Mars Express Radio Science Experiment MaRS MaRS Radio Science Data: Level 3 & 4 The retrieval

1. Mars Express Radio Science Experiment MaRS MaRS Radio Science Data: Level 3 & 4 The retrieval S.Tellmann, M.Pätzold ESAC June 2008

2. Overview LEVEL 3: • The data preparation • Calculation of bending angle and rayparameter • The Abel Transformation LEVEL 4: • The Neutral Atmosphere • Calculation of • Density • Temperature • Pressure • The Ionosphere • Calculation of the electron density

3. Level 3Retrieval of the Refractivity and the Radius

4. Level 3 Data Processing Flow Chart Input: Level 2 residual

5. Level 3 Data Processing Flow Chart Input: Level 2 residual Baseline fit correction

6. Starting Point: Residual • Starting point: Level 2 residual Offset Offset (and/or trend): Reason Uncertainties in Orbit

7. Baseline Fit Correction • Starting point: Level 2 residual radius: ~ 4000 km range for baseline fit Offset

8. Residual after Correction

9. Level 3 Data Processing Flow Chart Input: Level 2 residual Baseline fit correction Calculation of Measurement Geometry Occultation Plane

10. Next Goal: Calculation of Bending angle & Rayparameter a: bending angle a: rayparameter

11. Next Goal: Calculation of Bending angle & Rayparameter • Measurement geometry must be known: • Occultation Plane containing • Groundstation • Planet • Spacecraft • given by: • z: vector from groundstation to planet • r: vector perpendicular to z and • in this OCC plane a: bending angle a: rayparameter

12. Occultation (OCC) plane Calculation of state vectors for every measurement sample Earth direction PG/S,VG/S Radio Link PMEX,VMEX OCC plane at time tm MEX orbit

13. Level 3 Data Processing Flow Chart Input: Level 2 residual Baseline fit correction Calculation of Measurement Geometry Occultation Plane Calculation of Bending Angle & Rayparameter

14. Next Goal: Calculation of Bending angle & Rayparameter Solve equations from [Fjeldbo et al., 1971]: B ·( ) = ( ) where b11 = -vrs sin(be –br) + vzs cos(be– br) b12 = -vrt cos(ds – dr) + vzt sin(ds– dr) b21 = (rs+ zs)1/2 sin(be – g – br) b22 = zt cos(ds– dr) k1 = c Df/fs + vrs[cos(be – br) – cosbe] + vzs[sin(be – br) – sinbe] - vrt[sin(ds– dr) – sinds] – vzt[cos(ds – dr) – cosds] k2 = ztsin(ds – dr) + (rs2-zs2)1/2 sin(be –g– br) a: bending angle Dbr k1 Ddr k2 a: rayparameter

15. Calculation of Bending angle & Rayparameter bending angle a = dr + br rayparameter a = (rs2 + zs2)1/2 sin(be – br – g)

16. Level 3 Data Processing Flow Chart Input: Level 2 residual Baseline fit correction Calculation of Measurement Geometry Occultation Plane Calculation of Bending Angle & Rayparameter Abel Transformation Calculation of Refractivity & Radius

17. Calculation of Refractivity & Radius n Refractive index n Refractivity m Radius r

18. Algorithm for the calculation of the refractive index via an Abel transform Initialise a vector of dimension ‚i‘ To store the row integrals Current rayparameter of layer ‚i‘ Upper and lower boundary of the current row integral Bending angle of the current layer Call of the integration function and storing of the integral output Summing up of the array Zintegral

19. Algorithm for the calculation of the refractive index via an Abel transform Initialise a vector of dimension ‚i‘ To store the row integrals Current rayparameter of layer ‚i‘ Upper and lower boundary of the current row integral Bending angle of the current layer Call of the integration function and storing of the integral output INTEGRAL: Integration routine able to handle the pole Summing up of the array Zintegral

20. Calculation of Refractivity Bending Angle Refractivity a m radius [km] Abeltransform Refraktivität [deg * 106 ] Bending angle [deg * 106 ]

21. The Occultation Footpoints Earth direction x Spacecraft Occultation footpoint Moving over the surface of Mars

22. The Occultation Footpoints • Calculation of intersection point • of ray asymptotes using spherical • symmetry • Transformation of this vector • into planetary coordinates (lat, lon) • for every measurement value

23. Level 3 Data Processing Flow Chart Input: Level 2 residual Baseline fit correction Calculation of Measurement Geometry Occultation Plane Calculation of Bending Angle & Rayparameter Abel Transformation Calculation of Refractivity & Radius Calculation of Occultation Footpoints Main Output: Refractivity, Radius & OCC Footpoints

24. Level 4The Neutral Atmosphere

25. Starting Point: Refractivity Ionosphere: Negative Refraktivity higher than ~ 80 km altitude approx. 3480 km radius Transition Region: no significant bending approx. 60 km – 80 km altitude approx. 3450 km – 3480 km Neutral Atmosphere: positive Refractivity up to approx. 50 km altitude up to approx. 3450 km radius Ionopause Ionosphere Transition Region Neutral Atmosphere

26. The Neutral Number Density m : refractivity C1 : atmospheric constant k : Boltzman constant n : neutral number density • C1 is based on the atmospheric composition (CO2, N2, Ar) • C1 = 1.3063 10-6 K·m·s2/kgknown from laboratory measurements • [Hinson et al., 1999] .

27. Calculation of Pressure and Temperature • Ideal gas law relates Pressure, Temperature and Density • Hydrostatic equilibrium in well-mixed atmosphere: temperature can be derived directly from neutral number density

28. Calculation of Pressure and Temperature • Ideal gas law relates Pressure, Temperature and Density • Hydrostatic equilibrium in well-mixed atmosphere: temperature can be derived directly from neutral number density upper boundary condition

29. Upper boundary condition of temperature Tup = 150 K Tup = 160 K Tup = 170 K

30. Level 4 Neutral Atmosphere Data Processing Flow Chart Input: Refractivity Profile Calculation of Neutral Number Density Calculation of Temperature and Pressure Main Output: Profiles of Temperature, Pressure and Density

31. Level 4The Ionosphere

32. The Electron Density f0 : Radio link frequency Ne : electron density C3 = 40.31

33. The Electron Density

34. Temperature Profiles Northern Hemisphere 2007 Autumn 2005 Autumn 2005 Spring 2005 Spring 35.0°N

35. Temperature Profiles Northern Hemisphere 2007 Autumn 2005 Autumn 2005 Spring 2005 Spring Typical daytime profile middle latitude 35.0°N

36. Temperature Profiles Northern Hemisphere 2007 Autumn 2005 Autumn 2005 Spring 2005 Spring morning profile inversion in boundary layer 35.0°N

37. Temperature Profiles Northern Hemisphere 2007 Autumn 2005 Autumn 2005 Spring 2005 Spring Stationary wave structures 35.0°N

38. Comparison with Model: middle latitudes MaRS GCM low dust GCM med. dust GCM high dust

39. Comparison with Model: 60° N MaRS GCM low dust GCM med. dust GCM high dust

40. Comparison with Model: 63° N MaRS GCM low dust GCM med. dust GCM high dust

41. Comparison with Model: Winter Night MaRS GCM (LMD) altitude [km] altitude [km] Temperature [K] planetary latitude [deg] planetary latitude [deg]

42. Autumn profiles Ls = 227° – 235° Ls = 250° – 265° 2005 2007

43. Autumn & Winter profiles Ls = 227° – 235° Ls = 250° – 265° Ls = 345° – 15°