SMOS L2 OS ATBD - ARGANS

Tb_i 2 = Tb_meas_i 2
174
ICM-CSIC
LOCEAN/SA/CETP
IFREMER
SMOS L2 OS
Algorithm Theoretical
Baseline Document
where the value of Tb_meas_i 2 is given in the L1 output product.
Doc: SO-TN-ARG-GS-0007
Issue: 3 Rev: 9
Date: 25 January 2013
Page: 174
For model 1, a global figure will be given as a linear function of auxiliary parameters (SST,
SSS, wind speed – room must be kept for others parameters that might be needed) and of
polarization, considering the assumptions and limitations specified in each module of the
model.
Some experiments (Sabia et al., 2005) advise not using SSS as one of the constrained
parameters Pj, as the retrieved value tends to the a priori value. Until this is clarified we
propose using this term with a very big Pj (e.g. 100) to remove its impact on equation 4.14.1.
Case 2 – Model error taken into account
For a single measurement, the variance-covariance matrix for Tb mod (CEarth mod ) is diagonal in
the Earth reference frame:
C
mod
Earth
2
Th _
0
0
0
mod el
0
2
Tv _ mod el
0
0
0
0
2
T 3 _ mod el
0
0
0
0
2
T 4 _ mod el
where ²Th_model, ²Tv_model,²T3_model,²T4_model are the variances of the Tb mod components
(Th mod , Tv mod , T3 mod , T4 mod ) in the Earth reference frame. The correlation of the model error
between different measurements are neglected here.
The value of the model uncertainty is given by a global figure that takes into account the
assumptions and limitations specified in each module of each model. In this version of
ATBD, it is assumed to be constant and independent of polarization. Its value is given in the
TGRD in the Earth reference frame.
In the future, Tb_model could be given as an analytical function of auxiliary parameters (SST,
wind speed – with room kept for others parameters that might be needed), incidence angle
and polarization.
The method of transport of the error variances to the antenna reference frame is detailed
below.
The variance/covariance matrix in the antenna reference frame (C mod Ant) for Tb mod is given in
the antenna reference frame by:
C mod Ant = (MR4) C mod Earth (MR4) T
where MR4 is the rotation matrix described in § 4.12.1.2 and T represents the transposition
operation.