Algorithm Theoretical Based Document (ATBD) - CESBIO

SO-TN-ESL-SM-GS-0001
Issue 1.a
Date: 31/08/2006
SMOS level 2 processor
Soil moisture ATBD
When A_card is constant, this is the parameterized expression for a function which reduces to a cardioid when B_card
is taken equal to 0. Hence the name of "modified cardioid".
Or conversely:
A_card = m_card 2 / (m_card + ε' – B_card) U_card = tan -1 (ε"/(ε'-B_card) )
Eq 45
with: m_card = ( (ε'-B_card) 2 + ε" 2 ) 1/2
The optimal value for B_card is very close to 0.8.
These expressions are relevant because angular dependant radiometric data allow retrieving accurately the value of the
magnitude A_card. On the other hand, the retrieval accuracy on the polar angle U_card is extremely poor; indeed, the
emissivity is almost independent of U_card, to the extent that almost any a priori value can be stipulated for the angle
U_card.
Therefore, in cases considered above, SMOS data can still be used to derive an estimate for the magnitude A_card,
which will be referred to as the dielectric constant index.
This may be useful, as any additional independent information on the dielectric constant can then be used to infer the
full complex ε.
For the cases of vegetated soil or open water, values for A_card and U_card may be computed readily from the complex
dielectric constant (which is available from the retrieval), using the above equations (Eq 45), if necessary.
In the decision tree, the notation for the cardioid forward model is MD.
This model is a particular case in the sense that its implementation is not completely identical, depending whether it is
used for direct simulation or retrieval. In order to apply it:
Once values for ε' and ε" from TGRD relevant LUT have been obtained for each relevant fraction;
• For every fraction such that a fixed contribution is needed in the aggregated forward model, this contribution is
obtained using directly these ε' and ε" values and then taking care of surface roughness and possible vegetation
layer.
• For the non nominal fraction or group of fractions over which the retrieval is carried out:
• Build fraction weighted averages of ε' and ε " over the relevant fraction group;
• Obtain the a priori value for A_card and the reference value for U_card using equations (Eq 45)
• In the fwd model for iterative retrieval, A_card is floating; ε' and ε" are computed from A_card, U_card and the
constant B_card using Eq 44. Following steps (surface roughness, vegetation layer) are carried out in the usual
way. Depending on the decision tree, the vegetation optical thickness may be either a fixed or a floating
parameter.
• Using the retrieved A_card and the constant U_card and B_card, ε' and ε" can be computed and should appear
in the output product.
3.1.5 Other contributions to the radiometric signal
Corrective terms in the radiative transfer equation (RTE) refer to ionospheric (Faraday) rotation and sky and
atmospheric contributions. Faraday rotation is taken care of in the geometrical transformation from antenna to TOA
(sections 3.2.2.1.2 & 3.2.2.1.6); this section deals with the remaining contributions. It must be recalled that they should
not be considered as corrections to apply before the retrieval, but as corrective terms and factors to be included in the
forward models used in the retrieval.
As seen above, the RTE can be written:
TB P = TB atm + exp (-τ atm ) [TB atm +TB sk exp(-τ atm )] R1 + exp (-τ atm ) R2
Eq 46
Where aggregated terms R1 and R2, which do not depend on either atmospheric or sky contributions, are dealt with in
sections 3.1.2 to 3.1.4.
This section is focused on atmospheric and sky contribution, i.e. obtaining first TB atm & τ atm , next TB sk .
3.1.5.1 Atmospheric contributions
3.1.5.1.1 Theoretical description
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