Reply to comment by Pätzold et al. on "Mars Express radio-occultation data: A novel analysis approach"

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Reply to comment by Pätzold et al. on ”Mars Express radio-occultation data: A novel analysis approach”

M Grandin, P.-L Blelly, O Witasse, Aurélie Marchaudon

To cite this version:

M Grandin, P.-L Blelly, O Witasse, Aurélie Marchaudon. Reply to comment by Pätzold et al. on

”Mars Express radio-occultation data: A novel analysis approach”. Journal of Geophysical Research

Space Physics, American Geophysical Union/Wiley, 2016, �10.1002/2015JA022229�. �hal-03166305�

Reply to comment by Pätzold et al. on “Mars Express radio-occultation data: A novel analysis approach”

M. Grandin

, P.-L. Blelly

, O. Witasse

, and A. Marchaudon

1

Sodankylä Geophysical Observatory, University of Oulu, Sodankylä, Finland,

Université de Toulouse; UPS-OMP; IRAP, Toulouse, France,

CNRS; IRAP, Toulouse, France,

Scientific Support Office, European Space Agency, ESTEC, Noordwijk, Netherlands

Abstract We reply to the Comment by Pätzold et al. on our paper presenting a new analysis approach for Mars Express radio-occultation data. We address each of the main comments, showing that none of them invalidates the method itself, but rather, they underline aspects which could be considered to improve the model. One major issue raised by the Comment is the computation of the frequency residual values, as our model did not take into account the change in frequency between the uplink and the downlink. This problem has been given full consideration, and the corresponding part of the model has been corrected accordingly. The dayside profile analyzed in the original article has been reanalyzed with the updated version of the model, and the results are presented, which show overall improvements.

In their Comment, Pätzold et al. claim that the method presented in Grandin et al. [2014] to analyze radio-occultation data from Mars Express cannot be implemented. They provide a step-by-step list of the rea- sons why, according to them, it is impossible to couple the lower atmosphere with the ionosphere to retrieve full profiles. However, the majority of the points they raise do not question the method intrinsically but rather underline limitations in its implementation.

The first section of the Comment, titled “The standard radio science inversion method,” does not address any aspect of the Grandin et al. [2014] paper and simply summarizes the historical method to retrieve atmospheric and ionospheric profiles from radio-occultation experiments. It therefore raises no point on which we can respond, especially since the approach we present in our paper fundamentally differs from the radio science standard inversion.

Below we respond to the authors of the Comment on the relevant aspects they discuss. Section 1 addresses the comments on the implementation, while section 2 responds to the comments on the method itself. A detailed reply on the Comment related to the computation of the frequency residuals is given in section 3.

1. Reply to Comments on the Implementation

Several points in the Comment address issues related to the implementation of the method rather than the approach itself. Before replying briefly on these aspects, we simply remind that the aim of the paper has been since the beginning to present a new approach to analyze radio-occultation data from Mars Express. Our model is still being developed, and we are not yet in the stage of routine operation and systematic analysis of the radio-occultation measurements collected since the start of the Mars Express mission. The motiva- tion for developing a new approach was the fact that many soundings of the Martian environment using the radio-occultation technique correspond to regions located near the twilight terminator of the planet. In these regions, the ionosphere does not exhibit spherical symmetry, and applying the radio science inversion method is therefore questionable [see, e.g., Ao et al., 2015]. The method we present in Grandin et al. [2014]

precisely avoids making the assumption of spherical symmetry for the ionosphere, which is why our final aim will be to reach a version of the model allowing to analyze a great number of profiles.

Keeping that in mind, we thank M. Pätzold and his team for pointing out several aspects on which improvement is needed before we may reach this stage. On the advice to use the SOLAR2000 model [Tobiska et al., 2000] to estimate the solar EUV flux, we wish to mention that we are fully aware of the existence of several models of solar EUV flux and of their respective limitations, and our model can use different solar flux models: EUVAC [Richards et al., 1994], TOBISKA1998 [Tobiska and Eparvier, 1998], and the

REPLY

10.1002/2015JA022229

This article is a reply to Pätzold et al.

[2016] doi:10.1002/2015JA021955.

Key Points:

• Most points of the Comment are irrelevant

• The author of the Comment misunderstood the original paper

• The relevant points were taken into account

Correspondence to:

M. Grandin, mgrandin@sgo.fi

Citation:

Grandin, M., P.-L. Blelly, O. Witasse, and A. Marchaudon (2016), Reply to comment by Pätzold et al. on “Mars Express radio-occultation data: A novel analysis approach”, J. Geophys. Res.

Space Physics, 121, 10,592–10,598, doi:10.1002/2015JA022229.

Received 2 DEC 2015 Accepted 23 MAR 2016

Accepted article online 28 MAR 2016 Published online 18 OCT 2016

©2016. American Geophysical Union.

All Rights Reserved.

Journal of Geophysical Research: Space Physics 10.1002/2015JA022229

Figure 1. Refractivity profile obtained after the analysis of the 28 April 2007 radio-occultation data. The red line shows the results from the model, while the black line shows the upper part of the results from the standard inversion.

Flare Irradiance Spectral Model (FISM) [Chamberlin et al., 2007]. We think that this last one, covering the solar irra- diance spectrum on the 0.1–190 nm wavelength range with 1 nm resolu- tion based on TIMED observations, is certainly the most appropriate for such studies. Presently, we use the daily FISM solar spectrum provided by the LASP Interactive Solar Irradi- ance Data Center (LISIRD) website (http://lasp.colorado.edu/lisird/fism/).

However, we would like to mention that the atmosphere is a filter which smoothes the action of the solar flux, and therefore, the dependency on a specific model is not so critical.

Furthermore, the present ionospheric model is a photochemical model, which is much better than a Chapman model but less confident than a model including transport. Work is in progress in the inclusion of the transport in the model to describe better the layers above 180 km.

We also appreciate that using a constant refractive volume to derive the contribution of the neutral atmo- sphere to the refractivity is formally incorrect above 120 km altitude; yet as Pätzold et al. underline in their Comment, the influence of the neutral part on the refractivity above 100 km is negligible compared to the effect of the electrons. We therefore do not expect the simplification consisting in taking a constant refractive volume to have any dramatic effect on the analysis.

The production rates are provided by a kinetic model for suprathermal electrons based on the one used in the TRANSCAR model [Robineau et al., 1996; Lilensten and Blelly, 2002; Marchaudon and Blelly, 2015] without the transport, as in the altitude range considered (100–200 km) local processes dominate over transport. This model solves the primary production of suprathermal electrons in the range 0–1000 eV as a result of solar photoionization and secondary production and energy loss as a result of electron impact on the neutrals.

A few other minor remarks can be briefly addressed before moving on to the points which deserve a more detailed response. The reproach regarding the use of the expression “Doppler shift,” in the beginning of the section titled “The ‘novel approach’ and where it fails, step by step,” is unfounded. We simply invite the authors of the Comment to read more carefully the second paragraph of section 1 in Grandin et al. [2014]; they will see that our definition of the frequency residuals is essentially the same as in Ao et al. [2015].

In response to the technical question regarding the criterion used to terminate the optimization, we use a 𝜒

method in order to minimize the squared difference between our simulated frequency residual profile and the measurement by Mars Express Orbiter Radio Science (MaRS). This choice naturally gives more weight to the altitudes with higher frequency residual values.

We accept the remark that dust can be considered transparent for X band wavelengths. The hypothesis that dust could explain the discrepancies between our simulations and the measured data can therefore be ruled out.

Finally, the authors of the Comment insist on seeing a refractivity profile obtained with our method. Figure 1 gives the refractivity of the Martian environment as a function of altitude for the experiment of 28 April 2007 (red line). The features corresponding to the ionosphere can be easily identified between 100 and 200 km altitude, while the positive contribution below 80 km corresponds to the effect of the neutral atmosphere.

In the transition region between 80 and 100 km, the refractivity is near zero, as expected. However, it is impor-

tant to underline at this point that in our method, obtaining the refractivity is not one of the key objectives

but rather a simple step in the simulation. It is not the refractivity profile obtained from the inversion that we

aim at reproducing but the frequency residual profile, which is the only measured parameter. Comparing our refractivity profile to the one obtained with the radio science inversion method may therefore be interesting in order to estimate the effect of the symmetry assumption. However, this would make no sense if the aim of the comparison is to assess the validity of our approach, as the refractivity profile obtained with the radio science inversion method has been retrieved under the assumption of spherical symmetry, which we precisely aim at overcoming. In addition, we have to mention that we did not manage to find the Level 3 data files for MaRS experiments on the European Space Agency Planetary Science Archive. The full refractivity profiles obtained via the radio science inversion should in principle be present in Level 3 data files, while the temperature and density profiles are Level 4 data. Given that we only managed to obtain the Level 4 data for the experiments we studied, we are only able to display the refractivity profile above the minimum altitude (∼67 km) of the Level 4 data file corresponding to the ionospheric part. Indeed, the refractivity is present in this file, but it is not the case for the atmospheric part, which corresponds to a separate Level 4 data file. As a consequence, we show in black in Figure 1 the upper part of the refractivity profile obtained with the radio science inver- sion. While the overall features are similar to our profile, it is clear that differences can be noted. In particular, our profile shows less intense contributions in the ionosphere, especially for the secondary peak near 110 km altitude.

2. Reply to Comments on the Method Itself

The authors of the Comment claim that we “do not realize (…) that it is also not feasible to obtain informa- tion on the temperature of the neutral species. The derived temperature profile from radio-occultation is that for a well-mixed gas of the neutral atmosphere.” We agree with this Comment; in fact, we never produced any separate temperature profiles for the neutral constituants of the atmosphere. We indeed assume that the neutral atmosphere is a well-mixed gas when constructing the temperature and density profiles. As for pro- viding separate neutral density profiles in the lower atmosphere, the choices made in the model are already discussed in detail in the last paragraph of section 2.1.2 of the original paper.

The authors of the Comment also give a list of reasons why, according to them, it is impossible to obtain any information on the neutral atmosphere above 80 km altitude. We think that the authors of the Comment misunderstood our approach. We are aware of the fact that above that altitude, the contribution of the neu- tral species to the local refractivity is of the same order of magnitude or lower than the contribution of the electrons. However, as explained in the original paper, our approach couples the neutral and the charged com- ponents of the Martian environment by resolving the equations for photochemistry. It therefore imposes a strong constraint on the neutral atmosphere so as to obtain the adequate electron density profile to account for the frequency residual values corresponding to the ionosphere-dominated region.

Another criticism made on our method is its alleged bad altitude resolution compared to the radio science inversion method which is said to reach “an altitude resolution of 500 m”. It should be made clear at this point that the simulated and measured frequency residual profiles are not compared solely at the altitudes attained by a given ray. The cost function defined in the optimization procedure takes into account every measured point available in the MaRS data file (Level 2), using a linear interpolation between two simulated points. Obviously, this involves a smoothing of the retrieved profiles, but nothing prevents from computing raypaths with an increased altitude resolution to reduce this effect (except computation time). Also, future development is foreseen to interpolate the simulated points using a spline function, but we do not expect this change to be critical.

Contrary to what Pätzold et al. assume in their Comment, the profiles obtained after optimization are com- pletely different from the initial ones. Figure 2 illustrates this by showing simultaneously the initial and final atmospheric and ionospheric profiles for the experiment of 28 April 2007. We do not show every step of the optimization procedure, as this example required 13 iterations: the figure would therefore not be legible and it would not be of much interest. The figure will be further discussed in section 3.

Still in relation to the optimization procedure, the authors of the Comment express their wish for more infor-

mation regarding the range within which the parameters of the model can take their values. In order to

preserve the general pattern for the neutral temperature (described in section 2.1.1 of the original paper), the

optimization is not performed directly on the temperature values at certain altitudes but rather on normalized

coefficients depending on them. For instance, in order to guarantee that the mesosphere temperature

Journal of Geophysical Research: Space Physics 10.1002/2015JA022229

Figure 2. Comparison of the initial (red dashed line) and final (red solid line, with error bars) atmospheric temperature profiles for the experiment of 28 April 2007. The magenta line shows the neutral temperature profile given by the Mars Climate Database (MCD) v5.2 for the conditions of the experiment. The blue lines show the neutral temperature profile retrieved with the standard inversion method using a high (light blue), medium (medium blue), and low (dark blue) upper boundary conditions.

T

does indeed correspond to the minimum for the profile, the other ref- erence temperatures, denoted T

and T

, are expressed

T

= (1 + 𝛼 )T

(1) and

T

= 𝛽 Tm + (1 − 𝛽 )T

, (2) where 𝛼 and 𝛽 are the actual param- eters to be optimized. It is obvious, then, that 𝛼 > 0 and 0 < 𝛽 < 1. As arbitrary additional constraints, we impose that 𝛼< 3, so as to ensure that T

< 4T

, while T

must be comprised between 75 and 200 K (T

itself is of course also normalized during the optimization procedure). This aims at being a reasonable compromise to avoid constraining too strictly the pro- file while discarding completely unre- alistic profiles. It does not seem rel- evant to go into detail through each of the optimized parameters in this Reply; a similar approach has been adopted for the other parameters.

It is true that no detailed error and sensitivity analysis have been provided in the original paper. It is never- theless possible to provide estimates of uncertainties for the model parameters which are optimized. They can be obtained from the optimization algorithm [Marquardt, 1963], which includes the estimation of errors after the adjustment. Because most of the parameters which are adjusted in our model are temperatures at reference altitudes, it is therefore possible, for instance, to display the corresponding uncertainties for these specific points. Carrying a more thorough error analysis will definitely be a necessary step before being able to apply a systematic analysis of the collected radio-occultation profiles. It is part of the further developments

Figure 3. Simulated (red) and measured (dark blue) frequency residual profiles after a new analysis of the radio-occultation data of 28 April 2007. The thin black line shows the difference between these two curves, shifted by 0.2 Hz for legibility.

of the model, but it is beyond the scope of the original paper, and the question will be addressed when we start data processing with our method.

3. Correction of the Frequency Residual Computation

The most critical point raised by Pätzold and his team is undoubtedly the fre- quency residual computation, which was not implemented correctly in the version of the model presented in the origi- nal paper. We indeed did not take into account the change in the frequency between uplink and downlink transmis- sions. We had to change the algorithm to take into account the dual frequency.

After this correction, a new analysis has

been performed on the 28 April 2007

radio-occultation profile. The results are

given below.

Figure 4. Ionospheric density profiles, showing simulated electron (red), O

(dash-dotted blue), O

(solid blue), CO

(purple), and NO

(green) number densities and electron density (dark blue) obtained with the radio science classical inversion.

As underlined in the Comment, the fre- quency residuals were initially calculated assuming the same frequency and the same path within the Martian environ- ment for the uplink and the downlink transmissions. Given the important dif- ference between the uplink and down- link frequencies, the contribution of each step (uplink and downlink) to the mea- sured frequency residual is significantly different at ionospheric altitudes.

We therefore took into account this remark of the Comment and imple- mented a new method to compute the frequency residuals, following more closely the actual experiment.

Based on the transmitted uplink fre- quency provided in the MaRS data files, we calculate the trajectory of the radio wave in the Martian environment until it reaches the Mars Express spacecraft. Then, taking into account the Doppler shift observed at the spacecraft and using the transponder ratio provided by Pätzold et al., we determine the downlink frequency transmitted by Mars Express toward the ground station on Earth. This frequency is used to calculate the downlink path in the Martian environment, from which we can calculate the observed frequency at the ground station. We finally compare this frequency to the one predicted without the effects of the Martian environment in order to obtain the frequency residuals.

The analyzed radio-occultation profiles shown in the original paper have therefore been updated after imple- menting this correction to the model. Figures 2–5 show the results of a new analysis of the experiment of 28 April 2007. Interestingly, although the fit on the frequency residual profile (Figure 3) is not perfect, espe- cially in the 130–140 km altitude range, some problems mentioned in the discussion of the original paper seem to have been at least partially solved after this correction.

Figure 5. Ratios of the neutral densities below 50 km, comparing results of our model to the standard inversion (red) and the standard inversion to the MCD v5.2 profile (blue).

For instance, the neutral temperature values obtained with our method show slightly better agreement with the results of the standard inversion (see Figure 2). We show the three temper- ature profiles given by the standard inversion, which use low, medium, and high upper boundary conditions as explained by Pätzold et al. in their Comment. It is clear that at most alti- tudes, our retrieved profile is closer to the medium boundary condition profile, but the profiles diverge below 20 km. We are presently working on understanding the source of these discrepancies.

Nevertheless, since Pätzold et al. sug-

gested that we compare also our

retrieved temperature profile with the

one obtained using the Mars Climate

Journal of Geophysical Research: Space Physics 10.1002/2015JA022229

Table 1. Uncertainties on the Retrieved Exospheric Temperature and Reference Neutral Densities

Parameter Value Uncertainty Unit

T

307.5 ± 6.8 K

n

9 . 124 × 10

±4 . 779 × 10

m

n

ref

2 . 634 × 10

±5 . 382 × 10

m

n

ref

5 . 230 × 10

±1 . 527 × 10

m

Database (MCD) v5.2 from Laboratoire de Météorologie Dynamique (LMD), we also show in this figure the corresponding MCD profile (in magenta) for the condi- tions of the experiment. In spite of the differences at higher altitudes, one can notice that the agreement is good near the ground, while the standard inversion profiles show a lower temperature.

Some error bars on the adjusted temperature profile are provided in Figure 2. They have been obtained as described above, i.e., directly from the Levenberg-Marquardt algorithm outputs. One can note that the uncer- tainties are not evenly distributed over altitudes. Below 50 km, they are significantly lower than between 50 and 100 km, which may probably be explained by the greater signal-to-noise ratio on the frequency residual values. Uncertainties on T

as well as the reference neutral densities are given in Table 1.

The ionospheric profiles are shown in Figure 4. The overall agreement of the electron density profiles (our model and standard inversion) is fairly good, especially near the peak region. Above 200 km altitude, the uncertainties are too high to obtain confidence in the retrieved profiles, given that they correspond to extremely low values of frequency residuals. It is important at this point to underline the fact that no error bars can be easily provided on the electron density profile retrieved with our method. Indeed, the electron density is fully calculated by the model, based on the local photochemistry. As stated above, the optimization algorithm provides an error estimation on the adjusted parameters of the model (e.g., T

, T

, T

,…), not on the retrieved profiles themselves.

Figure 5 presents the ratio between our neutral density profile and the one obtained with the standard inver- sion, below 50 km altitude. One can see that the discrepancy is of the order of 15%, which represents about 1 km uncertainty in altitude. We also plot the ratio between the standard inversion profile and the reference model (MCD v5.2). The discrepancy is lower, except above 30 km. We still do not understand the origin of such discrepancy, as our temperature is close to the one given by the MCD. We think that the problem may be linked to the planetodetic/planetocentric altitude definition.

Finally, the features between 100 and 120 km altitude on the frequency residual profile are relatively well reproduced with the correction, although some inaccuracies remain. This was not the case before the correc- tion, and these features may originate from the change in frequency between the uplink and the downlink rather than only from the lower ionosphere structure. However, the fit is not good between 125 and 140 km;

again, this may be related to a problem of planetodetic/planetocentric altitude definition. We are presently working on understanding this issue.

4. Summary

We have replied to the most relevant comments made by Pätzold et al. regarding the novel approach to analyze radio-occultation data presented in the original paper Grandin et al. [2014].

Many remarks address the implementation of the method rather than the approach itself, and we agree that improvement is possible in many aspects, e.g., regarding the solar flux model.

Although Pätzold et al. aim at claiming that the method cannot be implemented, most of the remaining com- ments probably originate from a misunderstanding of the original paper. We hope that these points have now been made clear in this Reply.

One major improvement was, however, enabled thanks to the Comment. In the published version of the method, the computation of the frequency residuals indeed did not take into account the difference of fre- quency between the uplink and the downlink transmissions. The determination of the frequency residuals has therefore been revised accordingly, and the results presented in Figures 2–5 reveal dramatic improvement.

Further development of the method is foreseen, taking into account the previous comments and aiming at

improving the fit in the altitude range where it is not satisfactory.

References

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Acknowledgments

The authors acknowledge M. Pätzold (University of Cologne, Germany), Principal Investigator of Mars Express Radio Sci., 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 experiment simulations come from the SPICE database: http://naif.jpl.nasa.gov/naif/.

The neutral temperature profile used for comparison with the presented results has been obtained thanks to the Mars Climate Database v5.2:

http://www-mars.lmd.jussieu.fr/

mars/time/martian_time.html.