## Introduction

Atomic oxygen extends from about 80 km to above 300 km in altitude, but with more than 90% concentrated between 85 and 125 km (Fig. 1a). It plays an important role for the energy balance of the mesosphere and lower thermosphere (MLT), because it participates in exothermic chemical reactions and it contributes to radiative cooling1,2. The latter occurs mainly via emission from CO2 at 15 µm and NO at 5.3 µm. Both molecules are excited by collisions with ground state atomic oxygen. In particular, quenching of CO2 vibrational levels by collisions with atomic oxygen is important. Therefore, the knowledge about the distribution of atomic oxygen is crucial for retrieval of the kinetic temperature in the MLT from the 15 µm CO2 radiance3. In addition, direct radiative cooling by atomic oxygen occurs via the fine structure transition from the lowest excited state, 3P1, into the ground state, 3P2, at 63.2 µm (4.7448 THz)4. This is the dominant cooling mechanism above ~250 km. In the MLT the lifetime of atomic oxygen in the 3P1 state is several hours. Because of this long lifetime it can be transported over large distances before it releases its energy and therefore it might be used as tracer for the dynamical motions, vertical transport, tides, and winds5,6,7. This leads to a strong coupling between the dynamics and the photochemistry in the MLT with the energy being released significantly after and far away from the location, where the UV photon is absorbed. An accurate knowledge of the global distribution of atomic oxygen and its concentration profile as well as diurnal and annual variations are therefore essential for understanding the photochemistry and the energy budget of the MLT.

At the atmospheric conditions of the MLT the fine structure line at 4.7448 THz is thermally Doppler broadened with a line width of 12 MHz for emission originating at 100 km where the density of atomic oxygen is largest. Due to the increasing temperature, emission from the thermosphere is broader (25 MHz at altitudes >300 km). Direct observation of this transition requires airborne or space-borne instruments, because absorption by tropospheric water vapor prohibits observation with ground-based instruments. In addition, terahertz (THz) spectrometers are notoriously complex, in particular when it comes to airborne or space-borne applications. The 4.7-THz line has been observed a few times by rocket-borne instruments8. More observations with global coverage have been done with the Cryogenic Infrared Spectrometers and Telescopes for the Atmosphere (CRISTA) that flew on the space shuttle in the 1990s9,10. With this spectrometer atomic oxygen densities have been determined at altitudes from 130 to 175 km, which account for about 20% of the total atomic oxygen in the MLT. Below 130 km retrieval was not possible, because of the opacity of the transition and the limb view of CRISTA. Measurements of the fine-structure line have also been made with the Far-InfraRed Spectrometer (FIRS-2), a Fourier transform spectrometer on a high-altitude (38 km) balloon11. From 1989 to 2003 in total 31 spectra have been obtained and analyzed. But again, the line shape of the transition was not resolved. The radiances observed by FIRS-2 deviate by less than 15% from the computed ones using the Mass Spectrometer Incoherent Scatter (MSIS) model11,12.

Atomic oxygen concentrations can be inferred indirectly from measurements of the O(1S) green line, the O2 A-band or the emission from vibrationally excited OH. These methods rely on chemical reaction models and assumptions such as photochemical steady state, quenching rates, radiative lifetimes, and reaction coefficients. The OH emission has been measured with the SABER (Sounding of the Atmosphere using Broadband Emission Radiometry) infrared spectrometer and with the Scanning Imaging Absorption  Spectrometer for Atmospheric Chartography (SCIAMACHY)6,13,14. The O(1S) green line was measured by the Wind Imaging Interferometer (WINDII) and SCIAMACHY instruments15,16,17 and the O2 A-band airglow has been measured with SCIAMACHY and the Optical Spectrograph and InfraRed Imaging System (OSIRIS) on the Odin satellite18. With all instruments geographical and seasonal variations of the atomic oxygen concentration have been found. Initially, differences up to 60% are reported for concentrations derived from OH measurements with SABER and O(1S) measurements with SCIAMACHY16. A recent comparison based on an improved photochemical model reveals differences up to 20% between SABER, SCIAMACHY, WINDII, and OSIRIS measurements19. The new atomic oxygen concentrations are about 25% smaller than those originally derived19,20. Likewise, with an improved photochemical model it was found that the atomic oxygen concentrations derived from OH, O(1S), and O2 A band measurements with SCIAMACHY agree within 15% with each other, which is better than the agreement with SABER data derived from OH measurements21.

## Results and discussion

Direct observations of atomic oxygen are potentially more accurate. We have analyzed its emission at 4.7 THz measured with the GREAT spectrometer on SOFIA, the Stratospheric Observatory for Infrared Astronomy22,23. This is a by-product of the astronomical observations in the same frequency band. In fact, atomic oxygen has been observed in the atmosphere of Mars using GREAT24. Due to Doppler shift the line from the astronomical object is often significantly shifted (up to 3 GHz) from the atmospheric line. This allows analyzing the spectra of the atomic oxygen line in the Earth atmosphere for those astronomical objects, which are significantly Doppler shifted and not too much broadened, ensuring that the lines do not interfere.

Heterodyne spectroscopy has a number of differences compared to grating spectroscopy and Fourier-transform spectroscopy regarding the measurement of atomic oxygen in the atmosphere. First of all it provides a much higher spectral resolution. In the case of GREAT the spectral resolution of 6 MHz (full width at half maximum (FWHM), see “Methods” section) is limited by the line width of the local oscillator (LO)25. This is significantly smaller than the atomic oxygen line width. In comparison, CRISTA has a spectral resolution of 4.2 GHz8 and FIRS-2 has 120 MHz spectral resolution11. The resolving power of GREAT allows spectrally resolving the atomic oxygen line (Fig. 1b). Because of the high spectral resolution the problem of saturation of the atomic oxygen line can be overcome in the vertical sounding observation geometry of GREAT (see “Methods” section). This occurs in the center of the line while the line wings are not saturated and contain information about the atomic oxygen concentration at higher altitudes. The second advantage is the high sensitivity of the GREAT spectrometer. Its single-sideband noise temperature is 2200 K. This corresponds to a noise equivalent power (NEP) of 3 × 10−20 W within an integration time of 1 s. With this sensitivity GREAT is capable of measuring one spectrum with an integration time of 19 s. For comparison, 31 separate spectra have been measured with FIRS-2 each requiring between 11 and 16 min of integration time. It should be noted that GREAT is a rather large instrument, which, in its present form, cannot be implemented on a balloon or on a satellite. However, recent improvements in heterodyne technology, in particular high-frequency Schottky diode mixers26, compact quantum-cascade lasers as local oscillators27, and low-power CMOS (Complementary Metal-Oxide Semiconductor) backend spectrometers28 have initiated the development of balloon-borne and satellite instruments29,30.

The spectra, which are presented here, have been measured on 14 January 2015 between 1:15 and 4:15 am (flight ID 2015/01/14). The flight trajectory is shown in Fig. 1c. Essentially it is in south-north direction above the Pacific Ocean west of northern Mexico and California between 27° and 48° north latitude and 134° and 128° west longitude. The flight direction is from south to north and the telescope is viewing west. Three typical profiles obtained during this flight are shown in Fig. 2. They have been measured at three different elevations, as well as at different locations along the flight track and different altitudes. The measurement uncertainty in intensity is ±15%. It is caused by uncertainties of the absorption by water vapor and calibration uncertainties (see “Methods” section). At the lowest elevation of 29.1° the profile is the broadest with signs of saturation as the flat top indicates. With increasing elevation it becomes narrower and at the largest elevation of 50.6° saturation almost disappears, because the path through the atmosphere becomes shorter and less atomic oxygen is probed. It should be noted that most of the signal in the wings of the profile is from altitudes around 100 km. The red solid lines are radiative transfer calculations based on atomic oxygen column densities and temperature profiles from NRLMSISE-00 (US Naval Research Laboratory Mass Spectrometer and Incoherent Scatter Radar Exosphere − 2000)31. Each line profile is a convolution with the 6 MHz spectral resolution of the GREAT spectrometer. The elevation of the telescope as well as the absorption by the atmosphere between SOFIA and the MLT are also taken into account (see “Methods” section). The residuals (modeled minus measured data) are up to 15% and the largest deviations occur in the wings of the profiles, indicating that the atomic oxygen concentration is somewhat different from the model in particular at higher altitudes.

In order to analyze the accuracy of the model we have calculated the emission profiles assuming various deviations from the atomic oxygen concentration and temperature profiles of NRLMSISE-00 (Fig. 3). First, we have varied the concentration profile from 120 to 80% of the nominal concentration at all altitudes. The residuals show that the best agreement is obtained with the nominal concentrations from NRLMSISE-00. It should be noted that the residuals become more pronounced in the wings of the profile while the peak remains unchanged because of saturation. This underlines the importance of the high spectral resolution. When the temperature, T, is changed by ±5% while the concentration profile is kept nominal the emission becomes much stronger (T = +5%) or much weaker (T = −5%), because more or less atomic oxygen is excited. An important difference to the residuals for different atomic oxygen concentrations is that in this case the residual at the peak of the line changes significantly. In Fig. 3c calculated profiles are shown which are obtained by shifting the concentration profile by +5 km or −5 km relative to the nominal profile while keeping the temperature profile unchanged. Again, the deviation from the measured profile is pronounced. When the concentration profile is shifted by −5 km a single peak occurs and saturation of the emission is reduced. A double-peak emission profile appears when the concentration profile is shifted upwards, because the wings of the emission profile are less attenuated. They probe higher atmospheric layers and more atomic oxygen contributes to the signal.

Because NRLMSISE-00 is not a physics-based model, an agreement between this model and the GREAT measurements might be accidental. Therefore we compare the GREAT data with atomic oxygen profiles obtained with the SABER instrument. There is a set of nine SABER profiles, which was measured close to the geolocation and time of the GREAT measurements (see “Methods” section). This data has been measured along the flight track shown in Fig. 1c on 14 January 2015 between 0:22 and 0:30 am local time19. (ftp://saber.gats-inc.com/Version2_0/SABER_atox_Panka_etal_2018_GRL/SABER_o3p_oh_night_2015_v1.0.nc). The profiles extend from 80 to 100 km altitude. Since there are no measured data available for altitudes above 100 km we have combined SABER and NRLMSISE-00 atomic oxygen and temperature profiles. Below 100 km these consist of the SABER profile while above 100 km the NRLMSISE-00 profiles were taken. With these concentration and temperature profiles the expected atomic oxygen emission is calculated and compared with the measured emission (position B in Fig. 1c). The agreement between the GREAT and the SABER/NRLMSISE-00 profiles is similar as with the pure NRLMSISE-00 profiles (Fig. 4a). The differences are within the uncertainty of the GREAT measurement. Also, day-to-day variations of atomic oxygen and temperature as well as uncertainties of the SABER data and NRLMSISE-00 may contribute to the differences. An analysis of the altitude profiles is shown in Fig. 4b. Along with the combined SABER/NRLMSISE-00 profiles it displays a range (±1σ) of atomic oxygen concentration profiles, which are compatible with the GREAT spectra. At the peak this is an uncertainty of approx. ±40%. The range of profiles is derived by varying the atomic oxygen concentration profile, the temperature profile and the relative positon of both starting with the best fit NRLMSISE-00 profile. The variations of these parameters were determined, which provide residuals of less than the measurement uncertainty of ±15%. The combined SABER/NRLMSISE-00 profile falls into this range.

We now turn to the analysis of the flight path in Fig. 1c with 254 spectra. For each spectrum the radiance has been determined by integration of the emission profile and plotted as a function of flight time (Fig. 5). All data are corrected for absorption by atmospheric water vapor, which is determined by fitting the maximum of the saturated emission profiles (see “Methods” section). In contrast to Fig. 2a single value for the precipitable water vapor (pwv) content has been applied to all spectra (see “Methods” section). The calculated radiances take into account the atomic oxygen concentration and temperature profiles from NRLMSISE-00 and the elevation of the telescope. It should be noted that along the flight path the atomic oxygen concentration as well as the temperature predicted by NRLMSISE-00 change by less than ±5% at all altitudes between 50 and 400 km. If only the region with the highest concentration of atomic oxygen is considered (85–125 km) the changes are less than ±2%. The measured radiances agree with the calculated ones within the measurement uncertainty of ±15%. The radiance increases by about 20%, because the elevation of the telescope decreases leading to a longer path through the atmosphere and as a consequence to broader emission profiles and increased radiances (cf. Fig. 2). The shapes of the measured emission profiles along the flight path of SOFIA agree well with the predictions by NRLMSISE-00 and the corresponding atomic oxygen concentration profiles are well within the uncertainty of the GREAT measurement shown in Fig. 4b. It is worth noting that out of the 31 FIRS-2 radiances 26 are in the range of our measurement between 1.5 and 2.2 nW cm−2 sr−111.

The first spectrally resolved, direct measurement of atomic oxygen in the MLT through its fine-structure transition at 4.7 THz is presented. This is a very promising alternative to established indirect methods which rely on of photochemical models. It is an important step towards a conclusive understanding of the photochemistry, energy balance, and dynamics of the Earth atmosphere. This will be substantiated once the large amount of atomic oxygen data, which has been obtained with SOFIA, is completely analyzed. With the recently installed seven-pixel upGREAT heterodyne spectrometer even more data will be available. In particular, the fine-structure transition at 2.06 THz can be measured simultaneously, enabling measurements of wind speed and temperature profile. Beyond that, with the current progress in THz technology balloon-borne and space-borne heterodyne spectrometers become feasible. Combining such a THz spectrometer with optical instruments similar to SABER or SCIAMACHY will be even more advantageous for the determination of atomic oxygen in the MLT.

## Methods

The emission of the atomic oxygen fine structure line at 4.7448 THz is observed with GREAT, the German Receiver for Astronomy at Terahertz Frequencies. GREAT is regularly operated on board of the Stratospheric Observatory for Infrared Astronomy (SOFIA)22, which is a Boeing 747SP with a 2.5-m diameter telescope in the rear. The elevation of the telescope can be varied from about 20° to 60° and its azimuth is determined by the aircraft heading. At 100 km altitude the area of the sampled volume is about 5 m wide and 5 km long and the distance between two sampled volumes is approximately 15.5 km. This is determined by the spatial resolution of the 2.5-m diameter telescope of SOFIA, which has a diffraction limited beam width of 6 arcsec (FWHM), by the speed of the aircraft, and the integration time for one spectrum, which is 19 s.

GREAT is a heterodyne spectrometer with two frequency channels, one of them at 4.7 THz. The observing altitude of SOFIA is 12–14 km, meaning that the emission from atomic oxygen in the MLT will be present in nearly all of the astronomical atomic oxygen observations. Due to the velocity of astronomical objects relative to the Earth the atomic oxygen emission from these objects is usually Doppler shifted relative to the line in the Earth’s atmosphere. Thus the astronomical data nearly always contain the atomic oxygen line originating from the MLT. The GREAT heterodyne spectrometer relies on a hot-electron bolometer as mixer and a quantum-cascade laser (QCL) as local oscillator (LO)25,32. It has single-sideband noise temperature of 2200 K enabling a measurement time of 19 s per spectrum and an intermediate bandwidth ranging from 0.2 to 2.5 GHz. The backend spectrometer is a digital fast Fourier transform spectrometer33. Its channel spacing is 76.3 kHz, more than sufficient for the present observations, where we, in fact, used channel binning down to effectively 0.763 MHz channels. The spectral resolution is ultimately limited by the emission linewidth of the QCL LO, which is Gaussian-shaped with 6 MHz FWHM. The spectral resolution of the GREAT instrument has been determined prior to the flight in the laboratory be measuring reference spectra of CH3OH at a pressure of 1 hPa. From the analysis of these spectra a spectral resolution of 6 MHz (FWHM) was determined. This linewidth is taken into account when comparing the measured radiances with our radiative transfer model.

For radiometric calibration the GREAT spectrometer is equipped with two blackbody calibration sources. One has a temperature Thot of 294 K while the other one is cooled providing a temperature Tcold = 149 K. A measurement cycle for the atmospheric atomic oxygen line is as follows: First, the signals Chot and Ccold from the hot calibration source and the cold calibration source, respectively, are measured. Then the signal of the sky, Csky, with no astronomical source in the field-of-view of the telescope is measured. The calibrated signal, Scal, is determined according to

$$S_{{\rm{cal}}}\left( {T_{{\rm{sky}}},\;v} \right) = \frac{{C_{{\rm{sky}}} - C_{{\rm{hot}}}}}{{C_{{\rm{hot}}} - C_{{\rm{cold}}}}}\left( {B\left( {T_{{\rm{hot}}},\;v} \right) - B\left( {T_{{\rm{cold}}},\;v} \right)} \right) + B\left( {T_{{\rm{hot}}},\;v} \right).$$
(1)

Here, B(Thot, ν) and B(Tcold, ν) are the radiances of the hot and cold calibration source.

For analysis of the spectra we have implemented a radiative transfer code. In this code the atmospheric radiance is modelled by evaluating the following radiative transfer equation

$$R_{{\rm{int}}} = \mathop {\iint}\nolimits_{\nu ,z} {B_\nu \left( {T\left( z \right)} \right)\frac{{\partial \tau _\nu }}{{\partial z}}{\rm{d}}z{\rm{d}}\nu } ,$$
(2)

with Rint being the spectrally integrated radiance (nW cm−2 sr−1). T is the temperature at altitude z and ν is the frequency. Bν(T(z)) is the source function at altitude z. As has been shown in previous studies, local thermodynamic equilibrium (LTE) determines the population of atomic oxygen up to at least 350 km34. This is in agreement with FIRS-2 measurements, which show that more than 80% of the atomic oxygen radiance originates from below ~140 km and its distribution is well modelled assuming LTE11. Therefore Bν(T) is the Planck blackbody function. The monochromatic transmission τν is given by

$$\tau _\nu = {\rm{exp}}\left( { - \sigma _\nu u} \right).$$
(3)

Here σν is the absorption cross section and u is the optical mass along the line of sight. The absorption cross section is the product of the line strength S and the line profile of the atomic oxygen transition. Due to the low pressure this is a Doppler profile. At 4.7448 THz the FWHM of a Doppler profile varies from 12 MHz at 200 K (corresponding altitude approx. 100 km) to approx. 25 MHz at 850 K (corresponding altitudes >300 km). The line strength S depends on the temperature T. At Tref = 296 K it is S = 1.131 × 10−21 cm−1 atom−1 cm2) and can be calculated for other temperatures according to

$$S\left( T \right) = S\left( {T_{{\rm{ref}}}} \right)\frac{{Q\left( {T_{{\rm{ref}}}} \right)}}{{Q\left( T \right)}}\frac{{{\rm{exp}}\left( {\frac{{ - E_{\rm{L}}}}{{kT}}} \right)}}{{{\rm{exp}}\left( {\frac{{ - E_{\rm{L}}}}{{kT_{{\rm{ref}}}}}} \right)}}\frac{{1 - {\rm{exp}}\left( {\frac{{ - h}}{{kT}}} \right)}}{{1 - {\rm{exp}}\left( {\frac{h}{{kT_{{\rm{ref}}}}}} \right)}}$$
(4)

Here ν is the frequency, Q is the electronic partition function and EL is the energy of the lower state of the transition. EL is zero because the 3P2 is the ground state.

To calculate the radiance the atmosphere is divided into horizontally homogeneous spherical layers with a thickness d = 1 km starting at an altitude of 400 km and ending at 50 km. Absorption and scattering have been neglected. In each layer the transmission τν is calculated assuming an average temperature within the layer, which is taken from the NRLMSISE-00 temperature profile31. In each layer a portion of the incoming radiation is absorbed which is taken into account by an attenuation factor exp(−αν l) (ανː absorption coefficient at frequency ν, l: absorption length). The radiation which is thermally emitted by the layer is added. The absorption path length takes into account the elevation φ of the telescope.