2.1 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 2-D 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 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 and 80^∘ N or 80^∘ S and 50^∘ N depending on the satellite orientation. At low and middle latitudes, the same latitude is observed twice per orbit, with LT differences close to 12 h. Hence, gathering the observations between each maneuver allows us to piece together the complete diurnal cycle of the retrieved parameters.

Table 2SMILES2 observation characteristics.

^a Calibration measurements will be performed over the upper range. ^b Tangent point vertical displacement during the integration time.

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2.2 Spectral bands

Three spectral bands near 638, 763 GHz and 2 THz are measured simultaneously (Ochiai et al., 2018). The band at 638 GHz contains a strong stratospheric and lower mesospheric signal from ozone (O₃). 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 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 and 160 km, the abundance of O in its ground state, wind and temperature (Baron et al., 2015, 2019b).

Table 3The 763 GHz spectral band.

^∗ Estimated for a tangent height of 80 km including the antenna field of view and the scan velocity.

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Figure 2(a) Spectra at the Equator in daytime for tangent heights of 50, 70 and 90 km. The x coordinates are the intermediate frequency (IF). The yellow dashed lines indicate the noise standard deviation (2σ). The grey area shows the frequency range of 200 MHz in which the Zeeman radiative transfer model is used (only for the upper-side band). (b) Same as (a) but for 80^∘ N and nighttime winter conditions. The red labels indicate molecular lines in the upper-side band. The LO frequency is 763.5 GHz.

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The 763 GHz band (Table 3) is the band considered in this study. It contains lines of water vapor (H₂O) at 752.03 GHz and O₂ at 773.84 GHz (Fig. 2) that provide a strong signal in the MLT. It also contains other molecular lines, weaker but still suitable for our study: nitric oxide (NO, 751.67–752.00 and 773.02–773.05 GHz), O₃ (754.46 and 776.66 GHz) and carbon monoxide isotopologue (¹³CO) 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.

2.3 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 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 O₂ abundance considering that the volume mixing ratio of O₂ 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 volume-mixing ratio (VMR) as in the lower altitudes.

Figure 3(a) Energy levels of the O₂ transitions measured with MLS at 119 GHz (Schwartz et al., 2006), SMR at 487 GHz (Larsson et al., 2014) and SMILES-2. The degenerated energy levels ($M=-J\mathrm{\dots }J$) are indicated with black horizontal strokes. (b) Strength and polarization of the Zeeman components of the line chosen for SMILES-2. The components' frequency is computed for a magnetic field of 60 µT (0.6 Gs). The representation of the polarization states is adapted from Fig. 3.1 in Landi Degl'Innocenti and Landolfi (2004). The dashed lines represent perpendicular and parallel LOSs with respect to B (grey thick arrow).

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.

2.4 LOS altitude

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. Height registration for a complete scan is calculated differently in the lower part of the scan and in the range of interest (between ∼20 and 60 and between 60 and 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 O₂ line near 763 GHz and from O₃ lines 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 on board the satellite. Based on JEM/SMILES results, the expected precision on the retrieved LOS tangent heights will be 100 m or better (Ochiai et al., 2013).

3.1 Absorption matrix

The interaction between the radiation and the atmosphere are described by the 4×4 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 O₂ transition:

where ν is the frequency, z is the altitude, t denotes a spectroscopic transition of the species M that is not affected by the geomagnetic field, n_M ($n_{{\mathrm{O}}_{\mathrm{2}}}$) is the number density of M (O₂), 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 inclination angle of the magnetic field with respect to the LOS (Fig. 4a).

Table 4Zeeman transitions characteristics for the O₂ line at 773.84 GHz ($J:\mathrm{4}\to \mathrm{4}$ and =1). The relative strengths are normalized such as $\sum s_{\mathit{\pi }}=\sum s_{{\mathit{\sigma }}^{+}}=\sum s_{{\mathit{\sigma }}^{-}}=\mathrm{1}$ (Table 3.1 in Landi Degl'Innocenti and Landolfi, 2004). The frequency shift factors β_m are from Eq. (5).

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The frequencies ν_σ,π (Hz) are those of the Zeeman components (Fig. 3). They are dependent on the magnetic field (Larsson et al., 2014):

where g_s=2.002064, μ_b is the Bohr magneton ($\mathrm{9.27401}\times {\mathrm{10}}^{-\mathrm{24}}$ J T⁻¹), h_p is the Planck constant ($\mathrm{6.62618}\times {\mathrm{10}}^{-\mathrm{34}}$ m² kg s⁻¹) and

Here, the lower scripts u and l denote the upper and lower levels of the transition, respectively, and N, J, S and m are quantum numbers associated with the angular momentum, the spin, the total momentum N+S and the projection of J on the B axis.

Figure 4(a) Cartesian and spherical frames used for the radiative transfer calculation. The x and z axes are along the vertical axis (W) and the LOS, respectively. (b) Frame for describing the observation of the same air mass from the forward (ANT1) and aftward (ANT2) antennas. The background geomagnetic field (B) is at first approximation in the meridional plane.

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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).

3.2 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 nonpolarized radiation (Semel and López, 1999):

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, ${\mathit{b}}_{\mathrm{p}}\left(s\right)=\left[P\right(s),\mathrm{0},\mathrm{0},\mathrm{0}{]}^T$ describes the nonpolarized source function between s and s+ds, P(s) is the Planck function, and $\mathbf{\Lambda }(s,s+\mathrm{d}s)$ is 4×4 evolution operator matrix defined as follows:

Figure 5Upper panels: O₂ lines simulated for antenna-1 (blue) and antenna-2 (yellow) at 80^∘ N over the ascending orbit. Panels from left to right show the results for a detector with horizontal, $+\mathrm{45}{}^{\circ }$, vertical, $-\mathrm{45}{}^{\circ }$ and right-circular polarization. The dashed and full yellow thin lines are spectra calculated with an angular tilt of the antenna-2 detector of −20 and $+\mathrm{20}{}^{\circ }$. The black dashed lines are the measurement noise STD × 10 for antenna-1. Lower panels: same as upper panels but for the Equator.

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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 $\mathbf{\Lambda }(i,j)=\mathbf{\Lambda }(k,j)\cdot \mathbf{\Lambda }(i,k)$ with $i<k<j$ (the two matrices on the right-hand side of the equality do not commute).

4.1 Measured radiance

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

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 (Baron et al., 2018). 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 O₂ line (upper sideband). Outside this range, the nonpolarized 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 follows:

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

where b_d[n] is the nth component of the Stokes vector and (m,n) is $(-\mathrm{1},\mathrm{1})$, (1,1), $(-\mathrm{1},\mathrm{2})$, (1,2), $(-\mathrm{1},\mathrm{3})$ and (1,3) for horizontal, vertical, +45, $-\mathrm{45}{}^{\circ }$, right and left circular polarizations, respectively.

Figure 6Magnetic field (θ_1,2, ϕ_1,2,$\left|\mathit{B}\right|$ and Φ_b) and LOS (Φ_1,2) parameters (Fig. 4) with respect to latitudes. The blue (yellow) lines are for ANT1 (ANT2) data. The circle–dashed (square–full) lines are data on the descending (ascending) orbit branch. The grey arrows in panels 2 and 5 indicate the direction of the satellite motion.

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Figure 5 shows simulated spectra of the O₂ line over the Equator and at 80^∘ N when the satellite is moving toward north (ascending orbit branch). The tangent height is 100 km and the atmospheric conditions are representative of the Northern Hemisphere in wintertime (Baron et al., 2018). The magnetic field characteristics are zonal means inferred from a quiet solar day (Fig. 6). Spectra are shown for different radiometer's polarizations. Over the Equator, B is along the meridional direction and clear differences are seen between the radiances measured with both antennas, except if the detector has a vertical polarization. In that case, the radiometer detects only the σ^± lines independently of the LOS orientation. The antenna-1 spectrum measured with a radiometer with a horizontal polarization is sensitive to the π components which gives the visible double line shape. A receiver with a right-circular polarization measures mainly the σ⁺ components since the antenna-1 is nearly aligned with the magnetic field (${\mathit{\theta }}_{\mathrm{1}}=\mathrm{20}{}^{\circ }$ in Fig. 6). The spectrum looks like a single line with a frequency shift of $\mathrm{\Delta }\mathit{\nu }\approx \mathrm{420}({\mathit{\beta }}_{\mathrm{m}=-\mathrm{1}}+{\mathit{\beta }}_{\mathrm{m}=\mathrm{0}})=-\mathrm{21}$ kHz (Eq. 4), equivalent to a LOS wind of 8 m s⁻¹.

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, while the horizontally polarized one detects σ^± components (Fig. 3).

4.2 Retrieval setting

The geomagnetic field may exhibit rapid temporal and spatial variations that can be as large as hundreds of nanoteslas (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.

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 follows:

where the superscripts a₁ and a₂ denote that the parameters are associated with the antennas 1 and 2, respectively. The vector x describing the retrieved parameters contains the profiles of the chemical species having the most significant features in the MLT spectra, namely O₂, H₂O, O₃, 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 follows:

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 to 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)

where $\mathbf{K}=\frac{\mathrm{d}\mathit{y}}{\mathrm{d}\mathit{x}}$ 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 (Baron et al., 2018). The matrix S_y is the diagonal covariance matrix associated with the measurement noise:

and ${\mathbf{S}}_{y,i,i}$ is the noise induced variance on the ith component of the measurement vector y, T_sys is the system temperature (Table 3), δν is the frequency resolution (0.5 MHz) and δt is the spectrum integration time (0.25 s).

The radiative transfer model computes the Jacobian ${\mathbf{K}}_B=\partial {\mathit{y}}^{a_i}/\partial {\mathit{x}}_B$ with respect to antenna-i frame ($\mathit{\{}{\mathit{x}}_{\mathit{i}},{\mathit{y}}_{\mathit{i}},{\mathit{z}}_{\mathit{i}}\mathit{\}}$ in Fig. 4a). The matrix K_B is then computed in the atmospheric frame (Fig. 4):

where $q=\mathit{\{}\mathit{u},\mathit{v},\mathit{w}\mathit{\}}$ denote the atmospheric frame axes, and

where Φ_i is the angle between the antenna-i LOS and the meridional direction (Fig. 4a).

Figure 7Vertical profiles of atmospheric number density, temperature and VMRs of O₂, H₂O, O₃ and NO. They are representative of a Northern Hemisphere winter period (DJF), during daytime at 50^∘ S and the Equator (dashed-grey and red lines, respectively), and polar night at 80^∘ N (blue lines).

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5.1 Atmospheric density, temperature and LOS wind

The achieved precision of the atmospheric density (or O₂) 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 shows that spectral lines from other molecular species also have an impact on the O₂ 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 and thus indirectly improves the O₂ abundance retrieval. Similarly, including H₂O and O₃ lines leads to an improvement of the O₂ 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 O₂ line is the main source of information on the temperature near 90 km.

Figure 10Same as Fig. 9 but for LOS wind retrievals.

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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 O₂ 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.

Figures 9 and 10 show the achieved retrieval precisions for temperature and LOS wind, at altitudes between 80 and 110 km and for different polarization settings. Results are shown within the latitude range 50^∘ S–80^∘ N, for both antennas and for both the ascending and descending orbit branches. The results obtained with B=0 are also presented.

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 in the H₂O abundance explains the larger impact of the O₂ line on the 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.

The 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 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.

Figure 11Same as Fig. 9 but for the geomagnetic field components and altitudes between 85 and 105 km. The retrieval vertical resolution is 20 km.

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5.2 Geomagnetic field

Figure 11 shows the retrieval errors on the three components of B at 85 km and 105 km (vertical resolution of 20 km). The results strongly depend on the radiometer's polarization. Best performance is achieved with a $\pm \mathrm{45}{}^{\circ }$ linear polarization. Errors are clearly smaller when the retrieved component is aligned with the background magnetic field: the error on B_v is smallest at the Equator where B is horizontal and in the meridional plane, and the error on B_w minimizes at high latitudes where B is nearly vertical. The best sensitivity is found at 85 km where the precision is better than 400 nT for all components and at all latitudes, except for the zonal component (B_u) in the tropics. At high latitudes, errors are between 50 and 100 nT for the vertical component (B_w) and between 100 and 200 nT for the horizontal ones (B_u and B_v). At 105 km, errors increase, for example to 80–500 nT outside the tropics.

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 found with a slant polarization. Only the meridional component (B_v) can still be retrieved with a reasonable precision of 100–400 nT. At middle and high latitudes, best precision is found for B_w (30–50 nT at 85 km and 50–70 nT at 105 km). At 85 km, the error on B_v and B_u are between 200 and 300 and between 300 and 2000 nT, respectively. Large errors in B_u are found at 40^∘S and 70^∘ N where the LOS is aligned with the U and V axes (Φ₁ or Φ₂=0, Fig. 6).

Our results show that the sensitivity of the SMILES-2 instrument is high enough to potentially measure the electrojet-induced variations of B at high latitudes even under quiet sun conditions, provided that the data are properly averaged. Yee et al. (2017) used the Zeeman effect on the AURA/MLS O₂ line to derive variations of 100–200 nT in the intensity of B. During solar storms, the amplitude of the perturbations in the auroral regions could be considerably larger (several hundreds of nanoteslas) (Yee et al., 2017; Yamazaki and Maute, 2017) and could be detected with single measurements along the vertical and at least one horizontal component of B. Hence, SMILES-2 could allow us to infer information on the 3-D variations of the auroral electrojet.

Perturbations of the geomagnetic field near the Equator (30 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 equatorial jet will be more challenging, and a receiver with a slant polarization could be necessary.