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M Grandin, P.-L Blelly, O Witasse, Aurélie Marchaudon
To cite this version:
M Grandin, P.-L Blelly, O Witasse, Aurélie Marchaudon. Mars Express radio-occultation data: A
novel analysis approach. Journal of Geophysical Research Space Physics, American Geophysical
Union/Wiley, 2014, 119 (12), pp.10,621-10,632. �10.1002/2014ja020698�. �hal-03166297�
RESEARCH ARTICLE
10.1002/2014JA020698
Key Points:
• A direct approach of
radio-occultation data analysis has been implemented
• It enables a full-profile analysis of a given experiment
• Twilight terminator profiles can be retrieved with this method
Correspondence to:
M. Grandin, mgrandin@sgo.fi
Citation:
Grandin, M., P.-L. Blelly, O. Witasse, and A. Marchaudon, (2014), Mars Express radio-occultation data: A novel analysis approach,J. Geophys. Res. Space Physics, 119, doi:10.1002/2014JA020698.
Received 6 OCT 2014 Accepted 2 DEC 2014
Accepted article online 5 DEC 2014
Mars Express radio-occultation data: A novel analysis approach
M. Grandin
1,2, P.-L. Blelly
2,3, O. Witasse
4, and A. Marchaudon
2,31
Sodankylä Geophysical Observatory, University of Oulu, Sodankylä, Finland,
2Institut de Recherche en Astrophysique et Plan ´etologie, Université de Toulouse, Toulouse, France,
3Centre National de la Recherche Scientifique, UMR 5277, Toulouse, France,
4Scientific Support Office, European Space Agency, ESTEC, Noordwijk, Netherlands
Abstract The Mars Express Radio Science (MaRS) experiment on board Mars Express has been providing radio-occultation data since early 2004. The analysis method currently used to retrieve neutral atmosphere and ionosphere profiles is based on the resolution of a complex inverse problem. The solution to such a problem is obtained under strong assumptions on the atmosphere and the ionosphere and with some limitations. Here we developed a novel method for radio-occultation data analysis based on a direct approach which overcomes some of the difficulties related to the standard inversion. This new method is based on a numerical model of the atmosphere and the ionosphere of Mars computing the propagation of the radio waves from the spacecraft to the receiver on Earth. The main interest of such an approach lies in the intrinsic and coherent coupling between the neutral part and the ionized part of the planetary environment, which gives physical constrains on the retrieved profiles. We have applied this new method to radio occultation experiments performed by MaRS, and we present the results obtained in two different occultation configurations. We discuss the differences which emerge from the standard analysis and the gain that such a method can give to the analysis of planetary environments.
1. Introduction
Based on the refraction of radio waves within the atmosphere and the ionosphere of a planet,
radio-occultation has long been the main technique to derive information on planetary environments. At the end of the 1960s, radio-occultation experiments have been performed at Mars with Mariner IV [Kliore and Tito, 1967] and at Venus with Mariner V [Cain et al., 1967]. Many later interplanetary missions made further use of the technique, including the Viking missions launched in 1975 [Fjeldbo et al., 1977]. In the early 2000s, the Mars Global Surveyor and Mars Express missions also performed such experiments to provide the scientific community with hundreds of radio-occultation profiles of Mars [Hinson et al., 1999; Pätzold et al., 2004].
The principle of this method lies in the measurement of the Doppler shift of a radio signal sent by an orbiter around the given planet toward a ground receiver on Earth. As the probe gets occulted by the planet from the receiver’s point of view, the signal propagates more and more deeply through the planet’s ionosphere and atmosphere, whose refractive indices are concentration dependent and thereby inhomogeneous. This refractive index gradient bends the electromagnetic ray and a parallax appears. As a result, the Doppler shift observed by the receiver is slightly different from the predicted one assuming that there is no atmosphere/ionosphere. This Doppler shift difference is called frequency residual. Thanks to its measurement, it is possible to infer the bending angle of the ray due to the presence of the planetary envelope and to obtain information on neutral species temperature, pressure, and density profiles in the atmosphere and on the electron density profile in the ionosphere as functions of the altitude in the probed regions.
Most previous studies [e.g., Fjeldbo et al., 1971; Pätzold et al., 2007; Tellmann et al., 2013; Pätzold et al., 2005;
Peter et al., 2014] using radio-occultation data assume several properties, mainly stratified atmosphere and
ionosphere with spherical symmetry and a clear separation between neutral and ionized media. These
assumptions enable an inversion of the radio-occultation profile in order to obtain the aforementioned
information. However, such assumptions are not always verified, for instance near the twilight terminator
of the planet, and the inversion of the electron profile is likely not to give reliable information. Moreover,
atmosphere and ionosphere are strongly correlated; separating both domains imposes to leave apart the
transition region which contains valuable information on the coupling between the two regions. Thanks
Figure 1. Overall structure of the model.
to direct simulations, in which the trajectory of the radio wave within the planetary envelope is computed, these constrains may be released. This allows to expect more trustworthy results on atmosphere and ionosphere profiles, especially because the spherical symmetry assumption is not physically satisfying considering the temperature and electron density differences between the dayside and the nightside of the planet. Even on the dayside of the planet, local ionospheric structures such as planetary waves [Wang and Nielsen, 2003] and oblique ionospheric echoes most likely due to localized plasma density structures [Andrews et al., 2014] can break the spherical symmetry.
A description of the model is provided in section 2. Section 3 presents the results of the analysis of two Mars Express radio-occultation profiles using the model, followed by a discussion in section 4. Finally, a summary and a conclusion of this work are given in section 5.
2. Model Description
Although its structure makes it planet independent, the model has been more specifically designed to study data from the Mars Express mission. Since 2004, the Mars Express Radio Science (MaRS) experiment has provided hundreds of radio-occultation profiles which contain highly valuable information on the Martian ionosphere and neutral atmosphere [Pätzold et al., 2009].
The objective of the model is to provide a new analysis tool of Mars radio-occultation profiles which is able to retrieve the neutral temperature and densities in the atmosphere and the electron density in the ionosphere of the planet, accounting for the chemical couplings. The method we developed is novel, as it is based on direct simulations instead of an inverse problem solving, and it allows to analyze the “full radio-occultation profile” consistently, i.e., assuming no separation between the regions.
In this direct approach, we first consider a pattern for the atmosphere temperature profile, which can be adjusted through a set of parameters. We then derive the neutral atmosphere density and compute the electron density in the ionosphere, which enables to obtain the refractive index locally. For a given experiment characterized by certain orbit conditions (date, time, position, and pointing…), we study the propagation of a signal emitted by the probe toward the Earth-based receiver as it undergoes refraction in the planetary environment. From the computed trajectories of the radio wave, we derive the frequency residual profile for the experiment according to the model. The results of the simulation are then compared to the actual measurements, and an optimization procedure, based on a Levenberg-Marquardt algorithm, of the atmosphere parameters is enforced for the simulation to fit the data.
Figure 1 provides an overview of the analysis algorithm. The model can be split into three main physical modules: the neutral atmosphere model, the ionosphere model, and the frequency residual computation from ray trajectory integration. These modules are then coupled to a feedback-and-optimization block.
2.1. Atmosphere Model
2.1.1. Neutral Temperature Profile
First, a pattern for the neutral atmosphere temperature is chosen. This profile can be adjusted through a set of parameters (see below). Figure 2 shows an example of the chosen temperature profile for the neutrals.
This profile can be split into three regions:
1. in the thermosphere and exosphere (i.e., above 140 km altitude), we use an exponential Bates profile [Bates, 1959];
2. in the mesosphere (i.e., around 100 km altitude), the temperature reaches a flat minimum;
3. at lower altitudes (i.e., below 80 km altitude), we choose a piecewise constant temperature gradient.
100 150 200 250 300 350 0
50 100 150 200 250
Neutral temperature (K)
Altitude (km)
Figure 2. Example of a temperature profile as defined by the model. The values of the parameters for the exosphere and mesosphere parts are
𝜂m=105km,
Tm=120K,
Ta=180K,
Ta′=4.5K km
−1, and
T∞=290K.
The temperature profile is parametrized with the geopotential height, which takes into account the variation of the gravity acceleration due to the planet. The geopotential height, denoted 𝜂 , is defined according to the ground level where g
0≈ 3 . 71 m s
−2[Lodders and Fegley, 1998], and it therefore writes
𝜂 (z) = R
pz
R
p+ z (1)
where R
pis the local radius of Mars, for which the reference ellipsoid given by Ardalan et al. [2010]
is used.
The pattern of the temperature profile is adjustable through a set of parameters. For the thermosphere and exosphere Bates profile, as described in the appendix of Hedin et al. [1983], we have
T( 𝜂 ) = T
∞− ( T
∞− T
a)
e
−𝜎(𝜂−𝜂a)(2)
where T
∞represents the temperature limit for the neutrals in high exosphere, while T
ais the temperature at an empirically chosen reference altitude 𝜂
a= 140 km. The steepness of the exponential profile is determined by 𝜎 . This expression can be totally defined by a set of three independent parameters; we choose T
a, T
∞, and T
a′=
dTd𝜂
|| |
𝜂a= 𝜎 (T
∞− T
a).
The mesosphere rather-slowly-varying profile is rendered using an inverse parabola connected to the Bates profile and extended downward with a line segment between altitudes noted 𝜂
mand 𝜂
1, on which the temperature reaches its minimum value T
m. This gives two additional adjustment parameters, as we empirically fix 𝜂
1= 80 km.
Finally, the lower atmosphere is modeled by several layers with constant temperature gradient. The thickness of these layers has been set to 5 km, which represents fifteen additional parameters. This choice enables more flexibility than assuming a linear profile.
2.1.2. Neutral Density Profile Computation
Knowing the neutral temperature profile and under the hydrostatic equilibrium assumption, the density profiles of each neutral species can be computed. We have
dP
s= −m
sN
s( 𝜂 )g
0d 𝜂
where P
s= N
sk
BT is the pressure of the species s considered an ideal gas (k
Bthe Boltzmann constant) and N
sits density, with m
sthe molecular mass of the species and g
0the gravity acceleration at ground level.
Defining T ̄ =
TT∞
the normalized temperature, we introduce the atmosphere scaling height H
s0≡
kmBT∞sg0
. The integration of the obtained equation leads to
P
s( 𝜂 ) = P
srefexp (
− 1 H
s0∫
𝜂 𝜂ref
d 𝜂
′T ̄
)
P
refbeing the reference pressure at a reference altitude 𝜂
ref.
Finally, the neutral density is derived applying the ideal gas law again, which gives N
s( 𝜂 ) = N
srefT
refT ( 𝜂 ) exp (
− 1 H
s0∫
𝜂 𝜂ref
d 𝜂
′T ̄
)
(3)
where N
srefand T
refare, respectively, the neutral density of species s and the neutral temperature at
𝜂
ref= 110 km. T
refbeing constrained by the temperature profile model, the only additional free parameters
are the N
sref. As we consider a Martian atmosphere with three neutral species: CO
2, O, and N
2, we thus
introduce N
COref2, N
Oref, and N
Nref2.
In the lower atmosphere, we modify N
2and O densities so as to maintain a constant mixing ratio with CO
2, chosen to be, respectively, 0 . 5 × 10
−2for N
2/CO
2and 10
−3for O/CO
2, and below 70 km, the O density is exponentially reduced in order to render the fact that O is formed by photodissociation of CO
2and therefore shows a decreasing density at low altitudes [Peter et al., 2014]. This is not critical for the analysis, but it may prevent some biases at very low altitude. These last two features have been chosen only to provide more realistic N
2and O density profiles but do not pretend to reflect reality. Indeed, CO
2is largely predominant at low altitudes, and contributions of N
2and O to total neutral density therefore prove negligible [Nier and McElroy, 1977].
2.2. Ionosphere Model
The ionosphere model is based on a photochemical equilibrium: the ion production rate, which depends on the atmosphere, is balanced by dissociative recombination of the ions with the electrons. The electroneutrality allows then to derive the electron density.
2.2.1. Ion Production
The ion production rates are computed from a photochemical model developed for this study, which takes into account the solar flux received locally by the neutrals and the local solar zenith angle. The F
10.7index is used as a proxy for solar activity at the time of the experiment. It corresponds to a daily measurement of the 10.7 cm radio flux performed at the Pentictin Radio Observatory (Canada) at local noon. In the model, the F
10.7index is used to calibrate the solar EUV flux spectrum at the Earth orbit. We use the Solar EUV Flux Model for Aeronomic Calculations (EUVAC) model [Richards et al., 1994] to describe the solar flux. The values of the solar flux received at Earth are then normalized to the Martian orbit for the computation of the ion production rates in the Martian ionosphere. From the densities of the neutral species, the ion primary and secondary production rates due to the photoionization by the EUV fluxes at the time of the experiment can be determined. In this model, three ion species are formed by photoionization: CO
+2, O
+, and N
+2.
Because the F
10.7index does not render very well the high-energy spectrum of the solar flux [Woods et al., 2005], a correction coefficient has been introduced in order to enhance the X-and-UV part of the spectrum (wavelengths below 25 nm). The values of the solar flux at those wavelengths as defined by the model are multiplied by this coefficient, noted C
XUV. This fudge factor is an additional parameter for the optimization, which is allowed to vary from 1 to 50 so as to find a compromise between flexibility and plausible values.
2.2.2. Ion Photochemical Model and Electron Density Computation
The ionosphere model considers five ion species: CO
+2, O
+, O
+2, N
+2, and NO
+. Three of them are formed by photoionization (CO
+2, O
+, and N
+2), while the other two are created only through chemical reactions. These ions interact with the neutrals CO
2, O, and N
2as well as with the electrons; they are involved in 13 reactions given in Table 1 (after Schunk and Nagy [2000]). The (k
i) and ( 𝛼
i) stand for the reaction rates (in m
−3s
−1), some of them depending on the neutral temperature T in kelvin.
The ionosphere model computes the chemical equilibrium for this system of equations for given neutral densities. If we define N = (
n
O+2
, n
O+, n
CO+2
, n
N+2
, n
NO+)
Tand if we suppose N = N
0+ 𝛿 N, it can be written, at the first order:
d𝛿N
dt = + M
0N
0+ M
1𝛿 N (4)
where is the vector of the production rates of the ions in m
−3s
−1, M
0the chemical evolution matrix at order 0, and M
1the chemical evolution matrix at order 1, both depending on the neutral densities, the zero-order electron density and the reaction rates. M
1also depends on the zero-order ion densities.
The solution of equation (4) is then given by 𝛿 N = −[I
3− exp (
tM
1) ]M
1−1(
+ M
0N
0)
(5) with I
3the identity matrix. We integrate this equation with respect to time t using an Euler forward scheme.
2.3. Experiment Simulation 2.3.1. Ray Trajectory Integration
Once the atmosphere and ionosphere properties are set up, it is possible to compute the trajectory of a
radio wave within the planetary envelope.
Table 1. Chemical Reactions Considered in the Ionosphere Model and Their Reaction Rates (After Schunk and Nagy [2000])
O
+2+ N
2 →NO
++ NO
k1=5.0×10−22O
++ N
2 →NO
++ N
k2=1.5×10−16−5.9×10−17( T 300)
O
++ CO
2 →O
+2+ CO
k3=1.1×10−15CO
+2+ O
→O
+2+ CO
k4=1.64×10−16CO
+2+ O
→O
++ CO
2 k5=9.6×10−17N
+2+ CO
2 →CO
+2+ N
2 k6=8.0×10−16N
+2+ O
→O
++ N
2 k7=1.0×10−17(300 T)0.23
N
+2+ O
→NO
++ N
k8=1.4×10−16(300 T)0.44
O
+2+ e
− →O + O
𝛼1=1.6×10−13(300 T
)0.55
O
++ e
− →O
𝛼2=3.7×10−18(250T )0.7
CO
+2+ e
− →O + CO
𝛼3=1.14×10T −10N
+2+ e
− →N + N
𝛼4=1.8×10−13(300T )0.39
NO
++ e
− →N + O
𝛼5=4.2×10−13(300T )0.85
Indeed, locally, the refractive index n of a planetary envelope depends on the electron and neutral densities. Two contributions to the refractive index can be identified. If we introduce N the neutral density, the contribution of the neutral species can be expressed as
𝛿 n
1= ̄𝜅 N (6)
where ̄𝜅 = 1 . 804 × 10
−29m
3is the refractive volume of Mars neutral atmosphere, obtained from laboratory experiments and measurements of the Martian atmosphere composition by the Viking Landers [Hinson et al., 1999].
The second contribution is due to free electrons in the plasma and depends on the propagating wave frequency f . Its expression comes from classical plasma physics derivations and writes
𝛿 n
2≈ − 𝛼 N
ef
2(7)
with 𝛼 =
e28𝜋2𝜀0me
, e the elementary charge, 𝜀
0the vacuum permittivity, and m
ethe electron mass, and where N
erepresents the electron density number. The resulting refractive index can therefore be expressed:
n = 1 + ̄𝜅 N − 𝛼 N
ef
2(8)
Figure 3. Notations for refraction at elementary scale.
Knowing the local refractive index value, it is possible to compute the radio wave trajectory within the planetary envelope. Figure 3 summarizes the notations that will be used in the continuation.
The Eikonal equation derives from the Fermat principle and describes the equation of the raypath at some point M. If → − e
sis the unit vector along the ray at M (see Figure 3) and → − e
s⊥its oriented perpendicular vector in the tangent plane to the ray, we introduce
→ − 𝜈 the unit vector along the gradient of the refractive index n and
→ − 𝜏 its oriented perpendicular vector in the tangent plane. Then, we can write the equation of the raypath as
→ − ∇n = ‖‖ ‖
→ − ∇n ‖‖ ‖ → − 𝜈 = d ds
( n → − e
s)
= dn ds
→ − e
s+ n di ds
→ − e
s⊥Figure 4. Configuration and notations for the computation of the frequency residuals. The scales are not realistic on this sketch.
from which we can derive the equation for the ray bending:
di ds = ‖‖ ‖
→ − ∇n ‖‖ ‖ n
→ − 𝜈 ⋅ → − e
s⊥= − ‖‖ ‖
→ − ∇n ‖‖ ‖ n
→ − 𝜏 ⋅ → − e
s(9)
The ray path is then obtained by numerically integrating this equation with a second-order Runge-Kutta algorithm.
2.3.2. Interface With Orbit Data and Frequency Residual Computation In order to simulate a radio-occultation experiment, the knowledge of the geometric configuration proves mandatory. We need to know the position and velocity of the spacecraft, of Mars and of the receiving ground station, and also the solar zenith angle along the ray trajectory as well as the one-way light time between the emitter and the receiver. All these data are obtained thanks to the SPICE (Spacecraft, Planet, Instrument, C-matrix and Event kernels) database and routines developed by the Navigation Ancillary Information Facility (NAIF) within NASA [Acton, 1996].
The data deduced from the measurements performed by MaRS are a frequency residual profile. The frequency residual corresponds to the observed Doppler shift Δf
obs, measured by the receiver, corrected from the predicted one if the wave did not encounter any atmosphere Δf
pred. The frequency residual values provided by MaRS are corrected from any terrestrial atmosphere and ionosphere contributions so as to keep only the Martian environment effects.
For a two-way experiment, as is the case for Mars Express, the radio wave is emitted by the ground station, received, and immediately reemitted toward the Earth. A frequency-locked loop ensures that no perturbation on the frequency is generated by Mars Express during the reemission.
In our model, we compute the frequency residual corresponding to each simulated trajectory in order to obtain a profile against altitude thanks to multiple ray tracing as the probe gets occulted.
As shown in Figure 4, let → − v
mexand → − v
rec, respectively, be the velocity of Mars Express and the receiving ground station in the frame of Mars, and let → − u
inand → − u
outbe the unit vectors giving the direction of the radio wave propagation, respectively, before entering the Martian environment and after leaving it, if we consider a one-way propagation toward Mars Express. For a radio wave of frequency f , the frequency residual Δf writes
Δf = Δf
obs− Δf
pred= f c
( → − v
rec⋅ → − u
in− → − v
mex⋅ → − u
out)
− f c
( → − v
rec⋅ → − u
in− → − v
mex⋅ → − u
in)
= f c
[ → − v
mex⋅ ( → − u
in− → − u
out)]
(10) To obtain the two-way frequency residual, equation (10) has to be applied twice, using the same path within the Martian environment but taking into account that, during the about 20 min transit of the radio wave from and to the ground station, the velocity of the tracking station has slightly changed.
In the model as described above, the spinning of the planet is neglected. However, a thorough approach should take into account the Doppler shift experienced by the radio wave as seen within the atmosphere frame rotating around the spin axis of the planet. Since the refractivity in the ionosphere depends on the wave frequency, the aforementioned Doppler shift may affect the wave trajectory and the observed frequency residual.
The influence of the spinning has therefore been studied by computing the frequency residual profile
obtained when taking into account the Doppler shift due to the rotation, and comparing it to the profile
computed without the effects of the spinning. It turns out that the magnitude of the observed variations lies
below 10
−4Hz, while the noise level on the data can be estimated around 10
−2Hz on the cleanest profiles.
Table 2. Analyzed Radio-Occultation Profiles
Year 2007 2007
Day of year 118 134
Orbit number 4253 4311/4312
Ls
227.7◦ 237.3◦Target point latitude
34.5◦ 64.9◦Target point longitude
34.3◦ 171.6◦Target point solar zenith angle
64◦ 89◦Target point local solar time 9:41 14:26
F10.7
index value 86.1 74.4
Heliocentric distance (AU) 1.39 1.38
Distance from Earth (AU) 1.78 1.70
As a consequence, given the additional computational cost induced by this approach, it can be considered acceptable to neglect the influence of the spinning of the planet on the frequency residual profile.
2.4. Feedback Loop Implementation The last part of the model is the feedback loop. An optimization needs to be performed on the atmosphere parameters which constrain the model.
We use the Levenberg-Marquardt algorithm to perform the optimization [Marquardt, 1963].
For a run of the model, a realistic set of parameters for the atmosphere model is chosen, and about 50 successive trajectories are calculated. Each trajectory is computed for a certain position of Mars Express on its orbit during the ingress, showing a different bending angle which induces a frequency residual. A profile of frequency residual against altitude is therefore obtained for the chosen set of parameters.
This profile is then compared to the actual measurements, and the difference between the two enables by minimization to optimize the atmosphere parameters and to draw the neutral temperature and density profiles as well as the electron density profile corresponding to the probed region under the conditions of the experiment.
3. First Results of the Model
To validate this new approach of radio-occultation data analysis, the model has been tested on actual exper- iments. Two objectives have been pursued: first, comparing to a typical radio-occultation profile previously analyzed using the inversion method and interpreting the causes for discrepancies, and second, provid- ing an analysis of a profile for which the inversion method should not be applied—here we chose a profile located at the twilight terminator of Mars. Table 2 gives some key characteristics of the two experiments selected to illustrate this new analysis.
The model has first been tested on the experiment of 28 April 2007, since it shows a profile corresponding to the dayside atmosphere and ionosphere (solar zenith angle: 64
◦) and thus represents an ideal typical case. In
−0.4 −0.2 0 0.2 0.4
0 50 100 150 200 250
Residual (Hz)
Altitude (km)
MaRS data Model Error
Figure 5. Frequency residual simulation for the experiment of 28 April 2007. The light and dark thick lines, respectively, show the measurements by Mars Express and the frequency resid- ual simulated by the model. The thin line gives the difference between those curves, shifted by 0.2 Hz for visibility.
addition, for this experiment, the profiles obtained using the classical inversion method are available, which enables to determine whether the results of both methods are in agreement with each other. This way, it can be checked whether our new model provides plausible results. For this simulation, 49 successive trajectories have been computed, corresponding to probed altitudes ranging between 250 km and ground level.
The result of the frequency residual adjustment
is given in Figure 5. It can be seen that there is
good agreement between the simulated fre-
quency residual and the measured one at most
altitudes. The overall shape of the profile and
the orders of magnitude are well rendered
by the simulation. Especially, the residual peak
around 145 km is well reproduced by the
model. However, it still proves difficult to fit the
region between 110 and 130 km, in which
1015 1020 0
50 100 150 200 250
Neutral density (m
−3)
Altitude (km)
Total CO2 O N2 MaRS inversion
Figure 6. Neutral density for the experiment of 28 April 2007.
The total density and the contributions of each species are displayed, as well as the total neutral density obtained by the inversion method up to 50 km.
some clear fluctuations can be observed on the measurements. The thin curve gives the remaining error between the model and the measurements. It remains very low, except in the 110–130 km range of altitude and below 50 km, when the frequency residual values increase dramatically.
Figure 6 shows the adjusted neutral density profiles obtained in this analysis, with the con- tributions of each species. The thickest black line gives the results of the inversion method up to 50 km. There is very good agreement between the results of both methods. It must be noted that, above 45 km altitude, the inver- sion method does not provide any information on the neutral atmosphere. In addition, only the total neutral density can be retrieved by this method. At those altitudes, CO
2is by far the dominant species, and we remind that the O and N
2densities have been constrained at low altitude so as to provide plausible profiles that are, however, not influent on the measurements at these altitudes.
The neutral temperature profile is plotted in Figure 7, showing the modeled profile and the results of the inversion method, again up to 50 km. A clear difference between both methods can be noticed. This dif- ference probably arises from the fact that the inversion method requires to choose an upper boundary condition at 50 km [Tellmann and Pätzold, 2008]. Usually, this upper boundary condition is chosen within a range of possible values, and several possible solutions are often proposed (see, for instance, Figures 9–11 in [Pätzold et al., 2009]). On the contrary, in our model, the lower atmosphere temperature is constrained by the upper part of the profile, and no boundary condition needs to be set. The model therefore strongly cou- ples the lower and the upper neutral atmosphere as well as the ionosphere. It should also be highlighted that our analysis gives a whole temperature profile for the neutral species, enabling to estimate the exo- sphere temperature, which is not possible with the inversion method for which the neutral atmosphere is solved only up to ∼ 50 km.
As a by-product, the model provides not only the electron density profile but also the different contribu- tions of the main ion species. Figure 8 presents the results of the analysis and compares the electron density profile to the one obtained by the inversion method. Despite the fact that the maximum is the same in both cases and the location of the peaks are similar, there are significant differences. First, in the lower ionosphere,
100 150 200 250 300 350 400
0 50 100 150 200 250
Neutral temperature (K)
Altitude (km)
Model MaRS inversion
Figure 7. Neutral temperature profile for the experiment of 28 April 2007. The gray line shows the profile given by the model, while the results of the classical inversion are given in black up to 50 km.
typically below the main peak altitude, the model gives more electrons than derived from the inversion. This discrepancy can be explained between 110 and 130 km by the fact that the frequency residual is not well reproduced. Then, the topside electron density values obtained by the model are lower than the ones coming from the inversion. Given that above ∼200 km altitude, the frequency resid- ual values are very low, one can expect larger error bars on the retrieved profiles for both methods. Still, the topside frequency residual profile reproduced by the model shows excel- lent agreement with the MaRS data, and the solution proposed by the model is therefore consistent with the measurements.
In addition, contrary to the inversion method
which provides profiles in the occultation
108 1010 1012 0
50 100 150 200 250
Electron and ion density (m−3)
Altitude (km)
Electrons O2+
O+ CO2
+
NO+ MaRS inversion
Figure 8. Density profiles in the ionosphere for the experiment of 28 April 2007. The electron density as well as the contribu- tion of each ion species are displayed (N
+2density is too low to emerge in the window and is therefore not plotted). The black line gives the electron density obtained with the classical inversion method.
point region, the model enables to determine the physical parameters in the whole occul- tation plane, thus enabling to draw electron density or refractivity maps. For the experiment of 28 April 2007, the corresponding maps are given in Figure 9. The electron density map reveals that the model does take into account the dependence of the electron density from the solar zenith angle. To better illustrate this, Figure 10 gives the electron density profiles corresponding to the vertical black and gray lines which appear in the electron density map.
A clear evolution of the main peak altitude and density can be seen as the profiles are plotted in regions with higher and higher solar zenith angles.
Given the overall agreement between the simulations and the measurements, and as the results provided by the model prove rather similar to those of the inversion method for such a typical dayside experiment, our new approach seems satisfactory and may therefore be used to analyze other types of data sets.
We consequently used the model to analyze the experiment of 14 May 2007. In this case, the probed region is located at the twilight terminator of Mars (solar zenith angle: 89
◦). In principle, the classical inversion method should therefore not be applied, because of the ionosphere lack of symmetry in the region of the experiment. This method has nevertheless been applied to analyze this experiment. The results of our analy- sis are given in Figure 11, where they can be compared to those of the inversion method. The corresponding electron density map is shown in Figure 12. A horizontal black dash-dotted line has been plotted to show the path of the lowest ray before occultation, above which is located the region affecting the radio wave propagation during the experiment. It is clear that the terminator is situated within this region.
As can be noted, the overall agreement between the simulated frequency residual profile and the measure- ments proves satisfactory. Especially, the upper part fits really well, with a remaining error of the order of the noise level of the measurement. In the lower part, the error is larger, in particular below 50 km altitude. A possible explanation to this disagreement may lie in the presence of dust up to this range of altitudes, typ- ical for the considered solar longitude [Heavens et al., 2011], which might affect the refractive index in the lowest atmosphere.
Figure 9. Electron density and refractivity maps in the radio-occultation plane for the experiment of 28 April 2007. (top)
The four black and gray vertical lines show the locations where electron density profiles will be plotted in the next figure.
108 109 1010 1011 1012 0
50 100 150 200 250
Electron density (m
−3)
Altitude (km)
Figure 10. Electron density profiles at four different locations in the radio-occultation plane for the experiment of 28 April 2007.
The line styles correspond to those given in Figure 9 (top).
The electron density peaks around 180 km alti- tude, as the Sun is barely above the horizon in the target point region, where the profile is plotted. Interestingly, the classical inversion method gives electrons down to 90 km alti- tude, whereas the model does not reproduce this E region with such a low solar elevation. A possible explanation for this discrepancy may be that the classical inversion method, as it assumes spherical symmetry for the probed ionosphere, provides an averaged electron density over the whole studied region, thus adding the contribution of regions with a higher solar elevation.
The neutral temperatures show surprising fea- tures, with gradient inversions in the lower atmosphere. Interestingly, these features are also given by the classical inversion method.
They will be discussed in the next section.
Finally, the modeled neutral density, although showing peculiar features directly linked to those described for the neutral temperature profiles, proves in agreement with the results of the classical inversion method.
4. Discussion
The main benefit of the model is its coupling between the neutral and ionized media. Contrary to the classical inversion approach, which considers separately the neutral atmosphere below 50 km and the iono- sphere above 80 km, this model simulates the whole planetary envelope and is based on simple physical assumptions, such as the hydrostatic equilibrium and rather well-known photochemical reactions. One practical consequence of this coupling is to remove the uncertainty on the neutral temperature profile due to a needed upper boundary condition. The neutral temperature profile is given from ground level till the exosphere.
−0.4 −0.2 0 0.2 0.4
0 50 100 150 200 250
Residual (Hz)
Altitude (km)
MaRS data Model Error
108 1010 1012
0 50 100 150 200 250
Electron and ion density (m
−3)
Altitude (km)
Electrons O2+ O+ CO2+
NO+ MaRS inversion
100 150 200 250 300 350 400 0
50 100 150 200 250
Neutral temperature (K)
Altitude (km)
Model MaRS inversion
1015 1020
0 50 100 150 200 250
Neutral density (m
−3)
Altitude (km)
Total CO2 O N2 MaRS inversion
Figure 11. Results of the simulation for the experiment of 14 May 2007. (top left) The frequency residual profiles, (top
right) the electron and ion density profiles, (bottom left) the neutral temperature profiles, and (bottom right) the neutral
density profiles. Formats are the same as in Figures 5 to 8.
Figure 12. Electron density map in the radio-occultation plane for the experiment of 14 May 2007. The black dash-dotted line shows the trajectory of the lowest ray before occultation. Only the regions located above this line have some influence on radio wave propagation during the experiment.
As mentioned earlier, another major interest of this approach lies in the fact that strong assumptions on the planetary envelope symmetry can be avoided to retrieve the ionospheric profiles, enabling to study regions such as those located near the twilight terminator of the planet and in the nightside, where potentially inter- esting phenomena may occur. Indeed, the dependency on the solar zenith angle is taken into account at each point for ion and electron densities computation. Therefore, the simulations are able to represent in a quite realistic way the atmosphere and ionosphere even near the twilight terminator of the planet, which is confirmed by the successful results of the simulation applied to the experiment of 14 May 2007. In the case of the Mars Express mission, given the geometry, most studied regions have relatively large solar zenith angles, which means that this new technique can prove very useful to analyze the obtained profiles.
One should at that point address the sensitivity of the frequency residual profile associated with each of the adjusted parameters. Some of the parameters, such as T
a, T
a′, z
m, and N
Nref2, have little influence on the frequency residual profile. Some others only control the lower atmosphere part of the profile, like the stratosphere-and-troposphere temperature values. N
Orefmostly drives the main peak region, while T
m, T
∞, N
COref2, and C
XUVhave an impact on a wider range of altitudes.
Besides, the lower ionosphere is not yet modeled in a fully satisfactory way, as the 110–130 km frequency residual fluctuations are not rendered well by the simulation. A possible way to improve this aspect could be to use a more accurate solar flux representation in the photochemical part of the model with a finer wave- length resolution. It might be so that, at present stage, the C
XUVparameter obtained with the analysis is high because of the need to compensate a too coarse solar flux representation. This would result in overes- timating the ion production due to the shortest wavelengths at lower altitudes, where the adjustment is not fully satisfactory.
Finally, some nonpredictable phenomena may occur, especially in the lower atmosphere, such as dust storms, which may affect the radio wave propagation in the medium and therefore have an impact on the measurement. Only a few studies [e.g., Goldhirsh, 1982] have been made about X-band radio wave prop- agation in a dusty atmosphere, and it therefore proves difficult to model such effects. Compensating this refractive index perturbation by modifying the neutral density and temperature could results in producing features as observed in Figure 11 (bottom).
5. Conclusion
The model which has been presented above enables to simulate radio-occultation experiments performed by MaRS on board Mars Express. It first assumes neutral temperature and density profiles for the probed region, computes the electron density profile in the ionosphere, and then performs an optimization on these profiles in order to make the simulated frequency residual profile fit the actual measurements. This represents a completely novel approach of radio-occultation measurement analysis, coupling the iono- sphere and the neutral atmosphere, in which all the regions are considered together in the analysis process.
This allows for interdependencies between the lower and upper atmosphere on one side and between the atmosphere and the ionosphere on the other side.
It must be noted that, although this model has been developed for Mars, it remains to a large extent planet
independent. Indeed, these simulations could easily be applied to other missions on different planets, such
as Venus Express, provided an atmosphere and ionosphere model is implemented for the given planet.
The obtained results prove really encouraging and confirm the relevance of the method. This totally novel approach for radio-occultation data processing will enable to improve our analysis of MaRS data and may contribute—if performed on a great number of radio-occultation measurements—to develop new atmospheric and ionospheric models for Mars.
Future work will include analyzing more Mars Express radio-occultation data, in particular nighttime data [Withers et al., 2012]. Also, comparisons with electron density profiles and empirical model from the Mars Advanced Radar for Subsurface and Ionosphere Sounding (MARSIS) data [Sánchez-Cano et al., 2013] are envisaged, to further test and validate our new method.
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Acknowledgments
The authors acknowledge M. Pätzold (University of Cologne, Germany), Principal Investigator of Mars Express Radio Science, and the European Space Agency for making the data available on the Planetary Science Archive (http://www.rssd.esa.int/PSA).
The orbit data used for the experi- ment simulations come from the SPICE database: http://naif.jpl.nasa.gov/
naif/. The Martian Solar Longitudes (Ls values in Table 2) have been obtained thanks to the Mars Climate Database v5.1: http://www-mars.lmd.jussieu.fr/
mars/time/martian_time.html.
Alan Rodger thanks the reviewers for their assistance in evaluating this paper.
