SMOS L2 OS ATBD - ARGANS

120
ICM-CSIC
LOCEAN/SA/CETP
IFREMER
the sum over the Kirchhoff Integral harmonics to obtain
( , , , ) =
2m
ks ko
u10w
( ks,
ko)
cos2m(
siw),
(41)
o
m=
0
o
SMOS L2 OS
Algorithm Theoretical
Baseline Document
Doc: SO-TN-ARG-GS-0007
Issue: 3 Rev: 9
Date: 25 January 2013
Page: 120
where we have explicitly included the dependence of the final scattering coefficients on the
wind speed u 10 and wind direction w (towards which the wind is blowing), and where
m 2qsq
2
o
2 ks
k 1 o T s o
m
( , ) =
o
o(
k , k ) e(
qsqo)
2(0)
IK
qsqo
(42)
Note that the scattering coefficient harmonics are independent of wind direction. Moreover,
these harmonics only depend on the incoming and scattered radiation incidence angles, the
wind speed, and difference between the incoming and scattered radiation azimuth angles.
Thus, switching from vector notation to angles, we can write the scattering coefficients as
o(
10
o
m=
0
o,
o,
s,
s,
u10, w)
= 2m(
o,
s
o,
s,
u ) cos2m(
si
w),
4.7.5.3. The Semi-Empirical Geometrical Optics Scattering Model
While the models discussed in the preceding section are attractive because of their
applicability to a large range of scattering geometries and ocean surface roughness
conditions, they are difficult to empirically correct if their predictions are not accurate.
Indeed, we have found that the predictions obtained from both the Kirchhoff and SSA-1
models do not agree well with the scattered celestial sky brightness inferred from the data,
especially near the galactic plane where the sky brightness is strongest and also strongly
varying as a function of position in the celestial sky. In order to improve the predictions we
have adopted a geometrical optics model, which is more amenable to empirical adjustment
than the Kirchhoff and SSA-1 models.
Owing its analytical simplicity and flexibility, scattering models based upon the geometrical
optics approximation became widely used in the 1960s, there is a large body of literature on
the subject (see [26-32,35,36,38] and references therein), with applications ranging from the
interpretation of radar backscatter from the lunar surface to interpretation of microwave
emission and scattering from the rough ocean surface.
Taking the high-frequency limit of the Kirchhoff expression (35) for the scattering cross
sections, as is done in [28], we obtain the general form of the geometrical optics
approximation for the bistatic scattering cross sections,
o
2
4
2qsq
o
( ks , ko
) =
T ( , ) ( / ,
2
ks
ko
P qx
qz
q
( q q ) q q o
s
o
s
o
y
/ q
z
)
(77)
(43)