Salinity retrieval with scale model antenna pattern

Salinity retrieval with scale model antenna

pattern

S. Kim/F. WentzAquarius Workshop (GSFC)

2008.03

Tb2 retrieval accuracy: scale model (ascending)

Simple Faraday correction & before additional correction

TB2/2 in Kelvin

2001 Solar flux

2003 day 303 (IRI 2001 TEC)

error reaches +/- 3-4K

After

Faraday angle

Tb2 retrieval scale-model (descending)

Before additional correctionerror reaches -2K

After

Faraday angle

Scale model Tb1 retrieval accuracy (ascending)

Before additional Faraday correction

After

Scale model Tb1: descending

Before additional correction

After

Tb2 (with scale model) & Faraday rotation

Tb2 is strongly related to Faraday rotation(theoretical model Tb2 is offset by 1.5K; simple correction: T2 = (T22+T32))

Ascending horn 1 descending

K

latitude latitude

Faraday angleFaraday off

Simple correction

Faraday OnSimple correction

Theoretical model

Faraday offSimple correction


Scale model

Scale model antenna Stokes matrix (modified)

*2 2 *

2 2 * *

* * * * *

* * * * *

*

Im

Re Im

2Re Re Re Im Im

2Im 2Im Im Im Re R

Re

2Re

e

vv vh vv vh

a

hv hh hv hh hv hha

a vv hv vv hh vh hv vv hh vh hv

a

vv hv vh hh vv hh vh hv vv hh v

vv vh

vh

h

hh

g g g gV

g g g g g gH

U g g g g g g g g g gW

g g g g g g g g

g g

g g

g g g

*

R

R

R

R

hv

V

H

U

Wg

scale model antenna’s off-diagonal term is 10-40 times larger than theoretical’s

theoretical antennaIHORN = 1

0.9777995 0.0222005 0.0018323 0.0000360

0.0236619 0.9763381 -0.0016604 -0.0001937

-0.0012777 0.0011429 0.9584791 0.0017800

-0.0003209 -0.0001290 0.0001374 0.9443555

IHORN = 2

0.9698600 0.0301399 -0.0027432 -0.0008946

0.0281496 0.9718504 0.0045488 -0.0004253

-0.0016207 0.0014077 0.9382428 0.0007672

0.0001413 -0.0006906 -0.0013847 0.9365401

IHORN = 3

0.9659594 0.0340406 0.0014531 0.0007880

0.0334903 0.9665097 -0.0021459 -0.0001634

-0.0014786 0.0013045 0.9091309 -0.0004642

0.0000453 0.0003553 -0.0006897 0.9228344

scale model antennaHORN= 1(n1)

0.9853075 0.0168026 -0.0195433 -0.0085144

0.0154680 0.9870461 0.0065521 0.0043823

-0.0018744 -0.0224793 0.9034507 -0.2914306

0.0063599 -0.0261359 0.2846981 0.9142451

HORN= 2(p0)

0.9793472 0.0251813 -0.0082843 -0.0003378

0.0222499 0.9820560 -0.0088156 -0.0069168

0.0027088 -0.0392866 0.9340240 0.0511001

-0.0127451 0.0026349 -0.0496169 0.9496149

HORN= 3(p1)

0.9736289 0.0336871 -0.0206253 -0.0046420

0.0273845 0.9800099 0.0076234 0.0009958

0.0049451 -0.0272600 0.8377592 -0.3615281

0.0066785 -0.0258146 0.3477410 0.8623706

Scale model antenna Stokes matrix (classical)

2 2 2 2 * *12

2 2 2 2 * *12

2 2 2 212

12 2 2 21

22

*3

4

* *

*

*

*

Re

Re

Re

I

Im

e

m

R

vv vh hv hh vv vh hh hvvv vh h

vv vh

v

vv vh hv hh vv vh hh

v vh hh hv

hh v

v hh

A

vv vh hv hhA

Avv hv

hh

v

h

h

v h

A

v

g g g g g g g g g

g g g g

g g gT

g g g g

g

g g

g g g

g g

g g gT

T g

g g

g gT

g

* *

* * * *

1

2

*

*

* * *

* * 3

4

* Im

Im Im Im

Re

Re

aa bb ab ba

vv hv

BR

B

hh vh vv hv hh vh vv hh vh hv

R

BRv hv vv hh vh

aa bb ab ba

hv

BR

hh vh g g g g

g g g g g g g g g

T

g g g g g

T

Tg g g gT

g g

g

g

g

theoretical antennaIHORN = 1 1.0000000 0.0000000 0.0001719 0.0002297 0.0000000 0.9541376 0.0034927 0.0002297 -0.0000674 -0.0012103 0.9584791

0.0002297 -0.0000960 -0.0002249 0.0001374

0.9443555

IHORN = 2 0.9999999 -0.0000000 0.0018056 -0.0004693 -0.0000000 0.9417105 -0.0072920 -

0.0004693 -0.0001065 -0.0015142 0.9382428 -

0.0004693 0.0004160 -0.0002746 -0.0013847

0.9365401 IHORN = 3 1.0000000 0.0000000 -0.0006928 0.0009514 0.0000000 0.9324691 0.0035990 0.0009514 -0.0000870 -0.0013916 0.9091309

0.0009514 -0.0001550 0.0002003 -0.0006897

0.9228344

scale model antennaHORN= 1(n1)

1.0023122 -0.0002020 -0.0129912 -0.0128967 -0.0002020 0.9700415 -0.0260954 -

0.0128967 -0.0121768 0.0103024 0.9034507 -

0.0128967 0.0162479 -0.0098880 0.2846981 0.9142451 HORN= 2(p0)

1.0044172 0.0001113 -0.0170999 0.0065790 0.0001113 0.9569861 0.0005313 0.0065790 -0.0182889 0.0209977 0.9340240 0.0065790 -0.0076900 -0.0050551 0.0496169

0.9496149 HORN= 3(p1)

1.0073552 -0.0000392 -0.0130019 -0.0056378 -0.0000392 0.9462836 -0.0282487 -

0.0056378 -0.0111575 0.0161026 0.8377592 -

0.0056378 0.0162465 -0.0095681 0.3477410 0.8623706

Errors in Faraday correction

2 21 1 2 2 3 2 & A B A toa A A BT T T T T T

For uniform gain, no coupling, simple Faraday correction gives:

The simple correction would produce

TBtoa

TBR

TA

ionosphere

atmosphere

TAtoa

T’B

* *2,2 vv vh hh hv

1, 1, 21,

Re(g g + )1 sin(2 )B toa

A toa B toa fB toa

Tg gT G T

G T

24 2 2 * * * *

2, 2, vv hv vh hh 1, 2, vv hv vh hh 1,

2* * * *

1, 1,2 vv hv vh hh v h h v2, 2 2

2, 2,

2 Re(g g + ) sin(2 ) Re(g g + )

Re(g g + ) Re(G g + )1 2 sin(2 )

A toa B toa B toa B toa f B toa

B toa B toaB toa f

B toa B toa

T G T G g g T T g g T

T Tg g G gG T

G T G T

With coupling ( based on Le Vine et al 07)

* *

* *vv vh hh hv 2,

* *vv h

21, 1,

2 22, 2,

2 2

vv hv vh hh

v vh

2,

* *v

2,

v hv vh hhhh 1,3,

Re(g g )sin(2 )

Re(g g

Re(g g + )sin(2 )

R

(

)e(g g + )

G -g )cos(2 )

(

cos(

G -g )cos(2 )

2

A toa B toa

A toa f B toa

f B

f B toa

B toa

toa

f B toa

A toa

g g T

T gG T

T T

T

g T

g g T g gT

* *

vv hv vh

2 22,

2 2

2,

21 ,hh ,Re(g g

) +(G -g )sin(2 )

+(G -g )sin )+ ) (2

f Bf B to

B toa

toa

f B toa

a

g

T

Tg T

T

Additional Faraday correction

2,1,

1,

'1, s1 in(2 )B toa

fB toa

B toa B toaT TT

T

12, 2

,

2,

', 21 2 si ( n )B toa

B toaf

BB a

toatoT

T

TT

constant value for Tb1/Tb2 [10,7,4] for horn1,2,3

f (Faraday angle) is estimate as 0.5*atan(Ta3/Ta2)

No exact way to deconvolve the Faraday effect because of 4pi integration The additional correction is applied after APC (antenna pattern correction, A-matrix approach)

* *vv vh hh hv=Re(g g + )=[-0.013, -0.017, -0.013]g g

* *vv hv vh hh=Re(g g + )=[-0.013, -0.019, -0.012]g g

Performance of additional correction for Tb2

Faraday off


Faraday On

Additional Correction

Land fraction

Performance of additional correction for Tb1

Faraday off


Faraday On

Additional Correction

Land fraction

salinity retrieval accuracy: after additional correction

Ascending

Descending

salinity retrieval: scale model Scale model retrieval meets the SSS retrieval requirement

Optimal case (SST > 10C), land fraction < 1e-3, but with the strongest Faraday rotation effect of a year and the strong solar effect

With theoretical antenna pattern

With scale model antenna pattern

∆SSS (9sec) mean std dev

Inner horn -0.006 0.14

Middle horn -0.013 0.13

Outer horn -0.017 0.12

∆SSS(psu,6sec)

mean std dev


Middle horn 0.054 0.21

Outer horn 0.019 0.21

salinity retrieval: scale model All SST and land fraction < 1e-3

With theoretical antenna pattern

With scale model antenna pattern

∆SSS(psu) Mean std dev

Inner horn 0.013 0.44


Outer horn 0.052 0.41

∆SSS mean std dev



Outer horn -0.016 0.26

Practical considerations

We don’t know antenna pattern & Faraday angle But these may be estimated

By trial and error, determine Re(Gg*)/G2

[-0.014, -0.018, -0.012] empirical [-0.013, -0.019, -0.012] from scale-model pattern

Faraday angle: 0.5atan(ta3/ta2) Truth Faraday angle (forward simulation) works slightly better than 0.5atan()

Nominal values of Tb1, Tb2 are ok

Summary

Simulation of salinity retrieval is performed using the scale model antenna pattern Simple correction of the Faraday effect is not sufficient, leaving up to 3-4K error in TB2 retrieval (in worst-case Faraday condition) Additional Faraday correction is implemented Now TB1 and TB2 may be retrieved with less than 0.15K error; salinity may be retrieved with an accuracy better than 0.2psu.

Documents

Salinity retrieval with scale model antenna pattern