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
Where Y is the year, and M, D, HH, MM, SS respectively month, day, hour, minute and seconds. JD is the julian date
and U 0 the number of julian centuries since the reference epoch (1 JAN 2000). INT means selecting the integer part. Ω E
is the Earth rotation rate.
To have the time, the simplest is probably to extract the acquisition time of the first view of the node and then adding
for each view the SNAPSHOT_ID times the elementary integration time. Using a mean time for all the views could also
be considered. Similarly, the mean average angle between the two polarisations is also quite adequate.
In the following we will distinguish two polarizations for T sky . At present, existing galactic maps do not distinguish
between V and H pol but there is a polarization dependency, though not yet fully quantified.
a) Assuming a flat land
The galactic contribution reflected towards the radiometer, TB sk , to be introduced in Eq 9, can be computed from TB sky :
TB sk = TB sky (lat, lon, U T , θ , φ, p) =TB sky (δ,α,p) Eq 60
where p is one of the polarisations (H or V).
b) Taking into account the roughness of the land:
If the sky were homogeneous, it is expected that the introduction of the roughness would have a small effect in most
cases: for instance, when the reflection coefficient is modified by about 2.5% (at nadir)) and for a galactic noise of 5K,
neglecting the roughness effect would introduce an error of less than 0.1K.
Ideally it would be necessary at this level to introduce bistatic reflection coefficients, σ 0 ; in theory, the galactic noise
over the whole sky should be convoluted with these scattering coefficients. However since they are expected to
decrease rapidly away from specular reflection, the integration could be done over a narrow interval. This is
approximately taken care of by the integration that is necessary anyway due to the finite width of the synthetic antenna
beam (see next section).
Keeping this in mind and considering the magnitude of the very maximum galactic brightness temperature we might
encounter, (10-15 K) we believe that simplified approach using the direct model values could be used as a proxy (Eq
60) and that no significant spreading will occur.
In other words we assume that the reflectivity coefficients estimated through the direct model are deemed sufficient to
compute the reflected galactic contribution.
3.1.5.2.3.3 Integration over the antenna beam:
Finally it is necessary to integrate the reflected brightness temperature over the antenna pattern to obtain the sky
contribution to the signal exactly as for a ground element. When the antenna pattern is axially symmetric, according to
[88] it is possible to make the integration on δ and α and thence to precompute (TGRD) customized galactic maps
integrated over an average apodisation window after reflection on the surface. As the SMOS lobe varies across the FOV
and is not symmetric, this is not accurate but deemed sufficient for our purpose. Views with sky contributions above a
TH_SKY threshold will be flagged.
3.1.5.2.4 Error budget estimates (sensitivity analysis)
The main uncertainty is expected to come from inaccuracies of the galactic noise maps. In [89] the authors estimate the
accuracy on their maps (due to the calibration of the instrument) to be of 0.5K.
In addition to a constant bias, uncertainties are likely to appear on these maps near the equatorial galactic plane. In order
to estimate these uncertainties, the SSS ESL have compared the maps derived from the Stokert survey, commonly
called the Reich and Reich map, and the ones derived from the Effelsberg survey. Both maps include the continuum
radiation and the cosmic background; Stockert survey was performed with a 34mn angular resolution instrument while
Effelsberg used a 9mn angular resolution instrument. Stockert map for the northern hemisphere and Effelsberg maps are
available on the http://www.mpifr-bonn.mpg.de/survey.html site; the Stokert map for southern hemisphere was
provided by ESA. Stockert maps are global but region around Cassiopeia is excluded (no data) and strong sources are
suspected to be underestimated; Effelsberg survey is concentrated close to the equatorial plane (Cygnus excluded).
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