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Planetary and Space Science 55 (2007) 864–870

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Absorption and reflection of radio waves in the Martian ionosphere

E. Nielsena,�, D.D. Morganb, D.L. Kirchnerb, J. Plautc, G. Picardid

aMax Planck Institute for Solar System Research, 37191 Katlenburg-Lindau, GermanybDepartment of Physics and Astronomy, University of Iowa, Iowa City, IA 52242, USA

cJet Propulsion Laboratory, Pasadena, CA 91109, USAdInfocom Department, ‘‘La Sapienza’’ University of Rome, 00184 Rome, Italy

Received 13 July 2006; received in revised form 11 October 2006; accepted 11 October 2006

Available online 1 December 2006

Abstract

Radio wave absorption in the Martian ionosphere has been predicted and tested against MARSIS radar observations. Models of the

ionosphere densities and of absorption in a CO2 neutral atmosphere were used. The appearance of ground reflections in the MARSIS

observations is shown to be consistent with predictions of reflection and absorption of radio waves in the ionosphere. It is concluded that

the secondary density maximum, known to be typically present below the primary density peak, contributes considerably to the

absorption and thus to the appearance of ground reflections. It is the first time predicted radio wave absorption in a CO2 planetary

atmosphere has been tested against actual observations.

r 2006 Elsevier Ltd. All rights reserved.

Keywords: Mars; Ionosphere; Radio wave absorption; Top-side sounder

1. Introduction

The low frequency radar Mars Advanced Radar forSubsurface and Ionospheric Sounding (MARSIS) onboard the ESA mission Mars Express (MEX) is usedprimarily both to sound the ionosphere plasma and tosound the ground, surface and subsurface, for essentiallywater deposits in both liquid and frozen forms. The lowestaltitude of the spacecraft is �300 km well above the altitudeof the electron density maximum in the ionosphere. Thealtitude of the electron density maximum is typically�130 km. The ground sounding signal must thereforepenetrate the ionosphere twice before detection. Thus, for aground reflection to be detected the signal frequency mustbe larger than the maximum plasma frequency. If thiscondition is met, the ionosphere has two further effects onthe signal: it will cause dispersion of the signal phases, andit will attenuate the signal amplitude. In this work we donot consider the signal dispersion. Instead, we willdetermine how the appearance of a ground reflected signal

e front matter r 2006 Elsevier Ltd. All rights reserved.

s.2006.10.005

ing author. Tel.: +495556 979450.

ess: nielsen@mps.mpg.de (E. Nielsen).

in the observations is controlled by reflection and absorp-tion in the ionospheric plasma.Radio wave absorption in an atmosphere is controlled to

a large extent by the collision frequency of thermalelectrons with the neutral molecules. Since the majorneutral atmospheric component on Mars is CO2, which hasa much larger scattering cross section for thermal electronsthan does either oxygen or nitrogen, the absorption onMars, for the same electron density and signal frequency, ismuch more severe than in Earth’s atmosphere.

2. Observations and analysis

MARSIS can be operated either in a ground soundingmode or in the Active Ionosphere Sounder (AIS) mode.Here we use data obtained in the AIS mode. The radaroperates between 0.1 and 5.4MHz. A series of narrow nearmonochromatic signals are transmitted in sequence and foreach frequency the time delays to echoes are measured. Theechoes are either reflection from the ionosphere or from theground. The observations are presented in a spectrogramdisplaying the intensity of the echo signal as a function oftime delay (on the horizontal axis) and signal frequency

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Fig. 2. Data for orbit 2029. The minimum frequency for ground

reflections is decreasing as the solar zenith angle increases, associated

with a weakening of the solar radiation induced primary electron density

layer.

E. Nielsen et al. / Planetary and Space Science 55 (2007) 864–870 865

(on the vertical axis). An example of such a spectrogram isshown in Fig. 1. The virtual depth, which is half the delaytime multiplied by the vacuum speed of light, is given onthe top horizontal axis. The echo between 1.1 and 2.7MHzis an ionospheric reflection. The later echoes at higherfrequencies between 3.5 and 5.4MHz are the signalreflected from the ground. It is typical for the groundreflection that when present it appears for all frequenciesbetween a minimum frequency and the maximum fre-quency of the sounder. The distance to the target (theground) is the same for all frequencies, and since all signalstravel through the same ionosphere the delay times are onlyweakly increasing with decreasing frequency. This groundreflection is not always present in the spectrograms. Thereason is that the radar signal may be either reflected beforepenetrating the ionosphere because the sounding frequencyis less than the maximum plasma frequency, or be soseverely attenuated that the signal drops below the receivernoise level.

The primary electron density maximum in the Martianionosphere is a Chapman layer controlled by solarradiation, which therefore varies in height and in intensitywith solar zenith angle. It is to be expected that theminimum frequency for the ground reflection is to a largeextent controlled by the solar zenith angle. We thereforedisplay in Fig. 2 the appearance of ground reflectionsduring one orbit by presenting the minimum frequencyversus zenith angle. In this case the ground reflectionappeared first for a zenith angle of �60�. For smaller zenithangles the denser ionosphere probably caused attenuationsufficient to reduce the received signal below noise level.

Fig. 1. MARSIS Active Ionosphere Spectrogram displaying ionosphere

(at low frequencies) and ground reflections (at high frequencies). The slant

of the ground reflections towards higher delay time with decreasing

frequency is caused by decreasing propagation speed as the frequency

decreases. The ground reflection first appears at a minimum frequency of

�3:2MHz.

Ground reflections occurred for all zenith angles largerthan 60� up to 100�. These observations are reproduced inthe following using model calculations.Nielsen et al. (2006) found that the main electron density

peak is well approximated by a Chapman layer up to analtitude of 180–200 km, and exponentially decreasing withaltitude above that height. The density profile (Eqs. (1)–(3))is controlled by zenith angle and solar ionizing fluxintensity (F ¼ F10:7 cm flux) (see for example summaryin Nielsen, 2001 and references therein),

NeðhÞ ¼ No

� exp1

21�

h� hmax

H� Chðx; yÞ exp �

h� hmax

H

� �� �,

ð1Þ

where No is the subsolar maximum density, hmax thesubsolar altitude of maximum density, H the neutral scaleheight in the Chapman layer, y the solar zenith angle, h thealtitude, and

x ¼ ðRMars þ hÞ=H,

No ¼ 200n100:36 log F=120 ð103 el=cm3Þ,

hmax ¼ 120þ 10 log1

Chðx; yÞðkmÞ,

H ¼ 10n exp 0:16 lnF

100

� �ðkmÞ. ð2Þ

The plasma scale height above the Chapman layer is

H t ¼ 23n exp 0:55 lnF

50

� �ðkmÞ. (3)

Use of the Chapman function Chðy;xÞ takes into accountthat ionizing radiation extends past the terminator andallows analysis for zenith angles larger than 90�. In thisanalysis x ¼ 350 was used. In Fig. 3 there is an example of

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Fig. 3. Example of the primary density peak in the ionosphere model. At

5MHz the signal passes through the layer and is attenuated by 11.8 dB in

its way to and from the ground.

Fig. 4. Altitude profile of the electron momentum-transfer collision

frequency in Mars’s CO2 atmosphere.

E. Nielsen et al. / Planetary and Space Science 55 (2007) 864–870866

the model ionosphere for a zenith angle of 50� and a solarflux F10:7 ¼ 111 units. Neglecting the weak crustalmagnetic fields the sounder signal propagating into theionosphere is reflected where the signal frequency equalsthe plasma frequency

f p ðkHzÞ ¼ 8:98ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiNeðhÞ ðel=cm3Þ

q. (4)

The radar signal is attenuated by absorption in theionosphere

AðhÞ ¼ 4:61n104NeðhÞnðhÞ

o2ðhÞ þ n2ðhÞðdB=kmÞ, (5)

where o is the signal frequency (rad/s), and n ðs�1Þ themomentum-transfer electron-neutral collision frequency.The collision frequency is governed by the main molecularcomponent in the Martian atmosphere, which is CO2

(Detrick et al., 1997). For the relatively cool Martianionosphere the thermal mean energy is about 0.1 eV.Laboratory measurements in a CO2 gas of moleculesshow the collision frequency of such electrons to be closeto 10�7 per molecule=s (Hake and Phelps, 1967). Multi-plying the collision frequency per molecule by the CO2

concentration yields the altitude profile of the collisionfrequency, shown in Fig. 4. This profile is in very goodagreement with Schunk and Nagy (2000). Note that thesecollision frequencies are nearly a factor of 100 larger thanin Earth’s ionosphere. The reason is that the electroncollision frequency with N2 molecules, the dominantmolecule in Earth’s ionosphere, is much lower at

2� 10�9 per molecule=s. This suggests that strong radiowave absorption is a striking aspect of the Martianionosphere. The specific absorption (dB/km/electron)maximizes where the signal frequency equals the collisionfrequency; this occurs at altitudes of 80–90 km for therange of MARSIS AIS radar frequencies. Because thecollision frequency increases with decreasing altitude themain contribution to the total absorption of a signalpropagating through the ionosphere occurs below the peakdensity. The detailed density profile above the Chapmanlayer is of little importance in this respect. On the otherhand additional electron densities below the densitymaximum could have an important contribution to thetotal absorption, even if these densities are relatively small.To illustrate the reflection and absorption properties of

the ionosphere we calculate the absorption of radio wavesof frequencies between 3 and 4MHz (in steps of 0.2MHz)in a Chapman layer for a solar flux of F10:7 ¼ 70. Theresult is shown in Fig. 5. The absorption is only calculatedfor signals that penetrate the ionosphere. At 3MHz thesignal is only penetrating the layer for zenith angles 464�

and at 3.2MHz for angles 453�, etc. Thus, a groundreflection can only occur at these frequencies at zenithangles larger than these limiting angles. For 3.8 and4.0MHz there is penetration of the layer at all zenithangles. However, the absorption is very large at smallangles, approaching 40 dB at 4MHz. If we assume that anionospheric absorption larger than for example 20 dB willattenuate the signal below noise level, then a groundreflected signal will only occur for angles 442�. It appearsthat at lower frequencies the occurrence of groundreflection is limited by reflection in the layer, while at

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Fig. 5. Zenith angle variation of the absorption in a model ionosphere (for

solar F107 flux of 70). Calculations are for 3.0, 3.2, 3.4, 3.6, 3.8, and

4.0MHz. The low frequency curves terminate at the smallest zenith angle

where it is penetrate the ionosphere.

Fig. 6. Ground-reflection plots. The cross-hatched area is the region

where ground reflections occur. The larger the allowed absorption in the

ionosphere (20 dB in the top panel, and 10 dB in the bottom panel) the

larger the cross-hatched area.

E. Nielsen et al. / Planetary and Space Science 55 (2007) 864–870 867

higher frequencies the occurrence of ground reflection islimited by absorption in the ionosphere.

In a coordinate system with signal frequency versuszenith angle we can now determine the area in whichground reflection occurs, cross-hatched in Fig. 6. The toppanel is for an ionospheric absorption limit of 20 dB, andthe bottom panel for 10 dB. The border of the cross-hatched area marks the zenith angles and frequencieslimiting the appearance of ground reflections. Note that thelimiting values below �3MHz and for angles larger than�65� are identical in the two plots; they are controlled byreflections inside the layer. For larger frequencies andsmaller angles the limiting values differ because they arecontrolled by ionospheric absorption. When the allowedabsorption limit increases (here from 10 to 20 dB) theground wave appearance at higher frequencies spreadstowards lower zenith angles. This kind of plot is hereafterreferred to as a ‘ground-reflection plot’.

Before comparing these predictions with observations wemust also take into account the separation between radarand target (the ground). The attenuation owing to thisspatial separation is given by (T. Hagfors, privatecommunication)

Pr ¼ PtA2a2

4h2ðaþ hÞ2l2

, (6)

where A is the effective antenna area (calculated for a half-wave dipole gain of 1.64), a the radius of the spherical

target ð¼ RmarsÞ, l the signal wave length, and h thespacecraft altitude. The reflectivity of the target has beenset to unity. The range attenuation in dB is

Ar ¼ �10:0n logPr

Pt. (7)

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For a radius of 3398 km and an altitude of 300 km, Ar ¼

94:2 dB at 3MHz. For a total measurable attenuation of120 dB, this allows for maximum 25.8 dB ionosphericabsorption for that spacecraft altitude.

In Fig. 7 the observations shown in Fig. 2 are displayedin a ground-reflection plot representative of that orbit(2029). Between 70� and 80� there is a ledge where theminimum frequency tends to remain constant for increas-ing angle. This is an instrumental effect: the radar has a dipin radiated power between �2:7 and 2.9MHz. Theminimum frequency is overestimated to its value on thehigh frequency side of this dip. The real minimumfrequency eventually reappears on the low frequency sideof the dip at a corresponding higher zenith angle. Apartfrom this ledge, for large zenith angles (4�70�) there isgood agreement between prediction and observation. Thismeans that reflection and absorption at these high zenithangles are well described by the model. However, below�70� the maximum allowed absorption is clearly over-estimated: the data points are located inside the cross-hatched area rather than on the limiting border. These datapoints were obtained for spacecraft altitudes between 293and 358 km. The corresponding range attenuation leads tomaximum ionosphere attenuation (in the primary densitylayer—for which these calculations were made) between26.0 and 24.1 dB. Note, two cross-hatched areas are shown:one for each of these limiting absorptions. The solid-linecross-hatched area corresponds to 24.1 dB, and the dashed-and solid-line cross-hatched to 26.0 dB. These limiting

Fig. 7. The same data points as in Fig. 2 are plotted in a ground-reflection

plot. There is good agreement at low frequencies, while at high frequencies

the maximum allowed ionosphere absorption (adjusted for spacecraft

altitude is between 26.0 and 24.1 dB) is too large.

values are clearly too large and extend the cross-hatchedarea toward zenith angles that are much smaller than theobserved ones. In addition to absorption in the primarylayer there must be a further factor in the ionospherecausing absorption. Adding a zenith-angle-independentabsorption of 18 dB to the calculated absorption in theprimary layer brings the observations into much betteragreement with the prediction, in Fig. 8. The zenith-angle-dependent component of the absorption is the absorptioncalculated for the primary layer. For that component thelimiting values of absorption are 8.0–6.1 dB for the givenspacecraft altitude variation. This shows that a majorcontribution to the total absorption comes from a sourceother than the primary ionospheric layer. As expected thelimiting border at large zenith angles is not much affectedby this additional absorption component.The MARSIS radar is a top-side sounder, which

measures the electron density profile from high altitudesdown to the altitude of the maximum electron density. Ataltitudes below the altitude of maximum density thedensity profile is not accessible to sounder observations.So far in the calculations we have assumed that thebottom-side ionosphere was governed by the Chapmanlayer fitted to the observations above the density max-imum. The analysis so far suggests that this is not a validassumption. The additional absorption required to fit themeasurements to observations must arise owing to electrondensities in this region which are larger than predictedby the bottom-side Chapman layer. Since the collision

Fig. 8. Arbitrarily adding 18 dB to the calculated absorption brings also

the data at large frequencies in good agreement with the observed data.

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frequency increases downwards from the primary densitymaximum, even small density increases in this region maycontribute significantly to the total absorption.

The Martian ionosphere has been extensively observedusing the radio occultation technique, which allows thewhole density profile to be determined (from �60 to300 km) (Kliore, 1992). These observations show thattypically there is a secondary layer a few tens of kilometersbelow the density maximum of the primary layer. The extraabsorption implied by our analysis is likely to take place inthis secondary layer with a typical peak altitude at about110 km and a peak density about half the primarymaximum (Kliore, 1992; Rishbeth and Mendillo, 2004).We now insert a secondary layer in the model calculationswith a peak altitude at 110 km, a scale height of 10 km, andadjust the peak density to a good fit between calculationsand observations, in Fig. 9. With the secondary layerincluded the calculated absorption increases. The absorp-tion limits of 26.0 and 24.1 dB, derived considering thespacecraft altitude variation, lead now to a similar good fitof calculations and observations as in Fig. 8.

More recently Paetzold et al. (2005) reported a sporadicthird layer in the ionosphere of Mars. This layer couldappear with a peak density altitude between 65 and 110 km,and a mean density maximum of 8� 103 el=cm3. Instead ofthe secondary layer we now insert in the calculation a layerat 90 km altitude with peak density of 6� 103 el=cm3 and ascale height of 10 km. This layer yields a good fit of thedata to observations similar to that given by the secondarylayer. The result is similar to Fig. 9.

Fig. 9. Introducing the secondary ionosphere layer observed at Mars

(Kliore, 1992), brings the observations in good agreement with the

calculated total absorption in the ionosphere.

3. Discussion

The MARSIS radar is a low frequency top-side sounderorbiting above the main electron density layer in theMartian ionosphere. The radar operates at frequencies thatcover and somewhat exceed the range of plasma frequen-cies in the ionosphere. The radar can therefore be used tosound both the ionosphere and the ground. A reflectionfrom the ground is observed when the frequency is largerthan the maximum plasma frequency and when theabsorption in the ionosphere does not attenuate the radarsignal below detection limit. For a given spacecraft altitudethere is therefore an upper limit to the ionosphericabsorption allowing a ground reflection to be observed.The absorption limit depends on the details of theionospheric density profile as it varies with solar fluxintensity and solar zenith angle. The purpose of this work isto account for the typically observed pattern of groundreflections considering reflection and absorption of radiowaves in the ionosphere. This is the first time absorptioncalculations in the Martian ionosphere have been tested byobservations. We have used a model of the main (primary)density peak, which approximates the layer with a Chap-man layer both above (where MARSIS makes observa-tions, and we know this is a good approximation) andbelow. The absorption calculations are based mainly on anelectron-neutral collision frequency profile, which is setequal to the collision cross-section of thermal electronswith CO2 molecules times the CO2 density. It is noted thatthe collision frequencies at Mars are nearly a factor of 100larger than at similar altitudes in Earth’s ionosphere, whichmakes Mars a strong radio wave absorber. An example ofthe results of such calculations is shown in Fig. 6. Groundreflections appear in the cross-hatched area. For highzenith angles, and for low frequencies, the cut-off is causedby reflection of the radio wave inside the density layer. Atsmaller zenith angles, and for higher frequencies, the cut-off is controlled by absorption in the layer. For largerallowed absorption the area of ground reflections extendsfurther towards still smaller zenith angles.For a selected orbit (#2029) the minimum frequency for

which ground reflections occurred was determined as afunction of zenith angle. The data were compared topredictions for this orbit, in Fig. 7. Good agreementimplies that the data points should be located on(clustering around) the border of the cross-hatched area.At low frequencies there is a good agreement. This meansthat reflections inside the primary layer are well describedby the model. However, at higher frequencies the datapoints are located in the cross-hatched area, which meansthat there is stronger absorption occurring than is derivedfrom the model. Increasing the calculated absorption by18 dB brings the prediction into agreement with the datapoints. This agreement is shown in Fig. 8.We suggest that this additional absorption arises from a

secondary layer known to exist below the primary densitylayer. Including a secondary layer with typical parameter

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values in addition to the primary layer confirms that such aconfiguration can account for the MARSIS observations.Note that a more recently observed sporadic layer may bepresent at still lower altitudes. We find that such a layercould also account for the observations.

The secondary layer is thought to be the result ofionization by soft solar X-rays (Fox and Dalgarno, 1979).The sporadic third layer was suggested to be associatedwith ablation of meteorites in the atmosphere, therefore thesporadic occurrence (Paetzold et al., 2005). It is very likelythat other causes for absorption may play a role. Forexample, Morgan et al. (2006) have found that intervals ofground reflection absorption lasting up to two weekscoincide in time with high fluxes of solar energetic particlesin the 10MeV range. These events are observed at solarzenith angles up to 113�, well into the night side of Mars.Occurrence of absorption on the nightside is thought to bedue to the impinging particles having helical orbits ofplanetary-sized cyclotron radius, which are not clearlyshadowed by the planet.

Cosmic rays with energies affecting the ionospheredensities are channeled towards high latitudes on Earthdue to the dipole magnetic field. During these absorptionevents on Mars, which has a weak and sporadic magneticfield, most of the planet appears to be affected. Hard X-rays emitted at the onset of solar flares would cause shortlasting ð�1 hÞ density increases on the dayside Marsionosphere (e.g. Mendillo et al., 2006). Also local accel-eration processes could play a role. Recently inverted-Vevents were reported on Mars (Lundin and et al., 2006).

The observed variation of the minimum frequency ofground reflections are in very good agreement with thevariation predicted by propagation in the primary layer.This follows from the good fit in Fig. 8, where only aconstant increase in ionospheric absorption had to beincluded to obtain a match. It follows that the model forabsorption calculations in the primary layer is realistic.

The success of the absorption calculations together withthe multiple possible sources inducing increases in theionospheric electron densities, and thus causing absorp-tion, suggests that it is time to monitor the radio waveabsorption on Mars for the purpose of studying theoccurrence and nature of these processes. A simple lownoise monochromatic receiver placed on the surface of

Mars to record variations of the cosmic noise intensity as itchanges owing to changing absorption would serve such apurpose (Nielsen, 1998).

Acknowledgments

MARSIS was built and is jointly managed by the ItalianSpace Agency and NASA. Mars Express was built and isoperated by the European Space Agency. The research atthe University of Iowa was supported by NASA throughcontract 1224107 with the Jet Propulsion Laboratory.

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