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

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

2. Overview LEVEL 3: • The Bending Angle & the Rayparameter • The Refractive Index/Refractivity & Radius LEVEL 4: • The Neutral Atmosphere • Density • Temperature • Pressure • The Ionosphere • The Electron Density The Twoway Problem

3. Earth Occultations MEX f : signal transmitted from MEX f : signal received w/o atmosphere Df : classical Doppler shift send MEX w/o rec dop Neutral Atmosphere Mars Ionosphere w/o MEX f = f + Df send rec dop w/o f rec

4. Earth Occultations MEX f : signal transmitted from MEX f : signal received w/o atmosphere Df : classical Doppler shift f : signal received with atmosphere Df : frequency shift from atmosphere send Ray Asymptote MEX w/o rec dop a with Neutral Atmosphere rec Mars atm Ionosphere w/o MEX f = f + Df with f send rec dop rec w/o f rec with MEX f = f + Df + Df + Df dop iono send rec atm a : bending angle

5. Bending Angle & Rayparameter Retrieval based on geometrical optics [Fjeldbo et al., 1971] a : bending angle a : rayparameter

6. Bending Angle & Rayparameter Basic Idea: • Input: • Position of Spacecraft, • Groundstation & Mars • Velocity of Spacecraft, • Groundstation & Mars [Fjeldbo et al., 1971]

7. Doppler Effect For vEarth << vS/C:

8. The Refractivity • Calculation of Refractive index from bending angle and rayparameter • Reconstruction of a two-dimensional radial symmetric • distribution f(r) from its projection g(y) inverse Abeltransform [Pretzler et al., 1992] Abel transform: The twodimensional function is given by: Inverse Abel transform: [Jenkins, 1992]

9. The Refractivity • Inverse Abeltransform: Refractive Index: • Integration of bending angle and rayparameter over all layers • already traversed n1 n2 n3 n4

10. The Radius (ray peripasis) r : radius a : rayparameter n : refractive index

11. Refractivity Ionosphere: Negative Refractivity 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 Refractivity

12. Retrieval of atmospheric parameter f0 : Radio link frequency Ne : electron density C1, C3 : atm. constants k : Boltzman constant n: neutral number density Refractivity m(h): Neutral Atmosphere Ionosphere

13. The Ionosphere Refractivity m(h) in Ionosphere (h>60km): f0 : Radio link frequency Ne : electron density C3 : atm. constant Neutral Atmosphere Ionosphere

14. The Electron Density f0 : Radio link frequency Ne : electron density C3 = 40.31 m3/s2 • refractivity is ~1/ f2 • S-band is more sensitive to electron density than X-band

15. The Neutral Atmosphere Refractivity m(h) in neutral atmosphere (h<50km): C1: atm. constants k : Boltzman constant n: neutral number density Neutral Atmosphere Ionosphere Second term << first term

16. Neutral Atmosphere Neutral Number Density: Pressure (assuming hydrostatic equilibrium): Temperature: ideal gaslaw

17. The Twoway Problem

18. So far assumed: Oneway MEX f : signal transmitted from MEX f : signal received w/o atmosphere Df : classical Doppler shift f : signal received with atmosphere Df : frequency shift from atmosphere send MEX w/o rec dop a with Neutral Atmosphere rec Mars atm Ionosphere w/o MEX f = f + Df with f send rec dop rec w/o f rec with MEX f = f + Df + Df + Df dop iono send rec atm a : bending angle

19. But in Realty: Twoway Radio Link MEX Neutral Atmosphere Mars MEX Earth up f = f + Df rec send Ionosphere Up: X-band: 7.1 GHz Earth f send

20. The Twoway Problem MEX MEX f · k rec Neutralatmosphäre Mars MEX Earth up f = f + Df rec send Ionosphäre f = {f + Df }·k MEX Earth up send send Up: X-band: 7.1 GHz Earth f send

21. The Twoway Problem MEX a Neutral Atmosphere Mars MEX Earth up f = f + Df rec send Ionosphere f = {f + Df }·k MEX Earth up send send Earth Up: X-band: 7.1 GHz Down: X-band: 8.4 GHz S-band: 2.3 GHz f rec Earth f send up down Earth Earth f = k·f + k·Df + Df rec send

22. The Twoway Problem • Bending of Radio link on Uplink & Downlink • Difficult to seperate effects from Uplink & Downlink • Different dependency on Radio frequency in Ionosphere and Neutral atmosphere Neutral Atmosphere: Independent of frequency Ionosphere: m ~ 1/ f2

23. The Twoway Problem • Different frequencies on Uplink and Downlink • Ionospheric Bending is ~ 1/f2 Different bending on Uplink & Downlink • Bending in Neutral Atmosphere independent of frequency • Retrieval of bending angle and rayparameter is exclusively dependent on measurement geometry!!!! No frequency dependeny taken into account! Solution: • Retrieve Ionosphere and Neutral Atmosphere separately

24. Twoway Problem: The Ionosphere Best Solution: • Use Differential Doppler (~ pure Oneway S-band Downlink) • All effects ~ f are subtracted due to the use of to coherent frequencies Other solution: • Make an iterative solution: • solve for „mean Ionosphere“ • Calculate electron density refractivity for Uplink & Downlink • Make Raytracing: calculate bending in this „assumed“ atmosphere • Compare solution of ray tracing with true residual……

25. Twoway Problem: Neutral Atmosphere • Treat Uplink and Downlink explicitely with basic formulas from Oneway • Solve Uplink & Downlink in the way already described Literature: • Lipa, B. and Tyler, G.L., 1979. „Statistical and Computational Uncertainties in Atmospheric Profiles from Radio Occultation: Mariner 10 at Venus“, Icarus 39, 192 – 208. • Jenkins et al., 1994. „Radio Occultation Studies of the Venus Atmosphere with the Magellan Spacecraft“, Icarus 110, 79 – 49.