RADIOSCIENCE EXPERIMENTS TO MONITOR ATMOSPHERIC … · RADIOSCIENCE EXPERIMENTS TO MONITOR...

RADIOSCIENCE EXPERIMENTS TO MONITOR ATMOSPHERIC ANGULAR MOMENTUM VARIATIONS ONBOARD THE FORTHCOMING 2018 INSIGHT AND 2020 EXOMARS LANDERS. Ö. Karatekin, Royal Observatory of Belgium, Brussels, Belgium ([email protected]), V. Dehant Royal Observatory of Belgium, Brussels, Belgium ([email protected]), W. M. Folkner, Jet Propulsion Laboratory, JPL, Pasadena, USA ([email protected]), S. LeMaistre Royal Observatory of Bel-gium, Brussels, Belgium ([email protected]) S. Asmar, Jet Propulsion Laboratory, JPL, Pasadena, USA ([email protected]) A. Konopliv Jet Propulsion Laboratory, JPL, Pasadena, USA ([email protected]).

Introduction: LaRa onboard ExoMars 2020 surface platform

and RISE onboard InSight 2018 are radio science experiments designed to obtain coherent two-way Doppler measurements from the radio link between the Mars landers and Earth. The signals at the X-band radio frequencies will be generated and re-ceived by Earth-based giant antennas.

The Doppler measurements will be used to pre-

cisely determine the variations of the rotation rate (expressed as the Length-Of-Day (LOD) variations) and the orientation of the spin-axis of Mars in space (the long-term precession, polar motion and periodic nutations). These rotational data provide information on the interior structure such as the state, size and composition of the core as well as on the atmosphere of Mars.

The liquid core is expected to modify the period-

ic oscillations in the spin-axis orientation i.e, nuta-tions. The precession of the spin axis determines the polar moment of inertia (MOI) of the whole planet, which quantifies the mass concentration towards the center and is a major constraint for models of the interior structure of planets. In addition, since the changes in Mars rotation in seasonal scales are main-ly due to exchanges of angular momentum between the atmosphere and the ice caps, the measured rota-tion will deliver information on the Mars CO2 cycle.

LaRa and RISE will provide precise Doppler

measurements from which the motion of the landers in space can be calculated over a time period long enough to detect the signature of interior and to de-termine the effect of the atmosphere. The ultimate objectives of LaRa and RISE are to obtain infor-mation and constraints on the Martian interior, as well as on seasonal and inter-annual mass transfer between the atmosphere and the ice caps.

Atmosphere Surface interaction The interaction between the solid and fluid layers

of the Earth is the major cause of the fluctuations of the Earth rotation. In the absence of external forces,

the total angular momentum of the Earth is con-served and any change in the Atmospheric Angular Momentum (AAM) yields a change in the solid planet’s angular momentum. The same is true for Mars. Nevertheless, the causes and nature of angular momentum variations can be rather different.

Fig. 1 Rotation of Mars can be measured by radio range and Doppler, with the rotation of Earth measured relative to extragalactic radio sources with very-long-

baseline interferometry. AAM variations of a planet are associated with

the global atmospheric mass redistribution and the wind variability. On the Earth, the largest contribu-tion to angular momentum comes from the annual excitation caused principally by the Mousson regime and the seasonal variations of zonal winds. The an-gular momentum variability of Mars on the other hand is principally due to surface mass redistribution over seasonal time scales. The variation of angular momentum remains much smoother compared to that of the Earth. As a consequence, the amplifica-tion of the normal modes of the planet Mars due to the angular momentum is less significant compared to Earth. For both the Earth and Mars, the diurnal angular momentum variations are much smaller compared to the seasonal variations scales (Karate-kin et al., 2011).

The angular momentum variations can be ex-

pressed by introducing the atmospheric angular mo-mentum excitation functions (Barnes et al., 1983) and the loading effect, represented by the non-dimensional Love numbers (Munk and McDonald, 1960) which depend mainly on the elastic properties of the crust and the mantle. Several authors (Ca-zenave and Balmino, 1981; Defraigne et al., 2000; Van den Acker et al., 2002; Sanchez et al., 2003, 2004; Karatekin et al., 2006, Karatekin et al., 2011) estimated the seasonal variations of LOD from Vi-king lander surface pressure measurements as well as from GCM data, which includes the wind contribu-tion in addition.

Fig. 2 The variation of axial angular momentum based on MACDA assimilated dataset for years 25 and 26. Zonal means of equivalent visible total dust opacity at 610 Pa as a function latitude and solar longitude are shown above. The effect of dust are visible around Ls 220 for MY25 (Karatekin & Montabone 2014).

Recently, Karatekin & Montabone 2014 have in-

vestigated the seasonal angular momentum and rota-tion variations of Mars using the output from the Mars Analysis Correction Data Assimilation (MACDA) dataset v1.0. Studies of the dynamics of the Martian atmosphere are currently limited by the lack of continuous global observations of dynamical variables with a good temporal and spatial resolu-tion. A promising alternative approach is to assimi-late whatever available observations into a general circulation model. MACDA data set contains the reanalysis of fundamental atmospheric and surface variables for the planet Mars over three martian years, produced by assimilating data from spacecraft observations. Temperature and total dust opacities are assimilated into the Mars global circulation mod-el that is in use at the University of Oxford and at the Open University in the UK-LMD-MGCM, covering almost three complete martian seasonal cycles, be-tween martian years 24 through 27. We concentrate in this study the full Martian years 25 and 26. Figure 2 shows the temporal variation of wind and matter components of the axial angular momentum based on MACDA data set for years 25 and 26. The wind component, associated with the relative velocity of the fluid with respect to the solid planet, exhibit high frequency variability as well as seasonal changes. The matter component corresponds to the angular momentum of a rigid rotation of the fluid with the

planet, and is also called the pressure term. Its varia-tion is mainly seasonal. The effect of dust is visible in MY 25 around Ls =220o.

The angular momentum exchange between the

surface and the atmosphere, alters the planetary rota-tion, causing variations on the order of millisecond in Martian LOD over seasonal time scales whereas the polar motion effect is predicted to be in the order of tens of milliarcsecond (Karatekin et al., 2011).

The parameters of the rotation of Mars have been

determined using radio Doppler and ranging meas-urements from Martian orbiters and landers. These measurements had a signature on the measured radio signal due to the rotation of Mars about its spin axis and to the changes in Mars’ orientation. Accurate radio tracking of Mars orbiters is being performed nearly continuously since the arrival of MGS in 1997. Since then, the radio science data from orbiters (MGS, MO and MRO) combined with the data from Viking and Mars Pathfinder landers have been con-tinuously improving the determination of the Mars rotation parameters (see Konopliv et al., 2011). Fig-ure 3 shows the LOD variations computed from the GCM data as well as MACDA data for years 25 and 26 compared with the spacecraft observations from Konopliv et al., (2011). AMES (Haberle 2008) and LMD GCM (Climate Data Base version 4.2) have different assumptions for the dust content of the at-mosphere. MACDA and AMES GCM have higher temporal resolution whereas LMD MCD database considers only typical days over a martian month, hence LMD data is relatively smoother. The overall agreement between the observed and modeled ΔLOD is fairly good. Nevertheless, the present knowledge of LOD is not sufficient enough to differ between models and to constrain Mars CO2 cycle or winds. In addition, the accuracy of observations does not allow to determine nor the polar motion neither the interannual variability of LOD.

Figure 3. LOD variations computed from the GCM data)) as well as MACDA years 25 and 26 compared with the spacecraft observations from Konopliv et al., 2011 (blue shadowed region). The thickness of the shadowed region corresponds to the measurement uncertainties. (Karatekin & Montabone 2014)

The rotations of the planets with an atmosphere (such as Earth, Mars and Titan) constantly slow down and speed up, due to the angular momentum exchange between the surface and the atmosphere, altering the length of the day (LOD). Variations on the order of millisecond over seasonal time scales have been observed for Mars and Earth.Atmospheric angular momentum (AAM) variations of a planet are associated with the global atmospheric mass redistribution and the wind variability. In the present study, we investigate the seasonal angular momentum and rotation variations of Mars using the output from the Mars Analysis Correction Data Assimilation (MACDA) dataset v1.0 (Montabone et al. 2011). The corresponding LOD variations are compared with the existing geodetic observations based on orbiter tracking data as well as other GCM predictions. The results are discussed considering future observations of INSIGHT mission. Determination of LOD variations could help to better understand both the interior structure and the variability of the atmosphere.

ATMOSPHERIC MODEL: MACDA data set contains the reanalysis of fundamental atmospheric and surface variables for the planet Mars over three martian years, produced by assimilating data from spacecraft observations. Temperature and total dust opacities are assimilated into the Mars global circulation model that is in use at the University of Oxford and at the Open University in the UK-LMD-MGCM, covering almost three complete martian seasonal cycles, from 141 degrees solar longitude in martian Year (MY) 24 through 82 degrees solar longitude in MY 27. We concentrate in this study the full Martian years 25 and 26.

Mars Climate Database (MCD) of Laboratoire de Meteorologie Dynamique (LMD) (Forget et al., 1999) is used for comparison. This model can take into account several climatologies over a series of dust scenarios. We considered in this study the standard year, dust climatology.

Introduction

Surface Pressure Variations (MACDA vs MCD):

Conclusions and Perspectives

hAtm = �(u + �R cos ⇥)R cos ⇥

HAtm =�

VhdV

Atmospheric angular momentum (HAtm)

Results

Length of Day (LOD) variations :

Surface pressure averaged over the surface of the planet is plotted for Martian years 25 and 26. MCD data does not have any inter-annual variability and it is shown only for comparison. Mean annual surface pressure given by MCD is higher, 632 Pa, compared to 602 and 609 Pa for MACDA years 25 and 26 respectively. The three data sets (MACDA 25, MACDA 26 and MCD) show very similar seasonal variability. MACDA has higher temporal resolution whereas MCD database we used considers only typical days over a given Martian Month hence, LMD data is relatively smoother.

•MACDA data covering almost three complete martian seasonal cycles allow the study of inter-annual and seasonal variations of AAM. The most important inter-annual variations are observed on the wind component of axial AAM corresponding to ΔLOD .

•ΔLOD deduced from MACDA YR 25 and YR 26 is in good agreement with the geodetic observations. The difference with MACDA and MCD is mainly due to winds.

• Variations in atmospheric dust content shall cause inter-annual variations of both the AAM (wind components) and ΔLOD. The current ΔLOD observation do not provide interannual variability.

• In near future INSIGHT mission and in particular Rotation and Interior Structure Experiment (RISE) could provide interanual variations of ΔLOD and ΔAAM in synergy with TGO orbiter.

Observations: Multi-annual dust scenarios for Martian years 24 to 30 from a multi-instrument dataset of total dust opacity observations have been calculated by Montabone et al. 2012. This procedure includes gridding the observations on a pre-defined longitude-latitude grid with 1 sol resolution in time, and spatially interpolating the results to obtain complete daily maps of total dust opacity. For the purpose of producing the dust scenarios, dust opacity observations from various instruments including, Mars Global Surveyor Spectrometer (TES), Mars Odyssey / Thermal Emission Imaging System (THEMIS), Mars Exploration Rovers A “Spirit” and B “Opportunity”/Pancamcamera and Mars Reconnaissance Orbiter / Mars Climate Sounder (MCS) were collected.

Atmospheric Angular Momentum Variations:The angular momentum changes are calculated for Equatorial (X and Y) as well as axial (Z) respectively. The wind term is dominant in the equatorial (X and Y) components, which are associated with the polar motion. The matter term dominates the axial (Z) component, which is directly proportional to LOD variations. For Mars, mass exchange between the ice caps and the atmosphere due to sublimation/condensation plays the principal role both for the LOD and PM.

ATMOSPHERIC ANGULAR MOMENTUM AND ROTATION VARIATIONS OF MARS BETWEEN MARTIAN YEARS 25 AND 26

Ö. Karatekin1, Luca Montabone,2,31Royal Observatory of Belgium, Bruxelles, Belgium2 Department of Physics, University of Oxford, Oxford, United Kingdom, 3 Laboratoire de Météorologie Dynamique, Université Pierre et Marie Curie, Paris, France

The temporal variations of angular momentum is directly related to the changes in the solar insolation and the atmospheric dynamics. The angular momentum variability of Mars on the other hand is principally due to surface mass redistribution over seasonal time scales. Compared to Earth, Mars has a much more eccentric orbit. This introduces an asymmetry between the seasons and a dominant semi-annual signal in axial angular momentum. In addition to diurnal and annual components there is also an additional component with a period of 6–7 days due to the planetary atmospheric waves (See Karatekin et al. 2012).

The axial angular momentum variations based on MACDA data sets show a very similar behavior for years 25 and 26. The largest discrepancies on the matter term (Nevertheless the variations are very small) occurs around spring and autumn equinoxes, i.e. Ls~0 and 180. Wind component of the angular momentum show much larger fluctuations, over different timescales.

Time variation of the axial atmospheric angular momentum (Wind components) from MACDA data set for Martian years 25 and 26. The effect of dust are visible around Ls 220 and 320 for MY25 and MY26 respectively. Nevertheless there is not a strong correlation between the AAM and atmospheric dust content.

The parameters of the rotation of Mars have been determined using radio Doppler and ranging measurements from Martian orbiters and landers. These measurements had a signature on the measured radio signal due to the rotation of Mars about its spin axis and to the changes in Mars’ orientation. Accurate radio tracking of Mars orbiters is being performed nearly continuously since the arrival of MGS in 1997. Since then, the radio science data from orbiters (MGS, MO and MRO) combined with the data from Viking and Mars Pathfinder landers has been continuously improving the determination of the Mars rotation parameters (see Konopliv et al., 2011).

The LOD variations computed from the GCM data (red and blue lines) as well as MACDA years 25 and 26 are compared with the observations from Konopliv et al (2011) (blue shadowed region) in the next figure. The thickness of the shadowed region corresponds to the measurement uncertainties.

Total ΔLOD deduced from MACDA YR 25 and YR 26 (in red) is in good agreement with the observations. In the figure above, observations are indicated with shaded region in blue whose thickness corresponds to the measurement uncertainties (Konopliv et al., 2011). The observations do not contain inter-annual variability; The ΔLOD observations for MR 25 and MR 26 are exactly the same.

The angular momentum of a fluid particle is given as:

It corresponds to a particle moving with the same angular in the atmosphere velocity as the solid planet (Ω) and has a relative velocity u with respect to solid rotation. The total angular momentum of the fluid layer is given by the integral of the volume V of the fluid layer:

Using hydrostatic equilibrium assumptions, angular momentum can be expressed for a thin atmospheric layer with surface pressure Ps as:

velocity as the solid planet (O!

) and has a relative velocity v!

with

respect to solid rotation ð v!T ¼ v!þO!$ r!Þ. The total angular

momentum of the fluid layer is given by the integral of thevolume V of the fluid layer

H!¼Z

Vr!$ r v

!dVþ

Z

Vr!$ rðO

!$ r!ÞdV ð2Þ

Using hydrostatic equilibrium assumptions dp¼rg dr (with gthe surface gravity, and p the pressure) angular momentum canbe expressed for a thin atmospheric layer with surface pressure ps

as

H!¼Z

Vr!$ r v

!dVþ

Z

Sr!$ ðO

!$ r!Þ

ps

gdS ð3Þ

The first term of the right-hand side is associated with therelative velocity of the fluid with respect to the solid planet, and iscommonly referred to as the motion term (or wind/current term).The second term corresponds to the angular momentum of a rigidrotation of the fluid with the planet, and is called the matter term(or pressure term).

In the frame of Newtonian mechanics the time derivative ofthe angular momentum is equal to the total torque acting on thesystem. Consequently, if the system is isolated, its angularmomentum is a constant. This property is commonly used tostudy the effect of the solid–fluid interaction on planetaryrotation: the knowledge of the angular momentum variations ofthe fluid gives all the information on the changes of planetaryrotation.

We can look at the angular momentum budget from anotherpoint of view: considering the solid planet as a physical systeminteracting with the fluid layer, we can compute directlythe interaction torque due to the planet–fluid interaction (see r).The total torque can be decomposed into three main effects:(1) the pressure torque due to the action of fluid pressure on theplanetary surface, (2) the gravitational torque due to the gravita-tional interaction between the masses inside the planet and the

masses in the fluid layer, and (3) the friction torque associatedwith the relative motion of the fluid with respect to the surface.The total torque is computed from

G!¼Z

Sr!4 n!

T P dSþZ

Sr!4 n!

EP dSþZ

Sr!4 f!

dS ð4Þ

where n!

T is the unit vector normal to the planet surface, n!

E isthe unit vector normal to the equi-gravitational potential surface,

and f!

is the friction drag, or the friction force by unit of surface.As shown in re equatorial components of the torque (associatedwith polar motion and nutation) are dominated by the effect ofthe planet’s equatorial bulge: this ellipsoidal torque is the sum ofthe pressure torque and the gravitational torque acting on theequatorial bulge.

In most of the studies, the mass of the Earth’s atmosphere hasbeen assumed to be constant and the exchange of matter isignored. Nevertheless, GCMs, which are subjected to variousnumerical errors, do not always perfectly conserve the mass andangular momentum. Although these errors originate mostly formdiscretization problems and are insignificant from a dynamicalpoint of view, they contribute significantly to variation of therotational parameters for Earth, more precisely to LOD as shownby de Viron et al. (2002a). Obviously in the case of Mars wherethere are significant seasonal atmospheric mass changes due tocondensation and sublimation of CO2, it is even more important tosatisfy the mass and angular momentum conservations for anaccurate calculation of rotational parameters.

The angular momentum approach has been shown to be moresuccessful than the torque approach to estimate the effect of thefluid layers on the Earth’s rotation (see de Viron and Dehant, 2000).The reason is that the angular momentum approach is based on amean-like operation of well constrained quantities (large scalepressure and wind) that is quite insensitive to errors in the models,whereas the torque approach is based on delicate computation fromless known quantities (local pressure and friction drag).Nevertheless, the torque approach has been shown successful tointerpret the variation of the planetary rotation in terms of theinteractions force between the fluid and the solid planet (see Rchezet al., 2003). Consequently, it is interesting to investigate the fluideffects on the rotation of a planet by both approaches in parallel.

4. Basic comparison of Earth, Venus, and Mars rotationvariations from the fluid interaction point of view

The three terrestrial planets, Mars, Venus, and the Earth arecomparable in many ways. We will discuss only the propertiesrelevant to the angular momentum budget equation and theplanetary rotation. These parameters are shown in Table 2.

The changes in LOD are associated with angular momentumvariations of the solid planet along the axial axis (z-axis)

DLODLOD

¼&DHsolid

Hsolid¼&

DOO

ð5Þ

In the above equation, the changes in the polar moment ofinertia C of the solid planet due to the deformations are neglected.Assuming that the system is isolated, the change in total angularmomentum (the sum of the solid and atmospheric angularmomentum) is zero. Therefore, we can write

DLODLOD

¼&DHatm

Hsolidð6Þ

If the angular momentum of the fluid layer changes, it willinduce a change in the planetary rotation that is inversely

Ls (degrees)

∆ LO

D (m

s)

0 50 100 150 200 250 300 350-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8LMD GCM

Fig. 6. Seasonal LOD variations of Mars given in ms. Computed DLOD from theGCM data (red line) compared with the observations from Konopliv et al. (2006)(dark green region) and Konopliv et al. (2010) (blue region). The thickness of theshadowed regions corresponds to the measurement uncertainties. The time-variable three-dimensional wind and pressure field provided used for the GCMdata comes from Mars Climate Data Base of Laboratoire de Me!te!orologieDynamique (LMD) (Forget et al., 1999) (for interpretation of the references to colorin this figure legend, the reader is referred to the web version of this article).

O. Karatekin et al. / Planetary and Space Science 59 (2011) 923–933 927

The first term of the right-hand side is associated with the relative velocity of the fluid with respect to the solid planet, and is commonly referred to as the motion term (or wind/current term). The second term corresponds to the angular momentum of a rigid rotation of the fluid with the planet, and is called the matter term (or pressure term).The changes in LOD are associated with angular momentum variations of the solid planet along the axial axis (z-axis).ssuming that the system is isolated, the change in total angular momentum (the sum of the solid and atmospheric angular momentum) is zero. Therefore, we can write:

In reality, none of the planets is rigid, and they deform under tidal forces and surface mass redistributions. The angular momentum variations can be expressed equivalently by introducing the atmospheric angular momentum excitation functions (Barnes et al., 1983) and the loading effect, represented by the non-dimensional Love numbers (Munk and McDonald, 1960) which depend mainly on the elastic properties of the crust and the mantle.



with



H!¼Z

Vr!$ r v

!dVþ

Z

Vr!$ rðO

!$ r!ÞdV ð2Þ


as

H!¼Z

Vr!$ r v

!dVþ

Z

Sr!$ ðO

!$ r!Þ

ps

gdS ð3Þ





G!¼Z

Sr!4 n!

T P dSþZ

Sr!4 n!

EP dSþZ

Sr!4 f!

dS ð4Þ

where n!



and f!







DLODLOD

¼&DHsolid

Hsolid¼&

DOO

ð5Þ


DLODLOD

¼&DHatm

Hsolidð6Þ


Ls (degrees)

∆ LO

D (m

s)

0 50 100 150 200 250 300 350-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8LMD GCM



year 26year 25

year 26year 25

Acknowledgments This work was financially supported by the Belgian PRODEX program managed by the European Space Agency in collaboration with the Belgian Federal Science Policy Office

year 26year 25

year 25 year 26

year 25 year 26

into equivalent visible opacities and we normalised them at the reference pressure level of 610 Pa. 3. Product Observed or estimated total dust opacities (two-dimensional data) were gridded on a pre-defined time-space grid using the weighted binning methodology (acceptance criteria for the value at each grid point were defined) and, subsequently, incomplete maps were interpolated using the kriging interpolation method. The final result was a set of complete, regular, daily maps of equivalent visible total dust opacities at the reference pressure of 610 Pa from Ls ~105° in MY 24 to the end of MY 30. This series of maps was separated in Martian years of 669 sols each and the final product was exported as NetCDF files, ready to be interfaced to the LMD-MarsGCM or other numerical models . Note that MY 24 dust scenario is actually a hybrid scenario built using the first 224 sols of MY 25 to fill the lack of observations in MY 24 before Ls ~105°.

Figure 1: Zonal means of equivalent visible total dust opacity at 610 Pa as a function of latitude and solar longitude for seven Martian years. Data to produce these zonal means are extracted from the NetCDF dust scenario files. Acknowledgements We gratefully acknowledge the use of TES and THEMIS dust opacity retrievals provided by M. D. Smith of NASA Goddard Space Flight Center, the use of MCS dust opacity retrievals (and estimated total dust opacities) provided by D. Kass and the MCS team at NASA Jet Propulsion Laboratory, and the use of dust opacity observations from Spirit/Opportunity Pancam cameras (data from M. T. Lemmon). References [1] Smith M. D., Interannual variability in TES atmospheric observations of Mars during 1999-2003. Icarus 167, 148–165, 2004. [2] Smith, M., D., THEMIS observations of Mars aerosol optical depth from 2002-2008. Icarus doi: 10.1016/j.icarus.2009.03.027, 2009. [3] Lemmon, M.T., M.J. Wolff, M.D. Smith, R.T . Clancy, D. Banfield, G.A. Landis, A. Ghosh, P.H. Smith, N. Spanovich, B. Whitney, P. Whelley, R. Greeley, S. Thompson, J.F. Bell III, S.W. Squyres, Atmospheric Imaging Results from the Mars Exploration Rovers: Spirit and Opportunity. Science 306, 1753-1756, 2004. [4] Kleinbohl, A., J. T . Schofield, D. M. Kass, W. A. Abdo u, C. R. Backus, B. Sen, J. H. Shirley, W. G. Lawson, M. I. Richardson, F. W. Taylor, N. A. Teanby, and D. J. McCleese, Mars Climate Sounder lim b profile retrieval of atmospheric temperature, pressure, and dust and water ice opacity. J. Geophys. Res. 114, E10006, doi:10.1029/2009JE003358, 2009

Montabone, L.; Lewis, S. R.; Read, P. L., Mars Analysis Correction Data Assimilation (MACDA): MGS/TES v1.0, [Internet]. NCAS British Atmospheric Data Centre, 29 November 2011.Barnes, R.T.H., et al. 1983., Atmospheric angular momentum fluctuations, length-of-day changes and polar motion. Royal Society of London Proceedings Series A 387, 31-73. Munk, W. H., MacDonald, G. J. F. 1960. The rotation of the earth; a geophysical discussion. Cambridge [Eng.] University Press.

References: Forget, F., et al. 1999. Improved general circulation models of the Martian atmosphere from the surface to above 80 km. Journal of Geophysical Research 104, 24155-24176. Montabone, L., Millour, E., Forget, F., Lewis, S.R. 2012.\Seven-Year Climatology of Dust Opacity on Mars. European Planetary Science Congress 2012.Karatekin, O., et al. 2011.\ Atmospheric angular momentum variations of Earth, Mars and Venus at seasonal time scales. Planetary and Space Science 59, 923-933. Konopliv, A. S., et al. Mars high resolution gravity fields from MRO, Mars seasonal gravity, and other dynamical parameters. Icarus 211, 401-428.

The angular momentum for Equatorial (X and Y) and Axial (Z) components based on MACDA data set for years 25 and 26.

Figure: Zonal means of equivalent visible total dust opacity at 610 Pa as a function of latitude and solar longitude for Martian years 25 and 26 are given below:

Time variat ion of the axial atmospheric angular momentum (Matter components) from MACDA data set for Martian years 25 and 26. The interannual variation as well as the effect of dust is not significant. This is not surprising considering that the MACDA do not assimilate yet the surface pressure nor the seasonal surface `variation observations of CO2 ice.

Friday 25 April 14

The rotations of the planets with an atmosphere (such as Earth, Mars and Titan) constantly slow down and speed up, due to the angular momentum exchange between the surface and the atmosphere, altering the length of the day (LOD). Variations on the order of millisecond over seasonal time scales have been observed for Mars and Earth.Atmospheric angular momentum (AAM) variations of a planet are associated with the global atmospheric mass redistribution and the wind variability. In the present study, we investigate the seasonal angular momentum and rotation variations of Mars using the output from the Mars Analysis Correction Data Assimilation (MACDA) dataset v1.0 (Montabone et al. 2011). The corresponding LOD variations are compared with the existing geodetic observations based on orbiter tracking data as well as other GCM predictions. The results are discussed considering future observations of INSIGHT mission. Determination of LOD variations could help to better understand both the interior structure and the variability of the atmosphere.

ATMOSPHERIC MODEL: MACDA data set contains the reanalysis of fundamental atmospheric and surface variables for the planet Mars over three martian years, produced by assimilating data from spacecraft observations. Temperature and total dust opacities are assimilated into the Mars global circulation model that is in use at the University of Oxford and at the Open University in the UK-LMD-MGCM, covering almost three complete martian seasonal cycles, from 141 degrees solar longitude in martian Year (MY) 24 through 82 degrees solar longitude in MY 27. We concentrate in this study the full Martian years 25 and 26.

Mars Climate Database (MCD) of Laboratoire de Meteorologie Dynamique (LMD) (Forget et al., 1999) is used for comparison. This model can take into account several climatologies over a series of dust scenarios. We considered in this study the standard year, dust climatology.

Introduction

Surface Pressure Variations (MACDA vs MCD):

Conclusions and Perspectives

hAtm = �(u + �R cos ⇥)R cos ⇥

HAtm =�

VhdV

Atmospheric angular momentum (HAtm)

Results

Length of Day (LOD) variations :

Surface pressure averaged over the surface of the planet is plotted for Martian years 25 and 26. MCD data does not have any inter-annual variability and it is shown only for comparison. Mean annual surface pressure given by MCD is higher, 632 Pa, compared to 602 and 609 Pa for MACDA years 25 and 26 respectively. The three data sets (MACDA 25, MACDA 26 and MCD) show very similar seasonal variability. MACDA has higher temporal resolution whereas MCD database we used considers only typical days over a given Martian Month hence, LMD data is relatively smoother.

•MACDA data covering almost three complete martian seasonal cycles allow the study of inter-annual and seasonal variations of AAM. The most important inter-annual variations are observed on the wind component of axial AAM corresponding to ΔLOD .

•ΔLOD deduced from MACDA YR 25 and YR 26 is in good agreement with the geodetic observations. The difference with MACDA and MCD is mainly due to winds.

• Variations in atmospheric dust content shall cause inter-annual variations of both the AAM (wind components) and ΔLOD. The current ΔLOD observation do not provide interannual variability.

• In near future INSIGHT mission and in particular Rotation and Interior Structure Experiment (RISE) could provide interanual variations of ΔLOD and ΔAAM in synergy with TGO orbiter.

Observations: Multi-annual dust scenarios for Martian years 24 to 30 from a multi-instrument dataset of total dust opacity observations have been calculated by Montabone et al. 2012. This procedure includes gridding the observations on a pre-defined longitude-latitude grid with 1 sol resolution in time, and spatially interpolating the results to obtain complete daily maps of total dust opacity. For the purpose of producing the dust scenarios, dust opacity observations from various instruments including, Mars Global Surveyor Spectrometer (TES), Mars Odyssey / Thermal Emission Imaging System (THEMIS), Mars Exploration Rovers A “Spirit” and B “Opportunity”/Pancamcamera and Mars Reconnaissance Orbiter / Mars Climate Sounder (MCS) were collected.

Atmospheric Angular Momentum Variations:The angular momentum changes are calculated for Equatorial (X and Y) as well as axial (Z) respectively. The wind term is dominant in the equatorial (X and Y) components, which are associated with the polar motion. The matter term dominates the axial (Z) component, which is directly proportional to LOD variations. For Mars, mass exchange between the ice caps and the atmosphere due to sublimation/condensation plays the principal role both for the LOD and PM.

ATMOSPHERIC ANGULAR MOMENTUM AND ROTATION VARIATIONS OF MARS BETWEEN MARTIAN YEARS 25 AND 26

Ö. Karatekin1, Luca Montabone,2,31Royal Observatory of Belgium, Bruxelles, Belgium2 Department of Physics, University of Oxford, Oxford, United Kingdom, 3 Laboratoire de Météorologie Dynamique, Université Pierre et Marie Curie, Paris, France

The temporal variations of angular momentum is directly related to the changes in the solar insolation and the atmospheric dynamics. The angular momentum variability of Mars on the other hand is principally due to surface mass redistribution over seasonal time scales. Compared to Earth, Mars has a much more eccentric orbit. This introduces an asymmetry between the seasons and a dominant semi-annual signal in axial angular momentum. In addition to diurnal and annual components there is also an additional component with a period of 6–7 days due to the planetary atmospheric waves (See Karatekin et al. 2012).

The axial angular momentum variations based on MACDA data sets show a very similar behavior for years 25 and 26. The largest discrepancies on the matter term (Nevertheless the variations are very small) occurs around spring and autumn equinoxes, i.e. Ls~0 and 180. Wind component of the angular momentum show much larger fluctuations, over different timescales.

Time variation of the axial atmospheric angular momentum (Wind components) from MACDA data set for Martian years 25 and 26. The effect of dust are visible around Ls 220 and 320 for MY25 and MY26 respectively. Nevertheless there is not a strong correlation between the AAM and atmospheric dust content.

The parameters of the rotation of Mars have been determined using radio Doppler and ranging measurements from Martian orbiters and landers. These measurements had a signature on the measured radio signal due to the rotation of Mars about its spin axis and to the changes in Mars’ orientation. Accurate radio tracking of Mars orbiters is being performed nearly continuously since the arrival of MGS in 1997. Since then, the radio science data from orbiters (MGS, MO and MRO) combined with the data from Viking and Mars Pathfinder landers has been continuously improving the determination of the Mars rotation parameters (see Konopliv et al., 2011).

The LOD variations computed from the GCM data (red and blue lines) as well as MACDA years 25 and 26 are compared with the observations from Konopliv et al (2011) (blue shadowed region) in the next figure. The thickness of the shadowed region corresponds to the measurement uncertainties.

Total ΔLOD deduced from MACDA YR 25 and YR 26 (in red) is in good agreement with the observations. In the figure above, observations are indicated with shaded region in blue whose thickness corresponds to the measurement uncertainties (Konopliv et al., 2011). The observations do not contain inter-annual variability; The ΔLOD observations for MR 25 and MR 26 are exactly the same.

The angular momentum of a fluid particle is given as:

It corresponds to a particle moving with the same angular in the atmosphere velocity as the solid planet (Ω) and has a relative velocity u with respect to solid rotation. The total angular momentum of the fluid layer is given by the integral of the volume V of the fluid layer:

Using hydrostatic equilibrium assumptions, angular momentum can be expressed for a thin atmospheric layer with surface pressure Ps as:



with



H!¼Z

Vr!$ r v

!dVþ

Z

Vr!$ rðO

!$ r!ÞdV ð2Þ


as

H!¼Z

Vr!$ r v

!dVþ

Z

Sr!$ ðO

!$ r!Þ

ps

gdS ð3Þ





G!¼Z

Sr!4 n!

T P dSþZ

Sr!4 n!

EP dSþZ

Sr!4 f!

dS ð4Þ

where n!



and f!







DLODLOD

¼&DHsolid

Hsolid¼&

DOO

ð5Þ


DLODLOD

¼&DHatm

Hsolidð6Þ


Ls (degrees)

∆ LO

D (m

s)

0 50 100 150 200 250 300 350-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8LMD GCM



The first term of the right-hand side is associated with the relative velocity of the fluid with respect to the solid planet, and is commonly referred to as the motion term (or wind/current term). The second term corresponds to the angular momentum of a rigid rotation of the fluid with the planet, and is called the matter term (or pressure term).The changes in LOD are associated with angular momentum variations of the solid planet along the axial axis (z-axis).ssuming that the system is isolated, the change in total angular momentum (the sum of the solid and atmospheric angular momentum) is zero. Therefore, we can write:

In reality, none of the planets is rigid, and they deform under tidal forces and surface mass redistributions. The angular momentum variations can be expressed equivalently by introducing the atmospheric angular momentum excitation functions (Barnes et al., 1983) and the loading effect, represented by the non-dimensional Love numbers (Munk and McDonald, 1960) which depend mainly on the elastic properties of the crust and the mantle.



with



H!¼Z

Vr!$ r v

!dVþ

Z

Vr!$ rðO

!$ r!ÞdV ð2Þ


as

H!¼Z

Vr!$ r v

!dVþ

Z

Sr!$ ðO

!$ r!Þ

ps

gdS ð3Þ





G!¼Z

Sr!4 n!

T P dSþZ

Sr!4 n!

EP dSþZ

Sr!4 f!

dS ð4Þ

where n!



and f!







DLODLOD

¼&DHsolid

Hsolid¼&

DOO

ð5Þ


DLODLOD

¼&DHatm

Hsolidð6Þ


Ls (degrees)

∆ LO

D (m

s)

0 50 100 150 200 250 300 350-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8LMD GCM



year 26year 25

year 26year 25

Acknowledgments This work was financially supported by the Belgian PRODEX program managed by the European Space Agency in collaboration with the Belgian Federal Science Policy Office

year 26year 25

year 25 year 26

year 25 year 26

into equivalent visible opacities and we normalised them at the reference pressure level of 610 Pa. 3. Product Observed or estimated total dust opacities (two-dimensional data) were gridded on a pre-defined time-space grid using the weighted binning methodology (acceptance criteria for the value at each grid point were defined) and, subsequently, incomplete maps were interpolated using the kriging interpolation method. The final result was a set of complete, regular, daily maps of equivalent visible total dust opacities at the reference pressure of 610 Pa from Ls ~105° in MY 24 to the end of MY 30. This series of maps was separated in Martian years of 669 sols each and the final product was exported as NetCDF files, ready to be interfaced to the LMD-MarsGCM or other numerical models . Note that MY 24 dust scenario is actually a hybrid scenario built using the first 224 sols of MY 25 to fill the lack of observations in MY 24 before Ls ~105°.

Figure 1: Zonal means of equivalent visible total dust opacity at 610 Pa as a function of latitude and solar longitude for seven Martian years. Data to produce these zonal means are extracted from the NetCDF dust scenario files. Acknowledgements We gratefully acknowledge the use of TES and THEMIS dust opacity retrievals provided by M. D. Smith of NASA Goddard Space Flight Center, the use of MCS dust opacity retrievals (and estimated total dust opacities) provided by D. Kass and the MCS team at NASA Jet Propulsion Laboratory, and the use of dust opacity observations from Spirit/Opportunity Pancam cameras (data from M. T. Lemmon). References [1] Smith M. D., Interannual variability in TES atmospheric observations of Mars during 1999-2003. Icarus 167, 148–165, 2004. [2] Smith, M., D., THEMIS observations of Mars aerosol optical depth from 2002-2008. Icarus doi: 10.1016/j.icarus.2009.03.027, 2009. [3] Lemmon, M.T., M.J. Wolff, M.D. Smith, R.T . Clancy, D. Banfield, G.A. Landis, A. Ghosh, P.H. Smith, N. Spanovich, B. Whitney, P. Whelley, R. Greeley, S. Thompson, J.F. Bell III, S.W. Squyres, Atmospheric Imaging Results from the Mars Exploration Rovers: Spirit and Opportunity. Science 306, 1753-1756, 2004. [4] Kleinbohl, A., J. T . Schofield, D. M. Kass, W. A. Abdo u, C. R. Backus, B. Sen, J. H. Shirley, W. G. Lawson, M. I. Richardson, F. W. Taylor, N. A. Teanby, and D. J. McCleese, Mars Climate Sounder lim b profile retrieval of atmospheric temperature, pressure, and dust and water ice opacity. J. Geophys. Res. 114, E10006, doi:10.1029/2009JE003358, 2009

Montabone, L.; Lewis, S. R.; Read, P. L., Mars Analysis Correction Data Assimilation (MACDA): MGS/TES v1.0, [Internet]. NCAS British Atmospheric Data Centre, 29 November 2011.Barnes, R.T.H., et al. 1983., Atmospheric angular momentum fluctuations, length-of-day changes and polar motion. Royal Society of London Proceedings Series A 387, 31-73. Munk, W. H., MacDonald, G. J. F. 1960. The rotation of the earth; a geophysical discussion. Cambridge [Eng.] University Press.

References: Forget, F., et al. 1999. Improved general circulation models of the Martian atmosphere from the surface to above 80 km. Journal of Geophysical Research 104, 24155-24176. Montabone, L., Millour, E., Forget, F., Lewis, S.R. 2012.\Seven-Year Climatology of Dust Opacity on Mars. European Planetary Science Congress 2012.Karatekin, O., et al. 2011.\ Atmospheric angular momentum variations of Earth, Mars and Venus at seasonal time scales. Planetary and Space Science 59, 923-933. Konopliv, A. S., et al. Mars high resolution gravity fields from MRO, Mars seasonal gravity, and other dynamical parameters. Icarus 211, 401-428.

The angular momentum for Equatorial (X and Y) and Axial (Z) components based on MACDA data set for years 25 and 26.

Figure: Zonal means of equivalent visible total dust opacity at 610 Pa as a function of latitude and solar longitude for Martian years 25 and 26 are given below:

Time variat ion of the axial atmospheric angular momentum (Matter components) from MACDA data set for Martian years 25 and 26. The interannual variation as well as the effect of dust is not significant. This is not surprising considering that the MACDA do not assimilate yet the surface pressure nor the seasonal surface `variation observations of CO2 ice.

Friday 25 April 14

Forthcoming Radio Science Experiments Radio tracking of ExoMars Surface Platform

(LaRa) and InSIght (RISE) in X-band over will improve the current precision on LOD more than an order of magnitude (See Figure 4). Such a precision will permit to provide constraints on the details of the physical processes taking part in the angular momentum variations of the Martian atmosphere. In addition, with such a precision on ΔLOD and with longer tracking coverage it might be possible to see the inter-annual variations of the global-scale cycling of CO2 on Mars that could arise from the dust storm variability.

Fig. 4: ΔLOD estimates from simulated Lander radio sci-ence experiment with a direct link between Mars and the Earth in comparison with those based on LMD and AMES GCM. The predicted uncertainty ranges of Lander radio science experiment are shown between the corresponding lines (See Le Maistre et al., 2012 for further details.)

Conclusion: Forthcoming Radio Science experiments RISE

and LaRa, are expected to improve current knowledge of Mars rotation parameters by at least an order of magnitude. They will provide infor-mation not only on the interior structure but also on the details of the physical processes taking part in the seasonal and inter-annual angular momentum varia-tions of the Martian atmosphere and the sublimation / condensation cycle of atmospheric CO2.

References:

[1] Barnes, R.T.H., et al. 1983., Atmospheric angu-lar momentum fluctuations, length-of-day changes and polar motion. Royal Society of London Proceed-ings Series A 387, 31-73. [2] Munk, W. H., MacDonald, G. J. F. 1960. The rotation of the earth; a geophysical discussion. Cam-bridge [Eng.] University Press. [3] Karatekin Ö., Montabone L. 2014. Atmospheric Angular Momentum and Rotation Variations of Mars between Martian years 24 and 27. The 5th In-ternational Workshop on Mars Atmosphere: Model-

ling and Observations, Oxford University, Oxford, UK, January 13-16, 2014 [4] Montabone, L.; Lewis, S. R.; Read, P. L., 2011. Mars Analysis Correction Data Assimilation (MACDA): MGS/TES v1.0, [Internet]. NCAS Brit-ish Atmospheric Data Center. [5] Konopliv, A. S., et al. 2011. Mars high resolution gravity fields from MRO, Mars seasonal gravity, and other dynamical parameters. Icarus 211, 401-428. [6] Le Maistre, S., et al. 2012. Lander radio science experiment with a direct link between Mars and the Earth. Planetary and Space Science 68, 105-122. [7] Cazenave, A., Balmino, G., 1981. Meteorological effects on the seasonal variations of the rotation of Mars. Geophys. Res. Lett. 8, 245–248. [8] Defraigne, P., de Viron, O., Dehant, V., Van Hoolst, T., Hourdin, F., 2000. Mars rotation varia-tions induced by atmospheric CO2 and winds. J. Geophys. Res. (Planets) 105 (E10), 24563–24570. [9] Sanchez, B., Rowlands, D., Haberle, R., Schaeffer, J., 2003. Atmospheric rotational effects on Mars based on the NASA Ames general circula-tion model. J. Geophys. Res. (Planets) 108, 5040. [10] Sanchez, B., Haberle, R., Schaeffer, J., 2004. Atmospheric rotational effects on Mars based on the NASA Ames general circulation model: angular momentum approach. J. Geophys. Res., 109(E8), CiteID, E08005. doi:10.1029/2004JE002254. [11] Van den Acker, E., Van Hoolst, T., de Viron, O., Defraigne, P., Dehant, V., Forget, F., Hourdin, F., 2002. Influence of the winds and of the CO2 mass exchange between the atmosphere and the po-lar ice caps on Mars’ orientation parameters. J. Ge-ophys. Res.. doi:10.1029/2000JE001539. [12] Karatekin, O ., Van Hoolst, T., Tastet, J., de Viron, O., Dehant, V, 2006. The effects of seasonal mass redistribution and interior structure on Length-of-Day variations of Mars. Adv. Space Res. 38 (4), 561–828 JASR-D-04-01301R1. [13] Karatekin, Ö. et al., 2011. Atmospheric angular momentum variations of Earth, Mars and Venus at seasonal time scales., Planetary and Space Science 59 (2011) 923–933. [14] Haberle, R.M., Forget, F., Colaprete, A., Schaeffer, J., Boynton, W.V., Kelly, N.J., Chamber-lain, M.A., 2008. The effect of ground ice on the martian seasonal CO2 cycle. Planet. Space Sci. 56, 251–255.

(Karatekin et al., 2006). Nevertheless, such a precision will permitto provide constraints on the details of the physical processestaking part in the angular momentum variations of the Martianatmosphere. As shown in Fig. 14 precision better than 0.05 msecon total LOD variations is required to be able to assess the LODestimates obtained from AMES or LMD Global Circulation Model(GCM). Current solution precision is just above this precision (seeFig. 29 in Konopliv et al. (2011)) whereas a LaRa-like experimentwill reach a precision significantly better (see Fig. 14). In addition,with such a precision on DLOD and with longer tracking coverageit might be possible to see the inter-annual variations of theglobal-scale cycling of CO2 on Mars that could arise from the duststorm variability.

Moreover, the total DLOD can be expressed as the sum of amatter (loading) term and a wind (motion) term, where thematter component is the dominant term (wind componentrepresenting about 30% of the total DLOD). The seasonal varia-tions in the matter term are proportional to DJ2 and inverselyproportional to the polar moment of inertia C (Chao andRubincam, 1990). Then, the wind component can be expressed

as follows:

DLODwind ¼DLODtotal" _f23

MR2e

CDJ2, ð37Þ

where _f is the spin rate of Mars, M and Re its mass and equatorialradius (see Table 1). Thus, using the best precision obtained in oursimulation study for total DLOD (0.008 msec) with 700 days ofmission duration and the current knowledge on DJ2ð710"9) andC (0.364475%10"4), the expected precision on the wind termhas been deduced at 0.16 msec. This corresponds to about 150% ofthe discrepancy between wind contribution estimates from theLMD and from the AMES GCM as expressed in Section 8 inKonopliv et al. (2011). In conclusion it will be impossible toseparate wind and matter contributions with a LaRa-like experi-ment. We note, however, that such a precision on the windcomponent is limited by the current precision on DJ2 which is2 or 3 orders of magnitude worst than precision on total DLODthat could be obtained with a LaRa-like experiment.

Fig. 15 shows the uncertainties and true errors obtained on _Iand _c. We can see from this figure that about 150 days arerequired to improve our knowledge on these ‘‘precession para-meters’’, represented by the horizontal dotted lines. The preces-sion rate, currently known at the 0.3% level of precision, isobtained with a precision of about 0.05% after 700 days of missionduration. The inferred precision on the normalized polar momentof inertia C=R2

e is equal to 1.1%10"4. This is about five timesbetter than the current precision of 5%10"4 obtained byKonopliv et al. (2011) using their best precession solution (witha precision of 10 mas/year, see Table 6 in their paper). We notethat the same precision can be obtained faster by combining thesedata with data of a previous mission like Mars Pathfinder and/orViking.

Fig. 16 (left panel) shows the accuracy in the estimation of theFCN period as a function of the experiment duration. As s0

appears in a nonlinear Eq. (12), the partial derivative of theDoppler observable with respect to it depends on its own value.Thus the estimated uncertainty of s0, obtained from an iterativeleast squares solution applied to the simulated data, depends onhow close the actual FCN period is to one-third of a Martian yearsince the resonance drives the amplitudes of the liquid corecontribution (the closer to the resonance period, the larger the

0 30 60 90 120 150 180 210 240 270 300 330 360Ls (degrees)

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

∆LO

D (m

sec)

Fig. 14. DLOD estimates from both LMD and AMES GCM maps are shown with therange of estimates derived from the precisions foreseen by this study.

0 100 200 300 400 500 600 70010

-210

-2

10-1

10-1

100

100

101

101

102

102

103

103

I dot (m

as/y

ear)

true error 1uncertainty 1true error 2uncertainty 2

0 100 200 300 400 500 600 700

Mission duration (days)

10-2

10-2

10-1

10-1

100

100

101

101

102

102

103

103

ψ dot (m

as/y

ear)

Fig. 15. Estimated uncertainties in obliquity (_I) and precession ( _c) rates in mas/year as a function of the mission duration, with trigonometric nutation amplitudemodeling (1) and with transfer function nutation modeling (2). Dotted lines correspond to current precision. The FCN period is equal to "240 days.

S. Le Maistre et al. / Planetary and Space Science 68 (2012) 105–122 117

RADIOSCIENCE EXPERIMENTS TO MONITOR ATMOSPHERIC … · RADIOSCIENCE EXPERIMENTS TO MONITOR...

Documents

Transcript of RADIOSCIENCE EXPERIMENTS TO MONITOR ATMOSPHERIC … · RADIOSCIENCE EXPERIMENTS TO MONITOR...