The submillimeter sensor will be carried to Mars on a satellite weighing less than 100 kg. Such a small satellite needs special means to enter orbit. The selected method to achieve orbit is to use the atmospheric drag to perform aerocapture. Aerocapture has never been attempted successfully before – as far as we are aware – so the final orbital parameters are to some extent uncertain. A future work will discuss the orbit insertion and retention in details. For this work, we have opted to work simply with two sets of observations taken from an orbit with the Kepler element's semi-major axis of 6150 km and eccentricity of 0.5. This gives a periareion altitude of 400 km and an orbit time of 5 h and 20 min. We will show simulated observations as well as estimated errors for retrieved atmospheric quantities in limb-scanning mode near the periareion and in nadir-staring mode near the apoareion. The final orbit could differ from the one above, but the feasibility of the sensor is not strictly dependent on the details of the orbit. As long as the periareion is not too high, it will merely affect its spatial resolution.

The sensor is also limited in mass and power budget by the small scale of the platform itself. We will, for instance, not be able to change the local oscillator to be sensitive to different ranges than those selected on the design board. A schematic sketch of the instrument can be seen in Fig. . The spectrometer we plan to use is the chirp transform spectrometer designed for the Jupiter icy moon explorer's submillimeter wave instrument, with 10 000 channels over a 1 GHz range for examples on this type of spectrometer, see, e.g.,. The local oscillator will be at 481.15 GHz with a central intermediate frequency of 6 GHz. There will be no suppression of either of the sidebands, so the measured radiation will be between 474.65–475.65 and 486.65–487.65 GHz. The system noise temperature is expected to be about 2000 K in double-sideband mode. The antenna is planned to be 30 cm large and made of carbon fiber reinforced plastic. This achieves a 10 km vertical footprint at orbit altitudes below about 400 km, with a resolution half-width of about 0.14∘. A lower system noise would improve all results presented below, though the quoted number is as good as we expect the instrument will be at time of flight.

We plan to use two identical receiver systems with the same setups but fed different states of polarization. The polarization states will be separated using a feed horn antenna. This way, if one of the receiver chains experiences technical issues, we can use the other to keep measuring the atmosphere. In addition, while both chains work, we can measure the magnetic field. Molecular oxygen is affected by the Zeeman effect , so it is possible to sense the strongest crustal magnetic field through the state of polarization for more details, please see.

Because of the dual receiver systems, if we take a single measurement every second, the measurement alone produces about 160 kbps of data before any compression is applied. This exceeds our maximum transfer rate, so we will have to perform limited data reduction aboard the spacecraft. The software for this is not ready yet. The only reduction considered in this work is an averaging by pairing immediate neighboring channels to increase the effective width of a channel to 200 kHz. This is still well below the line width of the absorption lines that we consider here, so no physics is lost.

We use the Atmospheric Radiative Transfer Simulator ARTS; for all forward simulations. ARTS is a fully three-dimensional model with full polarization capabilities that has been used in numerous studies. Please see the two cited articles, other articles citing them, and the source code – available via a copyleft license at http://www.radiativetransfer.org/ (last access: 10 December 2018) – to understand the radiative transfer method of ARTS in more detail. All of the data used in this study can be found via the aforementioned link.

The standard scenario atmosphere is from daytime simulations by Laboratoire de Météorologie Dynamique's global circulation model for a solar angle of 0∘. The temperature and volume mixing ratio profiles for key species are shown in Fig. . The magnetic field is set to a constant 1 µT throughout the transfer, pointing along the line of sight of the transfer. We expect there to be large variations in some gases (i.e., gaseous water, ozone, and hydrogen peroxide) and in the strength of the magnetic field. In order to demonstrate how the error estimation changes as the forward model scenario changes, we perform the simulations at a 100 times lower volume mixing ratio of these gases and of the magnetic field. In this reduced case, we still keep the temperature and molecular oxygen mixing ratios the same as in the standard scenario. We do not set the wind speed in any scenario but perform retrievals of it from analytical expressions of its Jacobian.

A spectroscopic suite suitable for Mars was developed by , which we use for our simulations. It computes pressure broadening and shifting per atmospheric species rather than from a predefined atmospheric composition. We also use the carbon dioxide collision-induced absorption from as the continua shown in Fig. . These continua are key to low-altitude limb measurements and are the main reason we are focusing on the 400 GHz range rather than higher frequencies. Note that the continua are effectively twice as strong as normal since we will not suppress the lower or upper sidebands. A big problem with these continua is that they are only defined down to a temperature of 200 K. For lower temperatures, we simply extrapolate to these using the code by ignoring the warnings. Despite these issues, we still choose to include the continua since ignoring a potential 20–120 K signal would be catastrophic for the science of the mission. Clearly, the carbon dioxide continua have to be studied more for Mars atmospheric conditions since their influence is notably strong. Even if our extrapolation is the cause of most of the absorption that we see (because of some model artifact at lower temperatures), it is necessary to confirm that this is the case and to limit the influence of the continua.

We use the optimal estimation method described by to predict at what level of precision and resolution we will be able to measure atmospheric parameters. This is done by assuming a linear error. Errors tend to be linear near the target even if the retrieval process or underlying physics is non-linear. The computed error is from ex=SaJ⊤JSaJ⊤+Se-1ey=Sa-1+J⊤Se-1J-1J⊤Se-1ey, where Sa is the a priori covariance matrix, J is the Jacobian matrix, Se is a diagonal radiance error covariance matrix, and ey is a Gaussian realization of the measurement error. This realization is repeated a number of times to estimate the error on retrieved parameters. The measurement error covariance is set to be diagonal, having the square of the standard deviation of the measurement error at each point. For most of the simulations below, we assume a diagonal a priori covariance matrix. For the one figure where we do not assume this at the end, the correlation of this matrix is assumed to decrease exponentially the further the distance is from the diagonal, as described by , and the correlations between retrieved parameters (i.e., wind, temperature, magnetic field strength, O2, H2O, H2O2, and O3 volume mixing ratios) are still assumed to be zero. The a priori variance at each altitude level is from a standard deviation of the molecular oxygen mixing ratio of 100 ppmv, of the gaseous water mixing ratio of 1 ppmv, of the hydrogen peroxide and ozone mixing ratios of 10 ppbv, of the magnetic field strength of 10 µT, of the temperature of 10 K, and of the wind speed of 100 m s-1. These numbers were chosen because they are the closest order of magnitude standard deviations that produce a clear measurement response for each model parameter in the limb-scanning simulations at 1 s integration time. For some of these parameters, we will discuss what happens to the error estimations by increasing the standard deviation by 1 order of magnitude. The measurement response is defined as r=SaJ⊤JSaJ⊤+Se-1Ju=Sa-1+J⊤Se-1J-1J⊤Se-1Ju=Au, where u is a vector of ones, and A is the averaging kernel. We define a clear measurement response as max(r)>0.8. The trace of A gives the degrees of freedom of the retrieval system.

Note that the shape of the averaging kernels gives the altitude range where the measurements are sensitive to the atmospheric parameters, a combination of the instrument's statistical and physical vertical resolution. The degrees of freedom of the averaging kernel give a rough estimation of how many distinct parameters can be set over the entire profile altitude range, given the statistical constraints. A reduction in the degrees of freedom by, e.g., assuming a larger statistical correlation distance or by integrating the signal over a wider vertical slice of the atmosphere, should be followed by an increase in the precision of the retrieved parameter at the cost of a loss in vertical resolution. It is also possible to increase the precision of the retrieved model parameters by increasing the integration time to reduce the measurement noise. This has the cost of reducing the spatial resolution either vertically or horizontally. We will not consider this type of reduced resolution in this work, partly because such a reduction can be done by averaging measurements a posteriori so long as the original data are available in a high time resolution. The only test of resolution versus precision we make in this work is one where we vary the a priori correlation distance. Although a very crude estimation, it serves the purpose of finding a limit to the precision.

The simulated signal from 486.65 to 487.65 GHz and from 475.65 to 474.65 GHz is shown in Fig. . The signal shows two hydrogen peroxide absorption lines at 475.20 and 487.20 GHz, a single molecular oxygen absorption line at 487.25 GHz, a single ozone absorption line at 487.35 GHz, and a single gaseous water absorption line near the edge at 474.69 GHz. The limb view signal from molecular oxygen is saturated at the lowest tangent altitude (peaks of 95 K in the double-sideband view), but its signal is more reduced at higher altitudes. The gaseous water signal is also saturated at lower tangent altitudes but weakens greatly at higher tangent altitudes. The ozone signal is weak, about 5 K in strength at low altitudes, due to Ozone's consistently high mixing ratio at higher altitudes. The hydrogen peroxide signal is also weak, but much stronger than the ozone signal, at 10 K at low altitudes, but its strength decreases more rapidly at higher altitudes.

The estimated errors on the forward model parameters for limb-scanning observations are shown in Fig.  for a single second of integration time pointing at each of the tangent altitudes of Fig. . In addition to the signal in Fig. , we also present a case in Fig.  where the gaseous water, the hydrogen peroxide, and the ozone volume mixing ratios, as well as the magnetic field strength, are reduced by a factor of 100. Below, for simplicity, the atmosphere with less water is called “dry” and the atmosphere with more water is called “wet”. The estimated errors on the forward model parameters for nadir-staring mode are shown in Fig.  for a full 1 h of integration time.

For Figs. , , and :

In terms of molecular oxygen, expected error levels are of 25 ppmv with good measurement response from 10 to 30 km in the limb-scanning mode. In nadir-staring mode, the altitude range of good measurement response extends from 10 to 40 km, and the expected error is about 15 ppmv. Molecular oxygen is not expected to change at short timescales, so either scenario is good for the purpose of the mission to place a constraint on our knowledge of molecular oxygen variations. Longer integration times in limb-scanning mode, or staring at lower altitudes, could be useful for limiting the vertical profile of the molecule better, especially at lower altitudes. For instance, the very near-surface error achieves good measurement response by merely increasing the integration time to 2 s staring every 10 km from 5 to 35 km.

An estimation of the vertical resolution versus precision can be had by letting the correlation distance increase to large distances. In Fig. , we let the correlation distance vary from a diagonal a priori matrix to 1000 km for both nadir-staring and limb-scanning simulations. The figure shows the degrees of freedom of the averaging kernel at these different correlation distances versus the precision in the range where the measurement response is above 80 %. This way, the figure indicates that what we are trading for increased precision is lower degrees of freedom. Lower correlation distances tend to have more degrees of freedom. Since we discuss the uncorrelated case in precious subsection, we limit the discussion below to longer correlation distances, where the degrees of freedom are reduced. These represents a scenario where we assume that the state of the atmosphere at one level is highly correlated with that at every other level. This is a somewhat crude way to reduce the degrees of freedom of the problem, but it serves as an estimate of the error at a lower vertical resolution. For molecular oxygen, this highly correlated state reduces the estimated errors in the nadir-staring mode to about 10 ppmv and in the limb-scanning mode to about 15 ppmv. For gaseous water, the highly correlated state reduces the error estimation to 0.1 ppmv for both nadir-staring and limb-scanning modes. For hydrogen peroxide, the estimated errors are reduced in the highly correlated state to about 1 ppbv in nadir-staring mode and to 0.5 ppbv in limb-scanning mode. The limb-scanning mode retains more than 1 degree of freedom. For ozone, limb-scanning mode errors remain at about 2 ppbv in the highly correlated state, as its degrees of freedom are low to begin with for the uncorrelated a priori covariance matrix. The magnetic field in the highly correlated state has limb-scanning mode estimated errors at 1 µT and in nadir-staring mode at 0.5 µT. Since the magnetic field is highly correlated with vertical distance, these numbers might better represent the precision at which we can retrieve the magnetic field strength from a single profile than the errors estimated in the previous subsection. The temperature error estimation in the highly correlated case retains degrees of freedom in both nadir-staring and limb-scanning modes, meaning the retrieval system does not allow the trade that we are after. The errors are expected to be about 0.5 K. The wind speed errors are expected to be around 5 to 10 m s-1 in the highly correlated case.