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PhD Defence, September 10, 1999
Retrieval Analysis and Methodologies in Atmospheric Limb Sounding Using the GNSS Radio Occultation Technique
PhD Defence
by
Stig Syndergaard
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PhD Defence, September 10, 1999
Content of presentation
• The GNSS radio occultation principle
• Data processing and exemplar results
-----------------------------------------------
• Violation of spherical symmetry assumption
• Severe weather gradients• Earth’s oblateness
• Ionosphere calibration of data
• Conclusion and prospects
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PhD Defence, September 10, 1999
The GPS constellation
• 24 satellites
• Six 12 hour orbits
• Altitude: 20200 km
• Inclination: 55º
• Transmit dual frequency signals
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PhD Defence, September 10, 1999
LEO
GNSS
Earth
Io n o sp h e re
L E O = L ow E arth O rb ite r
N e u tra lA tm o sp h ere
G N S S = G lob al N av iga tio n S a te llite S y stem
= B en d in g an g le
S i g n a l f r e q u e n c i e s : f 1 = 1 . 5 7 5 4 2 G H z & f 2 = 1 . 2 2 7 6 0 G H z
R e f r a c t i v e i n d e x o f m e d i u m : 22211f
NC
T
ek
T
pk e
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PhD Defence, September 10, 1999
D o pp ler d ep end s o n
If the ray is bend , D opp le r is d iffe ren tthan exp ec ted from veloc ities on ly
v
v
G P S
G P S
L E O
L E O
The measurement is a phase (meters): LEO
GPS
dsL
Doppler dt
dL
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PhD Defence, September 10, 1999
a
a
r0
Tan g en t p o in t
S p h e r i c a l S y m m e t r y A s s u m p t i o n :
0
222
/ln2)(
r
drar
drdaa
A b e l T r a n s f o r m
a
adaa
ar
220
)(1exp)(
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PhD Defence, September 10, 1999
Standard deviation on retrieved refractivity
A b so lu te e rro r (N -u n its) R e la tiv e e rro r
Alt
itud
e (k
m)
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PhD Defence, September 10, 1999
Content of presentation
• The GNSS radio occultation principle
• Data processing and exemplar results
-----------------------------------------------
• Violation of spherical symmetry assumption
• Severe weather gradients• Earth’s oblateness
• Ionosphere calibration of data
• Conclusion and prospects
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PhD Defence, September 10, 1999
Data Processing Chain
Numerical differentiation
Geometry
Inversion using Abel Transform
Refractivity Equation
Hydrostatic Equilibrium
Equation of State
Phase
Doppler
Bending Angle
Refractive Index
Density
Pressure
Temperature
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PhD Defence, September 10, 1999
Tem p era tu re ( C )O
Alt
itud
e (k
m)
G P S _ 066 5_4 6 4 7 .4 N , 12 .0 E 23 :0 5 U TO O
R ad ioso nde 4 8 .3 N , 11 .6 E 2 3 :00 U TO O
N C E P 4 8 .1 N , 10 .8 E 24 :00 U TO O
E C M W F 48 .1 N , 1 0 .8 E 2 4 :00 U TO O
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PhD Defence, September 10, 1999
Tem p era tu re ( C )O
Alt
itud
e (k
m)
G P S _ 053 7_4 0 66 .1 N , 22 .6 E 19 :0 8 U TO O
R adioso nde 6 5 .6 N , 22 .1 E 18 :00 U TO O
N C E P 6 6 .6 N , 21 .2 E 18 :0 0 U TO O
E C M W F 66 .6 N , 2 1 .2 E 18 :00 U TO O
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PhD Defence, September 10, 1999
Accuracy 1-2 Kelvin between ~ 8 and ~ 40 km Above ~ 40 km: accuracy is limited by thermal noise and ionosphere residual Below ~ 8 km: water vapor may become dominant
Vertical Resolution First Fresnel Diameter: 0.5-1.5 km Improved if using diffraction theory
Horizontal Resolution Integrated effect over the entire ray path Most of the bending occurs over ~ 700 km Fresnel Diameter corresponds to ~ 100 km Tangent point moves ~ 100 km
Inversion is based on the assumption of local spherical symmetry
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PhD Defence, September 10, 1999
Content of presentation
• The GNSS radio occultation principle
• Data processing and exemplar results
-----------------------------------------------
• Violation of spherical symmetry assumption
• Severe weather gradients• Earth’s oblateness
• Ionosphere calibration of data
• Conclusion and prospects
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PhD Defence, September 10, 1999
Model temperature field of a severe front
2 01 0
0 CO
-1 0-2 0
-3 0-4 0
-5 0
-6 0
-6 0-7 0
-5 0
L atitud e (de g )
Alt
itud
e (k
m)
4 45 0 km
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PhD Defence, September 10, 1999
C ase 3
C ase 2
C ase 1
R ay p ro p a g a tio nd ire c tio n
L o n g itu d e (d eg )
Lat
itud
e (d
eg)
Tan g en tp o in ts
-65 -60 -55 -50 -45 -40 -35 -30-70
5
5
5
10
10
10
15
15
15
20
20
20
25
25
25
L atitu d e (d e g )
Altitude (km
)
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PhD Defence, September 10, 1999
Temperature profiles in the frontal zone
R etriev ed p ro file (c ase 2 )“T rue” p ro file a t tan ge n t po in t
W arm a nd c o ld p ro files
Tem p era tu re ( C )O
Alt
itud
e (k
m)
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PhD Defence, September 10, 1999
Retrieval errors in the frontal zone
C ase 3
C ase 2
C ase 1
Tem p era tu re e rro r ( C )O
Alt
itud
e (k
m)
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PhD Defence, September 10, 1999
Content of presentation
• The GNSS radio occultation principle
• Data processing and exemplar results
-----------------------------------------------
• Violation of spherical symmetry assumption
• Severe weather gradients• Earth’s oblateness
• Ionosphere calibration of data
• Conclusion and prospects
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PhD Defence, September 10, 1999
Correcting for the Earth’s oblateness
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PhD Defence, September 10, 1999
Before correction After correction
Earth’s oblateness
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PhD Defence, September 10, 1999
Content of presentation
• The GNSS radio occultation principle
• Data processing and exemplar results
-----------------------------------------------
• Violation of spherical symmetry assumption
• Severe weather gradients• Earth’s oblateness
• Ionosphere calibration of data
• Conclusion and prospects
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PhD Defence, September 10, 1999
T w o t r a d i t i o n a l i o n o s p h e r e c o r r e c t i o n m e t h o d s
1 ) P h a s e c o r r e c t i o n :
L N CN
fK
B N
fd s
L N CN
fK
B N
fd s
ne e
G P S
L E O
ne e
G P S
L E O
11
21
3
22
22
3
1
1
( )
( )
T h e t r a d i t i o n a l i o n o s p h e r e c o r r e c t e d p h a s e L C i s f o r m e d a t t h e s a m e t i m e s( s a m p l e s ) :
L tf L t f L t
f fN d s L tC n
G P S
L E O
F( )( ) ( )
( ) ( )
12
1 22
2
12
22 1
A s s u m p t i o n s : S a m e i n t e g r a t i o n p a t h s N e g l e c t i n g s e c o n d a n d h i g h e r o r d e r i o n o s p h e r e t e r m s
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PhD Defence, September 10, 1999
T w o t r a d i t i o n a l i o n o s p h e r e c o r r e c t i o n m e t h o d s
2 ) B e n d i n g a n g l e c o r r e c t i o n :
T h e i o n o s p h e r e c o r r e c t e d b e n d i n g a n g l e i s f o r m e d a t t h e s a m e i m p a c tp a r a m e t e r s [ V o r o b ’ e v a n d K r a s i l ’ n i k o v a ( 1 9 9 3 ) ] :
( )( ) ( )
af a f a
f f
12
1 22
2
12
22
A s s u m p t i o n s : S p h e r i c a l s y m m e t r y i n t h e i o n o s p h e r e a n d n e u t r a l a t m o s p h e r e N e g l e c t i n g s e c o n d a n d h i g h e r o r d e r i o n o s p h e r e t e r m s B e n d i n g a n g l e i s a l i n e a r f u n c t i o n a l o f r e f r a c t i v i t y
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PhD Defence, September 10, 1999
Model calculation of retrievals of the temperature in the case of a typical day-time, solar maximum ionosphere
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PhD Defence, September 10, 1999
Ionosphere calibration
The present calibration scheme (bending angle correction) is sufficientat night-time conditions or at solar minimum
At day-time, solar maximum, the ionosphere residual is the limitingerror source in the reconstruction of atmospheric parameters in thestratosphere [Kursinski et al. (1997)]
Sounding of the whole ionosphere (60-1000 km) could enable us toreconstruct the electron density structure, which would be valuable intrying to remove the residual [Gorbunov et al. (1996)]
Sounding of the neutral atmosphere (0-100 km) gives additionalinformation on the Total Electron Content (TEC) between theocculting satellites, which can be used in the calibration scheme[present study]
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PhD Defence, September 10, 1999
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PhD Defence, September 10, 1999
R e s i d u a l p h a s e p a t h e r r o r a f t e r t h e t r a d i t i o n a l p h a s e p a t h c o r r e c t i o n m e t h o d
L L
f f C
f fC FF F F F
12
1 22
2 1 2
12
22
( ) ( ) ( ) ( )
( D i s p e r s i o n r e s i d u a l t e r m )
K B f B f
f f
1 11
1 2 21
2
12
22
( S e c o n d o r d e r ‘ m a g n e t i c ’ t e r m )
1
1
1 ( )N d sn 2
2
1 ( )N d sn F n
F
N d s ( )1
1
1
N d se 2
2
N d se F e
F
N d s
T h e s e c o n d o r d e r t e r m c a n b e e s t i m a t e d u s i n g t h e T E C m e a s u r e m e n t sa n d a m a g n e t i c f i e l d m o d e l
H i g h e r o r d e r i o n o s p h e r e t e r m s a r e n e g l i g i b l e [ H a r d y e t a l . ( 1 9 9 3 ) ]
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PhD Defence, September 10, 1999
A n a l y t i c e x p r e s s i o n f o r t h e d i s p e r s i o n r e s i d u a l
S e r i e s e x p a n s i o n a n d u s i n g t h e a s s u m p t i o n o f s p h e r i c a l s y m m e t r ya l l o w s u s t o d e r i v e t h e r a y p a t h d i s p e r s i o n r e s i d u a l ( t o s e c o n d o r d e r ) :
2
22
12
22
1
2
21 11
ffff
CL
w h e r e
2
222
22
))
))
(()(
((
da
d
da
dD
da
dsNda
da
dD
TECTEC
TEC e
a i s t h e i m p a c t p a r a m e t e r f o r t h e i o n o s p h e r e ‘ f r e e ’ p a t hD i s t h e G P S - L E O r e d u c e d d i s t a n c e i s a d e f o c u s i n g f a c t o r d u e t o t h e n e u t r a l a t m o s p h e r e
F
e dsNTEC i s t h e T o t a l E l e c t r o n C o n t e n t a l o n g t h e ‘ f r e e ’ p a t h
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PhD Defence, September 10, 1999
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PhD Defence, September 10, 1999
Improved dual-frequency phase correction
The residual phase path error can be estimated from the TEC ,
dsN e2
, D , , a, and a magnetic field model
TEC , D , , and a can be estimated from the occultation data itself
dsN e2
is near proportional to TEC for tangent points below 50 km
The main difference between the bending angle correction and thisimproved phase correction lies in the ‘minor’ dispersion term
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PhD Defence, September 10, 1999
GPS/MET occultation no. 259, day 35, 1997
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PhD Defence, September 10, 1999
A t r i p l e x f r e q u e n c y c o m b i n a t i o n
W i t h a t h i r d f r e q u e n c y i t w o u l d b e p o s s i b l e t o e l i m i n a t e t h e t e r ma n d o b t a i n t h e f o l l o w i n g c o m b i n a t i o n ( n e g l e c t i n g t h e s e c o n d o r d e r‘ m a g n e t i c ’ t e r m )
23
22
21
3
21
22
21
43
21
23
42
23
22
41
32
22
14
322
12
34
212
32
24
13
)()()(
)()()(
fff
C
fffffffff
LfffLfffLfffL C
C a n b e g e n e r a l i z e d t o t a k e i n t o a c c o u n t t h e m a g n e t i c t e r m ( u s i n g am a g n e t i c f i e l d m o d e l )
W o r k s s u r p r i s i n g l y g o o d f o r a s y m m e t r i c a l c o n d i t i o n s a s w e l l
D r a w b a c k : A m p l i f i e s t h e r a n d o m n o i s e a p p r e c i a b l y i f t h e t h i r df r e q u e n c y i s t o o c l o s e t o L 1 o r L 2
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PhD Defence, September 10, 1999
Content of presentation
• The GNSS radio occultation principle
• Data processing and exemplar results
-----------------------------------------------
• Violation of spherical symmetry assumption
• Severe weather gradients• Earth’s oblateness
• Ionosphere calibration of data
• Conclusion and prospects
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PhD Defence, September 10, 1999
Summery & Conclusions (1)
GPS-Occultation data can be inverted to give highly accurate temperatureprofiles in the upper troposphere and the lower stratosphere
In the lower troposphere temperature can be obtained under dry conditions
In the upper stratosphere and above the accuracy is limited by thermal errorsand residual ionosphere effects
In regions of severe horizontal gradients like in a frontal system, the methodstill works well with maximum errors of a few C
Correction for the Earth’s oblateness is necessary
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PhD Defence, September 10, 1999
Summery & Conclusions (2)
Ionosphere phase path correction can be improved using the occultation TECinformation
The main difference between the ionosphere correction of bending angles andthe improved phase path correction method has been expressed mathematically
Both the bending angle correction and the improved phase path correctionassumes spherical symmetry in the ionosphere
A third frequency would enable a triplex frequency combination being almostinsensitive to ionospheric asymmetry conditions
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PhD Defence, September 10, 1999
Prospects
In the near future, GNSS receivers will be flown on a multitude of researchand Earth observation satellites
Bending angles or refractivity will in the future be assimilated into numericalweather prediction models
A large amount of data over years will also be valuable for monitoring ofclimate change
The technique can also be applied to obtain the electron density in theionosphere, and data may be used in combination with ground basedmeasurements to obtain better tomographic representations of the ionosphere
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PhD Defence, September 10, 1999
14 days of GPS/MET occultations