kim_wentz by mudoc123

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									         Salinity retrieval
with scale model antenna pattern



             S. Kim/F. Wentz
        Aquarius 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

Faraday angle




After
                      Tb2 retrieval scale-model (descending)


  Before additional correction
  error reaches -2K




Faraday angle




  After
        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
                    Theoretical model                                      Scale model
                                               Faraday
                    Faraday off                angle                       Faraday off
                    Simple                                                 Simple
                    correction                                             correction
                    Faraday On                                             Faraday On
                    Simple correction                                      Simple correction
               Scale model antenna Stokes matrix (modified)
 scale model antenna’s off-diagonal term is 10-40 times larger than theoretical’s
                                                                Re  g vv g vh                           Im  g vv g vh              
                        2                  2                                 *                                          *
                  g vv               g vh
      Va                                                                                                                                VR 
     H                                                        Re  g hv g hh                           Im  g hv g hh               
                        2                  2                                 *                                           *
                  g hv               g hh
      a                                                                                                                               HR 
     U a   2 Re  g g *  2 Re  g g *             Re  g vv g hh   Re  g vh g hv  
                                                                    *                  *
                                                                                                  Im  g vv g hh   Im  g vh g hv   U R 
                                                                                                                *                  *
                    vv hv              vh hh                                                                                       
       Wa  
                                                                                                 Re  gvv g hh   Re  g vh g hv     R 
                                                                                                                                            W
             2 Im  g vv g hv  2 Im  g vh g hh 
                            *                  *
                                                       Im  g vv g hh   Im  g vh g hv  
                                                                    *                  *                      *                  *
                                                                                                                                   

theoretical antenna                                                       scale model antenna
IHORN =            1                                                      HORN=         1(n1)
   0.9777995    0.0222005    0.0018323    0.0000360                         0.9853075 0.0168026 -0.0195433 -0.0085144
   0.0236619    0.9763381   -0.0016604   -0.0001937                         0.0154680 0.9870461 0.0065521 0.0043823
  -0.0012777    0.0011429    0.9584791    0.0017800                        -0.0018744 -0.0224793 0.9034507 -0.2914306
  -0.0003209   -0.0001290    0.0001374    0.9443555                         0.0063599 -0.0261359 0.2846981 0.9142451
 IHORN =           2                                                      HORN=          2(p0)
   0.9698600    0.0301399   -0.0027432   -0.0008946                       0.9793472 0.0251813 -0.0082843 -0.0003378
   0.0281496    0.9718504    0.0045488   -0.0004253                         0.0222499 0.9820560 -0.0088156 -0.0069168
  -0.0016207    0.0014077    0.9382428    0.0007672                         0.0027088 -0.0392866 0.9340240 0.0511001
   0.0001413   -0.0006906   -0.0013847    0.9365401                        -0.0127451 0.0026349 -0.0496169 0.9496149
 IHORN =           3                                                      HORN=          3(p1)
   0.9659594    0.0340406    0.0014531    0.0007880                         0.9736289 0.0336871 -0.0206253 -0.0046420
   0.0334903    0.9665097   -0.0021459   -0.0001634                         0.0273845 0.9800099 0.0076234 0.0009958
  -0.0014786    0.0013045    0.9091309   -0.0004642                         0.0049451 -0.0272600 0.8377592 -0.3615281
   0.0000453    0.0003553   -0.0006897    0.9228344                         0.0066785 -0.0258146 0.3477410 0.8623706
                    Scale model antenna Stokes matrix (classical)

 TA1  
            
          1 g 2  g 2  g 2  g 2
            2 vv        vh        hv         hh    g
                                                   1
                                                   2     vv
                                                              2
                                                                   g vh  g hv  g hh
                                                                       2        2        2
                                                                                                Re  g vv g vh  g hh g hv   Im  g vv g vh  g hh g hv  
                                                                                                             *           *                   *           *
                                                                                                                                                               TBR1 
            
T   1 g 2  g 2  g 2  g 2
 A 2    2 vv        vh        hv         hh    g
                                                   1
                                                   2     vv
                                                              2
                                                                   g vh  g hv  g hh
                                                                       2        2        2
                                                                                                Re  g vv g vh  g hh g hv   Im  gvv gvh  g hh g hv   TBR 2 
                                                                                                             *           *                   *           * 
                                                                                                                                                                     
TA3                                                                                                                                                        T 
             Re  g vv g hv  g hh g vh 
                            *           *
                                                          Re  g vv g hv  g hh g vh 
                                                                      *           *
                                                                                                 Re  g vv g hh  g vh g hv   Im  g aa gbb  g ab gba    BR 3 
                                                                                                             *           *                   *           *

TA 4                                                                                                                                                       TBR 4 
          
               Im  g vv g hv  g hh g vh 
                            *           *
                                                          Im  g vv g hv  g hh g vh 
                                                                      *           *
                                                                                                 Im  g vv g hh  gvh g hv  Re  g aa gbb  g ab gba  
                                                                                                             *           *                 *           *
                                                                                                                                                             



       theoretical antenna                                                          scale model antenna
       IHORN =       1                                                              HORN=        1(n1)
         1.0000000 0.0000000 0.0001719 0.0002297                                      1.0023122 -0.0002020 -0.0129912 -0.0128967
          0.0000000 0.9541376 0.0034927 0.0002297                                     -0.0002020 0.9700415 -0.0260954 -0.0128967
         -0.0000674 -0.0012103 0.9584791 0.0002297                                    -0.0121768 0.0103024 0.9034507 -0.0128967
         -0.0000960 -0.0002249 0.0001374 0.9443555                                     0.0162479 -0.0098880 0.2846981 0.9142451
                                                                                    HORN=         2(p0)
       IHORN =        2
                                                                                     1.0044172 0.0001113 -0.0170999 0.0065790
          0.9999999 -0.0000000 0.0018056 -0.0004693
         -0.0000000 0.9417105 -0.0072920 -0.0004693                                    0.0001113 0.9569861 0.0005313 0.0065790
         -0.0001065 -0.0015142 0.9382428 -0.0004693                                   -0.0182889 0.0209977 0.9340240 0.0065790
          0.0004160 -0.0002746 -0.0013847 0.9365401                                   -0.0076900 -0.0050551 0.0496169 0.9496149
       IHORN =        3                                                             HORN=         3(p1)
         1.0000000 0.0000000 -0.0006928 0.0009514                                    1.0073552 -0.0000392 -0.0130019 -0.0056378
          0.0000000 0.9324691 0.0035990 0.0009514                                     -0.0000392 0.9462836 -0.0282487 -0.0056378
         -0.0000870 -0.0013916 0.9091309 0.0009514                                    -0.0111575 0.0161026 0.8377592 -0.0056378
         -0.0001550 0.0002003 -0.0006897 0.9228344                                     0.0162465 -0.0095681 0.3477410 0.8623706
                                  Errors in Faraday correction                                                           TA
     For uniform gain, no coupling, simple Faraday correction gives:
     TA1  TB1 & TA2toa  TA22  TA23  TB 2


    With coupling ( based on Le Vine et al 07)                                                                                TBR
                                                                                                       TAtoa    ionosphere
 TA1,toa  G 2TB1,toa  Re(g vv g* +g hh g hv )sin(2 f )TB 2,toa
                                 vh
                                           *

                                                                                                       T’B atmosphere TBtoa
 TA2,toa  (G 2 -g 2 )cos(2 f )TB 2,toa  Re(g vv g*  g vh g hh )sin(2 f )TB 2,toa
                                                    hv
                                                               *


            (G 2 -g 2 )cos(2 f )TB 2,toa
 TA3,toa  Re(g vv g* v +g vh g hh )TB1,toa  Re(g vv g*  g vh g hh )cos(2 f )TB 2,toa +(G 2 -g 2 )sin(2 f )TB 2,toa
                    h
                                *
                                                       hv
                                                                  *


            Re(g vv g* +g vh g hh )TB1,toa +(G 2 -g 2 )sin (2 f )TB 2,toa
                      hv
                                *




     The simple correction would produce
                        Re(g vv g* +g hh g hv ) TB 2,toa
                                            *
                                                                     
 TA1,toa    G TB1,toa 1 
                 2                vh
                                                          sin(2 f ) 
                                 G2             TB1,toa             
                                                                    
                                                                                                                     2
TA2,toa  G 4TB22,toa  2G 2 Re(g vv g* +g vh g hh )TB1,toaTB 2,toa sin(2 f )  Re(g vv g* +g vh g hh )TB1,toa 
                                      hv
                                                *
                                                                                          hv
                                                                                                     *
                                                                                                                 
                                                                                                            2
                           Re(g vv g* +g vh g hh ) TB1,toa
                                              *
                                                                          Re(G v g* +Gh g v ) TB1,toa 
                                                                                       *
        G TB 2,toa
             2
                      1 2          hv
                                                            sin(2 f )           h
                                                                                                        
                                    G2             TB 2,toa              
                                                                                 G2           TB 2,toa 
                                                                                                        
                         Additional Faraday correction
   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)


                                  T                   
         TB' 1,toa  TB1,toa 1   B 2,toa sin(2 f ) 
                                  TB1,toa             
                                                      
         =Re(g vv g* +g hh g hv )=[-0.013, -0.017, -0.013]
                    vh
                              *




                                       TB1,toa
        TB' 2,toa  TB 2,toa 1  2               sin(2 f )
                                       TB 2,toa
         =Re(g vv g* +g vh g hh )=[-0.013, -0.019, -0.012]
                    hv
                              *




         constant value for Tb1/Tb2 [10,7,4] for horn1,2,3
         f (Faraday angle) is estimate as 0.5*atan(Ta3/Ta2)
                Performance of additional correction for Tb2




Faraday off



Faraday On
Simple
correction

Faraday On
Additional
Correction



Land fraction
                Performance of additional correction for Tb1




Faraday off



Faraday On
Simple
correction

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 scale model antenna pattern
         ∆SSS(psu,6sec)      mean           std dev

         Inner horn          -0.005          0.23

         Middle horn         0.054           0.21

         Outer horn          0.019           0.21


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

With scale model antenna pattern
          ∆SSS(psu)       Mean         std dev

        Inner horn        0.013         0.44

        Middle horn      -0.032         0.44

        Outer horn        0.052         0.41


With theoretical antenna pattern
             ∆SSS         mean         std dev

        Inner horn       -0.007         0.28

        Middle horn      -0.010         0.27

        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.

								
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