<p><b>kavulich@ucar.edu</b> 2013-05-01 11:47:42 -0600 (Wed, 01 May 2013)</p><p>-Reformat citations<br>
-Update "var.tex" to WRFV3 Technote version (old version is way outdated). Authored by Hans, so added him to authors<br>
</p><hr noshade><pre><font color="gray">Modified: trunk/wrfvar/3DVAR_technote/acknow.tex
===================================================================
--- trunk/wrfvar/3DVAR_technote/acknow.tex 2013-04-29 23:47:16 UTC (rev 425)
+++ trunk/wrfvar/3DVAR_technote/acknow.tex 2013-05-01 17:47:42 UTC (rev 426)
@@ -1,30 +1,38 @@
\chapter*{Acknowledgments}
-\addcontentsline{toc}{chapter}{</font>
<font color="blue">umberline{}Acknowledgments}
+\addcontentsline{toc}{chapter}{</font>
<font color="gray">umberline{}Acknowledgments}
-\hskip 15pt
+\hskip 15pt
Many people beyond this document's author list have
contributed to the development of the WRF-Var system.
\vskip 10pt
+Guidance for this guide was provided by several previous well-written papers and technical notes, including
+
+\begin{itemize}
+ \item Barker, D., W. Huang, Y.-R. Guo, and A. Bourgeois, 2003: A Three-dimensional Variational (3DVAR) Data Assimilation System for Use With MM5. NCAR Technical Note NCAR/TN-453+STR \citep{BarkerEA2003}
+ \item Skamarock, W., J.B. Klemp, J. Dudhia, D.O. Gill, D. Barker, M.G. Duda, X.-Y. Huang, and W. Wang, 2008: A Description of the Advanced Research WRF Version 3. NCAR Technical Note NCAR/TN-475+STR \citep{SkamarockEA2008}
+\end{itemize}
+
+\vskip 10pt
NCAR scientists (Dale)
\vskip 10pt
-SE achnowledgements (Zhang)
+SE acknowledgements (Zhang)
\vskip 10pt
-The development of WRF-Var represents an international team effort.
-We would like to acknowledge the following people for their
-contributions to the WRF-Var system: Mike McAtee, Roy Peck, Steve Rugg,
-Jerry Wegiel, Wan-Shu Wu, Dezso Devenyi, Mi-Seon Lee, Ki-Han Youn, Eunha Lim,
+The development of WRF-Var represents an international team effort.
+We would like to acknowledge the following people for their
+contributions to the WRF-Var system: Mike McAtee, Roy Peck, Steve Rugg,
+Jerry Wegiel, Wan-Shu Wu, Dezso Devenyi, Mi-Seon Lee, Ki-Han Youn, Eunha Lim,
Hyun-Cheol Shin, Shu-Hua Chen, Ananda Das, Ashish Routray, etc.....
\vskip 10pt
Tech note reviewers (Dale)
\vskip 10pt
-The WRF-Var effort is supported by the National Science Foundation
-(ATM and Office of Polar Programs), the US Air Force Weather Agency,
-NASA, the Korean Meteorological Administration, the Japanese Central
-Research Institute for the Power Industry, the Taiwanese Civil
-Aeronautics Administration and Central Weather Bureau, and the Beijing
+The WRF-Var effort is supported by the National Science Foundation
+(ATM and Office of Polar Programs), the US Air Force Weather Agency,
+NASA, the Korean Meteorological Administration, the Japanese Central
+Research Institute for the Power Industry, the Taiwanese Civil
+Aeronautics Administration and Central Weather Bureau, and the Beijing
Meteorological Bureau.
Modified: trunk/wrfvar/3DVAR_technote/be.tex
===================================================================
--- trunk/wrfvar/3DVAR_technote/be.tex 2013-04-29 23:47:16 UTC (rev 425)
+++ trunk/wrfvar/3DVAR_technote/be.tex 2013-05-01 17:47:42 UTC (rev 426)
@@ -10,8 +10,8 @@
WRF-Var is a freely available community variational data assimilation system. It is used in a number of applications spanning convective to synoptic scales, tropical to polar domains, and variable observation distributions. In addition, the WRF-Var system is used to provide initial conditions for a number of forecast models in addition to WRF, e.g. MM5, the Korean Meteorological Administration's (KMA's) global spectral model, and the Taiwanese Nonhydrostatic Forecast Model (NFS). Perhaps understandably, the issue of forecast error generation for WRF-Var applications is the number 1 user question to date. For all these reasons, it is therefore vital that an accurate, portable, flexible, and efficient utility to generate and tune forecast error statistics be made available for community use.
-In the next subsection, a brief overview of the role of forecast error covariances in variational data assimilation is given. Default forecast error statistics are supplied with the WRF-Var release. These data files are made available primarily for training purposes, i.e. to permit the user to configure and test the WRF-Var/WRF system in their own application. It is important to note that the default statistics are not intended for extended testing or real-time applications of WRF-Var. For those applications, there is no substitute to creating one's own forecast error covariances with the {\it gen\_be} utility, described in subsection (\ref{gen_be_sub}). Having created domain-specific statistics, it may then be necessary to further tune both forecast and observation error statistics. A variety of algorithms are supplied with WRF-Var to perform this tuning, and documented in Chapter (\ref{diagnostics}). These tuning algorithms include both innovation vector-based approaches \
citep{hollingsworth86}
-and variational tuning approaches \citep{desroziers01}. Clearly, the whole process of tuning error statistics for data assimilation is rather complex. However, it has been shown in many applications, that this work is vital if one is to produce the optimal analysis.
+In the next subsection, a brief overview of the role of forecast error covariances in variational data assimilation is given. Default forecast error statistics are supplied with the WRF-Var release. These data files are made available primarily for training purposes, i.e. to permit the user to configure and test the WRF-Var/WRF system in their own application. It is important to note that the default statistics are not intended for extended testing or real-time applications of WRF-Var. For those applications, there is no substitute to creating one's own forecast error covariances with the {\it gen\_be} utility, described in subsection (\ref{gen_be_sub}). Having created domain-specific statistics, it may then be necessary to further tune both forecast and observation error statistics. A variety of algorithms are supplied with WRF-Var to perform this tuning, and documented in Chapter (\ref{diagnostics}). These tuning algorithms include both innovation vector-based approaches \
cite{hollingsworth86}
+and variational tuning approaches \cite{desroziers01}. Clearly, the whole process of tuning error statistics for data assimilation is rather complex. However, it has been shown in many applications, that this work is vital if one is to produce the optimal analysis.
\section{Scientific Background}
@@ -24,7 +24,7 @@
\label{var-b}
\end{equation}
-</font>
<font color="blue">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 results is the same - an ensemble of model perturbation vectors from which estimates of background error may be derived. The new {\it gen$\_$be} code has been designed to work with either forecast
difference, or ensemble-based perturbations.
+</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 \cite{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 \cite{fisher03} makes use of ensemble forecast output, defining the ${\bf x'}$ vectors as ensemble perturbations (ensemble minus ensemble mean). In either approach, the end results is the same - an ensemble of model perturbation vectors from which estimates of background error may be derived. The new {\it gen$\_$be} code has been designed to work with either forecast di
fference, or ensemble-based perturbations.
In model-space variational data assimilation systems, the background error covariances are specified not in model space ${\bf x'}$, but in a control variable space ${\bf v}$, related to the model variables (e.g. wind components, temperature, humidity, and surface pressure) via a control variable transform U defined by
@@ -100,7 +100,7 @@
The standard control variables (i.e. those variable for which we assume cross-correlations are zero) in WRF-Var are streamfunction, "pseudo" relative humidity, and the unbalanced components of velocity potential, temperature, and surface pressure.
-The unbalanced control variables are defined as the difference between full and balanced (or correlated) components of the field. In this stage of the calculation of background errors, the 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 in WRF-Var's ${\rm U}_p$ transform, and are also used in gen\_be\_stage2a (see below). Currently, three regression analyses are performed resulting in three sets of regression coefficients (note: drop the perturbation notation from now on for clarity):
+The unbalanced control variables are defined as the difference between full and balanced (or correlated) components of the field. In this stage of the calculation of background errors, the balanced component of particular fields is modeled via a regression analysis of the field using specified predictor fields (e.g. streamfunction). (see \cite{wu02} for further details). The resulting regression coefficients are output for use in WRF-Var's ${\rm U}_p$ transform, and are also used in gen\_be\_stage2a (see below). Currently, three regression analyses are performed resulting in three sets of regression coefficients (note: drop the perturbation notation from now on for clarity):
\begin{itemize}\setlength{\parskip}{-4pt}
@@ -136,7 +136,7 @@
\subsection{gen\_be\_stage3 - Eigenvectors/values of Vertical Error Covariances}
-The gen\_be\_stage3 program calculates the statistics required for the vertical component of the control variable transform of WRF-Var. This involves the projection of 3D fields on model-levels onto empirical orthogonal functions (EOFs) of the vertical component of background error covariances \citep{barker04}.
+The gen\_be\_stage3 program calculates the statistics required for the vertical component of the control variable transform of WRF-Var. This involves the projection of 3D fields on model-levels onto empirical orthogonal functions (EOFs) of the vertical component of background error covariances \cite{barker04}.
The {\it gen$\_$be} code calculates both domain-averaged and local
@@ -152,7 +152,7 @@
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 \cite{barker04}.
Having calculated and stored eigenvectors and eigenvalues, the final
part of {\it gen$\_$be$\_$stage3} is to project the entire sequence of
@@ -172,11 +172,11 @@
In global applications (gen\_be\_stage4\_global). a spectral decomposition of the grid-point data is performed, and power spectra computed for each variable and vertical mode. Details of the spectral technique used to project gridpoint fields to spectral modes are given in Appendix B together with a description of the power spectra computed from the spectral modes.
-In regional applications (gen\_be\_stage4\_regional), a recursive filter is used to provide the horizontal correlations (\citet{barker04}). The error covariance inputs to the recursive filter is a correlation lengthscale (provided by gen\_be\_stage4\_regional), and a WRF-Var namelist parameters to define the correlations shape (the number of passes through the recursive filter). The calculation of horizontal lengthscales in gen\_be\_stage4\_regional is described in section 8c of (\citet{barker04}). Note: This is the most expensive part of the entire gen\_be process.
+In regional applications (gen\_be\_stage4\_regional), a recursive filter is used to provide the horizontal correlations (\cite{barker04}). The error covariance inputs to the recursive filter is a correlation lengthscale (provided by gen\_be\_stage4\_regional), and a WRF-Var namelist parameters to define the correlations shape (the number of passes through the recursive filter). The calculation of horizontal lengthscales in gen\_be\_stage4\_regional is described in section 8c of (\cite{barker04}). Note: This is the most expensive part of the entire gen\_be process.
Input: Projected 3D (i,j,m) control variable fields: $\psi$, $\chi_u$, $T_u$, and $r$, and $p_{su}$(i,j). (output from stage 3 and 2a)
-Processing (regional): Perform linear regression of horizontal correlations to calculate recursive filter lengthscales (see \citet{barker04}).
+Processing (regional): Perform linear regression of horizontal correlations to calculate recursive filter lengthscales (see \cite{barker04}).
Processing (global): Perform horizontal spectral decomposition, and compute power spectra for each field/mode (see Appendix B).
Modified: trunk/wrfvar/3DVAR_technote/cover.tex
===================================================================
--- trunk/wrfvar/3DVAR_technote/cover.tex 2013-04-29 23:47:16 UTC (rev 425)
+++ trunk/wrfvar/3DVAR_technote/cover.tex 2013-05-01 17:47:42 UTC (rev 426)
@@ -18,6 +18,7 @@
</font>
<font color="gray">ormalsize
Michael J. Kavulich, Jr.&&\\
Xin Zhang&&\\
+Xiang-Yu Huang&&\\
Dale M. Barker&&\\[10cm]
&&\\%[15cm]
\multicolumn{2}{r|}{Mesoscale and Microscale Meteorology Division}&\\ \hline
Deleted: trunk/wrfvar/3DVAR_technote/description.bbl
===================================================================
--- trunk/wrfvar/3DVAR_technote/description.bbl 2013-04-29 23:47:16 UTC (rev 425)
+++ trunk/wrfvar/3DVAR_technote/description.bbl 2013-05-01 17:47:42 UTC (rev 426)
@@ -1,275 +0,0 @@
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-Weygandt, S. S., A. Shapiro, K. K. Droegemeier, 2002b: Retrieval of model
-initial fields from single-Doppler observations of a supercell
-thunderstorm. Part II: Thermodynamic retrieval and numerical prediction.
-{\em Mon. Wea. Rev.}, {\bf 130}, 454-476.
-
-\bibitem[White(2000)]{white00}%
-White, A., 2000: A View of the Equations of Meteorological Dynamics and
-Various Approximations. Forecasting Research Scientific Paper,
-No. 58. UK Met Office.
-
-\bibitem[Wu et al.(2002)]{wu02}%
-Wu, W. -S., R. J. Purser, and D. F. Parrish, 2002: Three-Dimensional Variational
- Analysis with Spatially Inhomogeneous Covariances.
- {\em Mon. Wea. Rev.}, {\bf 130}, 2905--2916.
-
-\bibitem[Xiao et al.(2005)]{xiao05}%
-Xiao, Q., Y. H. Kuo, J. Sun, W. C. Lee, E. Lim, Y. R. Guo, and D. M. Barker,
-2005: Assimilation of Doppler radar observations with a regional 3D-Var
-system: Impact of Doppler velocities on forecasts of a heavy rainfall case.
-{\em J. Appl. Met.}, {\bf 44(6)}, 768--788.
-
-\bibitem[Xiao et al.(2006)]{xiao06}%
-Xiao, Q., Y.-H. Kuo, Y. Zhang, D. M. Barker, and D.-J. Won, 2006:
-A tropical cyclone bogus data assimilation scheme in the MM5 3D-Var system
-and numerical experiments with Typhoon Rusa (2002) near landfall.
-{\em J. Meteor. Soc. Japan}, {\bf 84(4)}, 671--689.
-
-\bibitem[Xiao et al.(2007)]{xiao07}%
-Xiao, Q., Y.-H. Kuo, J. Sun, W.-C. Lee, D. M. Barker, and E. Lim, 2007:
-An approach of radar reflectivity data assimilation and its assessment
-with the inland QPF of Typhoon Rusa (2002) at landfall.
-{\em J. Appl. Meteor. Climat.}, {\bf 46}, 14-22.
-
-\end{thebibliography}
Modified: trunk/wrfvar/3DVAR_technote/description.tex
===================================================================
--- trunk/wrfvar/3DVAR_technote/description.tex 2013-04-29 23:47:16 UTC (rev 425)
+++ trunk/wrfvar/3DVAR_technote/description.tex 2013-05-01 17:47:42 UTC (rev 426)
@@ -11,13 +11,11 @@
\usepackage{amsmath}
\usepackage{amssymb}
%
-% Use natbib package for the citations
+% Use bibtex package for the citations
\usepackage{natbib}
+\usepackage[nottoc]{tocbibind}
%\usepackage[square]{natbib}
%
-% Use locally modified jgr bibliography style
-\bibliographystyle{jgr}
-%
% Use changebar package for highlighting changes
\usepackage{changebar}
%
@@ -29,6 +27,9 @@
%\usepackage[colorlinks,citecolor=black,linkcolor=black,urlcolor=black]{hyperref}
\usepackage[colorlinks,citecolor=blue,linkcolor=red,urlcolor=cyan]{hyperref}
+% Use appendix package
+\usepackage[page]{appendix}
+
% Use packages longtable, pdflscape, endnotes, and color for namelist appendix, define gray
\usepackage{longtable,tabu}
\usepackage{pdflscape}
@@ -37,11 +38,6 @@
\definecolor{light-gray}{gray}{0.95}
\definecolor{gray}{gray}{0.5}
%
-%\usepackage{html}
-%\begin{htmlonly}
-% </font>
<font color="gray">ewcommand{\href}[2]{\htmladdnormallink{#2}{#1}}
-%\end{htmlonly}
-%
% Set up page layout
\setlength{\textwidth}{6.75in}
\setlength{\oddsidemargin}{-0.0in}
@@ -52,9 +48,6 @@
\setlength{\headsep}{0.5in}
\setlength{\topskip}{0.0in}
\setlength{\footskip}{0.5in}
-%\renewcommand{\baselinestretch}{2.0}
-%\setlength{\parindent}{0.0in}
-%\setlength{\parskip}{0.08in}
%
% Include some coding shortcuts
\def \eg{{\emph{e.g.} }}
@@ -69,7 +62,9 @@
%\pagestyle{fancy}
% preliminary pages
+\pdfbookmark{Cover}{Cover}
\include{cover}
+\pdfbookmark{\contentsname}{Contents}
\tableofcontents
\listoffigures
\listoftables
@@ -86,21 +81,21 @@
\include{obs}
\include{be}
\include{3dvar}
-% Next two lines MUST come right before the last chapter include
-\addtocontents{toc}{\contentsline {chapter}{}{}{}}
-\addtocontents{toc}{\contentsline {chapter}{Appendices}{}{}}
\include{se}
%\include{asf}
%
% appendices
-\appendix
+\begin{appendices}
\include{appena}
\begin{landscape}
\include{namelist}
+\include{acronyms}
\end{landscape}
+\end{appendices}
%
% bibliography
-\addcontentsline{toc}{chapter}{</font>
<font color="red">umberline{}References}
-\bibliography{description}
+%\addcontentsline{toc}{chapter}{</font>
<font color="gray">umberline{}Bibliography}
+\bibliography{refs}{}
+\bibliographystyle{agufull08}
\end{document}
Modified: trunk/wrfvar/3DVAR_technote/namelist.tex
===================================================================
--- trunk/wrfvar/3DVAR_technote/namelist.tex 2013-04-29 23:47:16 UTC (rev 425)
+++ trunk/wrfvar/3DVAR_technote/namelist.tex 2013-05-01 17:47:42 UTC (rev 426)
@@ -26,10 +26,10 @@
as max and min for each variable, as well as information about relative humidity corrections
\\ print\_detail\_xb & logical & 1 & .false. & Prints additional details about the background state
\\ print\_detail\_obs & logical & 1 & .false. & Prints additional details on \textit{every} ascii-formatted observation: this option can
- make log files \textit{extremely} long if a large number of observations are assimilated
+ make log files \textit{very} long if a large number of observations are assimilated
\\ print\_detail\_f\_obs & logical & 1 & .false. & Prints additional details about observation filtering when ``analysis\_type'' = ``QC-OBS''
\\ print\_detail\_map & logical & 1 & .false. & Prints additional details about the background/analysis domain.
-\\ print\_detail\_grad & logical & 1 & .false. & print\_detail\_grad
+\\ print\_detail\_grad & logical & 1 & .false. & Prints additional details about the cost function and cost function gradient
\\ print\_detail\_regression & logical & 1 & .false. & print\_detail\_regression
\\ print\_detail\_spectral & logical & 1 & .false. & print\_detail\_spectral
\\ print\_detail\_testing & logical & 1 & .false. & print\_detail\_testing
Modified: trunk/wrfvar/3DVAR_technote/var.tex
===================================================================
--- trunk/wrfvar/3DVAR_technote/var.tex 2013-04-29 23:47:16 UTC (rev 425)
+++ trunk/wrfvar/3DVAR_technote/var.tex 2013-05-01 17:47:42 UTC (rev 426)
@@ -80,10 +80,10 @@
\vspace{0.5cm}
b) Observations ${\bf y^{o}}$--- In the current version of WRF-Var, observations may be
-supplied either in a text (MM5 3D-Var) format or BUFR format (but not a
-combination of the two). An observation preprocessor (3DVAR$\_$OBSPROC)
-is supplied with the code release to perform basic quality control, assign
-observation errors, and reformat observations from the MM5 {\it little$\_$r} text
+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}
@@ -105,14 +105,20 @@
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 ${\bf x^{lbc}}$ (described in
-\citet{barker03}). Note: In cycling mode, only the {\it wrfbdy} lateral boundary condition
-files (${\bf x^{lbc}}$) output of SI/real are used, and not the {\it wrfinput} initial condition
-files (${\bf x^{b}}$). In cold-start mode, both are required.
+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,
+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
@@ -124,29 +130,25 @@
\subsection{Improved minimization and ``outer loop"}
-The default WRF-Var cost function minimization uses a modified version of the limited
-memory Quasi-Newton Method (QNM). Recently, an alternative Conjugate Gradient
-Method (CGM) has been implemented. Unlike the QNM technique, the CGM method
-restricts 3D-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
+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 background. The
+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 their O-B values are outside a prescribed range (typically several times the
-observation error standard deviation). This {\it errormax} test implicitly assumes the rejected
-large O-B values are due to a bad observation (O) rather than poor background (B).
-However, if it is the background B that is incorrect then the system will reject the most
-useful observations available to the assimilation system, i.e., those in areas where the
-first-guess is poor. The outer loop alleviates this effect by allowing observations
-rejected in previous iterations to be accepted if their new O-B falls within the required range
-in subsequent outer loops. The assimilation of nearby observations in previous iterations
-essentially provides a ``buddy check" to the observation in question.
+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{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 +162,11 @@
${\rm U}_{p}$.
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
@@ -291,27 +175,27 @@
(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). Surface observations with
-high temporal resolution also benefit from the use of FGAT.
+asynoptic, moving platforms (e.g., aircraft and satellite data).
\subsection{Radar Data Assimilation}
-Numerous modifications have been made in order to assimilate Doppler
-radar radial velocity and reflectivity observations. Firstly, vertical
-velocity increments are included in WRF-Var via the ``Richarson
-balance equation" that combines the continuity equation, adiabatic
-thermodynamic equation, and hydrostatic relation. Linear and adjoint
-codes of Richardson's equation have been incorporated into WRF-Var. In
-order to develop a capability for Doppler reflectivity assimilation,
-we use the total water as a control variable, requiring a partitioning
-of the moisture and water hydrometeor increments. A warm-rain
-parameterization is also included, 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. Finally, the observation operators for Doppler radial velocity
-and reflectivity are included in WRF-Var. Further details and results
-of the radial velocity work can be found in \citet{xiao05}. The radar
-reflectivity approach will be described in a future paper.
+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}
@@ -324,7 +208,7 @@
boundary conditions. Of course, there are also scientific questions
concerning the optimal mix of observations required for
global/regional models, and the choice of control variables and
-balance constraints. A unified global/regional 3D-Var system should
+balance constraints. A unified global/regional data assimilation system should
therefore be flexible to a variety of thinning/quality-control
algorithms and also to alternative formulations of the background
error covariance matrix. This flexibility has been a key design
@@ -343,8 +227,7 @@
correlation defined in spectral space is also a weakness---
anisotropies need to be defined in an alternative manner. One solution
to this problem is to replace the spectral correlations with
-grid-point correlations (e.g., in the Gridpoint Statistical
-Interpolation scheme under development at NCEP). An alternative
+grid-point correlations \citep{purser03}. An alternative
technique is to supplement the isotropic spectral correlations with an
anisotropic component derived via grid transformations, additional
control variables or 4D-Var. Research using the latter techniques is
@@ -386,8 +269,8 @@
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 usually estimated offline.
+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
@@ -405,17 +288,12 @@
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
-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
-required a new, efficient, portable forecast background error covariance calculation
-code to be written. There is also a demand for such a capability to be available and
-supported for the wider 3/4D-Var research community for application to their own
-geographic areas of interest (the default statistics supplied with the WRF-Var
-release are designed only as a starting point). 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 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
+forecast error statistics for use with the WRF-Var system is described.
The background error covariance matrix is defined as
@@ -436,15 +314,6 @@
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.
-
-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. In contrast, the background error code performs the
-inverse control variable transform ${\bf v}={\rm U}_{h}^{-1} {\rm U}_{v}^{-1} {\rm U}_{p}^{-1}{\bf x'}$ in order to
-accumulate statistics for each component of the control vector ${\bf v}$.
-
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
@@ -454,6 +323,14 @@
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
+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
+${\rm U}$ 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
@@ -501,12 +378,6 @@
\subsection{Multivariate Covariances: Regression coefficients and unbalanced variables}
-The WRF-Var system permits a variety of background error covariance
-models to be employed, as described in Section \ref{var-cvs}
-above.
-The utility {\it gen$\_$be} is used to provide background error
-statistics only for cv$\_$options 4 and 5.
-
The second stage
of {\it gen$\_$be (gen$\_$be$\_$stage2)} provides statistics for the
unbalanced fields $\chi_u$, $T_u$, and $P_{su}$ used as control
@@ -519,58 +390,54 @@
\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:
+performed resulting in three sets of regression coefficients (note:
The perturbation notation has been dropped for the
remainder of this chapter for clarity.):
\begin{itemize}\setlength{\parskip}{-4pt}
-\item Velocity potential/streamfunction regression: $\chi_b=c\psi$;
-\item Temperature/streamfunction regression: $T_{b,k1}=\sum_{k2}G_{k1,k2}\psi_{k2}$; and
-\item Surface pressure/streamfunction regression: $p_{sb}=\sum{k}W_{k}\psi_{k}$.
+\item Velocity potential/streamfunction regression: $\chi_b(k)=c(k)\psi(k)$;
+\item Temperature/streamfunction regression: $T_b(k)=\sum_{k1}G(k1,k)\psi(k1)$; and
+\item Surface pressure/streamfunction regression: $p_{sb}=\sum_{k1}W(k1)\psi(k1)$.
\end{itemize}
-Data is read from all $n_f \times n_e$ files and sorted into bins defined via the namelist
-option {\it bin$\_$type}. Regression coefficients $G(k1,k2)$ and $W(k)$ are computed
-individually for each bin (bin$\_$type=1 is used here, representing latitudinal dependence)
-in order to allow representation of differences between, for example, polar, mid-latitude, and
-tropical dynamical and physical processes. In addition, the scalar coefficient $c$ used to
-estimate velocity potential errors from those of streamfunction is calculated as a function
-of height to represent, for example, the impact of boundary-layer physics. Latitudinal/height
+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
+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
-discontinuities at the edges of latitude/height boxes.
+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 $\chi_u=\chi-c\psi$, $T_{u,k1}=T_{k1}-\sum_{k2}G_{k1,k2}\psi_{k2}$,
-and $p_{su}=p_s - \sum_{k} W_{k}\psi_{k}$. These fields are output for the
+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}
+control variable projections}
The third stage ({\it gen$\_$be$\_$stage3}) of {\it gen$\_$be}
calculates the statistics required for the vertical component of the
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.
The {\it gen$\_$be} code calculates both domain-averaged and local
values of the vertical component of the background error covariance
-matrix. The definition of local again depends on the value of the
-namelist variable bin$\_$type chosen. For example, for bin$\_$type=1,
-a $kz \times kz$ (where $kz$ is the number of vertical levels) vertical
-component of $\bf B$ is produced at every latitude (data is averaged
-over time and longitude) for each control variable. Eigendecomposition
-of the resulting climatological vertical error covariances ${\bf
+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
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
@@ -582,15 +449,57 @@
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. (It is however,
-still a fairly local change.)
+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
-are computed for each of the $kz$ vertical modes of the 3D control
-variables $\psi$, $\chi_u$, $T_u$, and $r$, and for the 2D control
+are computed for each of the $K$ vertical modes of the 3D control
+variables $\psi$, $\chi_u$, $T_u$, and relative humidity $r$, and for the 2D control
variable $p_{su}$ data. In contrast, in regional mode, horizontal
correlations are computed between grid-points of each 2D field, binned
as a function of distance. A Gaussian curve is then fitted to the data
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>