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Rosetta_CD\PR\what_is_RS.ppt, 04.09.2015 18:39AM, 1 Mars Express Radio Science Experiment MaRS MaRS Radio Science Data: Level 3 & 4 The retrieval S.Tellmann,

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Presentation on theme: "Rosetta_CD\PR\what_is_RS.ppt, 04.09.2015 18:39AM, 1 Mars Express Radio Science Experiment MaRS MaRS Radio Science Data: Level 3 & 4 The retrieval S.Tellmann,"— Presentation transcript:

1 Rosetta_CD\PR\what_is_RS.ppt, 04.09.2015 18:39AM, 1 Mars Express Radio Science Experiment MaRS MaRS Radio Science Data: Level 3 & 4 The retrieval S.Tellmann, M.Pätzold ESAC June 2008

2 Rosetta_CD\PR\what_is_RS_v4.ppt, 04.09.2015 18:39AM, 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 Rosetta_CD\PR\what_is_RS_v4.ppt, 04.09.2015 18:39AM, 3 Level 3 Retrieval of the Refractivity and the Radius

4 Rosetta_CD\PR\what_is_RS_v4.ppt, 04.09.2015 18:39AM, 4 Level 3 Data Processing Flow Chart Input: Level 2 residual

5 Rosetta_CD\PR\what_is_RS_v4.ppt, 04.09.2015 18:39AM, 5 Level 3 Data Processing Flow Chart Input: Level 2 residual Baseline fit correction

6 Rosetta_CD\PR\what_is_RS_v4.ppt, 04.09.2015 18:39AM, 6 Starting Point: Residual Starting point: Level 2 residual Offset Offset (and/or trend): Reason Uncertainties in Orbit

7 Rosetta_CD\PR\what_is_RS_v4.ppt, 04.09.2015 18:39AM, 7 Baseline Fit Correction Starting point: Level 2 residual Offset range for baseline fit radius: ~ 4000 km

8 Rosetta_CD\PR\what_is_RS_v4.ppt, 04.09.2015 18:39AM, 8 Residual after Correction

9 Rosetta_CD\PR\what_is_RS_v4.ppt, 04.09.2015 18:39AM, 9 Level 3 Data Processing Flow Chart Input: Level 2 residual Baseline fit correction Calculation of Measurement Geometry Occultation Plane

10 Rosetta_CD\PR\what_is_RS_v4.ppt, 04.09.2015 18:39AM, 10 Next Goal: Calculation of Bending angle & Rayparameter  : bending angle a: rayparameter

11 Rosetta_CD\PR\what_is_RS_v4.ppt, 04.09.2015 18:39AM, 11 Next Goal: Calculation of Bending angle & Rayparameter  : bending angle a: 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

12 Rosetta_CD\PR\what_is_RS_v4.ppt, 04.09.2015 18:39AM, 12 Occultation (OCC) plane Radio Link MEX orbit OCC plane at time t m Earth direction Calculation of state vectors for every measurement sample P MEX,V MEX P G/S,V G/S

13 Rosetta_CD\PR\what_is_RS_v4.ppt, 04.09.2015 18:39AM, 13 Level 3 Data Processing Flow Chart Input: Level 2 residual Baseline fit correction Calculation of Bending Angle & Rayparameter Calculation of Measurement Geometry Occultation Plane

14 Rosetta_CD\PR\what_is_RS_v4.ppt, 04.09.2015 18:39AM, 14 Next Goal: Calculation of Bending angle & Rayparameter  : bending angle a: rayparameter Solve equations from [Fjeldbo et al., 1971]: B · ( ) = ( ) where b 11 = -v rs sin(  e –  r ) + v zs cos(  e –  r ) b 12 = -v rt cos(  s –  r ) + v zt sin(  s –  r ) b 21 = (r s + z s ) 1/2 sin(b e –  –  r ) b 22 = z t cos(  s –  r ) k 1 = c  f/f s + v rs [cos(  e –  r ) – cos  e ] + v zs [sin(  e –  r ) – sin  e ] - v rt [sin(  s –  r ) – sin  s ] – v zt [cos(  s –  r ) – cos  s ] k 2 = z t sin(  s –  r ) + (r s 2 -z s 2 ) 1/2 sin(  e –  –  r )  r  r k1k1 k2k2

15 Rosetta_CD\PR\what_is_RS_v4.ppt, 04.09.2015 18:39AM, 15 bending angle  =  r +  r rayparameter a = (r s 2 + z s 2 ) 1/2 sin(  e –  r –  ) Calculation of Bending angle & Rayparameter

16 Rosetta_CD\PR\what_is_RS_v4.ppt, 04.09.2015 18:39AM, 16 Level 3 Data Processing Flow Chart Input: Level 2 residual Baseline fit correction Calculation of Bending Angle & Rayparameter Abel Transformation Calculation of Refractivity & Radius Calculation of Measurement Geometry Occultation Plane

17 Rosetta_CD\PR\what_is_RS_v4.ppt, 04.09.2015 18:39AM, 17 Calculation of Refractivity & Radius Refractive index n n Refractivity  Radius r

18 Rosetta_CD\PR\what_is_RS_v4.ppt, 04.09.2015 18:39AM, 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 Rosetta_CD\PR\what_is_RS_v4.ppt, 04.09.2015 18:39AM, 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 Summing up of the array Zintegral INTEGRAL: Integration routine able to handle the pole

20 Rosetta_CD\PR\what_is_RS_v4.ppt, 04.09.2015 18:39AM, 20 Calculation of Refractivity radius [km]   Bending Angle Refractivity Abeltransform Bending angle [deg * 10 6 ] Refraktivität [deg * 10 6 ]

21 Rosetta_CD\PR\what_is_RS_v4.ppt, 04.09.2015 18:39AM, 21 The Occultation Footpoints x Occultation footpoint Moving over the surface of Mars Spacecraft Earth direction

22 Rosetta_CD\PR\what_is_RS_v4.ppt, 04.09.2015 18:39AM, 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 Rosetta_CD\PR\what_is_RS_v4.ppt, 04.09.2015 18:39AM, 23 Level 3 Data Processing Flow Chart Input: Level 2 residual Baseline fit correction Calculation of Bending Angle & Rayparameter Abel Transformation Calculation of Refractivity & Radius Calculation of Measurement Geometry Occultation Plane Main Output: Refractivity, Radius & OCC Footpoints Calculation of Occultation Footpoints

24 Rosetta_CD\PR\what_is_RS_v4.ppt, 04.09.2015 18:39AM, 24 Level 4 The Neutral Atmosphere

25 Rosetta_CD\PR\what_is_RS_v4.ppt, 04.09.2015 18:39AM, 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 Neutral Atmosphere Ionosphere Ionopause Transition Region

26 Rosetta_CD\PR\what_is_RS_v4.ppt, 04.09.2015 18:39AM, 26 The Neutral Number Density  : refractivity C 1 : atmospheric constant k : Boltzman constant n : neutral number density C 1 is based on the atmospheric composition (CO 2, N 2, Ar) C 1 = 1.3063 10 -6 K·m·s 2 /kg known from laboratory measurements [Hinson et al., 1999].

27 Rosetta_CD\PR\what_is_RS_v4.ppt, 04.09.2015 18:39AM, 27 Ideal gas law relates Pressure, Temperature and Density Hydrostatic equilibrium in well-mixed atmosphere: temperature can be derived directly from neutral number density Calculation of Pressure and Temperature

28 Rosetta_CD\PR\what_is_RS_v4.ppt, 04.09.2015 18:39AM, 28 Ideal gas law relates Pressure, Temperature and Density Hydrostatic equilibrium in well-mixed atmosphere: temperature can be derived directly from neutral number density Calculation of Pressure and Temperature upper boundary condition

29 Rosetta_CD\PR\what_is_RS_v4.ppt, 04.09.2015 18:39AM, 29 Upper boundary condition of temperature T up = 150 K T up = 160 K T up = 170 K

30 Rosetta_CD\PR\what_is_RS_v4.ppt, 04.09.2015 18:39AM, 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 Rosetta_CD\PR\what_is_RS_v4.ppt, 04.09.2015 18:39AM, 31 Level 4 The Ionosphere

32 Rosetta_CD\PR\what_is_RS_v4.ppt, 04.09.2015 18:39AM, 32 The Electron Density f 0 : Radio link frequency N e : electron density C 3 = 40.31

33 Rosetta_CD\PR\what_is_RS_v4.ppt, 04.09.2015 18:39AM, 33 The Electron Density

34 Rosetta_CD\PR\what_is_RS_v4.ppt, 04.09.2015 18:39AM, 34 2007 Autumn 2005 Autumn 2005 Spring Temperature Profiles Northern Hemisphere 35.0°N

35 Rosetta_CD\PR\what_is_RS_v4.ppt, 04.09.2015 18:39AM, 35 2007 Autumn 2005 Autumn 2005 Spring Temperature Profiles Northern Hemisphere Typical daytime profile middle latitude 35.0°N

36 Rosetta_CD\PR\what_is_RS_v4.ppt, 04.09.2015 18:39AM, 36 2007 Autumn 2005 Autumn 2005 Spring Temperature Profiles Northern Hemisphere morning profile inversion in boundary layer 35.0°N

37 Rosetta_CD\PR\what_is_RS_v4.ppt, 04.09.2015 18:39AM, 37 2007 Autumn 2005 Autumn 2005 Spring Temperature Profiles Northern Hemisphere Stationary wave structures 35.0°N

38 Rosetta_CD\PR\what_is_RS_v4.ppt, 04.09.2015 18:39AM, 38 Comparison with Model: middle latitudes MaRS GCM low dust GCM med. dust GCM high dust

39 Rosetta_CD\PR\what_is_RS_v4.ppt, 04.09.2015 18:39AM, 39 Comparison with Model: 60° N MaRS GCM low dust GCM med. dust GCM high dust

40 Rosetta_CD\PR\what_is_RS_v4.ppt, 04.09.2015 18:39AM, 40 Comparison with Model: 63° N MaRS GCM low dust GCM med. dust GCM high dust

41 Rosetta_CD\PR\what_is_RS_v4.ppt, 04.09.2015 18:39AM, 41 Comparison with Model: Winter Night MaRS GCM (LMD) Temperature [K] altitude [km] planetary latitude [deg]

42 Rosetta_CD\PR\what_is_RS_v4.ppt, 04.09.2015 18:39AM, 42 Autumn profiles L s = 250° – 265° L s = 227° – 235° 2005 2007

43 Rosetta_CD\PR\what_is_RS_v4.ppt, 04.09.2015 18:39AM, 43 Autumn & Winter profiles L s = 250° – 265° L s = 227° – 235° L s = 345° – 15°

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