Lower panel: Lists at 80 K obtained in this work by DAS between 6545 and 6600 cm -1 (blue circles), in Ref. [] and Ref. [] for the tetradecad and icosad regions (grey circles). On the two panels, lines with lower state energy value derived by combining the present CRDS data at 296 K and the DAS data at 80 K are highlighted with light blue.

  Ref. [] for the description of the DAS spectrometer and cell cooled at liquid nitrogen temperature.Three DFB diodes were used to cover the 6545-6602 cm -1 interval. The comparison of the DAS spectrum at 80 K to the CRDS spectrum at room temperature presented in Fig.5illustrates the drastic change of the appearance of the spectrum by cooling. Depending on the lower state energy of the considered transitions, lines exhibit very different temperature dependence.

Fig. 5 .

 5 Fig. 5. Example of empirical lower state Jemp values derived for 13 CH4 transitions near 6584 cm -1 . Upper panel: CRDS spectrum at 297 K (P= 1.0 Torr) Lowerpanel: DAS spectrum at 80 K (P= 6.0 Torr) Empirical Jemp values derived by the 2T-method are indicated for the coinciding lines. Note the difference of sensitivity of the CRDS and DAS recordings.

The 13 CH4 4 .. 5 .

 1345 partition function for the corresponding temperatures was taken from HITRAN [6to the same transition at 296 K and 80 K were associated automatically when their line centers position coincidence criterion fixed to within 0.003 cm -1 . This value is about third of the Doppler full width of the13 CH4 line at 80 K and corresponds to the estimated combined error bars of the line center determinations. This position criterion allowed us deriving the Eemp values of 200 and 438 lines in the 6147-6200 cm -1 and 6547-6653 cm -1 interval, respectively. The associated lines are highlighted with light blue on Fig. As the sensitivity of the DAS recordings is significantly lower than that of the CRDS recordings, Eemp values were determined for most of the transitions of the 80 K dataset (about 80%). The lower state rotational quantum number, Jemp, was obtained using the rigid approximation, Eemp ≈ B0J(J+1) where B0= 5.214 cm -1 is the 13 CH4 principal rotational constant. The lower state empirical Jemp values were computed from As an example, the derived empirical J values have been indicated on the piece of the spectra displayed in Fig. In the displayed interval, the obtained Jemp values show a clear propensity to be close to integers. However, the insufficient sensitivity of the DAS recordings limits the accuracy of the intensity values at 80K and a significant number of Jemp values are not integer.

  present measurement will allow for a tuning of the calculated line positions according to experimental or empirical values.

Fig. 6 .

 6 Fig. 6. Comparison of the CRDS spectrum of 13 CH4 (P= 7.5 Torr) with the ab initio TheoReTS line list at 296 K. Upper panels: Overview between 6150 and 6650 cm -1 . The alternate colors correspond to recordings performed with different distributed feed-back diode lasers Lower panels: Enlargement around 6433 cm -1 showing the good agreement for the line intensities and significant deviations of the line positions TheoReTS list (blue sticks). On the lowest panel, the red symbols correspond to the CRDS line list.

  CH4 lines are missing in our list. The sum of the

		Sum of intensities (cm/molecule)	Number of lines	Number of Eemp
	This work	1.068×10 -21	13030	900 assignments /638 Eemp values
	TheoReTS [12]	1.076×10 -21	35427

Table 2 :

 2 Overview of the rovibrational assignments of the 13 CH4 spectrum at 296 K between 6284 and 6543 cm -1 . The vibrational sublevels are enumerated here for each band for a given symmetry type. The ranking n umbers within the Tetradecad are the following: a N= 1, N= 2, N= 3, and N= 4 for F2 1, F2 2, F2 3, F2 4; b N= 1 and N=2 for F1 1 and F1 2; c N=2, N=3, N= 4 and N=5 for E 1, E 2, E 3 and E 4; d N= 3, N=4, and N= 5 for F1 1, F1 2 and F1 3; e N= 2 and N= 3 for A1 1 and A1 2; f N= 5, N= 6 and N= 7 for F2 1, F2 2 and F2 3; g N= 1 and N =2 for A2 1 and A2 2.

	Band Sublevel	Band centre * (cm -1 )	Positions Nb. Jmin, Jmax
		F2 1 a	6342.372	58	1-8
		A1	6370.408	43	2-8
		F1 1 b	6393.259	100	1-8
	5v4	F2 2 a E	6413.726 6470.409	164 54	0-8 1-8
		F2 3 a	6470.611	88	0-8
		F1 2 b	6492.112	56	2-8
		F2 4 a	6501.303	101	1-8
		E 1 c	6589.064	33	4-8
		F1 1 d	6609.599	66	3-8
		A1 1 e	6626.582	1	8-8
	v2+4v4	F2 1 f	6628.235	22	6-8
		E 2 c	6651.817	4	4-8
		A2 1 g	6653.391	3	8-8
		F2 2 f	6687.808	36	5-8

) recordings at 1 Torr and 7.5 Torr are both available. Weaker lines are detected at 7.5 Torr but the strongest lines cannot be measured at that pressure. In that frequency interval, for each DFB laser diode, the line list was obtained by incorporating the 1 Torr line parameters of the strong lines in the 7.5 Torr line list.Then, impurity lines were systematically searched and removed from all the line lists. A significant number of water lines were detected above 6400 cm -1 . The presence of water is believed to be due to desorption from the cell. Water relative concentration was evaluated to be no more than

2×10 -3 . Lines of CO2 and very weak lines of acetylene were also identified with corresponding relative concentration less than 10 -4 and 5×10-7 . Finally, we checked that our lists do not include lines of the 12 CH4 major isotopologue, confirming the high isotopic purity of the used 13 CH4 sample.

Commenté [AC1]:Je comprends pas, cc'est evident?

Acknowledgments

This work was performed in the frame of the ANR project e_PYTHEAS (ANR-16-CE31-0005).