Upload
hector-johns
View
217
Download
0
Embed Size (px)
Citation preview
Ros
etta
_CD
\PR
\wha
t_is
_RS
.ppt
, 21
.04.
23 1
3:56
AM
, 1
Mars Express Radio Science Experiment MaRS
MaRS Radio Science Data:Level 3 & 4
Basics
S.Tellmann, M.Pätzold
ESACJune 2008
Ros
etta
_CD
\PR
\wha
t_is
_RS
_v4.
ppt,
04/
21/2
3 13
:56A
M,
2
OverviewLEVEL 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
Ros
etta
_CD
\PR
\wha
t_is
_RS
_v4.
ppt,
04/
21/2
3 13
:56A
M,
3
Earth Occultations
Ionosphere
Mars
Neutral Atmosphere
frecw/o
f = f + frecw/o
sendMEX
dop
MEXf : signal transmitted from MEX
f : signal received w/o atmosphere
f : classical Doppler shift
MEXsendw/orec
dop
Ros
etta
_CD
\PR
\wha
t_is
_RS
_v4.
ppt,
04/
21/2
3 13
:56A
M,
4
Earth Occultations
Ionosphere
Mars
Neutral Atmosphere
frecw/o
f = f + frecw/o
sendMEX
dop
MEXf : signal transmitted from MEX
f : signal received w/o atmosphere
f : classical Doppler shift
f : signal received with atmosphere
f : frequency shift from atmosphere
MEXsendw/orec
dop
recwith
f = f + f + f + frecwith MEX
send dop iono
atm
recwithf
atm
bending angle
Ray Asymptote
Ros
etta
_CD
\PR
\wha
t_is
_RS
_v4.
ppt,
04/
21/2
3 13
:56A
M,
5
Bending Angle & Rayparameter
Retrieval based on geometrical optics [Fjeldbo et al., 1971]
: bending anglea : rayparameter
Ros
etta
_CD
\PR
\wha
t_is
_RS
_v4.
ppt,
04/
21/2
3 13
:56A
M,
6
Bending Angle & Rayparameter
[Fjeldbo et al., 1971]
Basic Idea:
f fwithrec fwo
rec
Input:
• Position of Spacecraft, Groundstation & Mars• Velocity of Spacecraft, Groundstation & Mars
Ros
etta
_CD
\PR
\wha
t_is
_RS
_v4.
ppt,
04/
21/2
3 13
:56A
M,
7
Doppler Effect
ftransmit
frec
1 ntransmit
1 nrec
vc
For vEarth << vS/C:
fSCtransmit fEarth
rec 1 nSC nEarth
Ros
etta
_CD
\PR
\wha
t_is
_RS
_v4.
ppt,
04/
21/2
3 13
:56A
M,
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
The twodimensional function is given by:
[Pretzler et al., 1992]
[Jenkins, 1992]
Abel transform:
Inverse Abel transform:
Ros
etta
_CD
\PR
\wha
t_is
_RS
_v4.
ppt,
04/
21/2
3 13
:56A
M,
9
The Refractivity
• Inverse Abeltransform:
• Integration of bending angle and rayparameter over all layers already traversed
Refractive Index:
n1
n2n3
n4
Ros
etta
_CD
\PR
\wha
t_is
_RS
_v4.
ppt,
04/
21/2
3 13
:56A
M,
10
The Radius (ray peripasis)
r an
r : radiusa : rayparametern : refractive index
Ros
etta
_CD
\PR
\wha
t_is
_RS
_v4.
ppt,
04/
21/2
3 13
:56A
M,
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 radiusNeutral Atmosphere
Ionosphere
Ionopause
Transition Region
Refractivity
Ros
etta
_CD
\PR
\wha
t_is
_RS
_v4.
ppt,
04/
21/2
3 13
:56A
M,
12
Retrieval of atmospheric parameter
2
031 f
hNCkhnCh e
f0 : Radio link frequency
Ne : electron density
C1, C3 : atm. constants
k : Boltzman constant
n: neutral number densityNeutral Atmosphere Ionosphere
Refractivity (h):
Ros
etta
_CD
\PR
\wha
t_is
_RS
_v4.
ppt,
04/
21/2
3 13
:56A
M,
13
The Ionosphere
2
031 f
hNCkhnCh e
f0 : Radio link frequency
Ne : electron density
C3 : atm. constant
Neutral Atmosphere Ionosphere
Refractivity (h) in Ionosphere (h>60km):
Ros
etta
_CD
\PR
\wha
t_is
_RS
_v4.
ppt,
04/
21/2
3 13
:56A
M,
14
The Electron Density
h C3
Ne
f20
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
Ros
etta
_CD
\PR
\wha
t_is
_RS
_v4.
ppt,
04/
21/2
3 13
:56A
M,
15
The Neutral Atmosphere
2
031 f
hNCkhnCh e
Neutral Atmosphere Ionosphere
Refractivity (h) in neutral atmosphere (h<50km):
Second term << first term
C1: atm. constants
k : Boltzman constant
n: neutral number density
Ros
etta
_CD
\PR
\wha
t_is
_RS
_v4.
ppt,
04/
21/2
3 13
:56A
M,
16
Neutral Number Density:
Pressure (assuming hydrostatic equilibrium):
Temperature: ideal gaslaw
Neutral Atmosphere
gmnr
p
nk
pT
h C1n h
k
Ros
etta
_CD
\PR
\wha
t_is
_RS
_v4.
ppt,
04/
21/2
3 13
:56A
M,
17
The Twoway Problem
Ros
etta
_CD
\PR
\wha
t_is
_RS
_v4.
ppt,
04/
21/2
3 13
:56A
M,
18
Ionosphere
Mars
Neutral Atmosphere
frecw/o
f = f + frecw/o
sendMEX
dop
MEXf : signal transmitted from MEX
f : signal received w/o atmosphere
f : classical Doppler shift
f : signal received with atmosphere
f : frequency shift from atmosphere
MEXsendw/orec
dop
recwith
f = f + f + f + frecwith MEX
send dop iono
atm
recwithf
atm
bending angle
So far assumed: Oneway
Ros
etta
_CD
\PR
\wha
t_is
_RS
_v4.
ppt,
04/
21/2
3 13
:56A
M,
19
But in Realty: Twoway Radio Link
Ionosphere
Mars
Neutral Atmosphere
f
f = f + frec sendEarth
MEX
MEX up
Earth
send
Up: X-band: 7.1 GHz
Ros
etta
_CD
\PR
\wha
t_is
_RS
_v4.
ppt,
04/
21/2
3 13
:56A
M,
20
Ionosphäre
Mars
Neutralatmosphäre
f
f = f + frec sendEarth
MEX
MEX up
f = {f + f }·k MEX
send
Earth
Earth
send
send
up
f · kMEX
rec
The Twoway Problem
Up: X-band: 7.1 GHz
Ros
etta
_CD
\PR
\wha
t_is
_RS
_v4.
ppt,
04/
21/2
3 13
:56A
M,
21
Ionosphere
Mars
Neutral Atmosphere
f
f = f + frec sendEarth
MEX
f = k· f + k·f + fEarthrec
Earthsend
up down
fEarthrec
MEX up
f = {f + f }·k MEX
send
Earth
Earth
send
send
up
The Twoway Problem
Up: X-band: 7.1 GHzDown:X-band: 8.4 GHzS-band: 2.3 GHz
Ros
etta
_CD
\PR
\wha
t_is
_RS
_v4.
ppt,
04/
21/2
3 13
:56A
M,
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
2
031 f
hNCkhnCh e
Neutral Atmosphere:Independent of frequency Ionosphere: ~ 1/ f2
Ros
etta
_CD
\PR
\wha
t_is
_RS
_v4.
ppt,
04/
21/2
3 13
:56A
M,
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
Ros
etta
_CD
\PR
\wha
t_is
_RS
_v4.
ppt,
04/
21/2
3 13
:56A
M,
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……
Ros
etta
_CD
\PR
\wha
t_is
_RS
_v4.
ppt,
04/
21/2
3 13
:56A
M,
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.
fSCsend fSC
rec k