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    \noindent \href{http://asl.umbc.edu/~strow/}{L. Strow}\\
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\wwwheader 
  {L1B Clear Flag Methodology} 
  {http://asl.umbc.edu/pub/airs/exercises/clearmethod.html}
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\section{Definitions}

Our computed radiance, $R_c$ is given by
\begin{displaymath}
R_c = \epsilon B(T_s) \tau_{atm} + \int B d\tau
\end{displaymath}
where $T_s$ is the NCEP sea surface temperature, and $\tau_{atm}$ is the
atmospheric transmittance computed with the forward model using the
NCEP model fields for temperature and water vapor.  
\begin{displaymath}
R_s^C = \epsilon B(T_s)
\end{displaymath}
is the radiance if the atmospheric transmittance was zero, 
and
\begin{displaymath}
R_{obs} = \epsilon B(T_s^t) \tau_{atm}^t + \int B^t d\tau^t,
\end{displaymath}
is the observed radiance, where the superscripts denote ``true''
quantities. 
($R_c - R_s^c$) is our estimate of the ``atmospheric'' part of
$R_{obs}$, which we subtract from $R_{obs}$ in order to estimate just
the sea surface emission part of $R_{obs}$, or $\epsilon B(T^t_s)$.
$T^t_s(est)$ denotes our estimate of the true sea surface temperature.
Therefore, our final estimate of the sea surface temperature from an
observed radiance is
\begin{displaymath}
BT\left[ \frac{R_{obs} - (R_c - R_s^c)}{\epsilon} \right] = T_s^t(est)
\end{displaymath}
where $BT[]$ turns radiance into brightness temperature.  ($R_c -
R_s^c$) is very small for 2616 \wn (few tenths of a K), but up to 4K
or more at 900 \wn.

\section{Clear Flag}

I compute $T^t_s(est)$ for the 900 and 2616 \wn channels.  The
clear flag is derived from FOVS that return true for the following
three tests:

\begin{enumerate}
  \item Is Mitch Goldberg's L2 flag (fov\_clear\_flag) set?
  \item $| T^t_{s,2616 cm^{-1}}(est) - T_s | < 1K $
  \item $| T^t_{s,2616 cm^{-1}}(est) - T^t_{s,900 cm^{-1}}(est) | < 0.5K$
\end{enumerate}

Since we know the true sea surface temperature Test-\#2 above is quite
good.  However, in practice $T_s$ will have 0.5 - 1K errors, and
Test-\#3 might be quite important, although it is less sensitive.
Test-\#2 will help get rid of outliers that could make it through
Test-\#3.  

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