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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


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


The GPS constellation

• 24 satellites

• Six 12 hour orbits

• Altitude: 20200 km

• Inclination: 55º

• Transmit dual frequency signals


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


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


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)(


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)





-----------------------------------------------






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


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



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


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





-----------------------------------------------






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


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

)


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


Alt

itud

e (k

m)


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)





-----------------------------------------------






Correcting for the Earth’s oblateness


Before correction After correction

Earth’s oblateness





-----------------------------------------------






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


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


Model calculation of retrievals of the temperature in the case of a typical day-time, solar maximum ionosphere


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]


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 ) ]


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


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


GPS/MET occultation no. 259, day 35, 1997


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





-----------------------------------------------






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


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


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


14 days of GPS/MET occultations

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