SMOS L2 OS ATBD - ARGANS

161
4.10 Cardioid model
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: 161
As shown by Waldteufel et al. (2004), simultaneous retrieval of the real, ', and imaginary
part, ", of dielectric constant from SMOS Tb is an ill posed problem as the cost function,
rather than a single minimum, exhibit a minimum valley, that can be represented analytically
using a modified cardioid model. After carrying out the following change of variable:
' = A_card (1 + cos(U_card) ) cos (U_card) + B_card
" = A_card (1 + cos(U_card) ) sin (U_card)
which is equivalent to:
A_card = m_card 2 / (m_card + ' – B_card) U_card = tan -1 ("/('-B_card) )
with: m_card = ( ('-B_card) 2 + " 2 ) 1/2
with B_card = 0.8, it is possible to retrieve the parameter A_card with good accuracy: a
minimum of Chi2 is seen as a vertical line corresponding to a constant value of A_card and
various values of U_card. Local minima of Chi2 are also observed for unrealistic negative
values of A_card; as it will be described in the following, retrieval of such negative values
are avoided by taking an error on prior A_card over the ocean of 20 units or by initiating the
retrieval with low A_card value as low A_card are much better constrained.
With these definitions and considering direct emissivity models described above: for sea ice,
A_card=1.2 (U_card=0); over a flat sea, A_card ranges between 48 and 67 depending on SSS
and SST values and U_card between -0.9 and -0.5 radians.
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 A_card, U_card remaining undetermined.
We found that initiating the retrieval with low A_card prior value (A_card prior =1) and large
error on A_card (A_card =50) allows to avoid retrieval of negative A_card values while
avoiding biases on low A_card values and gives the same result over ocean pixels as taking
A_card prior deduced from mean SSS and SST.
Details on cardioid computation over the ocean are given by Boutin et al (submitted, see
Annex-2).
We suggest by default to use a minimalist model that includes the flat sea model plus
atmospheric and constant galactic noise correction (GN=3.7K) reflected by a flat sea in order
to minimize bias between effective A_card and A_card computed from retrieved SSS and
SST. The relevance of including galactic noise and atmosphere correction in this minimalist
model will be checked during AlgoVal tests.
Retrievals using the cardioid model use all the measurements available (including
outliers, those affected by ice, sky radiation, sun glint, etc.). This implies the bypass of
the measurement discrimination step.
[4.10.1]
[4.10.2]