Effect of water vapour absorption on hydroxyl temperatures measured from Svalbard

We model absorption by atmospheric water vapour of hydroxyl airglow emission using the HIghresolution TRANsmission molecular absorption database (HITRAN2012). Transmission coefficients are provided as a function of water vapour column density for the strongest OH Meinel emission lines in the (8–3), (5–1), (9–4), (8–4), and (6–2) vibrational bands. These coefficients are used to determine precise OH(8–3) rotational temperatures from spectra measured by the High Throughput Imaging Echelle Spectrograph (HiTIES), installed at the Kjell Henriksen Observatory (KHO), Svalbard. The method described in this paper also allows us to estimate atmospheric water vapour content using the HiTIES instrument.


Introduction
A layer of excited hydroxyl molecules near the mesopause is responsible for strong airglow emission that can be detected over a wide wavelength range.First identified by Meinel (1950a, b), this emission is produced by molecular vibration-rotation transitions.It is possible to derive rotational OH temperatures by determining ratios between emission lines.If one considers that the lower rotational and vibrational states have undergone enough collisions to be in local thermodynamic equilibrium (LTE), then the neutral atmospheric temperature can be assumed to match the rotational hydroxyl temperature.This method has been used by many authors to calculate mesospheric temperatures (e.g.French et al., 2000;Phillips et al., 2004;Suzuki et al., 2010;Holmen et al., 2014a).In this study, we use the same nomenclature as Phillips et al. (2004) to describe hydroxyl emissions, as detailed in Appendix A of that paper.
OH temperatures have been derived in previous works using different vibrational bands, depending on the wavelength range of the spectroscope in use.French et al. (2000) and Holmen et al. (2014a) measured the OH(6-2) band, Phillips et al. (2004) compared OH(6-2) band observations with measurements from OH(8-3), and Suzuki et al. (2010) made use of the OH(8-4) band.In this study, we use Hi-TIES, the High Throughput Imaging Echelle Spectrograph (Chakrabarti et al., 2001), part of the Spectrographic Imaging Facility (SIF), located at the Kjell Henriksen Observatory (KHO), Svalbard (78.148 • N, 16.043 • E), to record hydroxyl emission line intensities.We use the HiTIES filter panel with a bandpass from 728 to 740 nm, allowing measurement of the OH(8-3) band.The emission peak altitude is dependent on vibrational level (von Savigny et al., 2012), the mean thickness of the OH layer being about 8 km (Baker and Stair, 1988) with higher vibrational levels located at the top of the layer and vice versa.Due to the spread in altitude of the different vibrational excited states, there is expected to be a difference in the rotational temperatures derived from emission from different vibrational bands.The temperature difference between bands is thought to vary from a few kelvin to up to 20 K between bands with the largest difference in upper vibrational state ν (Cosby and Slanger, 2007;von Savigny et al., 2012;Noll et al., 2015Noll et al., , 2016)).
A difficulty in determining accurate temperatures from OH lines is the absorption of this emission by other atmospheric species, in particular water vapour.Phillips et al. (2004) found that water vapour absorption decreases the intensity of the OH(8-3) P 1 (4) line by 2.3 %, affecting the temperature derived using a ratio between this line and other Pbranch lines in the (8-3) band by up to 17 K.This calculation was carried out only for average winter conditions at Davis Station, Antarctica; however, this absorption is dependent on the concentration of water vapour in the atmosphere, which is highly variable, and will also be on average higher at lower latitudes.
To quantify the effects of atmospheric absorption on OH emission, Espy and Hammond (1995) modelled atmospheric absorption of a number of species (such as H 2 O, CO 2 , and O 3 ), as well as OH line profiles to provide transmission coefficients for OH Meinel rotational lines in a number of different vibrational bands.These coefficients are provided for four different atmospheric conditions: mid-and high-latitude summer, and mid-and high-latitude winter.Unfortunately, their table giving transmission coefficients for the OH(8-3) (Table 6) is a repeat of the OH(6-2) table (Table 5) and is thus erroneous.
In this work, we model water vapour absorption in the atmosphere and provide transmission of various OH Meinel band lines as a function of the concentration of atmospheric H 2 O. Whereas Espy and Hammond (1995) provided transmission values for four discrete concentrations of water vapour, here we provide the transmission as a continuous function of water vapour concentration.This paper is organised as follows: Sect. 2 describes the instruments, models, and methods used in this study; Sect. 3 provides the transmission coefficients for OH lines; and Sect. 4 shows the effect of water vapour absorption on temperatures derived from OH lines in the (8-3) vibrational band measured by HiTIES.

Modelling water vapour absorption
The transmission of emission at a given wavelength λ as it passes through the atmosphere can be determined using the Beer-Lambert law: where τ is the optical depth, σ abs H 2 O is the absorption cross section of H 2 O, n H 2 O is the number density of H 2 O, and z is the altitude.This expression gives the optical depth over a column of atmosphere between z = z OH , the altitude at which the hydroxyl emission occurs, and z = 0, where the instruments measuring the emission are located.Equation ( 1) is valid for a vertical beam, where there is only extinction in the beam (i.e.no emission within the beam or scattering into the beam).The transmission coefficient can then be obtained from (2) To determine the absorption cross section, we use the latest version of the HIgh-resolution TRANsmission molecular absorption database, HITRAN2012 (Rothman et al., 2013).This gives the H 2 O absorption cross section σ abs H 2 O for given temperature and pressure conditions, used to determine line broadening.Therefore to calculate transmission coefficients, we need atmospheric profiles of pressure p(z), temperature T (z), and water vapour number density n H 2 O (z).These are obtained from radiosonde measurements over Ny-Ålesund, Svalbard by Maturilli and Kayser (2016).Daily observations have been made since 1993.Since in Sect. 4 we take a week of OH line intensity measurements from December 2003 as an example to determine temperatures, we have used atmospheric profiles from this month from the Ny-Ålesund dataset.These are plotted in Fig. 1, where the thin coloured lines each represent a daily observation from December 2003 (all days of this month are included); the thick black lines are the mean of all the daily values and so represent a monthly average during winter.
Water vapour is principally located in the troposphere, at altitudes less than about 10 km.Therefore, we need only the atmospheric profiles below this altitude.To take into account varying water vapour column densities, the monthly mean profile from Fig. 1c is scaled such that the integrated column density matches the required value.We have tested using a selected daily profile instead of the monthly mean and obtain little difference in the results.
Atmospheric water vapour content is often provided as precipitable water vapour (PWV), normally expressed in millimetres, which is the height of a column of liquid water that would result from the condensation of all the water in a column of atmosphere.A PWV of 1 mm corresponds to a column density of 1 kg m −2 .Espy and Hammond (1995) consider PWVs of 29, 21, 8.5, and 4.2 mm, corresponding respectively to low-latitude summer, winter, high-latitude summer, and winter.

Determining hydroxyl temperatures
If we assume a Boltzmann distribution for the population of rotational levels, the intensity I of a Meinel band line is (Mies, 1974) where N ν is the total number of molecules in the ν vibrational level, A is the transition probability, J is the upper state total angular momentum quantum number, Q ν is the partition function, F is the energy level of the initial rotational level, T is the rotational temperature, h is Planck's constant, c is the speed of light, and k is Boltzmann's constant.
One method to obtain the temperature is to take the ratio of intensities of OH lines with different upper rotational states (Phillips et al., 2004).Thus, from Eq. (3), we obtain where the indices a and b represent the two emission lines from different upper states.
Values for the energy levels are taken from Coxon and Foster (1982).There is a discrepancy in the literature over transition probabilities that can affect the temperature values obtained from Eq. ( 4) by up to ∼ 10 − 20 K (Phillips et al., 2004;Perminov et al., 2007).The most common sources are Mies (1974), Langhoff et al. (1986), andTurnbull andLowe (1989).It is therefore important to be consistent with the set of transition probabilities used whenever comparing temperature results.In the results shown in this paper, we use the values from Mies (1974).

Wavelength
In order to ensure that the airglow layer is in LTE, we produce a Boltzmann plot (e.g.Sigernes et al., 2003) for each temperature retrieval performed.This consists of plotting ln {I / [A(2J + 1)]} as a function of (hc/k)F for each of the OH(8-3) P-branch lines measured by HiTIES.If Eq. ( 3) is valid, i.e. the airglow layer is in LTE, it can be seen that the plotted function should be linear and the slope is the rotational temperature T .As an example, the Boltzmann plot for the HiTIES spectrum in Fig. 2 (measured on 23 December 2003 at 22:30 UT) is shown in Fig. 3.The linear fit (solid black line) is determined using the three P 1 lines (blue symbols), since these have the highest intensities (and thus lower associated errors).The points corresponding to the P 2 lines (represented by red symbols in Fig. 3) follow the same linear fit, indicating that the airglow layer is indeed in LTE at this time.To assert that there is LTE, we use the same criteria as Table 3. Water vapour transmission at wavelengths of OH(9-4) lines.Vacuum wavelengths are from Rousselot et al. (2000), with conversion to air wavelengths undertaken as specified by Ciddor (1996).At each wavelength, water vapour transmission is given by a function of PWV: T λ = exp(−A × PWV), with PWV in mm.Rousselot et al. (2000), with conversion to air wavelengths undertaken as specified by Ciddor (1996).At each wavelength, water vapour transmission is given by a function of PWV: T λ = exp(−A × PWV), with PWV in mm.correcting the hydroxyl emission line intensities for this effect, we would obtain a bad linear fit and a significant error on the rotational temperature.

Wavelength
In the following section, Sect.3, we detail the results of water vapour absorption modelling, providing coefficients for scaling OH line intensities to take this into account.More details on the resulting temperatures determined from Hi-TIES measurements are shown in Sect. 4.  Rousselot et al. (2000), with conversion to air wavelengths undertaken as specified by Ciddor (1996).At each wavelength, water vapour transmission is given by a function of PWV: T λ = exp(−A × PWV), with PWV in mm.
Water vapour absorption lines originating in the troposphere are mainly subject to pressure-broadening.Using the HITRAN model, we find that for a temperature of about 300 K and a pressure of 1 bar (most H 2 O is concentrated near the Earth's surface), the full width at half maximum of an H 2 O line at a wavelength close to the OH(8-3)P 1 (4) line is about 0.1 Å.On the other hand, since OH emission is produced near the mesopause, the principal broadening mechanism is Doppler broadening.The full width at half maximum of such a Gaussian line profile is given by where λ 0 is the centre wavelength of the line.Applying Eq. ( 5) using the value of temperature determined in Sect.2.2 from the HiTIES spectrum in Fig. 2, T = 188.7 K, gives λ/λ 0 = 2.38 × 10 −6 .Therefore, at the wavelength of the most absorbed OH line in the HiTIES spectrum, P 1 (4), we obtain a full width at half maximum of 0.018 Å.We consider that this is sufficiently small compared to the width of the water vapour absorption lines that we do not calculate the precise shape of the OH lines to determine the H 2 O transmission values in Tables 1-5, instead only calculating the values at the line centre wavelength.
In addition, we do not take into account any Doppler shifts that may occur to the centre wavelengths, or effects of nonvertical lines of sight.Thus, the values given are only valid when observing in the zenith, assuming that any vertical flows are small.
The water vapour transmissions of OH(8-3) band emission lines, some of which are observed by the HiTIES instrument (see Fig. 2), are plotted in Fig. 4. The two lambdadoubled components of each line are shown, even though Hi-TIES does not have sufficiently high wavelength resolution to be able to distinguish these.Of the lines observed by Hi-TIES, it is mainly P 1 (4)e that is affected.For the case of the HiTIES observation from 23 December 2003 at 22:30 UT, described in Sect.2.2, a value of PWV of 2.7 mm was taken in order for the three hydroxyl temperatures (obtained from ratios P 1 (2) / P 1 (3), P 1 (2) / P 1 (4), and P 1 (3) / P 1 (4)) to match.This represents an absorption of 6.7 % of the OH(8-3)P 1 (4)e line.
In this study, we focus on the role of water vapour absorption; however, other species may also participate in the attenuation of hydroxyl line emission.As a test, we estimate the absorption by CO 2 of OH line emission using a similar method to that used for H 2 O absorption described in Sect.2.1.We use a profile of CO 2 density with altitude from Foucher et al. (2011), scaled to the high-latitude winter carbon dioxide column density given by Espy and Hammond (1995) of 7.103×10 21 molecules cm −2 .The HITRAN database is then used to determine CO 2 absorption cross sections.We find that the transmission coefficients at the centre wavelengths of all the OH lines included in Tables 1 to 5 are equal to 1. Thus, at the hydroxyl line wavelengths included   in this study, carbon dioxide does not appear to be a major absorber.

Hydroxyl temperatures
To test the transmission values determined in this paper, we incorporate these into a calculation of OH(8-3) temperatures from spectral measurements from the HiTIES instrument.
The resulting temperatures are plotted in Fig. 9. Twelve days of observations in December 2003 and January 2004 are used to obtain temperatures, using the method described in Sect.2.2.The three strongest P-branch lines are used -P 1 (2), P 1 (3), and P 1 (4) -meaning three temperature estimates can be obtained for each measured spectrum, since one temperature determination requires the ratio of two OH line intensities, as per Eq. ( 4).Without correction for water vapour absorption, the three mean daily temperatures are different by 10 to 20 K, similar to the discrepancies found by Phillips     (2004).This difference in temperature values is due to the absorption of the P 1 (4) line by H 2 O (see Sect. 3).The daily mean temperatures without taking into account water vapour absorption are shown in dashed coloured lines in Fig. 9a: in blue for temperatures obtained by taking the ratio of P 1 (2) and P 1 (3), in red for P 1 (2) and P 1 (4), and in yellow for P 1 (3) and P 1 (4).
To correct for the absorption of OH emission by water vapour, we use the expressions and coefficients given in Table 1 for each of the P-branch lines used to determine temperatures.Since the three OH lines used are from the same vibrational band, the emission for each of them is produced at the same altitude.Thus, any difference in temperature estimation obtained from different ratios of these lines' intensity is assumed to be due only to differing amounts of water vapour absorption that their emission undergoes before reaching the HiTIES detector.Therefore, the column density of water vapour (or PWV) is chosen such that the three temperature determinations give the same result.
In this fashion, we obtain the temperatures and PWV values plotted in black in Fig. 9.Here we show only tempera-tures obtained during clear-sky periods, i.e. with no auroral emission present.Each temperature estimation (represented by a black point in Fig. 9a) is calculated with OH(8-3) line intensities measured from a spectrum composed of 20 min of HiTIES observations.The corresponding values of PWV for each of these temperature calculations are shown by the black points in Fig. 9b.The daily mean of all of these values is shown by the black solid lines in both panels.
The daily mean OH rotational temperature shows a variation of around 20 K over the course of a 2-to 3-day period.This is similar to what has previously been observed by Suzuki et al. (2009) and Espy et al. (2003) in OH airglow temperature measurements in Antarctica.These studies concluded that such rapid changes in OH rotational temperatures were due to changes in the meridional component of the mesospheric wind, caused by gravity waves.It is possible that such a mechanism is also responsible for the time variation of the OH temperatures that we measure here.Such changes in OH temperatures over a few days have also been seen in the Arctic (Nielsen et al., 2002;Dyrland et al., 2010;Holmen et al., 2014b).

Figure 1 .
Figure 1.Atmospheric profiles used in the water vapour absorption model, measured by radiosonde over Ny-Ålesund, Svalbard, from Maturilli and Kayser (2016).Panel (a) shows the pressure as a function of altitude, panel (b) shows the temperature, and panel (c) shows the number density of H 2 O.The coloured lines each represent a daily observation during the month of December 2003; the mean profiles from this month are plotted in solid black lines with 1 standard deviation from the mean shown in dashed black lines.

Figure 2 .
Figure 2. Example clear-sky HiTIES spectrum, showing labelled OH emission lines.Taken on 23 December 2003 at 22:30 UT, with an integration time of 120 s.

Figure 3 .
Figure 3. Boltzmann plot determined from the OH(8-3) P-branch lines shown in the HiTIES spectrum from Fig. 2, taken on 23 December 2003 at 22:30 UT, with an integration time of 120 s.Blue symbols represent P 1 lines, and red symbols are P 2 lines.Crosses indicate intensities as measured by the HiTIES instrument, whereas open circles have been corrected for water vapour absorption.The solid black line is a linear fit to the water-vapour-corrected P 1 lines.The slope of this fit gives a rotational temperature of T = 188.7 K.

Figure 4 .
Figure 4. Water vapour transmission of the OH(8-3) lines, measured by HiTIES, as a function of precipitable water vapour (PWV).The left panel shows the Q-branch lines and the right panel, the P branch.Solid lines represent the e component of the lambda-doubled line, and the dashed lines represent the f component.

Figure 5 .
Figure 5. Water vapour transmission of the OH(5-1) lines as a function of precipitable water vapour (PWV).The left panel shows the Q-branch lines and the right panel, the P branch.Solid lines represent the e component of the lambda-doubled line, and the dashed lines represent the f component.

Figure 6 .
Figure 6.Water vapour transmission of the OH(9-4) P-branch lines as a function of precipitable water vapour (PWV).Solid lines represent the e component of the lambda-doubled line, and the dashed lines represent the f component.The Q-branch transmissions are not represented for this band since they are all equal to 1 within 0.01 % over the plotted range of PWV.

Figure 7 .
Figure 7. Water vapour transmission of the OH(6-2) lines as a function of precipitable water vapour (PWV).The left panel shows the Q-branch lines and the right panel, the P branch.Solid lines represent the e component of the lambda-doubled line, and the dashed lines represent the f component.

Figure 8 .
Figure 8. Water vapour transmission of the OH(8-4) lines as a function of precipitable water vapour (PWV).The left panel shows the Q-branch lines and the right panel, the P branch.Solid lines represent the e component of the lambda-doubled line, and the dashed lines represent the f component.

Table 4 .
line intensities is also shown in the Boltzmann plot of Fig.3.Circles are used to represent water vapourcorrected OH intensities, whereas crosses represent uncorrected intensities.From this figure it can be seen that the lines most absorbed by water vapour are P 1 (4) and P 2 (2).Without Water vapour transmission at wavelengths of OH(6-2) lines.Vacuum wavelengths are from

Table 5 .
Water vapour transmission at wavelengths of OH(8-4) lines.Vacuum wavelengths are from