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forced by differences between observed and predicted top-of-the-atmosphere (TOA)
brightness temperatures (BTs) for the different satellite SST channel wavelengths.
Calculation of the TOA-BTs requires use of a fast radiative transfer model. For this
purpose the Community Radiative Transfer Model (CRTM;
Han et al. 2006
)isbeing
integrated into the 3DVAR. In addition to the TOA forward model, CRTM provides
the tangent linear radiance sensitivities (Jacobians) with respect to the prior SST,
water vapor, and atmospheric temperature predictor variables as a function of the
infrared satellite 3.5, 11 and
12
m wavelengths. The physical SST inverse model
for a given channel is given by,
2
3
2
3
2
3
©
1
sst
J
sst
J
sst
J
sst
J
t
J
sst
J
q
•
BT
J
sst
•
•T
sst
•T
a
•Q
a
4
5
D
4
5
4
5
J
t
J
sst
©
t
J
t
J
t
J
t
J
q
(13.11)
BT
J
t
J
q
J
sst
J
q
J
t
©
q
J
q
J
q
•
BT
J
q
where
BT are the TOA-BT innovations, J
sst
,J
t
,andJ
q
are the radiative transfer
model Jacobians for SST, atmospheric temperature, and water vapor, respectively,
©
sst
,
•
Q
atm
are the
corrections output for each of the priors that take into account the variable SST
and temperature and water vapor content of the atmosphere at the time and location
of the radiance measurement. The prior corrections are calculated and summed
over the SST channels (3 channels at night, 2 channels during the day). With
this approach, coefficients that relate radiances to SST in the observation operator
are dynamically defined for each atmospheric situation observed. The method
removes atmospheric signals in the radiance data and extracts more information
on the SST, which improves the time consistency of the SST estimate, especially
in the tropics where water vapor variations create unrealistic sub-daily variations
in the empirically derived SST. However, the physical SST method requires careful
consideration of biases and error statistics of the NWP fields. Biases are expected
since the NWP information may represent areas that are both cloudy and clear, while
the satellite radiance data, by definition, are only available in clear-sky, cloud free
conditions. Accordingly, a bias correction step is under development following the
ideas developed by
Merchant et al.
(
2008
). Proper specification of the error statistics
of the priors is also required to correctly partition the observed TOA-BT differences
into the various sources of variability (atmospheric temperature, water vapor, or
sea surface temperature). Sensitivity experiments are underway to evaluate situation
dependent error statistics for the atmospheric temperature and water vapor priors
using the 96-member global NWP ensemble operational at FNMOC.
Implementation of the physical SST method via an observation operator will
have many advantages in the 3DVAR. First, in a coupled model forecast, the
prior SST will come from the coupled ocean model forecast and differences
between observed and predicted TOA-BTs will be computed using the coupled
model atmospheric state. This is a true example of coupled data assimilation: an
observation in one fluid (atmospheric radiances) creates an innovation in a different
fluid (ocean SST). Second, the method can easily be extended to incorporate the
©
t
,and
©
q
are the errors of the priors, and
•
T
sst
,
•
T
atm
,and
•
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