!BOI

!  !TITLE: The Grid-point Statistical Interpolation \\ Analysis Library Documentation \\ Version 0.00

!  !AUTHORS: Staff

!  !AFFILIATION: NCEP/NOAA and GMAO/NASA

!  !DATE: May 2004

!  !INTRODUCTION: Package Overview 
\setcounter{secnumdepth}{5}
\setlength{\parskip}{0.5em}
This document describes the Grid-point Statistical Interpolation (GSI) 
analysis system. This is a three-dimensional variational analysis system
capable of producing either global or regional analyses updates.

%....................................................................
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%   Useful latex abbreviations
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\def\calJ{{\cal J \{ }}
%\def\xx{{\bf x}}
%\def\yy{{\bf y}}
%\def\BB{{\bf B}}
%\def\RR{{\bf R}}
\def\hh{\mbox{\boldmath $h$}}
\def\xx{\mbox{\boldmath $x$}}
\def\yy{\mbox{\boldmath $y$}}
\def\BB{\mbox{\boldmath $B$}}
\def\RR{\mbox{\boldmath $R$}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%....................................................................
\subsection{Introduction}
%           ------------
\label{sec:Intro}

The Grid-point Statistical Interpolation (GSI) analysis system has been
introduced at NCEP as a candidate replacement for the Spectral-Statistical
Interpolation (SSI) analysis system motivated by the following two main
drivers: (i) to allow implementation of situation-dependent (flow-dependent)
background error statistics; and (ii) to facilitate maintenance of a unified analysis
system serving both the global and regional applications at NCEP. The GSI is a three-dimensional
variation procedure designed to assimilate observations at any given time
$t_k$ by minimizing the cost function
\begin{equation} 
 J(\xx_k) = ( \xx_k - \xx^b_k  )^T \BB^{-1} ( \xx_k - \xx^b_k )
          + ( \yy_k - \hh_k(\xx) )^T \RR^{-1} ( \yy_k - \hh_k(\xx) )
\end{equation} 
where $\xx^b_k$ is the $n$-vector background state, $yy_k$ is the $p_k$-vector
of observations, $\hh$ is the observation operator responsible for 
converting the background state onto the observables, and $\BB$ and $\RR$ are
the $n\times n$ background and $p_k\times p_k$ observation error covariance 
matrices respectively. The high dimensionality (order $10^7$) of the control 
$n$-vector $\xx_k$ is such that minimization of the cost function $J$ 
can only be achieved with gradient-based methods. 

%....................................................................
\subsection{Algorithm Description}
%           ---------------------
\label{sec:Algorithm}

\input About../symbols.tex

In this section we provide a brief description of the optimization algorithm used in GSI.

%  The following are the contents of About../gsisolver.tex (by JGuo) slightly modified to fit
%  this file properly. (RTodling)
\subsubsection{Conventions}

The notation used here is selected to reflect a balanced consideration of
\begin{enumerate}
\item variable names used in the GSI software,
\item symbols used in GEOS DAS literature,
\item symbols used in related literature of optimization algorithms, and
\item notation consistency throughout this note.
\end{enumerate}

In this document, a superscript often categorizes the symbol, such
$()^b$ for background,
$()^a$ for analysis, and
$()^g$ for initial guess.
Exceptions
include $()^T$ for matrix-transpose and $()^{-1}$ for matrix-inverse,
numbers for exponents, or otherwise being specified in the text.

On the other hand, a subscript often denotes the instantiation of the
symbol, {\it i.e.} symbols evaluated at specific locations or with
respect to specific variables.

\subsubsection{Cost Function $J(x)$}
A variational data assimilation problem tries to minimize the
cost function in the following form
\begin{align}	\label{eq:cost-in-x}
J(x) &= \onehalf
  \Bigl\{
	(x-x^b)^T
	\bP^{-1}
	(x-x^b)
	+
	\bigl[ \cH(x) - o \bigr]^T
	\bR^{-1}
	\bigl[ \cH(x) - o \bigr]
  \Bigr\}
\end{align}
with respect to a gridded field $x$,
where
\begin{align*}
  x^b &: \text{a given background field of $x$}		\\
  o &: \text{observations}				\\
  \bR &: \text{observation error covariance}		\\
  \bP &: \text{background error covariance}		\\
  \cH &: \text{observation operator}
\end{align*}

Define
\begin{gather}
\label{eq:xhatsave}
\xhatsave \equiv x - x^b
\end{gather}
Then in term of $x$-increment $\xhatsave$,
the cost function is
\begin{subequations}
\begin{align}
\label{eq:cost-in-xhatsave}
J(x) &= \onehalf
  \Bigl\{
	(\xhatsave)^T
	\bP^{-1}
	\xhatsave
	+
	\bigl[ \cH(x) - o \bigr]^T
	\bR^{-1}
	\bigl[ \cH(x) - o \bigr]
  \Bigr\}		\\
\label{eq:x-in-xhatsave}
x &= x^b + \xhatsave
\end{align}
\end{subequations}

Define a preconditioned increment vector
\begin{align}
  \yhatsave &\equiv \bP^{-1}\xhatsave
\end{align}
Then in term of $y$-increment $\yhatsave$, the cost function is
\begin{subequations}
\begin{align}
\label{eq:cost-in-yhatsave}
J(x) &= \onehalf
  \Bigl\{
	(\yhatsave)^T
	\bP
	\yhatsave
	+
	\bigl[ \cH(x) - o \bigr]^T
	\bR^{-1}
	\bigl[ \cH(x) - o \bigr]
  \Bigr\}
  \\
\label{eq:x-in-yhatsave}
x &= x^b + \bP \yhatsave
\end{align}
\end{subequations}

The minimization of Eq. (\ref{eq:cost-in-x}) with respect to
$x$ is equivalent to
the minimization of Eq. (\ref{eq:cost-in-xhatsave}) with respect to
$\xhatsave$, and in particular, is equivalent to
the minimization of Eq. (\ref{eq:cost-in-yhatsave}) with respect to
$\yhatsave$.

\subsubsection{Gradient of Cost Function, $\nabla_\yhatsave J$}

The first thing of an iterative optimization algorithm is
to evaluate the gradient of the cost function.
Denoted by $\nabla_\yhatsave J$, the
gradient of the cost function $J(x)$ in Eq. (\ref{eq:cost-in-yhatsave})
with respect to $\yhatsave$ at $x=x^b+\xhatsave$ is
\begin{align}
\label{eq:grad-in-yhatsave}
  \nabla_\yhatsave J
    &=	\xhatsave +
	\bP\bH_x^T \bR^{-1}
	\bigl[ \cH(x) - o \bigr]
\end{align}
where
\begin{align*}
  \bH_x &\equiv \left. \frac{\partial \cH(x)}{\partial x}
  		\right|_{x}
\end{align*}
based on identities
\begin{gather*}
  \frac{\partial \cH(x(\yhatsave))}{\partial \yhatsave}
    =	\frac{\partial \cH\bigl(x(\yhatsave)\bigr)}{\partial x}	\cdot
	\frac{\partial          x(\yhatsave)      }{\partial \yhatsave}
    =	\bH_x \bP	\\
  \bP^T = \bP
\end{gather*}

For a cost function minimization process started with a given initial
``guess'' field $x^g$, let
\begin{gather}
\label{eq:xhat}
  \xhat \equiv x - x^g
\end{gather}
then
\begin{align*}
  x = x^b + \xhatsave = x^g + \xhat.
\end{align*}
Eq.~(\ref{eq:grad-in-yhatsave}) becomes
\begin{align}
\label{eq:grad-wrt-yhatsave-in-xhat}
  \nabla_\yhatsave J
    &=	\xhatsave +
	\bP\bH_x^T \bR^{-1}
	\bigl[ \cH(x^g+\xhat) - o \bigr]
\end{align}
Or correspondingly
\begin{align}
\label{eq:grad-wrt-xhatsave-in-xhat}
  \nabla_\xhatsave J
    &=	\yhatsave +
	\bH_x^T \bR^{-1}
	\bigl[ \cH(x^g+\xhat) - o \bigr]
\end{align}


\subsubsection{Minimization Algorithm}

The objective of an iterative step in the cost function minimization
process utilizing the gradient defined by
Eq.~(\ref{eq:grad-wrt-yhatsave-in-xhat})
is to find the next correction step $\delta x$ which reduces
the cost function in $x$
\begin{align*}
  J(x+\delta x) < J(x);
\end{align*}
Or in $\xhat$
\begin{align*}
  J(\xhat+\delta\xhat) < J(\xhat).
\end{align*}
Note that $\delta\xhat \equiv \delta x$ by the definition of $\xhat$.

This minimization objective can be achieved through the
algorithm in the GSI system, shown in Fig.~\ref{alg:algo} in
mathematical terms, and in Fig.~\ref{alg:code} in
program terms.

\begin{figure}[ht]
\begin{center}
\includegraphics[scale=0.8]{About../algo-pcgsoi-math}
\caption{Routine {\tt PCGSOI()} in mathematical terms.}
\label{alg:algo}
\end{center}
\end{figure}

In Fig.~\ref{alg:algo},
the objective of code segment line 6-9 is to compute the gradient
with respect to $\xhat$ ({\em i.e.} $\xhatsave$) and $\yhatsave$,
respectively.  Line 10-13 is to compute the correction directions
in $\xhat$ ($\xhatsave$) and $\yhatsave$, where line 11 for
scalar $\beta$
is in agreement with Eqs.~(106) and (107) in Navon and Legler (1987),
in the ``one-step limited-memory BFGS quasi-Newton update'' form.
Line 14 is to compute the step-size
that minimize the cost function along the given correction direction
$\dirx_i$ or $\diry_i$, which
can also be noted as ``solve
\begin{align*}
0 &=(\dirx_i)^T\!\nabla_\xhat J	\\
  &=(\dirx_i)^T\!\yhatsave +
    (\dirx_i)^T\!\bH^T\Rinv
	\bigl(\cH(x_j^g+\xhat_{i-1}+\alpha_i\dirx_i)-o\bigr)	\\
  &=(\diry_i)^T\!\xhatsave +
    (\dirx_i)^T\!\bH^T\Rinv
	\bigl(\cH(x_j^g+\xhat_{i-1}+\alpha_i\dirx_i)-o\bigr)	\\
  &=(\diry_i)^T\!\nabla_\yhatsave J
\end{align*}
for $\alpha_i$''.
Line 15-17, is to compute the next values of $\xhat$ ($\xhatsave$)
and $\yhatsave$.

\begin{figure}[ht]
\begin{center}
\includegraphics[scale=0.8]{About../algo-pcgsoi-code}
\caption{Routine {\tt PCGSOI()} in program terms.
Note two new operators ${\bm L}$ and ${\bm L}^{-1}$.} \label{alg:code}
\end{center}
\end{figure}

The algorithm shown in Fig.~\ref{alg:algo} and Fig.~\ref{alg:code} is
known as the ``inner-loop'' of the minimization process in the GSI, or
\verb"SUBROUTINE PCGSOI()".  Note that beside that Fig.~\ref{alg:algo}
is in mathematical terms and Fig.~\ref{alg:code} is in program terms,
Fig.~\ref{alg:code} also identifies the difference between the source
grid-space defining background state $q^b$ and analysis $q^a$, and the
intermediate grid-space defining the guess state $x^g$ and the
increment state $\xhat$, and two linear operators
($\bL$ and $\bL^{-1}$) converting between
the two spaces back-and-forth.

The algorithm descriptions given in these two figures
include neither some configuration steps for the ``inner-loop'', nor
the so-called ``restart'' of the search directions.  Both are parts of
the algorithm known as the ``outer-loop'' of the process in the GSI,
or in \verb"SUBROUTINE GLBSOI()".

Figure~\ref{alg:twoloops} describes
the complete minimization process in its two level nested-loop form,
for the algorithm in routine \verb"GLBSOI()" as well as
its major lower level routines.
For convenience, some of these lower level
routines are marked as Fortran comments in the figure.
Note that the description of line 4-6 is highly simplified,
not an accurate representation of the complex details in this
part of the whole algorithm.

\begin{figure}[hb]
\begin{center}
\includegraphics[scale=0.8]{About../algo-glbsoi-code}
\caption{Minimization in two level nested loops
from routine {\tt GLBSOI()} down.
} \label{alg:twoloops}
\end{center}
\end{figure}

%\end{document}

%....................................................................
\subsection{General Input Datasets}
%           ----------------------
\label{sec:GenData}

\begin{center}
\begin{tabular}{|l|l|}\hline
{\bf Filename} & {\bf Description} \\
\hline
\hline
spectral\_coefficients      &   \\ 
transmittance\_coefficients &   \\
emissivity\_coefficients    &   \\
pcpinfo                     &   \\
satinfo                     &    \\
ozinfo                      &   \\
berror\_stats               & tuning parameters related to definition of background
                             error covariance \\
prepobs\_prep.bufrtable     & BUFR table for prepobs files \\
\hline
\end{tabular}
\end{center}

%....................................................................
\subsection{Observational Data}
%           ------------------
\label{sec:ObsData}

\begin{center}
\begin{tabular}{|l|l|l|}\hline
{\bf Instrument} & {\bf Satellite} & {\bf Description}\\
\hline
\hline
AMSU-A & NOAA-14/15/16/17  & TBD \\
AMSU-B & NOAA-14/15/16/17  & TBD \\
HIRS/2 & NOAA-14/15/16/17  & TBD \\
HIRS/3 & NOAA-14/15/16/17  & TBD \\
SBUV   & NOAA-16           & TBD \\
MSU    & NOAA-14           & TBD \\
TMI    & TRMM              & TBD \\
MODIS  & TERRA             & TBD \\
AIRS   & TERRA             & TBD \\
CERES  & TERRA             & TBD \\
\hline
\end{tabular}
\end{center}

\subsection{Header Information}
%           ------------------
\label{sec:HeaderInfo}

%....................................................................
\subsubsection{Storage requirements}
%              --------------------

%....................................................................
\subsection{Overview of the application program interface (API)}
%           ---------------------------------------------------
\label{sec:API}
\subsubsection{FORTRAN 90 interface}
%              --------------------
\label{sec:API90}

\subsubsection{FORTRAN 77 interface}
%              --------------------
\label{sec:API77}

\subsubsection{FORTRAN 77 write routines}
%              -------------------------
\label{sec:WriteGSI}

\subsubsection{FORTRAN 77 read routines}
%              -------------------------
\label{sec:ReadGSI}

\subsubsection{Query routines}
%              --------------
\label{sec:GSIQuery}

\subsection{Compatibility with different versions}
%           -------------------------------------

%..................................................................

\section{Software Installation and Usage}
%        -------------------------------
\label{sec:Software}
\subsection{Availability}
%           ------------
\label{sec:Avail}
A copy of this software can be obtained by from a CVS repository currently
residing at NASA/Goddard Space Flight Center. A CVS command allowing 
extraction of a copy of the GSI software has the general form: 
\begin{verbatim}
cvs -d ${UserID}@zeus.gsfc.nasa.gov:/CM/baseline/GEOS_DAS \
       checkout -r ${TAG} -d ${Out_SubDir} MODULE_NAME
\end{verbatim}
where the C-shell variable, \verb|UserID|, is a valid user
identification tag, \verb|TAG| is the CVS software tag version,
\verb|Out_SubDir| is the destination subdirectory on the local 
platform, and \verb|MODULE_NAME| is the name of the desired CVS
module to be extracted.

For example, a valid string for \verb|TAG| is 
\begin{verbatim}
ncep-gsi-1_2
\end{verbatim}
If the user identification name is \verb|ncep_nco| and the local
destination directory is \verb|gsi|, a valid CVS command to extract
a copy of the source code from the repository is
\begin{verbatim}
cvs -d ncep_nco@zeus.gsfc.nasa.gov:/CM/baseline/GEOS_DAS \
       checkout -r ncep-gsi-1_2 -d gsi gsi
\end{verbatim}
where \verb|gsi| is the module name in this case.

Once the software is copied to the user's local directory all valid
tags can be listed for a given GSI file using the command,
\begin{verbatim}
    cvs status -v $(FILE)
\end{verbatim}
where \verb|FILE| is a file extracted from CVS.  To get all versions
of the GSI library, the most logical choice for \verb|FILE| is
\verb|Makefile|.  The software can be updated to the desired version
by entering the command,
\begin{verbatim}
    cvs update -r ${TAG}
\end{verbatim}

\subsection{Dependencies and System Requirements}
%           ------------------------------------
\label{sec:System}

\subsection{Installation Instructions}
%           -------------------------
\label{sec:Install}
There are currently two ways the GSI executable can be built. 

\begin{description}

\item[Makefile] This file is used to compile using the make utility

\item[Makefile.conf.{\em ARCH}] where {\em ARCH} is the result of the
C-Shell UNIX command, {\tt uname~-s} or {\tt uname~-n}.  This include
file for the file, Makefile, contains all the machine dependent
configuration parameters necessary to build the software on the
desired platform.  

\item[Makefile.depend] This file contains the list of object files
with each entry containing the corresponding source code and the
header files that are referenced by the source code.

\item[configure] Script to link the make file to the appropriate
configuration file, Makefile.conf.{\em ARCH} (where ARCH is the result
of the C-Shell UNIX command, {\tt uname~-s}).  The command,
\begin{verbatim}

            ./configure

\end{verbatim}
should be performed so that the proper link is created.

\item   Enter:
\begin{verbatim}
             make lib
\end{verbatim}
The file will be slightly smaller than if the FORTRAN 90 modules are
included.  For a list of additional targets, enter
\begin{verbatim}
             make help
\end{verbatim}
\end{description}

\subsection{Library testing}
%           ---------------
\label{sec:Testing}

\subsection{Compiling GSI application program}
%           ----------------------------------

%.........................................................................

\newpage

\centerline{\huge\bf References}

\addcontentsline{toc}{section}{References}

\begin{description}

\item{}Derber, J., and Rosati

\item{}Purser R.J., W.-S. Wu, D. F. Parrish, N. M. Roberts, 2003: Numerical 
       aspects of the application of recursive filters to variational statistical 
       analysis. Part I: Spatially homogeneous and isotropic Gaussian covariances.
       {\it Mon. Wea. Rev.}, {\bf 131}, 1524-1535.

\item{}Purser R.J., W.-S. Wu, D. F. Parrish, N. M. Roberts, 2003: Numerical 
       aspects of the application of recursive filters to variational statistical 
       analysis.  Part II: Spatially inhomogeneous and anisotropic general covariances.
       {\it Mon. Wea. Rev.}, {\bf 131}, 1536-1548.

\item{}Wan-Shu, W., R. J. Purser, and D. F. Parrish, 2002: Three-dimensional
       variational analysis with spatially inhomogeneous covariances.
       {\it Mon. Wea. Rev.}, {\bf 130}, 2905-2916.

\end{description}

%..........................................................................

\newpage

\addcontentsline{toc}{section}{Revision History}

\vspace*{\fill}

\centerline{\huge\bf Revision History}

\bigskip

\bigskip

\begin{center}
\begin{tabular}{|l|l|l|l|}\hline
{\bf Version} & {\bf Version} & {\bf Pages Affected/}   & {\bf Aproval}\\
{\bf Number}  & {\bf Date}    & {\bf Extent of Changes} & {\bf Authority}\\
\hline
\hline
Version 0 & May  2004       & see  Changes/20040505.txt & ncep-gsi-2004\_05 \\
Version 0 & June 2004       & see  Changes/20040602.txt & ncep-gsi-2004\_06 \\
\hline
\end{tabular}
\end{center}

\vspace*{\fill}

\appendix

\addcontentsline{toc}{part}{APPENDIX}

\section{Resource Files}
\label{sec:RCFiles}

\begin{table}[h]
\caption{\small Namelists necessary to setup parameters to run GSI.}
\label{tab:namelist}
\end{table}
{\tiny
\begin{verbatim}
 &SETUP
   JCAP=@JCAP,NLAT=@NLAT,NLON=@NLON,nsig=@NSIG,
   miter=3,niter(1)=100,niter(2)=100,niter(3)=1,
   as=0.4,0.4,0.3,0.6,1.0,0.6,1.0,1.0,vs=0.5,hs=1.0,bw=0.
   grosst=10.0,grossw=10.0,grossrw=10.0,grossdw=10.0,grossp=10.0,grossq=10.0,
   grosspw=10.0,gencode=78,
   dfact=0.1,factqmin=0.05,deltim=300,
   ndat=27,jpch=493,npred=5,iguess=-1,
   hybrid=.false.,regional=.false.,oneobtest=.false.,
 /
 &OBS_INPUT
   dmesh(1)=145.0,dmesh(2)=240.,dmesh(3)=180.,
   dfile(1)='amsuabufr',dtype(1)='amsua',    id(1)=15, dload(1)=225.0, dval(1)=10.0, dthin(1)=1,
   dfile(2)='amsubbufr',dtype(2)='amsub',    id(2)=15, dload(2)=75.0,  dval(2)=3.0, dthin(2)=2,
   dfile(3)='hirs2bufr',dtype(3)='hirs/2',   id(3)=14, dload(3)=285.0, dval(3)=6.0, dthin(3)=3,
   dfile(4)='msubufr',  dtype(4)='msu',      id(4)=14, dload(4)=60.0,  dval(4)=2.0, dthin(4)=1,
   dfile(5)='prepqc',   dtype(5)='goes',     id(5)=10, dload(5)=270.0, dval(5)=6.0, dthin(5)=3
   dfile(6)='prepqc',   dtype(6)='goes',     id(6)=12, dload(6)=270.0, dval(6)=6.0, dthin(6)=3,
   dfile(7)='ssmi',     dtype(7)='pcp_ssm/i',id(7)=264,dload(7)=300.0, dval(7)=1.0, dthin(7)=-1,
   dfile(8)='tmi',      dtype(8)='pcp_tmi',  id(8)=211,dload(8)=300.0, dval(8)=1.0, dthin(8)=-1,
   dfile(9)='amsuabufr',dtype(9)='amsua',    id(9)=16, dload(9)=225.0, dval(9)=10.0, dthin(9)=1,
   dfile(10)='amsubbufr',dtype(10)='amsub',  id(10)=16,dload(10)=75.0, dval(10)=3.0, dthin(10)=2,
   dfile(11)='hirs3bufr',dtype(11)='hirs/3', id(11)=16,dload(11)=285.0,dval(11)=6.0, dthin(11)=3,
   dfile(12)='sbuvbufr', dtype(12)='sbuv2',  id(12)=16,dload(12)=75.0, dval(12)=1.0, dthin(12)=0,
   dfile(13)='amsuabufr',dtype(13)='amsua',  id(13)=17,dload(13)=225.0,dval(13)=10.0, dthin(13)=1,
   dfile(14)='amsubbufr',dtype(14)='amsub',  id(14)=17,dload(14)=75.0, dval(14)=3.0, dthin(14)=2,
   dfile(15)='hirs3bufr',dtype(15)='hirs/3', id(15)=17,dload(15)=285.0,dval(15)=6.0, dthin(15)=3,
   dfile(16)='goesimg',  dtype(16)='goesimg',id(16)=10,dload(16)=15.0, dval(16)=1.0, dthin(16)=3,
   dfile(17)='goesimg',  dtype(17)='goesimg',id(17)=12,dload(17)=15.0, dval(17)=1.0, dthin(17)=3,
   dfile(18)='airs',     dtype(18)='airs',   id(18)=49,dload(18)=4215.,dval(18)=20.0, dthin(18)=3,
   dfile(19)='airs',   dtype(19)='eos_amsua',id(19)=49,dload(19)=225.0,dval(19)=10.0, dthin(19)=1,
   dfile(20)='prepqc',    dtype(20)='t',     id(20)=0, dload(20)=2.483,dval(20)=1.0, dthin(20)=0,
   dfile(21)='prepqc',    dtype(21)='uv',    id(21)=0, dload(21)=3.478,dval(21)=1.0, dthin(21)=0,
   dfile(22)='prepqc',    dtype(22)='ps',    id(22)=0, dload(22)=1.000,dval(22)=1.0, dthin(22)=0,
   dfile(23)='prepqc',    dtype(23)='q',     id(23)=0, dload(23)=3.991,dval(23)=1.0, dthin(23)=0,
   dfile(24)='prepqc',    dtype(24)='pw',    id(24)=0, dload(24)=3.000,dval(24)=1.0, dthin(24)=0,
   dfile(25)='prepqc',    dtype(25)='dw',    id(25)=0, dload(25)=3.000,dval(25)=1.0, dthin(25)=0,
   dfile(26)='radarbufr', dtype(26)='rw',    id(26)=0, dload(26)=2.000,dval(26)=1.0, dthin(26)=0,
   dfile(27)='prepqc',    dtype(27)='spd',   id(27)=0, dload(27)=3.478,dval(27)=1.0, dthin(27)=0,
 /
 &SINGLEOB_TEST
   maginnov=0.1,magoberr=0.1,oneob_type='t',
   oblat=45.,oblon=180.,obpres=1000.,obdattim=2004041512,
   obhourset=0.,
 /
\end{verbatim}
}

\subsection{Glossary}
%           --------

\begin{center}
\begin{tabular}{ll}\hline
AIRS   & Atmospheric Infrared Sounder \\ 
AMSU   & Advanced Micorwave Sounding Unit \\
CERES  & Clouds and Earth's Radiant Energy System \\
HIRS   & High-Resolution Infrared Radiation Sounder \\
MODIS  & Moderate-Resolution Imaging Spectrometer \\
MSU    & Micorwave Sounding Unit \\
SBUV   & Solar Backscatter Ultraviolet radiometer \\
TMI    & TRMM Microwave Imager \\
TRMM   & Tropical Rainfall Measuring Mission \\
\hline
\end{tabular}
\end{center}

!EOI