Potential for the measurement of MLT wind, temperature, density and geomagnetic field with Superconducting Submillimeter-Wave Limb-Emission Sounder-2 (SMILES-2)

Submillimeter-Wave Limb-Emission Sounder-2 (SMILES-2) is a satellite mission proposed in Japan to probe the middle and upper-atmosphere (20–160 km). The main instrument is composed of 4-K cooled radiometers operating near 0.7 and 2 THz. It could measure the diurnal changes of the horizontal wind above 30 km, temperature above 20 km, ground-state atomic oxygen above 90 km, atmospheric density near the mesopause, as well as abundance of about 15 chemical species. In this study we have conducted simulations to assess the wind, temperature and density retrieval performance in the mesosphere 5 and lower thermosphere (60–110 km) using the radiometer at 760 GHz. It contains lines of water vapor (H2O), molecular oxygen (O2) and nitric oxide (NO) that are the strongest signals measured with SMILES-2 at these altitudes. The Zeeman effect on the O2 line due to the geomagnetic field (B) is considered, otherwise, the retrieval errors would be underestimated by a factor of 2 above 90 km. The optimal configuration for the radiometer’s polarization is found to be vertical linear. Considering a retrieval vertical resolution of 2.5 km, the line-of-sight wind is retrieved with a precision of 2–5 m s−1 up to 90 km and 10 30 m s−1 at 110 km. Temperature and atmospheric density are retrieved with a precision better than 5 K and 7% up to 90 km (30 K and 20% at 110 km). Errors induced by uncertainties on the vectorB are mitigated by retrieving it. The retrieval ofB is described as a side-product of the mission. At high-latitudes, precisions of 30–100 nT on the vertical component and 100–300 nT on the horizontal one could be obtained at 85 and 105 km (vertical resolution of 20 km). SMILES-2 could therefore provide the first measurements ofB close to the electrojets’ altitude, and the precision is enough to measure variations induced by solar 15 storms in the auroral regions.


Introduction
The mesosphere and lower thermosphere (MLT) is a transitional region (60-110 km) between atmospheric layers with very different characteristics, namely the stratosphere (15-60 km) and the thermosphere (90-400 km) (Smith, 2012;Shiotani et al., 2019). In the stratosphere, O 3 controls the chemical and radiative processes, hence it also regulates the temperature and the 20 dynamics. In the thermosphere, the chemistry and the radiative balance are mainly controlled by the oxygen atoms. In this region, wind and temperature exhibit large diurnal variations and are strongly influenced by tides generated in the lower atmosphere. The thermosphere is also the region of interactions between the ionized (plasma) and neutral atmosphere.
The mean physical characteristics of the MLT (wind, temperature and density) are primarily established by energy transfered from the troposphere via small-scale gravity waves (GWs) (Fritts and Alexander, 2003;Tsuda, 2014). Hence, the MLT state 25 deviates significantly from the radiative equilibrium as illustrated by the occurrence of the coldest point of the Earth system (≈ 150 K) in the summer polar mesopause. Waves with planetary scales also contribute to the upper atmosphere climate (general circulation) through their momentum and energy transport/deposition (Forbes et al., 2006;Pancheva and Mukhtarov, 2011). In particular, tides that are mainly driven by diurnally varying diabatic heating in the troposphere and the stratosphere, propagate upward, with their amplitude reaching a maximum in the MLT (Chapman and Lindzen, 1970;Sakazaki et al., 2015). 30 Hence, the MLT plays a key role in connecting the lower and upper atmosphere and also in linking both hemispheres (Xu et al., 2009;Karlsson and Becker, 2016). Furthermore, the increase of anthropogenic CO 2 is responsible for a cooling of 1-3 K/decade in the MLT that has been measured since the early 1990s (Beig, 2011).
The processes behind these phenomena are still not well quantified. The difficulty arises from the non-linear interactions between the GWs, tides, planetary waves, the background wind and the electromagnetic field (Sato et al., 2018;Immel et al., 35 2006). The system is further complicated by the interconnections between the dynamics and highly variable chemical species, as well as the very different temporal and spatial scales of these processes. Observations of the MLT, in particular of wind, temperature and density, are therefore essential to further our understanding of this region (Smith, 2012).
Continuous measurements of temperature and wind are performed from ground-based stations using lidars (Steinbrecht et al., 2009;Baumgarten, 2010), radars (Jacobi et al., 2015;Tsutsumi et al., 2017) and, up to 70 km, with millimeter radiome-40 ters (Rüfenacht et al., 2014). Density was recently monitored using meteor radars (Yi et al., 2018) but measurements remain scarce. Satellite observations of the MLT have also been performed for several decades. The missions currently in operation and capable of measuring at these altitudes are listed in Tab. 1. Temperature is measured with various techniques and spectral domains (Schwartz et al., 2006;Sica et al., 2008;Sheese et al., 2010;Christensen et al., 2015;Eastes et al., 2017;Englert et al., 2017), but discrepancies larger than 10 K can be found between these measurements above 80 km (García-Comas et al., 2014). 45 Baron et al. (2013) and Shepherd (2015) described the past and current wind measurements from space. Currently only TIDI and MLS (and soon MIGHTI) are capable of measuring MLT winds but with a poor sensitivity below 80 km (Niciejewski et al., 2006;Wu et al., 2008;Englert et al., 2017), and MLS, which is equipped with a single antenna, can only measure one component of the wind vector (it was not designed for wind measurement). with unprecedented precision and altitude coverage such as the temperature between 15-160 km, horizontal wind between 30-160 km, atmospheric density up to 110 km, ground state of atomic oxygen between 90-160 km and more than 15 trace gases' abundance (Baron et al., 2019a, b). The proposed satellite will be equipped with two antennas for the limb measurement of horizontal winds, and three radiometers near 0.7 and 2 THz cooled at 4 K, a technology successfully tested with JEM/SMILES (Kikuchi et al., 2010). With a precessing orbit and the high receiver precision, it will be possible to retrieve 70 diurnal variations of very weak signals as demonstrated with JEM/SMILES (Sakazaki et al., 2013;Khosravi et al., 2013).
In this study we discuss the potential for SMILES-2 to measure the main characteristics of the neutral MLT, namely wind, temperature and atmospheric density. An essential source of information is the O 2 transition at 773.8 GHz. As a magnetic dipole, O 2 is subject to the Zeeman effect induced by the Earth's magnetic field (B). Special care is taken to properly include this effect in the simulations in order to correctly assess the measurement performance. Retrieval errors induced by uncertainties 75 on B are mitigated by retrieving its three components simultaneously with other atmospheric parameters. The scientific interest of the retrieval of B is also discussed. In Sect. 2, the characteristics and principle of the observations are presented in details.
Sections 3 and 4 describe the Zeeman model and the retrieval setting, respectively. The retrieval errors are discussed in Sect. 5.
Finally, we summarize the results and discuss future analysis for SMILES-2.

Observation method
The observation characteristics are summarized in Table 2. The atmospheric limb is scanned from about 20 to 180 km. Scans are performed alternatively with two antennas looking at perpendicular directions to each other. Both antennas can probe the same atmospheric column with a 7 min delay ( Fig. 1), allowing us to derive the 2D horizontal winds. The same method will be used for SIW and more information is given in Baron et al. (2018). The limb geometry provides a high vertical resolution 85 of 2-3 km, and the zonal and meridional samplings at the equator are about 20 • (2200 km) and 6 • (650 km), respectively.
The orbit precesses with a period of about 3 months. The satellite orientation is reversed after every half precession cycle in order to keep the solar panels properly illuminated and the radiative-cooling panels in the shadow side. The latitude coverage is between 50 • S-80 • N or 80 • S-50 • N depending on the satellite orientation. At low and mid latitudes, the same latitude is observed twice per orbit, with LT differences close to 12 hours. Hence, gathering the observations between each maneuver 90 allows us to piece together the complete diurnal cycle of the retrieved parameters.

Spectral bands
Three spectral bands near 638 GHz, 763 GHz and 2 THz are measured simultaneously . The band at 638 GHz contains a strong stratospheric and lower mesospheric signal from ozone (O 3 ). This band is the same as that selected for SIW and its main characteristics are described in Baron et al. (2018). Two THz bands are measured alternatively, one 95 contains OH lines and the second one an O line (Ochiai et al., 2017;Baron et al., 2019a). The O line is used to retrieve between 90-160 km, the abundance of O in its ground-state, wind and temperature (Baron et al., 2015(Baron et al., , 2019b. and carbon monoxide isotopologue ( 13 CO) at 771.183 GHz. The bands have changed compared to those originally described by Ochiai et al. (2017), a change motivated to reduce the power consumption. In the new setting, the CO line is about 50 times weaker than that previously selected.

Qualitative description of the information content
Most of the lines in the spectral bands are emitted by chemical species in their ground state under local thermodynamic 105 equilibrium. The molecular abundance and the temperature are retrieved from the amplitude of the lines. Their Doppler shift  (2.5 kHz for 1 m s −1 ) is used to retrieve the line-of-sight (LOS) wind. The atmospheric density is derived from the O 2 abundance considering that the volume mixing ratio of O 2 is well known below 110 km (Schwartz et al., 2006).
Above about 70 km, the lines are broadened by the random molecular motions, i.e., Doppler broadening, and they do not carry direct information on the pressure (Appendix A). Consequently, the density of the molecule can be retrieved and not the 110 volume-mixing ratio (VMR) as in the lower altitudes. Molecular oxygen is a magnetic dipole that interacts with B. It is subject to the Zeeman effect (Lenoir, 1968) and the selected spectroscopic transition is split into σ ± and π components with different polarization states depending on the LOS orientation ( Fig. 3). The frequency separation of the spectral components is proportional to the amplitude of B.

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In this study, we consider LOS tangent heights between 60 and 110 km. They are provided as input for the inversion algorithm, therefore they must be known before inverting the spectra. Heights registration for a complete scan is calculated differently in the lower part of the scan and in the range of interest (between ∼20-60 km and 60-110 km, respectively).
Between 20 and 60 km, an approach similar to that used for Aura MLS (Schwartz et al., 2006) can be used. The LOS tangent pressure and atmospheric temperature would be retrieved simultaneously from the O 2 line near 763 GHz and from O 3 lines 120 in the 638 GHz band. The height of the pressure levels would then be derived from the hydrostatic equilibrium equation. The resulting precisions are estimated to be better than 1% and 75 m for the LOS tangent pressure and height, respectively (Baron et al., 2019b).
In the altitude range of interest (> 60 km), the LOS tangent heights are inferred from the extrapolation of those calculated previously for the lower altitudes and attitude data from the star-trackers and GPS onboard the satellite. Based on JEM/SMILES 125 results, the expected precision on the retrieved LOS tangent heights will be 100 m or better (Ochiai et al., 2013).

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The magnetic field characteristics (amplitude and orientation angles with respect to the LOS) are defined at the LOS tangent height (Fig. 4) and are assumed constant over the LOS. This approximation is the same as that used by Yee et al. (2017) and it is justified since most of the retrieved information comes from a thin altitude range around the tangent point.

Absorption matrix
The interaction between the radiation and the atmosphere are described by the 4x4 absorption matrix K: where I is the identity matrix, k a is the scalar absorption coefficient and K o is a matrix with off-diagonal components: The scalar absorption coefficient is computed using a line-by-line model and the Zeeman effect is only applied on the O 2 transition: where ν is the frequency, z the altitude, t denotes a spectroscopic transition of the species M that is not affected by the geomagnetic field, n M (n O2 ) is the number density of M (O 2 ), S t is the line strength, F is the Voigt function (Schreier et al., 2014;Larsson et al., 2014) and Γ t,z represents the parameters related to the linewidth (Appendix A). The angle θ is the 145 inclination angle of the magnetic field with respect to the LOS (Fig. 4, left panel).
where the lower scripts u and l denote the upper and lower levels of the transition, respectively, N , J, S and m are quantum numbers associated with the angular momentum, the spin, the total momemtum N + S and the projection of J on the B axis.
The coefficients of K o are derived from Landi Degl'Innocenti and Landolfi (2004) (Eq. 5.36): The parameters u ,v and q are computed by replacing the term F with F , the dispersive part of the complex Voigt function (See Appendix A and (Schreier et al., 2014)).

Radiative transfer
The LOS is divided in narrow ranges of size ds (typically 5 km long) in which the atmospheric parameters are considered constant. The change of the polarized radiance passing through an homogeneous range is derived from a matrix equation which is similar to the scalar radiative transfer one used for a non-polarized radiation (Semel and López, 1999): 165 where b a (s) is the Stokes vector at the position s on the LOS (the frequency dependence is omitted), "·" is the matrix multiplication operator, b p (s) = [P (s), 0, 0, 0] T describes the non-polarized source function between s and s + ds, P (s) is the Planck function, and Λ(s, s + ds) is 4 × 4 evolution operator matrix defined as: The integration over the LOS is performed by applying the scalar equation given by Urban et al. (2004) to Stokes parameters: where b a (sat) is the Stokes vector representing the radiation state at the antenna position, i is the index of the level at s i (i = 0 for the tangent point) and N is the number of levels above the tangent point. The cosmic background radiation is neglected.
We use the relationship Λ(i, j) = Λ(k, j) · Λ(i, k) with i < k < j (the two matrices on the right-side of the equality do not 175 commute).

Measured radiance
The measured radiance for antenna a (a =1 or 2) at the elevation angle θ and the IF ν is:

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where y a,u and y a,l are the atmospheric specific intensities in the upper and lower sidebands around the local oscillator frequency ν LO , R θ,ν represents the antenna and spectrometer functions and is the convolution operator . A simple case with a constant upper and lower sideband ratio is considered. The Zeeman model is only used within a bandwidth of 200 MHz encompassing the O 2 line (upper sideband). Outside this range, the non polarized radiative transfer model described in Baron et al. (2018) is used. In order to transform the Stokes vector (Eq. 9) to the specific intensity associated with the radiometer's polarization, we first rotate the vector from the atmospheric frame to the detector frame as: where b d is the Stokes vector in the instrument frame and M r (α d ) is the Mueller matrix for a rotation α d : The specific intensity y corresponding to the detector polarization is  Over the polar region, the spectra measured by both antennas are very similar since the vector B is almost vertical and perpendicular to both LOSs (Fig. 6). Only the Zeeman components π are detected with the receiver with vertical polarization 205 while the horizontally polarized one detects σ ± components (Fig. 3).

Retrieval setting
The geomagnetic field may exhibit rapid temporal and spatial variations that can be as large as hundreds nT (Doumbia et al., 2007;Yee et al., 2017). Such variations will be difficult to take into account when processing the data and may lead to retrieval errors with the same magnitude as those induced by the measurement noise.

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Such errors are mitigated by retrieving the three components of B simultaneously with other atmospheric parameters. It is done by using the scans of the same atmospheric column measured with the two antennas (Fig. 4). The measurement vector y is defined accordingly as: where the superscripts a 1 and a 2 denote that the parameters are associated with the antennas 1 and 2, respectively. The vector 215 x describing the retrieved parameters contains the profiles of the chemical species having the most significant features in the MLT spectra, namely O 2 , H 2 O, O 3 , NO and HDO (Fig. 2). It also includes the profiles of temperature T, LOS winds (LW) and the three components of B. It is defined as: where x Bw , x Bu , and x Bv are the profiles of the vertical, zonal and meridional components of B. The abundance and temperature profiles are retrieved for each antenna in order to account for differences between both scan locations. This is a similar approach as that used by Hagen et al. (2018) for the measurement of winds with the ground-based radiometer WIRA.
The retrieval error induced by the measurement noise is (Rodgers, 2000) 225 where K = dy dx is the Jacobian matrix of the retrieved parameters x and U is a diagonal matrix to ensure a stable inversion but with values large enough to allow us to neglect its effects in the altitude range where the retrievals are relevant . The matrix S y is the diagonal covariance matrix associated with the measurement noise: The radiative transfer model computes the Jacobian K B = ∂y ai /∂x B with respect to antenna-i frame ({x i , y i , z i } in left panel of Fig. 4). The matrix K B is then computed in the atmospheric frame ( Fig. 4):

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where q = {u, v, w} denote the atmospheric frame axes, and where Φ i is the angle between the antenna-i LOS and the meridional direction (left panel of Fig. 4). representative of the polar night. We did not find significant differences between daytime and nighttime except for the relative error on O 3 retrieval, which is photo-dissociated between 60-80 km. of the MLT. The precision is better than 10% above 95 km at 50 • S and above 78 km over the winter polar region (NH in this study). A precision of 10% or better is achieved above 95 km at 50 • S and 78 km in the winter polar region. The sensitivity to H 2 O decreases with increasing altitude, more sharply above 90 km. The precision is better than 1% up to 75 km in the SH and 65 km in the NH polar region.
The relative error on O 3 retrieval is ∼ 1% around 60 km and strongly increases with increasing altitude and outside of the 260 polar night, because of the daytime photo-dissociation of O 3 .

Atmospheric density, temperature and LOS wind
The achieved precision of the atmospheric density (or O 2 ) profile is better than 5% up to about 95 km at all latitudes. Above 90 km, the signal intensity drops significantly and errors quickly increase, up to 20% at 110 km. Outside of the 70-90 km range, there are significant differences between the error profiles calculated for the full-and narrow-band inversions. This

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shows that spectral lines from other molecular species also have an impact on the O 2 retrievals. This impact probably occurs through the temperature retrieval. For instance, over the winter polar region, the strong NO signal significantly improves the temperature retrievals, thus indirectly improves the O 2 abundance retrieval. Similarly, including H 2 O and O 3 lines leads to an improvement of the O 2 retrieval quality below 70 km.
For all latitudes, the temperature retrieval error is better than 5 K below 90 km and 30 K at 110 km. The O 2 line is the main 270 source of information on the temperature near 90 km.
The LOS wind, a key product for SMILES-2, is retrieved with a precision of 2-4 m s −1 up to 90 km. Above this altitude, the retrieval errors strongly increase, up to 20 m s −1 or more at 110 km. The O 2 line is the main source of information on the LOS wind above 70 km. Over the polar region and above 100 km, spectral lines of NO contribute significantly to the LOS wind retrievals. For atmospheric temperature and below 90 km, the Zeeman effect has a negligible impact on the retrieval errors. Differences can be seen only at high latitudes, where the decrease of the H 2 O abundance explains the larger impact of the O 2 line on the 280 retrieval. In terms of LOS wind retrieval, the Zeeman effect is negligible below 80 km. Above 90 km, the approximation B = 0 leads to a significant underestimation of the retrieval errors, with differences of up to a factor of 2. This clearly shows that the retrieval errors depend on the radiometer polarization, the LOS orientation and on the characteristics of the magnetic field.
Best overall precision is found for a radiometer with a linear vertical polarization. For instance, at NH high latitudes, the LOS wind retrieval error at 99 km is 6 m s −1 using a linear vertical polarization, but degrades to about 10 m s −1 for other 285 polarization settings. Furthermore, using the linear vertical polarization yields homogeneous results for different observation geometries: we could not find significant differences between ascending and descending orbits or between the two antennas. Contrary to the results shown in Sect. 5.1 where it was the optimal configuration, the linear vertical polarization yields a worse retrieval performance for B. In this case, the retrieval errors on B w and B u over the tropics are much larger than those   Perturbations of the geomagnetic field near the equator (30 nT and 80 nT for the surface vertical and horizontal components of B) are much smaller than the retrieval precision (Doumbia et al., 2007). Therefore, extracting interesting information on the 310 equatorial jet will be more challenging and a receiver with a slant polarization could be necessary.

Conclusions
This analysis demonstrates the potential of SMILES-2 for the measurement of the temperature, atmospheric density and LOS wind in the MLT (60-110 km). The retrieval precision was assessed, focusing on the SMILES-2 band at 760 GHz, the most suitable for such measurements. Special care was taken to properly include the Zeeman effect on the O 2 line. Our results showed that neglecting it could lead to underestimating the retrieval errors by a factor of up to 2 above 90 km. Because the O 2 line is polarized, the radiometer's polarization configuration had to be investigated. We found that the optimal configuration was vertical linear. The LOS wind is retrieved with a precision of 2-5 m s −1 up to 90 km (30 m s −1 at 110 km) and a vertical resolution of 2.5 km. Temperature and atmospheric density are retrieved with a precision better than 5 K (30 K) and 7% (20%) up to 90 km (110 km), respectively. The achieved precision of the wind measurements, a key product for SMILES-2, is 320 comparable to the requirements for the new ICON mission (Englert et al., 2017). However, unlike optical sensors, SMILES-2 can acquire high-precision measurements during day and night, and at all latitudes, even during auroral events. The low noise level achieved by the 4-K super-cooled radiometers is essential to achieve good performance above 90 km, where sensitivity becomes critical due to significantly weaker signals.
The retrieval of the geomagnetic field using the O 2 line was also discussed. We showed that valuable information on the 325 horizontal and vertical components of B could be determined directly near the E-region auroral electrojets. Yee et al. (2017) highlighted the need for such observations since, currently, only measurements from the ground or from low-orbit satellites spectral lines, has also been proposed to measure the Martian residual magnetic field (Larsson et al., 2013). Further analyses 330 should be conducted, to characterize more precisely the potential of SMILES-2 for the study of the 3D ionospheric electrojets.
The final instrumental setup is still under discussion. In terms of possible instrumental developments, the spectral bandwidth of the 763-GHz band might be reduced in the definitive configuration of SMILES-2. Narrowing the bandwidth by a factor of 2 (while ensuring a correct adjustment of the LO frequency) would cause minimal degradation of the measurement performance, limited to altitudes below about 40 km.

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Future work to improve MLT retrievals will include the two other SMILES-2 bands. Indeed, the atomic oxygen line at 2 THz contains temperature and wind information above 100 km. This line can help us to improve the wind retrieval precision to 10 m s −1 at 110 km (Baron et al., 2019b). In the 638-GHz band, a strong signal from O 3 will be measured below about 70 km in daytime and 90 km in nighttime. Furthermore, new parameters for the Zeeman model became recently available (Larsson et al., 2019). Applying the updated parameters should induce a change of the O 2 and O line intensities, of up to a few percent.

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The Zeeman effect on other spectral lines: OH, NO and ClO, should also be studied.

Appendix A: Spectroscopic parameters
The spectroscopic parameters are taken from the HITRAN database (Rothman et al., 2009). The line strength at the temperature T is: where k b = 1.380662 × 10 −23 J K −1 is the Bolzmann constant,ν 0 (cm −1 ) is the transition wavenumber, S H (T 0 ) is the HI-TRAN line strength (cm −1 cm 2 molecule −1 ), T 0 = 296 K, E L (cm −1 ) is the lowest energy of the transition. The partition function Q is calculated from tabulated values between 120 and 500 K, a range that encompasses the temperatures found between 50 and 130 km (Q(296) = 215.77). The constants C E = 10 2 h p c and C H = 10 −2 c allow the conversion of the HI- The dispersion profile used for the calculation of the coefficient q , u and v (Eq. 2) is given by: with v = ln 2 ν−ν0 ∆ν d and erfi(v) = 2/π v 0 exp(t 2 ) dt is the imaginary error function (Eq. 5.54 in Landi Degl'Innocenti and Landolfi (2004)).