<p><b>weiwang</b> 2008-05-13 11:53:47 -0600 (Tue, 13 May 2008)</p><p>update var from Dale<br>
</p><hr noshade><pre><font color="gray">Modified: trunk/wrf/technote/var.tex
===================================================================
--- trunk/wrf/technote/var.tex 2008-05-13 01:09:49 UTC (rev 67)
+++ trunk/wrf/technote/var.tex 2008-05-13 17:53:47 UTC (rev 68)
@@ -113,6 +113,13 @@
\section{Improvements to the WRF-Var Algorithm}
\label{var-upgrade}
+The latest version of WRF-Var (V3.0) contains a number of improvements relative
+to that described in the MM5 3DVAR technical note (\citet{barker03}). These are described below.
+It should also be noted that the public release of WRF-Var V3.0 contains only a subset of
+the capabilities of the full WRF-Var system. In particular, the direct assimilation of radiances,
+hybrid variational/ensemble data assimilation technique, and 4D-Var will be released once
+funding to support these complex algorithms is available.
+
\subsection{Improved vertical interpolation}
The original WRF 3D-Var system described in \citet{barker04} used height
@@ -142,11 +149,11 @@
in subsequent outer loops. The assimilation of nearby observations in previous iterations
essentially provides a ``buddy check" to the observation in question.
-\subsection{Flexible choice of control variables}
+\subsection{Choice of control variables}
\label{var-cvs}
-In practical variational data assimilation schemes, the background error covariance
-matrix ${\bf B}$ is computed not in model space ${\bf x}': u, v, T, q, p_{s}$, but in a
+A major change that users of previous versions of WRF-Var will notice, is the simplification
+of the background error covariance model used within WRF-Var. As before, the background error covariance matrix ${\bf B}$ is computed not in model space ${\bf x}': u, v, T, q, p_{s}$, but in a
control variable space ${\bf v}$ related to model space via the control variable transform ${\rm U}$,
i.e.,
@@ -160,129 +167,11 @@
${\rm U}_{p}$.
The components of ${\bf v}$ are chosen so that their error cross-correlations are negligible,
-thus permitting the matrix ${\bf B}$ to be block-diagonalized. The many varying applications
-(high/low resolution, polar/tropical, etc.) of WRF-Var require a flexible
-choice of background error model. This is achieved via a namelist option
-``cv$\_$options" as defined in Table \ref{var-cvtable}.
+thus permitting the matrix ${\bf B}$ to be block-diagonalized. The major change in WRF-Var V3.0
+is to simplify the control variable transform ${\rm U_p}$ to perform a simple statistical regression as described in subsection
+(\ref{var-b}) below. Testing in numerous applications has shown
+a general improvement of forecasts scores using this definition of balance, as compared to the dynamical geostrophic//cyclostrophic balance constraint defined in \citet{barker03}.
-\begin{table}[h]
-\begin{center}
-\begin{tabular}{|l|l|l|l|l|l|}
-\hline
-% Line 1
- { } &
- \ &
- \multicolumn{1}{c|}{2} &
- \multicolumn{1}{c|}{3} &
- \multicolumn{1}{c|}{4} &
- \multicolumn{1}{c|}{5} \\
- \raisebox{1.5ex}[0cm] {cv$\_$options} &
- \ &
- \multicolumn{1}{c|}{(original MM5)} &
- \multicolumn{1}{c|}{(NCEP)} &
- \multicolumn{1}{c|}{(Global)} &
- \multicolumn{1}{c|}{(Regional)}\\
- \hline
-% Line 2
- { } &
- \multicolumn{1}{c|}{ } &
- \multicolumn{4}{c|}{ }\\
- \raisebox{1.5ex}[0cm] {Analysis} &
- \multicolumn{1}{c|}{${\bf x}'$} &
- \multicolumn{4}{c|}{$u'$,$v'$,$T'$,$q'$,${p_s}'(i,j,k)$}\\
- \raisebox{1.5ex}[0cm] {Increment} &
- \multicolumn{1}{c|}{ } &
- \multicolumn{4}{c|}{ }\\
- \hline
-% Line 3
- { } &
- \multicolumn{1}{c|}{ } &
- \multicolumn{1}{c|}{ } &
- \multicolumn{3}{c|}{ }\\
- \raisebox{1.5ex}[0cm] {Change of} &
- \multicolumn{1}{c|}{${\rm U}_p$} &
- \multicolumn{1}{c|}{$\psi'$,$\chi'$,$p_u'$,$q'$} &
- \multicolumn{3}{c|}{$\psi'$,$\chi_u'$,$T_u'$,$r'$,$p_{su}'$}\\
- \raisebox{1.5ex}[0cm] {Variable} &
- \multicolumn{1}{c|}{ } &
- \multicolumn{1}{c|}{ } &
- \multicolumn{3}{c|}{ }\\
- \hline
-% Line 4
- { } &
- \multicolumn{1}{c|}{ } &
- \multicolumn{1}{c|}{ } &
- \multicolumn{1}{c|}{ } &
- \multicolumn{2}{c|}{ }\\
- \raisebox{1.5ex}[0cm] {Vertical} &
- \multicolumn{1}{c|}{${\rm U}_v$} &
- \multicolumn{1}{c|}{${\bf B}={\bf E}{\Lambda}{\bf E}^{T}$} &
- \multicolumn{1}{c|}{RF} &
- \multicolumn{2}{c|}{${\bf B}={\bf E}{\Lambda}{\bf E}^{T}$} \\
- \raisebox{1.5ex}[0cm] {Covariances} &
- \multicolumn{1}{c|}{ } &
- \multicolumn{1}{c|}{ } &
- \multicolumn{1}{c|}{ } &
- \multicolumn{2}{c|}{ }\\
- \hline
-% Line 5
- { } &
- \multicolumn{1}{c|}{ } &
- \multicolumn{2}{c|}{ } &
- \multicolumn{1}{c|}{ } &
- \multicolumn{1}{c|}{ }\\
- \raisebox{1.5ex}[0cm] {Horizontal} &
- \multicolumn{1}{c|}{${\rm U}_h$} &
- \multicolumn{2}{c|}{RF} &
- \multicolumn{1}{c|}{Spectral} &
- \multicolumn{1}{c|}{RF}\\
- \raisebox{1.5ex}[0cm] {Correlations} &
- \multicolumn{1}{c|}{ } &
- \multicolumn{2}{c|}{ } &
- \multicolumn{1}{c|}{ } &
- \multicolumn{1}{c|}{ }\\
- \hline
-% Line 6
- { } &
- \multicolumn{1}{c|}{ } &
- \multicolumn{2}{c|}{ } &
- \multicolumn{1}{c|}{ } &
- \multicolumn{1}{c|}{ }\\
- \raisebox{1.5ex}[0cm] {Control} &
- \multicolumn{1}{c|}{${\bf v}$ } &
- \multicolumn{1}{c|}{${\bf v}(i,j,m)$} &
- \multicolumn{1}{c|}{${\bf v}(i,j,k)$} &
- \multicolumn{1}{c|}{${\bf v}(l,n,m)$} &
- \multicolumn{1}{c|}{${\bf v}(i,j,m)$}\\
- \raisebox{1.5ex}[0cm] {Variables} &
- \multicolumn{1}{c|}{ } &
- \multicolumn{2}{c|}{ } &
- \multicolumn{1}{c|}{ } &
- \multicolumn{1}{c|}{ }\\
- \hline
-\end{tabular}
-\end{center}
-\caption{The definitions of the various stages of the control
- variable transform given by (\ref{var-cv}) for the unified global/regional
- WRF-Var system. Indices $(i,j,k)$ refer to grid-point
- space, index $m$ to vertical mode, and $l$, $n$ to global spectral mode.
- The variables are: $u, v$: velocity components; $T$: temperature; $q$: mixing ratio;
- $p_s$: surface pressure; $\psi$: streamfunction; $\chi$: velocity potential;
- $r$: relative humidity. The subscript $u$ indicates an unbalanced field. The acronym RF stands for recursive filter.}
-\label{var-cvtable}
-\end{table}
-
-Table \ref{var-cvtable} indicates that the only difference between global (cv$\_$options=4) and WRF
-regional (cv$\_$options=5) versions of the WRF-Var control variable
-transform is in the horizontal error correlations ${\rm U}_{h}$.
-Note also, the only difference between the old MM5
-background error model (cv$\_$options=2) and WRF regional (cv$\_$options=5) is in the
-${\rm U}_{p}$ transform. The former imposes a dynamical balance constraint via an
-unbalanced pressure control variable \citep{barker04}, whereas in the new regional
-covariance model, balance is imposed via statistical regression (see Section \ref{var-be} for
-details). This choice of control variables is considered more appropriate for the
-mass-based ARW solver.
-
\subsection{First Guess at Appropriate Time (FGAT)}
A First Guess at Appropriate Time (FGAT) procedure has been implemented in
@@ -405,7 +294,7 @@
required to specify and implement flow-dependent error covariances in 3/4D-Var is
significant.
-The NMC-method code developed for MM5 3D-Var \citep{barker04} is nearing the
+The NMC-method code developed for MM5 3D-Var \citet{barker04} is nearing the
end of its useful life. The development of a unified global/regional WRF-Var system, and
its application to a variety of models (e.g., ARW, MM5, KMA global model,
Taiwan's Nonhydrostatic Forecast System [NFS]) has
@@ -552,7 +441,7 @@
control variable transform. This calculation involves the projection
of 3D fields on model-levels onto empirical orthogonal functions
(EOFs) of the vertical component of background error covariances
-\citep{barker04}. For each 3D control variable ($\psi$, $\chi_u$,
+\citet{barker04}. For each 3D control variable ($\psi$, $\chi_u$,
$T_u$, and $r$), the vertical component of ${\bf B}$, is calculated
and an eigenvector decomposition performed. The resulting eigenvectors
${\bf E}$ and eigenvalues $\Lambda$ are saved for use in WRF-Var.
@@ -570,7 +459,7 @@
statistics are included in the dataset supplied to WRF-Var, allowing
the choice between homogeneous (domain-averaged) or local
(inhomogeneous) background error variances and vertical correlations
-to be chosen at run time \citep{barker04}.
+to be chosen at run time \citet{barker04}.
Having calculated and stored eigenvectors and eigenvalues, the final
part of {\it gen$\_$be$\_$stage3} is to project the entire sequence of
3D control variable fields into EOF space ${\bf v_v}=U_{v}^{-1}{\bf
@@ -594,3 +483,45 @@
as described in \citet{barker04} to provide correlation lengthscales
for use in the recursive filter algorithm.
+\section{WRF-Var V3.0 Software Engineering Improvements}
+\label{se}
+
+A major overhall of the WRF-Var software has been performed for V3.0. The following
+is a summary:
+
+\subsection{Memory improvements}
+
+The WRF-Var registry had become bloated with WRF and U4D-Var 2d and 3d state variables that were unused in
+3D-Var applications. These variables were allocated but uninitialised, and written to the analysis files. The removal
+of these dummy variable has resulted in a significant (10-50\% depending on application) reduction in the memory
+requirements of WRF-Var.
+
+\subsection{Four-Byte I/O}
+
+The WRF-Var algorithm requires eight-byte precision internally. However, it only needs to read and write 4-byte files.
+Switching from 8-byte to 4-byte output in V3.0 has improved I/O performance and halves file sizes.
+
+\subsection{Switch from RSL to RSL\_LITE}
+
+The switch from RSL to RSL\_LITE has been made in V3.0 as the latter possesses
+a simpler "lighter" communications layer, and has been shown to be scalable
+to arbitrary domain sizes (largest to date: 4500x4500) and numbers of processors
+(largest to date: 64K processors on Blue Gene). RSL\_LITE supports all capabilities of WRF,
+including Halo and periodic boundary exchanges, Distributed I/O, Nesting and moving nests,
+and parallel transposes. RSL\_LITE has also been simplified by dropping irregular decomposition,
+load balancing, and ragged edge nesting, and the initialisation techniques improved
+to avoid recalculation and give better scaling at higher processor counts.
+
+\subsection{Reorganisation of observation structures}
+
+The F90 derived data types used for observations have been rewritten to permit batches
+of observations to be passed to subroutine calls, especially interpolation ones and
+subsequently makes better use of cache memory.
+
+\subsection{Radar reflectivity operators redesigned}
+
+The efficiency of the coding of the radar observation operators has been improved.
+Previously, routines were called once per observation, which would then recalculate common
+factors before performing what was often just a one-line calculation. Re-writing the code
+in V3.0 to move the calculations inside loops in the calling routine allows them to work
+on batches of observations at a time, vastly improving cache hit rates and eliminating recalculation.
</font>
</pre>