<p><b>kavulich@ucar.edu</b> 2013-05-02 16:36:15 -0600 (Thu, 02 May 2013)</p><p>-Continuing work on quick-start chapter <br>
-Merging information from WRFV3 tech note. Much of this will not make the final cut, but should be a helpful guide<br>
</p><hr noshade><pre><font color="gray">Modified: trunk/wrfvar/3DVAR_technote/3dvar.tex
===================================================================
--- trunk/wrfvar/3DVAR_technote/3dvar.tex 2013-05-02 22:27:52 UTC (rev 427)
+++ trunk/wrfvar/3DVAR_technote/3dvar.tex 2013-05-02 22:36:15 UTC (rev 428)
@@ -4,7 +4,16 @@
\section{Running WRFDA\textendash 3DVAR}
\label{running}
+\section{Minimization}
+\label{minim}
+Unlike the QNM technique, the CGM method restricts WRF-Var's inner loop to be completely linear. This limitation is dealt with through the inclusion of an outer loop in WRF-Var, the purpose of which is to iterate towards nonlinear solutions (e.g., observation operators, balance constraints, and the forecast itself in 4D-Var) using the WRF-Var analysis from the previous iteration as new first guess. The outer loop is also used as a form of variational quality control as follows: observations are rejected if the magnitude of the observation minus first guess differences are larger than a specified threshold (typically several times the observation error standard deviation). This {\it errormax} test implicitly assumes the first guess is accurate. However, in cases when this assumption breaks down (i.e. in areas of large forecast error), there is a danger that good observations might be rejected in areas where they are most valuable. The outer loop alleviates this effect by allo
wing observations rejected in previous iterations to be accepted if their updated observation minus analysis differences pass the errormax QC check in in subsequent outer loops. The assimilation of nearby observations in previous iterations essentially provides a ``buddy check" to the observation in question.
+
\section{Output}
\label{output}
-We should detail ALL the output files and what the options mean
\ No newline at end of file
+We should detail ALL the output files and what the options mean
+
+\section{Radar Data Assimilation}
+\label{radar}
+
+A capability to assimilate Doppler radar radial velocity and reflectivity observations is available in WRF-Var \citep{xiao05, xiao07, xiao072, xiao08}. In order to calculate the vertical velocity increment as a result of assimilating the vertical velocity component of radial velocity, the Richarson balance equation, which combines the continuity equation, adiabatic thermodynamic equation and hydrostatic relation, and its linear and adjoint codes are introduced. For reflectivity assimilation, total water is used as a control variable. This requires a partitioning between water vapor and hydrometeor increments during the minimization procedure. A warm-rain parameterization is included to assist the calculation of hydrometeors, which includes condensation of water vapor into cloud, accretion of cloud by rain, automatic conversion of cloud to rain, and evaporation of rain to water vapor. The observation operators for Doppler radial velocity and reflectivity are included.
Modified: trunk/wrfvar/3DVAR_technote/be.tex
===================================================================
--- trunk/wrfvar/3DVAR_technote/be.tex 2013-05-02 22:27:52 UTC (rev 427)
+++ trunk/wrfvar/3DVAR_technote/be.tex 2013-05-02 22:36:15 UTC (rev 428)
@@ -2,8 +2,30 @@
\label{be}
+\subsection{Choice of control variables}
+\label{var-cvs}
+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.,
+\begin{equation}
+{\bf x}' = {\rm U}{\bf v}= {\rm U}_{p} {\rm U}_{v} {\rm U}_{h}{\bf v}.
+\label{var-cv}
+\end{equation}
+
+The expansion ${\rm U}={\rm U}_{p}
+{\rm U}_{v} {\rm U}_{h}$ represents the various stages of covariance modeling: horizontal correlations ${\rm U}_{h}$, vertical covariances ${\rm U}_{v}$, and multivariate covariances
+${\rm U}_{p}$.
+
+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 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}.
+
+
\section{Overview}
Forecast (first guess or background) error covariances are a vital input to any modern data assimilation system. They influence the analysis fit to observations and also completely define the analysis response away from observations. The latter impact is particularly important in data-sparse areas of the globe. Unlike ensemble filter data assimilation techniques (e.g. the Ensemble Adjustment Kalman Filter, the Ensemble Transform Kalman Filter), 3/4D-Var systems do not implicitly evolve forecast error covariances in real-time. Instead, climatologic statistics are typically estimated offline, and tuned to represent forecast errors for particular applications. This document describes the generation and tuning of forecast error covariances for the WRF-Var system.
Modified: trunk/wrfvar/3DVAR_technote/description.tex
===================================================================
--- trunk/wrfvar/3DVAR_technote/description.tex 2013-05-02 22:27:52 UTC (rev 427)
+++ trunk/wrfvar/3DVAR_technote/description.tex 2013-05-02 22:36:15 UTC (rev 428)
@@ -76,8 +76,6 @@
\setcounter{page}{1}
\include{quickstart}
\include{intro}
-\include{basics}
-\include{installation}
\include{obs}
\include{be}
\include{3dvar}
Modified: trunk/wrfvar/3DVAR_technote/intro.tex
===================================================================
--- trunk/wrfvar/3DVAR_technote/intro.tex 2013-05-02 22:27:52 UTC (rev 427)
+++ trunk/wrfvar/3DVAR_technote/intro.tex 2013-05-02 22:36:15 UTC (rev 428)
@@ -1,6 +1,8 @@
\chapter{Introduction}
\label{intro}
+This overview supplements the original description of the three-dimensional variational (3D-Var) algorithm found in \citet{barker04}.
+
Data assimilation is the technique by which \textbf{observations} are combined with an NWP product (the \textbf{first guess} or background forecast) and their respective error statistics to provide an improved estimate (the \textbf{analysis}) of the atmospheric (or oceanic, Jovian, etc.) state. Variational (Var) data assimilation achieves this through the iterative minimization of a prescribed cost (or penalty) function. Differences between the analysis and observations/first guess are penalized (damped) according to their perceived error.
The MMM Division of NCAR supports a unified (global/regional, multi-model, 3/4D-Var) model-space data assimilation system (WRFDA) for use by the NCAR staff and collaborators, and is also freely available to the general community, together with further documentation, test results, plans etc., from the WRFDA web-page (\url{http://www.mmm.ucar.edu/wrf/users/wrfda/index.html}).
Various components of the WRFDA system are shown in blue in the sketch below, to-gether with their relationship with the rest of the WRF system.
@@ -8,9 +10,53 @@
\section{Overview of Variational Data Assimilation}
\label{overview}
+The basic goal of any variational data assimilation system is to produce an optimal estimate of the true atmospheric state at analysis time through iterative solution of a prescribed cost-function \citep{ide97}:
+
+\begin{equation}
+J({\bf x}) = J_b({\bf x}) + J_o({\bf x}) = \frac{1}{2
+} ({\bf x}-{\bf x}^{b})^{T}{\bf B}^{-1}({\bf x}-{\bf x}^{b}) +
+\frac{1}{2}
+({\bf y}-{\bf y}^{o})^{T}({\bf E+F})^{-1}({\bf y}-{\bf y}^{o}).
+\label{cost_function}
+\end{equation}
+
+The variational problem can be summarized as the iterative minimization of (\ref{cost_function}) to find the analysis state ${\bf x}$ that minimizes $J({\bf x})$. This solution represents the {\it a posteriori} maximum likelihood (minimum variance) estimate of the true state of the atmosphere given the two sources of {\it a priori} data: the first guess (or background) ${\bf x^{b}}$ and observations ${\bf y^{o}}$ \citep{lorenc86}. The fit to individual data points is weighted by estimates of their errors: ${\bf B}$, ${\bf E}$, and ${\bf F}$ are the background, observation (instrumental), and representivity error covariance matrices, respectively. Representivity error is an estimate of inaccuracies introduced in the observation operator $H$ used to transform the gridded analysis ${\bf x}$ to observation space ${\bf y}=H({\bf x})$ for comparison against observations. This error will be resolution dependent and may also include a contribution from approximations (e.g., lineariz
ations) in $H$.
+
\section{Overview of WRFDA}
\label{overview-wrfda}
+
+As described in \citet{barker04}, the particular variational data assimilation algorithm adopted in WRF-Var is a model-space, incremental formulation of the variational problem. In this approach, observations, previous forecasts, their errors, and physical laws are combined to produce analysis increments ${\bf x^{a'}}$, which are added to the first guess ${\bf x^{b}}$ to provide an updated analysis.
+
+Figure \ref{var-sketch} illustrates the relationship between WRF-Var, the various datasets, and the other components of a typical NWP system (here ARW). The WRF-Var assimilation proceeds as described in \citet{barker04}. A number of recent upgrades to the WRF-Var algorithm will be described in Section \ref{var-upgrade}.
+
+%
+% Figure 9.1 WRFDA flowchart
+%
+\begin{figure}
+ \centering
+ \includegraphics[width=6.5in]{figures/wrfda_flowchart.pdf}
+ \caption{\label{var-sketch}Sketch showing the relationship between datasets (circles),
+ and algorithms (rectangles) of the ARW system.}
+\end{figure}
+
+The three inputs to WRF-Var are:
+
+\vspace{0.5cm}
+
+a) First guess ${\bf x^{b}}$--- In cold-start mode, this is typically a forecast/analysis from another model interpolated to the ARW grid (and variables) via the WRF SI and {\it real} programs. In cycling mode, the first guess is a short-range (typically 1--6 hour) ARW forecast.
+
+\vspace{0.5cm}
+
+b) Observations ${\bf y^{o}}$--- In the current version of WRF-Var, observations may be supplied either in PREPBUFR format ({\it ob\_format=1}) or an ASCII "little\_r" format ({\it ob\_format=2}). An observation preprocessor (3DVAR$\_$OBSPROC) is supplied with the code release to perform basic quality control, assign "total" observation errors (${\bf R = E+F}$ in Fig. \ref{var-sketch}), and reformat observations from the MM5 {\it little$\_$r} text format into 3D-Var's own text format. Details can be found in \citet{barker03, barker04}.
+
+\vspace{0.5cm}
+
+c) Background error covariances ${\bf B}$--- used to define the spatial and multivariate response of the analysis to an observation. In variational systems, these covariances are typically calculated off-line, and significant tuning is required to optimize performance for a particular application (e.g., \citet{ingleby01, wu02}). The amount of work required to do this satisfactorily is significant, and should not be underestimated. In order to assist the user, WRF developers supply the following: i) a default set of statistics used for the initial set up of a domain; ii) a utility {\it gen$\_$be} (described in Section \ref{var-be}) to process ensembles of forecasts into the appropriate control variable space; and iii) diagnostic routines to assess the accuracy of observation and background error statistics. These routines include both innovation vector-based approaches \citep{hollingsworth86} and variational tuning approaches \citep{desroziers01}.
+
+Following assimilation of all data, an analysis ${\bf x^{a}}$ is produced that must be merged with the existing lateral boundary conditions ${\bf x^{lbc}}$ in the {\it WRF\_BC} utility (\citet{barker03}). At this stage, the {\it wrfbdy} lateral boundary condition files (${\bf x^{lbc}}$) output of WPS/real is updated to make the lateral boundaries consistent with the analysis, and surface fields (e.g. SST) are also updated in the {\it wrfinput} analysis file.
+
+
\subsection{System requirements}
\label{system_requirements}
Modified: trunk/wrfvar/3DVAR_technote/obs.tex
===================================================================
--- trunk/wrfvar/3DVAR_technote/obs.tex 2013-05-02 22:27:52 UTC (rev 427)
+++ trunk/wrfvar/3DVAR_technote/obs.tex 2013-05-02 22:36:15 UTC (rev 428)
@@ -4,7 +4,7 @@
Guo, Rizvi
\section{Observation Preprocessing}
-In general, the observation processing system can be separated into 3 modules: 1) the decoder module to convert the observations in a variety of format from the external sources to a decoder format file, i.e. LITTLE\_R format here; 2) the 3DVAR\_OBSPROC module to perform the functions for which the first guess field information is not required; and 3) the WRFVar observation processing module to perform the functions for which the first guess field information is required. In this section, only the second one, 3DVAR\_OBSPROC, is discussed. The first one, the decoder module development, is the user's responsibility, and the third one, WRFVar observation processing such as innovation calculation, background check, etc., is included in the WRFVar code (\ref{xx}). The observation preprocessor program, 3DVAR\_OBSPROC, is coded with the Fortran-90.
+In general, the observation processing system can be separated into 3 modules: 1) the decoder module to convert the observations in a variety of format from the external sources to a decoder format file, i.e. LITTLE\_R format here; 2) the 3DVAR\_OBSPROC module to perform the functions for which the first guess field information is not required; and 3) the WRFVar observation processing module to perform the functions for which the first guess field information is required. In this section, only the second one, 3DVAR\_OBSPROC, is discussed. The first one, the decoder module development, is the user's responsibility, and the third one, WRFVar observation processing such as innovation calculation, background check, etc., is included in the WRFVar code (\ref{xx}). The observation preprocessor program, 3DVAR\_OBSPROC, is coded with the Fortran-90.
The observation preprocessing, 3DVAR\_OBSPROC, provides the "conventional" observations ${\it{Y^o}}$ for ingest into WRF-Var. Here the "conventional" observations include not only the synoptic data, such as TEMP, SYNOP, etc., but also some of the retrievals from satellite measurements, such as SATEM, QuikSCAT, AIRS, Ground-based GPSPW(ZTD), and Space-born GPS refractivity, and SSMI, etc. Currently, the 3DVAR\_OBSPROC supports 21 types of observations, each type is assigned with the WMO code as listed in the table 5.1. The 2-digit codes are standard WMO code, and the 3-digit codes are the expansion in 3DVAR\_OBSPROC.
@@ -59,13 +59,13 @@
19 & AIRSRET & 133 & AIRS retrieved soundings \\
\hline
20 & BOGUS & 135 & Bogus soundings \\
-\hline
+\hline
21 & QSCAT & 281 & QuikSCAT ocean surface wind \\
\hline
\end{tabular}
\end{center}
\vspace*{-5mm}
-\end{table}
+\end{table}
\subsection{Input files}
@@ -73,12 +73,12 @@
The {\it{namelist.3dvar\_obs}} file provides the necessary information to 3DVAR\_OBSPROC program, which contains nine records (see Appendix ). The most important informations are the LITTLE\_R observation filename, analysis time window, geographic location, and the analysis domain setting, etc. In this new released version of 3DVAR\_OBSPROC, an additional namelist-record, ${\it{record9}}$, indicates the format to the processed observation output file: prebufr, ascii, or both. Users must carefully edit this {\it{namelist.3dvar\_obs}} file to meet the requirements of the applications prior to run 3DVAR\_OBSPROC.
-The observation data file to input 3DVAR\_OBSPROC must be in LITTLE\_R format. The LITTLE\_R file is a report-based ascii file, all observation reports can be merged together, in any order, to form a LITTLE\_R file. A complete description of LITTLE\_R format can be found from $${http://www.mmm.ucar.edu/mm5/documents/MM5\_tut\_Web\_notes/OA/OA.htm}$$ in section 6.12. In this 3DVar application, the ground-based GPS PW (precipitable water) is included in end of the header record. Optionally, if there are 7-channel SSMI brightness temperature available, they should be included in end part of the header record after GPS PW.
+The observation data file to input 3DVAR\_OBSPROC must be in LITTLE\_R format. The LITTLE\_R file is a report-based ascii file, all observation reports can be merged together, in any order, to form a LITTLE\_R file. A complete description of LITTLE\_R format can be found from $${http://www.mmm.ucar.edu/mm5/documents/MM5\_tut\_Web\_notes/OA/OA.htm}$$ in section 6.12. In this 3DVar application, the ground-based GPS PW (precipitable water) is included in end of the header record. Optionally, if there are 7-channel SSMI brightness temperature available, they should be included in end part of the header record after GPS PW.
The LITTLE\_R file is easy to be manipulated by hand, for example, add or remove certain reports from a LITTLE\_R file to identify the impacts of those reports. However, the size of the ascii file is too large for some of the remote sensing data, thus it is hard to be transferred.
-
-Currently except the Radar and satellite radiance data, the space-born GPS Radio-Occultation observation in BUFR format, SSMI brightness temperature in HDF format, etc., can also be converted to LITTLE\_R format data and processed by 3DVAR\_OBSPROC (\ref{GPSRO}).
+Currently except the Radar and satellite radiance data, the space-born GPS Radio-Occultation observation in BUFR format, SSMI brightness temperature in HDF format, etc., can also be converted to LITTLE\_R format data and processed by 3DVAR\_OBSPROC (\ref{GPSRO}).
+
The observation error statistics file, ${\it{obserr.txt}}$, provided by our preprocessor includes the error specifications for 15 types of observations: SYNOP, SHIP, BUOY, METAR, PILOT, PROFILER, SOUND, SATEM, SATOB, AIREP, SSMI, AIRS, TOVS, SSMT1, and SSMT2, for the different observed parameters. For some types of observations, such as GPS PW (\ref{GPSPW}) and QuikSCAT sea surface wind (\ref{ascii}), the observation errors may be available from the LITTLE\_R file. If not available, a default observation errors will be assigned by 3DVAR\_OBSPROC.
The ${\it{prebufr\ table\ file}}$ provided by 3DVAR\_OBSPROC is used to write out a ${\it{prebufr}}$ format observation file (\ref{bufr}). When a new type of observation is introduced, this table file must be edited, otherwise that new type of observation will not be contained in the prebufr observation file although it is included in the ascii observation file.
@@ -87,7 +87,7 @@
\begin{itemize}
-\item
+\item
Read the namelist file and the LITTLE\_R observation data file and screen the observations
\vspace*{2mm}
@@ -101,7 +101,7 @@
Sort and the duplication check of the observations
\vspace*{2mm}
-To prepare the sort and duplication check of the observations, the pressure need to be recovered if it is missing at certain levels. Basically, this is done under two situations: (1) if both of pressure and height can be found at the levels above and below the missing level, $p1$, $p2$ and $h1$, $h2$, then from data at these two levels, the mean temperature, $T_m$, between them can be computed and
+To prepare the sort and duplication check of the observations, the pressure need to be recovered if it is missing at certain levels. Basically, this is done under two situations: (1) if both of pressure and height can be found at the levels above and below the missing level, $p1$, $p2$ and $h1$, $h2$, then from data at these two levels, the mean temperature, $T_m$, between them can be computed and
\begin{equation}
%$$
@@ -123,12 +123,14 @@
duplication check easier and faster.
-
+
\end{itemize}
\section{Observation Quality Control}
+The original WRF 3D-Var system described in \citet{barker04} used height interpolation for all observation operators. If an observation is reported as a function of pressure, then height is approximated using the hydrostatic relation. This step introduces an unnecessary source of error. The new WRF-Var system performs vertical interpolation in terms of the original observed coordinate, i.e., pressure or height.
+
\section{Observation Data Formats}
\subsection{BUFR}
@@ -137,6 +139,5 @@
\subsection{ASCII format}
\label{ascii}
-
\section{First Guess at Appropriate Time}
Modified: trunk/wrfvar/3DVAR_technote/quickstart.tex
===================================================================
--- trunk/wrfvar/3DVAR_technote/quickstart.tex 2013-05-02 22:27:52 UTC (rev 427)
+++ trunk/wrfvar/3DVAR_technote/quickstart.tex 2013-05-02 22:36:15 UTC (rev 428)
@@ -7,11 +7,13 @@
\section*{Installing WRFDA}
\label{quick-install}
-\subsubsection*{Obtaining the WRFDA source code}
+\subsubsection*{Obtaining the WRFDA source code and test data}
\label{quick-source}
Users can download the WRFDA source code from \url{http://www.mmm.ucar.edu/wrf/users/wrfda/download/get_source.html}. You will be required to register (for free) with an email address (which will be kept confidential) before downloading the code. After the source code has been downloaded, it must be unzipped (gunzip WRFDAV3.5.TAR.gz) and untarred (tar -xf WRFDAV3.5.TAR), which should result in the \texttt{WRFDA} directory being created.
+It is also strongly recommended that users download the WRFDA test data set.
+
\subsubsection*{Setting your system environment}
\label{quick-env}
@@ -37,4 +39,32 @@
It is also possible to use RTTOV, which is a different RTM maintained by EUMETSAT. For this and other details about RTMs see the section ``Radiative Transfer Models'' (\ref{RTM})
-
\ No newline at end of file
+\subsubsection*{Configure your installation for your machine}
+\label{quick-config}
+
+Enter the \texttt{WRFDA} directory and run the configure script:
+
+\begin{verbatim}
+ > cd WRFDA
+ > ./configure wrfda
+\end{verbatim}
+
+A list of configuration options should appear. Each option lists an operating system, a compiler type, and a parallelism option. Since the configuration script doesn't check which compilers are actually installed on your system, be sure to select only among the options that you have available to you. The available parallelism options are single-processor (serial), shared-memory parallel (smpar), distributed-memory parallel (dmpar), and distributed-memory with shared-memory parallel (sm+dm). However, shared-memory (smpar and sm+dm) options are not supported as of WRFDA Version 3.5, so we do not recommend selecting these options.
+
+\subsubsection*{Configure your installation for your machine}
+\label{quick-compile}
+
+To compile WRFDA, run the following command:
+
+\begin{verbatim}
+ > ./compile all_wrfvar >& compile.out
+\end{verbatim}
+
+To check for successful compilation, run the command:
+
+\begin{verbatim}
+>ls -l var/build/*exe var/obsproc/src/obsproc.exe
+\end{verbatim}
+
+If the compilation was successful, this command should list 44 executables. The main WRFDA executable is \texttt{da\_wrfvar.exe}; ensure this has been created before continuing.
+
Modified: trunk/wrfvar/3DVAR_technote/var.tex
===================================================================
--- trunk/wrfvar/3DVAR_technote/var.tex 2013-05-02 22:27:52 UTC (rev 427)
+++ trunk/wrfvar/3DVAR_technote/var.tex 2013-05-02 22:36:15 UTC (rev 428)
@@ -1,202 +1,42 @@
\chapter{Variational Data Assimilation}
\label{var_chap}
-An introduction to the basic ideas of variational data assimilation and
-the WRF-Var system is given in this chapter, followed by a brief
-overview of recent major improvements to WRF-Var. This overview
-supplements the original description of the three-dimensional
-variational (3D-Var) algorithm found in \citet{barker04}. One of the
-most important additions to WRF-Var is a new utility {\it gen$\_$be},
-used to calculate background error covariances for a user's own
-application; it is discussed in the latter half of this chapter. The
-WRF-Var system is evolving rapidly,
-and a future technical note will accompany the general release of the
-4D-Var component of WRF-Var. That technical note will include an
-extensive description of the entire WRF-Var system.
\section{Introduction}
\label{var-intro}
-The basic goal of any variational data assimilation system is to produce
-an optimal estimate of the true atmospheric state at analysis time
-through iterative solution of a prescribed cost-function \citep{ide97}:
-\begin{equation}
-J({\bf x}) = J_b({\bf x}) + J_o({\bf x}) = \frac{1}{2
-} ({\bf x}-{\bf x}^{b})^{T}{\bf B}^{-1}({\bf x}-{\bf x}^{b}) +
-\frac{1}{2}
-({\bf y}-{\bf y}^{o})^{T}({\bf E+F})^{-1}({\bf y}-{\bf y}^{o}).
-\label{cost_function}
-\end{equation}
-The variational problem can be summarized as the iterative minimization
-of (\ref{cost_function}) to find the analysis state ${\bf x}$ that
-minimizes $J({\bf x})$. This solution represents the {\it a posteriori}
-maximum likelihood (minimum variance) estimate of the true state of the
-atmosphere given the two sources of {\it a priori} data: the first guess
-(or background) ${\bf x^{b}}$ and observations ${\bf y^{o}}$
-\citep{lorenc86}. The fit to individual data points is weighted by
-estimates of their errors: ${\bf B}$, ${\bf E}$, and ${\bf F}$ are the
-background, observation (instrumental), and representivity error
-covariance matrices, respectively. Representivity error is an estimate of
-inaccuracies introduced in the observation operator $H$ used to
-transform the gridded analysis ${\bf x}$ to observation space ${\bf
-y}=H({\bf x})$ for comparison against observations. This error will be
-resolution dependent and may also include a contribution from
-approximations (e.g., linearizations) in $H$.
-
-As described in \citet{barker04}, the particular variational data
-assimilation algorithm adopted in WRF-Var is a model-space, incremental
-formulation of the variational problem. In this approach, observations,
-previous forecasts, their errors, and physical laws are combined to
-produce analysis increments ${\bf x^{a'}}$, which are added to the first
-guess ${\bf x^{b}}$ to provide an updated analysis.
-
-Figure \ref{var-sketch} illustrates the relationship between WRF-Var,
-the various datasets, and the other components of a typical NWP system
-(here ARW). The WRF-Var assimilation proceeds as described in
-\citet{barker04}. A number of recent upgrades to the WRF-Var algorithm
-will be described in Section \ref{var-upgrade}.
-
-%
-% Figure 9.1 var-sketch
-%
-\begin{figure}
- \centering
- \includegraphics[width=6.5in]{figures/var-sketch.pdf}
- \caption{\label{var-sketch}Sketch showing the relationship between datasets (circles),
- and algorithms (rectangles) of the ARW system.}
-\end{figure}
-
-The three inputs to WRF-Var are:
-
-\vspace{0.5cm}
-
-a) First guess ${\bf x^{b}}$--- In cold-start mode, this is typically a
-forecast/analysis from another model interpolated to the ARW grid (and variables) via the
-WRF SI and {\it real} programs. In cycling mode, the first guess
-is a short-range (typically 1--6 hour) ARW forecast.
-
-\vspace{0.5cm}
-
-b) Observations ${\bf y^{o}}$--- In the current version of WRF-Var, observations may be
-supplied either in PREPBUFR format ({\it ob\_format=1}) or an ASCII "little\_r" format
-({\it ob\_format=2}). An observation preprocessor (3DVAR$\_$OBSPROC)
-is supplied with the code release to perform basic quality control, assign "total"
-observation errors (${\bf R = E+F}$ in Fig. \ref{var-sketch}), and reformat observations from the MM5 {\it little$\_$r} text
-format into 3D-Var's own text format. Details can be found in \citet{barker03, barker04}.
-
-\vspace{0.5cm}
-
-c) Background error covariances ${\bf B}$--- used to define the spatial
-and multivariate response of the analysis to an observation. In
-variational systems, these covariances are typically calculated
-off-line, and significant tuning is required to optimize performance
-for a particular application (e.g., \citet{ingleby01, wu02}). The
-amount of work required to do this satisfactorily is significant, and
-should not be underestimated. In order to assist the user, WRF
-developers supply the following: i) a default set of statistics used
-for the initial set up of a domain; ii) a utility {\it gen$\_$be}
-(described in Section
-\ref{var-be}) to process ensembles of forecasts into the appropriate control variable
-space; and iii) diagnostic routines to assess the accuracy of
-observation and background error statistics. These routines include
-both innovation vector-based approaches \citep{hollingsworth86} and
-variational tuning approaches \citep{desroziers01}.
-
-Following assimilation of all data, an analysis ${\bf x^{a}}$ is produced that must be
-merged with the existing lateral boundary conditions ${\bf x^{lbc}}$ in the {\it WRF\_BC}
-utility (\citet{barker03}). At this stage, the {\it wrfbdy} lateral boundary condition
-files (${\bf x^{lbc}}$) output of WPS/real is updated to make the lateral boundaries consistent with the analysis, and surface fields (e.g. SST) are also updated in the {\it wrfinput} analysis file.
-
\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,
+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
-interpolation for all observation operators. If an observation is reported as a
-function of pressure, then height is approximated using the
-hydrostatic relation. This step introduces an unnecessary source of error.
-The new WRF-Var system performs vertical interpolation in terms of the
-original observed coordinate, i.e., pressure or height.
\subsection{Improved minimization and ``outer loop"}
-Prior to WRF-Var V3.0, the default WRF-Var cost function minimization used a modified
-version of the limited memory Quasi-Newton Method (QNM). In V3.0, an alternative
-Conjugate Gradient Method (CGM) has been implemented. Unlike the QNM technique,
-the CGM method restricts WRF-Var's inner loop to be completely linear. This limitation is dealt
-with through the inclusion of an outer loop in WRF-Var, the purpose of which is to iterate towards
-nonlinear solutions (e.g., observation operators, balance constraints, and the forecast itself in
-4D-Var) using the WRF-Var analysis from the previous iteration as new first guess. The
-outer loop is also used as a form of variational quality control as follows: observations are
-rejected if the magnitude of the observation minus first guess differences are larger than a
-specified threshold (typically several times the observation error standard deviation). This {\it errormax} test implicitly assumes the first guess is accurate. However, in cases when this assumption breaks
-down (i.e. in areas of large forecast error), there is a danger that good observations might be rejected in areas where they are most valuable. The outer loop alleviates this effect by allowing observations
-rejected in previous iterations to be accepted if their updated observation minus analysis differences
-pass the errormax QC check in in subsequent outer loops. The assimilation of nearby observations in previous iterations essentially provides a ``buddy check" to the observation in question.
-
-\subsection{Choice of control variables}
-\label{var-cvs}
+Prior to WRF-Var V3.0, the default WRF-Var cost function minimization used a modified
+version of the limited memory Quasi-Newton Method (QNM).
-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.,
-\begin{equation}
-{\bf x}' = {\rm U}{\bf v}= {\rm U}_{p} {\rm U}_{v} {\rm U}_{h}{\bf v}.
-\label{var-cv}
-\end{equation}
-
-The expansion ${\rm U}={\rm U}_{p}
-{\rm U}_{v} {\rm U}_{h}$ represents the various stages of covariance modeling: horizontal correlations ${\rm U}_{h}$, vertical covariances ${\rm U}_{v}$, and multivariate covariances
-${\rm U}_{p}$.
-
-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 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}.
-
\subsection{First Guess at Appropriate Time (FGAT)}
-A First Guess at Appropriate Time (FGAT) procedure has been implemented in
+A First Guess at Appropriate Time (FGAT) procedure has been implemented in
WRF-Var \citep{lee04}.
- The FGAT capability results in a more accurate calculation of innovation vectors
-(observation minus first guess difference), and hence a better use of observations when
-their valid time differs from that of the analysis.
-FGAT is most effective for the analysis of observations from
+ The FGAT capability results in a more accurate calculation of innovation vectors
+(observation minus first guess difference), and hence a better use of observations when
+their valid time differs from that of the analysis.
+FGAT is most effective for the analysis of observations from
asynoptic, moving platforms (e.g., aircraft and satellite data).
-\subsection{Radar Data Assimilation}
-A capability to assimilate Doppler radar radial velocity
-and reflectivity observations is available in WRF-Var
-\citep{xiao05, xiao07, xiao072, xiao08}.
-In order to calculate the vertical velocity increment as a result of
-assimilating the vertical velocity component of radial velocity,
-the Richarson balance equation, which combines the continuity
-equation, adiabatic thermodynamic equation and hydrostatic
-relation, and its linear and adjoint codes are introduced.
-For reflectivity assimilation, total water is used as a control variable.
-This requires a partitioning
-between water vapor and hydrometeor increments during the minimization procedure.
-A warm-rain parameterization is included to assist the calculation
-of hydrometeors, which includes condensation of water vapor
-into cloud, accretion of cloud by rain, automatic
-conversion of cloud to rain, and evaporation of rain to water vapor.
-The observation operators for Doppler radial velocity
-and reflectivity are included.
-
\subsection{Unified Regional/Global 3D-Var Assimilation}
There are many benefits to having a single data assimilation system
@@ -233,47 +73,47 @@
control variables or 4D-Var. Research using the latter techniques is
underway using the WRF-Var system.
-The WRF-Var code has been adapted to perform assimilation on a global, regular
+The WRF-Var code has been adapted to perform assimilation on a global, regular
latitude-longitude grid. The major modifications are as follows.
\vspace{0.5cm}
-a) Spectral to grid-point transformations (and their adjoints) have been included in 3D-Var
-to represent the horizontal component (${\rm U}_h$) of the background error covariance
+a) Spectral to grid-point transformations (and their adjoints) have been included in 3D-Var
+to represent the horizontal component (${\rm U}_h$) of the background error covariance
model.
\vspace{0.5cm}
-b) A new global WRF-Var registry was created to accommodate the
-output of global forecast models (currently only the Korean Meteorological
-Administration's (KMA) global model has been tested).
-The final analysis increments are written in binary format and added back to the global
+b) A new global WRF-Var registry was created to accommodate the
+output of global forecast models (currently only the Korean Meteorological
+Administration's (KMA) global model has been tested).
+The final analysis increments are written in binary format and added back to the global
first guess to provide the global analysis in the native model format.
\vspace{0.5cm}
-c) Changes have been made to allow for periodic boundary conditions in the East--West
+c) Changes have been made to allow for periodic boundary conditions in the East--West
direction.
\vspace{0.5cm}
-d) A number of minor changes have been made to treat the polar rows as special points
-(e.g., in the grid-point $\psi, \chi$ to $u,v$ wind conversion in the ${\rm U}_p$ transform and the
+d) A number of minor changes have been made to treat the polar rows as special points
+(e.g., in the grid-point $\psi, \chi$ to $u,v$ wind conversion in the ${\rm U}_p$ transform and the
observation operators for polar winds).
\section{Background Error Covariances}
\label{var-be}
-Forecast (``first guess" or ``background") error covariances are a vital input to variational
-data assimilation systems. They influence the analysis fit to observations and also
-completely define the analysis response away from observations. The latter impact is
-particularly important in data-sparse areas of the globe. Unlike ensemble filter data
-assimilation techniques (e.g., the Ensemble Adjustment Kalman Filter, the Ensemble
-Transform Kalman Filter), 3/4D-Var systems do not explicitly evolve forecast error
-covariances in real-time (although both 4D-Var and hybrid variational/ensemble data assimilation techniques currently being developed within WRF-Var implement flow-dependent covariances implicitly). Instead, climatologic statistics are usually estimated offline.
-The ``NMC-method", in which forecast error covariances are approximated using
-forecast difference (e.g., T+48 minus T+24) statistics, is a commonly used approach
-\citep{parrish92}. Experiments at ECMWF \citep{fisher03} indicate superior statistics may
+Forecast (``first guess" or ``background") error covariances are a vital input to variational
+data assimilation systems. They influence the analysis fit to observations and also
+completely define the analysis response away from observations. The latter impact is
+particularly important in data-sparse areas of the globe. Unlike ensemble filter data
+assimilation techniques (e.g., the Ensemble Adjustment Kalman Filter, the Ensemble
+Transform Kalman Filter), 3/4D-Var systems do not explicitly evolve forecast error
+covariances in real-time (although both 4D-Var and hybrid variational/ensemble data assimilation techniques currently being developed within WRF-Var implement flow-dependent covariances implicitly). Instead, climatologic statistics are usually estimated offline.
+The ``NMC-method", in which forecast error covariances are approximated using
+forecast difference (e.g., T+48 minus T+24) statistics, is a commonly used approach
+\citep{parrish92}. Experiments at ECMWF \citep{fisher03} indicate superior statistics may
be obtained using a cycling analysis/forecast ensemble prediction
system based on perturbed observations/physics.
@@ -281,61 +121,61 @@
covariances in 3D/4D-Var through, for example, grid transformations
\citep{desroziers97}, anisotropic recursive filters
\citep{wu02, purser03},
-or observation-space formulations of the variational
-problem \citep{daley01}. Flow-dependence may be enhanced in 4D-Var
-through the use of the forecast model to provide dynamical consistency to the evolving
-forecast state during 4D-Var's time window \citep{rabier98}. Still, the practical effort
-required to specify and implement flow-dependent error covariances in 3/4D-Var is
+or observation-space formulations of the variational
+problem \citep{daley01}. Flow-dependence may be enhanced in 4D-Var
+through the use of the forecast model to provide dynamical consistency to the evolving
+forecast state during 4D-Var's time window \citep{rabier98}. Still, the practical effort
+required to specify and implement flow-dependent error covariances in 3/4D-Var is
significant.
The development of a unified global/regional WRF-Var system, and its widespread use
in the WRF community has necessitated the development of a new, efficient, portable forecast background error covariance calculation code. Numerous applications have also indicated
-that superior results are obtained if one invests effort in calculating domain-specific
-error covariances, instead of using the the default statistics supplied with the WRF-Var
-release. In this section, the new {\it gen$\_$be} code developed by NCAR/MMM to generate
+that superior results are obtained if one invests effort in calculating domain-specific
+error covariances, instead of using the the default statistics supplied with the WRF-Var
+release. In this section, the new {\it gen$\_$be} code developed by NCAR/MMM to generate
forecast error statistics for use with the WRF-Var system is described.
-The background error covariance matrix is defined as
+The background error covariance matrix is defined as
\begin{equation}
{\bf B}=\overline{\epsilon \epsilon^{T}} \simeq \overline{{\bf x'}{\bf x'}^{T}},
\label{var-b}
\end{equation}
-</font>
<font color="blue">oindent where the overbar denotes an average over time and/or geographical area. The true
+</font>
<font color="gray">oindent where the overbar denotes an average over time and/or geographical area. The true
background error $\epsilon$ is not known in reality, but is assumed to be statistically
well-represented by a model state perturbation ${\bf x'}$. In the standard NMC-method
-\citep{parrish92}, the perturbation ${\bf x'}$ is given by the difference between
-two forecasts (e.g., 24 hour minus 12 hour) verifying at the same time. Climatological
-estimates of background error may then be obtained by averaging such forecast
-differences over a period of time (e.g., one month). An alternative strategy proposed by
-\citep{fisher03} makes use of ensemble forecast output, defining the ${\bf x'}$ vectors as
-ensemble perturbations (ensemble minus ensemble mean). In either approach, the end
-result is an ensemble of model perturbation vectors from which estimates of
-background error may be derived. The new {\it gen$\_$be} utility has been designed to work with
+\citep{parrish92}, the perturbation ${\bf x'}$ is given by the difference between
+two forecasts (e.g., 24 hour minus 12 hour) verifying at the same time. Climatological
+estimates of background error may then be obtained by averaging such forecast
+differences over a period of time (e.g., one month). An alternative strategy proposed by
+\citep{fisher03} makes use of ensemble forecast output, defining the ${\bf x'}$ vectors as
+ensemble perturbations (ensemble minus ensemble mean). In either approach, the end
+result is an ensemble of model perturbation vectors from which estimates of
+background error may be derived. The new {\it gen$\_$be} utility has been designed to work with
either forecast difference, or ensemble-based, perturbations.
-Using the NMC-method, ${\bf x}'={\bf x_{T2}}-{\bf x_{T1}}$ where $T2$ and $T1$
-are the forecast difference times (e.g., 48h minus 24h for global, 24h minus 12h for regional).
-Alternatively, for an ensemble-based approach, ${\bf x_{k}}'={\bf x_{k}}-\bar{\bf
-x}$, where the overbar is an average over ensemble members $k=1,n_{e}$. The total
-number of binary files produced by this stage is $n_{f} \times n_e$ where $n_f$ is the
-number of forecast times used (e.g., for 30 days with forecast every 12 hours, $n_f=60$).
-Using the NMC-method, $n_e=1$ (1 forecast difference per time). For ensemble-based
+Using the NMC-method, ${\bf x}'={\bf x_{T2}}-{\bf x_{T1}}$ where $T2$ and $T1$
+are the forecast difference times (e.g., 48h minus 24h for global, 24h minus 12h for regional).
+Alternatively, for an ensemble-based approach, ${\bf x_{k}}'={\bf x_{k}}-\bar{\bf
+x}$, where the overbar is an average over ensemble members $k=1,n_{e}$. The total
+number of binary files produced by this stage is $n_{f} \times n_e$ where $n_f$ is the
+number of forecast times used (e.g., for 30 days with forecast every 12 hours, $n_f=60$).
+Using the NMC-method, $n_e=1$ (1 forecast difference per time). For ensemble-based
statistics, $n_e$ is the number of ensemble members.
-As described above, the WRF-Var background error covariances are specified not in
-model space ${\bf x'}$, but in a control variable space ${\bf v}$, which is related to the model variables
-(e.g., wind components, temperature, humidity, and surface pressure) via the control
-variable transform defined in (\ref{var-cv}). Both (\ref{var-cv}) and
+As described above, the WRF-Var background error covariances are specified not in
+model space ${\bf x'}$, but in a control variable space ${\bf v}$, which is related to the model variables
+(e.g., wind components, temperature, humidity, and surface pressure) via the control
+variable transform defined in (\ref{var-cv}). Both (\ref{var-cv}) and
its adjoint are required in WRF-Var. To enable this, the (offline) background error utility is used
-to compute components of the forecast error covariance matrix modeled within the
+to compute components of the forecast error covariance matrix modeled within the
${\rm U}$ transform. This process is described in the following subsections.
The background error covariance generation code {\it gen$\_$be} is designed to process
-data from a variety of regional/global models (e.g., ARW, MM5, KMA global model,
-NFS, etc.), and process it in order to provide error
-covariance statistics for use in variational data assimilation systems. The initial,
-model-dependent ``stage 0" is illustrated in Fig. \ref{var-genbe0}.
+data from a variety of regional/global models (e.g., ARW, MM5, KMA global model,
+NFS, etc.), and process it in order to provide error
+covariance statistics for use in variational data assimilation systems. The initial,
+model-dependent ``stage 0" is illustrated in Fig. \ref{var-genbe0}.
%
% Figure 9.6 var-genbe0
@@ -343,38 +183,38 @@
\begin{figure}
\centering
\includegraphics[width=4.0in]{figures/var-genbe0.pdf}
- \caption{\label{var-genbe0}Sketch of the role of Stage 0 converters
- in transforming model-specific data (e.g., ARW, KMA global model, etc.) to standard
+ \caption{\label{var-genbe0}Sketch of the role of Stage 0 converters
+ in transforming model-specific data (e.g., ARW, KMA global model, etc.) to standard
perturbation fields and relevant metadata (e.g., latitude, height, land/sea, etc.).}
\end{figure}
-Alternative models use different grids, variables, data formats, etc., and so initial converters
-are required to transform model output into a set of standard perturbation fields (and metadata),
-and to output them in a standard binary format for further, model-independent processing. The
+Alternative models use different grids, variables, data formats, etc., and so initial converters
+are required to transform model output into a set of standard perturbation fields (and metadata),
+and to output them in a standard binary format for further, model-independent processing. The
standard grid-point fields are as follows.
\begin{itemize}\setlength{\parskip}{-4pt}
\item
- Perturbations: Streamfunction $\psi'(i,j,k)$, velocity potential $\chi'(i,j,k)$,
+ Perturbations: Streamfunction $\psi'(i,j,k)$, velocity potential $\chi'(i,j,k)$,
temperature $T'(i,j,k)$, relative humidity $r'(i,j,k)$, surface pressure $p_s'(i,j)$.
\item
- Full-fields: height $z(i,j,k)$, latitude $\phi(i,j)$. (These are required for the
-production of background error statistics stored in terms of physics variables,
-rather than tied to a specific grid. This flexibility is included in {\it gen$\_$be} through a
-namelist option to define the bins over which data is averaged in a variety of ways
-(e.g., latitude height, grid points). Land-sea and orographic effects may also be
+ Full-fields: height $z(i,j,k)$, latitude $\phi(i,j)$. (These are required for the
+production of background error statistics stored in terms of physics variables,
+rather than tied to a specific grid. This flexibility is included in {\it gen$\_$be} through a
+namelist option to define the bins over which data is averaged in a variety of ways
+(e.g., latitude height, grid points). Land-sea and orographic effects may also be
represented in this way.
\end{itemize}
In general, the {\it stage$\_$0} converters are developed and maintained by those supporting
-individual models. Only the WRF-to-standard-fields converter {\it gen$\_$be$\_$stage0$\_$wrf}
+individual models. Only the WRF-to-standard-fields converter {\it gen$\_$be$\_$stage0$\_$wrf}
is maintained and supported by the ARW effort.
\subsection{Removal of time-mean}
-In order to calculate covariances between fields, the average value must first be removed.
-This is performed in the first stage utility {\it gen$\_$be$\_$stage1}.
+In order to calculate covariances between fields, the average value must first be removed.
+This is performed in the first stage utility {\it gen$\_$be$\_$stage1}.
\subsection{Multivariate Covariances: Regression coefficients and unbalanced variables}
@@ -387,11 +227,11 @@
balanced component of particular fields is modeled via a regression
analysis of the field using specified predictor fields
(e.g., streamfunction; see
-\citet{wu02} for further details). The resulting regression coefficients
-are output for use
+\citet{wu02} for further details). The resulting regression coefficients
+are output for use
in WRF-Var's ${\rm U}_p$ transform. Currently, three regression analyses are
performed resulting in three sets of regression coefficients (note:
-The perturbation notation has been dropped for the
+The perturbation notation has been dropped for the
remainder of this chapter for clarity.):
\begin{itemize}\setlength{\parskip}{-4pt}
@@ -401,22 +241,22 @@
\end{itemize}
The summation over the vertical index $k1$ relates to the integral (hydrostatic) relationship between
-mass fields and the wind field. By default, the regression coefficients $c$, $G$, and $W$ do
-not vary horizontally, however options exists to relax this assumption via the {\it bin\_type}
-namelist variable in order to allow representation of differences between, for example, polar, mid-latitude, and tropical dynamical and physical processes. The scalar coefficient $c$ used to
+mass fields and the wind field. By default, the regression coefficients $c$, $G$, and $W$ do
+not vary horizontally, however options exists to relax this assumption via the {\it bin\_type}
+namelist variable in order to allow representation of differences between, for example, polar, mid-latitude, and tropical dynamical and physical processes. The scalar coefficient $c$ used to
estimate velocity potential errors from those of streamfunction is permitted to vary with model
-level in order to represent, for example, the impact of boundary-layer physics. Latitudinal/height
-smoothing of the resulting coefficients may be optionally performed to avoid artificial
+level in order to represent, for example, the impact of boundary-layer physics. Latitudinal/height
+smoothing of the resulting coefficients may be optionally performed to avoid artificial
discontinuities at the edges of latitude/height boxes (see the future WRF-Var technical note for
details of these "expert" features).
-Having computed regression coefficients, the unbalanced components of the fields are
-calculated as $\chi_{u}(k)=\chi(k)-c(k)\psi(k)$, $T_{u}(k)=T(k)-\sum_{k1}G(k1,k)\psi(k1)$,
-and $p_{su}=p_s - \sum_{k1} W(k1)\psi(k1)$. These fields are output for the
+Having computed regression coefficients, the unbalanced components of the fields are
+calculated as $\chi_{u}(k)=\chi(k)-c(k)\psi(k)$, $T_{u}(k)=T(k)-\sum_{k1}G(k1,k)\psi(k1)$,
+and $p_{su}=p_s - \sum_{k1} W(k1)\psi(k1)$. These fields are output for the
subsequent calculation of the spatial covariances as described below.
-\subsection{Vertical Covariances: Eigenvectors/eigenvalues and
-control variable projections}
+\subsection{Vertical Covariances: Eigenvectors/eigenvalues and
+control variable projections}
The third stage ({\it gen$\_$be$\_$stage3}) of {\it gen$\_$be}
calculates the statistics required for the vertical component of the
@@ -430,7 +270,7 @@
The {\it gen$\_$be} code calculates both domain-averaged and local
values of the vertical component of the background error covariance
-matrix. Eigendecomposition of the resulting $K\times K$ ($K$ is the number of
+matrix. Eigendecomposition of the resulting $K\times K$ ($K$ is the number of
vertical levels) climatological vertical error covariance matrix ${\bf
B}={\bf E}{\Lambda}{\bf E}^{T}$ results in both domain-averaged and
local eigenvectors $\bf E$ and eigenvalues $\Lambda$. Both sets of
@@ -443,13 +283,13 @@
3D control variable fields into EOF space ${\bf v_v}=U_{v}^{-1}{\bf
v_p}=\Lambda^{-1/2}{\bf E}^{T} {\bf v_p}$.
-\subsection{Horizontal Covariances: Recursive filter lengthscale (regional), or power
+\subsection{Horizontal Covariances: Recursive filter lengthscale (regional), or power
spectra (global)}
The last aspect of the climatological component of background error
covariance data required for WRF-Var is the horizontal error
correlations, the representation of which forms the largest difference
-between running WRF-Var in regional and global mode - the rest of
+between running WRF-Var in regional and global mode - the rest of
{\it gen\_be} is essentially the same for both regional and global models.
In a global application ({\it gen\_be\_stage4\_global}), power spectra
@@ -469,37 +309,37 @@
\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
+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.
+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
+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
+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
+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>