Spectral observations are an important diagnostic tool to probe the upper atmosphere, a region that is difficult to measure directly. Emissions from this region include optical airglow and aurorae, which are produced by the de-excitation of atoms or molecules in the upper mesosphere and the thermosphere. These emissions contain information on the state of the layers of atmosphere in which they are produced and also on the solar photons or precipitating energetic particles responsible for the excited states of the atmospheric species. Furthermore, since optical emissions from the upper atmosphere are produced over a wide range of altitudes, by simultaneously observing at different wavelengths, it is possible to build up a picture of the vertical structure of the upper atmosphere.

The neutral temperature is one parameter that is possible to determine from spectral observations in visible wavelengths. Making the assumption that the emitting species are in local thermodynamic equilibrium (LTE), the neutral temperature can be obtained by measuring emissions from the rotational bands of molecules. In this way, neutral temperatures have been determined from observations of airglow emissions from the OH layer located near the mesopause e.g.. It has also been possible to measure rotational temperatures from N2+ ions observed during aurorae e.g..

One difficulty with these measurements is that emissions from different species often occur at the same wavelengths. For example, past studies of OH temperatures (such as those listed above) have not been able to obtain measurements during periods of auroral activity, when auroral emissions contaminate the OH spectrum. To overcome this problem, we have developed a method to distinguish different emissions seen in the High Throughput Imaging Echelle Spectrograph, HiTIES , by fitting the spectrum, thus enabling us to measure temperatures at different altitudes simultaneously.

Our spectral fitting method also allows for the determination of the column density of water vapour, or precipitable water vapour (PWV), by measuring the absorption of upper atmospheric airglow emissions. There are multiple other methods traditionally used to measure PWV, either from the ground using the Global Navigation Satellite System (GNSS) e.g., from radiosondes e.g., or from satellite observations e.g.. However, polar regions pose certain difficulties for these methods. Indeed, there is a lack of stations for ground-based measurements, and satellite retrieval methods using microwave imagers require knowledge of the surface emissivity, which is large and highly variable over ice and snow . The optical ground-based measurement of PWV from airglow, described in this paper, allows for estimates of atmospheric water vapour column densities at high temporal resolution in the Arctic.

The instrument is described in Sect. , and the different emissions it measures are described in Sect. . Section  details the spectral fitting and temperature retrieval process. We have run a Monte Carlo simulation to quantify the uncertainties on parameter retrieval from the HiTIES spectra; the results of these retrieval tests are discussed in Sect. . Monte Carlo simulations also allow us to assess uncertainties on the laboratory measurements of quantum numbers required to determine OH temperatures, as described in Sect. .

The High Throughput Imaging Echelle Spectrograph has been measuring emissions from the upper polar atmosphere since the year 2000. It is a part of the Spectrographic Imaging Facility (SIF) located in the high Arctic on Svalbard at the Kjell Henriksen Observatory (78.148∘ N, 16.043∘ E). The spectrograph has an 8∘ slit that is centred on the magnetic zenith. Light entering the instrument passes through a collimator, before being diffracted by an echelle grating and re-imaged on an EMCCD detector. A mosaic of interference filters is used to separate overlapping diffraction orders, allowing for the simultaneous observation at high temporal and spectral resolution of non-contiguous spectral regions. Figure  shows a schematic diagram of the two mosaic filters that have been used the most often over the lifetime of the instrument. Each individual panel of the filters is centred in wavelength on a particular atmospheric emission of interest, although it should be noted that each panel may also contain emissions from multiple other species.

The instrument records images at a frequency of 2 Hz; however, depending on the brightness of the observed emissions, the spectra are typically post-integrated to between ∼10 and 120 s. The width of the spectrograph slit can be changed to adjust the spectral resolution, with higher resolution being a trade-off with the amount of light captured. In the 2015–2016 season, during which the data in Fig.  were recorded, the FWHM was 0.15 nm.

A number of different mosaic filters have been in use with the HiTIES instrument over its years of operation, with filters containing panels observing the wavelength region between 725 and 740 nm in use for most winter seasons since 2003. The spectral fitting described in this paper is applied to spectra in this panel, called the “O+ panel”, since it contains two doublets of auroral origin from the O+ ion (see Sect. ). The O+ panel is located in the top left corner of the four-panel mosaic, as drawn in Fig. a, and in the middle of the three-panel mosaic shown in Fig. b. Also observed in this panel are OH airglow emissions from the (8-3) Meinel band (see Sect. ) and N2 1P emissions from the (6-4) and (5-3) bands (see Sect. ).

An example of a spectrum recorded with the HiTIES O+ panel is plotted in Fig. a. The observations are shown in grey crosses and the thick black line represents a spectrum that has been fitted to the data using the method described in Sect. . The different components of the fit that summed together produce the think black line are plotted in coloured lines: OH lines in green, O+ lines in orange, and N2 band emission in purple.

There are several parameters of interest we aim to retrieve from each HiTIES spectrum that can provide us with information on the state of the upper atmosphere. These parameters are the following:

intensities of the OH and O+ emission lines and of the N2 emission;

The following, Sect.  to , describes the emission components measured by HiTIES in more detail.

A least-squares fitting routine is used to determine the parameters of the superposed emissions present in the measured HiTIES spectra. The OH and O+ lines are represented as Gaussians, all with the same FWHM, since the width is principally determined by the instrument function. Line centre wavelengths are fixed at the values given in Table . OH rotational states are split due to nuclear-spin–electron-orbit interactions, referred to as Λ doubling. The resulting Λ-doubled components are not spectrally resolved by HiTIES, meaning that the hydroxyl emission lines in Fig.  are made up of two components, labelled with the subscripts e and f (referring to the parity of the lower state) in Table . We fit a Gaussian for each Λ-doubled component and make the assumption that the two components of each OH vibrational–rotational transition are of equal intensity; thus we fix the peak height of the Gaussian representing the f component of each transition to have the same peak height as the e component.

The two O+ doublets are represented in the fit by four Gaussians centred at the wavelengths given in Table . From the Einstein coefficients of these transitions , we obtain the following constraints on the intensities of the O+ lines: I(2P1/20→2D3/20)=1.668×I(2P1/20→2D5/20),I(2P3/20→2D3/20)=0.540×I(2P3/20→2D5/20), where I is the line intensity. Equations () and () are included as constraints in the fitting process, allowing for 10 % variation in the coefficients.

We create a database of N2 model spectra at temperatures from 150 to 1150 K, with a resolution of 10 K and an instrument function FWHM appropriately chosen for the focus of the HiTIES instrument during a given season. The fitting routine finds the best match to the data out of this grid of modelled spectra, providing a direct retrieval of the N2 rotational temperature.

Each measured HiTIES spectrum is fitted with 30 parameters: 24 OH line peak intensities (modelled as 48 Gaussians with e and f components constrained to have the same height for the same rotational–vibrational transition), two O+ line intensities (modelled as four Gaussians, with constrained ratios between the upper and lower wavelength components of each doublet given in Eqs.  and ), the FWHM (assumed the same for all the OH and O+ Gaussians), the intensity and rotational temperature of the N2 emission, and a constant background intensity. Figure a shows the resulting fit to a spectrum recorded by HiTIES on 15 December 2015 at 01:40 UT; the data are shown in light grey and the fitted spectrum is a thick black line. Figure b shows the residuals of this fit, for which it can be seen that a good fit to the data is achieved with the chosen parameters. However, at the short wavelength end of the spectrum, there are a few emission features in the data that are not present in the fitted spectrum, in particular peaks near 727.3, 728.0, and 728.9 nm. We believe these peaks correspond to O2 emission, which is not included in our fit. Therefore, our fitted values of the Q-branch OH(8-3) lines, present at the short wavelength end of the HiTIES spectrum, are likely unreliable, so these OH lines are not used for the temperature retrieval.

With the fitted intensities of the P-branch OH lines, we determine the OH rotational temperature by constructing a Boltzmann plot (see Sect.  and Fig. ). The temperature retrieval is performed using the strongest P1 branch lines: P1(2), P1(3), P1(4), and P1(5).

Tropospheric water vapour absorption attenuates many of the emission lines measured with HiTIES. This effect must be taken into account for correct parameter retrieval from the fitting process. Modelling of the H2O absorption in each line is not just done for OH emission, as described in Sect. , but also for each O+ and N2 emission line. The HITRAN spectral database is used to determine the H2O absorption cross section, and water vapour absorption in the column of atmosphere above the instrument is calculated using the Beer–Lambert law see. We parameterise water vapour absorption with the coefficient ς given for the OH and O+ lines in Table , which is related to absorption (aλ) and transmission (tλ) coefficients by the following: tλ=1-aλ=exp-ς×PWV, where PWV is the precipitable water vapour in millimetres. PWV represents the height of a column of liquid water that would result from the condensation of all the water in a column of atmosphere. Thus, a PWV of 1 mm is equivalent to a column density of H2O of 1 kg m-2.

The spectral fitting and OH temperature retrieval process is run multiple times, each assuming a different given value of PWV. From the Boltzmann plot constructed with OH P-branch lines, the correlation coefficient R2 of the linear fit allowing for temperature retrieval is determined for each of these runs. The retrieved value of PWV for a given HiTIES spectrum is then taken as the PWV that maximises the Boltzmann plot correlation coefficient R2. An example of this process is shown in Fig.  for the spectrum from Fig. , taken on 15 December 2015 at 01:40 UT. Each blue point in Fig.  is a value of R2 from a Boltzmann plot constructed using the OH P-branch line intensities calculated by the spectral fitting routine, assuming a given value of the PWV between 0 and 10 mm. The value of PWV which maximises R2 is found by fitting the blue points in Fig . Since water vapour absorption is calculated using the Beer–Lambert law, which takes the form of an exponential, we find that the expression that provides the best fit to the R2 points is a sum of exponentials, R2=aexpb×PWV+cexpd×PWV, and thus the maximum of R2 is attained at a precipitable water vapour of PWV=1b-dln-cdab. To reduce computational time, we have found that it is sufficient to run the retrieval process at just five different values of PWV in order to determine the maximum of R2.

Considering that the main source of noise in a given spectrum is shot noise, we determine the uncertainties on the fitted line intensities (eI) using the following: eI=σresiduals×Npixels, where σresiduals is the standard deviation of the residuals and Npixels is the number of pixels on the detector contained in the FWHM of the emission line. In this way, we can obtain uncertainty estimates on the parameters retrieved from each particular spectrum. However, we would also like to determine the ranges of parameters over which the fitting process produces accurate results. For this reason, we carry out a Monte Carlo simulation in Sect. .

In order to estimate expected errors on the fitting and parameter retrieval process described in Sect. , we have performed a Monte Carlo simulation. Such a simulation also provides information on the region of parameter space over which the fitting method is valid. Synthetic spectra were generated containing OH, O+, and N2 components in different proportions and with different properties. The parameters of each synthetic spectrum were drawn randomly within the following ranges.

IOHin≡IOHP1(3)in=1300 R nm-1

The OH temperature measurements depend on possessing correct values of transition probabilities and energy terms. In particular, past studies have shown large differences in OH temperatures derived using different sources for the transition probabilities e.g.. To assess this effect on our retrieval process, we have constructed 10 000 synthetic spectra in the same manner as described in Sect. , except that they are constructed using transition probabilities from , whereas the retrieval process assumes transition probabilities from . The results of this Monte Carlo simulation are shown in Fig. , in which the same parameters are plotted as in the top row of Fig. ; namely, the fractional error on the OH temperature is plotted against the OH temperature (panel a), the N2 temperature (panel b), the O+ intensity (panel c), and the N2 intensity (panel d). The 2-D histograms in Fig.  are very similar to those in the top row of Fig. , in which the transition probabilities used both in constructing the synthetic spectra and in the retrieval process are from . The only difference is an offset of about 3 % to 4 %, corresponding to a difference in temperature of 6 to 8 K, assuming an OH temperature of around 200 K.

We take the same approach to ascertain the effect on OH temperatures of different sources for the OH energy levels. The fractional errors on the retrieval of TOH are plotted in Fig.  by constructing synthetic spectra with energy terms from and assuming values in the retrieval process. The mean values also show an offset from the 0 error line, but much smaller than for different transition probabilities, of about 0.5 % to 1 %, equivalent to 1 to 2 K at 200 K.

We have developed a new spectral fitting method that allows us to extract the intensity of simultaneous emissions in HiTIES spectra. These emissions – OH airglow, auroral O+, and N2 – originate from different atmospheric layers and their properties inform us of the state of the upper polar atmosphere. In particular, combining our spectral fitting method with a temperature retrieval process allows us to estimate neutral temperatures at different altitudes and the atmospheric column density of water vapour. In this paper, using a Monte Carlo simulation to retrieve the known parameters of synthetic spectra, we have shown the domains over which our spectral fitting and temperature retrieval processes are successful.

The Monte Carlo simulation shows that we can correctly retrieve OH temperatures, as long as any N2 emission is not too bright. Indeed, we find that the distribution of fractional errors on TOH has a standard deviation of less than 6 % when the maximum intensity of the N2 spectrum is less than the peak intensity of the strongest OH emission line seen in HiTIES, OH(8-3) P1(3). This uncertainty corresponds to about 12 K on an OH temperature of 200 K, obtained from a single spectrum typically integrated over 2 min of observing time. Since OH emission is present in almost all of our data, we can improve the errors on TOH by temporally averaging multiple observations. Thus, combining 15 consecutive 2 min measurements would reduce the absolute uncertainty from 12 to 3.1 K.

We have also evaluated the magnitude of errors on TOH that occurs from uncertainties in the OH transition probabilities. The offset measured between temperatures obtained using transition probabilities from and is about 4 % on average (roughly 8 K), reinforcing the fact that any comparisons between different OH temperature datasets must take this into account.

When there is sufficient N2 emission present, we can successfully determine the N2 temperature. The standard deviation of the distribution of fractional errors on TN2 is between 3 % and 5 % when the maximum intensity of the N2 spectrum is greater than 3.7 times the background level. In the spectral fitting procedure and the Monte Carlo simulations performed in this study, we have assumed that all of the N2 emission in the HiTIES spectrum is produced at a single temperature. This is not necessarily the case, especially if the N2 layer is extended in altitude. Therefore, in future we intend to modify our spectral fitting method to take into account the possible presence of N2 emission at different temperatures in a single spectrum.

showed that the ratio of the two O+ doublets observed by HiTIES at 732 and 733 nm can be used as a measure of the neutral temperature in the F-region ionosphere. We can determine this ratio, RO+, with a distribution of fractional errors of less than 5 % when the peak of the 732 nm O+ doublet is greater than 6 times the background emission.

As a by-product of the spectral fitting method, we have been able to estimate the amount of water vapour in the column of atmosphere above the HiTIES instrument: the precipitable water vapour or PWV. When OH lines are present in our data, which is almost at all times that the instrument is running, we can obtain high-cadence (at least every 10 min) measurements of the PWV.

In a number of follow-up studies, we will make use of the spectral fitting and temperature retrieval methods demonstrated here to explore trends in upper atmospheric neutral temperatures in the HiTIES dataset. As a first step, we shall compare OH(8-3) temperatures measured by HiTIES with OH(6-2) temperatures from the Silverbullet instrument operated by the University Centre in Svalbard (UNIS) e.g., also located at the Kjell Henriksen Observatory, and with OH temperatures derived from the SABER instrument onboard the TIMED satellite.