An Assessment of Microwave Moisture Retrievals over Land and Ocean

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					 An Assessment of AMSU-A
Moisture Retrievals over Land
         and Ocean


          Stan Kidder
         20 June 2006

                                1
Purpose of Study

To determine how accurately atmospheric
water vapor and liquid water can be
retrieved from AMSU-A data using
  1. A simplified forward model and
  2. Rodger’s (2000) maximum a posteriori
     (MAP) solution


                                          2
In Other Words

• To use a simplified atmosphere (in which
 everything is known) to determine the
 best that one can hope for in moisture
 retrieval accuracy and how various factors
 (especially surface emittance) influence
 this accuracy.



                                              3
The Forward Model

   TB(n) = enTstn                                          surface emission

                   + TA(1 - tn)                        atmospheric emission

                   + TA tn(1 - tn)(1 – en)                 surface reflection


TB = brightness temperature (K)     tn = atmospheric transmittance (unitless)
n = frequency (GHz)                 TS = surface temperature (K)
en = surface emittance (unitless)   TA = constant atmospheric temp (K)

                                                                            4
The Forward Model (cont.)
tn = to(n)                                 oxygen

      exp[−bL(n)L]                        cloud liquid water

      exp[−bV(n)V]                       water vapor


   to(n) = vertical transmittance of dry, cloud-free atmosphere
   L = vertically integrated cloud liquid water (kg m-2 or mm)
   V = vertically integrated water vapor (TPW, kg m-2 or mm)
   bL(n) = liquid water mass absorption coefficient (m2 kg-1)
   bV(n) = water vapor mass absorption coefficient (m2 kg-1)

                                                                  5
     Forward Model Constants*

n    (GHz)            23.8               31.4      50.3         52.8


to                   0.9746             0.9588    0.5937       0.1639


bL   (m2 kg-1)       0.0600             0.1035    0.2575       0.2822


bV    (m2 kg-1)    5.18510−3      2.78910−3    4.77710−3   5.03410−3


      *Determined using Liebe (1992).
                                                                       6
The Measurement Vector


                 Se = se2I4

                 se = 0.5 K
                   (“noise”)

                               7
The State Vector




                   8
A Priori




           9
A Priori Covariance




                      10
Surface Emittance

• Treated as a forward model parameter,
  that is, as a random variable which is not
  retrieved and thus adds error to the
  retrieved quantities
• The standard deviation of surface
  emittance is varied to evaluate the
  accuracy with which it must be known to
  achieve the desired accuracy of retrieval
                                               11
Mean Emittance

Channel             23.8             31.4              50.3              52.8
Ocean*             0.421            0.443             0.482             0.488
Land               0.950            0.950             0.950             0.950
*From Kohn (1995). TS = 300 K, WS = 5 m s-1, salinity = 35 ppt, zenith angle = 0




                                                                                   12
The Retrieval Scheme
• K = analytic Jacobian [Kij = ∂TB(νi)/ ∂xj]
• Rodgers’ iterative solution (eq. 5.8) with K
  being recalculated at every iteration:



• Convergence is achieved (eq. 5.29) when



                                                 13
Retrieval Error Covariance

• At convergence (Rodgers eq. 5.30):




                                       14
Model Parameter-Caused Error
• Rodgers eq. 3.16 & 3.27:




  Note that in the Dx equation, e stands for surface emittance, whereas, in
  the Gy equation, Se is the measurement covariance matrix.




                                                                              15
Procedure
1. Choose a state vector, and an emissivity
     vector, approximating the values as Gaussian
     variables
2.   Calculate the measurement vector with noise
3.   Retrieve the state vector using e0
4.   Repeat steps 1-3 1000 times
5.   Calculate the retrieval statistics as functions of
     emittance noise

                                                      16
Results

• Presented as a series of graphs showing
 the bias, standard deviation, and RMS
 error of retrieving TS, TA, L, and V.




                                            17
TS Ocean
                                           TS Ocean

           45
           40
           35
           30
           25                                                                    Bias
 Kelvins




           20                                                                    Std Dev
           15                                                                    RMS

           10
           5
           0
           -5   0.000   0.005     0.010     0.015     0.020      0.025   0.030

                                Std. Dev. of Surface Emittance



                                                                                           18
TS Land
                                            TS Land

           10
           9
           8
           7
           6                                                                     Bias
 Kelvins




           5                                                                     Std Dev
           4                                                                     RMS
           3
           2
           1
           0
                0.000   0.005     0.010     0.015     0.020      0.025   0.030
                                Std. Dev. of Surface Emittance



                                                                                           19
TA Ocean
                                           TA Ocean

           10


           8


           6
                                                                                 Bias
 Kelvins




           4                                                                     Std Dev
                                                                                 RMS
           2


           0
                0.000   0.005     0.010     0.015     0.020      0.025   0.030
           -2
                                Std. Dev. of Surface Emittance



                                                                                           20
TA Land
                                            TA Land

           10


           8


           6
                                                                                 Bias
 Kelvins




           4                                                                     Std Dev
                                                                                 RMS
           2


           0
                0.000   0.005     0.010     0.015      0.020     0.025   0.030
           -2
                                Std. Dev. of Surface Emittance



                                                                                           21
L Ocean
                                                  L Ocean

                0.25

                0.20

                0.15
 kg/m^2 or mm




                0.10                                                                     Bias
                                                                                         Std Dev
                0.05                                                                     RMS

                0.00
                        0.000   0.005     0.010     0.015     0.020      0.025   0.030
                -0.05

                -0.10
                                        Std. Dev. of Surface Emittance



                                                                                                   22
L Land
                                                   L Land

                0.60
                0.50
                0.40
                0.30
 kg/m^2 or mm




                0.20                                                                     Bias
                0.10                                                                     Std Dev
                0.00                                                                     RMS

                -0.10   0.000   0.005     0.010     0.015     0.020      0.025   0.030

                -0.20
                -0.30
                -0.40
                                        Std. Dev. of Surface Emittance



                                                                                                   23
V Ocean
                                                 V Ocean

                14

                12

                10
 kg/m^2 or mm




                8
                                                                                      Bias
                6                                                                     Std Dev
                                                                                      RMS
                4

                2

                0
                     0.000   0.005     0.010     0.015     0.020      0.025   0.030
                -2
                                     Std. Dev. of Surface Emittance



                                                                                                24
V Land
                                                  V Land

                80
                70
                60
                50
 kg/m^2 or mm




                40                                                                     Bias
                30                                                                     Std Dev
                20                                                                     RMS

                10
                 0
                -10   0.000   0.005     0.010     0.015     0.020      0.025   0.030

                -20
                                      Std. Dev. of Surface Emittance



                                                                                                 25
Conclusions
• Atmospheric temperature (TA) is accurately
    retrieved over land or ocean
•   Surface temperature (TS) is accurately retrieved
    over land, but poorly retrieved over ocean
•   Liquid water (L, CLW) is marginally retrieved
    over ocean, but lost in the noise over land
•   Water vapor (V, TPW) is accurately retrieved
    over ocean, but probably not retrievable over
    land with AMSU-A channels

                                                       26
Conclusions (cont.)
• Retrieving surface emittances instead of treating
    them as model parameters is unlikely to help
•   Adding AMSU-B channels would possibly help
    with land retrievals
•   Experiments with C1DOE should be performed
    to see if they support these results




                                                   27
References
Rodgers, C. D., 2000: Inverse Methods for Atmospheric
  Sounding: Theory and Practice. World Scientific, 238 pp.
Kohn, D. J., 1995: Refinement of a semi-empirical model
  for the microwave emissivity of the sea surface as a
  function of wind speed, M.S. thesis, meteorology dept.,
  Texas A&M University.
Liebe, H. J., 1992: Atmospheric Attenuation and Delay
   Rates from 1 to 1000 GHz. Institute for
   Telecommunication Sciences, NTIA/ITS.S1, 325
   BROADWAY, Boulder, CO 80303


                                                            28

				
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