SMOS L2 OS ATBD - ARGANS

VI
ICM-CSIC
LOCEAN/SA/CETP
IFREMER
SMOS L2 OS
Algorithm Theoretical
Baseline Document
Doc: SO-TN-ARG-GS-0007
Issue: 3 Rev: 9
Date: 25 January 2013
Page:A2- VI
From Figure 2, it is clear that the minimization of Chi2 parameter does not allow to retrieve a
single pair of (', ") while it allows to retrieve a single value of Acard, Ucard remaining
undetermined.
The retrieval is performed through the iterative Levenberg and Marquard (Marquardt 1963)
algorithm. Minimization is done over Tb measured and modelled at the antenna level, using
the following cost function:
chi2
1
mod
2
prior ret
Nm
meas T ( , 1,
2)
bi
T i
1,
2
bi P P
P P
P P 1 N
2
2
i 0
T
P1, P2
P
b i
where (P1, P2) are (Acard, surface temperature), Nm is the number of measurements in the
meas
i
mod
i
pixel, T b , radiometer measurements, T b modelled Tb and T , radiometric errors;
prior
P ,
ret
P and P are a priori value, retrieved value and a priori error on P1 and P2
parameters. The error on surface temperature is set to 1.5°C. Over the ocean, Acard prior is
deduced from mean SSS and SST, and Acard is taken as 20% of Acard a priori value (about
10). In case of sea-ice retrievals, several a priori values of Acard and Acard were tested in
order to avoid retrieval of negative Acard values while avoiding biases on low Acard values.
We found that initiating the retrieval with low Acard prior value (Acard prior =1) and large
error on Acard (Acard =50) meets this goal and gives the same result over ocean pixels as
taking Acard prior deduced from mean SSS and SST.
Two kinds of retrievals were performed: academic retrievals and semi-realistic retrievals:
Academic retrievals:
These retrievals were performed in order to look at the performance of the Acard retrieval, in
case of ocean-ice heterogeneous pixels or in case of biases on auxiliary parameters or on Tb.
Tb, entering in the retrieval, is modelled considering only parts of the direct model that are
impacted by these biases. Atmospheric effects, galactic noise reflection and Faraday rotation
are neglected.
bi
2
Eqn. 3