Mondelain

S Vasilchenko

A Campargue

S Kassi

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

µm windows by CRDS at room temperature

Keywords: Water vapor, self-continuum, foreign-continuum, MT_CKD model, CRDS, transparency windows

est destinée au dépôt

Introduction

Absorption of water vapour plays a key role in the radiative budget of the Earth's atmosphere [START_REF] Cubasch | Climate Change 2013: The Physical Science Basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change[END_REF]. This absorption corresponds to the sum of the narrow rovibrational absorption lines, hereafter named "local line monomer", with the broadband water vapour continuum, slowly varying in frequency. This latter contribution has its largest impact in transparency windows (or regions of weak monomer absorption) in contrast to the regions corresponding to the water vapour vibrational bands where the monomer contribution largely dominates. In a mixture of water vapour in air, like the Earth's atmosphere, two contributions of the continuum are present: (i) the self-continuum due to interactions between two water molecules and (ii) the foreign-continuum arising from interactions between water molecules and molecular oxygen and nitrogen. Despite decades of debates [START_REF] Shine | The Water Vapour Continuum: Brief History and Recent Developments[END_REF], the origin of the water continuum is unclear with different processes suggested to contribute: far wings of the rovibrational lines, water dimers (stable and metastable) 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].

The semi-empirical MT_CKD model (Mlawer-Tobin_Clough-Kneizys-Davies) [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] is the usual pragmatic way to take into account the continuum absorption contribution of the water vapour in atmospheric radiative transfer codes. This model assumes an empirical line profile applied to all the water monomer transitions, with intermediate and far line wings fitted to reproduce a selection of laboratory and atmospheric data. The MT_CKD model also includes an additional term called "weak interaction" term.

During the two last decades large efforts have been done to complete previous experimental data [START_REF] Burch | Continuum absorption by H 2 O[END_REF][START_REF] Burch | Continuum absorption by H 2 O in the 700 -1200 cm -1 and[END_REF][START_REF] Burch | Absorption by H 2 O in narrow windows between 3000 and 4200 cm -1[END_REF] and to better characterize the water vapour continuum, particularly in the infrared windows. Several laboratory studies were dedicated to the measurement of the self-continuum cross-sections using 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] and cavity-enhanced absorption spectroscopy (CEAS) including cavity ring down spectroscopy (CRDS) and optical feedback CEAS (OFCEAS) [START_REF] Cormier | Cavity ringdown spectroscopy measurements of the infrared water vapor continuum[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]. The FTS room temperature self-continuum cross-section values, in relatively good agreement to each other, were found largely higher than the MT_CKD_2.5 cross-sections in the centre of the 2.1 and 1.6 µm windows by factors greater than 20 [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] and 160 [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], respectively. On the other hand, as a result of their inherent higher sensitivity and high baseline stability, CEAS studies of our group provided datasets with reduced uncertainties. They were found in a much better agreement with the MT_CKD model [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]. Note that our CRDS and OFCEAS measurements [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] rely on the careful checking of the quadratic pressure dependence of the continuum absorption which provides a key criterion to ensure the gas phase origin of the spectrum baseline variation. This is not the case for the FTS results at room temperature which relied on single pressure spectra measurements in the windows. The latest version (3.2) of the MT_CKD self-continuum was constrained to the CEAS cross-sections in the 4.0, 2.1, 1.6 and 1.25 µm windows [17].

In fact, a pure quadratic pressure dependence was achieved in all our CRDS and OFCEAS studies of the water vapour self-continuum except in the 1.6 µm window where the weak continuum signal was found to include not only a pressure squared term but also a linear term in [START_REF] Mondelain | The water vapor self-continuum by CRDS at room temperature in the 1.6 µm transparency window[END_REF][START_REF] Mondelain | Temperature dependence of the water vapor self-continuum by cavity ring-down spectroscopy in the 1.6 µm transparency window[END_REF]. This linear term was tentatively interpreted as due to the adsorption of the water molecules on the high reflective mirrors of the CRDS cell. In this situation, the accuracy of our C s values in the 1.6 µm window was questioned [START_REF] Shine | The water vapour continuum in near-infrared windows -current understanding and prospects for its inclusion in spectroscopic databases[END_REF]. This is the reason why in the present contribution, we reconsider the 1.6 µm window where measurements are particularly demanding as a result of the weakness of the continuum in this window. In addition, the spectral coverage of this window will be extended on its two edges.

The foreign-continuum of water vapor in air is a major source of uncertainty to be constrained in Earth atmospheric models because, under standard conditions, it might account for a significant fraction of the absorbed incoming solar flux [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] Ptashnik | Water vapour foreign-continuum absorption in near-infrared windows from laboratory measurements[END_REF]. In the laboratory, the foreigncontinuum cross-sections are derived from spectra recorded with moist nitrogen (or air) which include both a foreign-and a self-contribution. As a result, the obtained foreign-continuum cross-sections, C F , are directly impacted by the self-continuum cross-sections values, derived separately with pure water vapor samples. The review included in [START_REF] Hartmann | Recent advances in collisional effects on spectra of molecular gases and their practical consequences[END_REF], indicates that only a few experimental studies of the water foreign-continuum are available. The reference [START_REF] Cormier | Infrared water vapor continuum absorption at atmospheric temperatures[END_REF] describing CRDS measurements at 944 cm -1 should be added to the seven references listed in Table 6 of Ref. [START_REF] Hartmann | Recent advances in collisional effects on spectra of molecular gases and their practical consequences[END_REF]. The FTS results obtained at NIST [START_REF] Baranov | The continuum absorption in H 2 O+N 2 mixtures in the 2000-3250 cm -1 spectral region at temperatures from 326 to[END_REF][START_REF] Baranov | H 2 O-N 2 collisioninduced absorption band intensity in the region of the N 2 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] and by 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] match and have led to a significant increase of the MT_CKD foreigncontinuum model in the transparency windows. Note that, in the limit of the reported error bars, the foreign-continuum has been found to be mostly temperature independent in the broad-band CAVIAR FTS measurements between 350 and 430 K. Similar weak temperature dependence results were reported in the infrared in the 296-363 K range [START_REF] Baranov | The continuum absorption in H 2 O+N 2 mixtures in the 2000-3250 cm -1 spectral region at temperatures from 326 to[END_REF][START_REF] Baranov | H 2 O-N 2 collisioninduced absorption band intensity in the region of the N 2 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].

In the following, we will present the experimental determination of the foreign-continuum by CRDS at room temperature for four new spectral points of the 2.3 µm window and the production of an extended dataset for the self-continuum cross-sections in the 1.6 µm window.

The rest of the paper is organized as follows. In the next section, the experimental setups used for the self-and foreign-continua measurements are detailed. The data analysis and the cross-sections retrievals are presented in Part 3 and 4 for the self-continuum in the 1.6 µm window and for the measurements in the 2.3 µm window, respectively. These two parts include a comparison to experimental data available in the literature and to the MT_CKD model, and a detailed analysis of the error budget. Notes a A previous determination (5.9(3)×10 -24 cm 2 molecule -1 atm -1 ) was obtained by OFCEAS in [START_REF] Ventrillard | Accurate measurements and temperature dependence of the water vapor self-continuum absorption in the 2.1 µm atmospheric window[END_REF].

b Previous CRDS measurements in the 5875-6665 cm -1 range (10 pts) were reported in [START_REF] Mondelain | The water vapor self-continuum by CRDS at room temperature in the 1.6 µm transparency window[END_REF][START_REF] Mondelain | Temperature dependence of the water vapor self-continuum by cavity ring-down spectroscopy in the 1.6 µm transparency window[END_REF].

Experimental setups and data acquisition

The CRDS spectrometers

Three cavity ring down spectrometers were used in this work. The 2.3 µm setup has been described in details in [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] Mondelain | The CO 2 absorption spectrum in the 2.3µm transparency window by high sensitivity CRDS: (II) Self-absorption continuum[END_REF] while readers are referred to [START_REF] Kassi | Cavity ring down spectroscopy with 5×10 -13 cm -1 sensitivity[END_REF] for the two setups used in the

= - (1)
With c the speed of light and the ring down time with the optical cavity empty or filled with a non-absorbing gas.

Depending on the spectral region, the minimal detectable absorption coefficient of our recorded spectra, α min , varies from 5×10 -11 cm -1 to a few 10 -10 cm -1 . Pressures were measured either with a 50 mbar or a 1000 mbar pressure gauge (ATM.1ST from STS, accuracy of ±0.1% of the full scale). The temperature of the CRDS cell was continuously measured by a temperature sensor (TSic 501 from IST, ±0.1 K accuracy) fixed on the external wall of the cavity enveloped by thermal insulation foam.

Self-continuum data acquisition

At the beginning of each day of measurements, the water sample was purified by cooling with liquid nitrogen and pumping on the residual vapour phase. To determine the self-continuum cross-sections, C S , the absorption coefficient at a selected spectral point was recorded during pressure ramps from 0 to 15 Torr (i.e. about 71% of the saturation pressure at 296 K). The only exception was for measurements near 5130 cm -1 where the water monomer contribution is particularly strong. Two spectra recorded in flow regime at 6 and 10 Torr were preferred to the spectral ramp at fixed frequency in order to better account for the water monomer contribution (see details below).

Foreign-continuum data acquisition

The measurements of the foreign-continuum absorption are more demanding as they require to vary either the water vapour partial pressure of a moist air sample at fixed high pressure (a few hundred Torr) or to vary the total pressure for a given water partial pressure by adding dry air to the CRDS sample. This last method used in [START_REF] Mondelain | The self-and foreign-absorption continua of water vapor by cavity ring-down spectroscopy near 2.35 µm[END_REF] is made difficult by the possible modification of the optical alignment of the CRDS setup due to the large pressure changes. In order to overcome this difficulty, we preferred the first method and recorded CRDS spectra for different water vapour partial pressures (determined from absorption lines as detailed in section 4.1), while maintaining the total pressure constant in the high finesse cavity. A purpose-built humidifier was developed and a flow of humidified air was injected into the CRDS cell for different controlled water vapour partial pressures up to about 6 Torr. The total pressure was regulated at 700 Torr, for most of the measurements, with a downstream proportional electrovalve controlled by a proportional-integral loop.

To vary the water vapour partial pressure in the dry air (Alphagaz 2 from Air Liquide), a syringe injection system, as described in details in [START_REF] Landsberg | Development of an OF-CEAS laser spectrometer for water vapor isotope measurements at low water concentrations[END_REF], was used (Fig. 1). In this system a water droplet formed at the end of the syringe needle evaporates continuously in the surrounding air flow of the mixing chamber. The evaporation rate is proportional to the surface area of the droplet in contact with air. When this evaporation rate equals to liquid water supply rate, a steady-state is reached. The partial pressure of water vapour depends also of the dry air flow which is regulated together with the total pressure. A small part of the humidified air is derived into the CRDS cell where the total pressure is regulated with a proportional valve. Depending on the liquid water injection rate and dry air flow, partial pressure of water vapour can be varied from 0 to 5.9 Torr in 700 Torr of air. This corresponds to a maximum relative humidity (RH) of 28% at 296 K. During the test phase, stabilities better than 0.3% were achieved over several tens of minutes for H 2 O partial pressure up to 3.5 Torr (17% RH at 296 K). Up to 6 Torr the system provides H 2 O partial pressure with stability better than the percent level. At higher pressure the system becomes less stable and no measurements were realized.

Self-continuum

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

, = ! " = #$ % ! , & #$ % " , ' (2)
where α cavity , α WML , α WCS and α WCF are the contributions due to the cavity, water vapor "monomer local lines" (WML), water vapor self-continuum (WCS) and foreign-continuum (WCF). C S and C F cross-sections are expressed in cm 2 molecule -1 atm -1 . Note that the negligible contribution of the Rayleigh scattering is omitted in Eq. (2). The data treatment of the pressure ramps is the same as described in our previous papers [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]. A simulation of the water vapor rovibrational spectrum, α WML , was performed at different pressures on the basis of the HITRAN2016 line list [START_REF] Gordon | The HITRAN2016 Molecular Spectroscopic Database[END_REF], using a Voigt profile and the standard [-25, +25 cm -1 ] convention cut off for the line wings. For each spectral point, the quantity (α tot -α WML ) = (α cavity + #$ % ! , recordings in the 1.6 µm window and the variation of the cross section versus the wavenumber. The C S values derived in this way are listed in Table 2 and presented in Fig. 3.

Self-continuum cross-sections retrieval

In the last column of Table 2, the monomer relative contribution to the total absorption, α WML/ (α WML +α WC ), is given at each spectra point. Obviously, the spectral points were chosen in order to minimize as much as possible the contribution of rovibrational lines. Overall, the monomer contribution represents less than 12 % for the spectral points below 6300 cm -1 and then increases up to 70 % on the high energy edge of the window. In the 2.3 µm window, self-continuum measurements were performed near 4720 cm -1 and in the 5121-5136 cm -1 interval. C S at 4720 cm -1 was already determined by OFCEAS in [START_REF] Ventrillard | Accurate measurements and temperature dependence of the water vapor self-continuum absorption in the 2.1 µm atmospheric window[END_REF] with a set of mirrors giving ring down times limited to 14 µs. The set of mirrors of our CRDS spectrometer provides ring down times of about 150 µs at 4720 cm -1 which should allow improving the sensitivity of the OFCEAS recordings. This is the reason why we decided to repeat the C S measurement at this spectral point. The C S derivation at 4720 cm -1 was based on pressure ramp recordings up to 15 Torr as in the 1.6 µm window. Similar quality of the pressure squared dependence was obtained. The derived C S value (6.3(2)×10 -24 cm 2 molecule -1 atm -1 ) is consistent with the OFCEAS value of 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] (5.9(3)×10 -24 cm 2 molecule -1 atm -1 ).

Two spectra at 10 Torr and one spectrum at 6 Torr were recorded over the 5121-5136 cm -1 interval accessible with the laser diode at disposal. Our choice to use a series of spectra instead of pressure ramps was motivated by the strong contribution of the monomer lines over the considered region. Indeed, in this situation, the uncertainty on the intensities of the strong lines located in the region (extended by ±25 cm -1 ) may have a strong impact on the derived foreign-continuum value. The recorded spectra were first corrected from the baseline retrieved from spectra recorded with the CRDS cell evacuated. Then the monomer contribution, simulated using the HITRAN2016 database, was subtracted. From the obtained residuals, eleven spectral points were selected in micro-windows between absorption lines. These points were chosen because we estimated that locally the monomer contribution (ranging between 39 and 92%) was satisfactorily accounted for by the HITRAN simulation.

For each spectral point, the C S values were derived from the remaining absorption (α tot -α WMLα cavity ) due to self-continuum (Eq. 2). As detailed below ( §3.4), the set of about 30 C S values was fitted by a linear function of the wavenumber. The recommended values at 5120 and 5135 cm -1 are included in Table 2.

Error budget

The stability of the spectrum baseline was checked over several hours from spectra recorded successively and found to be better than 2-5×10 -10 cm -1 i.e. at a level much below the level of the continuum absorption. In addition, the coincidence of the measured continuum absorption during increasing and decreasing pressure ramps together with the pure pressure squared dependence clearly indicate that the baseline instability during pressure ramps has a marginal contribution to the error budget. The error due to the measurement of the pressure is less than 0.04 Torr for the 50 mbar full range pressure gauge used for the self-continuum measurements and is thus also negligible.

For C S values derived from pressure ramps, the statistical error bars of the above pressure fits range between 0.03 and 2.3 %.

For a large part of the spectral points, the main source of uncertainty comes from the subtracted monomer contribution. This is especially true for the high energy edge of the 1.6 µm window and the 5130 cm -1 point where the monomer contribution represents between 20% and 72% of the total absorption above 6368 cm -1 and up to 92% of the total absorption around 5130 cm -1 (Table 2). Following the method proposed in Ref. [START_REF] Ptashnik | Evaluation of suitable spectral intervals for near-IR laboratory detection of water vapour continuum absorption[END_REF], we estimated the uncertainty due to the monomer lines by propagation of the uncertainties provided by HITRAN2016 for the different spectroscopic parameters of the water vapour lines. In practice, only the uncertainties on the line intensities and on the self-broadening coefficients, γ self , have to be considered. We performed two simulations, one with all line intensities increased by their respective error bar which led to a , - deviation from the usual HITRAN simulation and one with all γ self coefficients increased by their error bar which led to a , . /012 deviation. The uncertainty on α WML was obtained from:

, = 3, - & , . /012 & 4 /&
and is the dominant contribution to the error budget when the monomer contribution is important. At the opposite, in the centre of the 1.6 µm window, α WML represents no more than a few % and can be mostly neglected. In this case, a good indication about the error bar can be obtained from the dispersion of the experimental values. We have included in Fig. 3, the curve obtained from a 6 th order polynomial fit of the measurements between 5800 and 6700 cm -1 . The rms of the residuals is about 7×10 -26 cm 2 molecule -1 atm -1

i.e. about 25 % of the C s value at the centre of the window. The error bars included in Table 2 correspond to the largest value between , and 7×10 -26 cm 2 molecule -1 atm -1 and are believed to be conservative.

Comparison to literature values

The retrieved C S values in the 1.6 µm window listed in Table 2 are plotted in logarithmic scale in Fig. 4 together with the most relevant literature data, in particular the two series of measurements performed by FTS in Tomsk [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]. The present measurements in the 5702-6854 cm -1 range extend to the low-and high-energy edges of the window our previous CRDS datasets in the 5875-6665 cm -1 interval [START_REF] Mondelain | The water vapor self-continuum by CRDS at room temperature in the 1.6 µm transparency window[END_REF][START_REF] Mondelain | Temperature dependence of the water vapor self-continuum by cavity ring-down spectroscopy in the 1.6 µm transparency window[END_REF]. As mentioned above, in these previous works, the pressure dependence of the absorption continuum was found to include a linear pressure dependence. This linear contribution was relatively important in the centre of the window (see for example Fig. 4 of [START_REF] Mondelain | The water vapor self-continuum by CRDS at room temperature in the 1.6 µm transparency window[END_REF]) and prevented us to estimate properly the uncertainty on the C S values derived from the quadratic term. The overall agreement with the present recordings is satisfactory. Compared to Ref. [START_REF] Mondelain | Temperature dependence of the water vapor self-continuum by cavity ring-down spectroscopy in the 1.6 µm transparency window[END_REF], maximum deviations of about a factor of 2 are noted at 6022 and 6121 cm -1 . This is significantly above the combined error bars but the uncertainties in Ref. [START_REF] Mondelain | Temperature dependence of the water vapor self-continuum by cavity ring-down spectroscopy in the 1.6 µm transparency window[END_REF] were specified to exclude possible biases due to the adsorbate.

The higher quality of the present results performed with a new set of high reflective mirrors is illustrated by the purely quadratic pressure dependence obtained for all the measurement points (Fig. 2) and the reduced dispersion of the retrieved C S values (Fig. 3). The present results take thus precedence over the older ones.

The strong overestimation of the data retrieved from FTS spectra at room temperature in the centre of the 2.1 µm [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]] and 1.6 µm windows [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] has been discussed in details in of the absorption measured by Bicknell. The propagation of the large uncertainty on the used C F value leads to an uncertainty on C S larger than its absolute value. Fortuitously, the derived self-continuum cross-section (2.5×10 -25 cm 2 molecule -1 atm -1 ) is consistent with our measurements (see Fig. 4).

The overall agreement with the MT_CKD_3.2 semi-empirical cross-sections model is very good. This is not surprising as the MT_CKD_3.2 continuum was adjusted according to our previous CRDS results obtained below 6600 cm -1 [START_REF] Mondelain | Temperature dependence of the water vapor self-continuum by cavity ring-down spectroscopy in the 1.6 µm transparency window[END_REF]. We note that the agreement extends to the new measurement points above this wavenumber. Important differences (up to a factor 2.3) are nevertheless observed on the newly measured low energy edge around 5700 cm -1 .

The experimental results indicate that the MT_CKD continuum should be significantly reduced in this region

Figure 5. Overview of the experimental self-continuum cross-sections, C S , reported in the literature and retrieved in this work (blue diamonds) for the 2.3 µm window and comparison to the MT_CKD_3.2 continuum. Literature values include FTS values from

Ref. [START_REF] Ptashnik | Near-infrared water vapour self-continuum at close to room temperature[END_REF] (Tomsk2013), Ref. [START_REF] Ptashnik | Water vapor continuum absorption in near-IR atmospheric windows[END_REF] (Tomsk2015) and CAVIAR [START_REF] Ptashnik | Water vapor self-continuum absorption in near-infrared windows derived from laboratory measurements[END_REF]. The C S value at 4605 cm -1 (purple star) was derived from the measurement of Bicknell et al. by interferometric calorimetry of a water vapour+N 2 mixture [START_REF] Bicknell | Search for low-absorption regions in the 1.6-and 2.1-µm atmospheric windows[END_REF]; the plotted value is corrected from the foreign-contribution (see Text). Open red circles correspond to the OFCEAS and CRDS values of 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] and Refs [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], respectively. In the insert, the series of measurements performed from three spectra near 5130 cm -1 are highlighted with diamonds filled with different colors. The recommended values correspond to the black solid line obtained from a fit of the measurement points.

The new C S values between 5120 and 5137 cm -1 concern the high energy edge of the 2.3 µm window where CRDS measurements were missing. As mentioned above, they were obtained from a series of three spectra recorded at 6 and 10 Torr and extend over the 5121-5138 cm -1 interval. The different series of measurement points, highlighted in the insert of The present and previous CRDS and OFCEAS data in the 2.3 µm window [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] Ventrillard | Accurate measurements and temperature dependence of the water vapor self-continuum absorption in the 2.1 µm atmospheric window[END_REF] are plotted in Fig. 5 together with FTS data from Refs. [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]. Similarly to the 1.6 µm window, the current 3.2 version of the MT_CKD continuum was adjusted to our previous measurements below 4800 cm -1 [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] Ventrillard | Accurate measurements and temperature dependence of the water vapor self-continuum absorption in the 2.1 µm atmospheric window[END_REF]. Near 5130 cm -1 , the present results are found to be about a factor 1.5 smaller than MT_CKD_3.2 values. The agreement with the FTS values, in particular with Tomsk2015 [START_REF] Ptashnik | Water vapor continuum absorption in near-IR atmospheric windows[END_REF], is significantly better than for the other CRDS spectral points of the window. This agreement results from the strong value of C S at 5130 cm -1 (about 4×10 -23 cm 2 molecule -1 atm -1 ) which is close to the mostly constant FTS values reported near room temperature between 4400 and 5000 cm -1 [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] and between 5700 and 6700 cm -1 [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] and that can be considered as the detectivity threshold of the CAVIAR and Tomsk setups.

We have also considered the room temperature measurement reported by Bicknell et al. by calorimetric interferometry near 4605 cm -1 for a mixture of 14.7 Torr of water vapour in N 2 at a total pressure of 770 Torr [START_REF] Bicknell | Search for low-absorption regions in the 1.6-and 2.1-µm atmospheric windows[END_REF]. The calculated monomer contribution (7×10 -9 cm -1 ) was subtracted from the total absorption (1.0×10 -7 cm -1 ) obtained from Fig. 8 of Ref. [START_REF] Bicknell | Search for low-absorption regions in the 1.6-and 2.1-µm atmospheric windows[END_REF]. The foreign-contribution in the conditions of Ref. [START_REF] Bicknell | Search for low-absorption regions in the 1.6-and 2.1-µm atmospheric windows[END_REF] was determined using the C F value (6.7×10 -26 cm 2 molecule -1 atm -1 ) interpolated from our C F determinations at 4522.0 and 4724.1 cm -1 (see below and Table 1). As a result, we obtain a C S value of 6.7×10 -24 cm 2 molecule -1 atm -1 , included in Fig. 5, which shows a very good consistency with our results.

4 Foreign-continuum

Cross-section retrieval

As mentioned above the foreign-continuum measurements were performed on the basis of spectra recorded over a few cm -1 around 4435, 4522, 4720 and 4999 cm -1 . The recordings were performed in flow regime with constant total pressure (generally 700 Torr) and different partial pressures of water vapour up to 6 Torr. For each water concentration, two successive spectra were recorded to check the concentration stability. All the spectra were first corrected from the background spectrum obtained with dry air at the same total pressure to ensure no change in the mirror alignment. As very small losses due to Rayleigh scattering are mostly identical in this background and in the moist air spectra, the Rayleigh contribution was omitted in Eq. ( 2). For each recorded spectrum, the water vapour partial pressure, , was determined from a line profile fit of a few isolated water lines. Water lines with low uncertainty intensity values were taken from the HITRAN2016 database. The water monomer contribution was then simulated for the experimental conditions of the recordings -, P tot , Tusing the HITRAN2016 database and the usual [-25 cm -1 , +25 cm -1 ] line profile cut-off. This α WML contribution was then subtracted from (α tot -α cavity ) together with the absorption contribution of the self-continuum, α WCF . The latter was calculated using the self-continuum cross-section values determined in our previous works and the value at 4720 cm -1 updated in this work (see Table 1). Figure 6 shows the different contributions to the absorption continuum near 4520 cm -1 . For a partial pressure of water vapour of about 6 Torr in air at a total pressure of 700

Torr, the self-and foreign-contributions have similar amplitude, the monomer lines contribution being smaller at this spectral point. The different foreign-continuum crosssection values given in Table 1, were retrieved from the fitted slope of (α totα cavityα WMLα WCS ) versus ' (see Eq. 2). Fig. 7 shows the achieved linear dependence for four measurement points. Figure 7. Foreign-continuum absorptions at the selected spectral points and corresponding fitted slopes (solid lines).

Comparison to literature values

The comparison of the available experimental determination of the foreign-continuum crosssections in the 2.3 µm window to the MT_CKD_3.2 values is presented in Fig. 8.

Experimental data at room temperature are limited to the present determinations around four spectral points and our previous CRDS data point at 4250 cm -1 [START_REF] Mondelain | The self-and foreign-absorption continua of water vapor by cavity ring-down spectroscopy near 2.35 µm[END_REF]. The CAVIAR consortium reported foreign-continuum absorption by FTS between 1. In the centre of the window, the CRDS dataset shows a disagreement of typically a factor 5 with the cross-sections given by the MT_CKD_3.2 model. The agreement is much better for the two measurement points on the low and high energy range of the window (at 4250 and 4999 cm -1 , respectively). In fact the MT_CKD foreign-continuum was recently significantly increased in the 2.3 µm window, taking into account our CRDS value at 4250 cm -1 [START_REF] Mondelain | The self-and foreign-absorption continua of water vapor by cavity ring-down spectroscopy near 2.35 µm[END_REF] and the NIST values [START_REF] Baranov | The water vapour self-and water-nitrogen continuum absorption in the 1000 and 2500 cm -1 atmospheric windows[END_REF] (the MT_CKD_2.5 is included in Fig. 8, for comparison). The obtained CRDS results indicate that the MT_CKD foreign-continuum should be significantly increased in the centre of the window, too. [START_REF] Ptashnik | Water vapour foreign-continuum absorption in near-infrared windows from laboratory measurements[END_REF] (open black circles) and the CRDS value at 4250 cm -1 of Ref. [START_REF] Mondelain | The self-and foreign-absorption continua of water vapor by cavity ring-down spectroscopy near 2.35 µm[END_REF].

Error budget

Uncertainties on the derived C F values have been calculated with the error propagation approach using Eq. 2 and assuming uncorrelated variables. In general, error bars on C F are expected to be larger than those on C S , as the foreign continuum is the residuals obtained after subtraction of the self-continuum and monomer contributions. From spectra recorded successively with the same amount of water vapour, the baseline stability was evaluated to be in the 5-8×10 -10 cm -1 range, depending on the measurement point. Uncertainties on temperature and total pressure are deduced from the accuracies given by the temperature sensor and pressure gauges manufacturers and are mostly negligible. The C S values and corresponding error bars were taken in our original paper (see Table 1), except near 4724 cm -1 where we used the results obtained in this work.

The water vapour partial pressure is a major error source as it impacts both the self-continuum contribution proportional to & and the monomer contribution proportional to . As mentioned above, this quantity was retrieved from the area of well-isolated H 2 O lines fitted with a Voigt profile using their HITRAN2016 intensity values. The relative uncertainty on is mostly determined by the error bar on the intensity value, the uncertainty on the fitted area being negligible. It leads to error bars on the order of 5% for all the measurement points but the 4999.0 cm -1 spectral point where a 10 % value was adopted.

The uncertainty due to the monomer contribution, α WML , was calculated in the same way as Combining the different error sources, we obtained, for each spectral point, the error bar on " for each value (see Fig. 7). The final C F uncertainty included in Table 1 was calculated as the square root of the variance of the linear fit of the foreign absorption coefficient versus ' as illustrated in Fig. 7. In this fit, each data point was weighted according to its error bar, the weight being taken as the inverse of the squared uncertainty.

Finally, we considered the possible contribution of the N 2 collision induced absorption (CIA) band near 4630 cm -1 to the foreign-continuum measurements at 4720 cm -1 . This weak CIA band corresponds to the 2-0 first overtone band of N 2 . Experimentally, it was investigated at room temperature [START_REF] Shapiro | The collision-induced fundamental and first overtone bands of oxygen and nitrogen[END_REF] and at 97.5 K [START_REF] Mckellar | Low-temperature infrared absorption of gaseous N 2 and N 2 + H 2 in the 2.0-2.5 µm region: Application to the atmospheres of Titan and Triton[END_REF], a long time ago. Very recently, Hartmann et al.

performed classical molecular dynamic simulations (CMDS) of the 2-0 N 2 CIA [START_REF] Hartmann | Collision-induced absorption by N 2 near 2.16µm: Calculations, model, and consequences for atmospheric remote sensing[END_REF] and achieved a very satisfactory agreement with these pioneer experimental works. Note that, near its maximum, the amplitude of the CIA absorption for N 2 at 1 atm is about 10 -8 cm -1 , i.e. on the same order of magnitude as the absorption due to the foreign-continuum of 5 Torr of water vapour in 1 atm of air. The experimental procedure adopted in this work for the foreigncontinuum measurements excludes a possible bias due to the contribution of the N 2 2-0 CIA.

Indeed, the baseline of the background spectrum recorded with dry air at 700 Torr includes the N 2 CIA in air which is thus subtracted from the spectrum of moist air. A marginal contribution of the CIA may nevertheless be possible due to the fact that for a given total pressure, a few Torr of air in the background spectrum are replaced by water vapour. The enhancement of the N 2 CIA by water vapour has been evidenced by Baranov [25] in the region of the 1-0 fundamental band. Nevertheless, CMDS calculations indicate that for the 2-0 pressure conditions.

Conclusion

In the present work, the accuracy of the self-continuum cross-sections of water vapor has been improved by CRDS in the 1.6 µm window and at the 4720 cm -1 spectral point of the 2.3 µm window. In addition, the spectral coverage of the 1.6 µm window was extended at low and high energies and a new spectral point of the 2.3 µm window was measured at 5130 cm -1 . In the context of the debate about the large discrepancies between FTS and laser-based measurements at room temperature in the transparency windows [START_REF] Shine | The water vapour continuum in near-infrared windows -current understanding and prospects for its inclusion in spectroscopic databases[END_REF], our first measurements in the 1.6 µm were questioned because a non purely quadratic pressure squared dependence was observed. In these earlier CRDS works, the sensitivity of the CRDS technique allowed evidencing and measuring a small absorption signal proportional to the water vapor pressure which was attributed to water adsorbed on the mirrors used at that time. This linear term added some uncertainty to the derived C S values. In the present recordings performed with a better set of high reflective mirrors, a pure pressure squared dependence is obtained for all the measurement points. Although showing a general agreement with the present more accurate results, cross section values reported in Refs. [START_REF] Mondelain | The water vapor self-continuum by CRDS at room temperature in the 1.6 µm transparency window[END_REF][START_REF] Mondelain | Temperature dependence of the water vapor self-continuum by cavity ring-down spectroscopy in the 1.6 µm transparency window[END_REF] were partly affected by errors related to adsorption.

As the 3.2 version of the MT_CKD model in the 2.3 and 1.6 µm windows was constrained according to our previous measurements, the overall agreement is very good. The most significant deviations concern newly measured spectral points in the low energy edge of the 1.6 µm window near 5700 cm -1 and in the high energy edge of the 2.3 µm window near 5130 cm -1 where measurements are lower than MT_CKD by about a factor of 2 and 1.5, respectively.

In general, accurate measurements of the water vapor foreign-continuum are more demanding as the C F cross-sections are directly impacted by the uncertainty on the water vapor partial pressure in moist air used for the measurements and by the uncertainties on the selfcontinuum and on the water monomer contributions. In this work, C F values were newly determined with error bars ranging between 4 and 22 % at four spectral points of the 2.3 µm window, between 4430 and 5000 cm -1 . The measurements are found consistent with the previous CRDS measurement at 4250 cm -1 [START_REF] Mondelain | The self-and foreign-absorption continua of water vapor by cavity ring-down spectroscopy near 2.35 µm[END_REF] which has led to an increase of the MT_CKD foreign continuum at this spectral point. The new measurements confirm the underestimation of the MT_CKD continuum in the centre of the 2.3 µm window where an increase by a factor of 5 is suggested.

Figure 1 .

 1 Figure 1. Scheme of the air humidifier based on a syringe injection system.

Figure 2 .

 2 Figure 2. Self-continuum absorption versus the squared water vapor pressure during pressure ramps up to 15 Torr for different spectral points of the 1.6 µm window. The self-continuum cross-section values were derived from the linear fits (black lines).

Notea

  The listed C s values were derived from the frequency dependence of C s values at various measurement points in the 5121-5138 cm -1 interval. Depending of the selected spectral point, the monomer contribution represents between 39 and 92 % of the total absorption (see Text and insert in Fig.4).

Figure 3 .

 3 Figure3. Overview of the self-continuum cross-sections, C S , in the 1.6 µm window. Black stars show the CRDS values of Ref.[START_REF] Mondelain | Temperature dependence of the water vapor self-continuum by cavity ring-down spectroscopy in the 1.6 µm transparency window[END_REF]. The grey curve corresponds to a 6 th order polynomial fit of the present measurements (blue diamonds) in the 5800-6700 cm -1 interval: %= ∑ ) * +with a i coefficient values of 2.69348×10 -17 , -2.60041×10 -20 , 1.04584×10 -23 , -2.24283×10 -27 , 2.70491×10 -31 , -1.73944×10 -35 and 4.65967×10 -40 .

Fig. 5 ,

 5 show a clear increase with the wavenumber values. The set of about 30 C S values was fitted by a linear function of the wavenumber. The corresponding fitted values at 5120 and 5135 cm -1 are given in Table2. Taking into account the statistical averaging of the error bars which are mostly due to the uncertainties on the water monomer, we estimate to ~2×10 -23 cm 2 molecule -1 atm -1 the resulting error bars which represents 54% and 42% of the C s value at 5120 cm -1 and 5135 cm -1 , respectively. Note that only 2% dispersion is observed around the linear function fitted to the ~30 C S values in the 5121-5138 cm -1 interval which might indicate that the estimated error bar are overestimated.

Figure 6 .

 6 Figure 6. Part of the spectrum recorded around 4522 cm -1 for a mixture of water vapour in air (5.85 Torr of H 2 O in 693.35 Torr of air) and corrected from the background spectrum recorded with dry air at the same total pressure. The "local line monomer", self-continuum and foreign-continuum contributions are indicated. The red arrow shows one of the selected measurement points.

1 and 5 8 .

 58 µm at high temperatures (350-431 K) with an absorption path length of 17.7 m. The chosen elevated temperatures allow increasing the water vapour partial pressure of the recordings between 266 and 600 mbar. Compared to our measurement conditions (less than 6 Torr of water in air at about 1 atm), these high water vapour pressure values combined with air pressure of about 4 atm led to an increase of the foreign-continuum absorption signal by two or three orders of magnitude. The FTS recordings between 350 and 431 K did not reveal temperature dependence greater than the uncertainty in those measurements. The C F values at the 400 K average temperature reported by Ptatshnik et al. [22] are plotted on Fig. Note that the MT_CKD foreign-continuum also included in the figure is assumed to be temperature independent. Our room temperature C F values are systematically below the FTS values (at 400 K) by a factor between 2 and 4. Although the FTS values were reported with very large error bars (between 30 and 93 %), the CRDS values fall outside the 1σ FTS confidence interval except at 4724 cm -1 . If these FTS values at 400 K are confirmed, it would indicate that the foreign-continuum exhibits small positive temperature dependence.

Figure 8 .

 8 Figure 8. Overview of the foreign-continuum cross-sections, C F , reported in the literature and retrieved in this work for the 2.3 µm window and comparison to the MT_CKD model in its versions 3.2 (red) and 2.5 (black). Previous experimental determinations are limited to the CAVIAR FTS valuesat 400 K from Ref.[START_REF] Ptashnik | Water vapour foreign-continuum absorption in near-infrared windows from laboratory measurements[END_REF] (open black circles) and the CRDS value at 4250 cm -1 of Ref.[START_REF] Mondelain | The self-and foreign-absorption continua of water vapor by cavity ring-down spectroscopy near 2.35 µm[END_REF].

presented in Section 3 . 3

 33 for the self-continuum. The error bars on the line intensities, selfbroadening and air-broadening coefficients were considered together with the uncertainty on the water vapour pressure. Four simulations, , , were performed, each of them with either, the intensities, γ self , γ air coefficients or values increased by their error bar. The uncertainty on α WML was obtained from: ,

Table 1 .

 1 Spectral points selected for the present continua measurements by CRDS in the 2.3 and 1.6 µm windows and corresponding self-and foreign-continuum cross-sections values. TW (This work) marks the newly derived values.

	Window Approx. center	Measurement points (cm -1 )	C S (cm 2 molecule -1 atm -1 )	C F (cm 2 molecule -1 atm -1 )
		4432.6	1.19(6)×10 -23 [15]	1.26(5)×10 -25 (TW)
	4700 cm -1	4436.3 4522.0	1.18(6)×10 -23 [15] 9.33(25)×10 -24 [14]	1.15(5)×10 -25 (TW) 8.10(36)×10 -26 (TW)
	(2.1 µm)	4724.1	6.30(16)×10 -24 (TW) a	4.44(43)×10 -26 (TW)
		4999.0	7.76(39)×10 -24 [16]	8.3(18)×10 -26 (TW)
		5121-5136 (10 pts)	3.70(20)×10 -23 -4.80(20)×10 -23 (TW)
	6300 cm -1 (1.6 µm)	5702-6854 (30 pts)	2.3×10 -25 -1.9×10 -23 (TW) b

are listed in Table 1. The set of DFB laser diodes at disposal

	absorbing gas, α(ν), is then derived from the fitted RD time, at the laser frequency ν, with the
	following equation:
	1.6 µm region. Briefly, a distributed feedback (DFB) laser diode (either from Eblana
	Photonics or NEL) is coupled into a high finesse cavity composed of two mirrors with highly
	reflective coatings. The different measurement points in the 2.3 µm window (near 4435, 4522,
	4724, 4999 and 5130 cm -1 ) allows for a continuous coverage of the 1.6 µm window. Thirty spectral points were selected
	to sample the 5702-6854 cm -1 spectral range. Each spectrometer employed mirrors (from
	Layertec) with coatings optimized for each of the spectral range of interest. Resonance
	between the laser emitted frequency, measured with a wavelength meter (model 621-A IR
	from Bristol), and a longitudinal mode of the optical cavity is achieved by dithering the cavity
	length with the output mirror mounted on a piezoelectric transducer. After filling of 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 absorption coefficient of the

Table 2 .

 2 Self-continuum cross-sections in the 1.6 and 2.3 µm windows and corresponding relative contribution of the "local line monomer" to the total absorption. During the whole period of measurements temperature varied between 296 K and 298.5 K.

	ν cm -1	C S cm 2 molecule -1 atm -1	α WML/ (α WML +α WC ) %
		2.3 µm window
	4724.07	6.30(16)×10 -24	4.0
	5120.00	3.7(20)×10 -23	a
	5135.00	4.8(20)×10 -23	a
		1.6 µm window
	5702.13	5.83(13)×10 -24	11.91
	5752.04	4.43(6)×10 -24	10.07
	5780.40	3.66(7)×10 -24	6.57
	5816.58	3.04(7)×10 -24	3.53
	5842.21	2.68(7)×10 -24	3.70
	5875.22	1.97(7)×10 -24	3.65
	5905.72	1.59(7)×10 -24	2.72
	5934.64	1.31(7)×10 -24	2.07
	5971.09	1.04(7)×10 -24	5.33
	6022.06	8.7(7)×10 -25	3.09
	6064.57	6.5(7)×10 -25	6.08
	6076.35	6.4(7)×10 -25	15.28
	6082.69	5.8(7)×10 -25	1.18
	6121.24	4.9(7)×10 -25	1.95
	6164.68	3.3(7)×10 -25	1.44
	6224.09	2.8(7)×10 -25	2.53
	6311.03	2.5(7)×10 -25	12.87
	6368.98	2.4(7)×10 -25	18.72
	6422.57	3.2(7)×10 -25	19.82
	6511.97	4.8(7)×10 -25	38.77
	6562.18	5.8(7)×10 -25	32.85
	6613.97	1.00(7)×10 -24	40.56
	6637.62	1.46(10)×10 -24	39.78
	6665.27	2.14(14)×10 -24	39.49
	6683.95	3.59(96)×10 -24	72.08
	6714.74	7.3(10)×10 -24	66.33
	6739.76	9.30(96)×10 -24	57.07
	6762.79	1.56(17)×10 -23	58.11
	6808.32	1.59(17)×10 -23	62.63
	6854.65	1.87(10)×10 -23	42.26

&was plotted versus & and fitted by a linear function. The constant term corresponds to the absorption losses of the empty cavity, α cavity , while the self-continuum cross-section is obtained from the fitted value of the linear coefficient in & . Fig.2illustrates the pure quadratic dependence achieved in the present

Acknowledgments

This project is supported by the Labex OSUG@2020 (ANR10 LABX56) and the LEFE-ChAt program from CNRS-INSU. The authors want to thank J.-M. Hartmann (LMD) for providing them classical molecular dynamic calculations of the N 2 CIA in a N 2 -H 2 O mixture.

our previous contributions (see for example Ref. [START_REF] Campargue | Accurate laboratory determination of the near infrared water vapor self-continuum: A test of the MT_CKD model[END_REF]). To our opinion, the FTS sensitivity and baseline stability of the FTS setups used are not sufficient for such measurements of weak continua. As a rule, reported C S values should be systematically supported by a solid study of the pressure dependence of the absorption signal. For example no pressure dependence was reported in the FTS room temperature studies of Refs. [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]. Literature values were obtained by FTS in Ref. [START_REF] Ptashnik | Near-infrared water vapour self-continuum at close to room temperature[END_REF] (Tomsk2013), Ref. [START_REF] Ptashnik | Water vapor continuum absorption in near-IR atmospheric windows[END_REF] (Tomsk2015) and Ref. [START_REF] Ptashnik | Water vapor self-continuum absorption in near-infrared windows derived from laboratory measurements[END_REF] (CAVIAR), by photoacoustic spectroscopy in Ref. [START_REF] Kapitanov | Photoacoustic measurements of the water vapor continuum absorption in the 1.6 µm window[END_REF]), by interferometric calorimetry in Ref. [START_REF] Bicknell | Search for low-absorption regions in the 1.6-and 2.1-µm atmospheric windows[END_REF](pink star) and by CRDS in Ref. [START_REF] Mondelain | The water vapor self-continuum by CRDS at room temperature in the 1.6 µm transparency window[END_REF](grey triangles) and Ref. [START_REF] Mondelain | Temperature dependence of the water vapor self-continuum by cavity ring-down spectroscopy in the 1.6 µm transparency window[END_REF] (black stars)

A photoacoustic measurement was very recently reported by Kapitanov et al. [START_REF] Kapitanov | Photoacoustic measurements of the water vapor continuum absorption in the 1.6 µm window[END_REF] for the room temperature self-continuum at 6177 cm -1 . The reported C S value (5.4±0.8×10 -24 cm 2 molecule -1 atm -1 ) included in Fig. 4, is intermediate between the FTS and CRDS values. For completeness, the value at 6150 cm -1 reported by Bicknell et al. by calorimetric interferometry [START_REF] Bicknell | Search for low-absorption regions in the 1.6-and 2.1-µm atmospheric windows[END_REF] is added. Bicknell et al. performed only measurements for water vapor in N 2 at a total pressure of 770 Torr. The plotted C S value at 6150 cm -1 is derived from the total continuum absorption of 3.2±0.3×10 -8 cm -1 measured in [START_REF] Bicknell | Search for low-absorption regions in the 1.6-and 2.1-µm atmospheric windows[END_REF] after subtraction of the foreign-continuum contribution. The latter is obtained from the CAVIAR foreign cross-section measured at 400 K in [START_REF] Ptashnik | Water vapour foreign-continuum absorption in near-infrared windows from laboratory measurements[END_REF] (C F = 3.2±2.8×10 -26 cm 2 molecule -1 atmosphere -1 ) assuming no temperature dependence. No water vapour partial pressure was given in [START_REF] Bicknell | Search for low-absorption regions in the 1.6-and 2.1-µm atmospheric windows[END_REF] but a value of 25 Torr was estimated in [START_REF] Ptashnik | Near-infrared water vapour self-continuum at close to room temperature[END_REF]. As a result, the foreign-continuum is calculated to contribute to about 75 %